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venv/lib/python3.13/site-packages/scipy/sparse/__init__.py
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venv/lib/python3.13/site-packages/scipy/sparse/__init__.py
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"""
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===================================
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Sparse arrays (:mod:`scipy.sparse`)
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===================================
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.. currentmodule:: scipy.sparse
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.. toctree::
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:hidden:
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sparse.csgraph
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sparse.linalg
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sparse.migration_to_sparray
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SciPy 2-D sparse array package for numeric data.
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.. note::
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This package is switching to an array interface, compatible with
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NumPy arrays, from the older matrix interface. We recommend that
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you use the array objects (`bsr_array`, `coo_array`, etc.) for
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all new work.
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When using the array interface, please note that:
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- ``x * y`` no longer performs matrix multiplication, but
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element-wise multiplication (just like with NumPy arrays). To
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make code work with both arrays and matrices, use ``x @ y`` for
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matrix multiplication.
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- Operations such as ``sum``, that used to produce dense matrices, now
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produce arrays, whose multiplication behavior differs similarly.
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- Sparse arrays use array style *slicing* operations, returning scalars,
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1D, or 2D sparse arrays. If you need 2D results, use an appropriate index.
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E.g. ``A[:, i, None]`` or ``A[:, [i]]``.
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- All index arrays for a given sparse array should be of same dtype.
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For example, for CSR format, ``indices`` and ``indptr`` should have
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the same dtype. For COO, each array in `coords` should have same dtype.
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The construction utilities (`eye`, `kron`, `random`, `diags`, etc.)
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have appropriate replacements (see :ref:`sparse-construction-functions`).
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For more information see
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:ref:`Migration from spmatrix to sparray <migration_to_sparray>`.
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Submodules
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==========
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.. autosummary::
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csgraph - Compressed sparse graph routines
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linalg - Sparse linear algebra routines
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Sparse array classes
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====================
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.. autosummary::
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:toctree: generated/
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bsr_array - Block Sparse Row array
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coo_array - A sparse array in COOrdinate format
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csc_array - Compressed Sparse Column array
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csr_array - Compressed Sparse Row array
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dia_array - Sparse array with DIAgonal storage
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dok_array - Dictionary Of Keys based sparse array
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lil_array - Row-based list of lists sparse array
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sparray - Sparse array base class
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.. _sparse-construction-functions:
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Building sparse arrays
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----------------------
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.. autosummary::
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:toctree: generated/
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diags_array - Return a sparse array from diagonals
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eye_array - Sparse MxN array whose k-th diagonal is all ones
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random_array - Random values in a given shape array
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block_array - Build a sparse array from sub-blocks
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.. _combining-arrays:
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Combining arrays
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----------------
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.. autosummary::
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:toctree: generated/
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kron - Kronecker product of two sparse arrays
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kronsum - Kronecker sum of sparse arrays
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block_diag - Build a block diagonal sparse array
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tril - Lower triangular portion of a sparse array
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triu - Upper triangular portion of a sparse array
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hstack - Stack sparse arrays horizontally (column wise)
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vstack - Stack sparse arrays vertically (row wise)
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Sparse tools
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------------
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.. autosummary::
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:toctree: generated/
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save_npz - Save a sparse array to a file using ``.npz`` format.
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load_npz - Load a sparse array from a file using ``.npz`` format.
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find - Return the indices and values of the nonzero elements
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get_index_dtype - determine a good dtype for index arrays.
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safely_cast_index_arrays - cast index array dtype or raise if shape too big
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Identifying sparse arrays
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-------------------------
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.. autosummary::
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:toctree: generated/
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issparse - Check if the argument is a sparse object (array or matrix).
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Sparse matrix classes
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=====================
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.. autosummary::
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:toctree: generated/
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bsr_matrix - Block Sparse Row matrix
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coo_matrix - A sparse matrix in COOrdinate format
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csc_matrix - Compressed Sparse Column matrix
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csr_matrix - Compressed Sparse Row matrix
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dia_matrix - Sparse matrix with DIAgonal storage
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dok_matrix - Dictionary Of Keys based sparse matrix
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lil_matrix - Row-based list of lists sparse matrix
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spmatrix - Sparse matrix base class
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Building sparse matrices
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------------------------
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.. autosummary::
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:toctree: generated/
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eye - Sparse MxN matrix whose k-th diagonal is all ones
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identity - Identity matrix in sparse matrix format
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diags - Return a sparse matrix from diagonals
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spdiags - Return a sparse matrix from diagonals
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bmat - Build a sparse matrix from sparse sub-blocks
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random - Random values in a given shape matrix
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rand - Random values in a given shape matrix (old interface)
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**Combining matrices use the same functions as for** :ref:`combining-arrays`.
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Identifying sparse matrices
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---------------------------
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.. autosummary::
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:toctree: generated/
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issparse
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isspmatrix
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isspmatrix_csc
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isspmatrix_csr
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isspmatrix_bsr
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isspmatrix_lil
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isspmatrix_dok
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isspmatrix_coo
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isspmatrix_dia
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Warnings
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========
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.. autosummary::
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:toctree: generated/
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SparseEfficiencyWarning
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SparseWarning
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Usage information
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=================
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There are seven available sparse array types:
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1. csc_array: Compressed Sparse Column format
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2. csr_array: Compressed Sparse Row format
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3. bsr_array: Block Sparse Row format
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4. lil_array: List of Lists format
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5. dok_array: Dictionary of Keys format
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6. coo_array: COOrdinate format (aka IJV, triplet format)
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7. dia_array: DIAgonal format
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To construct an array efficiently, use any of `coo_array`,
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`dok_array` or `lil_array`. `dok_array` and `lil_array`
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support basic slicing and fancy indexing with a similar syntax
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to NumPy arrays. The COO format does not support indexing (yet)
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but can also be used to efficiently construct arrays using coord
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and value info.
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Despite their similarity to NumPy arrays, it is **strongly discouraged**
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to use NumPy functions directly on these arrays because NumPy typically
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treats them as generic Python objects rather than arrays, leading to
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unexpected (and incorrect) results. If you do want to apply a NumPy
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function to these arrays, first check if SciPy has its own implementation
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for the given sparse array class, or **convert the sparse array to
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a NumPy array** (e.g., using the `toarray` method of the class)
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before applying the method.
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All conversions among the CSR, CSC, and COO formats are efficient,
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linear-time operations.
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To perform manipulations such as multiplication or inversion, first
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convert the array to either CSC or CSR format. The `lil_array`
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format is row-based, so conversion to CSR is efficient, whereas
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conversion to CSC is less so.
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Matrix vector product
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---------------------
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To do a vector product between a 2D sparse array and a vector use
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the matmul operator (i.e., ``@``) which performs a dot product (like the
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``dot`` method):
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>>> import numpy as np
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>>> from scipy.sparse import csr_array
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>>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
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>>> v = np.array([1, 0, -1])
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>>> A @ v
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array([ 1, -3, -1], dtype=int64)
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The CSR format is especially suitable for fast matrix vector products.
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Example 1
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---------
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Construct a 1000x1000 `lil_array` and add some values to it:
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>>> from scipy.sparse import lil_array
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>>> from scipy.sparse.linalg import spsolve
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>>> from numpy.linalg import solve, norm
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>>> from numpy.random import rand
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>>> A = lil_array((1000, 1000))
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>>> A[0, :100] = rand(100)
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>>> A.setdiag(rand(1000))
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Now convert it to CSR format and solve A x = b for x:
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>>> A = A.tocsr()
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>>> b = rand(1000)
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>>> x = spsolve(A, b)
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Convert it to a dense array and solve, and check that the result
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is the same:
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>>> x_ = solve(A.toarray(), b)
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Now we can compute norm of the error with:
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>>> err = norm(x-x_)
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>>> err < 1e-9
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True
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It should be small :)
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Example 2
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---------
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Construct an array in COO format:
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>>> from scipy import sparse
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>>> from numpy import array
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>>> I = array([0,3,1,0])
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>>> J = array([0,3,1,2])
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>>> V = array([4,5,7,9])
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>>> A = sparse.coo_array((V,(I,J)),shape=(4,4))
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Notice that the indices do not need to be sorted.
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Duplicate (i,j) entries are summed when converting to CSR or CSC.
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>>> I = array([0,0,1,3,1,0,0])
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>>> J = array([0,2,1,3,1,0,0])
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>>> V = array([1,1,1,1,1,1,1])
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>>> B = sparse.coo_array((V,(I,J)),shape=(4,4)).tocsr()
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This is useful for constructing finite-element stiffness and mass matrices.
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Further details
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---------------
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CSR column indices are not necessarily sorted. Likewise for CSC row
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indices. Use the ``.sorted_indices()`` and ``.sort_indices()`` methods when
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sorted indices are required (e.g., when passing data to other libraries).
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"""
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# Original code by Travis Oliphant.
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# Modified and extended by Ed Schofield, Robert Cimrman,
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# Nathan Bell, and Jake Vanderplas.
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import warnings as _warnings
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import importlib as _importlib
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from ._base import *
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from ._csr import *
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from ._csc import *
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from ._lil import *
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from ._dok import *
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from ._coo import *
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from ._dia import *
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from ._bsr import *
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from ._construct import *
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from ._extract import *
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from ._matrix import spmatrix
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from ._matrix_io import *
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from ._sputils import get_index_dtype, safely_cast_index_arrays
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# Deprecated namespaces, to be removed in v2.0.0
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from . import (
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base, bsr, compressed, construct, coo, csc, csr, data, dia, dok, extract,
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lil, sparsetools, sputils
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)
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_submodules = ["csgraph", "linalg"]
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__all__ = [s for s in dir() if not s.startswith('_')] + _submodules
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# Filter PendingDeprecationWarning for np.matrix introduced with numpy 1.15
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msg = 'the matrix subclass is not the recommended way'
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_warnings.filterwarnings('ignore', message=msg)
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def __dir__():
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return __all__
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def __getattr__(name):
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if name in _submodules:
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return _importlib.import_module(f'scipy.sparse.{name}')
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else:
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try:
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return globals()[name]
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except KeyError:
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raise AttributeError(
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f"Module 'scipy.sparse' has no attribute '{name}'"
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)
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from scipy._lib._testutils import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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1613
venv/lib/python3.13/site-packages/scipy/sparse/_base.py
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1613
venv/lib/python3.13/site-packages/scipy/sparse/_base.py
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880
venv/lib/python3.13/site-packages/scipy/sparse/_bsr.py
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venv/lib/python3.13/site-packages/scipy/sparse/_bsr.py
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"""Compressed Block Sparse Row format"""
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__docformat__ = "restructuredtext en"
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__all__ = ['bsr_array', 'bsr_matrix', 'isspmatrix_bsr']
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from warnings import warn
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import numpy as np
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from scipy._lib._util import copy_if_needed
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from ._matrix import spmatrix
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from ._data import _data_matrix, _minmax_mixin
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from ._compressed import _cs_matrix
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from ._base import issparse, _formats, _spbase, sparray
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from ._sputils import (isshape, getdtype, getdata, to_native, upcast,
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check_shape)
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from . import _sparsetools
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from ._sparsetools import (bsr_matvec, bsr_matvecs, csr_matmat_maxnnz,
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bsr_matmat, bsr_transpose, bsr_sort_indices,
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bsr_tocsr)
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class _bsr_base(_cs_matrix, _minmax_mixin):
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_format = 'bsr'
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def __init__(self, arg1, shape=None, dtype=None, copy=False,
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blocksize=None, *, maxprint=None):
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_data_matrix.__init__(self, arg1, maxprint=maxprint)
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if issparse(arg1):
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if arg1.format == self.format and copy:
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arg1 = arg1.copy()
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else:
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arg1 = arg1.tobsr(blocksize=blocksize)
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self.indptr, self.indices, self.data, self._shape = (
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arg1.indptr, arg1.indices, arg1.data, arg1._shape
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)
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elif isinstance(arg1,tuple):
|
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if isshape(arg1):
|
||||
# it's a tuple of matrix dimensions (M,N)
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self._shape = check_shape(arg1)
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M,N = self.shape
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# process blocksize
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||||
if blocksize is None:
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blocksize = (1,1)
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||||
else:
|
||||
if not isshape(blocksize):
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||||
raise ValueError(f'invalid blocksize={blocksize}')
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blocksize = tuple(blocksize)
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self.data = np.zeros((0,) + blocksize, getdtype(dtype, default=float))
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|
||||
R,C = blocksize
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||||
if (M % R) != 0 or (N % C) != 0:
|
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raise ValueError('shape must be multiple of blocksize')
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|
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# Select index dtype large enough to pass array and
|
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# scalar parameters to sparsetools
|
||||
idx_dtype = self._get_index_dtype(maxval=max(M//R, N//C, R, C))
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self.indices = np.zeros(0, dtype=idx_dtype)
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self.indptr = np.zeros(M//R + 1, dtype=idx_dtype)
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|
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elif len(arg1) == 2:
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# (data,(row,col)) format
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coo = self._coo_container(arg1, dtype=dtype, shape=shape)
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||||
bsr = coo.tobsr(blocksize=blocksize)
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self.indptr, self.indices, self.data, self._shape = (
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bsr.indptr, bsr.indices, bsr.data, bsr._shape
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||||
)
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|
||||
elif len(arg1) == 3:
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# (data,indices,indptr) format
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(data, indices, indptr) = arg1
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# Select index dtype large enough to pass array and
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# scalar parameters to sparsetools
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maxval = 1
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if shape is not None:
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maxval = max(shape)
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if blocksize is not None:
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||||
maxval = max(maxval, max(blocksize))
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||||
idx_dtype = self._get_index_dtype((indices, indptr), maxval=maxval,
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||||
check_contents=True)
|
||||
if not copy:
|
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copy = copy_if_needed
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||||
self.indices = np.array(indices, copy=copy, dtype=idx_dtype)
|
||||
self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype)
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||||
self.data = getdata(data, copy=copy, dtype=dtype)
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||||
if self.data.ndim != 3:
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||||
raise ValueError(
|
||||
f'BSR data must be 3-dimensional, got shape={self.data.shape}'
|
||||
)
|
||||
if blocksize is not None:
|
||||
if not isshape(blocksize):
|
||||
raise ValueError(f'invalid blocksize={blocksize}')
|
||||
if tuple(blocksize) != self.data.shape[1:]:
|
||||
raise ValueError(
|
||||
f'mismatching blocksize={blocksize}'
|
||||
f' vs {self.data.shape[1:]}'
|
||||
)
|
||||
else:
|
||||
raise ValueError('unrecognized bsr_array constructor usage')
|
||||
else:
|
||||
# must be dense
|
||||
try:
|
||||
arg1 = np.asarray(arg1)
|
||||
except Exception as e:
|
||||
raise ValueError("unrecognized form for "
|
||||
f"{self.format}_matrix constructor") from e
|
||||
if isinstance(self, sparray) and arg1.ndim != 2:
|
||||
raise ValueError(f"BSR arrays don't support {arg1.ndim}D input. Use 2D")
|
||||
arg1 = self._coo_container(arg1, dtype=dtype).tobsr(blocksize=blocksize)
|
||||
self.indptr, self.indices, self.data, self._shape = (
|
||||
arg1.indptr, arg1.indices, arg1.data, arg1._shape
|
||||
)
|
||||
|
||||
if shape is not None:
|
||||
self._shape = check_shape(shape)
|
||||
else:
|
||||
if self.shape is None:
|
||||
# shape not already set, try to infer dimensions
|
||||
try:
|
||||
M = len(self.indptr) - 1
|
||||
N = self.indices.max() + 1
|
||||
except Exception as e:
|
||||
raise ValueError('unable to infer matrix dimensions') from e
|
||||
else:
|
||||
R,C = self.blocksize
|
||||
self._shape = check_shape((M*R,N*C))
|
||||
|
||||
if self.shape is None:
|
||||
if shape is None:
|
||||
# TODO infer shape here
|
||||
raise ValueError('need to infer shape')
|
||||
else:
|
||||
self._shape = check_shape(shape)
|
||||
|
||||
if dtype is not None:
|
||||
self.data = self.data.astype(getdtype(dtype, self.data), copy=False)
|
||||
|
||||
self.check_format(full_check=False)
|
||||
|
||||
def check_format(self, full_check=True):
|
||||
"""Check whether the array/matrix respects the BSR format.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
full_check : bool, optional
|
||||
If `True`, run rigorous check, scanning arrays for valid values.
|
||||
Note that activating those check might copy arrays for casting,
|
||||
modifying indices and index pointers' inplace.
|
||||
If `False`, run basic checks on attributes. O(1) operations.
|
||||
Default is `True`.
|
||||
"""
|
||||
M,N = self.shape
|
||||
R,C = self.blocksize
|
||||
|
||||
# index arrays should have integer data types
|
||||
if self.indptr.dtype.kind != 'i':
|
||||
warn(f"indptr array has non-integer dtype ({self.indptr.dtype.name})",
|
||||
stacklevel=2)
|
||||
if self.indices.dtype.kind != 'i':
|
||||
warn(f"indices array has non-integer dtype ({self.indices.dtype.name})",
|
||||
stacklevel=2)
|
||||
|
||||
# check array shapes
|
||||
if self.indices.ndim != 1 or self.indptr.ndim != 1:
|
||||
raise ValueError("indices, and indptr should be 1-D")
|
||||
if self.data.ndim != 3:
|
||||
raise ValueError("data should be 3-D")
|
||||
|
||||
# check index pointer
|
||||
if (len(self.indptr) != M//R + 1):
|
||||
raise ValueError(
|
||||
f"index pointer size ({len(self.indptr)}) should be ({M//R + 1})"
|
||||
)
|
||||
if (self.indptr[0] != 0):
|
||||
raise ValueError("index pointer should start with 0")
|
||||
|
||||
# check index and data arrays
|
||||
if (len(self.indices) != len(self.data)):
|
||||
raise ValueError("indices and data should have the same size")
|
||||
if (self.indptr[-1] > len(self.indices)):
|
||||
raise ValueError("Last value of index pointer should be less than "
|
||||
"the size of index and data arrays")
|
||||
|
||||
self.prune()
|
||||
|
||||
if full_check:
|
||||
# check format validity (more expensive)
|
||||
if self.nnz > 0:
|
||||
if self.indices.max() >= N//C:
|
||||
raise ValueError(
|
||||
f"column index values must be < {N//C}"
|
||||
f" (now max {self.indices.max()})"
|
||||
)
|
||||
if self.indices.min() < 0:
|
||||
raise ValueError("column index values must be >= 0")
|
||||
if np.diff(self.indptr).min() < 0:
|
||||
raise ValueError("index pointer values must form a "
|
||||
"non-decreasing sequence")
|
||||
|
||||
idx_dtype = self._get_index_dtype((self.indices, self.indptr))
|
||||
self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
|
||||
self.indices = np.asarray(self.indices, dtype=idx_dtype)
|
||||
self.data = to_native(self.data)
|
||||
# if not self.has_sorted_indices():
|
||||
# warn('Indices were not in sorted order. Sorting indices.')
|
||||
# self.sort_indices(check_first=False)
|
||||
|
||||
@property
|
||||
def blocksize(self) -> tuple:
|
||||
"""Block size of the matrix."""
|
||||
return self.data.shape[1:]
|
||||
|
||||
def _getnnz(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError("_getnnz over an axis is not implemented "
|
||||
"for BSR format")
|
||||
R, C = self.blocksize
|
||||
return int(self.indptr[-1]) * R * C
|
||||
|
||||
_getnnz.__doc__ = _spbase._getnnz.__doc__
|
||||
|
||||
def count_nonzero(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError(
|
||||
"count_nonzero over axis is not implemented for BSR format."
|
||||
)
|
||||
return np.count_nonzero(self._deduped_data())
|
||||
|
||||
count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
|
||||
|
||||
def __repr__(self):
|
||||
_, fmt = _formats[self.format]
|
||||
sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
|
||||
b = 'x'.join(str(x) for x in self.blocksize)
|
||||
return (
|
||||
f"<{fmt} sparse {sparse_cls} of dtype '{self.dtype}'\n"
|
||||
f"\twith {self.nnz} stored elements (blocksize={b}) and shape {self.shape}>"
|
||||
)
|
||||
|
||||
def diagonal(self, k=0):
|
||||
rows, cols = self.shape
|
||||
if k <= -rows or k >= cols:
|
||||
return np.empty(0, dtype=self.data.dtype)
|
||||
R, C = self.blocksize
|
||||
y = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
|
||||
dtype=upcast(self.dtype))
|
||||
_sparsetools.bsr_diagonal(k, rows // R, cols // C, R, C,
|
||||
self.indptr, self.indices,
|
||||
np.ravel(self.data), y)
|
||||
return y
|
||||
|
||||
diagonal.__doc__ = _spbase.diagonal.__doc__
|
||||
|
||||
##########################
|
||||
# NotImplemented methods #
|
||||
##########################
|
||||
|
||||
def __getitem__(self,key):
|
||||
raise NotImplementedError
|
||||
|
||||
def __setitem__(self,key,val):
|
||||
raise NotImplementedError
|
||||
|
||||
######################
|
||||
# Arithmetic methods #
|
||||
######################
|
||||
|
||||
def _add_dense(self, other):
|
||||
return self.tocoo(copy=False)._add_dense(other)
|
||||
|
||||
def _matmul_vector(self, other):
|
||||
M,N = self.shape
|
||||
R,C = self.blocksize
|
||||
|
||||
result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
|
||||
|
||||
bsr_matvec(M//R, N//C, R, C,
|
||||
self.indptr, self.indices, self.data.ravel(),
|
||||
other, result)
|
||||
|
||||
return result
|
||||
|
||||
def _matmul_multivector(self,other):
|
||||
R,C = self.blocksize
|
||||
M,N = self.shape
|
||||
n_vecs = other.shape[1] # number of column vectors
|
||||
|
||||
result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
|
||||
|
||||
bsr_matvecs(M//R, N//C, n_vecs, R, C,
|
||||
self.indptr, self.indices, self.data.ravel(),
|
||||
other.ravel(), result.ravel())
|
||||
|
||||
return result
|
||||
|
||||
def _matmul_sparse(self, other):
|
||||
M, K1 = self.shape
|
||||
K2, N = other.shape
|
||||
|
||||
R,n = self.blocksize
|
||||
|
||||
# convert to this format
|
||||
if other.format == "bsr":
|
||||
C = other.blocksize[1]
|
||||
else:
|
||||
C = 1
|
||||
|
||||
if other.format == "csr" and n == 1:
|
||||
other = other.tobsr(blocksize=(n,C), copy=False) # lightweight conversion
|
||||
else:
|
||||
other = other.tobsr(blocksize=(n,C))
|
||||
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices,
|
||||
other.indptr, other.indices))
|
||||
|
||||
bnnz = csr_matmat_maxnnz(M//R, N//C,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
other.indptr.astype(idx_dtype),
|
||||
other.indices.astype(idx_dtype))
|
||||
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices,
|
||||
other.indptr, other.indices),
|
||||
maxval=bnnz)
|
||||
indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
|
||||
indices = np.empty(bnnz, dtype=idx_dtype)
|
||||
data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype))
|
||||
|
||||
bsr_matmat(bnnz, M//R, N//C, R, C, n,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
np.ravel(self.data),
|
||||
other.indptr.astype(idx_dtype),
|
||||
other.indices.astype(idx_dtype),
|
||||
np.ravel(other.data),
|
||||
indptr,
|
||||
indices,
|
||||
data)
|
||||
|
||||
data = data.reshape(-1,R,C)
|
||||
|
||||
# TODO eliminate zeros
|
||||
|
||||
return self._bsr_container(
|
||||
(data, indices, indptr), shape=(M, N), blocksize=(R, C)
|
||||
)
|
||||
|
||||
######################
|
||||
# Conversion methods #
|
||||
######################
|
||||
|
||||
def tobsr(self, blocksize=None, copy=False):
|
||||
"""Convert this array/matrix into Block Sparse Row Format.
|
||||
|
||||
With copy=False, the data/indices may be shared between this
|
||||
array/matrix and the resultant bsr_array/bsr_matrix.
|
||||
|
||||
If blocksize=(R, C) is provided, it will be used for determining
|
||||
block size of the bsr_array/bsr_matrix.
|
||||
"""
|
||||
if blocksize not in [None, self.blocksize]:
|
||||
return self.tocsr().tobsr(blocksize=blocksize)
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
def tocsr(self, copy=False):
|
||||
M, N = self.shape
|
||||
R, C = self.blocksize
|
||||
nnz = self.nnz
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices),
|
||||
maxval=max(nnz, N))
|
||||
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||||
indices = np.empty(nnz, dtype=idx_dtype)
|
||||
data = np.empty(nnz, dtype=upcast(self.dtype))
|
||||
|
||||
bsr_tocsr(M // R, # n_brow
|
||||
N // C, # n_bcol
|
||||
R, C,
|
||||
self.indptr.astype(idx_dtype, copy=False),
|
||||
self.indices.astype(idx_dtype, copy=False),
|
||||
self.data,
|
||||
indptr,
|
||||
indices,
|
||||
data)
|
||||
return self._csr_container((data, indices, indptr), shape=self.shape)
|
||||
|
||||
tocsr.__doc__ = _spbase.tocsr.__doc__
|
||||
|
||||
def tocsc(self, copy=False):
|
||||
return self.tocsr(copy=False).tocsc(copy=copy)
|
||||
|
||||
tocsc.__doc__ = _spbase.tocsc.__doc__
|
||||
|
||||
def tocoo(self, copy=True):
|
||||
"""Convert this array/matrix to COOrdinate format.
|
||||
|
||||
When copy=False the data array will be shared between
|
||||
this array/matrix and the resultant coo_array/coo_matrix.
|
||||
"""
|
||||
|
||||
M,N = self.shape
|
||||
R,C = self.blocksize
|
||||
|
||||
indptr_diff = np.diff(self.indptr)
|
||||
if indptr_diff.dtype.itemsize > np.dtype(np.intp).itemsize:
|
||||
# Check for potential overflow
|
||||
indptr_diff_limited = indptr_diff.astype(np.intp)
|
||||
if np.any(indptr_diff_limited != indptr_diff):
|
||||
raise ValueError("Matrix too big to convert")
|
||||
indptr_diff = indptr_diff_limited
|
||||
|
||||
idx_dtype = self._get_index_dtype(maxval=max(M, N))
|
||||
row = (R * np.arange(M//R, dtype=idx_dtype)).repeat(indptr_diff)
|
||||
row = row.repeat(R*C).reshape(-1,R,C)
|
||||
row += np.tile(np.arange(R, dtype=idx_dtype).reshape(-1,1), (1,C))
|
||||
row = row.reshape(-1)
|
||||
|
||||
col = ((C * self.indices).astype(idx_dtype, copy=False)
|
||||
.repeat(R*C).reshape(-1,R,C))
|
||||
col += np.tile(np.arange(C, dtype=idx_dtype), (R,1))
|
||||
col = col.reshape(-1)
|
||||
|
||||
data = self.data.reshape(-1)
|
||||
|
||||
if copy:
|
||||
data = data.copy()
|
||||
|
||||
return self._coo_container(
|
||||
(data, (row, col)), shape=self.shape
|
||||
)
|
||||
|
||||
def toarray(self, order=None, out=None):
|
||||
return self.tocoo(copy=False).toarray(order=order, out=out)
|
||||
|
||||
toarray.__doc__ = _spbase.toarray.__doc__
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
if axes is not None and axes != (1, 0):
|
||||
raise ValueError("Sparse matrices do not support "
|
||||
"an 'axes' parameter because swapping "
|
||||
"dimensions is the only logical permutation.")
|
||||
|
||||
R, C = self.blocksize
|
||||
M, N = self.shape
|
||||
NBLK = self.nnz//(R*C)
|
||||
|
||||
if self.nnz == 0:
|
||||
return self._bsr_container((N, M), blocksize=(C, R),
|
||||
dtype=self.dtype, copy=copy)
|
||||
|
||||
indptr = np.empty(N//C + 1, dtype=self.indptr.dtype)
|
||||
indices = np.empty(NBLK, dtype=self.indices.dtype)
|
||||
data = np.empty((NBLK, C, R), dtype=self.data.dtype)
|
||||
|
||||
bsr_transpose(M//R, N//C, R, C,
|
||||
self.indptr, self.indices, self.data.ravel(),
|
||||
indptr, indices, data.ravel())
|
||||
|
||||
return self._bsr_container((data, indices, indptr),
|
||||
shape=(N, M), copy=copy)
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
##############################################################
|
||||
# methods that examine or modify the internal data structure #
|
||||
##############################################################
|
||||
|
||||
def eliminate_zeros(self):
|
||||
"""Remove zero elements in-place."""
|
||||
|
||||
if not self.nnz:
|
||||
return # nothing to do
|
||||
|
||||
R,C = self.blocksize
|
||||
M,N = self.shape
|
||||
|
||||
mask = (self.data != 0).reshape(-1,R*C).sum(axis=1) # nonzero blocks
|
||||
|
||||
nonzero_blocks = mask.nonzero()[0]
|
||||
|
||||
self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks]
|
||||
|
||||
# modifies self.indptr and self.indices *in place*
|
||||
_sparsetools.csr_eliminate_zeros(M//R, N//C, self.indptr,
|
||||
self.indices, mask)
|
||||
self.prune()
|
||||
|
||||
def sum_duplicates(self):
|
||||
"""Eliminate duplicate array/matrix entries by adding them together
|
||||
|
||||
The is an *in place* operation
|
||||
"""
|
||||
if self.has_canonical_format:
|
||||
return
|
||||
self.sort_indices()
|
||||
R, C = self.blocksize
|
||||
M, N = self.shape
|
||||
|
||||
# port of _sparsetools.csr_sum_duplicates
|
||||
n_row = M // R
|
||||
nnz = 0
|
||||
row_end = 0
|
||||
for i in range(n_row):
|
||||
jj = row_end
|
||||
row_end = self.indptr[i+1]
|
||||
while jj < row_end:
|
||||
j = self.indices[jj]
|
||||
x = self.data[jj]
|
||||
jj += 1
|
||||
while jj < row_end and self.indices[jj] == j:
|
||||
x += self.data[jj]
|
||||
jj += 1
|
||||
self.indices[nnz] = j
|
||||
self.data[nnz] = x
|
||||
nnz += 1
|
||||
self.indptr[i+1] = nnz
|
||||
|
||||
self.prune() # nnz may have changed
|
||||
self.has_canonical_format = True
|
||||
|
||||
def sort_indices(self):
|
||||
"""Sort the indices of this array/matrix *in place*
|
||||
"""
|
||||
if self.has_sorted_indices:
|
||||
return
|
||||
|
||||
R,C = self.blocksize
|
||||
M,N = self.shape
|
||||
|
||||
bsr_sort_indices(M//R, N//C, R, C, self.indptr, self.indices, self.data.ravel())
|
||||
|
||||
self.has_sorted_indices = True
|
||||
|
||||
def prune(self):
|
||||
"""Remove empty space after all non-zero elements.
|
||||
"""
|
||||
|
||||
R,C = self.blocksize
|
||||
M,N = self.shape
|
||||
|
||||
if len(self.indptr) != M//R + 1:
|
||||
raise ValueError("index pointer has invalid length")
|
||||
|
||||
bnnz = self.indptr[-1]
|
||||
|
||||
if len(self.indices) < bnnz:
|
||||
raise ValueError("indices array has too few elements")
|
||||
if len(self.data) < bnnz:
|
||||
raise ValueError("data array has too few elements")
|
||||
|
||||
self.data = self.data[:bnnz]
|
||||
self.indices = self.indices[:bnnz]
|
||||
|
||||
# utility functions
|
||||
def _binopt(self, other, op, in_shape=None, out_shape=None):
|
||||
"""Apply the binary operation fn to two sparse matrices."""
|
||||
|
||||
# Ideally we'd take the GCDs of the blocksize dimensions
|
||||
# and explode self and other to match.
|
||||
other = self.__class__(other, blocksize=self.blocksize)
|
||||
|
||||
# e.g. bsr_plus_bsr, etc.
|
||||
fn = getattr(_sparsetools, self.format + op + self.format)
|
||||
|
||||
R,C = self.blocksize
|
||||
|
||||
max_bnnz = len(self.data) + len(other.data)
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices,
|
||||
other.indptr, other.indices),
|
||||
maxval=max_bnnz)
|
||||
indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
|
||||
indices = np.empty(max_bnnz, dtype=idx_dtype)
|
||||
|
||||
bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_']
|
||||
if op in bool_ops:
|
||||
data = np.empty(R*C*max_bnnz, dtype=np.bool_)
|
||||
else:
|
||||
data = np.empty(R*C*max_bnnz, dtype=upcast(self.dtype,other.dtype))
|
||||
|
||||
fn(self.shape[0]//R, self.shape[1]//C, R, C,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
self.data,
|
||||
other.indptr.astype(idx_dtype),
|
||||
other.indices.astype(idx_dtype),
|
||||
np.ravel(other.data),
|
||||
indptr,
|
||||
indices,
|
||||
data)
|
||||
|
||||
actual_bnnz = indptr[-1]
|
||||
indices = indices[:actual_bnnz]
|
||||
data = data[:R*C*actual_bnnz]
|
||||
|
||||
if actual_bnnz < max_bnnz/2:
|
||||
indices = indices.copy()
|
||||
data = data.copy()
|
||||
|
||||
data = data.reshape(-1,R,C)
|
||||
|
||||
return self.__class__((data, indices, indptr), shape=self.shape)
|
||||
|
||||
# needed by _data_matrix
|
||||
def _with_data(self,data,copy=True):
|
||||
"""Returns a matrix with the same sparsity structure as self,
|
||||
but with different data. By default the structure arrays
|
||||
(i.e. .indptr and .indices) are copied.
|
||||
"""
|
||||
if copy:
|
||||
return self.__class__((data,self.indices.copy(),self.indptr.copy()),
|
||||
shape=self.shape,dtype=data.dtype)
|
||||
else:
|
||||
return self.__class__((data,self.indices,self.indptr),
|
||||
shape=self.shape,dtype=data.dtype)
|
||||
|
||||
# # these functions are used by the parent class
|
||||
# # to remove redundancy between bsc_matrix and bsr_matrix
|
||||
# def _swap(self,x):
|
||||
# """swap the members of x if this is a column-oriented matrix
|
||||
# """
|
||||
# return (x[0],x[1])
|
||||
|
||||
def _broadcast_to(self, shape, copy=False):
|
||||
return _spbase._broadcast_to(self, shape, copy)
|
||||
|
||||
|
||||
def isspmatrix_bsr(x):
|
||||
"""Is `x` of a bsr_matrix type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a bsr matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a bsr matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import bsr_array, bsr_matrix, csr_matrix, isspmatrix_bsr
|
||||
>>> isspmatrix_bsr(bsr_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_bsr(bsr_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_bsr(csr_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, bsr_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class bsr_array(_bsr_base, sparray):
|
||||
"""
|
||||
Block Sparse Row format sparse array.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
bsr_array(D, [blocksize=(R,C)])
|
||||
where D is a 2-D ndarray.
|
||||
|
||||
bsr_array(S, [blocksize=(R,C)])
|
||||
with another sparse array or matrix S (equivalent to S.tobsr())
|
||||
|
||||
bsr_array((M, N), [blocksize=(R,C), dtype])
|
||||
to construct an empty sparse array with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
bsr_array((data, ij), [blocksize=(R,C), shape=(M, N)])
|
||||
where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
|
||||
|
||||
bsr_array((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard BSR representation where the block column
|
||||
indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
|
||||
and their corresponding block values are stored in
|
||||
``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
|
||||
supplied, the array dimensions are inferred from the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
BSR format data array of the array
|
||||
indices
|
||||
BSR format index array of the array
|
||||
indptr
|
||||
BSR format index pointer array of the array
|
||||
blocksize
|
||||
Block size
|
||||
has_sorted_indices : bool
|
||||
Whether indices are sorted
|
||||
has_canonical_format : bool
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
**Summary of BSR format**
|
||||
|
||||
The Block Sparse Row (BSR) format is very similar to the Compressed
|
||||
Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
|
||||
sub matrices like the last example below. Such sparse block matrices often
|
||||
arise in vector-valued finite element discretizations. In such cases, BSR is
|
||||
considerably more efficient than CSR and CSC for many sparse arithmetic
|
||||
operations.
|
||||
|
||||
**Blocksize**
|
||||
|
||||
The blocksize (R,C) must evenly divide the shape of the sparse array (M,N).
|
||||
That is, R and C must satisfy the relationship ``M % R = 0`` and
|
||||
``N % C = 0``.
|
||||
|
||||
If no blocksize is specified, a simple heuristic is applied to determine
|
||||
an appropriate blocksize.
|
||||
|
||||
**Canonical Format**
|
||||
|
||||
In canonical format, there are no duplicate blocks and indices are sorted
|
||||
per row.
|
||||
|
||||
**Limitations**
|
||||
|
||||
Block Sparse Row format sparse arrays do not support slicing.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import bsr_array
|
||||
>>> bsr_array((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> col = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3 ,4, 5, 6])
|
||||
>>> bsr_array((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
|
||||
>>> bsr_array((data,indices,indptr), shape=(6, 6)).toarray()
|
||||
array([[1, 1, 0, 0, 2, 2],
|
||||
[1, 1, 0, 0, 2, 2],
|
||||
[0, 0, 0, 0, 3, 3],
|
||||
[0, 0, 0, 0, 3, 3],
|
||||
[4, 4, 5, 5, 6, 6],
|
||||
[4, 4, 5, 5, 6, 6]])
|
||||
|
||||
"""
|
||||
|
||||
|
||||
class bsr_matrix(spmatrix, _bsr_base):
|
||||
"""
|
||||
Block Sparse Row format sparse matrix.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
bsr_matrix(D, [blocksize=(R,C)])
|
||||
where D is a 2-D ndarray.
|
||||
|
||||
bsr_matrix(S, [blocksize=(R,C)])
|
||||
with another sparse array or matrix S (equivalent to S.tobsr())
|
||||
|
||||
bsr_matrix((M, N), [blocksize=(R,C), dtype])
|
||||
to construct an empty sparse matrix with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
|
||||
where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
|
||||
|
||||
bsr_matrix((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard BSR representation where the block column
|
||||
indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
|
||||
and their corresponding block values are stored in
|
||||
``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
|
||||
supplied, the matrix dimensions are inferred from the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
BSR format data array of the matrix
|
||||
indices
|
||||
BSR format index array of the matrix
|
||||
indptr
|
||||
BSR format index pointer array of the matrix
|
||||
blocksize
|
||||
Block size
|
||||
has_sorted_indices : bool
|
||||
Whether indices are sorted
|
||||
has_canonical_format : bool
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
**Summary of BSR format**
|
||||
|
||||
The Block Sparse Row (BSR) format is very similar to the Compressed
|
||||
Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
|
||||
sub matrices like the last example below. Such sparse block matrices often
|
||||
arise in vector-valued finite element discretizations. In such cases, BSR is
|
||||
considerably more efficient than CSR and CSC for many sparse arithmetic
|
||||
operations.
|
||||
|
||||
**Blocksize**
|
||||
|
||||
The blocksize (R,C) must evenly divide the shape of the sparse matrix (M,N).
|
||||
That is, R and C must satisfy the relationship ``M % R = 0`` and
|
||||
``N % C = 0``.
|
||||
|
||||
If no blocksize is specified, a simple heuristic is applied to determine
|
||||
an appropriate blocksize.
|
||||
|
||||
**Canonical Format**
|
||||
|
||||
In canonical format, there are no duplicate blocks and indices are sorted
|
||||
per row.
|
||||
|
||||
**Limitations**
|
||||
|
||||
Block Sparse Row format sparse matrices do not support slicing.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import bsr_matrix
|
||||
>>> bsr_matrix((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> col = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3 ,4, 5, 6])
|
||||
>>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
|
||||
>>> bsr_matrix((data,indices,indptr), shape=(6, 6)).toarray()
|
||||
array([[1, 1, 0, 0, 2, 2],
|
||||
[1, 1, 0, 0, 2, 2],
|
||||
[0, 0, 0, 0, 3, 3],
|
||||
[0, 0, 0, 0, 3, 3],
|
||||
[4, 4, 5, 5, 6, 6],
|
||||
[4, 4, 5, 5, 6, 6]])
|
||||
|
||||
"""
|
||||
|
||||
1328
venv/lib/python3.13/site-packages/scipy/sparse/_compressed.py
Normal file
1328
venv/lib/python3.13/site-packages/scipy/sparse/_compressed.py
Normal file
File diff suppressed because it is too large
Load diff
1454
venv/lib/python3.13/site-packages/scipy/sparse/_construct.py
Normal file
1454
venv/lib/python3.13/site-packages/scipy/sparse/_construct.py
Normal file
File diff suppressed because it is too large
Load diff
1581
venv/lib/python3.13/site-packages/scipy/sparse/_coo.py
Normal file
1581
venv/lib/python3.13/site-packages/scipy/sparse/_coo.py
Normal file
File diff suppressed because it is too large
Load diff
367
venv/lib/python3.13/site-packages/scipy/sparse/_csc.py
Normal file
367
venv/lib/python3.13/site-packages/scipy/sparse/_csc.py
Normal file
|
|
@ -0,0 +1,367 @@
|
|||
"""Compressed Sparse Column matrix format"""
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['csc_array', 'csc_matrix', 'isspmatrix_csc']
|
||||
|
||||
|
||||
import numpy as np
|
||||
|
||||
from ._matrix import spmatrix
|
||||
from ._base import _spbase, sparray
|
||||
from ._sparsetools import csr_tocsc, expandptr
|
||||
from ._sputils import upcast
|
||||
|
||||
from ._compressed import _cs_matrix
|
||||
|
||||
|
||||
class _csc_base(_cs_matrix):
|
||||
_format = 'csc'
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
if axes is not None and axes != (1, 0):
|
||||
raise ValueError("Sparse arrays/matrices do not support "
|
||||
"an 'axes' parameter because swapping "
|
||||
"dimensions is the only logical permutation.")
|
||||
|
||||
M, N = self.shape
|
||||
|
||||
return self._csr_container((self.data, self.indices,
|
||||
self.indptr), (N, M), copy=copy)
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
def __iter__(self):
|
||||
yield from self.tocsr()
|
||||
|
||||
def tocsc(self, copy=False):
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
tocsc.__doc__ = _spbase.tocsc.__doc__
|
||||
|
||||
def tocsr(self, copy=False):
|
||||
M,N = self.shape
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices),
|
||||
maxval=max(self.nnz, N))
|
||||
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||||
indices = np.empty(self.nnz, dtype=idx_dtype)
|
||||
data = np.empty(self.nnz, dtype=upcast(self.dtype))
|
||||
|
||||
csr_tocsc(N, M,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
self.data,
|
||||
indptr,
|
||||
indices,
|
||||
data)
|
||||
|
||||
A = self._csr_container(
|
||||
(data, indices, indptr),
|
||||
shape=self.shape, copy=False
|
||||
)
|
||||
A.has_sorted_indices = True
|
||||
return A
|
||||
|
||||
tocsr.__doc__ = _spbase.tocsr.__doc__
|
||||
|
||||
def nonzero(self):
|
||||
# CSC can't use _cs_matrix's .nonzero method because it
|
||||
# returns the indices sorted for self transposed.
|
||||
|
||||
# Get row and col indices, from _cs_matrix.tocoo
|
||||
major_dim, minor_dim = self._swap(self.shape)
|
||||
minor_indices = self.indices
|
||||
major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype)
|
||||
expandptr(major_dim, self.indptr, major_indices)
|
||||
row, col = self._swap((major_indices, minor_indices))
|
||||
|
||||
# Remove explicit zeros
|
||||
nz_mask = self.data != 0
|
||||
row = row[nz_mask]
|
||||
col = col[nz_mask]
|
||||
|
||||
# Sort them to be in C-style order
|
||||
ind = np.argsort(row, kind='mergesort')
|
||||
row = row[ind]
|
||||
col = col[ind]
|
||||
|
||||
return row, col
|
||||
|
||||
nonzero.__doc__ = _cs_matrix.nonzero.__doc__
|
||||
|
||||
def _getrow(self, i):
|
||||
"""Returns a copy of row i of the matrix, as a (1 x n)
|
||||
CSR matrix (row vector).
|
||||
"""
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < 0:
|
||||
i += M
|
||||
if i < 0 or i >= M:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
return self._get_submatrix(minor=i).tocsr()
|
||||
|
||||
def _getcol(self, i):
|
||||
"""Returns a copy of column i of the matrix, as a (m x 1)
|
||||
CSC matrix (column vector).
|
||||
"""
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < 0:
|
||||
i += N
|
||||
if i < 0 or i >= N:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
return self._get_submatrix(major=i, copy=True)
|
||||
|
||||
def _get_intXarray(self, row, col):
|
||||
return self._major_index_fancy(col)._get_submatrix(minor=row)
|
||||
|
||||
def _get_intXslice(self, row, col):
|
||||
if col.step in (1, None):
|
||||
return self._get_submatrix(major=col, minor=row, copy=True)
|
||||
return self._major_slice(col)._get_submatrix(minor=row)
|
||||
|
||||
def _get_sliceXint(self, row, col):
|
||||
if row.step in (1, None):
|
||||
return self._get_submatrix(major=col, minor=row, copy=True)
|
||||
return self._get_submatrix(major=col)._minor_slice(row)
|
||||
|
||||
def _get_sliceXarray(self, row, col):
|
||||
return self._major_index_fancy(col)._minor_slice(row)
|
||||
|
||||
def _get_arrayXint(self, row, col):
|
||||
res = self._get_submatrix(major=col)._minor_index_fancy(row)
|
||||
if row.ndim > 1:
|
||||
return res.reshape(row.shape)
|
||||
return res
|
||||
|
||||
def _get_arrayXslice(self, row, col):
|
||||
return self._major_slice(col)._minor_index_fancy(row)
|
||||
|
||||
# these functions are used by the parent class (_cs_matrix)
|
||||
# to remove redundancy between csc_array and csr_matrix
|
||||
@staticmethod
|
||||
def _swap(x):
|
||||
"""swap the members of x if this is a column-oriented matrix
|
||||
"""
|
||||
return x[1], x[0]
|
||||
|
||||
|
||||
def isspmatrix_csc(x):
|
||||
"""Is `x` of csc_matrix type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a csc matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a csc matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import csc_array, csc_matrix, coo_matrix, isspmatrix_csc
|
||||
>>> isspmatrix_csc(csc_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_csc(csc_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_csc(coo_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, csc_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class csc_array(_csc_base, sparray):
|
||||
"""
|
||||
Compressed Sparse Column array.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
csc_array(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
csc_array(S)
|
||||
with another sparse array or matrix S (equivalent to S.tocsc())
|
||||
|
||||
csc_array((M, N), [dtype])
|
||||
to construct an empty array with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
csc_array((data, (row_ind, col_ind)), [shape=(M, N)])
|
||||
where ``data``, ``row_ind`` and ``col_ind`` satisfy the
|
||||
relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
|
||||
|
||||
csc_array((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard CSC representation where the row indices for
|
||||
column i are stored in ``indices[indptr[i]:indptr[i+1]]``
|
||||
and their corresponding values are stored in
|
||||
``data[indptr[i]:indptr[i+1]]``. If the shape parameter is
|
||||
not supplied, the array dimensions are inferred from
|
||||
the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
CSC format data array of the array
|
||||
indices
|
||||
CSC format index array of the array
|
||||
indptr
|
||||
CSC format index pointer array of the array
|
||||
has_sorted_indices
|
||||
has_canonical_format
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the CSC format
|
||||
- efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
|
||||
- efficient column slicing
|
||||
- fast matrix vector products (CSR, BSR may be faster)
|
||||
|
||||
Disadvantages of the CSC format
|
||||
- slow row slicing operations (consider CSR)
|
||||
- changes to the sparsity structure are expensive (consider LIL or DOK)
|
||||
|
||||
Canonical format
|
||||
- Within each column, indices are sorted by row.
|
||||
- There are no duplicate entries.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csc_array
|
||||
>>> csc_array((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> col = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csc_array((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 4],
|
||||
[0, 0, 5],
|
||||
[2, 3, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csc_array((data, indices, indptr), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 4],
|
||||
[0, 0, 5],
|
||||
[2, 3, 6]])
|
||||
|
||||
"""
|
||||
|
||||
|
||||
class csc_matrix(spmatrix, _csc_base):
|
||||
"""
|
||||
Compressed Sparse Column matrix.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
csc_matrix(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
csc_matrix(S)
|
||||
with another sparse array or matrix S (equivalent to S.tocsc())
|
||||
|
||||
csc_matrix((M, N), [dtype])
|
||||
to construct an empty matrix with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
csc_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
|
||||
where ``data``, ``row_ind`` and ``col_ind`` satisfy the
|
||||
relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
|
||||
|
||||
csc_matrix((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard CSC representation where the row indices for
|
||||
column i are stored in ``indices[indptr[i]:indptr[i+1]]``
|
||||
and their corresponding values are stored in
|
||||
``data[indptr[i]:indptr[i+1]]``. If the shape parameter is
|
||||
not supplied, the matrix dimensions are inferred from
|
||||
the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
CSC format data array of the matrix
|
||||
indices
|
||||
CSC format index array of the matrix
|
||||
indptr
|
||||
CSC format index pointer array of the matrix
|
||||
has_sorted_indices
|
||||
has_canonical_format
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the CSC format
|
||||
- efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
|
||||
- efficient column slicing
|
||||
- fast matrix vector products (CSR, BSR may be faster)
|
||||
|
||||
Disadvantages of the CSC format
|
||||
- slow row slicing operations (consider CSR)
|
||||
- changes to the sparsity structure are expensive (consider LIL or DOK)
|
||||
|
||||
Canonical format
|
||||
- Within each column, indices are sorted by row.
|
||||
- There are no duplicate entries.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csc_matrix
|
||||
>>> csc_matrix((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> col = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csc_matrix((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 4],
|
||||
[0, 0, 5],
|
||||
[2, 3, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 4],
|
||||
[0, 0, 5],
|
||||
[2, 3, 6]])
|
||||
|
||||
"""
|
||||
|
||||
Binary file not shown.
558
venv/lib/python3.13/site-packages/scipy/sparse/_csr.py
Normal file
558
venv/lib/python3.13/site-packages/scipy/sparse/_csr.py
Normal file
|
|
@ -0,0 +1,558 @@
|
|||
"""Compressed Sparse Row matrix format"""
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['csr_array', 'csr_matrix', 'isspmatrix_csr']
|
||||
|
||||
import numpy as np
|
||||
|
||||
from ._matrix import spmatrix
|
||||
from ._base import _spbase, sparray
|
||||
from ._sparsetools import (csr_tocsc, csr_tobsr, csr_count_blocks,
|
||||
get_csr_submatrix, csr_sample_values)
|
||||
from ._sputils import upcast
|
||||
|
||||
from ._compressed import _cs_matrix
|
||||
|
||||
|
||||
class _csr_base(_cs_matrix):
|
||||
_format = 'csr'
|
||||
_allow_nd = (1, 2)
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
if axes is not None and axes != (1, 0):
|
||||
raise ValueError("Sparse arrays/matrices do not support "
|
||||
"an 'axes' parameter because swapping "
|
||||
"dimensions is the only logical permutation.")
|
||||
|
||||
if self.ndim == 1:
|
||||
return self.copy() if copy else self
|
||||
M, N = self.shape
|
||||
return self._csc_container((self.data, self.indices,
|
||||
self.indptr), shape=(N, M), copy=copy)
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
def tolil(self, copy=False):
|
||||
if self.ndim != 2:
|
||||
raise ValueError("Cannot convert a 1d sparse array to lil format")
|
||||
lil = self._lil_container(self.shape, dtype=self.dtype)
|
||||
|
||||
self.sum_duplicates()
|
||||
ptr,ind,dat = self.indptr,self.indices,self.data
|
||||
rows, data = lil.rows, lil.data
|
||||
|
||||
for n in range(self.shape[0]):
|
||||
start = ptr[n]
|
||||
end = ptr[n+1]
|
||||
rows[n] = ind[start:end].tolist()
|
||||
data[n] = dat[start:end].tolist()
|
||||
|
||||
return lil
|
||||
|
||||
tolil.__doc__ = _spbase.tolil.__doc__
|
||||
|
||||
def tocsr(self, copy=False):
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
tocsr.__doc__ = _spbase.tocsr.__doc__
|
||||
|
||||
def tocsc(self, copy=False):
|
||||
if self.ndim != 2:
|
||||
raise ValueError("Cannot convert a 1d sparse array to csc format")
|
||||
M, N = self.shape
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices),
|
||||
maxval=max(self.nnz, M))
|
||||
indptr = np.empty(N + 1, dtype=idx_dtype)
|
||||
indices = np.empty(self.nnz, dtype=idx_dtype)
|
||||
data = np.empty(self.nnz, dtype=upcast(self.dtype))
|
||||
|
||||
csr_tocsc(M, N,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
self.data,
|
||||
indptr,
|
||||
indices,
|
||||
data)
|
||||
|
||||
A = self._csc_container((data, indices, indptr), shape=self.shape)
|
||||
A.has_sorted_indices = True
|
||||
return A
|
||||
|
||||
tocsc.__doc__ = _spbase.tocsc.__doc__
|
||||
|
||||
def tobsr(self, blocksize=None, copy=True):
|
||||
if self.ndim != 2:
|
||||
raise ValueError("Cannot convert a 1d sparse array to bsr format")
|
||||
if blocksize is None:
|
||||
from ._spfuncs import estimate_blocksize
|
||||
return self.tobsr(blocksize=estimate_blocksize(self))
|
||||
|
||||
elif blocksize == (1,1):
|
||||
arg1 = (self.data.reshape(-1,1,1),self.indices,self.indptr)
|
||||
return self._bsr_container(arg1, shape=self.shape, copy=copy)
|
||||
|
||||
else:
|
||||
R,C = blocksize
|
||||
M,N = self.shape
|
||||
|
||||
if R < 1 or C < 1 or M % R != 0 or N % C != 0:
|
||||
raise ValueError(f'invalid blocksize {blocksize}')
|
||||
|
||||
blks = csr_count_blocks(M,N,R,C,self.indptr,self.indices)
|
||||
|
||||
idx_dtype = self._get_index_dtype((self.indptr, self.indices),
|
||||
maxval=max(N//C, blks))
|
||||
indptr = np.empty(M//R+1, dtype=idx_dtype)
|
||||
indices = np.empty(blks, dtype=idx_dtype)
|
||||
data = np.zeros((blks,R,C), dtype=self.dtype)
|
||||
|
||||
csr_tobsr(M, N, R, C,
|
||||
self.indptr.astype(idx_dtype),
|
||||
self.indices.astype(idx_dtype),
|
||||
self.data,
|
||||
indptr, indices, data.ravel())
|
||||
|
||||
return self._bsr_container(
|
||||
(data, indices, indptr), shape=self.shape
|
||||
)
|
||||
|
||||
tobsr.__doc__ = _spbase.tobsr.__doc__
|
||||
|
||||
# these functions are used by the parent class (_cs_matrix)
|
||||
# to remove redundancy between csc_matrix and csr_array
|
||||
@staticmethod
|
||||
def _swap(x):
|
||||
"""swap the members of x if this is a column-oriented matrix
|
||||
"""
|
||||
return x
|
||||
|
||||
def __iter__(self):
|
||||
if self.ndim == 1:
|
||||
zero = self.dtype.type(0)
|
||||
u = 0
|
||||
for v, d in zip(self.indices, self.data):
|
||||
for _ in range(v - u):
|
||||
yield zero
|
||||
yield d
|
||||
u = v + 1
|
||||
for _ in range(self.shape[0] - u):
|
||||
yield zero
|
||||
return
|
||||
|
||||
indptr = np.zeros(2, dtype=self.indptr.dtype)
|
||||
# return 1d (sparray) or 2drow (spmatrix)
|
||||
shape = self.shape[1:] if isinstance(self, sparray) else (1, self.shape[1])
|
||||
i0 = 0
|
||||
for i1 in self.indptr[1:]:
|
||||
indptr[1] = i1 - i0
|
||||
indices = self.indices[i0:i1]
|
||||
data = self.data[i0:i1]
|
||||
yield self.__class__((data, indices, indptr), shape=shape, copy=True)
|
||||
i0 = i1
|
||||
|
||||
def _getrow(self, i):
|
||||
"""Returns a copy of row i of the matrix, as a (1 x n)
|
||||
CSR matrix (row vector).
|
||||
"""
|
||||
if self.ndim == 1:
|
||||
if i not in (0, -1):
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
return self.reshape((1, self.shape[0]), copy=True)
|
||||
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < 0:
|
||||
i += M
|
||||
if i < 0 or i >= M:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
indptr, indices, data = get_csr_submatrix(
|
||||
M, N, self.indptr, self.indices, self.data, i, i + 1, 0, N)
|
||||
return self.__class__((data, indices, indptr), shape=(1, N),
|
||||
dtype=self.dtype, copy=False)
|
||||
|
||||
def _getcol(self, i):
|
||||
"""Returns a copy of column i. A (m x 1) sparse array (column vector).
|
||||
"""
|
||||
if self.ndim == 1:
|
||||
raise ValueError("getcol not provided for 1d arrays. Use indexing A[j]")
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < 0:
|
||||
i += N
|
||||
if i < 0 or i >= N:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
indptr, indices, data = get_csr_submatrix(
|
||||
M, N, self.indptr, self.indices, self.data, 0, M, i, i + 1)
|
||||
return self.__class__((data, indices, indptr), shape=(M, 1),
|
||||
dtype=self.dtype, copy=False)
|
||||
|
||||
def _get_int(self, idx):
|
||||
spot = np.flatnonzero(self.indices == idx)
|
||||
if spot.size:
|
||||
return self.data[spot[0]]
|
||||
return self.data.dtype.type(0)
|
||||
|
||||
def _get_slice(self, idx):
|
||||
if idx == slice(None):
|
||||
return self.copy()
|
||||
if idx.step in (1, None):
|
||||
ret = self._get_submatrix(0, idx, copy=True)
|
||||
return ret.reshape(ret.shape[-1])
|
||||
return self._minor_slice(idx)
|
||||
|
||||
def _get_array(self, idx):
|
||||
idx_dtype = self._get_index_dtype(self.indices)
|
||||
idx = np.asarray(idx, dtype=idx_dtype)
|
||||
if idx.size == 0:
|
||||
return self.__class__([], dtype=self.dtype)
|
||||
|
||||
M, N = 1, self.shape[0]
|
||||
row = np.zeros_like(idx, dtype=idx_dtype)
|
||||
col = np.asarray(idx, dtype=idx_dtype)
|
||||
val = np.empty(row.size, dtype=self.dtype)
|
||||
csr_sample_values(M, N, self.indptr, self.indices, self.data,
|
||||
row.size, row, col, val)
|
||||
|
||||
new_shape = col.shape if col.shape[0] > 1 else (col.shape[0],)
|
||||
return self.__class__(val.reshape(new_shape))
|
||||
|
||||
def _get_intXarray(self, row, col):
|
||||
return self._getrow(row)._minor_index_fancy(col)
|
||||
|
||||
def _get_intXslice(self, row, col):
|
||||
if col.step in (1, None):
|
||||
return self._get_submatrix(row, col, copy=True)
|
||||
# TODO: uncomment this once it's faster:
|
||||
# return self._getrow(row)._minor_slice(col)
|
||||
|
||||
M, N = self.shape
|
||||
start, stop, stride = col.indices(N)
|
||||
|
||||
ii, jj = self.indptr[row:row+2]
|
||||
row_indices = self.indices[ii:jj]
|
||||
row_data = self.data[ii:jj]
|
||||
|
||||
if stride > 0:
|
||||
ind = (row_indices >= start) & (row_indices < stop)
|
||||
else:
|
||||
ind = (row_indices <= start) & (row_indices > stop)
|
||||
|
||||
if abs(stride) > 1:
|
||||
ind &= (row_indices - start) % stride == 0
|
||||
|
||||
row_indices = (row_indices[ind] - start) // stride
|
||||
row_data = row_data[ind]
|
||||
row_indptr = np.array([0, len(row_indices)])
|
||||
|
||||
if stride < 0:
|
||||
row_data = row_data[::-1]
|
||||
row_indices = abs(row_indices[::-1])
|
||||
|
||||
shape = (1, max(0, int(np.ceil(float(stop - start) / stride))))
|
||||
return self.__class__((row_data, row_indices, row_indptr), shape=shape,
|
||||
dtype=self.dtype, copy=False)
|
||||
|
||||
def _get_sliceXint(self, row, col):
|
||||
if row.step in (1, None):
|
||||
return self._get_submatrix(row, col, copy=True)
|
||||
return self._major_slice(row)._get_submatrix(minor=col)
|
||||
|
||||
def _get_sliceXarray(self, row, col):
|
||||
return self._major_slice(row)._minor_index_fancy(col)
|
||||
|
||||
def _get_arrayXint(self, row, col):
|
||||
res = self._major_index_fancy(row)._get_submatrix(minor=col)
|
||||
if row.ndim > 1:
|
||||
return res.reshape(row.shape)
|
||||
return res
|
||||
|
||||
def _get_arrayXslice(self, row, col):
|
||||
if col.step not in (1, None):
|
||||
col = np.arange(*col.indices(self.shape[1]))
|
||||
return self._get_arrayXarray(row, col)
|
||||
return self._major_index_fancy(row)._get_submatrix(minor=col)
|
||||
|
||||
def _set_int(self, idx, x):
|
||||
self._set_many(0, idx, x)
|
||||
|
||||
def _set_array(self, idx, x):
|
||||
x = np.broadcast_to(x, idx.shape)
|
||||
self._set_many(np.zeros_like(idx), idx, x)
|
||||
|
||||
|
||||
def isspmatrix_csr(x):
|
||||
"""Is `x` of csr_matrix type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a csr matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a csr matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import csr_array, csr_matrix, coo_matrix, isspmatrix_csr
|
||||
>>> isspmatrix_csr(csr_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_csr(csr_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_csr(coo_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, csr_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class csr_array(_csr_base, sparray):
|
||||
"""
|
||||
Compressed Sparse Row array.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
csr_array(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
csr_array(S)
|
||||
with another sparse array or matrix S (equivalent to S.tocsr())
|
||||
|
||||
csr_array((M, N), [dtype])
|
||||
to construct an empty array with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
csr_array((data, (row_ind, col_ind)), [shape=(M, N)])
|
||||
where ``data``, ``row_ind`` and ``col_ind`` satisfy the
|
||||
relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
|
||||
|
||||
csr_array((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard CSR representation where the column indices for
|
||||
row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
|
||||
corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``.
|
||||
If the shape parameter is not supplied, the array dimensions
|
||||
are inferred from the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
CSR format data array of the array
|
||||
indices
|
||||
CSR format index array of the array
|
||||
indptr
|
||||
CSR format index pointer array of the array
|
||||
has_sorted_indices
|
||||
has_canonical_format
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the CSR format
|
||||
- efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
|
||||
- efficient row slicing
|
||||
- fast matrix vector products
|
||||
|
||||
Disadvantages of the CSR format
|
||||
- slow column slicing operations (consider CSC)
|
||||
- changes to the sparsity structure are expensive (consider LIL or DOK)
|
||||
|
||||
Canonical Format
|
||||
- Within each row, indices are sorted by column.
|
||||
- There are no duplicate entries.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csr_array
|
||||
>>> csr_array((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> col = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csr_array((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csr_array((data, indices, indptr), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
Duplicate entries are summed together:
|
||||
|
||||
>>> row = np.array([0, 1, 2, 0])
|
||||
>>> col = np.array([0, 1, 1, 0])
|
||||
>>> data = np.array([1, 2, 4, 8])
|
||||
>>> csr_array((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[9, 0, 0],
|
||||
[0, 2, 0],
|
||||
[0, 4, 0]])
|
||||
|
||||
As an example of how to construct a CSR array incrementally,
|
||||
the following snippet builds a term-document array from texts:
|
||||
|
||||
>>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
|
||||
>>> indptr = [0]
|
||||
>>> indices = []
|
||||
>>> data = []
|
||||
>>> vocabulary = {}
|
||||
>>> for d in docs:
|
||||
... for term in d:
|
||||
... index = vocabulary.setdefault(term, len(vocabulary))
|
||||
... indices.append(index)
|
||||
... data.append(1)
|
||||
... indptr.append(len(indices))
|
||||
...
|
||||
>>> csr_array((data, indices, indptr), dtype=int).toarray()
|
||||
array([[2, 1, 0, 0],
|
||||
[0, 1, 1, 1]])
|
||||
|
||||
"""
|
||||
|
||||
|
||||
class csr_matrix(spmatrix, _csr_base):
|
||||
"""
|
||||
Compressed Sparse Row matrix.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
csr_matrix(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
csr_matrix(S)
|
||||
with another sparse array or matrix S (equivalent to S.tocsr())
|
||||
|
||||
csr_matrix((M, N), [dtype])
|
||||
to construct an empty matrix with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
csr_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
|
||||
where ``data``, ``row_ind`` and ``col_ind`` satisfy the
|
||||
relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
|
||||
|
||||
csr_matrix((data, indices, indptr), [shape=(M, N)])
|
||||
is the standard CSR representation where the column indices for
|
||||
row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
|
||||
corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``.
|
||||
If the shape parameter is not supplied, the matrix dimensions
|
||||
are inferred from the index arrays.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
CSR format data array of the matrix
|
||||
indices
|
||||
CSR format index array of the matrix
|
||||
indptr
|
||||
CSR format index pointer array of the matrix
|
||||
has_sorted_indices
|
||||
has_canonical_format
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the CSR format
|
||||
- efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
|
||||
- efficient row slicing
|
||||
- fast matrix vector products
|
||||
|
||||
Disadvantages of the CSR format
|
||||
- slow column slicing operations (consider CSC)
|
||||
- changes to the sparsity structure are expensive (consider LIL or DOK)
|
||||
|
||||
Canonical Format
|
||||
- Within each row, indices are sorted by column.
|
||||
- There are no duplicate entries.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csr_matrix
|
||||
>>> csr_matrix((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> row = np.array([0, 0, 1, 2, 2, 2])
|
||||
>>> col = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
>>> indptr = np.array([0, 2, 3, 6])
|
||||
>>> indices = np.array([0, 2, 2, 0, 1, 2])
|
||||
>>> data = np.array([1, 2, 3, 4, 5, 6])
|
||||
>>> csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()
|
||||
array([[1, 0, 2],
|
||||
[0, 0, 3],
|
||||
[4, 5, 6]])
|
||||
|
||||
Duplicate entries are summed together:
|
||||
|
||||
>>> row = np.array([0, 1, 2, 0])
|
||||
>>> col = np.array([0, 1, 1, 0])
|
||||
>>> data = np.array([1, 2, 4, 8])
|
||||
>>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
|
||||
array([[9, 0, 0],
|
||||
[0, 2, 0],
|
||||
[0, 4, 0]])
|
||||
|
||||
As an example of how to construct a CSR matrix incrementally,
|
||||
the following snippet builds a term-document matrix from texts:
|
||||
|
||||
>>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
|
||||
>>> indptr = [0]
|
||||
>>> indices = []
|
||||
>>> data = []
|
||||
>>> vocabulary = {}
|
||||
>>> for d in docs:
|
||||
... for term in d:
|
||||
... index = vocabulary.setdefault(term, len(vocabulary))
|
||||
... indices.append(index)
|
||||
... data.append(1)
|
||||
... indptr.append(len(indices))
|
||||
...
|
||||
>>> csr_matrix((data, indices, indptr), dtype=int).toarray()
|
||||
array([[2, 1, 0, 0],
|
||||
[0, 1, 1, 1]])
|
||||
|
||||
"""
|
||||
|
||||
569
venv/lib/python3.13/site-packages/scipy/sparse/_data.py
Normal file
569
venv/lib/python3.13/site-packages/scipy/sparse/_data.py
Normal file
|
|
@ -0,0 +1,569 @@
|
|||
"""Base class for sparse matrice with a .data attribute
|
||||
|
||||
subclasses must provide a _with_data() method that
|
||||
creates a new matrix with the same sparsity pattern
|
||||
as self but with a different data array
|
||||
|
||||
"""
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
|
||||
from ._base import _spbase, sparray, _ufuncs_with_fixed_point_at_zero
|
||||
from ._sputils import isscalarlike, validateaxis
|
||||
|
||||
__all__ = []
|
||||
|
||||
|
||||
# TODO implement all relevant operations
|
||||
# use .data.__methods__() instead of /=, *=, etc.
|
||||
class _data_matrix(_spbase):
|
||||
def __init__(self, arg1, *, maxprint=None):
|
||||
_spbase.__init__(self, arg1, maxprint=maxprint)
|
||||
|
||||
@property
|
||||
def dtype(self):
|
||||
return self.data.dtype
|
||||
|
||||
@dtype.setter
|
||||
def dtype(self, newtype):
|
||||
self.data.dtype = newtype
|
||||
|
||||
def _deduped_data(self):
|
||||
if hasattr(self, 'sum_duplicates'):
|
||||
self.sum_duplicates()
|
||||
return self.data
|
||||
|
||||
def __abs__(self):
|
||||
return self._with_data(abs(self._deduped_data()))
|
||||
|
||||
def __round__(self, ndigits=0):
|
||||
return self._with_data(np.around(self._deduped_data(), decimals=ndigits))
|
||||
|
||||
def _real(self):
|
||||
return self._with_data(self.data.real)
|
||||
|
||||
def _imag(self):
|
||||
return self._with_data(self.data.imag)
|
||||
|
||||
def __neg__(self):
|
||||
if self.dtype.kind == 'b':
|
||||
raise NotImplementedError('negating a boolean sparse array is not '
|
||||
'supported')
|
||||
return self._with_data(-self.data)
|
||||
|
||||
def __imul__(self, other): # self *= other
|
||||
if isscalarlike(other):
|
||||
self.data *= other
|
||||
return self
|
||||
return NotImplemented
|
||||
|
||||
def __itruediv__(self, other): # self /= other
|
||||
if isscalarlike(other):
|
||||
recip = 1.0 / other
|
||||
self.data *= recip
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
def astype(self, dtype, casting='unsafe', copy=True):
|
||||
dtype = np.dtype(dtype)
|
||||
if self.dtype != dtype:
|
||||
matrix = self._with_data(
|
||||
self.data.astype(dtype, casting=casting, copy=True),
|
||||
copy=True
|
||||
)
|
||||
return matrix._with_data(matrix._deduped_data(), copy=False)
|
||||
elif copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
astype.__doc__ = _spbase.astype.__doc__
|
||||
|
||||
def conjugate(self, copy=True):
|
||||
if np.issubdtype(self.dtype, np.complexfloating):
|
||||
return self._with_data(self.data.conjugate(), copy=copy)
|
||||
elif copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
conjugate.__doc__ = _spbase.conjugate.__doc__
|
||||
|
||||
def copy(self):
|
||||
return self._with_data(self.data.copy(), copy=True)
|
||||
|
||||
copy.__doc__ = _spbase.copy.__doc__
|
||||
|
||||
def power(self, n, dtype=None):
|
||||
"""
|
||||
This function performs element-wise power.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
n : scalar
|
||||
n is a non-zero scalar (nonzero avoids dense ones creation)
|
||||
If zero power is desired, special case it to use `np.ones`
|
||||
|
||||
dtype : If dtype is not specified, the current dtype will be preserved.
|
||||
|
||||
Raises
|
||||
------
|
||||
NotImplementedError : if n is a zero scalar
|
||||
If zero power is desired, special case it to use
|
||||
``np.ones(A.shape, dtype=A.dtype)``
|
||||
"""
|
||||
if not isscalarlike(n):
|
||||
raise NotImplementedError("input is not scalar")
|
||||
if not n:
|
||||
raise NotImplementedError(
|
||||
"zero power is not supported as it would densify the matrix.\n"
|
||||
"Use `np.ones(A.shape, dtype=A.dtype)` for this case."
|
||||
)
|
||||
|
||||
data = self._deduped_data()
|
||||
if dtype is not None:
|
||||
data = data.astype(dtype, copy=False)
|
||||
return self._with_data(data ** n)
|
||||
|
||||
###########################
|
||||
# Multiplication handlers #
|
||||
###########################
|
||||
|
||||
def _mul_scalar(self, other):
|
||||
return self._with_data(self.data * other)
|
||||
|
||||
|
||||
# Add the numpy unary ufuncs for which func(0) = 0 to _data_matrix.
|
||||
for npfunc in _ufuncs_with_fixed_point_at_zero:
|
||||
name = npfunc.__name__
|
||||
|
||||
def _create_method(op):
|
||||
def method(self):
|
||||
result = op(self._deduped_data())
|
||||
return self._with_data(result, copy=True)
|
||||
|
||||
method.__doc__ = (f"Element-wise {name}.\n\n"
|
||||
f"See `numpy.{name}` for more information.")
|
||||
method.__name__ = name
|
||||
|
||||
return method
|
||||
|
||||
setattr(_data_matrix, name, _create_method(npfunc))
|
||||
|
||||
|
||||
def _find_missing_index(ind, n):
|
||||
for k, a in enumerate(ind):
|
||||
if k != a:
|
||||
return k
|
||||
|
||||
k += 1
|
||||
if k < n:
|
||||
return k
|
||||
else:
|
||||
return -1
|
||||
|
||||
|
||||
class _minmax_mixin:
|
||||
"""Mixin for min and max methods.
|
||||
|
||||
These are not implemented for dia_matrix, hence the separate class.
|
||||
"""
|
||||
|
||||
def _min_or_max_axis(self, axis, min_or_max, explicit):
|
||||
# already checked that self.shape[axis] is not zero
|
||||
N = self.shape[axis]
|
||||
M = self.shape[1 - axis]
|
||||
idx_dtype = self._get_index_dtype(maxval=M)
|
||||
|
||||
mat = self.tocsc() if axis == 0 else self.tocsr()
|
||||
mat.sum_duplicates()
|
||||
|
||||
major_index, value = mat._minor_reduce(min_or_max)
|
||||
if not explicit:
|
||||
not_full = np.diff(mat.indptr)[major_index] < N
|
||||
value[not_full] = min_or_max(value[not_full], 0)
|
||||
|
||||
mask = value != 0
|
||||
major_index = np.compress(mask, major_index).astype(idx_dtype, copy=False)
|
||||
value = np.compress(mask, value)
|
||||
|
||||
if isinstance(self, sparray):
|
||||
coords = (major_index,)
|
||||
shape = (M,)
|
||||
return self._coo_container((value, coords), shape=shape, dtype=self.dtype)
|
||||
|
||||
if axis == 0:
|
||||
return self._coo_container(
|
||||
(value, (np.zeros(len(value), dtype=idx_dtype), major_index)),
|
||||
dtype=self.dtype, shape=(1, M)
|
||||
)
|
||||
else:
|
||||
return self._coo_container(
|
||||
(value, (major_index, np.zeros(len(value), dtype=idx_dtype))),
|
||||
dtype=self.dtype, shape=(M, 1)
|
||||
)
|
||||
|
||||
def _min_or_max(self, axis, out, min_or_max, explicit):
|
||||
if out is not None:
|
||||
raise ValueError("Sparse min/max does not support an 'out' parameter.")
|
||||
|
||||
axis = validateaxis(axis, ndim=self.ndim)
|
||||
|
||||
if axis is None:
|
||||
if 0 in self.shape:
|
||||
raise ValueError("zero-size array to reduction operation")
|
||||
|
||||
zero = self.dtype.type(0)
|
||||
if self.nnz == 0:
|
||||
return zero
|
||||
m = min_or_max.reduce(self._deduped_data().ravel())
|
||||
if self.nnz != math.prod(self.shape) and not explicit:
|
||||
m = min_or_max(zero, m)
|
||||
return m
|
||||
|
||||
if any(self.shape[d] == 0 for d in axis):
|
||||
raise ValueError("zero-size array to reduction operation")
|
||||
|
||||
if self.ndim == 2:
|
||||
# note: 2D ensures that len(axis)==1 so we pass in the int axis[0]
|
||||
return self._min_or_max_axis(axis[0], min_or_max, explicit)
|
||||
return self._min_or_max_axis_nd(axis, min_or_max, explicit)
|
||||
|
||||
def _argminmax_axis(self, axis, argminmax, compare, explicit):
|
||||
zero = self.dtype.type(0)
|
||||
|
||||
mat = self.tocsc() if axis == 0 else self.tocsr()
|
||||
mat.sum_duplicates()
|
||||
|
||||
ret_size, line_size = mat._swap(mat.shape)
|
||||
ret = np.zeros(ret_size, dtype=int)
|
||||
|
||||
nz_lines, = np.nonzero(np.diff(mat.indptr))
|
||||
for i in nz_lines:
|
||||
p, q = mat.indptr[i:i + 2]
|
||||
data = mat.data[p:q]
|
||||
indices = mat.indices[p:q]
|
||||
extreme_index = argminmax(data)
|
||||
extreme_value = data[extreme_index]
|
||||
if explicit:
|
||||
if q - p > 0:
|
||||
ret[i] = indices[extreme_index]
|
||||
else:
|
||||
if compare(extreme_value, zero) or q - p == line_size:
|
||||
ret[i] = indices[extreme_index]
|
||||
else:
|
||||
zero_ind = _find_missing_index(indices, line_size)
|
||||
if extreme_value == zero:
|
||||
ret[i] = min(extreme_index, zero_ind)
|
||||
else:
|
||||
ret[i] = zero_ind
|
||||
|
||||
if isinstance(self, sparray):
|
||||
return ret
|
||||
|
||||
if axis == 1:
|
||||
ret = ret.reshape(-1, 1)
|
||||
|
||||
return self._ascontainer(ret)
|
||||
|
||||
def _argminmax(self, axis, out, argminmax, compare, explicit):
|
||||
if out is not None:
|
||||
minmax = "argmin" if argminmax == np.argmin else "argmax"
|
||||
raise ValueError(f"Sparse {minmax} does not support an 'out' parameter.")
|
||||
|
||||
axis = validateaxis(axis, ndim=self.ndim)
|
||||
|
||||
if axis is not None:
|
||||
if any(self.shape[i] == 0 for i in axis):
|
||||
minmax = "argmin" if argminmax == np.argmin else "argmax"
|
||||
raise ValueError(f"Cannot apply {minmax} along a zero-sized dimension.")
|
||||
|
||||
if self.ndim == 2:
|
||||
# note: 2D ensures that len(axis)==1 so we pass in the int axis[0]
|
||||
return self._argminmax_axis(axis[0], argminmax, compare, explicit)
|
||||
return self._argminmax_axis_nd(axis, argminmax, compare, explicit)
|
||||
|
||||
if 0 in self.shape:
|
||||
minmax = "argmin" if argminmax == np.argmin else "argmax"
|
||||
raise ValueError(f"Cannot apply {minmax} to an empty matrix.")
|
||||
|
||||
if self.nnz == 0:
|
||||
if explicit:
|
||||
minmax = "argmin" if argminmax == np.argmin else "argmax"
|
||||
raise ValueError(f"Cannot apply {minmax} to zero matrix "
|
||||
"when explicit=True.")
|
||||
return 0
|
||||
|
||||
zero = self.dtype.type(0)
|
||||
mat = self.tocoo()
|
||||
# Convert to canonical form: no duplicates, sorted indices.
|
||||
mat.sum_duplicates()
|
||||
extreme_index = argminmax(mat.data)
|
||||
if explicit:
|
||||
return extreme_index
|
||||
extreme_value = mat.data[extreme_index]
|
||||
|
||||
if mat.ndim > 2:
|
||||
mat = mat.reshape(-1)
|
||||
# If the min value is less than zero, or max is greater than zero,
|
||||
# then we do not need to worry about implicit zeros.
|
||||
# And we use a "cheap test" for the rare case of no implicit zeros.
|
||||
maxnnz = math.prod(self.shape)
|
||||
if compare(extreme_value, zero) or mat.nnz == maxnnz:
|
||||
# cast to Python int to avoid overflow and RuntimeError
|
||||
if mat.ndim == 1: # includes nD case that was reshaped above
|
||||
return int(mat.col[extreme_index])
|
||||
# ndim == 2
|
||||
num_col = mat.shape[-1]
|
||||
return int(mat.row[extreme_index]) * num_col + int(mat.col[extreme_index])
|
||||
|
||||
# At this stage, any implicit zero could be the min or max value.
|
||||
# After sum_duplicates(), the `row` and `col` arrays are guaranteed to
|
||||
# be sorted in C-order, which means the linearized indices are sorted.
|
||||
if mat.ndim == 1: # includes nD case that was reshaped above
|
||||
linear_indices = mat.coords[-1]
|
||||
else: # ndim == 2
|
||||
num_col = mat.shape[-1]
|
||||
linear_indices = mat.row * num_col + mat.col
|
||||
first_implicit_zero_index = _find_missing_index(linear_indices, maxnnz)
|
||||
if extreme_value == zero:
|
||||
return min(first_implicit_zero_index, extreme_index)
|
||||
return first_implicit_zero_index
|
||||
|
||||
def max(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return the maximum of the array/matrix or maximum along an axis.
|
||||
|
||||
By default, all elements are taken into account, not just the non-zero ones.
|
||||
But with `explicit` set, only the stored elements are considered.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None} optional
|
||||
Axis along which the sum is computed. The default is to
|
||||
compute the maximum over all elements, returning
|
||||
a scalar (i.e., `axis` = `None`).
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except
|
||||
for the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only the stored elements will be considered.
|
||||
If a row/column is empty, the sparse.coo_array returned
|
||||
has no stored element (i.e. an implicit zero) for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
amax : coo_array or scalar
|
||||
Maximum of `a`. If `axis` is None, the result is a scalar value.
|
||||
If `axis` is given, the result is a sparse.coo_array of dimension
|
||||
``a.ndim - 1``.
|
||||
|
||||
See Also
|
||||
--------
|
||||
min : The minimum value of a sparse array/matrix along a given axis.
|
||||
numpy.max : NumPy's implementation of 'max'
|
||||
|
||||
"""
|
||||
return self._min_or_max(axis, out, np.maximum, explicit)
|
||||
|
||||
def min(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return the minimum of the array/matrix or maximum along an axis.
|
||||
|
||||
By default, all elements are taken into account, not just the non-zero ones.
|
||||
But with `explicit` set, only the stored elements are considered.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None} optional
|
||||
Axis along which the sum is computed. The default is to
|
||||
compute the minimum over all elements, returning
|
||||
a scalar (i.e., `axis` = `None`).
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except for
|
||||
the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only the stored elements will be considered.
|
||||
If a row/column is empty, the sparse.coo_array returned
|
||||
has no stored element (i.e. an implicit zero) for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
amin : coo_matrix or scalar
|
||||
Minimum of `a`. If `axis` is None, the result is a scalar value.
|
||||
If `axis` is given, the result is a sparse.coo_array of dimension
|
||||
``a.ndim - 1``.
|
||||
|
||||
See Also
|
||||
--------
|
||||
max : The maximum value of a sparse array/matrix along a given axis.
|
||||
numpy.min : NumPy's implementation of 'min'
|
||||
|
||||
"""
|
||||
return self._min_or_max(axis, out, np.minimum, explicit)
|
||||
|
||||
def nanmax(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return the maximum, ignoring any Nans, along an axis.
|
||||
|
||||
Return the maximum, ignoring any Nans, of the array/matrix along an axis.
|
||||
By default this takes all elements into account, but with `explicit` set,
|
||||
only stored elements are considered.
|
||||
|
||||
.. versionadded:: 1.11.0
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None} optional
|
||||
Axis along which the maximum is computed. The default is to
|
||||
compute the maximum over all elements, returning
|
||||
a scalar (i.e., `axis` = `None`).
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except
|
||||
for the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only the stored elements will be considered.
|
||||
If a row/column is empty, the sparse.coo_array returned
|
||||
has no stored element (i.e. an implicit zero) for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
amax : coo_array or scalar
|
||||
Maximum of `a`. If `axis` is None, the result is a scalar value.
|
||||
If `axis` is given, the result is a sparse.coo_array of dimension
|
||||
``a.ndim - 1``.
|
||||
|
||||
See Also
|
||||
--------
|
||||
nanmin : The minimum value of a sparse array/matrix along a given axis,
|
||||
ignoring NaNs.
|
||||
max : The maximum value of a sparse array/matrix along a given axis,
|
||||
propagating NaNs.
|
||||
numpy.nanmax : NumPy's implementation of 'nanmax'.
|
||||
|
||||
"""
|
||||
return self._min_or_max(axis, out, np.fmax, explicit)
|
||||
|
||||
def nanmin(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return the minimum, ignoring any Nans, along an axis.
|
||||
|
||||
Return the minimum, ignoring any Nans, of the array/matrix along an axis.
|
||||
By default this takes all elements into account, but with `explicit` set,
|
||||
only stored elements are considered.
|
||||
|
||||
.. versionadded:: 1.11.0
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None} optional
|
||||
Axis along which the minimum is computed. The default is to
|
||||
compute the minimum over all elements, returning
|
||||
a scalar (i.e., `axis` = `None`).
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except for
|
||||
the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only the stored elements will be considered.
|
||||
If a row/column is empty, the sparse.coo_array returned
|
||||
has no stored element (i.e. an implicit zero) for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
amin : coo_array or scalar
|
||||
Minimum of `a`. If `axis` is None, the result is a scalar value.
|
||||
If `axis` is given, the result is a sparse.coo_array of dimension
|
||||
``a.ndim - 1``.
|
||||
|
||||
See Also
|
||||
--------
|
||||
nanmax : The maximum value of a sparse array/matrix along a given axis,
|
||||
ignoring NaNs.
|
||||
min : The minimum value of a sparse array/matrix along a given axis,
|
||||
propagating NaNs.
|
||||
numpy.nanmin : NumPy's implementation of 'nanmin'.
|
||||
|
||||
"""
|
||||
return self._min_or_max(axis, out, np.fmin, explicit)
|
||||
|
||||
def argmax(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return indices of maximum elements along an axis.
|
||||
|
||||
By default, implicit zero elements are taken into account. If there are
|
||||
several minimum values, the index of the first occurrence is returned.
|
||||
If `explicit` is set, only explicitly stored elements will be considered.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None}, optional
|
||||
Axis along which the argmax is computed. If None (default), index
|
||||
of the maximum element in the flatten data is returned.
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except for
|
||||
the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only explicitly stored elements will be considered.
|
||||
If axis is not None and an axis has no stored elements, argmax
|
||||
is undefined, so the index ``0`` is returned for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
ind : numpy.matrix or int
|
||||
Indices of maximum elements. If matrix, its size along `axis` is 1.
|
||||
"""
|
||||
return self._argminmax(axis, out, np.argmax, np.greater, explicit)
|
||||
|
||||
def argmin(self, axis=None, out=None, *, explicit=False):
|
||||
"""Return indices of minimum elements along an axis.
|
||||
|
||||
By default, implicit zero elements are taken into account. If there are
|
||||
several minimum values, the index of the first occurrence is returned.
|
||||
If `explicit` is set, only explicitly stored elements will be considered.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : {-2, -1, 0, 1, None}, optional
|
||||
Axis along which the argmin is computed. If None (default), index
|
||||
of the minimum element in the flatten data is returned.
|
||||
|
||||
out : None, optional
|
||||
This argument is in the signature *solely* for NumPy
|
||||
compatibility reasons. Do not pass in anything except for
|
||||
the default value, as this argument is not used.
|
||||
|
||||
explicit : {False, True} optional (default: False)
|
||||
When set to True, only explicitly stored elements will be considered.
|
||||
If axis is not None and an axis has no stored elements, argmin
|
||||
is undefined, so the index ``0`` is returned for that row/column.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
ind : numpy.matrix or int
|
||||
Indices of minimum elements. If matrix, its size along `axis` is 1.
|
||||
"""
|
||||
return self._argminmax(axis, out, np.argmin, np.less, explicit)
|
||||
677
venv/lib/python3.13/site-packages/scipy/sparse/_dia.py
Normal file
677
venv/lib/python3.13/site-packages/scipy/sparse/_dia.py
Normal file
|
|
@ -0,0 +1,677 @@
|
|||
"""Sparse DIAgonal format"""
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['dia_array', 'dia_matrix', 'isspmatrix_dia']
|
||||
|
||||
import numpy as np
|
||||
|
||||
from .._lib._util import copy_if_needed
|
||||
from ._matrix import spmatrix
|
||||
from ._base import issparse, _formats, _spbase, sparray
|
||||
from ._data import _data_matrix
|
||||
from ._sputils import (
|
||||
isdense, isscalarlike, isshape, upcast_char, getdtype, get_sum_dtype,
|
||||
validateaxis, check_shape
|
||||
)
|
||||
from ._sparsetools import dia_matmat, dia_matvec, dia_matvecs
|
||||
|
||||
|
||||
class _dia_base(_data_matrix):
|
||||
_format = 'dia'
|
||||
|
||||
def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
|
||||
_data_matrix.__init__(self, arg1, maxprint=maxprint)
|
||||
|
||||
if issparse(arg1):
|
||||
if arg1.format == "dia":
|
||||
if copy:
|
||||
arg1 = arg1.copy()
|
||||
self.data = arg1.data
|
||||
self.offsets = arg1.offsets
|
||||
self._shape = check_shape(arg1.shape)
|
||||
else:
|
||||
if arg1.format == self.format and copy:
|
||||
A = arg1.copy()
|
||||
else:
|
||||
A = arg1.todia()
|
||||
self.data = A.data
|
||||
self.offsets = A.offsets
|
||||
self._shape = check_shape(A.shape)
|
||||
elif isinstance(arg1, tuple):
|
||||
if isshape(arg1):
|
||||
# It's a tuple of matrix dimensions (M, N)
|
||||
# create empty matrix
|
||||
self._shape = check_shape(arg1)
|
||||
self.data = np.zeros((0,0), getdtype(dtype, default=float))
|
||||
idx_dtype = self._get_index_dtype(maxval=max(self.shape))
|
||||
self.offsets = np.zeros((0), dtype=idx_dtype)
|
||||
else:
|
||||
try:
|
||||
# Try interpreting it as (data, offsets)
|
||||
data, offsets = arg1
|
||||
except Exception as e:
|
||||
message = 'unrecognized form for dia_array constructor'
|
||||
raise ValueError(message) from e
|
||||
else:
|
||||
if shape is None:
|
||||
raise ValueError('expected a shape argument')
|
||||
if not copy:
|
||||
copy = copy_if_needed
|
||||
self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
|
||||
offsets = np.array(arg1[1],
|
||||
dtype=self._get_index_dtype(maxval=max(shape)),
|
||||
copy=copy)
|
||||
self.offsets = np.atleast_1d(offsets)
|
||||
self._shape = check_shape(shape)
|
||||
else:
|
||||
# must be dense, convert to COO first, then to DIA
|
||||
try:
|
||||
arg1 = np.asarray(arg1)
|
||||
except Exception as e:
|
||||
raise ValueError("unrecognized form for "
|
||||
f"{self.format}_matrix constructor") from e
|
||||
if isinstance(self, sparray) and arg1.ndim != 2:
|
||||
raise ValueError(f"DIA arrays don't support {arg1.ndim}D input. Use 2D")
|
||||
A = self._coo_container(arg1, dtype=dtype, shape=shape).todia()
|
||||
self.data = A.data
|
||||
self.offsets = A.offsets
|
||||
self._shape = check_shape(A.shape)
|
||||
|
||||
if dtype is not None:
|
||||
newdtype = getdtype(dtype)
|
||||
self.data = self.data.astype(newdtype)
|
||||
|
||||
# check format
|
||||
if self.offsets.ndim != 1:
|
||||
raise ValueError('offsets array must have rank 1')
|
||||
|
||||
if self.data.ndim != 2:
|
||||
raise ValueError('data array must have rank 2')
|
||||
|
||||
if self.data.shape[0] != len(self.offsets):
|
||||
raise ValueError(
|
||||
f'number of diagonals ({self.data.shape[0]}) does not match the number '
|
||||
f'of offsets ({len(self.offsets)})'
|
||||
)
|
||||
if len(np.unique(self.offsets)) != len(self.offsets):
|
||||
raise ValueError('offset array contains duplicate values')
|
||||
|
||||
def __repr__(self):
|
||||
_, fmt = _formats[self.format]
|
||||
sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
|
||||
d = self.data.shape[0]
|
||||
return (
|
||||
f"<{fmt} sparse {sparse_cls} of dtype '{self.dtype}'\n"
|
||||
f"\twith {self.nnz} stored elements ({d} diagonals) and shape {self.shape}>"
|
||||
)
|
||||
|
||||
def _data_mask(self):
|
||||
"""Returns a mask of the same shape as self.data, where
|
||||
mask[i,j] is True when data[i,j] corresponds to a stored element."""
|
||||
num_rows, num_cols = self.shape
|
||||
offset_inds = np.arange(self.data.shape[1])
|
||||
row = offset_inds - self.offsets[:,None]
|
||||
mask = (row >= 0)
|
||||
mask &= (row < num_rows)
|
||||
mask &= (offset_inds < num_cols)
|
||||
return mask
|
||||
|
||||
def count_nonzero(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError(
|
||||
"count_nonzero over an axis is not implemented for DIA format"
|
||||
)
|
||||
mask = self._data_mask()
|
||||
return np.count_nonzero(self.data[mask])
|
||||
|
||||
count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
|
||||
|
||||
def _getnnz(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError("_getnnz over an axis is not implemented "
|
||||
"for DIA format")
|
||||
M,N = self.shape
|
||||
nnz = 0
|
||||
for k in self.offsets:
|
||||
if k > 0:
|
||||
nnz += min(M,N-k)
|
||||
else:
|
||||
nnz += min(M+k,N)
|
||||
return int(nnz)
|
||||
|
||||
_getnnz.__doc__ = _spbase._getnnz.__doc__
|
||||
|
||||
def sum(self, axis=None, dtype=None, out=None):
|
||||
axis = validateaxis(axis)
|
||||
|
||||
res_dtype = get_sum_dtype(self.dtype)
|
||||
num_rows, num_cols = self.shape
|
||||
ret = None
|
||||
|
||||
if axis == (0,):
|
||||
mask = self._data_mask()
|
||||
x = (self.data * mask).sum(axis=0)
|
||||
if x.shape[0] == num_cols:
|
||||
res = x
|
||||
else:
|
||||
res = np.zeros(num_cols, dtype=x.dtype)
|
||||
res[:x.shape[0]] = x
|
||||
ret = self._ascontainer(res, dtype=res_dtype)
|
||||
|
||||
else: # axis is None or (1,)
|
||||
row_sums = np.zeros((num_rows, 1), dtype=res_dtype)
|
||||
one = np.ones(num_cols, dtype=res_dtype)
|
||||
dia_matvec(num_rows, num_cols, len(self.offsets),
|
||||
self.data.shape[1], self.offsets, self.data, one, row_sums)
|
||||
|
||||
row_sums = self._ascontainer(row_sums)
|
||||
|
||||
if axis is None:
|
||||
return row_sums.sum(dtype=dtype, out=out)
|
||||
|
||||
ret = self._ascontainer(row_sums.sum(axis=axis))
|
||||
|
||||
return ret.sum(axis=(), dtype=dtype, out=out)
|
||||
|
||||
sum.__doc__ = _spbase.sum.__doc__
|
||||
|
||||
def _add_sparse(self, other, sub=False):
|
||||
# If other is not DIA format, let them handle us instead.
|
||||
if not isinstance(other, _dia_base):
|
||||
return other._add_sparse(self)
|
||||
|
||||
# Fast path for exact equality of the sparsity structure.
|
||||
if np.array_equal(self.offsets, other.offsets):
|
||||
return self._with_data(self.data - other.data if sub else
|
||||
self.data + other.data)
|
||||
|
||||
# Find the union of the offsets (which will be sorted and unique).
|
||||
new_offsets = np.union1d(self.offsets, other.offsets)
|
||||
self_idx = np.searchsorted(new_offsets, self.offsets)
|
||||
other_idx = np.searchsorted(new_offsets, other.offsets)
|
||||
|
||||
self_d = self.data.shape[1]
|
||||
other_d = other.data.shape[1]
|
||||
# Fast path for a sparsity structure where the final offsets are a
|
||||
# permutation of the existing offsets and the diagonal lengths match.
|
||||
if self_d == other_d and len(new_offsets) == len(self.offsets):
|
||||
new_data = self.data[_invert_index(self_idx)]
|
||||
if sub:
|
||||
new_data[other_idx, :] -= other.data
|
||||
else:
|
||||
new_data[other_idx, :] += other.data
|
||||
elif self_d == other_d and len(new_offsets) == len(other.offsets):
|
||||
if sub:
|
||||
new_data = -other.data[_invert_index(other_idx)]
|
||||
else:
|
||||
new_data = other.data[_invert_index(other_idx)]
|
||||
new_data[self_idx, :] += self.data
|
||||
else:
|
||||
# Maximum diagonal length of the result.
|
||||
d = min(self.shape[0] + new_offsets[-1], self.shape[1])
|
||||
|
||||
# Add all diagonals to a freshly allocated data array.
|
||||
new_data = np.zeros(
|
||||
(len(new_offsets), d),
|
||||
dtype=np.result_type(self.data, other.data),
|
||||
)
|
||||
new_data[self_idx, :self_d] += self.data[:, :d]
|
||||
if sub:
|
||||
new_data[other_idx, :other_d] -= other.data[:, :d]
|
||||
else:
|
||||
new_data[other_idx, :other_d] += other.data[:, :d]
|
||||
return self._dia_container((new_data, new_offsets), shape=self.shape)
|
||||
|
||||
def _sub_sparse(self, other):
|
||||
# If other is not DIA format, use default handler.
|
||||
if not isinstance(other, _dia_base):
|
||||
return super()._sub_sparse(other)
|
||||
|
||||
return self._add_sparse(other, sub=True)
|
||||
|
||||
def _mul_scalar(self, other):
|
||||
return self._with_data(self.data * other)
|
||||
|
||||
def multiply(self, other):
|
||||
if isscalarlike(other):
|
||||
return self._mul_scalar(other)
|
||||
|
||||
if isdense(other):
|
||||
if other.ndim > 2:
|
||||
return self.toarray() * other
|
||||
|
||||
# Use default handler for pathological cases.
|
||||
if 0 in self.shape or 1 in self.shape or 0 in other.shape:
|
||||
return super().multiply(other)
|
||||
|
||||
other = np.atleast_2d(other)
|
||||
other_rows, other_cols = other.shape
|
||||
rows, cols = self.shape
|
||||
L = min(self.data.shape[1], cols)
|
||||
data = self.data[:, :L].astype(np.result_type(self.data, other))
|
||||
if other_rows == 1:
|
||||
data *= other[0, :L]
|
||||
elif other_rows != rows:
|
||||
raise ValueError('inconsistent shapes')
|
||||
else:
|
||||
j = np.arange(L)
|
||||
if L > rows:
|
||||
i = (j - self.offsets[:, None]) % rows
|
||||
else: # can use faster method
|
||||
i = j - self.offsets[:, None] % rows
|
||||
if other_cols == 1:
|
||||
j = 0
|
||||
elif other_cols != cols:
|
||||
raise ValueError('inconsistent shapes')
|
||||
data *= other[i, j]
|
||||
return self._with_data(data)
|
||||
|
||||
# If other is not DIA format or needs broadcasting (unreasonable
|
||||
# use case for DIA anyway), use default handler.
|
||||
if not isinstance(other, _dia_base) or other.shape != self.shape:
|
||||
return super().multiply(other)
|
||||
|
||||
# Find common offsets (unique diagonals don't contribute)
|
||||
# and indices corresponding to them in multiplicand and multiplier.
|
||||
offsets, self_idx, other_idx = \
|
||||
np.intersect1d(self.offsets, other.offsets,
|
||||
assume_unique=True, return_indices=True)
|
||||
# Only overlapping length of diagonals can have non-zero products.
|
||||
L = min(self.data.shape[1], other.data.shape[1])
|
||||
data = self.data[self_idx, :L] * other.data[other_idx, :L]
|
||||
return self._dia_container((data, offsets), shape=self.shape)
|
||||
|
||||
def _matmul_vector(self, other):
|
||||
x = other
|
||||
|
||||
y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
|
||||
x.dtype.char))
|
||||
|
||||
L = self.data.shape[1]
|
||||
|
||||
M,N = self.shape
|
||||
|
||||
dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data,
|
||||
x.ravel(), y.ravel())
|
||||
|
||||
return y
|
||||
|
||||
def _matmul_multivector(self, other):
|
||||
res = np.zeros((self.shape[0], other.shape[1]),
|
||||
dtype=np.result_type(self.data, other))
|
||||
dia_matvecs(*self.shape, *self.data.shape, self.offsets, self.data,
|
||||
other.shape[1], other, res)
|
||||
return res
|
||||
|
||||
def _matmul_sparse(self, other):
|
||||
# If other is not DIA format, use default handler.
|
||||
if not isinstance(other, _dia_base):
|
||||
return super()._matmul_sparse(other)
|
||||
|
||||
# If any dimension is zero, return empty array immediately.
|
||||
if 0 in self.shape or 0 in other.shape:
|
||||
return self._dia_container((self.shape[0], other.shape[1]))
|
||||
|
||||
offsets, data = dia_matmat(*self.shape, *self.data.shape,
|
||||
self.offsets, self.data,
|
||||
other.shape[1], *other.data.shape,
|
||||
other.offsets, other.data)
|
||||
return self._dia_container((data.reshape(len(offsets), -1), offsets),
|
||||
(self.shape[0], other.shape[1]))
|
||||
|
||||
def _setdiag(self, values, k=0):
|
||||
M, N = self.shape
|
||||
|
||||
if values.ndim == 0:
|
||||
# broadcast
|
||||
values_n = np.inf
|
||||
else:
|
||||
values_n = len(values)
|
||||
|
||||
if k < 0:
|
||||
n = min(M + k, N, values_n)
|
||||
min_index = 0
|
||||
max_index = n
|
||||
else:
|
||||
n = min(M, N - k, values_n)
|
||||
min_index = k
|
||||
max_index = k + n
|
||||
|
||||
if values.ndim != 0:
|
||||
# allow also longer sequences
|
||||
values = values[:n]
|
||||
|
||||
data_rows, data_cols = self.data.shape
|
||||
if k in self.offsets:
|
||||
if max_index > data_cols:
|
||||
data = np.zeros((data_rows, max_index), dtype=self.data.dtype)
|
||||
data[:, :data_cols] = self.data
|
||||
self.data = data
|
||||
self.data[self.offsets == k, min_index:max_index] = values
|
||||
else:
|
||||
self.offsets = np.append(self.offsets, self.offsets.dtype.type(k))
|
||||
m = max(max_index, data_cols)
|
||||
data = np.zeros((data_rows + 1, m), dtype=self.data.dtype)
|
||||
data[:-1, :data_cols] = self.data
|
||||
data[-1, min_index:max_index] = values
|
||||
self.data = data
|
||||
|
||||
def todia(self, copy=False):
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
todia.__doc__ = _spbase.todia.__doc__
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
if axes is not None and axes != (1, 0):
|
||||
raise ValueError("Sparse arrays/matrices do not support "
|
||||
"an 'axes' parameter because swapping "
|
||||
"dimensions is the only logical permutation.")
|
||||
|
||||
num_rows, num_cols = self.shape
|
||||
max_dim = max(self.shape)
|
||||
|
||||
# flip diagonal offsets
|
||||
offsets = -self.offsets
|
||||
|
||||
# re-align the data matrix
|
||||
r = np.arange(len(offsets), dtype=np.intc)[:, None]
|
||||
c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None]
|
||||
pad_amount = max(0, max_dim-self.data.shape[1])
|
||||
data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount),
|
||||
dtype=self.data.dtype)))
|
||||
data = data[r, c]
|
||||
return self._dia_container((data, offsets), shape=(
|
||||
num_cols, num_rows), copy=copy)
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
def diagonal(self, k=0):
|
||||
rows, cols = self.shape
|
||||
if k <= -rows or k >= cols:
|
||||
return np.empty(0, dtype=self.data.dtype)
|
||||
idx, = np.nonzero(self.offsets == k)
|
||||
first_col = max(0, k)
|
||||
last_col = min(rows + k, cols)
|
||||
result_size = last_col - first_col
|
||||
if idx.size == 0:
|
||||
return np.zeros(result_size, dtype=self.data.dtype)
|
||||
result = self.data[idx[0], first_col:last_col]
|
||||
padding = result_size - len(result)
|
||||
if padding > 0:
|
||||
result = np.pad(result, (0, padding), mode='constant')
|
||||
return result
|
||||
|
||||
diagonal.__doc__ = _spbase.diagonal.__doc__
|
||||
|
||||
def tocsc(self, copy=False):
|
||||
if self.nnz == 0:
|
||||
return self._csc_container(self.shape, dtype=self.dtype)
|
||||
|
||||
num_rows, num_cols = self.shape
|
||||
num_offsets, offset_len = self.data.shape
|
||||
offset_inds = np.arange(offset_len)
|
||||
|
||||
row = offset_inds - self.offsets[:,None]
|
||||
mask = (row >= 0)
|
||||
mask &= (row < num_rows)
|
||||
mask &= (offset_inds < num_cols)
|
||||
mask &= (self.data != 0)
|
||||
|
||||
idx_dtype = self._get_index_dtype(maxval=max(self.shape))
|
||||
indptr = np.zeros(num_cols + 1, dtype=idx_dtype)
|
||||
indptr[1:offset_len+1] = np.cumsum(mask.sum(axis=0)[:num_cols])
|
||||
if offset_len < num_cols:
|
||||
indptr[offset_len+1:] = indptr[offset_len]
|
||||
indices = row.T[mask.T].astype(idx_dtype, copy=False)
|
||||
data = self.data.T[mask.T]
|
||||
return self._csc_container((data, indices, indptr), shape=self.shape,
|
||||
dtype=self.dtype)
|
||||
|
||||
tocsc.__doc__ = _spbase.tocsc.__doc__
|
||||
|
||||
def tocoo(self, copy=False):
|
||||
num_rows, num_cols = self.shape
|
||||
num_offsets, offset_len = self.data.shape
|
||||
offset_inds = np.arange(offset_len)
|
||||
|
||||
row = offset_inds - self.offsets[:,None]
|
||||
mask = (row >= 0)
|
||||
mask &= (row < num_rows)
|
||||
mask &= (offset_inds < num_cols)
|
||||
mask &= (self.data != 0)
|
||||
row = row[mask]
|
||||
col = np.tile(offset_inds, num_offsets)[mask.ravel()]
|
||||
idx_dtype = self._get_index_dtype(
|
||||
arrays=(self.offsets,), maxval=max(self.shape)
|
||||
)
|
||||
row = row.astype(idx_dtype, copy=False)
|
||||
col = col.astype(idx_dtype, copy=False)
|
||||
data = self.data[mask]
|
||||
# Note: this cannot set has_canonical_format=True, because despite the
|
||||
# lack of duplicates, we do not generate sorted indices.
|
||||
return self._coo_container(
|
||||
(data, (row, col)), shape=self.shape, dtype=self.dtype, copy=False
|
||||
)
|
||||
|
||||
tocoo.__doc__ = _spbase.tocoo.__doc__
|
||||
|
||||
# needed by _data_matrix
|
||||
def _with_data(self, data, copy=True):
|
||||
"""Returns a matrix with the same sparsity structure as self,
|
||||
but with different data. By default the structure arrays are copied.
|
||||
"""
|
||||
if copy:
|
||||
return self._dia_container(
|
||||
(data, self.offsets.copy()), shape=self.shape
|
||||
)
|
||||
else:
|
||||
return self._dia_container(
|
||||
(data, self.offsets), shape=self.shape
|
||||
)
|
||||
|
||||
def resize(self, *shape):
|
||||
shape = check_shape(shape)
|
||||
M, N = shape
|
||||
# we do not need to handle the case of expanding N
|
||||
self.data = self.data[:, :N]
|
||||
|
||||
if (M > self.shape[0] and
|
||||
np.any(self.offsets + self.shape[0] < self.data.shape[1])):
|
||||
# explicitly clear values that were previously hidden
|
||||
mask = (self.offsets[:, None] + self.shape[0] <=
|
||||
np.arange(self.data.shape[1]))
|
||||
self.data[mask] = 0
|
||||
|
||||
self._shape = shape
|
||||
|
||||
resize.__doc__ = _spbase.resize.__doc__
|
||||
|
||||
|
||||
def _invert_index(idx):
|
||||
"""Helper function to invert an index array."""
|
||||
inv = np.zeros_like(idx)
|
||||
inv[idx] = np.arange(len(idx))
|
||||
return inv
|
||||
|
||||
|
||||
def isspmatrix_dia(x):
|
||||
"""Is `x` of dia_matrix type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a dia matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a dia matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import dia_array, dia_matrix, coo_matrix, isspmatrix_dia
|
||||
>>> isspmatrix_dia(dia_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_dia(dia_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_dia(coo_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, dia_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class dia_array(_dia_base, sparray):
|
||||
"""
|
||||
Sparse array with DIAgonal storage.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
dia_array(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
dia_array(S)
|
||||
with another sparse array or matrix S (equivalent to S.todia())
|
||||
|
||||
dia_array((M, N), [dtype])
|
||||
to construct an empty array with shape (M, N),
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
dia_array((data, offsets), shape=(M, N))
|
||||
where the ``data[k,:]`` stores the diagonal entries for
|
||||
diagonal ``offsets[k]`` (See example below)
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
DIA format data array of the array
|
||||
offsets
|
||||
DIA format offset array of the array
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
Sparse arrays with DIAgonal storage do not support slicing.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import dia_array
|
||||
>>> dia_array((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
|
||||
>>> offsets = np.array([0, -1, 2])
|
||||
>>> dia_array((data, offsets), shape=(4, 4)).toarray()
|
||||
array([[1, 0, 3, 0],
|
||||
[1, 2, 0, 4],
|
||||
[0, 2, 3, 0],
|
||||
[0, 0, 3, 4]])
|
||||
|
||||
>>> from scipy.sparse import dia_array
|
||||
>>> n = 10
|
||||
>>> ex = np.ones(n)
|
||||
>>> data = np.array([ex, 2 * ex, ex])
|
||||
>>> offsets = np.array([-1, 0, 1])
|
||||
>>> dia_array((data, offsets), shape=(n, n)).toarray()
|
||||
array([[2., 1., 0., ..., 0., 0., 0.],
|
||||
[1., 2., 1., ..., 0., 0., 0.],
|
||||
[0., 1., 2., ..., 0., 0., 0.],
|
||||
...,
|
||||
[0., 0., 0., ..., 2., 1., 0.],
|
||||
[0., 0., 0., ..., 1., 2., 1.],
|
||||
[0., 0., 0., ..., 0., 1., 2.]])
|
||||
"""
|
||||
|
||||
|
||||
class dia_matrix(spmatrix, _dia_base):
|
||||
"""
|
||||
Sparse matrix with DIAgonal storage.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
dia_matrix(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
dia_matrix(S)
|
||||
with another sparse array or matrix S (equivalent to S.todia())
|
||||
|
||||
dia_matrix((M, N), [dtype])
|
||||
to construct an empty matrix with shape (M, N),
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
dia_matrix((data, offsets), shape=(M, N))
|
||||
where the ``data[k,:]`` stores the diagonal entries for
|
||||
diagonal ``offsets[k]`` (See example below)
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
DIA format data array of the matrix
|
||||
offsets
|
||||
DIA format offset array of the matrix
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
Sparse matrices with DIAgonal storage do not support slicing.
|
||||
|
||||
Examples
|
||||
--------
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import dia_matrix
|
||||
>>> dia_matrix((3, 4), dtype=np.int8).toarray()
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 0, 0]], dtype=int8)
|
||||
|
||||
>>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
|
||||
>>> offsets = np.array([0, -1, 2])
|
||||
>>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
|
||||
array([[1, 0, 3, 0],
|
||||
[1, 2, 0, 4],
|
||||
[0, 2, 3, 0],
|
||||
[0, 0, 3, 4]])
|
||||
|
||||
>>> from scipy.sparse import dia_matrix
|
||||
>>> n = 10
|
||||
>>> ex = np.ones(n)
|
||||
>>> data = np.array([ex, 2 * ex, ex])
|
||||
>>> offsets = np.array([-1, 0, 1])
|
||||
>>> dia_matrix((data, offsets), shape=(n, n)).toarray()
|
||||
array([[2., 1., 0., ..., 0., 0., 0.],
|
||||
[1., 2., 1., ..., 0., 0., 0.],
|
||||
[0., 1., 2., ..., 0., 0., 0.],
|
||||
...,
|
||||
[0., 0., 0., ..., 2., 1., 0.],
|
||||
[0., 0., 0., ..., 1., 2., 1.],
|
||||
[0., 0., 0., ..., 0., 1., 2.]])
|
||||
"""
|
||||
669
venv/lib/python3.13/site-packages/scipy/sparse/_dok.py
Normal file
669
venv/lib/python3.13/site-packages/scipy/sparse/_dok.py
Normal file
|
|
@ -0,0 +1,669 @@
|
|||
"""Dictionary Of Keys based matrix"""
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['dok_array', 'dok_matrix', 'isspmatrix_dok']
|
||||
|
||||
import itertools
|
||||
import numpy as np
|
||||
|
||||
from ._matrix import spmatrix
|
||||
from ._base import _spbase, sparray, issparse
|
||||
from ._index import IndexMixin
|
||||
from ._sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
|
||||
upcast, upcast_scalar, check_shape)
|
||||
|
||||
|
||||
class _dok_base(_spbase, IndexMixin, dict):
|
||||
_format = 'dok'
|
||||
_allow_nd = (1, 2)
|
||||
|
||||
def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
|
||||
_spbase.__init__(self, arg1, maxprint=maxprint)
|
||||
|
||||
if isinstance(arg1, tuple) and isshape(arg1, allow_nd=self._allow_nd):
|
||||
self._shape = check_shape(arg1, allow_nd=self._allow_nd)
|
||||
self._dict = {}
|
||||
self.dtype = getdtype(dtype, default=float)
|
||||
elif issparse(arg1): # Sparse ctor
|
||||
if arg1.format == self.format:
|
||||
arg1 = arg1.copy() if copy else arg1
|
||||
else:
|
||||
arg1 = arg1.todok()
|
||||
|
||||
if dtype is not None:
|
||||
arg1 = arg1.astype(dtype, copy=False)
|
||||
|
||||
self._dict = arg1._dict
|
||||
self._shape = check_shape(arg1.shape, allow_nd=self._allow_nd)
|
||||
self.dtype = getdtype(arg1.dtype)
|
||||
else: # Dense ctor
|
||||
try:
|
||||
arg1 = np.asarray(arg1)
|
||||
except Exception as e:
|
||||
raise TypeError('Invalid input format.') from e
|
||||
|
||||
if arg1.ndim > 2:
|
||||
raise ValueError(f"DOK arrays don't yet support {arg1.ndim}D input.")
|
||||
|
||||
if arg1.ndim == 1:
|
||||
if dtype is not None:
|
||||
arg1 = arg1.astype(dtype)
|
||||
self._dict = {i: v for i, v in enumerate(arg1) if v != 0}
|
||||
self.dtype = getdtype(arg1.dtype)
|
||||
else:
|
||||
d = self._coo_container(arg1, shape=shape, dtype=dtype).todok()
|
||||
self._dict = d._dict
|
||||
self.dtype = getdtype(d.dtype)
|
||||
self._shape = check_shape(arg1.shape, allow_nd=self._allow_nd)
|
||||
|
||||
def update(self, val):
|
||||
# Prevent direct usage of update
|
||||
raise NotImplementedError("Direct update to DOK sparse format is not allowed.")
|
||||
|
||||
def _getnnz(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError(
|
||||
"_getnnz over an axis is not implemented for DOK format."
|
||||
)
|
||||
return len(self._dict)
|
||||
|
||||
def count_nonzero(self, axis=None):
|
||||
if axis is not None:
|
||||
raise NotImplementedError(
|
||||
"count_nonzero over an axis is not implemented for DOK format."
|
||||
)
|
||||
return sum(x != 0 for x in self.values())
|
||||
|
||||
_getnnz.__doc__ = _spbase._getnnz.__doc__
|
||||
count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
|
||||
|
||||
def __len__(self):
|
||||
return len(self._dict)
|
||||
|
||||
def __contains__(self, key):
|
||||
return key in self._dict
|
||||
|
||||
def setdefault(self, key, default=None, /):
|
||||
return self._dict.setdefault(key, default)
|
||||
|
||||
def __delitem__(self, key, /):
|
||||
del self._dict[key]
|
||||
|
||||
def clear(self):
|
||||
return self._dict.clear()
|
||||
|
||||
def pop(self, /, *args):
|
||||
return self._dict.pop(*args)
|
||||
|
||||
def __reversed__(self):
|
||||
raise TypeError("reversed is not defined for dok_array type")
|
||||
|
||||
def __or__(self, other):
|
||||
type_names = f"{type(self).__name__} and {type(other).__name__}"
|
||||
raise TypeError(f"unsupported operand type for |: {type_names}")
|
||||
|
||||
def __ror__(self, other):
|
||||
type_names = f"{type(self).__name__} and {type(other).__name__}"
|
||||
raise TypeError(f"unsupported operand type for |: {type_names}")
|
||||
|
||||
def __ior__(self, other):
|
||||
type_names = f"{type(self).__name__} and {type(other).__name__}"
|
||||
raise TypeError(f"unsupported operand type for |: {type_names}")
|
||||
|
||||
def popitem(self):
|
||||
return self._dict.popitem()
|
||||
|
||||
def items(self):
|
||||
return self._dict.items()
|
||||
|
||||
def keys(self):
|
||||
return self._dict.keys()
|
||||
|
||||
def values(self):
|
||||
return self._dict.values()
|
||||
|
||||
def get(self, key, default=0.0):
|
||||
"""This provides dict.get method functionality with type checking"""
|
||||
if key in self._dict:
|
||||
return self._dict[key]
|
||||
if isintlike(key) and self.ndim == 1:
|
||||
key = (key,)
|
||||
if self.ndim != len(key):
|
||||
raise IndexError(f'Index {key} length needs to match self.shape')
|
||||
try:
|
||||
for i in key:
|
||||
assert isintlike(i)
|
||||
except (AssertionError, TypeError, ValueError) as e:
|
||||
raise IndexError('Index must be or consist of integers.') from e
|
||||
key = tuple(i + M if i < 0 else i for i, M in zip(key, self.shape))
|
||||
if any(i < 0 or i >= M for i, M in zip(key, self.shape)):
|
||||
raise IndexError('Index out of bounds.')
|
||||
if self.ndim == 1:
|
||||
key = key[0]
|
||||
return self._dict.get(key, default)
|
||||
|
||||
# 1D get methods
|
||||
def _get_int(self, idx):
|
||||
return self._dict.get(idx, self.dtype.type(0))
|
||||
|
||||
def _get_slice(self, idx):
|
||||
i_range = range(*idx.indices(self.shape[0]))
|
||||
return self._get_array(list(i_range))
|
||||
|
||||
def _get_array(self, idx):
|
||||
idx = np.asarray(idx)
|
||||
if idx.ndim == 0:
|
||||
val = self._dict.get(int(idx), self.dtype.type(0))
|
||||
return np.array(val, stype=self.dtype)
|
||||
new_dok = self._dok_container(idx.shape, dtype=self.dtype)
|
||||
dok_vals = [self._dict.get(i, 0) for i in idx.ravel()]
|
||||
if dok_vals:
|
||||
if len(idx.shape) == 1:
|
||||
for i, v in enumerate(dok_vals):
|
||||
if v:
|
||||
new_dok._dict[i] = v
|
||||
else:
|
||||
new_idx = np.unravel_index(np.arange(len(dok_vals)), idx.shape)
|
||||
new_idx = new_idx[0] if len(new_idx) == 1 else zip(*new_idx)
|
||||
for i, v in zip(new_idx, dok_vals, strict=True):
|
||||
if v:
|
||||
new_dok._dict[i] = v
|
||||
return new_dok
|
||||
|
||||
# 2D get methods
|
||||
def _get_intXint(self, row, col):
|
||||
return self._dict.get((row, col), self.dtype.type(0))
|
||||
|
||||
def _get_intXslice(self, row, col):
|
||||
return self._get_sliceXslice(slice(row, row + 1), col)
|
||||
|
||||
def _get_sliceXint(self, row, col):
|
||||
return self._get_sliceXslice(row, slice(col, col + 1))
|
||||
|
||||
def _get_sliceXslice(self, row, col):
|
||||
row_start, row_stop, row_step = row.indices(self.shape[0])
|
||||
col_start, col_stop, col_step = col.indices(self.shape[1])
|
||||
row_range = range(row_start, row_stop, row_step)
|
||||
col_range = range(col_start, col_stop, col_step)
|
||||
shape = (len(row_range), len(col_range))
|
||||
# Switch paths only when advantageous
|
||||
# (count the iterations in the loops, adjust for complexity)
|
||||
if len(self) >= 2 * shape[0] * shape[1]:
|
||||
# O(nr*nc) path: loop over <row x col>
|
||||
return self._get_columnXarray(row_range, col_range)
|
||||
# O(nnz) path: loop over entries of self
|
||||
newdok = self._dok_container(shape, dtype=self.dtype)
|
||||
for key in self.keys():
|
||||
i, ri = divmod(int(key[0]) - row_start, row_step)
|
||||
if ri != 0 or i < 0 or i >= shape[0]:
|
||||
continue
|
||||
j, rj = divmod(int(key[1]) - col_start, col_step)
|
||||
if rj != 0 or j < 0 or j >= shape[1]:
|
||||
continue
|
||||
newdok._dict[i, j] = self._dict[key]
|
||||
return newdok
|
||||
|
||||
def _get_intXarray(self, row, col):
|
||||
return self._get_columnXarray([row], col.ravel())
|
||||
|
||||
def _get_arrayXint(self, row, col):
|
||||
res = self._get_columnXarray(row.ravel(), [col])
|
||||
if row.ndim > 1:
|
||||
return res.reshape(row.shape)
|
||||
return res
|
||||
|
||||
def _get_sliceXarray(self, row, col):
|
||||
row = list(range(*row.indices(self.shape[0])))
|
||||
return self._get_columnXarray(row, col)
|
||||
|
||||
def _get_arrayXslice(self, row, col):
|
||||
col = list(range(*col.indices(self.shape[1])))
|
||||
return self._get_columnXarray(row, col)
|
||||
|
||||
def _get_columnXarray(self, row, col):
|
||||
# outer indexing
|
||||
newdok = self._dok_container((len(row), len(col)), dtype=self.dtype)
|
||||
|
||||
for i, r in enumerate(row):
|
||||
for j, c in enumerate(col):
|
||||
v = self._dict.get((r, c), 0)
|
||||
if v:
|
||||
newdok._dict[i, j] = v
|
||||
return newdok
|
||||
|
||||
def _get_arrayXarray(self, row, col):
|
||||
# inner indexing
|
||||
i, j = map(np.atleast_2d, np.broadcast_arrays(row, col))
|
||||
newdok = self._dok_container(i.shape, dtype=self.dtype)
|
||||
|
||||
for key in itertools.product(range(i.shape[0]), range(i.shape[1])):
|
||||
v = self._dict.get((i[key], j[key]), 0)
|
||||
if v:
|
||||
newdok._dict[key] = v
|
||||
return newdok
|
||||
|
||||
# 1D set methods
|
||||
def _set_int(self, idx, x):
|
||||
if x:
|
||||
self._dict[idx] = x
|
||||
elif idx in self._dict:
|
||||
del self._dict[idx]
|
||||
|
||||
def _set_array(self, idx, x):
|
||||
idx_set = idx.ravel()
|
||||
x_set = x.ravel()
|
||||
if len(idx_set) != len(x_set):
|
||||
if len(x_set) == 1:
|
||||
x_set = np.full(len(idx_set), x_set[0], dtype=self.dtype)
|
||||
else:
|
||||
raise ValueError("Need len(index)==len(data) or len(data)==1")
|
||||
for i, v in zip(idx_set, x_set):
|
||||
if v:
|
||||
self._dict[i] = v
|
||||
elif i in self._dict:
|
||||
del self._dict[i]
|
||||
|
||||
# 2D set methods
|
||||
def _set_intXint(self, row, col, x):
|
||||
key = (row, col)
|
||||
if x:
|
||||
self._dict[key] = x
|
||||
elif key in self._dict:
|
||||
del self._dict[key]
|
||||
|
||||
def _set_arrayXarray(self, row, col, x):
|
||||
row = list(map(int, row.ravel()))
|
||||
col = list(map(int, col.ravel()))
|
||||
x = x.ravel()
|
||||
self._dict.update(zip(zip(row, col), x))
|
||||
|
||||
for i in np.nonzero(x == 0)[0]:
|
||||
key = (row[i], col[i])
|
||||
if self._dict[key] == 0:
|
||||
# may have been superseded by later update
|
||||
del self._dict[key]
|
||||
|
||||
def __add__(self, other):
|
||||
if isscalarlike(other):
|
||||
res_dtype = upcast_scalar(self.dtype, other)
|
||||
new = self._dok_container(self.shape, dtype=res_dtype)
|
||||
# Add this scalar to each element.
|
||||
for key in itertools.product(*[range(d) for d in self.shape]):
|
||||
aij = self._dict.get(key, 0) + other
|
||||
if aij:
|
||||
new[key] = aij
|
||||
elif issparse(other):
|
||||
if other.shape != self.shape:
|
||||
raise ValueError("Matrix dimensions are not equal.")
|
||||
res_dtype = upcast(self.dtype, other.dtype)
|
||||
new = self._dok_container(self.shape, dtype=res_dtype)
|
||||
new._dict = self._dict.copy()
|
||||
if other.format == "dok":
|
||||
o_items = other.items()
|
||||
else:
|
||||
other = other.tocoo()
|
||||
if self.ndim == 1:
|
||||
o_items = zip(other.coords[0], other.data)
|
||||
else:
|
||||
o_items = zip(zip(*other.coords), other.data)
|
||||
with np.errstate(over='ignore'):
|
||||
new._dict.update((k, new[k] + v) for k, v in o_items)
|
||||
elif isdense(other):
|
||||
new = self.todense() + other
|
||||
else:
|
||||
return NotImplemented
|
||||
return new
|
||||
|
||||
def __radd__(self, other):
|
||||
return self + other # addition is commutative
|
||||
|
||||
def __neg__(self):
|
||||
if self.dtype.kind == 'b':
|
||||
raise NotImplementedError(
|
||||
'Negating a sparse boolean matrix is not supported.'
|
||||
)
|
||||
new = self._dok_container(self.shape, dtype=self.dtype)
|
||||
new._dict.update((k, -v) for k, v in self.items())
|
||||
return new
|
||||
|
||||
def _mul_scalar(self, other):
|
||||
res_dtype = upcast_scalar(self.dtype, other)
|
||||
# Multiply this scalar by every element.
|
||||
new = self._dok_container(self.shape, dtype=res_dtype)
|
||||
new._dict.update(((k, v * other) for k, v in self.items()))
|
||||
return new
|
||||
|
||||
def _matmul_vector(self, other):
|
||||
res_dtype = upcast(self.dtype, other.dtype)
|
||||
|
||||
# vector @ vector
|
||||
if self.ndim == 1:
|
||||
if issparse(other):
|
||||
if other.format == "dok":
|
||||
keys = self.keys() & other.keys()
|
||||
else:
|
||||
keys = self.keys() & other.tocoo().coords[0]
|
||||
return res_dtype(sum(self._dict[k] * other._dict[k] for k in keys))
|
||||
elif isdense(other):
|
||||
return res_dtype(sum(other[k] * v for k, v in self.items()))
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
# matrix @ vector
|
||||
result = np.zeros(self.shape[0], dtype=res_dtype)
|
||||
for (i, j), v in self.items():
|
||||
result[i] += v * other[j]
|
||||
return result
|
||||
|
||||
def _matmul_multivector(self, other):
|
||||
result_dtype = upcast(self.dtype, other.dtype)
|
||||
# vector @ multivector
|
||||
if self.ndim == 1:
|
||||
# works for other 1d or 2d
|
||||
return sum(v * other[j] for j, v in self._dict.items())
|
||||
|
||||
# matrix @ multivector
|
||||
M = self.shape[0]
|
||||
new_shape = (M,) if other.ndim == 1 else (M, other.shape[1])
|
||||
result = np.zeros(new_shape, dtype=result_dtype)
|
||||
for (i, j), v in self.items():
|
||||
result[i] += v * other[j]
|
||||
return result
|
||||
|
||||
def __imul__(self, other):
|
||||
if isscalarlike(other):
|
||||
self._dict.update((k, v * other) for k, v in self.items())
|
||||
return self
|
||||
return NotImplemented
|
||||
|
||||
def __truediv__(self, other):
|
||||
if isscalarlike(other):
|
||||
res_dtype = upcast_scalar(self.dtype, other)
|
||||
new = self._dok_container(self.shape, dtype=res_dtype)
|
||||
new._dict.update(((k, v / other) for k, v in self.items()))
|
||||
return new
|
||||
return self.tocsr() / other
|
||||
|
||||
def __itruediv__(self, other):
|
||||
if isscalarlike(other):
|
||||
self._dict.update((k, v / other) for k, v in self.items())
|
||||
return self
|
||||
return NotImplemented
|
||||
|
||||
def __reduce__(self):
|
||||
# this approach is necessary because __setstate__ is called after
|
||||
# __setitem__ upon unpickling and since __init__ is not called there
|
||||
# is no shape attribute hence it is not possible to unpickle it.
|
||||
return dict.__reduce__(self)
|
||||
|
||||
def diagonal(self, k=0):
|
||||
if self.ndim == 2:
|
||||
return super().diagonal(k)
|
||||
raise ValueError("diagonal requires two dimensions")
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
if self.ndim == 1:
|
||||
return self.copy()
|
||||
|
||||
if axes is not None and axes != (1, 0):
|
||||
raise ValueError(
|
||||
"Sparse arrays/matrices do not support "
|
||||
"an 'axes' parameter because swapping "
|
||||
"dimensions is the only logical permutation."
|
||||
)
|
||||
|
||||
M, N = self.shape
|
||||
new = self._dok_container((N, M), dtype=self.dtype, copy=copy)
|
||||
new._dict.update((((right, left), val) for (left, right), val in self.items()))
|
||||
return new
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
def copy(self):
|
||||
new = self._dok_container(self.shape, dtype=self.dtype)
|
||||
new._dict.update(self._dict)
|
||||
return new
|
||||
|
||||
copy.__doc__ = _spbase.copy.__doc__
|
||||
|
||||
@classmethod
|
||||
def fromkeys(cls, iterable, value=1, /):
|
||||
tmp = dict.fromkeys(iterable, value)
|
||||
if isinstance(next(iter(tmp)), tuple):
|
||||
shape = tuple(max(idx) + 1 for idx in zip(*tmp))
|
||||
else:
|
||||
shape = (max(tmp) + 1,)
|
||||
result = cls(shape, dtype=type(value))
|
||||
result._dict = tmp
|
||||
return result
|
||||
|
||||
def tocoo(self, copy=False):
|
||||
nnz = self.nnz
|
||||
if nnz == 0:
|
||||
return self._coo_container(self.shape, dtype=self.dtype)
|
||||
|
||||
idx_dtype = self._get_index_dtype(maxval=max(self.shape))
|
||||
data = np.fromiter(self.values(), dtype=self.dtype, count=nnz)
|
||||
# handle 1d keys specially b/c not a tuple
|
||||
inds = zip(*self.keys()) if self.ndim > 1 else (self.keys(),)
|
||||
coords = tuple(np.fromiter(ix, dtype=idx_dtype, count=nnz) for ix in inds)
|
||||
A = self._coo_container((data, coords), shape=self.shape, dtype=self.dtype)
|
||||
A.has_canonical_format = True
|
||||
return A
|
||||
|
||||
tocoo.__doc__ = _spbase.tocoo.__doc__
|
||||
|
||||
def todok(self, copy=False):
|
||||
if copy:
|
||||
return self.copy()
|
||||
return self
|
||||
|
||||
todok.__doc__ = _spbase.todok.__doc__
|
||||
|
||||
def tocsc(self, copy=False):
|
||||
if self.ndim == 1:
|
||||
raise NotImplementedError("tocsr() not valid for 1d sparse array")
|
||||
return self.tocoo(copy=False).tocsc(copy=copy)
|
||||
|
||||
tocsc.__doc__ = _spbase.tocsc.__doc__
|
||||
|
||||
def resize(self, *shape):
|
||||
shape = check_shape(shape, allow_nd=self._allow_nd)
|
||||
if len(shape) != len(self.shape):
|
||||
# TODO implement resize across dimensions
|
||||
raise NotImplementedError
|
||||
|
||||
if self.ndim == 1:
|
||||
newN = shape[-1]
|
||||
for i in list(self._dict):
|
||||
if i >= newN:
|
||||
del self._dict[i]
|
||||
self._shape = shape
|
||||
return
|
||||
|
||||
newM, newN = shape
|
||||
M, N = self.shape
|
||||
if newM < M or newN < N:
|
||||
# Remove all elements outside new dimensions
|
||||
for i, j in list(self.keys()):
|
||||
if i >= newM or j >= newN:
|
||||
del self._dict[i, j]
|
||||
self._shape = shape
|
||||
|
||||
resize.__doc__ = _spbase.resize.__doc__
|
||||
|
||||
# Added for 1d to avoid `tocsr` from _base.py
|
||||
def astype(self, dtype, casting='unsafe', copy=True):
|
||||
dtype = np.dtype(dtype)
|
||||
if self.dtype != dtype:
|
||||
result = self._dok_container(self.shape, dtype=dtype)
|
||||
data = np.array(list(self._dict.values()), dtype=dtype)
|
||||
result._dict = dict(zip(self._dict, data))
|
||||
return result
|
||||
elif copy:
|
||||
return self.copy()
|
||||
return self
|
||||
|
||||
|
||||
def isspmatrix_dok(x):
|
||||
"""Is `x` of dok_array type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a dok matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a dok matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import dok_array, dok_matrix, coo_matrix, isspmatrix_dok
|
||||
>>> isspmatrix_dok(dok_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_dok(dok_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_dok(coo_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, dok_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class dok_array(_dok_base, sparray):
|
||||
"""
|
||||
Dictionary Of Keys based sparse array.
|
||||
|
||||
This is an efficient structure for constructing sparse
|
||||
arrays incrementally.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
dok_array(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
dok_array(S)
|
||||
with another sparse array or matrix S (equivalent to S.todok())
|
||||
|
||||
dok_array((M,N), [dtype])
|
||||
create the array with initial shape (M,N)
|
||||
dtype is optional, defaulting to dtype='d'
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
Number of nonzero elements
|
||||
size
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
- Allows for efficient O(1) access of individual elements.
|
||||
- Duplicates are not allowed.
|
||||
- Can be efficiently converted to a coo_array once constructed.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import dok_array
|
||||
>>> S = dok_array((5, 5), dtype=np.float32)
|
||||
>>> for i in range(5):
|
||||
... for j in range(5):
|
||||
... S[i, j] = i + j # Update element
|
||||
|
||||
"""
|
||||
|
||||
|
||||
class dok_matrix(spmatrix, _dok_base):
|
||||
"""
|
||||
Dictionary Of Keys based sparse matrix.
|
||||
|
||||
This is an efficient structure for constructing sparse
|
||||
matrices incrementally.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
dok_matrix(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
dok_matrix(S)
|
||||
with another sparse array or matrix S (equivalent to S.todok())
|
||||
|
||||
dok_matrix((M,N), [dtype])
|
||||
create the matrix with initial shape (M,N)
|
||||
dtype is optional, defaulting to dtype='d'
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
Number of nonzero elements
|
||||
size
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
- Allows for efficient O(1) access of individual elements.
|
||||
- Duplicates are not allowed.
|
||||
- Can be efficiently converted to a coo_matrix once constructed.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import dok_matrix
|
||||
>>> S = dok_matrix((5, 5), dtype=np.float32)
|
||||
>>> for i in range(5):
|
||||
... for j in range(5):
|
||||
... S[i, j] = i + j # Update element
|
||||
|
||||
"""
|
||||
|
||||
def set_shape(self, shape):
|
||||
new_matrix = self.reshape(shape, copy=False).asformat(self.format)
|
||||
self.__dict__ = new_matrix.__dict__
|
||||
|
||||
def get_shape(self):
|
||||
"""Get shape of a sparse matrix."""
|
||||
return self._shape
|
||||
|
||||
shape = property(fget=get_shape, fset=set_shape)
|
||||
|
||||
def __reversed__(self):
|
||||
return self._dict.__reversed__()
|
||||
|
||||
def __or__(self, other):
|
||||
if isinstance(other, _dok_base):
|
||||
return self._dict | other._dict
|
||||
return self._dict | other
|
||||
|
||||
def __ror__(self, other):
|
||||
if isinstance(other, _dok_base):
|
||||
return self._dict | other._dict
|
||||
return self._dict | other
|
||||
|
||||
def __ior__(self, other):
|
||||
if isinstance(other, _dok_base):
|
||||
self._dict |= other._dict
|
||||
else:
|
||||
self._dict |= other
|
||||
return self
|
||||
178
venv/lib/python3.13/site-packages/scipy/sparse/_extract.py
Normal file
178
venv/lib/python3.13/site-packages/scipy/sparse/_extract.py
Normal file
|
|
@ -0,0 +1,178 @@
|
|||
"""Functions to extract parts of sparse matrices
|
||||
"""
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['find', 'tril', 'triu']
|
||||
|
||||
|
||||
from ._coo import coo_matrix, coo_array
|
||||
from ._base import sparray
|
||||
|
||||
|
||||
def find(A):
|
||||
"""Return the indices and values of the nonzero elements of a matrix
|
||||
|
||||
Parameters
|
||||
----------
|
||||
A : dense or sparse array or matrix
|
||||
Matrix whose nonzero elements are desired.
|
||||
|
||||
Returns
|
||||
-------
|
||||
(I,J,V) : tuple of arrays
|
||||
I,J, and V contain the row indices, column indices, and values
|
||||
of the nonzero entries.
|
||||
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import csr_array, find
|
||||
>>> A = csr_array([[7.0, 8.0, 0],[0, 0, 9.0]])
|
||||
>>> find(A)
|
||||
(array([0, 0, 1], dtype=int32),
|
||||
array([0, 1, 2], dtype=int32),
|
||||
array([ 7., 8., 9.]))
|
||||
|
||||
"""
|
||||
|
||||
A = coo_array(A, copy=True)
|
||||
A.sum_duplicates()
|
||||
# remove explicit zeros
|
||||
nz_mask = A.data != 0
|
||||
return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask]
|
||||
|
||||
|
||||
def tril(A, k=0, format=None):
|
||||
"""Return the lower triangular portion of a sparse array or matrix
|
||||
|
||||
Returns the elements on or below the k-th diagonal of A.
|
||||
- k = 0 corresponds to the main diagonal
|
||||
- k > 0 is above the main diagonal
|
||||
- k < 0 is below the main diagonal
|
||||
|
||||
Parameters
|
||||
----------
|
||||
A : dense or sparse array or matrix
|
||||
Matrix whose lower trianglar portion is desired.
|
||||
k : integer : optional
|
||||
The top-most diagonal of the lower triangle.
|
||||
format : string
|
||||
Sparse format of the result, e.g. format="csr", etc.
|
||||
|
||||
Returns
|
||||
-------
|
||||
L : sparse matrix
|
||||
Lower triangular portion of A in sparse format.
|
||||
|
||||
See Also
|
||||
--------
|
||||
triu : upper triangle in sparse format
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import csr_array, tril
|
||||
>>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
|
||||
... dtype='int32')
|
||||
>>> A.toarray()
|
||||
array([[1, 2, 0, 0, 3],
|
||||
[4, 5, 0, 6, 7],
|
||||
[0, 0, 8, 9, 0]], dtype=int32)
|
||||
>>> tril(A).toarray()
|
||||
array([[1, 0, 0, 0, 0],
|
||||
[4, 5, 0, 0, 0],
|
||||
[0, 0, 8, 0, 0]], dtype=int32)
|
||||
>>> tril(A).nnz
|
||||
4
|
||||
>>> tril(A, k=1).toarray()
|
||||
array([[1, 2, 0, 0, 0],
|
||||
[4, 5, 0, 0, 0],
|
||||
[0, 0, 8, 9, 0]], dtype=int32)
|
||||
>>> tril(A, k=-1).toarray()
|
||||
array([[0, 0, 0, 0, 0],
|
||||
[4, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0]], dtype=int32)
|
||||
>>> tril(A, format='csc')
|
||||
<Compressed Sparse Column sparse array of dtype 'int32'
|
||||
with 4 stored elements and shape (3, 5)>
|
||||
|
||||
"""
|
||||
coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix
|
||||
|
||||
# convert to COOrdinate format where things are easy
|
||||
A = coo_sparse(A, copy=False)
|
||||
mask = A.row + k >= A.col
|
||||
|
||||
row = A.row[mask]
|
||||
col = A.col[mask]
|
||||
data = A.data[mask]
|
||||
new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype)
|
||||
return new_coo.asformat(format)
|
||||
|
||||
|
||||
def triu(A, k=0, format=None):
|
||||
"""Return the upper triangular portion of a sparse array or matrix
|
||||
|
||||
Returns the elements on or above the k-th diagonal of A.
|
||||
- k = 0 corresponds to the main diagonal
|
||||
- k > 0 is above the main diagonal
|
||||
- k < 0 is below the main diagonal
|
||||
|
||||
Parameters
|
||||
----------
|
||||
A : dense or sparse array or matrix
|
||||
Matrix whose upper trianglar portion is desired.
|
||||
k : integer : optional
|
||||
The bottom-most diagonal of the upper triangle.
|
||||
format : string
|
||||
Sparse format of the result, e.g. format="csr", etc.
|
||||
|
||||
Returns
|
||||
-------
|
||||
L : sparse array or matrix
|
||||
Upper triangular portion of A in sparse format.
|
||||
Sparse array if A is a sparse array, otherwise matrix.
|
||||
|
||||
See Also
|
||||
--------
|
||||
tril : lower triangle in sparse format
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import csr_array, triu
|
||||
>>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
|
||||
... dtype='int32')
|
||||
>>> A.toarray()
|
||||
array([[1, 2, 0, 0, 3],
|
||||
[4, 5, 0, 6, 7],
|
||||
[0, 0, 8, 9, 0]], dtype=int32)
|
||||
>>> triu(A).toarray()
|
||||
array([[1, 2, 0, 0, 3],
|
||||
[0, 5, 0, 6, 7],
|
||||
[0, 0, 8, 9, 0]], dtype=int32)
|
||||
>>> triu(A).nnz
|
||||
8
|
||||
>>> triu(A, k=1).toarray()
|
||||
array([[0, 2, 0, 0, 3],
|
||||
[0, 0, 0, 6, 7],
|
||||
[0, 0, 0, 9, 0]], dtype=int32)
|
||||
>>> triu(A, k=-1).toarray()
|
||||
array([[1, 2, 0, 0, 3],
|
||||
[4, 5, 0, 6, 7],
|
||||
[0, 0, 8, 9, 0]], dtype=int32)
|
||||
>>> triu(A, format='csc')
|
||||
<Compressed Sparse Column sparse array of dtype 'int32'
|
||||
with 8 stored elements and shape (3, 5)>
|
||||
|
||||
"""
|
||||
coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix
|
||||
|
||||
# convert to COOrdinate format where things are easy
|
||||
A = coo_sparse(A, copy=False)
|
||||
mask = A.row + k <= A.col
|
||||
|
||||
row = A.row[mask]
|
||||
col = A.col[mask]
|
||||
data = A.data[mask]
|
||||
new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype)
|
||||
return new_coo.asformat(format)
|
||||
444
venv/lib/python3.13/site-packages/scipy/sparse/_index.py
Normal file
444
venv/lib/python3.13/site-packages/scipy/sparse/_index.py
Normal file
|
|
@ -0,0 +1,444 @@
|
|||
"""Indexing mixin for sparse array/matrix classes.
|
||||
"""
|
||||
import numpy as np
|
||||
from ._sputils import isintlike
|
||||
from ._base import sparray, issparse
|
||||
|
||||
INT_TYPES = (int, np.integer)
|
||||
|
||||
|
||||
def _broadcast_arrays(a, b):
|
||||
"""
|
||||
Same as np.broadcast_arrays(a, b) but old writeability rules.
|
||||
|
||||
NumPy >= 1.17.0 transitions broadcast_arrays to return
|
||||
read-only arrays. Set writeability explicitly to avoid warnings.
|
||||
Retain the old writeability rules, as our Cython code assumes
|
||||
the old behavior.
|
||||
"""
|
||||
x, y = np.broadcast_arrays(a, b)
|
||||
x.flags.writeable = a.flags.writeable
|
||||
y.flags.writeable = b.flags.writeable
|
||||
return x, y
|
||||
|
||||
|
||||
class IndexMixin:
|
||||
"""
|
||||
This class provides common dispatching and validation logic for indexing.
|
||||
"""
|
||||
def __getitem__(self, key):
|
||||
index, new_shape = self._validate_indices(key)
|
||||
|
||||
# 1D array
|
||||
if len(index) == 1:
|
||||
idx = index[0]
|
||||
if isinstance(idx, np.ndarray):
|
||||
if idx.shape == ():
|
||||
idx = idx.item()
|
||||
if isinstance(idx, INT_TYPES):
|
||||
res = self._get_int(idx)
|
||||
elif isinstance(idx, slice):
|
||||
res = self._get_slice(idx)
|
||||
else: # assume array idx
|
||||
res = self._get_array(idx)
|
||||
|
||||
# package the result and return
|
||||
if not isinstance(self, sparray):
|
||||
return res
|
||||
# handle np.newaxis in idx when result would otherwise be a scalar
|
||||
if res.shape == () and new_shape != ():
|
||||
if len(new_shape) == 1:
|
||||
return self.__class__([res], shape=new_shape, dtype=self.dtype)
|
||||
if len(new_shape) == 2:
|
||||
return self.__class__([[res]], shape=new_shape, dtype=self.dtype)
|
||||
return res.reshape(new_shape)
|
||||
|
||||
# 2D array
|
||||
row, col = index
|
||||
|
||||
# Dispatch to specialized methods.
|
||||
if isinstance(row, INT_TYPES):
|
||||
if isinstance(col, INT_TYPES):
|
||||
res = self._get_intXint(row, col)
|
||||
elif isinstance(col, slice):
|
||||
res = self._get_intXslice(row, col)
|
||||
elif col.ndim == 1:
|
||||
res = self._get_intXarray(row, col)
|
||||
elif col.ndim == 2:
|
||||
res = self._get_intXarray(row, col)
|
||||
else:
|
||||
raise IndexError('index results in >2 dimensions')
|
||||
elif isinstance(row, slice):
|
||||
if isinstance(col, INT_TYPES):
|
||||
res = self._get_sliceXint(row, col)
|
||||
elif isinstance(col, slice):
|
||||
if row == slice(None) and row == col:
|
||||
res = self.copy()
|
||||
else:
|
||||
res = self._get_sliceXslice(row, col)
|
||||
elif col.ndim == 1:
|
||||
res = self._get_sliceXarray(row, col)
|
||||
else:
|
||||
raise IndexError('index results in >2 dimensions')
|
||||
else:
|
||||
if isinstance(col, INT_TYPES):
|
||||
res = self._get_arrayXint(row, col)
|
||||
elif isinstance(col, slice):
|
||||
res = self._get_arrayXslice(row, col)
|
||||
# arrayXarray preprocess
|
||||
elif (row.ndim == 2 and row.shape[1] == 1
|
||||
and (col.ndim == 1 or col.shape[0] == 1)):
|
||||
# outer indexing
|
||||
res = self._get_columnXarray(row[:, 0], col.ravel())
|
||||
else:
|
||||
# inner indexing
|
||||
row, col = _broadcast_arrays(row, col)
|
||||
if row.shape != col.shape:
|
||||
raise IndexError('number of row and column indices differ')
|
||||
if row.size == 0:
|
||||
res = self.__class__(np.atleast_2d(row).shape, dtype=self.dtype)
|
||||
else:
|
||||
res = self._get_arrayXarray(row, col)
|
||||
|
||||
# handle spmatrix (must be 2d, dont let 1d new_shape start reshape)
|
||||
if not isinstance(self, sparray):
|
||||
if new_shape == () or (len(new_shape) == 1 and res.ndim != 0):
|
||||
# res handles cases not inflated by None
|
||||
return res
|
||||
if len(new_shape) == 1:
|
||||
# shape inflated to 1D by None in index. Make 2D
|
||||
new_shape = (1,) + new_shape
|
||||
# reshape if needed (when None changes shape, e.g. A[1,:,None])
|
||||
return res if new_shape == res.shape else res.reshape(new_shape)
|
||||
|
||||
# package the result and return
|
||||
if res.shape != new_shape:
|
||||
# handle formats that support indexing but not 1D (lil for now)
|
||||
if self.format == "lil" and len(new_shape) != 2:
|
||||
if res.shape == ():
|
||||
return self._coo_container([res], shape = new_shape)
|
||||
return res.tocoo().reshape(new_shape)
|
||||
return res.reshape(new_shape)
|
||||
return res
|
||||
|
||||
def __setitem__(self, key, x):
|
||||
index, _ = self._validate_indices(key)
|
||||
|
||||
# 1D array
|
||||
if len(index) == 1:
|
||||
idx = index[0]
|
||||
|
||||
if issparse(x):
|
||||
x = x.toarray()
|
||||
else:
|
||||
x = np.asarray(x, dtype=self.dtype)
|
||||
|
||||
if isinstance(idx, INT_TYPES):
|
||||
if x.size != 1:
|
||||
raise ValueError('Trying to assign a sequence to an item')
|
||||
self._set_int(idx, x.flat[0])
|
||||
return
|
||||
|
||||
if isinstance(idx, slice):
|
||||
# check for simple case of slice that gives 1 item
|
||||
# Note: Python `range` does not use lots of memory
|
||||
idx_range = range(*idx.indices(self.shape[0]))
|
||||
N = len(idx_range)
|
||||
if N == 1 and x.size == 1:
|
||||
self._set_int(idx_range[0], x.flat[0])
|
||||
return
|
||||
idx = np.arange(*idx.indices(self.shape[0]))
|
||||
idx_shape = idx.shape
|
||||
else:
|
||||
idx_shape = idx.squeeze().shape
|
||||
# broadcast scalar to full 1d
|
||||
if x.squeeze().shape != idx_shape:
|
||||
x = np.broadcast_to(x, idx.shape)
|
||||
if x.size != 0:
|
||||
self._set_array(idx, x)
|
||||
return
|
||||
|
||||
# 2D array
|
||||
row, col = index
|
||||
|
||||
if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
|
||||
x = np.asarray(x, dtype=self.dtype)
|
||||
if x.size != 1:
|
||||
raise ValueError('Trying to assign a sequence to an item')
|
||||
self._set_intXint(row, col, x.flat[0])
|
||||
return
|
||||
|
||||
if isinstance(row, slice):
|
||||
row = np.arange(*row.indices(self.shape[0]))[:, None]
|
||||
else:
|
||||
row = np.atleast_1d(row)
|
||||
|
||||
if isinstance(col, slice):
|
||||
col = np.arange(*col.indices(self.shape[1]))[None, :]
|
||||
if row.ndim == 1:
|
||||
row = row[:, None]
|
||||
else:
|
||||
col = np.atleast_1d(col)
|
||||
|
||||
i, j = _broadcast_arrays(row, col)
|
||||
if i.shape != j.shape:
|
||||
raise IndexError('number of row and column indices differ')
|
||||
|
||||
if issparse(x):
|
||||
if 0 in x.shape:
|
||||
return
|
||||
if i.ndim == 1:
|
||||
# Inner indexing, so treat them like row vectors.
|
||||
i = i[None]
|
||||
j = j[None]
|
||||
x = x.tocoo(copy=False).reshape(x._shape_as_2d, copy=True)
|
||||
broadcast_row = x.shape[0] == 1 and i.shape[0] != 1
|
||||
broadcast_col = x.shape[1] == 1 and i.shape[1] != 1
|
||||
if not ((broadcast_row or x.shape[0] == i.shape[0]) and
|
||||
(broadcast_col or x.shape[1] == i.shape[1])):
|
||||
raise ValueError('shape mismatch in assignment')
|
||||
x.sum_duplicates()
|
||||
self._set_arrayXarray_sparse(i, j, x)
|
||||
else:
|
||||
# Make x and i into the same shape
|
||||
x = np.asarray(x, dtype=self.dtype)
|
||||
if x.squeeze().shape != i.squeeze().shape:
|
||||
x = np.broadcast_to(x, i.shape)
|
||||
if x.size == 0:
|
||||
return
|
||||
x = x.reshape(i.shape)
|
||||
self._set_arrayXarray(i, j, x)
|
||||
|
||||
def _validate_indices(self, key):
|
||||
"""Returns two tuples: (index tuple, requested shape tuple)"""
|
||||
# single ellipsis
|
||||
if key is Ellipsis:
|
||||
return (slice(None),) * self.ndim, self.shape
|
||||
|
||||
if not isinstance(key, tuple):
|
||||
key = [key]
|
||||
|
||||
ellps_pos = None
|
||||
index_1st = []
|
||||
prelim_ndim = 0
|
||||
for i, idx in enumerate(key):
|
||||
if idx is Ellipsis:
|
||||
if ellps_pos is not None:
|
||||
raise IndexError('an index can only have a single ellipsis')
|
||||
ellps_pos = i
|
||||
elif idx is None:
|
||||
index_1st.append(idx)
|
||||
elif isinstance(idx, slice) or isintlike(idx):
|
||||
index_1st.append(idx)
|
||||
prelim_ndim += 1
|
||||
elif (ix := _compatible_boolean_index(idx, self.ndim)) is not None:
|
||||
index_1st.append(ix)
|
||||
prelim_ndim += ix.ndim
|
||||
elif issparse(idx):
|
||||
# TODO: make sparse matrix indexing work for sparray
|
||||
raise IndexError(
|
||||
'Indexing with sparse matrices is not supported '
|
||||
'except boolean indexing where matrix and index '
|
||||
'are equal shapes.')
|
||||
else: # dense array
|
||||
index_1st.append(np.asarray(idx))
|
||||
prelim_ndim += 1
|
||||
ellip_slices = (self.ndim - prelim_ndim) * [slice(None)]
|
||||
if ellip_slices:
|
||||
if ellps_pos is None:
|
||||
index_1st.extend(ellip_slices)
|
||||
else:
|
||||
index_1st = index_1st[:ellps_pos] + ellip_slices + index_1st[ellps_pos:]
|
||||
|
||||
# second pass (have processed ellipsis and preprocessed arrays)
|
||||
idx_shape = []
|
||||
index_ndim = 0
|
||||
index = []
|
||||
array_indices = []
|
||||
for i, idx in enumerate(index_1st):
|
||||
if idx is None:
|
||||
idx_shape.append(1)
|
||||
elif isinstance(idx, slice):
|
||||
index.append(idx)
|
||||
Ms = self._shape[index_ndim]
|
||||
len_slice = len(range(*idx.indices(Ms)))
|
||||
idx_shape.append(len_slice)
|
||||
index_ndim += 1
|
||||
elif isintlike(idx):
|
||||
N = self._shape[index_ndim]
|
||||
if not (-N <= idx < N):
|
||||
raise IndexError(f'index ({idx}) out of range')
|
||||
idx = int(idx + N if idx < 0 else idx)
|
||||
index.append(idx)
|
||||
index_ndim += 1
|
||||
# bool array (checked in first pass)
|
||||
elif idx.dtype.kind == 'b':
|
||||
ix = idx
|
||||
tmp_ndim = index_ndim + ix.ndim
|
||||
mid_shape = self._shape[index_ndim:tmp_ndim]
|
||||
if ix.shape != mid_shape:
|
||||
raise IndexError(
|
||||
f"bool index {i} has shape {mid_shape} instead of {ix.shape}"
|
||||
)
|
||||
index.extend(ix.nonzero())
|
||||
array_indices.extend(range(index_ndim, tmp_ndim))
|
||||
index_ndim = tmp_ndim
|
||||
else: # dense array
|
||||
N = self._shape[index_ndim]
|
||||
idx = self._asindices(idx, N)
|
||||
index.append(idx)
|
||||
array_indices.append(index_ndim)
|
||||
index_ndim += 1
|
||||
if index_ndim > self.ndim:
|
||||
raise IndexError(
|
||||
f'invalid index ndim. Array is {self.ndim}D. Index needs {index_ndim}D'
|
||||
)
|
||||
if len(array_indices) > 1:
|
||||
idx_arrays = _broadcast_arrays(*(index[i] for i in array_indices))
|
||||
if any(idx_arrays[0].shape != ix.shape for ix in idx_arrays[1:]):
|
||||
shapes = " ".join(str(ix.shape) for ix in idx_arrays)
|
||||
msg = (f'shape mismatch: indexing arrays could not be broadcast '
|
||||
f'together with shapes {shapes}')
|
||||
raise IndexError(msg)
|
||||
# TODO: handle this for nD (adjacent arrays stay, separated move to start)
|
||||
idx_shape = list(idx_arrays[0].shape) + idx_shape
|
||||
elif len(array_indices) == 1:
|
||||
arr_index = array_indices[0]
|
||||
arr_shape = list(index[arr_index].shape)
|
||||
idx_shape = idx_shape[:arr_index] + arr_shape + idx_shape[arr_index:]
|
||||
if (ndim := len(idx_shape)) > 2:
|
||||
raise IndexError(f'Only 1D or 2D arrays allowed. Index makes {ndim}D')
|
||||
return tuple(index), tuple(idx_shape)
|
||||
|
||||
def _asindices(self, idx, length):
|
||||
"""Convert `idx` to a valid index for an axis with a given length.
|
||||
|
||||
Subclasses that need special validation can override this method.
|
||||
"""
|
||||
try:
|
||||
x = np.asarray(idx)
|
||||
except (ValueError, TypeError, MemoryError) as e:
|
||||
raise IndexError('invalid index') from e
|
||||
|
||||
if x.ndim not in (1, 2):
|
||||
raise IndexError('Index dimension must be 1 or 2')
|
||||
|
||||
if x.size == 0:
|
||||
return x
|
||||
|
||||
# Check bounds
|
||||
max_indx = x.max()
|
||||
if max_indx >= length:
|
||||
raise IndexError(f'index ({max_indx}) out of range')
|
||||
|
||||
min_indx = x.min()
|
||||
if min_indx < 0:
|
||||
if min_indx < -length:
|
||||
raise IndexError(f'index ({min_indx}) out of range')
|
||||
if x is idx or not x.flags.owndata:
|
||||
x = x.copy()
|
||||
x[x < 0] += length
|
||||
return x
|
||||
|
||||
def _getrow(self, i):
|
||||
"""Return a copy of row i of the matrix, as a (1 x n) row vector.
|
||||
"""
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < -M or i >= M:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
if i < 0:
|
||||
i += M
|
||||
return self._get_intXslice(i, slice(None))
|
||||
|
||||
def _getcol(self, i):
|
||||
"""Return a copy of column i of the matrix, as a (m x 1) column vector.
|
||||
"""
|
||||
M, N = self.shape
|
||||
i = int(i)
|
||||
if i < -N or i >= N:
|
||||
raise IndexError(f'index ({i}) out of range')
|
||||
if i < 0:
|
||||
i += N
|
||||
return self._get_sliceXint(slice(None), i)
|
||||
|
||||
def _get_int(self, idx):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_slice(self, idx):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_array(self, idx):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_intXint(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_intXarray(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_intXslice(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_sliceXint(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_sliceXslice(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_sliceXarray(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_arrayXint(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_arrayXslice(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_columnXarray(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _get_arrayXarray(self, row, col):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _set_int(self, idx, x):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _set_array(self, idx, x):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _set_intXint(self, row, col, x):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _set_arrayXarray(self, row, col, x):
|
||||
raise NotImplementedError()
|
||||
|
||||
def _set_arrayXarray_sparse(self, row, col, x):
|
||||
# Fall back to densifying x
|
||||
x = np.asarray(x.toarray(), dtype=self.dtype)
|
||||
x, _ = _broadcast_arrays(x, row)
|
||||
self._set_arrayXarray(row, col, x)
|
||||
|
||||
|
||||
def _compatible_boolean_index(idx, desired_ndim):
|
||||
"""Check for boolean array or array-like. peek before asarray for array-like"""
|
||||
# use attribute ndim to indicate a compatible array and check dtype
|
||||
# if not, look at 1st element as quick rejection of bool, else slower asanyarray
|
||||
if not hasattr(idx, 'ndim'):
|
||||
# is first element boolean?
|
||||
try:
|
||||
ix = next(iter(idx), None)
|
||||
for _ in range(desired_ndim):
|
||||
if isinstance(ix, bool):
|
||||
break
|
||||
ix = next(iter(ix), None)
|
||||
else:
|
||||
return None
|
||||
except TypeError:
|
||||
return None
|
||||
# since first is boolean, construct array and check all elements
|
||||
idx = np.asanyarray(idx)
|
||||
|
||||
if idx.dtype.kind == 'b':
|
||||
return idx
|
||||
return None
|
||||
632
venv/lib/python3.13/site-packages/scipy/sparse/_lil.py
Normal file
632
venv/lib/python3.13/site-packages/scipy/sparse/_lil.py
Normal file
|
|
@ -0,0 +1,632 @@
|
|||
"""List of Lists sparse matrix class
|
||||
"""
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['lil_array', 'lil_matrix', 'isspmatrix_lil']
|
||||
|
||||
from bisect import bisect_left
|
||||
|
||||
import numpy as np
|
||||
|
||||
from ._matrix import spmatrix
|
||||
from ._base import _spbase, sparray, issparse
|
||||
from ._index import IndexMixin, INT_TYPES, _broadcast_arrays
|
||||
from ._sputils import (getdtype, isshape, isscalarlike, upcast_scalar,
|
||||
check_shape, check_reshape_kwargs)
|
||||
from . import _csparsetools
|
||||
|
||||
|
||||
class _lil_base(_spbase, IndexMixin):
|
||||
_format = 'lil'
|
||||
|
||||
def __init__(self, arg1, shape=None, dtype=None, copy=False, *, maxprint=None):
|
||||
_spbase.__init__(self, arg1, maxprint=maxprint)
|
||||
self.dtype = getdtype(dtype, arg1, default=float)
|
||||
|
||||
# First get the shape
|
||||
if issparse(arg1):
|
||||
if arg1.format == "lil" and copy:
|
||||
A = arg1.copy()
|
||||
else:
|
||||
A = arg1.tolil()
|
||||
|
||||
if dtype is not None:
|
||||
newdtype = getdtype(dtype)
|
||||
A = A.astype(newdtype, copy=False)
|
||||
|
||||
self._shape = check_shape(A.shape)
|
||||
self.dtype = A.dtype
|
||||
self.rows = A.rows
|
||||
self.data = A.data
|
||||
elif isinstance(arg1,tuple):
|
||||
if isshape(arg1):
|
||||
if shape is not None:
|
||||
raise ValueError('invalid use of shape parameter')
|
||||
M, N = arg1
|
||||
self._shape = check_shape((M, N))
|
||||
self.rows = np.empty((M,), dtype=object)
|
||||
self.data = np.empty((M,), dtype=object)
|
||||
for i in range(M):
|
||||
self.rows[i] = []
|
||||
self.data[i] = []
|
||||
else:
|
||||
raise TypeError('unrecognized lil_array constructor usage')
|
||||
else:
|
||||
# assume A is dense
|
||||
try:
|
||||
A = self._ascontainer(arg1)
|
||||
except TypeError as e:
|
||||
raise TypeError('unsupported matrix type') from e
|
||||
if isinstance(self, sparray) and A.ndim != 2:
|
||||
raise ValueError(f"LIL arrays don't support {A.ndim}D input. Use 2D")
|
||||
A = self._csr_container(A, dtype=dtype).tolil()
|
||||
|
||||
self._shape = check_shape(A.shape)
|
||||
self.dtype = getdtype(A.dtype)
|
||||
self.rows = A.rows
|
||||
self.data = A.data
|
||||
|
||||
def __iadd__(self,other):
|
||||
self[:,:] = self + other
|
||||
return self
|
||||
|
||||
def __isub__(self,other):
|
||||
self[:,:] = self - other
|
||||
return self
|
||||
|
||||
def __imul__(self,other):
|
||||
if isscalarlike(other):
|
||||
self[:,:] = self * other
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
def __itruediv__(self,other):
|
||||
if isscalarlike(other):
|
||||
self[:,:] = self / other
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
# Whenever the dimensions change, empty lists should be created for each
|
||||
# row
|
||||
|
||||
def _getnnz(self, axis=None):
|
||||
if axis is None:
|
||||
return sum([len(rowvals) for rowvals in self.data])
|
||||
if axis < 0:
|
||||
axis += 2
|
||||
if axis == 0:
|
||||
out = np.zeros(self.shape[1], dtype=np.intp)
|
||||
for row in self.rows:
|
||||
out[row] += 1
|
||||
return out
|
||||
elif axis == 1:
|
||||
return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp)
|
||||
else:
|
||||
raise ValueError('axis out of bounds')
|
||||
|
||||
_getnnz.__doc__ = _spbase._getnnz.__doc__
|
||||
|
||||
def count_nonzero(self, axis=None):
|
||||
if axis is None:
|
||||
return sum(np.count_nonzero(rowvals) for rowvals in self.data)
|
||||
|
||||
if axis < 0:
|
||||
axis += 2
|
||||
if axis == 0:
|
||||
out = np.zeros(self.shape[1], dtype=np.intp)
|
||||
for row, data in zip(self.rows, self.data):
|
||||
mask = [c for c, d in zip(row, data) if d != 0]
|
||||
out[mask] += 1
|
||||
return out
|
||||
elif axis == 1:
|
||||
return np.array(
|
||||
[np.count_nonzero(rowvals) for rowvals in self.data], dtype=np.intp,
|
||||
)
|
||||
else:
|
||||
raise ValueError('axis out of bounds')
|
||||
|
||||
count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
|
||||
|
||||
def getrowview(self, i):
|
||||
"""Returns a view of the 'i'th row (without copying).
|
||||
"""
|
||||
new = self._lil_container((1, self.shape[1]), dtype=self.dtype)
|
||||
new.rows[0] = self.rows[i]
|
||||
new.data[0] = self.data[i]
|
||||
return new
|
||||
|
||||
def getrow(self, i):
|
||||
"""Returns a copy of the 'i'th row.
|
||||
"""
|
||||
M, N = self.shape
|
||||
if i < 0:
|
||||
i += M
|
||||
if i < 0 or i >= M:
|
||||
raise IndexError('row index out of bounds')
|
||||
new = self._lil_container((1, N), dtype=self.dtype)
|
||||
new.rows[0] = self.rows[i][:]
|
||||
new.data[0] = self.data[i][:]
|
||||
return new
|
||||
|
||||
def __getitem__(self, key):
|
||||
# Fast path for simple (int, int) indexing.
|
||||
if (isinstance(key, tuple) and len(key) == 2 and
|
||||
isinstance(key[0], INT_TYPES) and
|
||||
isinstance(key[1], INT_TYPES)):
|
||||
# lil_get1 handles validation for us.
|
||||
return self._get_intXint(*key)
|
||||
# Everything else takes the normal path.
|
||||
return IndexMixin.__getitem__(self, key)
|
||||
|
||||
def _asindices(self, idx, N):
|
||||
# LIL routines handle bounds-checking for us, so don't do it here.
|
||||
try:
|
||||
x = np.asarray(idx)
|
||||
except (ValueError, TypeError, MemoryError) as e:
|
||||
raise IndexError('invalid index') from e
|
||||
if x.ndim not in (1, 2):
|
||||
raise IndexError('Index dimension must be <= 2')
|
||||
return x
|
||||
|
||||
def _get_intXint(self, row, col):
|
||||
v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows,
|
||||
self.data, row, col)
|
||||
return self.dtype.type(v)
|
||||
|
||||
def _get_sliceXint(self, row, col):
|
||||
row = range(*row.indices(self.shape[0]))
|
||||
return self._get_row_ranges(row, slice(col, col+1))
|
||||
|
||||
def _get_arrayXint(self, row, col):
|
||||
res = self._get_row_ranges(row.ravel(), slice(col, col+1))
|
||||
if row.ndim > 1:
|
||||
return res.reshape(row.shape)
|
||||
return res
|
||||
|
||||
def _get_intXslice(self, row, col):
|
||||
return self._get_row_ranges((row,), col)
|
||||
|
||||
def _get_sliceXslice(self, row, col):
|
||||
row = range(*row.indices(self.shape[0]))
|
||||
return self._get_row_ranges(row, col)
|
||||
|
||||
def _get_arrayXslice(self, row, col):
|
||||
return self._get_row_ranges(row, col)
|
||||
|
||||
def _get_intXarray(self, row, col):
|
||||
row = np.array(row, dtype=col.dtype, ndmin=1)
|
||||
return self._get_columnXarray(row, col)
|
||||
|
||||
def _get_sliceXarray(self, row, col):
|
||||
row = np.arange(*row.indices(self.shape[0]))
|
||||
return self._get_columnXarray(row, col)
|
||||
|
||||
def _get_columnXarray(self, row, col):
|
||||
# outer indexing
|
||||
row, col = _broadcast_arrays(row[:,None], col)
|
||||
return self._get_arrayXarray(row, col)
|
||||
|
||||
def _get_arrayXarray(self, row, col):
|
||||
# inner indexing
|
||||
i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col))
|
||||
new = self._lil_container(i.shape, dtype=self.dtype)
|
||||
_csparsetools.lil_fancy_get(self.shape[0], self.shape[1],
|
||||
self.rows, self.data,
|
||||
new.rows, new.data,
|
||||
i, j)
|
||||
return new
|
||||
|
||||
def _get_row_ranges(self, rows, col_slice):
|
||||
"""
|
||||
Fast path for indexing in the case where column index is slice.
|
||||
|
||||
This gains performance improvement over brute force by more
|
||||
efficient skipping of zeros, by accessing the elements
|
||||
column-wise in order.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
rows : sequence or range
|
||||
Rows indexed. If range, must be within valid bounds.
|
||||
col_slice : slice
|
||||
Columns indexed
|
||||
|
||||
"""
|
||||
j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
|
||||
col_range = range(j_start, j_stop, j_stride)
|
||||
nj = len(col_range)
|
||||
new = self._lil_container((len(rows), nj), dtype=self.dtype)
|
||||
|
||||
_csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1],
|
||||
self.rows, self.data,
|
||||
new.rows, new.data,
|
||||
rows,
|
||||
j_start, j_stop, j_stride, nj)
|
||||
|
||||
return new
|
||||
|
||||
def _set_intXint(self, row, col, x):
|
||||
_csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
|
||||
self.data, row, col, x)
|
||||
|
||||
def _set_arrayXarray(self, row, col, x):
|
||||
i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x))
|
||||
_csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
|
||||
self.rows, self.data,
|
||||
i, j, x)
|
||||
|
||||
def _set_arrayXarray_sparse(self, row, col, x):
|
||||
# Fall back to densifying x
|
||||
x = np.asarray(x.toarray(), dtype=self.dtype)
|
||||
x, _ = _broadcast_arrays(x, row)
|
||||
self._set_arrayXarray(row, col, x)
|
||||
|
||||
def __setitem__(self, key, x):
|
||||
if isinstance(key, tuple) and len(key) == 2:
|
||||
row, col = key
|
||||
# Fast path for simple (int, int) indexing.
|
||||
if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
|
||||
x = self.dtype.type(x)
|
||||
if x.size > 1:
|
||||
raise ValueError("Trying to assign a sequence to an item")
|
||||
return self._set_intXint(row, col, x)
|
||||
# Fast path for full-matrix sparse assignment.
|
||||
if (isinstance(row, slice) and isinstance(col, slice) and
|
||||
row == slice(None) and col == slice(None) and
|
||||
issparse(x) and x.shape == self.shape):
|
||||
x = self._lil_container(x, dtype=self.dtype)
|
||||
self.rows = x.rows
|
||||
self.data = x.data
|
||||
return
|
||||
# Everything else takes the normal path.
|
||||
IndexMixin.__setitem__(self, key, x)
|
||||
|
||||
def _mul_scalar(self, other):
|
||||
if other == 0:
|
||||
# Multiply by zero: return the zero matrix
|
||||
new = self._lil_container(self.shape, dtype=self.dtype)
|
||||
else:
|
||||
res_dtype = upcast_scalar(self.dtype, other)
|
||||
|
||||
new = self.copy()
|
||||
new = new.astype(res_dtype)
|
||||
# Multiply this scalar by every element.
|
||||
for j, rowvals in enumerate(new.data):
|
||||
new.data[j] = [val*other for val in rowvals]
|
||||
return new
|
||||
|
||||
def __truediv__(self, other): # self / other
|
||||
if isscalarlike(other):
|
||||
new = self.copy()
|
||||
new.dtype = np.result_type(self, other)
|
||||
# Divide every element by this scalar
|
||||
for j, rowvals in enumerate(new.data):
|
||||
new.data[j] = [val/other for val in rowvals]
|
||||
return new
|
||||
else:
|
||||
return self.tocsr() / other
|
||||
|
||||
def copy(self):
|
||||
M, N = self.shape
|
||||
new = self._lil_container(self.shape, dtype=self.dtype)
|
||||
# This is ~14x faster than calling deepcopy() on rows and data.
|
||||
_csparsetools.lil_get_row_ranges(M, N, self.rows, self.data,
|
||||
new.rows, new.data, range(M),
|
||||
0, N, 1, N)
|
||||
return new
|
||||
|
||||
copy.__doc__ = _spbase.copy.__doc__
|
||||
|
||||
def reshape(self, *args, **kwargs):
|
||||
shape = check_shape(args, self.shape)
|
||||
order, copy = check_reshape_kwargs(kwargs)
|
||||
|
||||
# Return early if reshape is not required
|
||||
if shape == self.shape:
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
new = self._lil_container(shape, dtype=self.dtype)
|
||||
|
||||
if order == 'C':
|
||||
ncols = self.shape[1]
|
||||
for i, row in enumerate(self.rows):
|
||||
for col, j in enumerate(row):
|
||||
new_r, new_c = np.unravel_index(i * ncols + j, shape)
|
||||
new[new_r, new_c] = self[i, j]
|
||||
elif order == 'F':
|
||||
nrows = self.shape[0]
|
||||
for i, row in enumerate(self.rows):
|
||||
for col, j in enumerate(row):
|
||||
new_r, new_c = np.unravel_index(i + j * nrows, shape, order)
|
||||
new[new_r, new_c] = self[i, j]
|
||||
else:
|
||||
raise ValueError("'order' must be 'C' or 'F'")
|
||||
|
||||
return new
|
||||
|
||||
reshape.__doc__ = _spbase.reshape.__doc__
|
||||
|
||||
def resize(self, *shape):
|
||||
shape = check_shape(shape)
|
||||
new_M, new_N = shape
|
||||
M, N = self.shape
|
||||
|
||||
if new_M < M:
|
||||
self.rows = self.rows[:new_M]
|
||||
self.data = self.data[:new_M]
|
||||
elif new_M > M:
|
||||
self.rows = np.resize(self.rows, new_M)
|
||||
self.data = np.resize(self.data, new_M)
|
||||
for i in range(M, new_M):
|
||||
self.rows[i] = []
|
||||
self.data[i] = []
|
||||
|
||||
if new_N < N:
|
||||
for row, data in zip(self.rows, self.data):
|
||||
trunc = bisect_left(row, new_N)
|
||||
del row[trunc:]
|
||||
del data[trunc:]
|
||||
|
||||
self._shape = shape
|
||||
|
||||
resize.__doc__ = _spbase.resize.__doc__
|
||||
|
||||
def toarray(self, order=None, out=None):
|
||||
d = self._process_toarray_args(order, out)
|
||||
for i, row in enumerate(self.rows):
|
||||
for pos, j in enumerate(row):
|
||||
d[i, j] = self.data[i][pos]
|
||||
return d
|
||||
|
||||
toarray.__doc__ = _spbase.toarray.__doc__
|
||||
|
||||
def transpose(self, axes=None, copy=False):
|
||||
return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False)
|
||||
|
||||
transpose.__doc__ = _spbase.transpose.__doc__
|
||||
|
||||
def tolil(self, copy=False):
|
||||
if copy:
|
||||
return self.copy()
|
||||
else:
|
||||
return self
|
||||
|
||||
tolil.__doc__ = _spbase.tolil.__doc__
|
||||
|
||||
def tocsr(self, copy=False):
|
||||
M, N = self.shape
|
||||
if M == 0 or N == 0:
|
||||
return self._csr_container((M, N), dtype=self.dtype)
|
||||
|
||||
# construct indptr array
|
||||
if M*N <= np.iinfo(np.int32).max:
|
||||
# fast path: it is known that 64-bit indexing will not be needed.
|
||||
idx_dtype = np.int32
|
||||
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||||
indptr[0] = 0
|
||||
_csparsetools.lil_get_lengths(self.rows, indptr[1:])
|
||||
np.cumsum(indptr, out=indptr)
|
||||
nnz = indptr[-1]
|
||||
else:
|
||||
idx_dtype = self._get_index_dtype(maxval=N)
|
||||
lengths = np.empty(M, dtype=idx_dtype)
|
||||
_csparsetools.lil_get_lengths(self.rows, lengths)
|
||||
nnz = lengths.sum(dtype=np.int64)
|
||||
idx_dtype = self._get_index_dtype(maxval=max(N, nnz))
|
||||
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||||
indptr[0] = 0
|
||||
np.cumsum(lengths, dtype=idx_dtype, out=indptr[1:])
|
||||
|
||||
indices = np.empty(nnz, dtype=idx_dtype)
|
||||
data = np.empty(nnz, dtype=self.dtype)
|
||||
_csparsetools.lil_flatten_to_array(self.rows, indices)
|
||||
_csparsetools.lil_flatten_to_array(self.data, data)
|
||||
|
||||
# init csr matrix
|
||||
return self._csr_container((data, indices, indptr), shape=self.shape)
|
||||
|
||||
tocsr.__doc__ = _spbase.tocsr.__doc__
|
||||
|
||||
|
||||
def _prepare_index_for_memoryview(i, j, x=None):
|
||||
"""
|
||||
Convert index and data arrays to form suitable for passing to the
|
||||
Cython fancy getset routines.
|
||||
|
||||
The conversions are necessary since to (i) ensure the integer
|
||||
index arrays are in one of the accepted types, and (ii) to ensure
|
||||
the arrays are writable so that Cython memoryview support doesn't
|
||||
choke on them.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
i, j
|
||||
Index arrays
|
||||
x : optional
|
||||
Data arrays
|
||||
|
||||
Returns
|
||||
-------
|
||||
i, j, x
|
||||
Re-formatted arrays (x is omitted, if input was None)
|
||||
|
||||
"""
|
||||
if i.dtype > j.dtype:
|
||||
j = j.astype(i.dtype)
|
||||
elif i.dtype < j.dtype:
|
||||
i = i.astype(j.dtype)
|
||||
|
||||
if not i.flags.writeable or i.dtype not in (np.int32, np.int64):
|
||||
i = i.astype(np.intp)
|
||||
if not j.flags.writeable or j.dtype not in (np.int32, np.int64):
|
||||
j = j.astype(np.intp)
|
||||
|
||||
if x is not None:
|
||||
if not x.flags.writeable:
|
||||
x = x.copy()
|
||||
return i, j, x
|
||||
else:
|
||||
return i, j
|
||||
|
||||
|
||||
def isspmatrix_lil(x):
|
||||
"""Is `x` of lil_matrix type?
|
||||
|
||||
Parameters
|
||||
----------
|
||||
x
|
||||
object to check for being a lil matrix
|
||||
|
||||
Returns
|
||||
-------
|
||||
bool
|
||||
True if `x` is a lil matrix, False otherwise
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse import lil_array, lil_matrix, coo_matrix, isspmatrix_lil
|
||||
>>> isspmatrix_lil(lil_matrix([[5]]))
|
||||
True
|
||||
>>> isspmatrix_lil(lil_array([[5]]))
|
||||
False
|
||||
>>> isspmatrix_lil(coo_matrix([[5]]))
|
||||
False
|
||||
"""
|
||||
return isinstance(x, lil_matrix)
|
||||
|
||||
|
||||
# This namespace class separates array from matrix with isinstance
|
||||
class lil_array(_lil_base, sparray):
|
||||
"""
|
||||
Row-based LIst of Lists sparse array.
|
||||
|
||||
This is a structure for constructing sparse arrays incrementally.
|
||||
Note that inserting a single item can take linear time in the worst case;
|
||||
to construct the array efficiently, make sure the items are pre-sorted by
|
||||
index, per row.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
lil_array(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
lil_array(S)
|
||||
with another sparse array or matrix S (equivalent to S.tolil())
|
||||
|
||||
lil_array((M, N), [dtype])
|
||||
to construct an empty array with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the array
|
||||
shape : 2-tuple
|
||||
Shape of the array
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
LIL format data array of the array
|
||||
rows
|
||||
LIL format row index array of the array
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
Sparse arrays can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the LIL format
|
||||
- supports flexible slicing
|
||||
- changes to the array sparsity structure are efficient
|
||||
|
||||
Disadvantages of the LIL format
|
||||
- arithmetic operations LIL + LIL are slow (consider CSR or CSC)
|
||||
- slow column slicing (consider CSC)
|
||||
- slow matrix vector products (consider CSR or CSC)
|
||||
|
||||
Intended Usage
|
||||
- LIL is a convenient format for constructing sparse arrays
|
||||
- once an array has been constructed, convert to CSR or
|
||||
CSC format for fast arithmetic and matrix vector operations
|
||||
- consider using the COO format when constructing large arrays
|
||||
|
||||
Data Structure
|
||||
- An array (``self.rows``) of rows, each of which is a sorted
|
||||
list of column indices of non-zero elements.
|
||||
- The corresponding nonzero values are stored in similar
|
||||
fashion in ``self.data``.
|
||||
|
||||
"""
|
||||
|
||||
|
||||
class lil_matrix(spmatrix, _lil_base):
|
||||
"""
|
||||
Row-based LIst of Lists sparse matrix.
|
||||
|
||||
This is a structure for constructing sparse matrices incrementally.
|
||||
Note that inserting a single item can take linear time in the worst case;
|
||||
to construct the matrix efficiently, make sure the items are pre-sorted by
|
||||
index, per row.
|
||||
|
||||
This can be instantiated in several ways:
|
||||
lil_matrix(D)
|
||||
where D is a 2-D ndarray
|
||||
|
||||
lil_matrix(S)
|
||||
with another sparse array or matrix S (equivalent to S.tolil())
|
||||
|
||||
lil_matrix((M, N), [dtype])
|
||||
to construct an empty matrix with shape (M, N)
|
||||
dtype is optional, defaulting to dtype='d'.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
dtype : dtype
|
||||
Data type of the matrix
|
||||
shape : 2-tuple
|
||||
Shape of the matrix
|
||||
ndim : int
|
||||
Number of dimensions (this is always 2)
|
||||
nnz
|
||||
size
|
||||
data
|
||||
LIL format data array of the matrix
|
||||
rows
|
||||
LIL format row index array of the matrix
|
||||
T
|
||||
|
||||
Notes
|
||||
-----
|
||||
Sparse matrices can be used in arithmetic operations: they support
|
||||
addition, subtraction, multiplication, division, and matrix power.
|
||||
|
||||
Advantages of the LIL format
|
||||
- supports flexible slicing
|
||||
- changes to the matrix sparsity structure are efficient
|
||||
|
||||
Disadvantages of the LIL format
|
||||
- arithmetic operations LIL + LIL are slow (consider CSR or CSC)
|
||||
- slow column slicing (consider CSC)
|
||||
- slow matrix vector products (consider CSR or CSC)
|
||||
|
||||
Intended Usage
|
||||
- LIL is a convenient format for constructing sparse matrices
|
||||
- once a matrix has been constructed, convert to CSR or
|
||||
CSC format for fast arithmetic and matrix vector operations
|
||||
- consider using the COO format when constructing large matrices
|
||||
|
||||
Data Structure
|
||||
- An array (``self.rows``) of rows, each of which is a sorted
|
||||
list of column indices of non-zero elements.
|
||||
- The corresponding nonzero values are stored in similar
|
||||
fashion in ``self.data``.
|
||||
|
||||
"""
|
||||
169
venv/lib/python3.13/site-packages/scipy/sparse/_matrix.py
Normal file
169
venv/lib/python3.13/site-packages/scipy/sparse/_matrix.py
Normal file
|
|
@ -0,0 +1,169 @@
|
|||
class spmatrix:
|
||||
"""This class provides a base class for all sparse matrix classes.
|
||||
|
||||
It cannot be instantiated. Most of the work is provided by subclasses.
|
||||
"""
|
||||
_allow_nd = (2,)
|
||||
|
||||
@property
|
||||
def _bsr_container(self):
|
||||
from ._bsr import bsr_matrix
|
||||
return bsr_matrix
|
||||
|
||||
@property
|
||||
def _coo_container(self):
|
||||
from ._coo import coo_matrix
|
||||
return coo_matrix
|
||||
|
||||
@property
|
||||
def _csc_container(self):
|
||||
from ._csc import csc_matrix
|
||||
return csc_matrix
|
||||
|
||||
@property
|
||||
def _csr_container(self):
|
||||
from ._csr import csr_matrix
|
||||
return csr_matrix
|
||||
|
||||
@property
|
||||
def _dia_container(self):
|
||||
from ._dia import dia_matrix
|
||||
return dia_matrix
|
||||
|
||||
@property
|
||||
def _dok_container(self):
|
||||
from ._dok import dok_matrix
|
||||
return dok_matrix
|
||||
|
||||
@property
|
||||
def _lil_container(self):
|
||||
from ._lil import lil_matrix
|
||||
return lil_matrix
|
||||
|
||||
# Restore matrix multiplication
|
||||
def __mul__(self, other):
|
||||
return self._matmul_dispatch(other)
|
||||
|
||||
def __rmul__(self, other):
|
||||
return self._rmatmul_dispatch(other)
|
||||
|
||||
# Restore matrix power
|
||||
def __pow__(self, power):
|
||||
from .linalg import matrix_power
|
||||
|
||||
return matrix_power(self, power)
|
||||
|
||||
## Backward compatibility
|
||||
|
||||
def set_shape(self, shape):
|
||||
"""Set the shape of the matrix in-place"""
|
||||
# Make sure copy is False since this is in place
|
||||
# Make sure format is unchanged because we are doing a __dict__ swap
|
||||
new_self = self.reshape(shape, copy=False).asformat(self.format)
|
||||
self.__dict__ = new_self.__dict__
|
||||
|
||||
def get_shape(self):
|
||||
"""Get the shape of the matrix"""
|
||||
return self._shape
|
||||
|
||||
shape = property(fget=get_shape, fset=set_shape,
|
||||
doc="Shape of the matrix")
|
||||
|
||||
def asfptype(self):
|
||||
"""Upcast matrix to a floating point format (if necessary)"""
|
||||
return self._asfptype()
|
||||
|
||||
def getmaxprint(self):
|
||||
"""Maximum number of elements to display when printed."""
|
||||
return self._getmaxprint()
|
||||
|
||||
def getformat(self):
|
||||
"""Matrix storage format"""
|
||||
return self.format
|
||||
|
||||
def getnnz(self, axis=None):
|
||||
"""Number of stored values, including explicit zeros.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
axis : None, 0, or 1
|
||||
Select between the number of values across the whole array, in
|
||||
each column, or in each row.
|
||||
"""
|
||||
return self._getnnz(axis=axis)
|
||||
|
||||
def getH(self):
|
||||
"""Return the Hermitian transpose of this matrix.
|
||||
|
||||
See Also
|
||||
--------
|
||||
numpy.matrix.getH : NumPy's implementation of `getH` for matrices
|
||||
"""
|
||||
return self.conjugate().transpose()
|
||||
|
||||
def getcol(self, j):
|
||||
"""Returns a copy of column j of the matrix, as an (m x 1) sparse
|
||||
matrix (column vector).
|
||||
"""
|
||||
return self._getcol(j)
|
||||
|
||||
def getrow(self, i):
|
||||
"""Returns a copy of row i of the matrix, as a (1 x n) sparse
|
||||
matrix (row vector).
|
||||
"""
|
||||
return self._getrow(i)
|
||||
|
||||
def todense(self, order=None, out=None):
|
||||
"""
|
||||
Return a dense representation of this sparse matrix.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
order : {'C', 'F'}, optional
|
||||
Whether to store multi-dimensional data in C (row-major)
|
||||
or Fortran (column-major) order in memory. The default
|
||||
is 'None', which provides no ordering guarantees.
|
||||
Cannot be specified in conjunction with the `out`
|
||||
argument.
|
||||
|
||||
out : ndarray, 2-D, optional
|
||||
If specified, uses this array (or `numpy.matrix`) as the
|
||||
output buffer instead of allocating a new array to
|
||||
return. The provided array must have the same shape and
|
||||
dtype as the sparse matrix on which you are calling the
|
||||
method.
|
||||
|
||||
Returns
|
||||
-------
|
||||
arr : numpy.matrix, 2-D
|
||||
A NumPy matrix object with the same shape and containing
|
||||
the same data represented by the sparse matrix, with the
|
||||
requested memory order. If `out` was passed and was an
|
||||
array (rather than a `numpy.matrix`), it will be filled
|
||||
with the appropriate values and returned wrapped in a
|
||||
`numpy.matrix` object that shares the same memory.
|
||||
"""
|
||||
return super().todense(order, out)
|
||||
|
||||
@classmethod
|
||||
def __class_getitem__(cls, arg, /):
|
||||
"""
|
||||
Return a parametrized wrapper around the `~scipy.sparse.spmatrix` type.
|
||||
|
||||
.. versionadded:: 1.16.0
|
||||
|
||||
Returns
|
||||
-------
|
||||
alias : types.GenericAlias
|
||||
A parametrized `~scipy.sparse.spmatrix` type.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import coo_matrix
|
||||
|
||||
>>> coo_matrix[np.int8]
|
||||
scipy.sparse._coo.coo_matrix[numpy.int8]
|
||||
"""
|
||||
from types import GenericAlias
|
||||
return GenericAlias(cls, arg)
|
||||
167
venv/lib/python3.13/site-packages/scipy/sparse/_matrix_io.py
Normal file
167
venv/lib/python3.13/site-packages/scipy/sparse/_matrix_io.py
Normal file
|
|
@ -0,0 +1,167 @@
|
|||
import numpy as np
|
||||
import scipy as sp
|
||||
|
||||
__all__ = ['save_npz', 'load_npz']
|
||||
|
||||
|
||||
# Make loading safe vs. malicious input
|
||||
PICKLE_KWARGS = dict(allow_pickle=False)
|
||||
|
||||
|
||||
def save_npz(file, matrix, compressed=True):
|
||||
""" Save a sparse matrix or array to a file using ``.npz`` format.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
file : str or file-like object
|
||||
Either the file name (string) or an open file (file-like object)
|
||||
where the data will be saved. If file is a string, the ``.npz``
|
||||
extension will be appended to the file name if it is not already
|
||||
there.
|
||||
matrix: spmatrix or sparray
|
||||
The sparse matrix or array to save.
|
||||
Supported formats: ``csc``, ``csr``, ``bsr``, ``dia`` or ``coo``.
|
||||
compressed : bool, optional
|
||||
Allow compressing the file. Default: True
|
||||
|
||||
See Also
|
||||
--------
|
||||
scipy.sparse.load_npz: Load a sparse matrix from a file using ``.npz`` format.
|
||||
numpy.savez: Save several arrays into a ``.npz`` archive.
|
||||
numpy.savez_compressed : Save several arrays into a compressed ``.npz`` archive.
|
||||
|
||||
Examples
|
||||
--------
|
||||
Store sparse matrix to disk, and load it again:
|
||||
|
||||
>>> import numpy as np
|
||||
>>> import scipy as sp
|
||||
>>> sparse_matrix = sp.sparse.csc_matrix([[0, 0, 3], [4, 0, 0]])
|
||||
>>> sparse_matrix
|
||||
<Compressed Sparse Column sparse matrix of dtype 'int64'
|
||||
with 2 stored elements and shape (2, 3)>
|
||||
>>> sparse_matrix.toarray()
|
||||
array([[0, 0, 3],
|
||||
[4, 0, 0]], dtype=int64)
|
||||
|
||||
>>> sp.sparse.save_npz('/tmp/sparse_matrix.npz', sparse_matrix)
|
||||
>>> sparse_matrix = sp.sparse.load_npz('/tmp/sparse_matrix.npz')
|
||||
|
||||
>>> sparse_matrix
|
||||
<Compressed Sparse Column sparse matrix of dtype 'int64'
|
||||
with 2 stored elements and shape (2, 3)>
|
||||
>>> sparse_matrix.toarray()
|
||||
array([[0, 0, 3],
|
||||
[4, 0, 0]], dtype=int64)
|
||||
"""
|
||||
arrays_dict = {}
|
||||
if matrix.format in ('csc', 'csr', 'bsr'):
|
||||
arrays_dict.update(indices=matrix.indices, indptr=matrix.indptr)
|
||||
elif matrix.format == 'dia':
|
||||
arrays_dict.update(offsets=matrix.offsets)
|
||||
elif matrix.format == 'coo':
|
||||
arrays_dict.update(row=matrix.row, col=matrix.col)
|
||||
else:
|
||||
msg = f'Save is not implemented for sparse matrix of format {matrix.format}.'
|
||||
raise NotImplementedError(msg)
|
||||
arrays_dict.update(
|
||||
format=matrix.format.encode('ascii'),
|
||||
shape=matrix.shape,
|
||||
data=matrix.data
|
||||
)
|
||||
if isinstance(matrix, sp.sparse.sparray):
|
||||
arrays_dict.update(_is_array=True)
|
||||
if compressed:
|
||||
np.savez_compressed(file, **arrays_dict)
|
||||
else:
|
||||
np.savez(file, **arrays_dict)
|
||||
|
||||
|
||||
def load_npz(file):
|
||||
""" Load a sparse array/matrix from a file using ``.npz`` format.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
file : str or file-like object
|
||||
Either the file name (string) or an open file (file-like object)
|
||||
where the data will be loaded.
|
||||
|
||||
Returns
|
||||
-------
|
||||
result : csc_array, csr_array, bsr_array, dia_array or coo_array
|
||||
A sparse array/matrix containing the loaded data.
|
||||
|
||||
Raises
|
||||
------
|
||||
OSError
|
||||
If the input file does not exist or cannot be read.
|
||||
|
||||
See Also
|
||||
--------
|
||||
scipy.sparse.save_npz: Save a sparse array/matrix to a file using ``.npz`` format.
|
||||
numpy.load: Load several arrays from a ``.npz`` archive.
|
||||
|
||||
Examples
|
||||
--------
|
||||
Store sparse array/matrix to disk, and load it again:
|
||||
|
||||
>>> import numpy as np
|
||||
>>> import scipy as sp
|
||||
>>> sparse_array = sp.sparse.csc_array([[0, 0, 3], [4, 0, 0]])
|
||||
>>> sparse_array
|
||||
<Compressed Sparse Column sparse array of dtype 'int64'
|
||||
with 2 stored elements and shape (2, 3)>
|
||||
>>> sparse_array.toarray()
|
||||
array([[0, 0, 3],
|
||||
[4, 0, 0]], dtype=int64)
|
||||
|
||||
>>> sp.sparse.save_npz('/tmp/sparse_array.npz', sparse_array)
|
||||
>>> sparse_array = sp.sparse.load_npz('/tmp/sparse_array.npz')
|
||||
|
||||
>>> sparse_array
|
||||
<Compressed Sparse Column sparse array of dtype 'int64'
|
||||
with 2 stored elements and shape (2, 3)>
|
||||
>>> sparse_array.toarray()
|
||||
array([[0, 0, 3],
|
||||
[4, 0, 0]], dtype=int64)
|
||||
|
||||
In this example we force the result to be csr_array from csr_matrix
|
||||
>>> sparse_matrix = sp.sparse.csc_matrix([[0, 0, 3], [4, 0, 0]])
|
||||
>>> sp.sparse.save_npz('/tmp/sparse_matrix.npz', sparse_matrix)
|
||||
>>> tmp = sp.sparse.load_npz('/tmp/sparse_matrix.npz')
|
||||
>>> sparse_array = sp.sparse.csr_array(tmp)
|
||||
"""
|
||||
with np.load(file, **PICKLE_KWARGS) as loaded:
|
||||
sparse_format = loaded.get('format')
|
||||
if sparse_format is None:
|
||||
raise ValueError(f'The file {file} does not contain '
|
||||
f'a sparse array or matrix.')
|
||||
sparse_format = sparse_format.item()
|
||||
|
||||
if not isinstance(sparse_format, str):
|
||||
# Play safe with Python 2 vs 3 backward compatibility;
|
||||
# files saved with SciPy < 1.0.0 may contain unicode or bytes.
|
||||
sparse_format = sparse_format.decode('ascii')
|
||||
|
||||
if loaded.get('_is_array'):
|
||||
sparse_type = sparse_format + '_array'
|
||||
else:
|
||||
sparse_type = sparse_format + '_matrix'
|
||||
|
||||
try:
|
||||
cls = getattr(sp.sparse, f'{sparse_type}')
|
||||
except AttributeError as e:
|
||||
raise ValueError(f'Unknown format "{sparse_type}"') from e
|
||||
|
||||
if sparse_format in ('csc', 'csr', 'bsr'):
|
||||
return cls((loaded['data'], loaded['indices'], loaded['indptr']),
|
||||
shape=loaded['shape'])
|
||||
elif sparse_format == 'dia':
|
||||
return cls((loaded['data'], loaded['offsets']),
|
||||
shape=loaded['shape'])
|
||||
elif sparse_format == 'coo':
|
||||
return cls((loaded['data'], (loaded['row'], loaded['col'])),
|
||||
shape=loaded['shape'])
|
||||
else:
|
||||
raise NotImplementedError(f'Load is not implemented for '
|
||||
f'sparse matrix of format {sparse_format}.')
|
||||
Binary file not shown.
76
venv/lib/python3.13/site-packages/scipy/sparse/_spfuncs.py
Normal file
76
venv/lib/python3.13/site-packages/scipy/sparse/_spfuncs.py
Normal file
|
|
@ -0,0 +1,76 @@
|
|||
""" Functions that operate on sparse matrices
|
||||
"""
|
||||
|
||||
__all__ = ['count_blocks','estimate_blocksize']
|
||||
|
||||
from ._base import issparse
|
||||
from ._csr import csr_array
|
||||
from ._sparsetools import csr_count_blocks
|
||||
|
||||
|
||||
def estimate_blocksize(A,efficiency=0.7):
|
||||
"""Attempt to determine the blocksize of a sparse matrix
|
||||
|
||||
Returns a blocksize=(r,c) such that
|
||||
- A.nnz / A.tobsr( (r,c) ).nnz > efficiency
|
||||
"""
|
||||
if not (issparse(A) and A.format in ("csc", "csr")):
|
||||
A = csr_array(A)
|
||||
|
||||
if A.nnz == 0:
|
||||
return (1,1)
|
||||
|
||||
if not 0 < efficiency < 1.0:
|
||||
raise ValueError('efficiency must satisfy 0.0 < efficiency < 1.0')
|
||||
|
||||
high_efficiency = (1.0 + efficiency) / 2.0
|
||||
nnz = float(A.nnz)
|
||||
M,N = A.shape
|
||||
|
||||
if M % 2 == 0 and N % 2 == 0:
|
||||
e22 = nnz / (4 * count_blocks(A,(2,2)))
|
||||
else:
|
||||
e22 = 0.0
|
||||
|
||||
if M % 3 == 0 and N % 3 == 0:
|
||||
e33 = nnz / (9 * count_blocks(A,(3,3)))
|
||||
else:
|
||||
e33 = 0.0
|
||||
|
||||
if e22 > high_efficiency and e33 > high_efficiency:
|
||||
e66 = nnz / (36 * count_blocks(A,(6,6)))
|
||||
if e66 > efficiency:
|
||||
return (6,6)
|
||||
else:
|
||||
return (3,3)
|
||||
else:
|
||||
if M % 4 == 0 and N % 4 == 0:
|
||||
e44 = nnz / (16 * count_blocks(A,(4,4)))
|
||||
else:
|
||||
e44 = 0.0
|
||||
|
||||
if e44 > efficiency:
|
||||
return (4,4)
|
||||
elif e33 > efficiency:
|
||||
return (3,3)
|
||||
elif e22 > efficiency:
|
||||
return (2,2)
|
||||
else:
|
||||
return (1,1)
|
||||
|
||||
|
||||
def count_blocks(A,blocksize):
|
||||
"""For a given blocksize=(r,c) count the number of occupied
|
||||
blocks in a sparse matrix A
|
||||
"""
|
||||
r,c = blocksize
|
||||
if r < 1 or c < 1:
|
||||
raise ValueError('r and c must be positive')
|
||||
|
||||
if issparse(A):
|
||||
if A.format == "csr":
|
||||
M,N = A.shape
|
||||
return csr_count_blocks(M,N,r,c,A.indptr,A.indices)
|
||||
elif A.format == "csc":
|
||||
return count_blocks(A.T,(c,r))
|
||||
return count_blocks(csr_array(A),blocksize)
|
||||
632
venv/lib/python3.13/site-packages/scipy/sparse/_sputils.py
Normal file
632
venv/lib/python3.13/site-packages/scipy/sparse/_sputils.py
Normal file
|
|
@ -0,0 +1,632 @@
|
|||
""" Utility functions for sparse matrix module
|
||||
"""
|
||||
|
||||
import sys
|
||||
from typing import Any, Literal, Union
|
||||
import operator
|
||||
import numpy as np
|
||||
from math import prod
|
||||
import scipy.sparse as sp
|
||||
from scipy._lib._util import np_long, np_ulong
|
||||
|
||||
|
||||
__all__ = ['upcast', 'getdtype', 'getdata', 'isscalarlike', 'isintlike',
|
||||
'isshape', 'issequence', 'isdense', 'ismatrix', 'get_sum_dtype',
|
||||
'broadcast_shapes']
|
||||
|
||||
supported_dtypes = [np.bool_, np.byte, np.ubyte, np.short, np.ushort, np.intc,
|
||||
np.uintc, np_long, np_ulong, np.longlong, np.ulonglong,
|
||||
np.float32, np.float64, np.longdouble,
|
||||
np.complex64, np.complex128, np.clongdouble]
|
||||
|
||||
_upcast_memo = {}
|
||||
|
||||
|
||||
def upcast(*args):
|
||||
"""Returns the nearest supported sparse dtype for the
|
||||
combination of one or more types.
|
||||
|
||||
upcast(t0, t1, ..., tn) -> T where T is a supported dtype
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> from scipy.sparse._sputils import upcast
|
||||
>>> upcast('int32')
|
||||
<class 'numpy.int32'>
|
||||
>>> upcast('bool')
|
||||
<class 'numpy.bool'>
|
||||
>>> upcast('int32','float32')
|
||||
<class 'numpy.float64'>
|
||||
>>> upcast('bool',complex,float)
|
||||
<class 'numpy.complex128'>
|
||||
|
||||
"""
|
||||
|
||||
t = _upcast_memo.get(hash(args))
|
||||
if t is not None:
|
||||
return t
|
||||
|
||||
upcast = np.result_type(*args)
|
||||
|
||||
for t in supported_dtypes:
|
||||
if np.can_cast(upcast, t):
|
||||
_upcast_memo[hash(args)] = t
|
||||
return t
|
||||
|
||||
raise TypeError(f'no supported conversion for types: {args!r}')
|
||||
|
||||
|
||||
def upcast_char(*args):
|
||||
"""Same as `upcast` but taking dtype.char as input (faster)."""
|
||||
t = _upcast_memo.get(args)
|
||||
if t is not None:
|
||||
return t
|
||||
t = upcast(*map(np.dtype, args))
|
||||
_upcast_memo[args] = t
|
||||
return t
|
||||
|
||||
|
||||
def upcast_scalar(dtype, scalar):
|
||||
"""Determine data type for binary operation between an array of
|
||||
type `dtype` and a scalar.
|
||||
"""
|
||||
return (np.array([0], dtype=dtype) * scalar).dtype
|
||||
|
||||
|
||||
def downcast_intp_index(arr):
|
||||
"""
|
||||
Down-cast index array to np.intp dtype if it is of a larger dtype.
|
||||
|
||||
Raise an error if the array contains a value that is too large for
|
||||
intp.
|
||||
"""
|
||||
if arr.dtype.itemsize > np.dtype(np.intp).itemsize:
|
||||
if arr.size == 0:
|
||||
return arr.astype(np.intp)
|
||||
maxval = arr.max()
|
||||
minval = arr.min()
|
||||
if maxval > np.iinfo(np.intp).max or minval < np.iinfo(np.intp).min:
|
||||
raise ValueError("Cannot deal with arrays with indices larger "
|
||||
"than the machine maximum address size "
|
||||
"(e.g. 64-bit indices on 32-bit machine).")
|
||||
return arr.astype(np.intp)
|
||||
return arr
|
||||
|
||||
|
||||
def to_native(A):
|
||||
"""
|
||||
Ensure that the data type of the NumPy array `A` has native byte order.
|
||||
|
||||
`A` must be a NumPy array. If the data type of `A` does not have native
|
||||
byte order, a copy of `A` with a native byte order is returned. Otherwise
|
||||
`A` is returned.
|
||||
"""
|
||||
dt = A.dtype
|
||||
if dt.isnative:
|
||||
# Don't call `asarray()` if A is already native, to avoid unnecessarily
|
||||
# creating a view of the input array.
|
||||
return A
|
||||
return np.asarray(A, dtype=dt.newbyteorder('native'))
|
||||
|
||||
|
||||
def getdtype(dtype, a=None, default=None):
|
||||
"""Form a supported numpy dtype based on input arguments.
|
||||
|
||||
Returns a valid ``numpy.dtype`` from `dtype` if not None,
|
||||
or else ``a.dtype`` if possible, or else the given `default`
|
||||
if not None, or else raise a ``TypeError``.
|
||||
|
||||
The resulting ``dtype`` must be in ``supported_dtypes``:
|
||||
bool_, int8, uint8, int16, uint16, int32, uint32,
|
||||
int64, uint64, longlong, ulonglong, float32, float64,
|
||||
longdouble, complex64, complex128, clongdouble
|
||||
"""
|
||||
if dtype is None:
|
||||
try:
|
||||
newdtype = a.dtype
|
||||
except AttributeError as e:
|
||||
if default is not None:
|
||||
newdtype = np.dtype(default)
|
||||
else:
|
||||
raise TypeError("could not interpret data type") from e
|
||||
else:
|
||||
newdtype = np.dtype(dtype)
|
||||
|
||||
if newdtype not in supported_dtypes:
|
||||
supported_dtypes_fmt = ", ".join(t.__name__ for t in supported_dtypes)
|
||||
raise ValueError(f"scipy.sparse does not support dtype {newdtype}. "
|
||||
f"The only supported types are: {supported_dtypes_fmt}.")
|
||||
return newdtype
|
||||
|
||||
|
||||
def getdata(obj, dtype=None, copy=False) -> np.ndarray:
|
||||
"""
|
||||
This is a wrapper of `np.array(obj, dtype=dtype, copy=copy)`
|
||||
that will generate a warning if the result is an object array.
|
||||
"""
|
||||
data = np.array(obj, dtype=dtype, copy=copy)
|
||||
# Defer to getdtype for checking that the dtype is OK.
|
||||
# This is called for the validation only; we don't need the return value.
|
||||
getdtype(data.dtype)
|
||||
return data
|
||||
|
||||
|
||||
def safely_cast_index_arrays(A, idx_dtype=np.int32, msg=""):
|
||||
"""Safely cast sparse array indices to `idx_dtype`.
|
||||
|
||||
Check the shape of `A` to determine if it is safe to cast its index
|
||||
arrays to dtype `idx_dtype`. If any dimension in shape is larger than
|
||||
fits in the dtype, casting is unsafe so raise ``ValueError``.
|
||||
If safe, cast the index arrays to `idx_dtype` and return the result
|
||||
without changing the input `A`. The caller can assign results to `A`
|
||||
attributes if desired or use the recast index arrays directly.
|
||||
|
||||
Unless downcasting is needed, the original index arrays are returned.
|
||||
You can test e.g. ``A.indptr is new_indptr`` to see if downcasting occurred.
|
||||
|
||||
.. versionadded:: 1.15.0
|
||||
|
||||
Parameters
|
||||
----------
|
||||
A : sparse array or matrix
|
||||
The array for which index arrays should be downcast.
|
||||
idx_dtype : dtype
|
||||
Desired dtype. Should be an integer dtype (default: ``np.int32``).
|
||||
Most of scipy.sparse uses either int64 or int32.
|
||||
msg : string, optional
|
||||
A string to be added to the end of the ValueError message
|
||||
if the array shape is too big to fit in `idx_dtype`.
|
||||
The error message is ``f"<index> values too large for {msg}"``
|
||||
It should indicate why the downcasting is needed, e.g. "SuperLU",
|
||||
and defaults to f"dtype {idx_dtype}".
|
||||
|
||||
Returns
|
||||
-------
|
||||
idx_arrays : ndarray or tuple of ndarrays
|
||||
Based on ``A.format``, index arrays are returned after casting to `idx_dtype`.
|
||||
For CSC/CSR, returns ``(indices, indptr)``.
|
||||
For COO, returns ``coords``.
|
||||
For DIA, returns ``offsets``.
|
||||
For BSR, returns ``(indices, indptr)``.
|
||||
|
||||
Raises
|
||||
------
|
||||
ValueError
|
||||
If the array has shape that would not fit in the new dtype, or if
|
||||
the sparse format does not use index arrays.
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy import sparse
|
||||
>>> data = [3]
|
||||
>>> coords = (np.array([3]), np.array([1])) # Note: int64 arrays
|
||||
>>> A = sparse.coo_array((data, coords))
|
||||
>>> A.coords[0].dtype
|
||||
dtype('int64')
|
||||
|
||||
>>> # rescast after construction, raising exception if shape too big
|
||||
>>> coords = sparse.safely_cast_index_arrays(A, np.int32)
|
||||
>>> A.coords[0] is coords[0] # False if casting is needed
|
||||
False
|
||||
>>> A.coords = coords # set the index dtype of A
|
||||
>>> A.coords[0].dtype
|
||||
dtype('int32')
|
||||
"""
|
||||
if not msg:
|
||||
msg = f"dtype {idx_dtype}"
|
||||
# check for safe downcasting
|
||||
max_value = np.iinfo(idx_dtype).max
|
||||
|
||||
if A.format in ("csc", "csr"):
|
||||
# indptr[-1] is max b/c indptr always sorted
|
||||
if A.indptr[-1] > max_value:
|
||||
raise ValueError(f"indptr values too large for {msg}")
|
||||
|
||||
# check shape vs dtype
|
||||
if max(*A.shape) > max_value:
|
||||
if (A.indices > max_value).any():
|
||||
raise ValueError(f"indices values too large for {msg}")
|
||||
|
||||
indices = A.indices.astype(idx_dtype, copy=False)
|
||||
indptr = A.indptr.astype(idx_dtype, copy=False)
|
||||
return indices, indptr
|
||||
|
||||
elif A.format == "coo":
|
||||
if max(*A.shape) > max_value:
|
||||
if any((co > max_value).any() for co in A.coords):
|
||||
raise ValueError(f"coords values too large for {msg}")
|
||||
return tuple(co.astype(idx_dtype, copy=False) for co in A.coords)
|
||||
|
||||
elif A.format == "dia":
|
||||
if max(*A.shape) > max_value:
|
||||
if (A.offsets > max_value).any():
|
||||
raise ValueError(f"offsets values too large for {msg}")
|
||||
offsets = A.offsets.astype(idx_dtype, copy=False)
|
||||
return offsets
|
||||
|
||||
elif A.format == 'bsr':
|
||||
R, C = A.blocksize
|
||||
if A.indptr[-1] * R > max_value:
|
||||
raise ValueError("indptr values too large for {msg}")
|
||||
if max(*A.shape) > max_value:
|
||||
if (A.indices * C > max_value).any():
|
||||
raise ValueError(f"indices values too large for {msg}")
|
||||
indices = A.indices.astype(idx_dtype, copy=False)
|
||||
indptr = A.indptr.astype(idx_dtype, copy=False)
|
||||
return indices, indptr
|
||||
|
||||
else:
|
||||
raise TypeError(f'Format {A.format} is not associated with index arrays. '
|
||||
'DOK and LIL have dict and list, not array.')
|
||||
|
||||
|
||||
def get_index_dtype(arrays=(), maxval=None, check_contents=False):
|
||||
"""
|
||||
Based on input (integer) arrays `a`, determine a suitable index data
|
||||
type that can hold the data in the arrays.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
arrays : tuple of array_like
|
||||
Input arrays whose types/contents to check
|
||||
maxval : float, optional
|
||||
Maximum value needed
|
||||
check_contents : bool, optional
|
||||
Whether to check the values in the arrays and not just their types.
|
||||
Default: False (check only the types)
|
||||
|
||||
Returns
|
||||
-------
|
||||
dtype : dtype
|
||||
Suitable index data type (int32 or int64)
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy import sparse
|
||||
>>> # select index dtype based on shape
|
||||
>>> shape = (3, 3)
|
||||
>>> idx_dtype = sparse.get_index_dtype(maxval=max(shape))
|
||||
>>> data = [1.1, 3.0, 1.5]
|
||||
>>> indices = np.array([0, 1, 0], dtype=idx_dtype)
|
||||
>>> indptr = np.array([0, 2, 3, 3], dtype=idx_dtype)
|
||||
>>> A = sparse.csr_array((data, indices, indptr), shape=shape)
|
||||
>>> A.indptr.dtype
|
||||
dtype('int32')
|
||||
|
||||
>>> # select based on larger of existing arrays and shape
|
||||
>>> shape = (3, 3)
|
||||
>>> idx_dtype = sparse.get_index_dtype(A.indptr, maxval=max(shape))
|
||||
>>> idx_dtype
|
||||
<class 'numpy.int32'>
|
||||
"""
|
||||
# not using intc directly due to misinteractions with pythran
|
||||
if np.intc().itemsize != 4:
|
||||
return np.int64
|
||||
|
||||
int32min = np.int32(np.iinfo(np.int32).min)
|
||||
int32max = np.int32(np.iinfo(np.int32).max)
|
||||
|
||||
if maxval is not None:
|
||||
maxval = np.int64(maxval)
|
||||
if maxval > int32max:
|
||||
return np.int64
|
||||
|
||||
if isinstance(arrays, np.ndarray):
|
||||
arrays = (arrays,)
|
||||
|
||||
for arr in arrays:
|
||||
arr = np.asarray(arr)
|
||||
if not np.can_cast(arr.dtype, np.int32):
|
||||
if check_contents:
|
||||
if arr.size == 0:
|
||||
# a bigger type not needed
|
||||
continue
|
||||
elif np.issubdtype(arr.dtype, np.integer):
|
||||
maxval = arr.max()
|
||||
minval = arr.min()
|
||||
if minval >= int32min and maxval <= int32max:
|
||||
# a bigger type not needed
|
||||
continue
|
||||
return np.int64
|
||||
return np.int32
|
||||
|
||||
|
||||
def get_sum_dtype(dtype: np.dtype) -> np.dtype:
|
||||
"""Mimic numpy's casting for np.sum"""
|
||||
if dtype.kind == 'u' and np.can_cast(dtype, np.uint):
|
||||
return np.uint
|
||||
if np.can_cast(dtype, np.int_):
|
||||
return np.int_
|
||||
return dtype
|
||||
|
||||
|
||||
def isscalarlike(x) -> bool:
|
||||
"""Is x either a scalar, an array scalar, or a 0-dim array?"""
|
||||
return np.isscalar(x) or (isdense(x) and x.ndim == 0)
|
||||
|
||||
|
||||
def isintlike(x) -> bool:
|
||||
"""Is x appropriate as an index into a sparse matrix? Returns True
|
||||
if it can be cast safely to a machine int.
|
||||
"""
|
||||
# Fast-path check to eliminate non-scalar values. operator.index would
|
||||
# catch this case too, but the exception catching is slow.
|
||||
if np.ndim(x) != 0:
|
||||
return False
|
||||
try:
|
||||
operator.index(x)
|
||||
except (TypeError, ValueError):
|
||||
try:
|
||||
loose_int = bool(int(x) == x)
|
||||
except (TypeError, ValueError):
|
||||
return False
|
||||
if loose_int:
|
||||
msg = "Inexact indices into sparse matrices are not allowed"
|
||||
raise ValueError(msg)
|
||||
return loose_int
|
||||
return True
|
||||
|
||||
|
||||
def isshape(x, nonneg=False, *, allow_nd=(2,)) -> bool:
|
||||
"""Is x a valid tuple of dimensions?
|
||||
|
||||
If nonneg, also checks that the dimensions are non-negative.
|
||||
Shapes of length in the tuple allow_nd are allowed.
|
||||
"""
|
||||
ndim = len(x)
|
||||
if ndim not in allow_nd:
|
||||
return False
|
||||
|
||||
for d in x:
|
||||
if not isintlike(d):
|
||||
return False
|
||||
if nonneg and d < 0:
|
||||
return False
|
||||
return True
|
||||
|
||||
|
||||
def issequence(t) -> bool:
|
||||
return ((isinstance(t, list | tuple) and
|
||||
(len(t) == 0 or np.isscalar(t[0]))) or
|
||||
(isinstance(t, np.ndarray) and (t.ndim == 1)))
|
||||
|
||||
|
||||
def ismatrix(t) -> bool:
|
||||
return ((isinstance(t, list | tuple) and
|
||||
len(t) > 0 and issequence(t[0])) or
|
||||
(isinstance(t, np.ndarray) and t.ndim == 2))
|
||||
|
||||
|
||||
def isdense(x) -> bool:
|
||||
return isinstance(x, np.ndarray)
|
||||
|
||||
|
||||
def validateaxis(axis, *, ndim=2) -> tuple[int, ...] | None:
|
||||
if axis is None:
|
||||
return None
|
||||
|
||||
if axis == ():
|
||||
raise ValueError(
|
||||
"sparse does not accept 0D axis (). Either use toarray (for dense) "
|
||||
"or copy (for sparse)."
|
||||
)
|
||||
|
||||
if not isinstance(axis, tuple):
|
||||
# If not a tuple, check that the provided axis is actually
|
||||
# an integer and raise a TypeError similar to NumPy's
|
||||
if not np.issubdtype(np.dtype(type(axis)), np.integer):
|
||||
raise TypeError(f'axis must be an integer/tuple of ints, not {type(axis)}')
|
||||
axis = (axis,)
|
||||
|
||||
canon_axis = []
|
||||
for ax in axis:
|
||||
if not isintlike(ax):
|
||||
raise TypeError(f"axis must be an integer. (given {ax})")
|
||||
if ax < 0:
|
||||
ax += ndim
|
||||
if ax < 0 or ax >= ndim:
|
||||
raise ValueError("axis out of range for ndim")
|
||||
canon_axis.append(ax)
|
||||
|
||||
len_axis = len(canon_axis)
|
||||
if len_axis != len(set(canon_axis)):
|
||||
raise ValueError("duplicate value in axis")
|
||||
elif len_axis > ndim:
|
||||
raise ValueError("axis tuple has too many elements")
|
||||
elif len_axis == ndim:
|
||||
return None
|
||||
else:
|
||||
return tuple(canon_axis)
|
||||
|
||||
|
||||
def check_shape(args, current_shape=None, *, allow_nd=(2,)) -> tuple[int, ...]:
|
||||
"""Imitate numpy.matrix handling of shape arguments
|
||||
|
||||
Parameters
|
||||
----------
|
||||
args : array_like
|
||||
Data structures providing information about the shape of the sparse array.
|
||||
current_shape : tuple, optional
|
||||
The current shape of the sparse array or matrix.
|
||||
If None (default), the current shape will be inferred from args.
|
||||
allow_nd : tuple of ints, optional default: (2,)
|
||||
If shape does not have a length in the tuple allow_nd an error is raised.
|
||||
|
||||
Returns
|
||||
-------
|
||||
new_shape: tuple
|
||||
The new shape after validation.
|
||||
"""
|
||||
if len(args) == 0:
|
||||
raise TypeError("function missing 1 required positional argument: 'shape'")
|
||||
if len(args) == 1:
|
||||
try:
|
||||
shape_iter = iter(args[0])
|
||||
except TypeError:
|
||||
new_shape = (operator.index(args[0]), )
|
||||
else:
|
||||
new_shape = tuple(operator.index(arg) for arg in shape_iter)
|
||||
else:
|
||||
new_shape = tuple(operator.index(arg) for arg in args)
|
||||
|
||||
if current_shape is None:
|
||||
if len(new_shape) not in allow_nd:
|
||||
raise ValueError(f'shape must have length in {allow_nd}. Got {new_shape=}')
|
||||
if any(d < 0 for d in new_shape):
|
||||
raise ValueError("'shape' elements cannot be negative")
|
||||
else:
|
||||
# Check the current size only if needed
|
||||
current_size = prod(current_shape)
|
||||
|
||||
# Check for negatives
|
||||
negative_indexes = [i for i, x in enumerate(new_shape) if x < 0]
|
||||
if not negative_indexes:
|
||||
new_size = prod(new_shape)
|
||||
if new_size != current_size:
|
||||
raise ValueError(f'cannot reshape array of size {current_size}'
|
||||
f' into shape {new_shape}')
|
||||
elif len(negative_indexes) == 1:
|
||||
skip = negative_indexes[0]
|
||||
specified = prod(new_shape[:skip] + new_shape[skip+1:])
|
||||
unspecified, remainder = divmod(current_size, specified)
|
||||
if remainder != 0:
|
||||
err_shape = tuple('newshape' if x < 0 else x for x in new_shape)
|
||||
raise ValueError(f'cannot reshape array of size {current_size}'
|
||||
f' into shape {err_shape}')
|
||||
new_shape = new_shape[:skip] + (unspecified,) + new_shape[skip+1:]
|
||||
else:
|
||||
raise ValueError('can only specify one unknown dimension')
|
||||
|
||||
if len(new_shape) not in allow_nd:
|
||||
raise ValueError(f'shape must have length in {allow_nd}. Got {new_shape=}')
|
||||
|
||||
return new_shape
|
||||
|
||||
|
||||
def broadcast_shapes(*shapes):
|
||||
"""Check if shapes can be broadcast and return resulting shape
|
||||
|
||||
This is similar to the NumPy ``broadcast_shapes`` function but
|
||||
does not check memory consequences of the resulting dense matrix.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
*shapes : tuple of shape tuples
|
||||
The tuple of shapes to be considered for broadcasting.
|
||||
Shapes should be tuples of non-negative integers.
|
||||
|
||||
Returns
|
||||
-------
|
||||
new_shape : tuple of integers
|
||||
The shape that results from broadcasting th input shapes.
|
||||
"""
|
||||
if not shapes:
|
||||
return ()
|
||||
shapes = [shp if isinstance(shp, tuple | list) else (shp,) for shp in shapes]
|
||||
big_shp = max(shapes, key=len)
|
||||
out = list(big_shp)
|
||||
for shp in shapes:
|
||||
if shp is big_shp:
|
||||
continue
|
||||
for i, x in enumerate(shp, start=-len(shp)):
|
||||
if x != 1 and x != out[i]:
|
||||
if out[i] != 1:
|
||||
raise ValueError("shapes cannot be broadcast to a single shape.")
|
||||
out[i] = x
|
||||
return (*out,)
|
||||
|
||||
|
||||
def check_reshape_kwargs(kwargs):
|
||||
"""Unpack keyword arguments for reshape function.
|
||||
|
||||
This is useful because keyword arguments after star arguments are not
|
||||
allowed in Python 2, but star keyword arguments are. This function unpacks
|
||||
'order' and 'copy' from the star keyword arguments (with defaults) and
|
||||
throws an error for any remaining.
|
||||
"""
|
||||
|
||||
order = kwargs.pop('order', 'C')
|
||||
copy = kwargs.pop('copy', False)
|
||||
if kwargs: # Some unused kwargs remain
|
||||
raise TypeError("reshape() got unexpected keywords arguments: "
|
||||
f"{', '.join(kwargs.keys())}")
|
||||
return order, copy
|
||||
|
||||
|
||||
def is_pydata_spmatrix(m) -> bool:
|
||||
"""
|
||||
Check whether object is pydata/sparse matrix, avoiding importing the module.
|
||||
"""
|
||||
base_cls = getattr(sys.modules.get('sparse'), 'SparseArray', None)
|
||||
return base_cls is not None and isinstance(m, base_cls)
|
||||
|
||||
|
||||
def convert_pydata_sparse_to_scipy(
|
||||
arg: Any,
|
||||
target_format: None | Literal["csc", "csr"] = None,
|
||||
accept_fv: Any = None,
|
||||
) -> Union[Any, "sp.spmatrix"]:
|
||||
"""
|
||||
Convert a pydata/sparse array to scipy sparse matrix,
|
||||
pass through anything else.
|
||||
"""
|
||||
if is_pydata_spmatrix(arg):
|
||||
# The `accept_fv` keyword is new in PyData Sparse 0.15.4 (May 2024),
|
||||
# remove the `except` once the minimum supported version is >=0.15.4
|
||||
try:
|
||||
arg = arg.to_scipy_sparse(accept_fv=accept_fv)
|
||||
except TypeError:
|
||||
arg = arg.to_scipy_sparse()
|
||||
if target_format is not None:
|
||||
arg = arg.asformat(target_format)
|
||||
elif arg.format not in ("csc", "csr"):
|
||||
arg = arg.tocsc()
|
||||
return arg
|
||||
|
||||
|
||||
###############################################################################
|
||||
# Wrappers for NumPy types that are deprecated
|
||||
|
||||
# Numpy versions of these functions raise deprecation warnings, the
|
||||
# ones below do not.
|
||||
|
||||
def matrix(*args, **kwargs):
|
||||
return np.array(*args, **kwargs).view(np.matrix)
|
||||
|
||||
|
||||
def asmatrix(data, dtype=None):
|
||||
if isinstance(data, np.matrix) and (dtype is None or data.dtype == dtype):
|
||||
return data
|
||||
return np.asarray(data, dtype=dtype).view(np.matrix)
|
||||
|
||||
###############################################################################
|
||||
|
||||
|
||||
def _todata(s) -> np.ndarray:
|
||||
"""Access nonzero values, possibly after summing duplicates.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
s : sparse array
|
||||
Input sparse array.
|
||||
|
||||
Returns
|
||||
-------
|
||||
data: ndarray
|
||||
Nonzero values of the array, with shape (s.nnz,)
|
||||
|
||||
"""
|
||||
if isinstance(s, sp._data._data_matrix):
|
||||
return s._deduped_data()
|
||||
|
||||
if isinstance(s, sp.dok_array):
|
||||
return np.fromiter(s.values(), dtype=s.dtype, count=s.nnz)
|
||||
|
||||
if isinstance(s, sp.lil_array):
|
||||
data = np.empty(s.nnz, dtype=s.dtype)
|
||||
sp._csparsetools.lil_flatten_to_array(s.data, data)
|
||||
return data
|
||||
|
||||
return s.tocoo()._deduped_data()
|
||||
24
venv/lib/python3.13/site-packages/scipy/sparse/base.py
Normal file
24
venv/lib/python3.13/site-packages/scipy/sparse/base.py
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'SparseEfficiencyWarning',
|
||||
'SparseWarning',
|
||||
'issparse',
|
||||
'isspmatrix',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="base",
|
||||
private_modules=["_base"], all=__all__,
|
||||
attribute=name)
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/bsr.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/bsr.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'bsr_matrix',
|
||||
'isspmatrix_bsr',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="bsr",
|
||||
private_modules=["_bsr"], all=__all__,
|
||||
attribute=name)
|
||||
20
venv/lib/python3.13/site-packages/scipy/sparse/compressed.py
Normal file
20
venv/lib/python3.13/site-packages/scipy/sparse/compressed.py
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'SparseEfficiencyWarning',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="compressed",
|
||||
private_modules=["_compressed"], all=__all__,
|
||||
attribute=name)
|
||||
38
venv/lib/python3.13/site-packages/scipy/sparse/construct.py
Normal file
38
venv/lib/python3.13/site-packages/scipy/sparse/construct.py
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'block_diag',
|
||||
'bmat',
|
||||
'bsr_matrix',
|
||||
'coo_matrix',
|
||||
'csc_matrix',
|
||||
'csr_matrix',
|
||||
'dia_matrix',
|
||||
'diags',
|
||||
'eye',
|
||||
'get_index_dtype',
|
||||
'hstack',
|
||||
'identity',
|
||||
'issparse',
|
||||
'kron',
|
||||
'kronsum',
|
||||
'rand',
|
||||
'random',
|
||||
'spdiags',
|
||||
'vstack',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="construct",
|
||||
private_modules=["_construct"], all=__all__,
|
||||
attribute=name)
|
||||
23
venv/lib/python3.13/site-packages/scipy/sparse/coo.py
Normal file
23
venv/lib/python3.13/site-packages/scipy/sparse/coo.py
Normal file
|
|
@ -0,0 +1,23 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'SparseEfficiencyWarning',
|
||||
'coo_matrix',
|
||||
'isspmatrix_coo',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="coo",
|
||||
private_modules=["_coo"], all=__all__,
|
||||
attribute=name)
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/csc.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/csc.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'csc_matrix',
|
||||
'isspmatrix_csc',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="csc",
|
||||
private_modules=["_csc"], all=__all__,
|
||||
attribute=name)
|
||||
|
|
@ -0,0 +1,210 @@
|
|||
r"""
|
||||
Compressed sparse graph routines (:mod:`scipy.sparse.csgraph`)
|
||||
==============================================================
|
||||
|
||||
.. currentmodule:: scipy.sparse.csgraph
|
||||
|
||||
Fast graph algorithms based on sparse matrix representations.
|
||||
|
||||
Contents
|
||||
--------
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
connected_components -- determine connected components of a graph
|
||||
laplacian -- compute the laplacian of a graph
|
||||
shortest_path -- compute the shortest path between points on a positive graph
|
||||
dijkstra -- use Dijkstra's algorithm for shortest path
|
||||
floyd_warshall -- use the Floyd-Warshall algorithm for shortest path
|
||||
bellman_ford -- use the Bellman-Ford algorithm for shortest path
|
||||
johnson -- use Johnson's algorithm for shortest path
|
||||
yen -- use Yen's algorithm for K-shortest paths between to nodes.
|
||||
breadth_first_order -- compute a breadth-first order of nodes
|
||||
depth_first_order -- compute a depth-first order of nodes
|
||||
breadth_first_tree -- construct the breadth-first tree from a given node
|
||||
depth_first_tree -- construct a depth-first tree from a given node
|
||||
minimum_spanning_tree -- construct the minimum spanning tree of a graph
|
||||
reverse_cuthill_mckee -- compute permutation for reverse Cuthill-McKee ordering
|
||||
maximum_flow -- solve the maximum flow problem for a graph
|
||||
maximum_bipartite_matching -- compute a maximum matching of a bipartite graph
|
||||
min_weight_full_bipartite_matching - compute a minimum weight full matching of a bipartite graph
|
||||
structural_rank -- compute the structural rank of a graph
|
||||
NegativeCycleError
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
construct_dist_matrix
|
||||
csgraph_from_dense
|
||||
csgraph_from_masked
|
||||
csgraph_masked_from_dense
|
||||
csgraph_to_dense
|
||||
csgraph_to_masked
|
||||
reconstruct_path
|
||||
|
||||
Graph Representations
|
||||
---------------------
|
||||
This module uses graphs which are stored in a matrix format. A
|
||||
graph with N nodes can be represented by an (N x N) adjacency matrix G.
|
||||
If there is a connection from node i to node j, then G[i, j] = w, where
|
||||
w is the weight of the connection. For nodes i and j which are
|
||||
not connected, the value depends on the representation:
|
||||
|
||||
- for dense array representations, non-edges are represented by
|
||||
G[i, j] = 0, infinity, or NaN.
|
||||
|
||||
- for dense masked representations (of type np.ma.MaskedArray), non-edges
|
||||
are represented by masked values. This can be useful when graphs with
|
||||
zero-weight edges are desired.
|
||||
|
||||
- for sparse array representations, non-edges are represented by
|
||||
non-entries in the matrix. This sort of sparse representation also
|
||||
allows for edges with zero weights.
|
||||
|
||||
As a concrete example, imagine that you would like to represent the following
|
||||
undirected graph::
|
||||
|
||||
G
|
||||
|
||||
(0)
|
||||
/ \
|
||||
1 2
|
||||
/ \
|
||||
(2) (1)
|
||||
|
||||
This graph has three nodes, where node 0 and 1 are connected by an edge of
|
||||
weight 2, and nodes 0 and 2 are connected by an edge of weight 1.
|
||||
We can construct the dense, masked, and sparse representations as follows,
|
||||
keeping in mind that an undirected graph is represented by a symmetric matrix::
|
||||
|
||||
>>> import numpy as np
|
||||
>>> G_dense = np.array([[0, 2, 1],
|
||||
... [2, 0, 0],
|
||||
... [1, 0, 0]])
|
||||
>>> G_masked = np.ma.masked_values(G_dense, 0)
|
||||
>>> from scipy.sparse import csr_array
|
||||
>>> G_sparse = csr_array(G_dense)
|
||||
|
||||
This becomes more difficult when zero edges are significant. For example,
|
||||
consider the situation when we slightly modify the above graph::
|
||||
|
||||
G2
|
||||
|
||||
(0)
|
||||
/ \
|
||||
0 2
|
||||
/ \
|
||||
(2) (1)
|
||||
|
||||
This is identical to the previous graph, except nodes 0 and 2 are connected
|
||||
by an edge of zero weight. In this case, the dense representation above
|
||||
leads to ambiguities: how can non-edges be represented if zero is a meaningful
|
||||
value? In this case, either a masked or sparse representation must be used
|
||||
to eliminate the ambiguity::
|
||||
|
||||
>>> import numpy as np
|
||||
>>> G2_data = np.array([[np.inf, 2, 0 ],
|
||||
... [2, np.inf, np.inf],
|
||||
... [0, np.inf, np.inf]])
|
||||
>>> G2_masked = np.ma.masked_invalid(G2_data)
|
||||
>>> from scipy.sparse.csgraph import csgraph_from_dense
|
||||
>>> # G2_sparse = csr_array(G2_data) would give the wrong result
|
||||
>>> G2_sparse = csgraph_from_dense(G2_data, null_value=np.inf)
|
||||
>>> G2_sparse.data
|
||||
array([ 2., 0., 2., 0.])
|
||||
|
||||
Here we have used a utility routine from the csgraph submodule in order to
|
||||
convert the dense representation to a sparse representation which can be
|
||||
understood by the algorithms in submodule. By viewing the data array, we
|
||||
can see that the zero values are explicitly encoded in the graph.
|
||||
|
||||
Directed vs. undirected
|
||||
^^^^^^^^^^^^^^^^^^^^^^^
|
||||
Matrices may represent either directed or undirected graphs. This is
|
||||
specified throughout the csgraph module by a boolean keyword. Graphs are
|
||||
assumed to be directed by default. In a directed graph, traversal from node
|
||||
i to node j can be accomplished over the edge G[i, j], but not the edge
|
||||
G[j, i]. Consider the following dense graph::
|
||||
|
||||
>>> import numpy as np
|
||||
>>> G_dense = np.array([[0, 1, 0],
|
||||
... [2, 0, 3],
|
||||
... [0, 4, 0]])
|
||||
|
||||
When ``directed=True`` we get the graph::
|
||||
|
||||
---1--> ---3-->
|
||||
(0) (1) (2)
|
||||
<--2--- <--4---
|
||||
|
||||
In a non-directed graph, traversal from node i to node j can be
|
||||
accomplished over either G[i, j] or G[j, i]. If both edges are not null,
|
||||
and the two have unequal weights, then the smaller of the two is used.
|
||||
|
||||
So for the same graph, when ``directed=False`` we get the graph::
|
||||
|
||||
(0)--1--(1)--3--(2)
|
||||
|
||||
Note that a symmetric matrix will represent an undirected graph, regardless
|
||||
of whether the 'directed' keyword is set to True or False. In this case,
|
||||
using ``directed=True`` generally leads to more efficient computation.
|
||||
|
||||
The routines in this module accept as input either scipy.sparse representations
|
||||
(csr, csc, or lil format), masked representations, or dense representations
|
||||
with non-edges indicated by zeros, infinities, and NaN entries.
|
||||
""" # noqa: E501
|
||||
|
||||
__docformat__ = "restructuredtext en"
|
||||
|
||||
__all__ = ['connected_components',
|
||||
'laplacian',
|
||||
'shortest_path',
|
||||
'floyd_warshall',
|
||||
'dijkstra',
|
||||
'bellman_ford',
|
||||
'johnson',
|
||||
'yen',
|
||||
'breadth_first_order',
|
||||
'depth_first_order',
|
||||
'breadth_first_tree',
|
||||
'depth_first_tree',
|
||||
'minimum_spanning_tree',
|
||||
'reverse_cuthill_mckee',
|
||||
'maximum_flow',
|
||||
'maximum_bipartite_matching',
|
||||
'min_weight_full_bipartite_matching',
|
||||
'structural_rank',
|
||||
'construct_dist_matrix',
|
||||
'reconstruct_path',
|
||||
'csgraph_masked_from_dense',
|
||||
'csgraph_from_dense',
|
||||
'csgraph_from_masked',
|
||||
'csgraph_to_dense',
|
||||
'csgraph_to_masked',
|
||||
'NegativeCycleError']
|
||||
|
||||
from ._laplacian import laplacian
|
||||
from ._shortest_path import (
|
||||
shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, yen,
|
||||
NegativeCycleError
|
||||
)
|
||||
from ._traversal import (
|
||||
breadth_first_order, depth_first_order, breadth_first_tree,
|
||||
depth_first_tree, connected_components
|
||||
)
|
||||
from ._min_spanning_tree import minimum_spanning_tree
|
||||
from ._flow import maximum_flow
|
||||
from ._matching import (
|
||||
maximum_bipartite_matching, min_weight_full_bipartite_matching
|
||||
)
|
||||
from ._reordering import reverse_cuthill_mckee, structural_rank
|
||||
from ._tools import (
|
||||
construct_dist_matrix, reconstruct_path, csgraph_from_dense,
|
||||
csgraph_to_dense, csgraph_masked_from_dense, csgraph_from_masked,
|
||||
csgraph_to_masked
|
||||
)
|
||||
|
||||
from scipy._lib._testutils import PytestTester
|
||||
test = PytestTester(__name__)
|
||||
del PytestTester
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
|
|
@ -0,0 +1,563 @@
|
|||
"""
|
||||
Laplacian of a compressed-sparse graph
|
||||
"""
|
||||
|
||||
import numpy as np
|
||||
from scipy.sparse import issparse
|
||||
from scipy.sparse.linalg import LinearOperator
|
||||
from scipy.sparse._sputils import convert_pydata_sparse_to_scipy, is_pydata_spmatrix
|
||||
|
||||
|
||||
###############################################################################
|
||||
# Graph laplacian
|
||||
def laplacian(
|
||||
csgraph,
|
||||
normed=False,
|
||||
return_diag=False,
|
||||
use_out_degree=False,
|
||||
*,
|
||||
copy=True,
|
||||
form="array",
|
||||
dtype=None,
|
||||
symmetrized=False,
|
||||
):
|
||||
"""
|
||||
Return the Laplacian of a directed graph.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
csgraph : array_like or sparse array or matrix, 2 dimensions
|
||||
compressed-sparse graph, with shape (N, N).
|
||||
normed : bool, optional
|
||||
If True, then compute symmetrically normalized Laplacian.
|
||||
Default: False.
|
||||
return_diag : bool, optional
|
||||
If True, then also return an array related to vertex degrees.
|
||||
Default: False.
|
||||
use_out_degree : bool, optional
|
||||
If True, then use out-degree instead of in-degree.
|
||||
This distinction matters only if the graph is asymmetric.
|
||||
Default: False.
|
||||
copy: bool, optional
|
||||
If False, then change `csgraph` in place if possible,
|
||||
avoiding doubling the memory use.
|
||||
Default: True, for backward compatibility.
|
||||
form: 'array', or 'function', or 'lo'
|
||||
Determines the format of the output Laplacian:
|
||||
|
||||
* 'array' is a numpy array;
|
||||
* 'function' is a pointer to evaluating the Laplacian-vector
|
||||
or Laplacian-matrix product;
|
||||
* 'lo' results in the format of the `LinearOperator`.
|
||||
|
||||
Choosing 'function' or 'lo' always avoids doubling
|
||||
the memory use, ignoring `copy` value.
|
||||
Default: 'array', for backward compatibility.
|
||||
dtype: None or one of numeric numpy dtypes, optional
|
||||
The dtype of the output. If ``dtype=None``, the dtype of the
|
||||
output matches the dtype of the input csgraph, except for
|
||||
the case ``normed=True`` and integer-like csgraph, where
|
||||
the output dtype is 'float' allowing accurate normalization,
|
||||
but dramatically increasing the memory use.
|
||||
Default: None, for backward compatibility.
|
||||
symmetrized: bool, optional
|
||||
If True, then the output Laplacian is symmetric/Hermitian.
|
||||
The symmetrization is done by ``csgraph + csgraph.T.conj``
|
||||
without dividing by 2 to preserve integer dtypes if possible
|
||||
prior to the construction of the Laplacian.
|
||||
The symmetrization will increase the memory footprint of
|
||||
sparse matrices unless the sparsity pattern is symmetric or
|
||||
`form` is 'function' or 'lo'.
|
||||
Default: False, for backward compatibility.
|
||||
|
||||
Returns
|
||||
-------
|
||||
lap : ndarray, or sparse array or matrix, or `LinearOperator`
|
||||
The N x N Laplacian of csgraph. It will be a NumPy array (dense)
|
||||
if the input was dense, or a sparse array otherwise, or
|
||||
the format of a function or `LinearOperator` if
|
||||
`form` equals 'function' or 'lo', respectively.
|
||||
diag : ndarray, optional
|
||||
The length-N main diagonal of the Laplacian matrix.
|
||||
For the normalized Laplacian, this is the array of square roots
|
||||
of vertex degrees or 1 if the degree is zero.
|
||||
|
||||
Notes
|
||||
-----
|
||||
The Laplacian matrix of a graph is sometimes referred to as the
|
||||
"Kirchhoff matrix" or just the "Laplacian", and is useful in many
|
||||
parts of spectral graph theory.
|
||||
In particular, the eigen-decomposition of the Laplacian can give
|
||||
insight into many properties of the graph, e.g.,
|
||||
is commonly used for spectral data embedding and clustering.
|
||||
|
||||
The constructed Laplacian doubles the memory use if ``copy=True`` and
|
||||
``form="array"`` which is the default.
|
||||
Choosing ``copy=False`` has no effect unless ``form="array"``
|
||||
or the matrix is sparse in the ``coo`` format, or dense array, except
|
||||
for the integer input with ``normed=True`` that forces the float output.
|
||||
|
||||
Sparse input is reformatted into ``coo`` if ``form="array"``,
|
||||
which is the default.
|
||||
|
||||
If the input adjacency matrix is not symmetric, the Laplacian is
|
||||
also non-symmetric unless ``symmetrized=True`` is used.
|
||||
|
||||
Diagonal entries of the input adjacency matrix are ignored and
|
||||
replaced with zeros for the purpose of normalization where ``normed=True``.
|
||||
The normalization uses the inverse square roots of row-sums of the input
|
||||
adjacency matrix, and thus may fail if the row-sums contain
|
||||
negative or complex with a non-zero imaginary part values.
|
||||
|
||||
The normalization is symmetric, making the normalized Laplacian also
|
||||
symmetric if the input csgraph was symmetric.
|
||||
|
||||
References
|
||||
----------
|
||||
.. [1] Laplacian matrix. https://en.wikipedia.org/wiki/Laplacian_matrix
|
||||
|
||||
Examples
|
||||
--------
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csgraph
|
||||
|
||||
Our first illustration is the symmetric graph
|
||||
|
||||
>>> G = np.arange(4) * np.arange(4)[:, np.newaxis]
|
||||
>>> G
|
||||
array([[0, 0, 0, 0],
|
||||
[0, 1, 2, 3],
|
||||
[0, 2, 4, 6],
|
||||
[0, 3, 6, 9]])
|
||||
|
||||
and its symmetric Laplacian matrix
|
||||
|
||||
>>> csgraph.laplacian(G)
|
||||
array([[ 0, 0, 0, 0],
|
||||
[ 0, 5, -2, -3],
|
||||
[ 0, -2, 8, -6],
|
||||
[ 0, -3, -6, 9]])
|
||||
|
||||
The non-symmetric graph
|
||||
|
||||
>>> G = np.arange(9).reshape(3, 3)
|
||||
>>> G
|
||||
array([[0, 1, 2],
|
||||
[3, 4, 5],
|
||||
[6, 7, 8]])
|
||||
|
||||
has different row- and column sums, resulting in two varieties
|
||||
of the Laplacian matrix, using an in-degree, which is the default
|
||||
|
||||
>>> L_in_degree = csgraph.laplacian(G)
|
||||
>>> L_in_degree
|
||||
array([[ 9, -1, -2],
|
||||
[-3, 8, -5],
|
||||
[-6, -7, 7]])
|
||||
|
||||
or alternatively an out-degree
|
||||
|
||||
>>> L_out_degree = csgraph.laplacian(G, use_out_degree=True)
|
||||
>>> L_out_degree
|
||||
array([[ 3, -1, -2],
|
||||
[-3, 8, -5],
|
||||
[-6, -7, 13]])
|
||||
|
||||
Constructing a symmetric Laplacian matrix, one can add the two as
|
||||
|
||||
>>> L_in_degree + L_out_degree.T
|
||||
array([[ 12, -4, -8],
|
||||
[ -4, 16, -12],
|
||||
[ -8, -12, 20]])
|
||||
|
||||
or use the ``symmetrized=True`` option
|
||||
|
||||
>>> csgraph.laplacian(G, symmetrized=True)
|
||||
array([[ 12, -4, -8],
|
||||
[ -4, 16, -12],
|
||||
[ -8, -12, 20]])
|
||||
|
||||
that is equivalent to symmetrizing the original graph
|
||||
|
||||
>>> csgraph.laplacian(G + G.T)
|
||||
array([[ 12, -4, -8],
|
||||
[ -4, 16, -12],
|
||||
[ -8, -12, 20]])
|
||||
|
||||
The goal of normalization is to make the non-zero diagonal entries
|
||||
of the Laplacian matrix to be all unit, also scaling off-diagonal
|
||||
entries correspondingly. The normalization can be done manually, e.g.,
|
||||
|
||||
>>> G = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
|
||||
>>> L, d = csgraph.laplacian(G, return_diag=True)
|
||||
>>> L
|
||||
array([[ 2, -1, -1],
|
||||
[-1, 2, -1],
|
||||
[-1, -1, 2]])
|
||||
>>> d
|
||||
array([2, 2, 2])
|
||||
>>> scaling = np.sqrt(d)
|
||||
>>> scaling
|
||||
array([1.41421356, 1.41421356, 1.41421356])
|
||||
>>> (1/scaling)*L*(1/scaling)
|
||||
array([[ 1. , -0.5, -0.5],
|
||||
[-0.5, 1. , -0.5],
|
||||
[-0.5, -0.5, 1. ]])
|
||||
|
||||
Or using ``normed=True`` option
|
||||
|
||||
>>> L, d = csgraph.laplacian(G, return_diag=True, normed=True)
|
||||
>>> L
|
||||
array([[ 1. , -0.5, -0.5],
|
||||
[-0.5, 1. , -0.5],
|
||||
[-0.5, -0.5, 1. ]])
|
||||
|
||||
which now instead of the diagonal returns the scaling coefficients
|
||||
|
||||
>>> d
|
||||
array([1.41421356, 1.41421356, 1.41421356])
|
||||
|
||||
Zero scaling coefficients are substituted with 1s, where scaling
|
||||
has thus no effect, e.g.,
|
||||
|
||||
>>> G = np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0]])
|
||||
>>> G
|
||||
array([[0, 0, 0],
|
||||
[0, 0, 1],
|
||||
[0, 1, 0]])
|
||||
>>> L, d = csgraph.laplacian(G, return_diag=True, normed=True)
|
||||
>>> L
|
||||
array([[ 0., -0., -0.],
|
||||
[-0., 1., -1.],
|
||||
[-0., -1., 1.]])
|
||||
>>> d
|
||||
array([1., 1., 1.])
|
||||
|
||||
Only the symmetric normalization is implemented, resulting
|
||||
in a symmetric Laplacian matrix if and only if its graph is symmetric
|
||||
and has all non-negative degrees, like in the examples above.
|
||||
|
||||
The output Laplacian matrix is by default a dense array or a sparse
|
||||
array or matrix inferring its class, shape, format, and dtype from
|
||||
the input graph matrix:
|
||||
|
||||
>>> G = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]]).astype(np.float32)
|
||||
>>> G
|
||||
array([[0., 1., 1.],
|
||||
[1., 0., 1.],
|
||||
[1., 1., 0.]], dtype=float32)
|
||||
>>> csgraph.laplacian(G)
|
||||
array([[ 2., -1., -1.],
|
||||
[-1., 2., -1.],
|
||||
[-1., -1., 2.]], dtype=float32)
|
||||
|
||||
but can alternatively be generated matrix-free as a LinearOperator:
|
||||
|
||||
>>> L = csgraph.laplacian(G, form="lo")
|
||||
>>> L
|
||||
<3x3 _CustomLinearOperator with dtype=float32>
|
||||
>>> L(np.eye(3))
|
||||
array([[ 2., -1., -1.],
|
||||
[-1., 2., -1.],
|
||||
[-1., -1., 2.]])
|
||||
|
||||
or as a lambda-function:
|
||||
|
||||
>>> L = csgraph.laplacian(G, form="function")
|
||||
>>> L
|
||||
<function _laplace.<locals>.<lambda> at 0x0000012AE6F5A598>
|
||||
>>> L(np.eye(3))
|
||||
array([[ 2., -1., -1.],
|
||||
[-1., 2., -1.],
|
||||
[-1., -1., 2.]])
|
||||
|
||||
The Laplacian matrix is used for
|
||||
spectral data clustering and embedding
|
||||
as well as for spectral graph partitioning.
|
||||
Our final example illustrates the latter
|
||||
for a noisy directed linear graph.
|
||||
|
||||
>>> from scipy.sparse import diags_array, random_array
|
||||
>>> from scipy.sparse.linalg import lobpcg
|
||||
|
||||
Create a directed linear graph with ``N=35`` vertices
|
||||
using a sparse adjacency matrix ``G``:
|
||||
|
||||
>>> N = 35
|
||||
>>> G = diags_array(np.ones(N - 1), offsets=1, format="csr")
|
||||
|
||||
Fix a random seed ``rng`` and add a random sparse noise to the graph ``G``:
|
||||
|
||||
>>> rng = np.random.default_rng()
|
||||
>>> G += 1e-2 * random_array((N, N), density=0.1, rng=rng)
|
||||
|
||||
Set initial approximations for eigenvectors:
|
||||
|
||||
>>> X = rng.random((N, 2))
|
||||
|
||||
The constant vector of ones is always a trivial eigenvector
|
||||
of the non-normalized Laplacian to be filtered out:
|
||||
|
||||
>>> Y = np.ones((N, 1))
|
||||
|
||||
Alternating (1) the sign of the graph weights allows determining
|
||||
labels for spectral max- and min- cuts in a single loop.
|
||||
Since the graph is undirected, the option ``symmetrized=True``
|
||||
must be used in the construction of the Laplacian.
|
||||
The option ``normed=True`` cannot be used in (2) for the negative weights
|
||||
here as the symmetric normalization evaluates square roots.
|
||||
The option ``form="lo"`` in (2) is matrix-free, i.e., guarantees
|
||||
a fixed memory footprint and read-only access to the graph.
|
||||
Calling the eigenvalue solver ``lobpcg`` (3) computes the Fiedler vector
|
||||
that determines the labels as the signs of its components in (5).
|
||||
Since the sign in an eigenvector is not deterministic and can flip,
|
||||
we fix the sign of the first component to be always +1 in (4).
|
||||
|
||||
>>> for cut in ["max", "min"]:
|
||||
... G = -G # 1.
|
||||
... L = csgraph.laplacian(G, symmetrized=True, form="lo") # 2.
|
||||
... _, eves = lobpcg(L, X, Y=Y, largest=False, tol=1e-2) # 3.
|
||||
... eves *= np.sign(eves[0, 0]) # 4.
|
||||
... print(cut + "-cut labels:\\n", 1 * (eves[:, 0]>0)) # 5.
|
||||
max-cut labels:
|
||||
[1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1]
|
||||
min-cut labels:
|
||||
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
|
||||
|
||||
As anticipated for a (slightly noisy) linear graph,
|
||||
the max-cut strips all the edges of the graph coloring all
|
||||
odd vertices into one color and all even vertices into another one,
|
||||
while the balanced min-cut partitions the graph
|
||||
in the middle by deleting a single edge.
|
||||
Both determined partitions are optimal.
|
||||
"""
|
||||
is_pydata_sparse = is_pydata_spmatrix(csgraph)
|
||||
if is_pydata_sparse:
|
||||
pydata_sparse_cls = csgraph.__class__
|
||||
csgraph = convert_pydata_sparse_to_scipy(csgraph)
|
||||
if csgraph.ndim != 2 or csgraph.shape[0] != csgraph.shape[1]:
|
||||
raise ValueError('csgraph must be a square matrix or array')
|
||||
|
||||
if normed and (
|
||||
np.issubdtype(csgraph.dtype, np.signedinteger)
|
||||
or np.issubdtype(csgraph.dtype, np.uint)
|
||||
):
|
||||
csgraph = csgraph.astype(np.float64)
|
||||
|
||||
if form == "array":
|
||||
create_lap = (
|
||||
_laplacian_sparse if issparse(csgraph) else _laplacian_dense
|
||||
)
|
||||
else:
|
||||
create_lap = (
|
||||
_laplacian_sparse_flo
|
||||
if issparse(csgraph)
|
||||
else _laplacian_dense_flo
|
||||
)
|
||||
|
||||
degree_axis = 1 if use_out_degree else 0
|
||||
|
||||
lap, d = create_lap(
|
||||
csgraph,
|
||||
normed=normed,
|
||||
axis=degree_axis,
|
||||
copy=copy,
|
||||
form=form,
|
||||
dtype=dtype,
|
||||
symmetrized=symmetrized,
|
||||
)
|
||||
if is_pydata_sparse:
|
||||
lap = pydata_sparse_cls.from_scipy_sparse(lap)
|
||||
if return_diag:
|
||||
return lap, d
|
||||
return lap
|
||||
|
||||
|
||||
def _setdiag_dense(m, d):
|
||||
step = len(d) + 1
|
||||
m.flat[::step] = d
|
||||
|
||||
|
||||
def _laplace(m, d):
|
||||
return lambda v: v * d[:, np.newaxis] - m @ v
|
||||
|
||||
|
||||
def _laplace_normed(m, d, nd):
|
||||
laplace = _laplace(m, d)
|
||||
return lambda v: nd[:, np.newaxis] * laplace(v * nd[:, np.newaxis])
|
||||
|
||||
|
||||
def _laplace_sym(m, d):
|
||||
return (
|
||||
lambda v: v * d[:, np.newaxis]
|
||||
- m @ v
|
||||
- np.transpose(np.conjugate(np.transpose(np.conjugate(v)) @ m))
|
||||
)
|
||||
|
||||
|
||||
def _laplace_normed_sym(m, d, nd):
|
||||
laplace_sym = _laplace_sym(m, d)
|
||||
return lambda v: nd[:, np.newaxis] * laplace_sym(v * nd[:, np.newaxis])
|
||||
|
||||
|
||||
def _linearoperator(mv, shape, dtype):
|
||||
return LinearOperator(matvec=mv, matmat=mv, shape=shape, dtype=dtype)
|
||||
|
||||
|
||||
def _laplacian_sparse_flo(graph, normed, axis, copy, form, dtype, symmetrized):
|
||||
# The keyword argument `copy` is unused and has no effect here.
|
||||
del copy
|
||||
|
||||
if dtype is None:
|
||||
dtype = graph.dtype
|
||||
|
||||
graph_sum = np.asarray(graph.sum(axis=axis)).ravel()
|
||||
graph_diagonal = graph.diagonal()
|
||||
diag = graph_sum - graph_diagonal
|
||||
if symmetrized:
|
||||
graph_sum += np.asarray(graph.sum(axis=1 - axis)).ravel()
|
||||
diag = graph_sum - graph_diagonal - graph_diagonal
|
||||
|
||||
if normed:
|
||||
isolated_node_mask = diag == 0
|
||||
w = np.where(isolated_node_mask, 1, np.sqrt(diag))
|
||||
if symmetrized:
|
||||
md = _laplace_normed_sym(graph, graph_sum, 1.0 / w)
|
||||
else:
|
||||
md = _laplace_normed(graph, graph_sum, 1.0 / w)
|
||||
if form == "function":
|
||||
return md, w.astype(dtype, copy=False)
|
||||
elif form == "lo":
|
||||
m = _linearoperator(md, shape=graph.shape, dtype=dtype)
|
||||
return m, w.astype(dtype, copy=False)
|
||||
else:
|
||||
raise ValueError(f"Invalid form: {form!r}")
|
||||
else:
|
||||
if symmetrized:
|
||||
md = _laplace_sym(graph, graph_sum)
|
||||
else:
|
||||
md = _laplace(graph, graph_sum)
|
||||
if form == "function":
|
||||
return md, diag.astype(dtype, copy=False)
|
||||
elif form == "lo":
|
||||
m = _linearoperator(md, shape=graph.shape, dtype=dtype)
|
||||
return m, diag.astype(dtype, copy=False)
|
||||
else:
|
||||
raise ValueError(f"Invalid form: {form!r}")
|
||||
|
||||
|
||||
def _laplacian_sparse(graph, normed, axis, copy, form, dtype, symmetrized):
|
||||
# The keyword argument `form` is unused and has no effect here.
|
||||
del form
|
||||
|
||||
if dtype is None:
|
||||
dtype = graph.dtype
|
||||
|
||||
needs_copy = False
|
||||
if graph.format in ('lil', 'dok'):
|
||||
m = graph.tocoo()
|
||||
else:
|
||||
m = graph
|
||||
if copy:
|
||||
needs_copy = True
|
||||
|
||||
if symmetrized:
|
||||
m += m.T.conj()
|
||||
|
||||
w = np.asarray(m.sum(axis=axis)).ravel() - m.diagonal()
|
||||
if normed:
|
||||
m = m.tocoo(copy=needs_copy)
|
||||
isolated_node_mask = (w == 0)
|
||||
w = np.where(isolated_node_mask, 1, np.sqrt(w))
|
||||
m.data /= w[m.row]
|
||||
m.data /= w[m.col]
|
||||
m.data *= -1
|
||||
m.setdiag(1 - isolated_node_mask)
|
||||
else:
|
||||
if m.format == 'dia':
|
||||
m = m.copy()
|
||||
else:
|
||||
m = m.tocoo(copy=needs_copy)
|
||||
m.data *= -1
|
||||
m.setdiag(w)
|
||||
|
||||
return m.astype(dtype, copy=False), w.astype(dtype)
|
||||
|
||||
|
||||
def _laplacian_dense_flo(graph, normed, axis, copy, form, dtype, symmetrized):
|
||||
|
||||
if copy:
|
||||
m = np.array(graph)
|
||||
else:
|
||||
m = np.asarray(graph)
|
||||
|
||||
if dtype is None:
|
||||
dtype = m.dtype
|
||||
|
||||
graph_sum = m.sum(axis=axis)
|
||||
graph_diagonal = m.diagonal()
|
||||
diag = graph_sum - graph_diagonal
|
||||
if symmetrized:
|
||||
graph_sum += m.sum(axis=1 - axis)
|
||||
diag = graph_sum - graph_diagonal - graph_diagonal
|
||||
|
||||
if normed:
|
||||
isolated_node_mask = diag == 0
|
||||
w = np.where(isolated_node_mask, 1, np.sqrt(diag))
|
||||
if symmetrized:
|
||||
md = _laplace_normed_sym(m, graph_sum, 1.0 / w)
|
||||
else:
|
||||
md = _laplace_normed(m, graph_sum, 1.0 / w)
|
||||
if form == "function":
|
||||
return md, w.astype(dtype, copy=False)
|
||||
elif form == "lo":
|
||||
m = _linearoperator(md, shape=graph.shape, dtype=dtype)
|
||||
return m, w.astype(dtype, copy=False)
|
||||
else:
|
||||
raise ValueError(f"Invalid form: {form!r}")
|
||||
else:
|
||||
if symmetrized:
|
||||
md = _laplace_sym(m, graph_sum)
|
||||
else:
|
||||
md = _laplace(m, graph_sum)
|
||||
if form == "function":
|
||||
return md, diag.astype(dtype, copy=False)
|
||||
elif form == "lo":
|
||||
m = _linearoperator(md, shape=graph.shape, dtype=dtype)
|
||||
return m, diag.astype(dtype, copy=False)
|
||||
else:
|
||||
raise ValueError(f"Invalid form: {form!r}")
|
||||
|
||||
|
||||
def _laplacian_dense(graph, normed, axis, copy, form, dtype, symmetrized):
|
||||
|
||||
if form != "array":
|
||||
raise ValueError(f'{form!r} must be "array"')
|
||||
|
||||
if dtype is None:
|
||||
dtype = graph.dtype
|
||||
|
||||
if copy:
|
||||
m = np.array(graph)
|
||||
else:
|
||||
m = np.asarray(graph)
|
||||
|
||||
if dtype is None:
|
||||
dtype = m.dtype
|
||||
|
||||
if symmetrized:
|
||||
m += m.T.conj()
|
||||
np.fill_diagonal(m, 0)
|
||||
w = m.sum(axis=axis)
|
||||
if normed:
|
||||
isolated_node_mask = (w == 0)
|
||||
w = np.where(isolated_node_mask, 1, np.sqrt(w))
|
||||
m /= w
|
||||
m /= w[:, np.newaxis]
|
||||
m *= -1
|
||||
_setdiag_dense(m, 1 - isolated_node_mask)
|
||||
else:
|
||||
m *= -1
|
||||
_setdiag_dense(m, w)
|
||||
|
||||
return m.astype(dtype, copy=False), w.astype(dtype, copy=False)
|
||||
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|
|
@ -0,0 +1,66 @@
|
|||
import numpy as np
|
||||
from scipy.sparse import issparse
|
||||
from scipy.sparse._sputils import convert_pydata_sparse_to_scipy
|
||||
from scipy.sparse.csgraph._tools import (
|
||||
csgraph_to_dense, csgraph_from_dense,
|
||||
csgraph_masked_from_dense, csgraph_from_masked
|
||||
)
|
||||
|
||||
DTYPE = np.float64
|
||||
|
||||
|
||||
def validate_graph(csgraph, directed, dtype=DTYPE,
|
||||
csr_output=True, dense_output=True,
|
||||
copy_if_dense=False, copy_if_sparse=False,
|
||||
null_value_in=0, null_value_out=np.inf,
|
||||
infinity_null=True, nan_null=True):
|
||||
"""Routine for validation and conversion of csgraph inputs"""
|
||||
if not (csr_output or dense_output):
|
||||
raise ValueError("Internal: dense or csr output must be true")
|
||||
|
||||
accept_fv = [null_value_in]
|
||||
if infinity_null:
|
||||
accept_fv.append(np.inf)
|
||||
if nan_null:
|
||||
accept_fv.append(np.nan)
|
||||
csgraph = convert_pydata_sparse_to_scipy(csgraph, accept_fv=accept_fv)
|
||||
|
||||
# if undirected and csc storage, then transposing in-place
|
||||
# is quicker than later converting to csr.
|
||||
if (not directed) and issparse(csgraph) and csgraph.format == "csc":
|
||||
csgraph = csgraph.T
|
||||
|
||||
if issparse(csgraph):
|
||||
if csr_output:
|
||||
csgraph = csgraph.tocsr(copy=copy_if_sparse).astype(DTYPE, copy=False)
|
||||
else:
|
||||
csgraph = csgraph_to_dense(csgraph, null_value=null_value_out)
|
||||
elif np.ma.isMaskedArray(csgraph):
|
||||
if dense_output:
|
||||
mask = csgraph.mask
|
||||
csgraph = np.array(csgraph.data, dtype=DTYPE, copy=copy_if_dense)
|
||||
csgraph[mask] = null_value_out
|
||||
else:
|
||||
csgraph = csgraph_from_masked(csgraph)
|
||||
else:
|
||||
if dense_output:
|
||||
csgraph = csgraph_masked_from_dense(csgraph,
|
||||
copy=copy_if_dense,
|
||||
null_value=null_value_in,
|
||||
nan_null=nan_null,
|
||||
infinity_null=infinity_null)
|
||||
mask = csgraph.mask
|
||||
csgraph = np.asarray(csgraph.data, dtype=DTYPE)
|
||||
csgraph[mask] = null_value_out
|
||||
else:
|
||||
csgraph = csgraph_from_dense(csgraph, null_value=null_value_in,
|
||||
infinity_null=infinity_null,
|
||||
nan_null=nan_null)
|
||||
|
||||
if csgraph.ndim != 2:
|
||||
raise ValueError("compressed-sparse graph must be 2-D")
|
||||
|
||||
if csgraph.shape[0] != csgraph.shape[1]:
|
||||
raise ValueError("compressed-sparse graph must be shape (N, N)")
|
||||
|
||||
return csgraph
|
||||
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|
|
@ -0,0 +1,119 @@
|
|||
import numpy as np
|
||||
from numpy.testing import assert_equal, assert_array_almost_equal
|
||||
from scipy.sparse import csgraph, csr_array
|
||||
|
||||
|
||||
def test_weak_connections():
|
||||
Xde = np.array([[0, 1, 0],
|
||||
[0, 0, 0],
|
||||
[0, 0, 0]])
|
||||
|
||||
Xsp = csgraph.csgraph_from_dense(Xde, null_value=0)
|
||||
|
||||
for X in Xsp, Xde:
|
||||
n_components, labels =\
|
||||
csgraph.connected_components(X, directed=True,
|
||||
connection='weak')
|
||||
|
||||
assert_equal(n_components, 2)
|
||||
assert_array_almost_equal(labels, [0, 0, 1])
|
||||
|
||||
|
||||
def test_strong_connections():
|
||||
X1de = np.array([[0, 1, 0],
|
||||
[0, 0, 0],
|
||||
[0, 0, 0]])
|
||||
X2de = X1de + X1de.T
|
||||
|
||||
X1sp = csgraph.csgraph_from_dense(X1de, null_value=0)
|
||||
X2sp = csgraph.csgraph_from_dense(X2de, null_value=0)
|
||||
|
||||
for X in X1sp, X1de:
|
||||
n_components, labels =\
|
||||
csgraph.connected_components(X, directed=True,
|
||||
connection='strong')
|
||||
|
||||
assert_equal(n_components, 3)
|
||||
labels.sort()
|
||||
assert_array_almost_equal(labels, [0, 1, 2])
|
||||
|
||||
for X in X2sp, X2de:
|
||||
n_components, labels =\
|
||||
csgraph.connected_components(X, directed=True,
|
||||
connection='strong')
|
||||
|
||||
assert_equal(n_components, 2)
|
||||
labels.sort()
|
||||
assert_array_almost_equal(labels, [0, 0, 1])
|
||||
|
||||
|
||||
def test_strong_connections2():
|
||||
X = np.array([[0, 0, 0, 0, 0, 0],
|
||||
[1, 0, 1, 0, 0, 0],
|
||||
[0, 0, 0, 1, 0, 0],
|
||||
[0, 0, 1, 0, 1, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 1, 0]])
|
||||
n_components, labels =\
|
||||
csgraph.connected_components(X, directed=True,
|
||||
connection='strong')
|
||||
assert_equal(n_components, 5)
|
||||
labels.sort()
|
||||
assert_array_almost_equal(labels, [0, 1, 2, 2, 3, 4])
|
||||
|
||||
|
||||
def test_weak_connections2():
|
||||
X = np.array([[0, 0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 1, 0, 0],
|
||||
[0, 0, 1, 0, 1, 0],
|
||||
[0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 1, 0]])
|
||||
n_components, labels =\
|
||||
csgraph.connected_components(X, directed=True,
|
||||
connection='weak')
|
||||
assert_equal(n_components, 2)
|
||||
labels.sort()
|
||||
assert_array_almost_equal(labels, [0, 0, 1, 1, 1, 1])
|
||||
|
||||
|
||||
def test_ticket1876():
|
||||
# Regression test: this failed in the original implementation
|
||||
# There should be two strongly-connected components; previously gave one
|
||||
g = np.array([[0, 1, 1, 0],
|
||||
[1, 0, 0, 1],
|
||||
[0, 0, 0, 1],
|
||||
[0, 0, 1, 0]])
|
||||
n_components, labels = csgraph.connected_components(g, connection='strong')
|
||||
|
||||
assert_equal(n_components, 2)
|
||||
assert_equal(labels[0], labels[1])
|
||||
assert_equal(labels[2], labels[3])
|
||||
|
||||
|
||||
def test_fully_connected_graph():
|
||||
# Fully connected dense matrices raised an exception.
|
||||
# https://github.com/scipy/scipy/issues/3818
|
||||
g = np.ones((4, 4))
|
||||
n_components, labels = csgraph.connected_components(g)
|
||||
assert_equal(n_components, 1)
|
||||
|
||||
|
||||
def test_int64_indices_undirected():
|
||||
# See https://github.com/scipy/scipy/issues/18716
|
||||
g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
|
||||
assert g.indices.dtype == np.int64
|
||||
n, labels = csgraph.connected_components(g, directed=False)
|
||||
assert n == 1
|
||||
assert_array_almost_equal(labels, [0, 0])
|
||||
|
||||
|
||||
def test_int64_indices_directed():
|
||||
# See https://github.com/scipy/scipy/issues/18716
|
||||
g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
|
||||
assert g.indices.dtype == np.int64
|
||||
n, labels = csgraph.connected_components(g, directed=True,
|
||||
connection='strong')
|
||||
assert n == 2
|
||||
assert_array_almost_equal(labels, [1, 0])
|
||||
|
||||
|
|
@ -0,0 +1,61 @@
|
|||
import numpy as np
|
||||
from numpy.testing import assert_array_almost_equal
|
||||
from scipy.sparse import csr_array
|
||||
from scipy.sparse.csgraph import csgraph_from_dense, csgraph_to_dense
|
||||
|
||||
|
||||
def test_csgraph_from_dense():
|
||||
np.random.seed(1234)
|
||||
G = np.random.random((10, 10))
|
||||
some_nulls = (G < 0.4)
|
||||
all_nulls = (G < 0.8)
|
||||
|
||||
for null_value in [0, np.nan, np.inf]:
|
||||
G[all_nulls] = null_value
|
||||
with np.errstate(invalid="ignore"):
|
||||
G_csr = csgraph_from_dense(G, null_value=0)
|
||||
|
||||
G[all_nulls] = 0
|
||||
assert_array_almost_equal(G, G_csr.toarray())
|
||||
|
||||
for null_value in [np.nan, np.inf]:
|
||||
G[all_nulls] = 0
|
||||
G[some_nulls] = null_value
|
||||
with np.errstate(invalid="ignore"):
|
||||
G_csr = csgraph_from_dense(G, null_value=0)
|
||||
|
||||
G[all_nulls] = 0
|
||||
assert_array_almost_equal(G, G_csr.toarray())
|
||||
|
||||
|
||||
def test_csgraph_to_dense():
|
||||
np.random.seed(1234)
|
||||
G = np.random.random((10, 10))
|
||||
nulls = (G < 0.8)
|
||||
G[nulls] = np.inf
|
||||
|
||||
G_csr = csgraph_from_dense(G)
|
||||
|
||||
for null_value in [0, 10, -np.inf, np.inf]:
|
||||
G[nulls] = null_value
|
||||
assert_array_almost_equal(G, csgraph_to_dense(G_csr, null_value))
|
||||
|
||||
|
||||
def test_multiple_edges():
|
||||
# create a random square matrix with an even number of elements
|
||||
np.random.seed(1234)
|
||||
X = np.random.random((10, 10))
|
||||
Xcsr = csr_array(X)
|
||||
|
||||
# now double-up every other column
|
||||
Xcsr.indices[::2] = Xcsr.indices[1::2]
|
||||
|
||||
# normal sparse toarray() will sum the duplicated edges
|
||||
Xdense = Xcsr.toarray()
|
||||
assert_array_almost_equal(Xdense[:, 1::2],
|
||||
X[:, ::2] + X[:, 1::2])
|
||||
|
||||
# csgraph_to_dense chooses the minimum of each duplicated edge
|
||||
Xdense = csgraph_to_dense(Xcsr)
|
||||
assert_array_almost_equal(Xdense[:, 1::2],
|
||||
np.minimum(X[:, ::2], X[:, 1::2]))
|
||||
|
|
@ -0,0 +1,209 @@
|
|||
import numpy as np
|
||||
from numpy.testing import assert_array_equal
|
||||
import pytest
|
||||
|
||||
from scipy.sparse import csr_array, csc_array, csr_matrix
|
||||
from scipy.sparse.csgraph import maximum_flow
|
||||
from scipy.sparse.csgraph._flow import (
|
||||
_add_reverse_edges, _make_edge_pointers, _make_tails
|
||||
)
|
||||
|
||||
methods = ['edmonds_karp', 'dinic']
|
||||
|
||||
def test_raises_on_dense_input():
|
||||
with pytest.raises(TypeError):
|
||||
graph = np.array([[0, 1], [0, 0]])
|
||||
maximum_flow(graph, 0, 1)
|
||||
maximum_flow(graph, 0, 1, method='edmonds_karp')
|
||||
|
||||
|
||||
def test_raises_on_csc_input():
|
||||
with pytest.raises(TypeError):
|
||||
graph = csc_array([[0, 1], [0, 0]])
|
||||
maximum_flow(graph, 0, 1)
|
||||
maximum_flow(graph, 0, 1, method='edmonds_karp')
|
||||
|
||||
|
||||
def test_raises_on_floating_point_input():
|
||||
with pytest.raises(ValueError):
|
||||
graph = csr_array([[0, 1.5], [0, 0]], dtype=np.float64)
|
||||
maximum_flow(graph, 0, 1)
|
||||
maximum_flow(graph, 0, 1, method='edmonds_karp')
|
||||
|
||||
|
||||
def test_raises_on_non_square_input():
|
||||
with pytest.raises(ValueError):
|
||||
graph = csr_array([[0, 1, 2], [2, 1, 0]])
|
||||
maximum_flow(graph, 0, 1)
|
||||
|
||||
|
||||
def test_raises_when_source_is_sink():
|
||||
with pytest.raises(ValueError):
|
||||
graph = csr_array([[0, 1], [0, 0]])
|
||||
maximum_flow(graph, 0, 0)
|
||||
maximum_flow(graph, 0, 0, method='edmonds_karp')
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
@pytest.mark.parametrize('source', [-1, 2, 3])
|
||||
def test_raises_when_source_is_out_of_bounds(source, method):
|
||||
with pytest.raises(ValueError):
|
||||
graph = csr_array([[0, 1], [0, 0]])
|
||||
maximum_flow(graph, source, 1, method=method)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
@pytest.mark.parametrize('sink', [-1, 2, 3])
|
||||
def test_raises_when_sink_is_out_of_bounds(sink, method):
|
||||
with pytest.raises(ValueError):
|
||||
graph = csr_array([[0, 1], [0, 0]])
|
||||
maximum_flow(graph, 0, sink, method=method)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_simple_graph(method):
|
||||
# This graph looks as follows:
|
||||
# (0) --5--> (1)
|
||||
graph = csr_array([[0, 5], [0, 0]])
|
||||
res = maximum_flow(graph, 0, 1, method=method)
|
||||
assert res.flow_value == 5
|
||||
expected_flow = np.array([[0, 5], [-5, 0]])
|
||||
assert_array_equal(res.flow.toarray(), expected_flow)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_return_type(method):
|
||||
graph = csr_array([[0, 5], [0, 0]])
|
||||
assert isinstance(maximum_flow(graph, 0, 1, method=method).flow, csr_array)
|
||||
graph = csr_matrix([[0, 5], [0, 0]])
|
||||
assert isinstance(maximum_flow(graph, 0, 1, method=method).flow, csr_matrix)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_bottle_neck_graph(method):
|
||||
# This graph cannot use the full capacity between 0 and 1:
|
||||
# (0) --5--> (1) --3--> (2)
|
||||
graph = csr_array([[0, 5, 0], [0, 0, 3], [0, 0, 0]])
|
||||
res = maximum_flow(graph, 0, 2, method=method)
|
||||
assert res.flow_value == 3
|
||||
expected_flow = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
|
||||
assert_array_equal(res.flow.toarray(), expected_flow)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_backwards_flow(method):
|
||||
# This example causes backwards flow between vertices 3 and 4,
|
||||
# and so this test ensures that we handle that accordingly. See
|
||||
# https://stackoverflow.com/q/38843963/5085211
|
||||
# for more information.
|
||||
graph = csr_array([[0, 10, 0, 0, 10, 0, 0, 0],
|
||||
[0, 0, 10, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 10, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0, 0, 10],
|
||||
[0, 0, 0, 10, 0, 10, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0, 10, 0],
|
||||
[0, 0, 0, 0, 0, 0, 0, 10],
|
||||
[0, 0, 0, 0, 0, 0, 0, 0]])
|
||||
res = maximum_flow(graph, 0, 7, method=method)
|
||||
assert res.flow_value == 20
|
||||
expected_flow = np.array([[0, 10, 0, 0, 10, 0, 0, 0],
|
||||
[-10, 0, 10, 0, 0, 0, 0, 0],
|
||||
[0, -10, 0, 10, 0, 0, 0, 0],
|
||||
[0, 0, -10, 0, 0, 0, 0, 10],
|
||||
[-10, 0, 0, 0, 0, 10, 0, 0],
|
||||
[0, 0, 0, 0, -10, 0, 10, 0],
|
||||
[0, 0, 0, 0, 0, -10, 0, 10],
|
||||
[0, 0, 0, -10, 0, 0, -10, 0]])
|
||||
assert_array_equal(res.flow.toarray(), expected_flow)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_example_from_clrs_chapter_26_1(method):
|
||||
# See page 659 in CLRS second edition, but note that the maximum flow
|
||||
# we find is slightly different than the one in CLRS; we push a flow of
|
||||
# 12 to v_1 instead of v_2.
|
||||
graph = csr_array([[0, 16, 13, 0, 0, 0],
|
||||
[0, 0, 10, 12, 0, 0],
|
||||
[0, 4, 0, 0, 14, 0],
|
||||
[0, 0, 9, 0, 0, 20],
|
||||
[0, 0, 0, 7, 0, 4],
|
||||
[0, 0, 0, 0, 0, 0]])
|
||||
res = maximum_flow(graph, 0, 5, method=method)
|
||||
assert res.flow_value == 23
|
||||
expected_flow = np.array([[0, 12, 11, 0, 0, 0],
|
||||
[-12, 0, 0, 12, 0, 0],
|
||||
[-11, 0, 0, 0, 11, 0],
|
||||
[0, -12, 0, 0, -7, 19],
|
||||
[0, 0, -11, 7, 0, 4],
|
||||
[0, 0, 0, -19, -4, 0]])
|
||||
assert_array_equal(res.flow.toarray(), expected_flow)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_disconnected_graph(method):
|
||||
# This tests the following disconnected graph:
|
||||
# (0) --5--> (1) (2) --3--> (3)
|
||||
graph = csr_array([[0, 5, 0, 0],
|
||||
[0, 0, 0, 0],
|
||||
[0, 0, 9, 3],
|
||||
[0, 0, 0, 0]])
|
||||
res = maximum_flow(graph, 0, 3, method=method)
|
||||
assert res.flow_value == 0
|
||||
expected_flow = np.zeros((4, 4), dtype=np.int32)
|
||||
assert_array_equal(res.flow.toarray(), expected_flow)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_add_reverse_edges_large_graph(method):
|
||||
# Regression test for https://github.com/scipy/scipy/issues/14385
|
||||
n = 100_000
|
||||
indices = np.arange(1, n)
|
||||
indptr = np.array(list(range(n)) + [n - 1])
|
||||
data = np.ones(n - 1, dtype=np.int32)
|
||||
graph = csr_array((data, indices, indptr), shape=(n, n))
|
||||
res = maximum_flow(graph, 0, n - 1, method=method)
|
||||
assert res.flow_value == 1
|
||||
expected_flow = graph - graph.transpose()
|
||||
assert_array_equal(res.flow.data, expected_flow.data)
|
||||
assert_array_equal(res.flow.indices, expected_flow.indices)
|
||||
assert_array_equal(res.flow.indptr, expected_flow.indptr)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("a,b_data_expected", [
|
||||
([[]], []),
|
||||
([[0], [0]], []),
|
||||
([[1, 0, 2], [0, 0, 0], [0, 3, 0]], [1, 2, 0, 0, 3]),
|
||||
([[9, 8, 7], [4, 5, 6], [0, 0, 0]], [9, 8, 7, 4, 5, 6, 0, 0])])
|
||||
def test_add_reverse_edges(a, b_data_expected):
|
||||
"""Test that the reversal of the edges of the input graph works
|
||||
as expected.
|
||||
"""
|
||||
a = csr_array(a, dtype=np.int32, shape=(len(a), len(a)))
|
||||
b = _add_reverse_edges(a)
|
||||
assert_array_equal(b.data, b_data_expected)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("a,expected", [
|
||||
([[]], []),
|
||||
([[0]], []),
|
||||
([[1]], [0]),
|
||||
([[0, 1], [10, 0]], [1, 0]),
|
||||
([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 3, 4, 1, 2])
|
||||
])
|
||||
def test_make_edge_pointers(a, expected):
|
||||
a = csr_array(a, dtype=np.int32)
|
||||
rev_edge_ptr = _make_edge_pointers(a)
|
||||
assert_array_equal(rev_edge_ptr, expected)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("a,expected", [
|
||||
([[]], []),
|
||||
([[0]], []),
|
||||
([[1]], [0]),
|
||||
([[0, 1], [10, 0]], [0, 1]),
|
||||
([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 0, 1, 2, 2])
|
||||
])
|
||||
def test_make_tails(a, expected):
|
||||
a = csr_array(a, dtype=np.int32)
|
||||
tails = _make_tails(a)
|
||||
assert_array_equal(tails, expected)
|
||||
|
|
@ -0,0 +1,368 @@
|
|||
import pytest
|
||||
import numpy as np
|
||||
from numpy.testing import assert_allclose
|
||||
from pytest import raises as assert_raises
|
||||
from scipy import sparse
|
||||
|
||||
from scipy.sparse import csgraph
|
||||
from scipy._lib._util import np_long, np_ulong
|
||||
|
||||
|
||||
def check_int_type(mat):
|
||||
return np.issubdtype(mat.dtype, np.signedinteger) or np.issubdtype(
|
||||
mat.dtype, np_ulong
|
||||
)
|
||||
|
||||
|
||||
def test_laplacian_value_error():
|
||||
for t in int, float, complex:
|
||||
for m in ([1, 1],
|
||||
[[[1]]],
|
||||
[[1, 2, 3], [4, 5, 6]],
|
||||
[[1, 2], [3, 4], [5, 5]]):
|
||||
A = np.array(m, dtype=t)
|
||||
assert_raises(ValueError, csgraph.laplacian, A)
|
||||
|
||||
|
||||
def _explicit_laplacian(x, normed=False):
|
||||
if sparse.issparse(x):
|
||||
x = x.toarray()
|
||||
x = np.asarray(x)
|
||||
y = -1.0 * x
|
||||
for j in range(y.shape[0]):
|
||||
y[j,j] = x[j,j+1:].sum() + x[j,:j].sum()
|
||||
if normed:
|
||||
d = np.diag(y).copy()
|
||||
d[d == 0] = 1.0
|
||||
y /= d[:,None]**.5
|
||||
y /= d[None,:]**.5
|
||||
return y
|
||||
|
||||
|
||||
def _check_symmetric_graph_laplacian(mat, normed, copy=True):
|
||||
if not hasattr(mat, 'shape'):
|
||||
mat = eval(mat, dict(np=np, sparse=sparse))
|
||||
|
||||
if sparse.issparse(mat):
|
||||
sp_mat = mat
|
||||
mat = sp_mat.toarray()
|
||||
else:
|
||||
sp_mat = sparse.csr_array(mat)
|
||||
|
||||
mat_copy = np.copy(mat)
|
||||
sp_mat_copy = sparse.csr_array(sp_mat, copy=True)
|
||||
|
||||
n_nodes = mat.shape[0]
|
||||
explicit_laplacian = _explicit_laplacian(mat, normed=normed)
|
||||
laplacian = csgraph.laplacian(mat, normed=normed, copy=copy)
|
||||
sp_laplacian = csgraph.laplacian(sp_mat, normed=normed,
|
||||
copy=copy)
|
||||
|
||||
if copy:
|
||||
assert_allclose(mat, mat_copy)
|
||||
_assert_allclose_sparse(sp_mat, sp_mat_copy)
|
||||
else:
|
||||
if not (normed and check_int_type(mat)):
|
||||
assert_allclose(laplacian, mat)
|
||||
if sp_mat.format == 'coo':
|
||||
_assert_allclose_sparse(sp_laplacian, sp_mat)
|
||||
|
||||
assert_allclose(laplacian, sp_laplacian.toarray())
|
||||
|
||||
for tested in [laplacian, sp_laplacian.toarray()]:
|
||||
if not normed:
|
||||
assert_allclose(tested.sum(axis=0), np.zeros(n_nodes))
|
||||
assert_allclose(tested.T, tested)
|
||||
assert_allclose(tested, explicit_laplacian)
|
||||
|
||||
|
||||
def test_symmetric_graph_laplacian():
|
||||
symmetric_mats = (
|
||||
'np.arange(10) * np.arange(10)[:, np.newaxis]',
|
||||
'np.ones((7, 7))',
|
||||
'np.eye(19)',
|
||||
'sparse.diags([1, 1], [-1, 1], shape=(4, 4))',
|
||||
'sparse.diags([1, 1], [-1, 1], shape=(4, 4)).toarray()',
|
||||
'sparse.diags([1, 1], [-1, 1], shape=(4, 4)).todense()',
|
||||
'np.vander(np.arange(4)) + np.vander(np.arange(4)).T'
|
||||
)
|
||||
for mat in symmetric_mats:
|
||||
for normed in True, False:
|
||||
for copy in True, False:
|
||||
_check_symmetric_graph_laplacian(mat, normed, copy)
|
||||
|
||||
|
||||
def _assert_allclose_sparse(a, b, **kwargs):
|
||||
# helper function that can deal with sparse matrices
|
||||
if sparse.issparse(a):
|
||||
a = a.toarray()
|
||||
if sparse.issparse(b):
|
||||
b = b.toarray()
|
||||
assert_allclose(a, b, **kwargs)
|
||||
|
||||
|
||||
def _check_laplacian_dtype_none(
|
||||
A, desired_L, desired_d, normed, use_out_degree, copy, dtype, arr_type
|
||||
):
|
||||
mat = arr_type(A, dtype=dtype)
|
||||
L, d = csgraph.laplacian(
|
||||
mat,
|
||||
normed=normed,
|
||||
return_diag=True,
|
||||
use_out_degree=use_out_degree,
|
||||
copy=copy,
|
||||
dtype=None,
|
||||
)
|
||||
if normed and check_int_type(mat):
|
||||
assert L.dtype == np.float64
|
||||
assert d.dtype == np.float64
|
||||
_assert_allclose_sparse(L, desired_L, atol=1e-12)
|
||||
_assert_allclose_sparse(d, desired_d, atol=1e-12)
|
||||
else:
|
||||
assert L.dtype == dtype
|
||||
assert d.dtype == dtype
|
||||
desired_L = np.asarray(desired_L).astype(dtype)
|
||||
desired_d = np.asarray(desired_d).astype(dtype)
|
||||
_assert_allclose_sparse(L, desired_L, atol=1e-12)
|
||||
_assert_allclose_sparse(d, desired_d, atol=1e-12)
|
||||
|
||||
if not copy:
|
||||
if not (normed and check_int_type(mat)):
|
||||
if type(mat) is np.ndarray:
|
||||
assert_allclose(L, mat)
|
||||
elif mat.format == "coo":
|
||||
_assert_allclose_sparse(L, mat)
|
||||
|
||||
|
||||
def _check_laplacian_dtype(
|
||||
A, desired_L, desired_d, normed, use_out_degree, copy, dtype, arr_type
|
||||
):
|
||||
mat = arr_type(A, dtype=dtype)
|
||||
L, d = csgraph.laplacian(
|
||||
mat,
|
||||
normed=normed,
|
||||
return_diag=True,
|
||||
use_out_degree=use_out_degree,
|
||||
copy=copy,
|
||||
dtype=dtype,
|
||||
)
|
||||
assert L.dtype == dtype
|
||||
assert d.dtype == dtype
|
||||
desired_L = np.asarray(desired_L).astype(dtype)
|
||||
desired_d = np.asarray(desired_d).astype(dtype)
|
||||
_assert_allclose_sparse(L, desired_L, atol=1e-12)
|
||||
_assert_allclose_sparse(d, desired_d, atol=1e-12)
|
||||
|
||||
if not copy:
|
||||
if not (normed and check_int_type(mat)):
|
||||
if type(mat) is np.ndarray:
|
||||
assert_allclose(L, mat)
|
||||
elif mat.format == 'coo':
|
||||
_assert_allclose_sparse(L, mat)
|
||||
|
||||
|
||||
INT_DTYPES = (np.intc, np_long, np.longlong)
|
||||
REAL_DTYPES = (np.float32, np.float64, np.longdouble)
|
||||
COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
|
||||
DTYPES = INT_DTYPES + REAL_DTYPES + COMPLEX_DTYPES
|
||||
|
||||
|
||||
@pytest.mark.parametrize("dtype", DTYPES)
|
||||
@pytest.mark.parametrize("arr_type", [np.array,
|
||||
sparse.csr_matrix,
|
||||
sparse.coo_matrix,
|
||||
sparse.csr_array,
|
||||
sparse.coo_array])
|
||||
@pytest.mark.parametrize("copy", [True, False])
|
||||
@pytest.mark.parametrize("normed", [True, False])
|
||||
@pytest.mark.parametrize("use_out_degree", [True, False])
|
||||
def test_asymmetric_laplacian(use_out_degree, normed,
|
||||
copy, dtype, arr_type):
|
||||
# adjacency matrix
|
||||
A = [[0, 1, 0],
|
||||
[4, 2, 0],
|
||||
[0, 0, 0]]
|
||||
A = arr_type(np.array(A), dtype=dtype)
|
||||
A_copy = A.copy()
|
||||
|
||||
if not normed and use_out_degree:
|
||||
# Laplacian matrix using out-degree
|
||||
L = [[1, -1, 0],
|
||||
[-4, 4, 0],
|
||||
[0, 0, 0]]
|
||||
d = [1, 4, 0]
|
||||
|
||||
if normed and use_out_degree:
|
||||
# normalized Laplacian matrix using out-degree
|
||||
L = [[1, -0.5, 0],
|
||||
[-2, 1, 0],
|
||||
[0, 0, 0]]
|
||||
d = [1, 2, 1]
|
||||
|
||||
if not normed and not use_out_degree:
|
||||
# Laplacian matrix using in-degree
|
||||
L = [[4, -1, 0],
|
||||
[-4, 1, 0],
|
||||
[0, 0, 0]]
|
||||
d = [4, 1, 0]
|
||||
|
||||
if normed and not use_out_degree:
|
||||
# normalized Laplacian matrix using in-degree
|
||||
L = [[1, -0.5, 0],
|
||||
[-2, 1, 0],
|
||||
[0, 0, 0]]
|
||||
d = [2, 1, 1]
|
||||
|
||||
_check_laplacian_dtype_none(
|
||||
A,
|
||||
L,
|
||||
d,
|
||||
normed=normed,
|
||||
use_out_degree=use_out_degree,
|
||||
copy=copy,
|
||||
dtype=dtype,
|
||||
arr_type=arr_type,
|
||||
)
|
||||
|
||||
_check_laplacian_dtype(
|
||||
A_copy,
|
||||
L,
|
||||
d,
|
||||
normed=normed,
|
||||
use_out_degree=use_out_degree,
|
||||
copy=copy,
|
||||
dtype=dtype,
|
||||
arr_type=arr_type,
|
||||
)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("fmt", ['csr', 'csc', 'coo', 'lil',
|
||||
'dok', 'dia', 'bsr'])
|
||||
@pytest.mark.parametrize("normed", [True, False])
|
||||
@pytest.mark.parametrize("copy", [True, False])
|
||||
def test_sparse_formats(fmt, normed, copy):
|
||||
mat = sparse.diags_array([1, 1], offsets=[-1, 1], shape=(4, 4), format=fmt)
|
||||
_check_symmetric_graph_laplacian(mat, normed, copy)
|
||||
|
||||
|
||||
@pytest.mark.parametrize(
|
||||
"arr_type", [np.asarray,
|
||||
sparse.csr_matrix,
|
||||
sparse.coo_matrix,
|
||||
sparse.csr_array,
|
||||
sparse.coo_array]
|
||||
)
|
||||
@pytest.mark.parametrize("form", ["array", "function", "lo"])
|
||||
def test_laplacian_symmetrized(arr_type, form):
|
||||
# adjacency matrix
|
||||
n = 3
|
||||
mat = arr_type(np.arange(n * n).reshape(n, n))
|
||||
L_in, d_in = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
form=form,
|
||||
)
|
||||
L_out, d_out = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
use_out_degree=True,
|
||||
form=form,
|
||||
)
|
||||
Ls, ds = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
symmetrized=True,
|
||||
form=form,
|
||||
)
|
||||
Ls_normed, ds_normed = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
symmetrized=True,
|
||||
normed=True,
|
||||
form=form,
|
||||
)
|
||||
mat += mat.T
|
||||
Lss, dss = csgraph.laplacian(mat, return_diag=True, form=form)
|
||||
Lss_normed, dss_normed = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
normed=True,
|
||||
form=form,
|
||||
)
|
||||
|
||||
assert_allclose(ds, d_in + d_out)
|
||||
assert_allclose(ds, dss)
|
||||
assert_allclose(ds_normed, dss_normed)
|
||||
|
||||
d = {}
|
||||
for L in ["L_in", "L_out", "Ls", "Ls_normed", "Lss", "Lss_normed"]:
|
||||
if form == "array":
|
||||
d[L] = eval(L)
|
||||
else:
|
||||
d[L] = eval(L)(np.eye(n, dtype=mat.dtype))
|
||||
|
||||
_assert_allclose_sparse(d["Ls"], d["L_in"] + d["L_out"].T)
|
||||
_assert_allclose_sparse(d["Ls"], d["Lss"])
|
||||
_assert_allclose_sparse(d["Ls_normed"], d["Lss_normed"])
|
||||
|
||||
|
||||
@pytest.mark.parametrize(
|
||||
"arr_type", [np.asarray,
|
||||
sparse.csr_matrix,
|
||||
sparse.coo_matrix,
|
||||
sparse.csr_array,
|
||||
sparse.coo_array]
|
||||
)
|
||||
@pytest.mark.parametrize("dtype", DTYPES)
|
||||
@pytest.mark.parametrize("normed", [True, False])
|
||||
@pytest.mark.parametrize("symmetrized", [True, False])
|
||||
@pytest.mark.parametrize("use_out_degree", [True, False])
|
||||
@pytest.mark.parametrize("form", ["function", "lo"])
|
||||
def test_format(dtype, arr_type, normed, symmetrized, use_out_degree, form):
|
||||
n = 3
|
||||
mat = [[0, 1, 0], [4, 2, 0], [0, 0, 0]]
|
||||
mat = arr_type(np.array(mat), dtype=dtype)
|
||||
Lo, do = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
normed=normed,
|
||||
symmetrized=symmetrized,
|
||||
use_out_degree=use_out_degree,
|
||||
dtype=dtype,
|
||||
)
|
||||
La, da = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
normed=normed,
|
||||
symmetrized=symmetrized,
|
||||
use_out_degree=use_out_degree,
|
||||
dtype=dtype,
|
||||
form="array",
|
||||
)
|
||||
assert_allclose(do, da)
|
||||
_assert_allclose_sparse(Lo, La)
|
||||
|
||||
L, d = csgraph.laplacian(
|
||||
mat,
|
||||
return_diag=True,
|
||||
normed=normed,
|
||||
symmetrized=symmetrized,
|
||||
use_out_degree=use_out_degree,
|
||||
dtype=dtype,
|
||||
form=form,
|
||||
)
|
||||
assert_allclose(d, do)
|
||||
assert d.dtype == dtype
|
||||
Lm = L(np.eye(n, dtype=mat.dtype)).astype(dtype)
|
||||
_assert_allclose_sparse(Lm, Lo, rtol=2e-7, atol=2e-7)
|
||||
x = np.arange(6).reshape(3, 2)
|
||||
if not (normed and dtype in INT_DTYPES):
|
||||
assert_allclose(L(x), Lo @ x)
|
||||
else:
|
||||
# Normalized Lo is casted to integer, but L() is not
|
||||
pass
|
||||
|
||||
|
||||
def test_format_error_message():
|
||||
with pytest.raises(ValueError, match="Invalid form: 'toto'"):
|
||||
_ = csgraph.laplacian(np.eye(1), form='toto')
|
||||
|
|
@ -0,0 +1,307 @@
|
|||
from itertools import product
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_array_equal, assert_equal
|
||||
import pytest
|
||||
|
||||
from scipy.sparse import csr_array, coo_array, diags_array
|
||||
from scipy.sparse.csgraph import (
|
||||
maximum_bipartite_matching, min_weight_full_bipartite_matching
|
||||
)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_raises_on_dense_input():
|
||||
with pytest.raises(TypeError):
|
||||
graph = np.array([[0, 1], [0, 0]])
|
||||
maximum_bipartite_matching(graph)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_empty_graph():
|
||||
graph = csr_array((0, 0))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
expected_matching = np.array([])
|
||||
assert_array_equal(expected_matching, x)
|
||||
assert_array_equal(expected_matching, y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_empty_left_partition():
|
||||
graph = csr_array((2, 0))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
assert_array_equal(np.array([]), x)
|
||||
assert_array_equal(np.array([-1, -1]), y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_empty_right_partition():
|
||||
graph = csr_array((0, 3))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
assert_array_equal(np.array([-1, -1, -1]), x)
|
||||
assert_array_equal(np.array([]), y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_graph_with_no_edges():
|
||||
graph = csr_array((2, 2))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
assert_array_equal(np.array([-1, -1]), x)
|
||||
assert_array_equal(np.array([-1, -1]), y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_graph_that_causes_augmentation():
|
||||
# In this graph, column 1 is initially assigned to row 1, but it should be
|
||||
# reassigned to make room for row 2.
|
||||
graph = csr_array([[1, 1], [1, 0]])
|
||||
x = maximum_bipartite_matching(graph, perm_type='column')
|
||||
y = maximum_bipartite_matching(graph, perm_type='row')
|
||||
expected_matching = np.array([1, 0])
|
||||
assert_array_equal(expected_matching, x)
|
||||
assert_array_equal(expected_matching, y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_graph_with_more_rows_than_columns():
|
||||
graph = csr_array([[1, 1], [1, 0], [0, 1]])
|
||||
x = maximum_bipartite_matching(graph, perm_type='column')
|
||||
y = maximum_bipartite_matching(graph, perm_type='row')
|
||||
assert_array_equal(np.array([0, -1, 1]), x)
|
||||
assert_array_equal(np.array([0, 2]), y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_graph_with_more_columns_than_rows():
|
||||
graph = csr_array([[1, 1, 0], [0, 0, 1]])
|
||||
x = maximum_bipartite_matching(graph, perm_type='column')
|
||||
y = maximum_bipartite_matching(graph, perm_type='row')
|
||||
assert_array_equal(np.array([0, 2]), x)
|
||||
assert_array_equal(np.array([0, -1, 1]), y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_explicit_zeros_count_as_edges():
|
||||
data = [0, 0]
|
||||
indices = [1, 0]
|
||||
indptr = [0, 1, 2]
|
||||
graph = csr_array((data, indices, indptr), shape=(2, 2))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
expected_matching = np.array([1, 0])
|
||||
assert_array_equal(expected_matching, x)
|
||||
assert_array_equal(expected_matching, y)
|
||||
|
||||
|
||||
def test_maximum_bipartite_matching_feasibility_of_result():
|
||||
# This is a regression test for GitHub issue #11458
|
||||
data = np.ones(50, dtype=int)
|
||||
indices = [11, 12, 19, 22, 23, 5, 22, 3, 8, 10, 5, 6, 11, 12, 13, 5, 13,
|
||||
14, 20, 22, 3, 15, 3, 13, 14, 11, 12, 19, 22, 23, 5, 22, 3, 8,
|
||||
10, 5, 6, 11, 12, 13, 5, 13, 14, 20, 22, 3, 15, 3, 13, 14]
|
||||
indptr = [0, 5, 7, 10, 10, 15, 20, 22, 22, 23, 25, 30, 32, 35, 35, 40, 45,
|
||||
47, 47, 48, 50]
|
||||
graph = csr_array((data, indices, indptr), shape=(20, 25))
|
||||
x = maximum_bipartite_matching(graph, perm_type='row')
|
||||
y = maximum_bipartite_matching(graph, perm_type='column')
|
||||
assert (x != -1).sum() == 13
|
||||
assert (y != -1).sum() == 13
|
||||
# Ensure that each element of the matching is in fact an edge in the graph.
|
||||
for u, v in zip(range(graph.shape[0]), y):
|
||||
if v != -1:
|
||||
assert graph[u, v]
|
||||
for u, v in zip(x, range(graph.shape[1])):
|
||||
if u != -1:
|
||||
assert graph[u, v]
|
||||
|
||||
|
||||
def test_matching_large_random_graph_with_one_edge_incident_to_each_vertex():
|
||||
np.random.seed(42)
|
||||
A = diags_array(np.ones(25), offsets=0, format='csr')
|
||||
rand_perm = np.random.permutation(25)
|
||||
rand_perm2 = np.random.permutation(25)
|
||||
|
||||
Rrow = np.arange(25)
|
||||
Rcol = rand_perm
|
||||
Rdata = np.ones(25, dtype=int)
|
||||
Rmat = csr_array((Rdata, (Rrow, Rcol)))
|
||||
|
||||
Crow = rand_perm2
|
||||
Ccol = np.arange(25)
|
||||
Cdata = np.ones(25, dtype=int)
|
||||
Cmat = csr_array((Cdata, (Crow, Ccol)))
|
||||
# Randomly permute identity matrix
|
||||
B = Rmat @ A @ Cmat
|
||||
|
||||
# Row permute
|
||||
perm = maximum_bipartite_matching(B, perm_type='row')
|
||||
Rrow = np.arange(25)
|
||||
Rcol = perm
|
||||
Rdata = np.ones(25, dtype=int)
|
||||
Rmat = csr_array((Rdata, (Rrow, Rcol)))
|
||||
C1 = Rmat @ B
|
||||
|
||||
# Column permute
|
||||
perm2 = maximum_bipartite_matching(B, perm_type='column')
|
||||
Crow = perm2
|
||||
Ccol = np.arange(25)
|
||||
Cdata = np.ones(25, dtype=int)
|
||||
Cmat = csr_array((Cdata, (Crow, Ccol)))
|
||||
C2 = B @ Cmat
|
||||
|
||||
# Should get identity matrix back
|
||||
assert_equal(any(C1.diagonal() == 0), False)
|
||||
assert_equal(any(C2.diagonal() == 0), False)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('num_rows,num_cols', [(0, 0), (2, 0), (0, 3)])
|
||||
def test_min_weight_full_matching_trivial_graph(num_rows, num_cols):
|
||||
biadjacency = csr_array((num_cols, num_rows))
|
||||
biadjacency1 = coo_array((num_cols, num_rows))
|
||||
|
||||
row_ind, col_ind = min_weight_full_bipartite_matching(biadjacency)
|
||||
assert len(row_ind) == 0
|
||||
assert len(col_ind) == 0
|
||||
|
||||
row_ind1, col_ind1 = min_weight_full_bipartite_matching(biadjacency1)
|
||||
assert len(row_ind1) == 0
|
||||
assert len(col_ind1) == 0
|
||||
|
||||
|
||||
@pytest.mark.parametrize('biadjacency',
|
||||
[
|
||||
[[1, 1, 1], [1, 0, 0], [1, 0, 0]],
|
||||
[[1, 1, 1], [0, 0, 1], [0, 0, 1]],
|
||||
[[1, 0, 0, 1], [1, 1, 0, 1], [0, 0, 0, 0]],
|
||||
[[1, 0, 0], [2, 0, 0]],
|
||||
[[0, 1, 0], [0, 2, 0]],
|
||||
[[1, 0], [2, 0], [5, 0]]
|
||||
])
|
||||
def test_min_weight_full_matching_infeasible_problems(biadjacency):
|
||||
with pytest.raises(ValueError):
|
||||
min_weight_full_bipartite_matching(csr_array(biadjacency))
|
||||
with pytest.raises(ValueError):
|
||||
min_weight_full_bipartite_matching(coo_array(biadjacency))
|
||||
|
||||
|
||||
def test_min_weight_full_matching_large_infeasible():
|
||||
# Regression test for GitHub issue #17269
|
||||
a = np.asarray([
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001],
|
||||
[0.0, 0.11687445, 0.0, 0.0, 0.01319788, 0.07509257, 0.0,
|
||||
0.0, 0.0, 0.74228317, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.81087935, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.8408466, 0.0, 0.0, 0.0, 0.0, 0.01194389,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.82994211, 0.0, 0.0, 0.0, 0.11468516, 0.0, 0.0, 0.0,
|
||||
0.11173505, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0],
|
||||
[0.18796507, 0.0, 0.04002318, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75883335,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.71545464, 0.0, 0.0, 0.0, 0.0, 0.0, 0.02748488,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.78470564, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14829198,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.10870609, 0.0, 0.0, 0.0, 0.8918677, 0.0, 0.0, 0.0, 0.06306644,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.63844085, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7442354, 0.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09850549, 0.0, 0.0, 0.18638258,
|
||||
0.2769244, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.73182464, 0.0, 0.0, 0.46443561,
|
||||
0.38589284, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
|
||||
[0.29510278, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09666032, 0.0,
|
||||
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
|
||||
])
|
||||
with pytest.raises(ValueError, match='no full matching exists'):
|
||||
min_weight_full_bipartite_matching(csr_array(a))
|
||||
with pytest.raises(ValueError, match='no full matching exists'):
|
||||
min_weight_full_bipartite_matching(coo_array(a))
|
||||
|
||||
|
||||
@pytest.mark.thread_unsafe
|
||||
def test_explicit_zero_causes_warning():
|
||||
biadjacency = csr_array(((2, 0, 3), (0, 1, 1), (0, 2, 3)))
|
||||
with pytest.warns(UserWarning):
|
||||
min_weight_full_bipartite_matching(biadjacency)
|
||||
with pytest.warns(UserWarning):
|
||||
min_weight_full_bipartite_matching(biadjacency.tocoo())
|
||||
|
||||
|
||||
# General test for linear sum assignment solvers to make it possible to rely
|
||||
# on the same tests for scipy.optimize.linear_sum_assignment.
|
||||
def linear_sum_assignment_assertions(
|
||||
solver, array_type, sign, test_case
|
||||
):
|
||||
cost_matrix, expected_cost = test_case
|
||||
maximize = sign == -1
|
||||
cost_matrix = sign * array_type(cost_matrix)
|
||||
expected_cost = sign * np.array(expected_cost)
|
||||
|
||||
row_ind, col_ind = solver(cost_matrix, maximize=maximize)
|
||||
assert_array_equal(row_ind, np.sort(row_ind))
|
||||
assert_array_equal(expected_cost,
|
||||
np.array(cost_matrix[row_ind, col_ind]).flatten())
|
||||
|
||||
cost_matrix = cost_matrix.T
|
||||
row_ind, col_ind = solver(cost_matrix, maximize=maximize)
|
||||
assert_array_equal(row_ind, np.sort(row_ind))
|
||||
assert_array_equal(np.sort(expected_cost),
|
||||
np.sort(np.array(
|
||||
cost_matrix[row_ind, col_ind])).flatten())
|
||||
|
||||
|
||||
linear_sum_assignment_test_cases = product(
|
||||
[-1, 1],
|
||||
[
|
||||
# Square
|
||||
([[400, 150, 400],
|
||||
[400, 450, 600],
|
||||
[300, 225, 300]],
|
||||
[150, 400, 300]),
|
||||
|
||||
# Rectangular variant
|
||||
([[400, 150, 400, 1],
|
||||
[400, 450, 600, 2],
|
||||
[300, 225, 300, 3]],
|
||||
[150, 2, 300]),
|
||||
|
||||
([[10, 10, 8],
|
||||
[9, 8, 1],
|
||||
[9, 7, 4]],
|
||||
[10, 1, 7]),
|
||||
|
||||
# Square
|
||||
([[10, 10, 8, 11],
|
||||
[9, 8, 1, 1],
|
||||
[9, 7, 4, 10]],
|
||||
[10, 1, 4]),
|
||||
|
||||
# Rectangular variant
|
||||
([[10, float("inf"), float("inf")],
|
||||
[float("inf"), float("inf"), 1],
|
||||
[float("inf"), 7, float("inf")]],
|
||||
[10, 1, 7])
|
||||
])
|
||||
|
||||
|
||||
@pytest.mark.parametrize('sign,test_case', linear_sum_assignment_test_cases)
|
||||
def test_min_weight_full_matching_small_inputs(sign, test_case):
|
||||
linear_sum_assignment_assertions(
|
||||
min_weight_full_bipartite_matching, csr_array, sign, test_case)
|
||||
|
|
@ -0,0 +1,197 @@
|
|||
import pytest
|
||||
|
||||
import numpy as np
|
||||
import scipy.sparse as sp
|
||||
import scipy.sparse.csgraph as spgraph
|
||||
from scipy._lib import _pep440
|
||||
|
||||
from numpy.testing import assert_equal
|
||||
|
||||
try:
|
||||
import sparse
|
||||
except Exception:
|
||||
sparse = None
|
||||
|
||||
pytestmark = pytest.mark.skipif(sparse is None,
|
||||
reason="pydata/sparse not installed")
|
||||
|
||||
|
||||
msg = "pydata/sparse (0.15.1) does not implement necessary operations"
|
||||
|
||||
|
||||
sparse_params = (pytest.param("COO"),
|
||||
pytest.param("DOK", marks=[pytest.mark.xfail(reason=msg)]))
|
||||
|
||||
|
||||
def check_sparse_version(min_ver):
|
||||
if sparse is None:
|
||||
return pytest.mark.skip(reason="sparse is not installed")
|
||||
return pytest.mark.skipif(
|
||||
_pep440.parse(sparse.__version__) < _pep440.Version(min_ver),
|
||||
reason=f"sparse version >= {min_ver} required"
|
||||
)
|
||||
|
||||
|
||||
@pytest.fixture(params=sparse_params)
|
||||
def sparse_cls(request):
|
||||
return getattr(sparse, request.param)
|
||||
|
||||
|
||||
@pytest.fixture
|
||||
def graphs(sparse_cls):
|
||||
graph = [
|
||||
[0, 1, 1, 0, 0],
|
||||
[0, 0, 1, 0, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 1],
|
||||
[0, 0, 0, 0, 0],
|
||||
]
|
||||
A_dense = np.array(graph)
|
||||
A_sparse = sparse_cls(A_dense)
|
||||
return A_dense, A_sparse
|
||||
|
||||
|
||||
@pytest.mark.parametrize(
|
||||
"func",
|
||||
[
|
||||
spgraph.shortest_path,
|
||||
spgraph.dijkstra,
|
||||
spgraph.floyd_warshall,
|
||||
spgraph.bellman_ford,
|
||||
spgraph.johnson,
|
||||
spgraph.reverse_cuthill_mckee,
|
||||
spgraph.maximum_bipartite_matching,
|
||||
spgraph.structural_rank,
|
||||
]
|
||||
)
|
||||
def test_csgraph_equiv(func, graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
actual = func(A_sparse)
|
||||
desired = func(sp.csc_array(A_dense))
|
||||
assert_equal(actual, desired)
|
||||
|
||||
|
||||
def test_connected_components(graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
func = spgraph.connected_components
|
||||
|
||||
actual_comp, actual_labels = func(A_sparse)
|
||||
desired_comp, desired_labels, = func(sp.csc_array(A_dense))
|
||||
|
||||
assert actual_comp == desired_comp
|
||||
assert_equal(actual_labels, desired_labels)
|
||||
|
||||
|
||||
def test_laplacian(graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
sparse_cls = type(A_sparse)
|
||||
func = spgraph.laplacian
|
||||
|
||||
actual = func(A_sparse)
|
||||
desired = func(sp.csc_array(A_dense))
|
||||
|
||||
assert isinstance(actual, sparse_cls)
|
||||
|
||||
assert_equal(actual.todense(), desired.todense())
|
||||
|
||||
|
||||
@pytest.mark.parametrize(
|
||||
"func", [spgraph.breadth_first_order, spgraph.depth_first_order]
|
||||
)
|
||||
def test_order_search(graphs, func):
|
||||
A_dense, A_sparse = graphs
|
||||
|
||||
actual = func(A_sparse, 0)
|
||||
desired = func(sp.csc_array(A_dense), 0)
|
||||
|
||||
assert_equal(actual, desired)
|
||||
|
||||
|
||||
@pytest.mark.parametrize(
|
||||
"func", [spgraph.breadth_first_tree, spgraph.depth_first_tree]
|
||||
)
|
||||
def test_tree_search(graphs, func):
|
||||
A_dense, A_sparse = graphs
|
||||
sparse_cls = type(A_sparse)
|
||||
|
||||
actual = func(A_sparse, 0)
|
||||
desired = func(sp.csc_array(A_dense), 0)
|
||||
|
||||
assert isinstance(actual, sparse_cls)
|
||||
|
||||
assert_equal(actual.todense(), desired.todense())
|
||||
|
||||
|
||||
def test_minimum_spanning_tree(graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
sparse_cls = type(A_sparse)
|
||||
func = spgraph.minimum_spanning_tree
|
||||
|
||||
actual = func(A_sparse)
|
||||
desired = func(sp.csc_array(A_dense))
|
||||
|
||||
assert isinstance(actual, sparse_cls)
|
||||
|
||||
assert_equal(actual.todense(), desired.todense())
|
||||
|
||||
|
||||
def test_maximum_flow(graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
sparse_cls = type(A_sparse)
|
||||
func = spgraph.maximum_flow
|
||||
|
||||
actual = func(A_sparse, 0, 2)
|
||||
desired = func(sp.csr_array(A_dense), 0, 2)
|
||||
|
||||
assert actual.flow_value == desired.flow_value
|
||||
assert isinstance(actual.flow, sparse_cls)
|
||||
|
||||
assert_equal(actual.flow.todense(), desired.flow.todense())
|
||||
|
||||
|
||||
def test_min_weight_full_bipartite_matching(graphs):
|
||||
A_dense, A_sparse = graphs
|
||||
func = spgraph.min_weight_full_bipartite_matching
|
||||
|
||||
actual = func(A_sparse[0:2, 1:3])
|
||||
A_csc = sp.csc_array(A_dense)
|
||||
desired = func(A_csc[0:2, 1:3])
|
||||
desired1 = func(A_csc[0:2, 1:3].tocoo())
|
||||
|
||||
assert_equal(actual, desired)
|
||||
assert_equal(actual, desired1)
|
||||
|
||||
|
||||
@check_sparse_version("0.15.4")
|
||||
@pytest.mark.parametrize(
|
||||
"func",
|
||||
[
|
||||
spgraph.shortest_path,
|
||||
spgraph.dijkstra,
|
||||
spgraph.floyd_warshall,
|
||||
spgraph.bellman_ford,
|
||||
spgraph.johnson,
|
||||
spgraph.minimum_spanning_tree,
|
||||
]
|
||||
)
|
||||
@pytest.mark.parametrize(
|
||||
"fill_value, comp_func",
|
||||
[(np.inf, np.isposinf), (np.nan, np.isnan)],
|
||||
)
|
||||
def test_nonzero_fill_value(graphs, func, fill_value, comp_func):
|
||||
A_dense, A_sparse = graphs
|
||||
A_sparse = A_sparse.astype(float)
|
||||
A_sparse.fill_value = fill_value
|
||||
sparse_cls = type(A_sparse)
|
||||
|
||||
actual = func(A_sparse)
|
||||
desired = func(sp.csc_array(A_dense))
|
||||
|
||||
if func == spgraph.minimum_spanning_tree:
|
||||
assert isinstance(actual, sparse_cls)
|
||||
assert comp_func(actual.fill_value)
|
||||
actual = actual.todense()
|
||||
actual[comp_func(actual)] = 0.0
|
||||
assert_equal(actual, desired.todense())
|
||||
else:
|
||||
assert_equal(actual, desired)
|
||||
|
|
@ -0,0 +1,70 @@
|
|||
import numpy as np
|
||||
from numpy.testing import assert_equal
|
||||
from scipy.sparse.csgraph import reverse_cuthill_mckee, structural_rank
|
||||
from scipy.sparse import csc_array, csr_array, coo_array
|
||||
|
||||
|
||||
def test_graph_reverse_cuthill_mckee():
|
||||
A = np.array([[1, 0, 0, 0, 1, 0, 0, 0],
|
||||
[0, 1, 1, 0, 0, 1, 0, 1],
|
||||
[0, 1, 1, 0, 1, 0, 0, 0],
|
||||
[0, 0, 0, 1, 0, 0, 1, 0],
|
||||
[1, 0, 1, 0, 1, 0, 0, 0],
|
||||
[0, 1, 0, 0, 0, 1, 0, 1],
|
||||
[0, 0, 0, 1, 0, 0, 1, 0],
|
||||
[0, 1, 0, 0, 0, 1, 0, 1]], dtype=int)
|
||||
|
||||
graph = csr_array(A)
|
||||
perm = reverse_cuthill_mckee(graph)
|
||||
correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
|
||||
assert_equal(perm, correct_perm)
|
||||
|
||||
# Test int64 indices input
|
||||
graph.indices = graph.indices.astype('int64')
|
||||
graph.indptr = graph.indptr.astype('int64')
|
||||
perm = reverse_cuthill_mckee(graph, True)
|
||||
assert_equal(perm, correct_perm)
|
||||
|
||||
|
||||
def test_graph_reverse_cuthill_mckee_ordering():
|
||||
data = np.ones(63,dtype=int)
|
||||
rows = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2,
|
||||
2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
|
||||
6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9,
|
||||
9, 10, 10, 10, 10, 10, 11, 11, 11, 11,
|
||||
12, 12, 12, 13, 13, 13, 13, 14, 14, 14,
|
||||
14, 15, 15, 15, 15, 15])
|
||||
cols = np.array([0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2,
|
||||
7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7, 13,
|
||||
15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13,
|
||||
1, 9, 11, 0, 2, 8, 10, 15, 1, 3, 9, 11,
|
||||
4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14,
|
||||
5, 7, 10, 13, 15])
|
||||
graph = csr_array((data, (rows,cols)))
|
||||
perm = reverse_cuthill_mckee(graph)
|
||||
correct_perm = np.array([12, 14, 4, 6, 10, 8, 2, 15,
|
||||
0, 13, 7, 5, 9, 11, 1, 3])
|
||||
assert_equal(perm, correct_perm)
|
||||
|
||||
|
||||
def test_graph_structural_rank():
|
||||
# Test square matrix #1
|
||||
A = csc_array([[1, 1, 0],
|
||||
[1, 0, 1],
|
||||
[0, 1, 0]])
|
||||
assert_equal(structural_rank(A), 3)
|
||||
|
||||
# Test square matrix #2
|
||||
rows = np.array([0,0,0,0,0,1,1,2,2,3,3,3,3,3,3,4,4,5,5,6,6,7,7])
|
||||
cols = np.array([0,1,2,3,4,2,5,2,6,0,1,3,5,6,7,4,5,5,6,2,6,2,4])
|
||||
data = np.ones_like(rows)
|
||||
B = coo_array((data,(rows,cols)), shape=(8,8))
|
||||
assert_equal(structural_rank(B), 6)
|
||||
|
||||
#Test non-square matrix
|
||||
C = csc_array([[1, 0, 2, 0],
|
||||
[2, 0, 4, 0]])
|
||||
assert_equal(structural_rank(C), 2)
|
||||
|
||||
#Test tall matrix
|
||||
assert_equal(structural_rank(C.T), 2)
|
||||
|
|
@ -0,0 +1,540 @@
|
|||
from io import StringIO
|
||||
import warnings
|
||||
import numpy as np
|
||||
from numpy.testing import assert_array_almost_equal, assert_array_equal, assert_allclose
|
||||
from pytest import raises as assert_raises
|
||||
from scipy.sparse.csgraph import (shortest_path, dijkstra, johnson,
|
||||
bellman_ford, construct_dist_matrix, yen,
|
||||
NegativeCycleError)
|
||||
import scipy.sparse
|
||||
from scipy.io import mmread
|
||||
import pytest
|
||||
|
||||
directed_G = np.array([[0, 3, 3, 0, 0],
|
||||
[0, 0, 0, 2, 4],
|
||||
[0, 0, 0, 0, 0],
|
||||
[1, 0, 0, 0, 0],
|
||||
[2, 0, 0, 2, 0]], dtype=float)
|
||||
|
||||
# Undirected version of directed_G
|
||||
undirected_G = np.array([[0, 3, 3, 1, 2],
|
||||
[3, 0, 0, 2, 4],
|
||||
[3, 0, 0, 0, 0],
|
||||
[1, 2, 0, 0, 2],
|
||||
[2, 4, 0, 2, 0]], dtype=float)
|
||||
|
||||
unweighted_G = (directed_G > 0).astype(float)
|
||||
|
||||
# Correct shortest path lengths for directed_G and undirected_G
|
||||
directed_SP = [[0, 3, 3, 5, 7],
|
||||
[3, 0, 6, 2, 4],
|
||||
[np.inf, np.inf, 0, np.inf, np.inf],
|
||||
[1, 4, 4, 0, 8],
|
||||
[2, 5, 5, 2, 0]]
|
||||
|
||||
directed_2SP_0_to_3 = [[-9999, 0, -9999, 1, -9999],
|
||||
[-9999, 0, -9999, 4, 1]]
|
||||
|
||||
undirected_SP = np.array([[0, 3, 3, 1, 2],
|
||||
[3, 0, 6, 2, 4],
|
||||
[3, 6, 0, 4, 5],
|
||||
[1, 2, 4, 0, 2],
|
||||
[2, 4, 5, 2, 0]], dtype=float)
|
||||
|
||||
undirected_SP_limit_2 = np.array([[0, np.inf, np.inf, 1, 2],
|
||||
[np.inf, 0, np.inf, 2, np.inf],
|
||||
[np.inf, np.inf, 0, np.inf, np.inf],
|
||||
[1, 2, np.inf, 0, 2],
|
||||
[2, np.inf, np.inf, 2, 0]], dtype=float)
|
||||
|
||||
undirected_SP_limit_0 = np.ones((5, 5), dtype=float) - np.eye(5)
|
||||
undirected_SP_limit_0[undirected_SP_limit_0 > 0] = np.inf
|
||||
|
||||
# Correct predecessors for directed_G and undirected_G
|
||||
directed_pred = np.array([[-9999, 0, 0, 1, 1],
|
||||
[3, -9999, 0, 1, 1],
|
||||
[-9999, -9999, -9999, -9999, -9999],
|
||||
[3, 0, 0, -9999, 1],
|
||||
[4, 0, 0, 4, -9999]], dtype=float)
|
||||
|
||||
undirected_pred = np.array([[-9999, 0, 0, 0, 0],
|
||||
[1, -9999, 0, 1, 1],
|
||||
[2, 0, -9999, 0, 0],
|
||||
[3, 3, 0, -9999, 3],
|
||||
[4, 4, 0, 4, -9999]], dtype=float)
|
||||
|
||||
# Other graphs
|
||||
directed_sparse_zero_G = scipy.sparse.csr_array(
|
||||
(
|
||||
[0, 1, 2, 3, 1],
|
||||
([0, 1, 2, 3, 4], [1, 2, 0, 4, 3]),
|
||||
),
|
||||
shape=(5, 5),
|
||||
)
|
||||
|
||||
directed_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
|
||||
[3, 0, 1, np.inf, np.inf],
|
||||
[2, 2, 0, np.inf, np.inf],
|
||||
[np.inf, np.inf, np.inf, 0, 3],
|
||||
[np.inf, np.inf, np.inf, 1, 0]]
|
||||
|
||||
undirected_sparse_zero_G = scipy.sparse.csr_array(
|
||||
(
|
||||
[0, 0, 1, 1, 2, 2, 1, 1],
|
||||
([0, 1, 1, 2, 2, 0, 3, 4], [1, 0, 2, 1, 0, 2, 4, 3])
|
||||
),
|
||||
shape=(5, 5),
|
||||
)
|
||||
|
||||
undirected_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
|
||||
[0, 0, 1, np.inf, np.inf],
|
||||
[1, 1, 0, np.inf, np.inf],
|
||||
[np.inf, np.inf, np.inf, 0, 1],
|
||||
[np.inf, np.inf, np.inf, 1, 0]]
|
||||
|
||||
directed_negative_weighted_G = np.array([[0, 0, 0],
|
||||
[-1, 0, 0],
|
||||
[0, -1, 0]], dtype=float)
|
||||
|
||||
directed_negative_weighted_SP = np.array([[0, np.inf, np.inf],
|
||||
[-1, 0, np.inf],
|
||||
[-2, -1, 0]], dtype=float)
|
||||
|
||||
methods = ['auto', 'FW', 'D', 'BF', 'J']
|
||||
|
||||
|
||||
def test_dijkstra_limit():
|
||||
limits = [0, 2, np.inf]
|
||||
results = [undirected_SP_limit_0,
|
||||
undirected_SP_limit_2,
|
||||
undirected_SP]
|
||||
|
||||
def check(limit, result):
|
||||
SP = dijkstra(undirected_G, directed=False, limit=limit)
|
||||
assert_array_almost_equal(SP, result)
|
||||
|
||||
for limit, result in zip(limits, results):
|
||||
check(limit, result)
|
||||
|
||||
|
||||
def test_directed():
|
||||
def check(method):
|
||||
SP = shortest_path(directed_G, method=method, directed=True,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP, directed_SP)
|
||||
|
||||
for method in methods:
|
||||
check(method)
|
||||
|
||||
|
||||
def test_undirected():
|
||||
def check(method, directed_in):
|
||||
if directed_in:
|
||||
SP1 = shortest_path(directed_G, method=method, directed=False,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP1, undirected_SP)
|
||||
else:
|
||||
SP2 = shortest_path(undirected_G, method=method, directed=True,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP2, undirected_SP)
|
||||
|
||||
for method in methods:
|
||||
for directed_in in (True, False):
|
||||
check(method, directed_in)
|
||||
|
||||
|
||||
def test_directed_sparse_zero():
|
||||
# test directed sparse graph with zero-weight edge and two connected components
|
||||
def check(method):
|
||||
SP = shortest_path(directed_sparse_zero_G, method=method, directed=True,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP, directed_sparse_zero_SP)
|
||||
|
||||
for method in methods:
|
||||
check(method)
|
||||
|
||||
|
||||
def test_undirected_sparse_zero():
|
||||
def check(method, directed_in):
|
||||
if directed_in:
|
||||
SP1 = shortest_path(directed_sparse_zero_G, method=method, directed=False,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP1, undirected_sparse_zero_SP)
|
||||
else:
|
||||
SP2 = shortest_path(undirected_sparse_zero_G, method=method, directed=True,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP2, undirected_sparse_zero_SP)
|
||||
|
||||
for method in methods:
|
||||
for directed_in in (True, False):
|
||||
check(method, directed_in)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('directed, SP_ans',
|
||||
((True, directed_SP),
|
||||
(False, undirected_SP)))
|
||||
@pytest.mark.parametrize('indices', ([0, 2, 4], [0, 4], [3, 4], [0, 0]))
|
||||
def test_dijkstra_indices_min_only(directed, SP_ans, indices):
|
||||
SP_ans = np.array(SP_ans)
|
||||
indices = np.array(indices, dtype=np.int64)
|
||||
min_ind_ans = indices[np.argmin(SP_ans[indices, :], axis=0)]
|
||||
min_d_ans = np.zeros(SP_ans.shape[0], SP_ans.dtype)
|
||||
for k in range(SP_ans.shape[0]):
|
||||
min_d_ans[k] = SP_ans[min_ind_ans[k], k]
|
||||
min_ind_ans[np.isinf(min_d_ans)] = -9999
|
||||
|
||||
SP, pred, sources = dijkstra(directed_G,
|
||||
directed=directed,
|
||||
indices=indices,
|
||||
min_only=True,
|
||||
return_predecessors=True)
|
||||
assert_array_almost_equal(SP, min_d_ans)
|
||||
assert_array_equal(min_ind_ans, sources)
|
||||
SP = dijkstra(directed_G,
|
||||
directed=directed,
|
||||
indices=indices,
|
||||
min_only=True,
|
||||
return_predecessors=False)
|
||||
assert_array_almost_equal(SP, min_d_ans)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('n', (10, 100, 1000))
|
||||
def test_dijkstra_min_only_random(n):
|
||||
rng = np.random.default_rng(7345782358920239234)
|
||||
data = scipy.sparse.random_array((n, n), density=0.5, format='lil',
|
||||
rng=rng, dtype=np.float64)
|
||||
data.setdiag(np.zeros(n, dtype=np.bool_))
|
||||
# choose some random vertices
|
||||
v = np.arange(n)
|
||||
rng.shuffle(v)
|
||||
indices = v[:int(n*.1)]
|
||||
ds, pred, sources = dijkstra(data,
|
||||
directed=True,
|
||||
indices=indices,
|
||||
min_only=True,
|
||||
return_predecessors=True)
|
||||
for k in range(n):
|
||||
p = pred[k]
|
||||
s = sources[k]
|
||||
while p != -9999:
|
||||
assert sources[p] == s
|
||||
p = pred[p]
|
||||
|
||||
|
||||
@pytest.mark.parametrize('n', (10, 100))
|
||||
@pytest.mark.parametrize("method", ['FW', 'J', 'BF'])
|
||||
@pytest.mark.parametrize('directed', (True, False))
|
||||
def test_star_graph(n, method, directed):
|
||||
# Build the star graph
|
||||
star_arr = np.zeros((n, n), dtype=float)
|
||||
star_center_idx = 0
|
||||
star_arr[star_center_idx, :] = star_arr[:, star_center_idx] = range(n)
|
||||
G = scipy.sparse.csr_matrix(star_arr, shape=(n, n))
|
||||
# Build the distances matrix
|
||||
SP_solution = np.zeros((n, n), dtype=float)
|
||||
SP_solution[:] = star_arr[star_center_idx]
|
||||
for idx in range(1, n):
|
||||
SP_solution[idx] += star_arr[idx, star_center_idx]
|
||||
np.fill_diagonal(SP_solution, 0)
|
||||
|
||||
SP = shortest_path(G, method=method, directed=directed)
|
||||
assert_allclose(
|
||||
SP_solution, SP
|
||||
)
|
||||
|
||||
|
||||
def test_dijkstra_random():
|
||||
# reproduces the hang observed in gh-17782
|
||||
n = 10
|
||||
indices = [0, 4, 4, 5, 7, 9, 0, 6, 2, 3, 7, 9, 1, 2, 9, 2, 5, 6]
|
||||
indptr = [0, 0, 2, 5, 6, 7, 8, 12, 15, 18, 18]
|
||||
data = [0.33629, 0.40458, 0.47493, 0.42757, 0.11497, 0.91653, 0.69084,
|
||||
0.64979, 0.62555, 0.743, 0.01724, 0.99945, 0.31095, 0.15557,
|
||||
0.02439, 0.65814, 0.23478, 0.24072]
|
||||
graph = scipy.sparse.csr_array((data, indices, indptr), shape=(n, n))
|
||||
dijkstra(graph, directed=True, return_predecessors=True)
|
||||
|
||||
|
||||
def test_gh_17782_segfault():
|
||||
text = """%%MatrixMarket matrix coordinate real general
|
||||
84 84 22
|
||||
2 1 4.699999809265137e+00
|
||||
6 14 1.199999973177910e-01
|
||||
9 6 1.199999973177910e-01
|
||||
10 16 2.012000083923340e+01
|
||||
11 10 1.422000026702881e+01
|
||||
12 1 9.645999908447266e+01
|
||||
13 18 2.012000083923340e+01
|
||||
14 13 4.679999828338623e+00
|
||||
15 11 1.199999973177910e-01
|
||||
16 12 1.199999973177910e-01
|
||||
18 15 1.199999973177910e-01
|
||||
32 2 2.299999952316284e+00
|
||||
33 20 6.000000000000000e+00
|
||||
33 32 5.000000000000000e+00
|
||||
36 9 3.720000028610229e+00
|
||||
36 37 3.720000028610229e+00
|
||||
36 38 3.720000028610229e+00
|
||||
37 44 8.159999847412109e+00
|
||||
38 32 7.903999328613281e+01
|
||||
43 20 2.400000000000000e+01
|
||||
43 33 4.000000000000000e+00
|
||||
44 43 6.028000259399414e+01
|
||||
"""
|
||||
data = mmread(StringIO(text), spmatrix=False)
|
||||
dijkstra(data, directed=True, return_predecessors=True)
|
||||
|
||||
|
||||
def test_shortest_path_indices():
|
||||
indices = np.arange(4)
|
||||
|
||||
def check(func, indshape):
|
||||
outshape = indshape + (5,)
|
||||
SP = func(directed_G, directed=False,
|
||||
indices=indices.reshape(indshape))
|
||||
assert_array_almost_equal(SP, undirected_SP[indices].reshape(outshape))
|
||||
|
||||
for indshape in [(4,), (4, 1), (2, 2)]:
|
||||
for func in (dijkstra, bellman_ford, johnson, shortest_path):
|
||||
check(func, indshape)
|
||||
|
||||
assert_raises(ValueError, shortest_path, directed_G, method='FW',
|
||||
indices=indices)
|
||||
|
||||
|
||||
def test_predecessors():
|
||||
SP_res = {True: directed_SP,
|
||||
False: undirected_SP}
|
||||
pred_res = {True: directed_pred,
|
||||
False: undirected_pred}
|
||||
|
||||
def check(method, directed):
|
||||
SP, pred = shortest_path(directed_G, method, directed=directed,
|
||||
overwrite=False,
|
||||
return_predecessors=True)
|
||||
assert_array_almost_equal(SP, SP_res[directed])
|
||||
assert_array_almost_equal(pred, pred_res[directed])
|
||||
|
||||
for method in methods:
|
||||
for directed in (True, False):
|
||||
check(method, directed)
|
||||
|
||||
|
||||
def test_construct_shortest_path():
|
||||
def check(method, directed):
|
||||
SP1, pred = shortest_path(directed_G,
|
||||
directed=directed,
|
||||
overwrite=False,
|
||||
return_predecessors=True)
|
||||
SP2 = construct_dist_matrix(directed_G, pred, directed=directed)
|
||||
assert_array_almost_equal(SP1, SP2)
|
||||
|
||||
for method in methods:
|
||||
for directed in (True, False):
|
||||
check(method, directed)
|
||||
|
||||
@pytest.mark.parametrize("directed", [True, False])
|
||||
def test_construct_dist_matrix_predecessors_error(directed):
|
||||
SP1, pred = shortest_path(directed_G,
|
||||
directed=directed,
|
||||
overwrite=False,
|
||||
return_predecessors=True)
|
||||
assert_raises(TypeError, construct_dist_matrix,
|
||||
directed_G, pred.astype(np.int64), directed)
|
||||
|
||||
|
||||
def test_unweighted_path():
|
||||
def check(method, directed):
|
||||
SP1 = shortest_path(directed_G,
|
||||
directed=directed,
|
||||
overwrite=False,
|
||||
unweighted=True)
|
||||
SP2 = shortest_path(unweighted_G,
|
||||
directed=directed,
|
||||
overwrite=False,
|
||||
unweighted=False)
|
||||
assert_array_almost_equal(SP1, SP2)
|
||||
|
||||
for method in methods:
|
||||
for directed in (True, False):
|
||||
check(method, directed)
|
||||
|
||||
|
||||
def test_negative_cycles():
|
||||
# create a small graph with a negative cycle
|
||||
graph = np.ones([5, 5])
|
||||
graph.flat[::6] = 0
|
||||
graph[1, 2] = -2
|
||||
|
||||
def check(method, directed):
|
||||
assert_raises(NegativeCycleError, shortest_path, graph, method,
|
||||
directed)
|
||||
|
||||
for directed in (True, False):
|
||||
for method in ['FW', 'J', 'BF']:
|
||||
check(method, directed)
|
||||
|
||||
assert_raises(NegativeCycleError, yen, graph, 0, 1, 1,
|
||||
directed=directed)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("method", ['FW', 'J', 'BF'])
|
||||
def test_negative_weights(method):
|
||||
SP = shortest_path(directed_negative_weighted_G, method, directed=True)
|
||||
assert_allclose(SP, directed_negative_weighted_SP, atol=1e-10)
|
||||
|
||||
|
||||
def test_masked_input():
|
||||
np.ma.masked_equal(directed_G, 0)
|
||||
|
||||
def check(method):
|
||||
SP = shortest_path(directed_G, method=method, directed=True,
|
||||
overwrite=False)
|
||||
assert_array_almost_equal(SP, directed_SP)
|
||||
|
||||
for method in methods:
|
||||
check(method)
|
||||
|
||||
|
||||
def test_overwrite():
|
||||
G = np.array([[0, 3, 3, 1, 2],
|
||||
[3, 0, 0, 2, 4],
|
||||
[3, 0, 0, 0, 0],
|
||||
[1, 2, 0, 0, 2],
|
||||
[2, 4, 0, 2, 0]], dtype=float)
|
||||
foo = G.copy()
|
||||
shortest_path(foo, overwrite=False)
|
||||
assert_array_equal(foo, G)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('method', methods)
|
||||
def test_buffer(method):
|
||||
# Smoke test that sparse matrices with read-only buffers (e.g., those from
|
||||
# joblib workers) do not cause::
|
||||
#
|
||||
# ValueError: buffer source array is read-only
|
||||
#
|
||||
G = scipy.sparse.csr_array([[1.]])
|
||||
G.data.flags['WRITEABLE'] = False
|
||||
shortest_path(G, method=method)
|
||||
|
||||
|
||||
def test_NaN_warnings():
|
||||
with warnings.catch_warnings(record=True) as record:
|
||||
shortest_path(np.array([[0, 1], [np.nan, 0]]))
|
||||
for r in record:
|
||||
assert r.category is not RuntimeWarning
|
||||
|
||||
|
||||
def test_sparse_matrices():
|
||||
# Test that using lil,csr and csc sparse matrix do not cause error
|
||||
G_dense = np.array([[0, 3, 0, 0, 0],
|
||||
[0, 0, -1, 0, 0],
|
||||
[0, 0, 0, 2, 0],
|
||||
[0, 0, 0, 0, 4],
|
||||
[0, 0, 0, 0, 0]], dtype=float)
|
||||
SP = shortest_path(G_dense)
|
||||
G_csr = scipy.sparse.csr_array(G_dense)
|
||||
G_csc = scipy.sparse.csc_array(G_dense)
|
||||
G_lil = scipy.sparse.lil_array(G_dense)
|
||||
assert_array_almost_equal(SP, shortest_path(G_csr))
|
||||
assert_array_almost_equal(SP, shortest_path(G_csc))
|
||||
assert_array_almost_equal(SP, shortest_path(G_lil))
|
||||
|
||||
|
||||
def test_yen_directed():
|
||||
distances, predecessors = yen(
|
||||
directed_G,
|
||||
source=0,
|
||||
sink=3,
|
||||
K=2,
|
||||
return_predecessors=True
|
||||
)
|
||||
assert_allclose(distances, [5., 9.])
|
||||
assert_allclose(predecessors, directed_2SP_0_to_3)
|
||||
|
||||
|
||||
def test_yen_dense():
|
||||
dense_undirected_G = np.array([
|
||||
[0, 3, 3, 1, 2],
|
||||
[3, 0, 7, 6, 5],
|
||||
[3, 7, 0, 4, 0],
|
||||
[1, 6, 4, 0, 2],
|
||||
[2, 5, 0, 2, 0]], dtype=float)
|
||||
distances = yen(
|
||||
dense_undirected_G,
|
||||
source=0,
|
||||
sink=4,
|
||||
K=5,
|
||||
directed=False,
|
||||
)
|
||||
assert_allclose(distances, [2., 3., 8., 9., 11.])
|
||||
|
||||
|
||||
def test_yen_undirected():
|
||||
distances = yen(
|
||||
undirected_G,
|
||||
source=0,
|
||||
sink=3,
|
||||
K=4,
|
||||
directed=False,
|
||||
)
|
||||
assert_allclose(distances, [1., 4., 5., 8.])
|
||||
|
||||
|
||||
def test_yen_unweighted():
|
||||
# Ask for more paths than there are, verify only the available paths are returned
|
||||
distances, predecessors = yen(
|
||||
directed_G,
|
||||
source=0,
|
||||
sink=3,
|
||||
K=4,
|
||||
unweighted=True,
|
||||
return_predecessors=True,
|
||||
)
|
||||
assert_allclose(distances, [2., 3.])
|
||||
assert_allclose(predecessors, directed_2SP_0_to_3)
|
||||
|
||||
|
||||
def test_yen_no_paths():
|
||||
distances = yen(
|
||||
directed_G,
|
||||
source=2,
|
||||
sink=3,
|
||||
K=1,
|
||||
)
|
||||
assert distances.size == 0
|
||||
|
||||
|
||||
def test_yen_negative_weights():
|
||||
distances = yen(
|
||||
directed_negative_weighted_G,
|
||||
source=2,
|
||||
sink=0,
|
||||
K=1,
|
||||
)
|
||||
assert_allclose(distances, [-2.])
|
||||
|
||||
|
||||
@pytest.mark.parametrize("min_only", (True, False))
|
||||
@pytest.mark.parametrize("directed", (True, False))
|
||||
@pytest.mark.parametrize("return_predecessors", (True, False))
|
||||
@pytest.mark.parametrize("index_dtype", (np.int32, np.int64))
|
||||
@pytest.mark.parametrize("indices", (None, [1]))
|
||||
def test_20904(min_only, directed, return_predecessors, index_dtype, indices):
|
||||
"""Test two failures from gh-20904: int32 and indices-as-None."""
|
||||
adj_mat = scipy.sparse.eye_array(4, format="csr")
|
||||
adj_mat = scipy.sparse.csr_array(
|
||||
(
|
||||
adj_mat.data,
|
||||
adj_mat.indices.astype(index_dtype),
|
||||
adj_mat.indptr.astype(index_dtype),
|
||||
),
|
||||
)
|
||||
dijkstra(
|
||||
adj_mat,
|
||||
directed,
|
||||
indices=indices,
|
||||
min_only=min_only,
|
||||
return_predecessors=return_predecessors,
|
||||
)
|
||||
|
|
@ -0,0 +1,66 @@
|
|||
"""Test the minimum spanning tree function"""
|
||||
import numpy as np
|
||||
from numpy.testing import assert_
|
||||
import numpy.testing as npt
|
||||
from scipy.sparse import csr_array
|
||||
from scipy.sparse.csgraph import minimum_spanning_tree
|
||||
|
||||
|
||||
def test_minimum_spanning_tree():
|
||||
|
||||
# Create a graph with two connected components.
|
||||
graph = [[0,1,0,0,0],
|
||||
[1,0,0,0,0],
|
||||
[0,0,0,8,5],
|
||||
[0,0,8,0,1],
|
||||
[0,0,5,1,0]]
|
||||
graph = np.asarray(graph)
|
||||
|
||||
# Create the expected spanning tree.
|
||||
expected = [[0,1,0,0,0],
|
||||
[0,0,0,0,0],
|
||||
[0,0,0,0,5],
|
||||
[0,0,0,0,1],
|
||||
[0,0,0,0,0]]
|
||||
expected = np.asarray(expected)
|
||||
|
||||
# Ensure minimum spanning tree code gives this expected output.
|
||||
csgraph = csr_array(graph)
|
||||
mintree = minimum_spanning_tree(csgraph)
|
||||
mintree_array = mintree.toarray()
|
||||
npt.assert_array_equal(mintree_array, expected,
|
||||
'Incorrect spanning tree found.')
|
||||
|
||||
# Ensure that the original graph was not modified.
|
||||
npt.assert_array_equal(csgraph.toarray(), graph,
|
||||
'Original graph was modified.')
|
||||
|
||||
# Now let the algorithm modify the csgraph in place.
|
||||
mintree = minimum_spanning_tree(csgraph, overwrite=True)
|
||||
npt.assert_array_equal(mintree.toarray(), expected,
|
||||
'Graph was not properly modified to contain MST.')
|
||||
|
||||
np.random.seed(1234)
|
||||
for N in (5, 10, 15, 20):
|
||||
|
||||
# Create a random graph.
|
||||
graph = 3 + np.random.random((N, N))
|
||||
csgraph = csr_array(graph)
|
||||
|
||||
# The spanning tree has at most N - 1 edges.
|
||||
mintree = minimum_spanning_tree(csgraph)
|
||||
assert_(mintree.nnz < N)
|
||||
|
||||
# Set the sub diagonal to 1 to create a known spanning tree.
|
||||
idx = np.arange(N-1)
|
||||
graph[idx,idx+1] = 1
|
||||
csgraph = csr_array(graph)
|
||||
mintree = minimum_spanning_tree(csgraph)
|
||||
|
||||
# We expect to see this pattern in the spanning tree and otherwise
|
||||
# have this zero.
|
||||
expected = np.zeros((N, N))
|
||||
expected[idx, idx+1] = 1
|
||||
|
||||
npt.assert_array_equal(mintree.toarray(), expected,
|
||||
'Incorrect spanning tree found.')
|
||||
|
|
@ -0,0 +1,148 @@
|
|||
import numpy as np
|
||||
import pytest
|
||||
from numpy.testing import assert_array_almost_equal
|
||||
from scipy.sparse import csr_array, csr_matrix, coo_array, coo_matrix
|
||||
from scipy.sparse.csgraph import (breadth_first_tree, depth_first_tree,
|
||||
csgraph_to_dense, csgraph_from_dense, csgraph_masked_from_dense)
|
||||
|
||||
|
||||
def test_graph_breadth_first():
|
||||
csgraph = np.array([[0, 1, 2, 0, 0],
|
||||
[1, 0, 0, 0, 3],
|
||||
[2, 0, 0, 7, 0],
|
||||
[0, 0, 7, 0, 1],
|
||||
[0, 3, 0, 1, 0]])
|
||||
csgraph = csgraph_from_dense(csgraph, null_value=0)
|
||||
|
||||
bfirst = np.array([[0, 1, 2, 0, 0],
|
||||
[0, 0, 0, 0, 3],
|
||||
[0, 0, 0, 7, 0],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0]])
|
||||
|
||||
for directed in [True, False]:
|
||||
bfirst_test = breadth_first_tree(csgraph, 0, directed)
|
||||
assert_array_almost_equal(csgraph_to_dense(bfirst_test),
|
||||
bfirst)
|
||||
|
||||
|
||||
def test_graph_depth_first():
|
||||
csgraph = np.array([[0, 1, 2, 0, 0],
|
||||
[1, 0, 0, 0, 3],
|
||||
[2, 0, 0, 7, 0],
|
||||
[0, 0, 7, 0, 1],
|
||||
[0, 3, 0, 1, 0]])
|
||||
csgraph = csgraph_from_dense(csgraph, null_value=0)
|
||||
|
||||
dfirst = np.array([[0, 1, 0, 0, 0],
|
||||
[0, 0, 0, 0, 3],
|
||||
[0, 0, 0, 0, 0],
|
||||
[0, 0, 7, 0, 0],
|
||||
[0, 0, 0, 1, 0]])
|
||||
|
||||
for directed in [True, False]:
|
||||
dfirst_test = depth_first_tree(csgraph, 0, directed)
|
||||
assert_array_almost_equal(csgraph_to_dense(dfirst_test), dfirst)
|
||||
|
||||
|
||||
def test_return_type():
|
||||
from .._laplacian import laplacian
|
||||
from .._min_spanning_tree import minimum_spanning_tree
|
||||
|
||||
np_csgraph = np.array([[0, 1, 2, 0, 0],
|
||||
[1, 0, 0, 0, 3],
|
||||
[2, 0, 0, 7, 0],
|
||||
[0, 0, 7, 0, 1],
|
||||
[0, 3, 0, 1, 0]])
|
||||
csgraph = csr_array(np_csgraph)
|
||||
assert isinstance(laplacian(csgraph), coo_array)
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_array)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
|
||||
|
||||
csgraph = csgraph_from_dense(np_csgraph, null_value=0)
|
||||
assert isinstance(csgraph, csr_array)
|
||||
assert isinstance(laplacian(csgraph), coo_array)
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_array)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
|
||||
|
||||
csgraph = csgraph_masked_from_dense(np_csgraph, null_value=0)
|
||||
assert isinstance(csgraph, np.ma.MaskedArray)
|
||||
assert csgraph._baseclass is np.ndarray
|
||||
# laplacian doesnt work with masked arrays so not here
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_array)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_array)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_array)
|
||||
|
||||
# start of testing with matrix/spmatrix types
|
||||
with np.testing.suppress_warnings() as sup:
|
||||
sup.filter(DeprecationWarning, "the matrix subclass.*")
|
||||
sup.filter(PendingDeprecationWarning, "the matrix subclass.*")
|
||||
|
||||
nm_csgraph = np.matrix([[0, 1, 2, 0, 0],
|
||||
[1, 0, 0, 0, 3],
|
||||
[2, 0, 0, 7, 0],
|
||||
[0, 0, 7, 0, 1],
|
||||
[0, 3, 0, 1, 0]])
|
||||
|
||||
csgraph = csr_matrix(nm_csgraph)
|
||||
assert isinstance(laplacian(csgraph), coo_matrix)
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
|
||||
csgraph = csgraph_from_dense(nm_csgraph, null_value=0)
|
||||
assert isinstance(csgraph, csr_matrix)
|
||||
assert isinstance(laplacian(csgraph), coo_matrix)
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
|
||||
mm_csgraph = csgraph_masked_from_dense(nm_csgraph, null_value=0)
|
||||
assert isinstance(mm_csgraph, np.ma.MaskedArray)
|
||||
# laplacian doesnt work with masked arrays so not here
|
||||
assert isinstance(minimum_spanning_tree(csgraph), csr_matrix)
|
||||
for directed in [True, False]:
|
||||
assert isinstance(depth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
assert isinstance(breadth_first_tree(csgraph, 0, directed), csr_matrix)
|
||||
# end of testing with matrix/spmatrix types
|
||||
|
||||
|
||||
def test_graph_breadth_first_trivial_graph():
|
||||
csgraph = np.array([[0]])
|
||||
csgraph = csgraph_from_dense(csgraph, null_value=0)
|
||||
|
||||
bfirst = np.array([[0]])
|
||||
|
||||
for directed in [True, False]:
|
||||
bfirst_test = breadth_first_tree(csgraph, 0, directed)
|
||||
assert_array_almost_equal(csgraph_to_dense(bfirst_test), bfirst)
|
||||
|
||||
|
||||
def test_graph_depth_first_trivial_graph():
|
||||
csgraph = np.array([[0]])
|
||||
csgraph = csgraph_from_dense(csgraph, null_value=0)
|
||||
|
||||
bfirst = np.array([[0]])
|
||||
|
||||
for directed in [True, False]:
|
||||
bfirst_test = depth_first_tree(csgraph, 0, directed)
|
||||
assert_array_almost_equal(csgraph_to_dense(bfirst_test),
|
||||
bfirst)
|
||||
|
||||
|
||||
@pytest.mark.parametrize('directed', [True, False])
|
||||
@pytest.mark.parametrize('tree_func', [breadth_first_tree, depth_first_tree])
|
||||
def test_int64_indices(tree_func, directed):
|
||||
# See https://github.com/scipy/scipy/issues/18716
|
||||
g = csr_array(([1], np.array([[0], [1]], dtype=np.int64)), shape=(2, 2))
|
||||
assert g.indices.dtype == np.int64
|
||||
tree = tree_func(g, 0, directed=directed)
|
||||
assert_array_almost_equal(csgraph_to_dense(tree), [[0, 1], [0, 0]])
|
||||
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/csr.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/csr.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'csr_matrix',
|
||||
'isspmatrix_csr',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="csr",
|
||||
private_modules=["_csr"], all=__all__,
|
||||
attribute=name)
|
||||
18
venv/lib/python3.13/site-packages/scipy/sparse/data.py
Normal file
18
venv/lib/python3.13/site-packages/scipy/sparse/data.py
Normal file
|
|
@ -0,0 +1,18 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ : list[str] = []
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="data",
|
||||
private_modules=["_data"], all=__all__,
|
||||
attribute=name)
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/dia.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/dia.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'dia_matrix',
|
||||
'isspmatrix_dia',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="dia",
|
||||
private_modules=["_dia"], all=__all__,
|
||||
attribute=name)
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/dok.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/dok.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'dok_matrix',
|
||||
'isspmatrix_dok',
|
||||
'spmatrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="dok",
|
||||
private_modules=["_dok"], all=__all__,
|
||||
attribute=name)
|
||||
23
venv/lib/python3.13/site-packages/scipy/sparse/extract.py
Normal file
23
venv/lib/python3.13/site-packages/scipy/sparse/extract.py
Normal file
|
|
@ -0,0 +1,23 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'coo_matrix',
|
||||
'find',
|
||||
'tril',
|
||||
'triu',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="extract",
|
||||
private_modules=["_extract"], all=__all__,
|
||||
attribute=name)
|
||||
22
venv/lib/python3.13/site-packages/scipy/sparse/lil.py
Normal file
22
venv/lib/python3.13/site-packages/scipy/sparse/lil.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
# This file is not meant for public use and will be removed in SciPy v2.0.0.
|
||||
# Use the `scipy.sparse` namespace for importing the functions
|
||||
# included below.
|
||||
|
||||
from scipy._lib.deprecation import _sub_module_deprecation
|
||||
|
||||
|
||||
__all__ = [ # noqa: F822
|
||||
'isspmatrix_lil',
|
||||
'lil_array',
|
||||
'lil_matrix',
|
||||
]
|
||||
|
||||
|
||||
def __dir__():
|
||||
return __all__
|
||||
|
||||
|
||||
def __getattr__(name):
|
||||
return _sub_module_deprecation(sub_package="sparse", module="lil",
|
||||
private_modules=["_lil"], all=__all__,
|
||||
attribute=name)
|
||||
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