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env-llmeval/lib/python3.10/site-packages/sympy/matrices/benchmarks/bench_matrix.py

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+from sympy.core.numbers import Integer
+from sympy.matrices.dense import (eye, zeros)
+
+i3 = Integer(3)
+M = eye(100)
+
+
+def timeit_Matrix__getitem_ii():
+    M[3, 3]
+
+
+def timeit_Matrix__getitem_II():
+    M[i3, i3]
+
+
+def timeit_Matrix__getslice():
+    M[:, :]
+
+
+def timeit_Matrix_zeronm():
+    zeros(100, 100)

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/fourier.py

@@ -0,0 +1,91 @@
+from sympy.core.sympify import _sympify
+from sympy.matrices.expressions import MatrixExpr
+from sympy.core.numbers import I
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+
+
+class DFT(MatrixExpr):
+    r"""
+    Returns a discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import n
+    >>> from sympy.matrices.expressions.fourier import DFT
+    >>> DFT(3)
+    DFT(3)
+    >>> DFT(3).as_explicit()
+    Matrix([
+    [sqrt(3)/3,                sqrt(3)/3,                sqrt(3)/3],
+    [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3,  sqrt(3)*exp(2*I*pi/3)/3],
+    [sqrt(3)/3,  sqrt(3)*exp(2*I*pi/3)/3, sqrt(3)*exp(-2*I*pi/3)/3]])
+    >>> DFT(n).shape
+    (n, n)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/DFT_matrix
+
+    """
+
+    def __new__(cls, n):
+        n = _sympify(n)
+        cls._check_dim(n)
+
+        obj = super().__new__(cls, n)
+        return obj
+
+    n = property(lambda self: self.args[0])  # type: ignore
+    shape = property(lambda self: (self.n, self.n))  # type: ignore
+
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return IDFT(self.n)
+
+
+class IDFT(DFT):
+    r"""
+    Returns an inverse discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.expressions.fourier import DFT, IDFT
+    >>> IDFT(3)
+    IDFT(3)
+    >>> IDFT(4)*DFT(4)
+    I
+
+    See Also
+    ========
+
+    DFT
+
+    """
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(-i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return DFT(self.n)

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/kronecker.py

@@ -0,0 +1,434 @@
+"""Implementation of the Kronecker product"""
+from functools import reduce
+from math import prod
+
+from sympy.core import Mul, sympify
+from sympy.functions import adjoint
+from sympy.matrices.common import ShapeError
+from sympy.matrices.expressions.matexpr import MatrixExpr
+from sympy.matrices.expressions.transpose import transpose
+from sympy.matrices.expressions.special import Identity
+from sympy.matrices.matrices import MatrixBase
+from sympy.strategies import (
+    canon, condition, distribute, do_one, exhaust, flatten, typed, unpack)
+from sympy.strategies.traverse import bottom_up
+from sympy.utilities import sift
+
+from .matadd import MatAdd
+from .matmul import MatMul
+from .matpow import MatPow
+
+
+def kronecker_product(*matrices):
+    """
+    The Kronecker product of two or more arguments.
+
+    This computes the explicit Kronecker product for subclasses of
+    ``MatrixBase`` i.e. explicit matrices. Otherwise, a symbolic
+    ``KroneckerProduct`` object is returned.
+
+
+    Examples
+    ========
+
+    For ``MatrixSymbol`` arguments a ``KroneckerProduct`` object is returned.
+    Elements of this matrix can be obtained by indexing, or for MatrixSymbols
+    with known dimension the explicit matrix can be obtained with
+    ``.as_explicit()``
+
+    >>> from sympy import kronecker_product, MatrixSymbol
+    >>> A = MatrixSymbol('A', 2, 2)
+    >>> B = MatrixSymbol('B', 2, 2)
+    >>> kronecker_product(A)
+    A
+    >>> kronecker_product(A, B)
+    KroneckerProduct(A, B)
+    >>> kronecker_product(A, B)[0, 1]
+    A[0, 0]*B[0, 1]
+    >>> kronecker_product(A, B).as_explicit()
+    Matrix([
+        [A[0, 0]*B[0, 0], A[0, 0]*B[0, 1], A[0, 1]*B[0, 0], A[0, 1]*B[0, 1]],
+        [A[0, 0]*B[1, 0], A[0, 0]*B[1, 1], A[0, 1]*B[1, 0], A[0, 1]*B[1, 1]],
+        [A[1, 0]*B[0, 0], A[1, 0]*B[0, 1], A[1, 1]*B[0, 0], A[1, 1]*B[0, 1]],
+        [A[1, 0]*B[1, 0], A[1, 0]*B[1, 1], A[1, 1]*B[1, 0], A[1, 1]*B[1, 1]]])
+
+    For explicit matrices the Kronecker product is returned as a Matrix
+
+    >>> from sympy import Matrix, kronecker_product
+    >>> sigma_x = Matrix([
+    ... [0, 1],
+    ... [1, 0]])
+    ...
+    >>> Isigma_y = Matrix([
+    ... [0, 1],
+    ... [-1, 0]])
+    ...
+    >>> kronecker_product(sigma_x, Isigma_y)
+    Matrix([
+    [ 0, 0,  0, 1],
+    [ 0, 0, -1, 0],
+    [ 0, 1,  0, 0],
+    [-1, 0,  0, 0]])
+
+    See Also
+    ========
+        KroneckerProduct
+
+    """
+    if not matrices:
+        raise TypeError("Empty Kronecker product is undefined")
+    if len(matrices) == 1:
+        return matrices[0]
+    else:
+        return KroneckerProduct(*matrices).doit()
+
+
+class KroneckerProduct(MatrixExpr):
+    """
+    The Kronecker product of two or more arguments.
+
+    The Kronecker product is a non-commutative product of matrices.
+    Given two matrices of dimension (m, n) and (s, t) it produces a matrix
+    of dimension (m s, n t).
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the product, use the function
+    ``kronecker_product()`` or call the ``.doit()`` or  ``.as_explicit()``
+    methods.
+
+    >>> from sympy import KroneckerProduct, MatrixSymbol
+    >>> A = MatrixSymbol('A', 5, 5)
+    >>> B = MatrixSymbol('B', 5, 5)
+    >>> isinstance(KroneckerProduct(A, B), KroneckerProduct)
+    True
+    """
+    is_KroneckerProduct = True
+
+    def __new__(cls, *args, check=True):
+        args = list(map(sympify, args))
+        if all(a.is_Identity for a in args):
+            ret = Identity(prod(a.rows for a in args))
+            if all(isinstance(a, MatrixBase) for a in args):
+                return ret.as_explicit()
+            else:
+                return ret
+
+        if check:
+            validate(*args)
+        return super().__new__(cls, *args)
+
+    @property
+    def shape(self):
+        rows, cols = self.args[0].shape
+        for mat in self.args[1:]:
+            rows *= mat.rows
+            cols *= mat.cols
+        return (rows, cols)
+
+    def _entry(self, i, j, **kwargs):
+        result = 1
+        for mat in reversed(self.args):
+            i, m = divmod(i, mat.rows)
+            j, n = divmod(j, mat.cols)
+            result *= mat[m, n]
+        return result
+
+    def _eval_adjoint(self):
+        return KroneckerProduct(*list(map(adjoint, self.args))).doit()
+
+    def _eval_conjugate(self):
+        return KroneckerProduct(*[a.conjugate() for a in self.args]).doit()
+
+    def _eval_transpose(self):
+        return KroneckerProduct(*list(map(transpose, self.args))).doit()
+
+    def _eval_trace(self):
+        from .trace import trace
+        return Mul(*[trace(a) for a in self.args])
+
+    def _eval_determinant(self):
+        from .determinant import det, Determinant
+        if not all(a.is_square for a in self.args):
+            return Determinant(self)
+
+        m = self.rows
+        return Mul(*[det(a)**(m/a.rows) for a in self.args])
+
+    def _eval_inverse(self):
+        try:
+            return KroneckerProduct(*[a.inverse() for a in self.args])
+        except ShapeError:
+            from sympy.matrices.expressions.inverse import Inverse
+            return Inverse(self)
+
+    def structurally_equal(self, other):
+        '''Determine whether two matrices have the same Kronecker product structure
+
+        Examples
+        ========
+
+        >>> from sympy import KroneckerProduct, MatrixSymbol, symbols
+        >>> m, n = symbols(r'm, n', integer=True)
+        >>> A = MatrixSymbol('A', m, m)
+        >>> B = MatrixSymbol('B', n, n)
+        >>> C = MatrixSymbol('C', m, m)
+        >>> D = MatrixSymbol('D', n, n)
+        >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(C, D))
+        True
+        >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(D, C))
+        False
+        >>> KroneckerProduct(A, B).structurally_equal(C)
+        False
+        '''
+        # Inspired by BlockMatrix
+        return (isinstance(other, KroneckerProduct)
+                and self.shape == other.shape
+                and len(self.args) == len(other.args)
+                and all(a.shape == b.shape for (a, b) in zip(self.args, other.args)))
+
+    def has_matching_shape(self, other):
+        '''Determine whether two matrices have the appropriate structure to bring matrix
+        multiplication inside the KroneckerProdut
+
+        Examples
+        ========
+        >>> from sympy import KroneckerProduct, MatrixSymbol, symbols
+        >>> m, n = symbols(r'm, n', integer=True)
+        >>> A = MatrixSymbol('A', m, n)
+        >>> B = MatrixSymbol('B', n, m)
+        >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(B, A))
+        True
+        >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(A, B))
+        False
+        >>> KroneckerProduct(A, B).has_matching_shape(A)
+        False
+        '''
+        return (isinstance(other, KroneckerProduct)
+                and self.cols == other.rows
+                and len(self.args) == len(other.args)
+                and all(a.cols == b.rows for (a, b) in zip(self.args, other.args)))
+
+    def _eval_expand_kroneckerproduct(self, **hints):
+        return flatten(canon(typed({KroneckerProduct: distribute(KroneckerProduct, MatAdd)}))(self))
+
+    def _kronecker_add(self, other):
+        if self.structurally_equal(other):
+            return self.__class__(*[a + b for (a, b) in zip(self.args, other.args)])
+        else:
+            return self + other
+
+    def _kronecker_mul(self, other):
+        if self.has_matching_shape(other):
+            return self.__class__(*[a*b for (a, b) in zip(self.args, other.args)])
+        else:
+            return self * other
+
+    def doit(self, **hints):
+        deep = hints.get('deep', True)
+        if deep:
+            args = [arg.doit(**hints) for arg in self.args]
+        else:
+            args = self.args
+        return canonicalize(KroneckerProduct(*args))
+
+
+def validate(*args):
+    if not all(arg.is_Matrix for arg in args):
+        raise TypeError("Mix of Matrix and Scalar symbols")
+
+
+# rules
+
+def extract_commutative(kron):
+    c_part = []
+    nc_part = []
+    for arg in kron.args:
+        c, nc = arg.args_cnc()
+        c_part.extend(c)
+        nc_part.append(Mul._from_args(nc))
+
+    c_part = Mul(*c_part)
+    if c_part != 1:
+        return c_part*KroneckerProduct(*nc_part)
+    return kron
+
+
+def matrix_kronecker_product(*matrices):
+    """Compute the Kronecker product of a sequence of SymPy Matrices.
+
+    This is the standard Kronecker product of matrices [1].
+
+    Parameters
+    ==========
+
+    matrices : tuple of MatrixBase instances
+        The matrices to take the Kronecker product of.
+
+    Returns
+    =======
+
+    matrix : MatrixBase
+        The Kronecker product matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.matrices.expressions.kronecker import (
+    ... matrix_kronecker_product)
+
+    >>> m1 = Matrix([[1,2],[3,4]])
+    >>> m2 = Matrix([[1,0],[0,1]])
+    >>> matrix_kronecker_product(m1, m2)
+    Matrix([
+    [1, 0, 2, 0],
+    [0, 1, 0, 2],
+    [3, 0, 4, 0],
+    [0, 3, 0, 4]])
+    >>> matrix_kronecker_product(m2, m1)
+    Matrix([
+    [1, 2, 0, 0],
+    [3, 4, 0, 0],
+    [0, 0, 1, 2],
+    [0, 0, 3, 4]])
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Kronecker_product
+    """
+    # Make sure we have a sequence of Matrices
+    if not all(isinstance(m, MatrixBase) for m in matrices):
+        raise TypeError(
+            'Sequence of Matrices expected, got: %s' % repr(matrices)
+        )
+
+    # Pull out the first element in the product.
+    matrix_expansion = matrices[-1]
+    # Do the kronecker product working from right to left.
+    for mat in reversed(matrices[:-1]):
+        rows = mat.rows
+        cols = mat.cols
+        # Go through each row appending kronecker product to.
+        # running matrix_expansion.
+        for i in range(rows):
+            start = matrix_expansion*mat[i*cols]
+            # Go through each column joining each item
+            for j in range(cols - 1):
+                start = start.row_join(
+                    matrix_expansion*mat[i*cols + j + 1]
+                )
+            # If this is the first element, make it the start of the
+            # new row.
+            if i == 0:
+                next = start
+            else:
+                next = next.col_join(start)
+        matrix_expansion = next
+
+    MatrixClass = max(matrices, key=lambda M: M._class_priority).__class__
+    if isinstance(matrix_expansion, MatrixClass):
+        return matrix_expansion
+    else:
+        return MatrixClass(matrix_expansion)
+
+
+def explicit_kronecker_product(kron):
+    # Make sure we have a sequence of Matrices
+    if not all(isinstance(m, MatrixBase) for m in kron.args):
+        return kron
+
+    return matrix_kronecker_product(*kron.args)
+
+
+rules = (unpack,
+         explicit_kronecker_product,
+         flatten,
+         extract_commutative)
+
+canonicalize = exhaust(condition(lambda x: isinstance(x, KroneckerProduct),
+                                 do_one(*rules)))
+
+
+def _kronecker_dims_key(expr):
+    if isinstance(expr, KroneckerProduct):
+        return tuple(a.shape for a in expr.args)
+    else:
+        return (0,)
+
+
+def kronecker_mat_add(expr):
+    args = sift(expr.args, _kronecker_dims_key)
+    nonkrons = args.pop((0,), None)
+    if not args:
+        return expr
+
+    krons = [reduce(lambda x, y: x._kronecker_add(y), group)
+             for group in args.values()]
+
+    if not nonkrons:
+        return MatAdd(*krons)
+    else:
+        return MatAdd(*krons) + nonkrons
+
+
+def kronecker_mat_mul(expr):
+    # modified from block matrix code
+    factor, matrices = expr.as_coeff_matrices()
+
+    i = 0
+    while i < len(matrices) - 1:
+        A, B = matrices[i:i+2]
+        if isinstance(A, KroneckerProduct) and isinstance(B, KroneckerProduct):
+            matrices[i] = A._kronecker_mul(B)
+            matrices.pop(i+1)
+        else:
+            i += 1
+
+    return factor*MatMul(*matrices)
+
+
+def kronecker_mat_pow(expr):
+    if isinstance(expr.base, KroneckerProduct) and all(a.is_square for a in expr.base.args):
+        return KroneckerProduct(*[MatPow(a, expr.exp) for a in expr.base.args])
+    else:
+        return expr
+
+
+def combine_kronecker(expr):
+    """Combine KronekeckerProduct with expression.
+
+    If possible write operations on KroneckerProducts of compatible shapes
+    as a single KroneckerProduct.
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.expressions import combine_kronecker
+    >>> from sympy import MatrixSymbol, KroneckerProduct, symbols
+    >>> m, n = symbols(r'm, n', integer=True)
+    >>> A = MatrixSymbol('A', m, n)
+    >>> B = MatrixSymbol('B', n, m)
+    >>> combine_kronecker(KroneckerProduct(A, B)*KroneckerProduct(B, A))
+    KroneckerProduct(A*B, B*A)
+    >>> combine_kronecker(KroneckerProduct(A, B)+KroneckerProduct(B.T, A.T))
+    KroneckerProduct(A + B.T, B + A.T)
+    >>> C = MatrixSymbol('C', n, n)
+    >>> D = MatrixSymbol('D', m, m)
+    >>> combine_kronecker(KroneckerProduct(C, D)**m)
+    KroneckerProduct(C**m, D**m)
+    """
+    def haskron(expr):
+        return isinstance(expr, MatrixExpr) and expr.has(KroneckerProduct)
+
+    rule = exhaust(
+        bottom_up(exhaust(condition(haskron, typed(
+            {MatAdd: kronecker_mat_add,
+             MatMul: kronecker_mat_mul,
+             MatPow: kronecker_mat_pow})))))
+    result = rule(expr)
+    doit = getattr(result, 'doit', None)
+    if doit is not None:
+        return doit()
+    else:
+        return result

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_adjoint.py

@@ -0,0 +1,34 @@
+from sympy.core import symbols, S
+from sympy.functions import adjoint, conjugate, transpose
+from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
+from sympy.matrices import eye, Matrix
+
+n, m, l, k, p = symbols('n m l k p', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+
+
+def test_adjoint():
+    Sq = MatrixSymbol('Sq', n, n)
+
+    assert Adjoint(A).shape == (m, n)
+    assert Adjoint(A*B).shape == (l, n)
+    assert adjoint(Adjoint(A)) == A
+    assert isinstance(Adjoint(Adjoint(A)), Adjoint)
+
+    assert conjugate(Adjoint(A)) == Transpose(A)
+    assert transpose(Adjoint(A)) == Adjoint(Transpose(A))
+
+    assert Adjoint(eye(3)).doit() == eye(3)
+
+    assert Adjoint(S(5)).doit() == S(5)
+
+    assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
+
+    assert adjoint(trace(Sq)) == conjugate(trace(Sq))
+    assert trace(adjoint(Sq)) == conjugate(trace(Sq))
+
+    assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
+
+    assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A)

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py

@@ -0,0 +1,445 @@
+from sympy.matrices.expressions.trace import Trace
+from sympy.testing.pytest import raises, slow
+from sympy.matrices.expressions.blockmatrix import (
+    block_collapse, bc_matmul, bc_block_plus_ident, BlockDiagMatrix,
+    BlockMatrix, bc_dist, bc_matadd, bc_transpose, bc_inverse,
+    blockcut, reblock_2x2, deblock)
+from sympy.matrices.expressions import (MatrixSymbol, Identity,
+        Inverse, trace, Transpose, det, ZeroMatrix, OneMatrix)
+from sympy.matrices.common import NonInvertibleMatrixError
+from sympy.matrices import (
+    Matrix, ImmutableMatrix, ImmutableSparseMatrix)
+from sympy.core import Tuple, symbols, Expr, S
+from sympy.functions import transpose, im, re
+
+i, j, k, l, m, n, p = symbols('i:n, p', integer=True)
+A = MatrixSymbol('A', n, n)
+B = MatrixSymbol('B', n, n)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+G = MatrixSymbol('G', n, n)
+H = MatrixSymbol('H', n, n)
+b1 = BlockMatrix([[G, H]])
+b2 = BlockMatrix([[G], [H]])
+
+def test_bc_matmul():
+    assert bc_matmul(H*b1*b2*G) == BlockMatrix([[(H*G*G + H*H*H)*G]])
+
+def test_bc_matadd():
+    assert bc_matadd(BlockMatrix([[G, H]]) + BlockMatrix([[H, H]])) == \
+            BlockMatrix([[G+H, H+H]])
+
+def test_bc_transpose():
+    assert bc_transpose(Transpose(BlockMatrix([[A, B], [C, D]]))) == \
+            BlockMatrix([[A.T, C.T], [B.T, D.T]])
+
+def test_bc_dist_diag():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    C = MatrixSymbol('C', l, l)
+    X = BlockDiagMatrix(A, B, C)
+
+    assert bc_dist(X+X).equals(BlockDiagMatrix(2*A, 2*B, 2*C))
+
+def test_block_plus_ident():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    Z = MatrixSymbol('Z', n + m, n + m)
+    assert bc_block_plus_ident(X + Identity(m + n) + Z) == \
+            BlockDiagMatrix(Identity(n), Identity(m)) + X + Z
+
+def test_BlockMatrix():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, k)
+    C = MatrixSymbol('C', l, m)
+    D = MatrixSymbol('D', l, k)
+    M = MatrixSymbol('M', m + k, p)
+    N = MatrixSymbol('N', l + n, k + m)
+    X = BlockMatrix(Matrix([[A, B], [C, D]]))
+
+    assert X.__class__(*X.args) == X
+
+    # block_collapse does nothing on normal inputs
+    E = MatrixSymbol('E', n, m)
+    assert block_collapse(A + 2*E) == A + 2*E
+    F = MatrixSymbol('F', m, m)
+    assert block_collapse(E.T*A*F) == E.T*A*F
+
+    assert X.shape == (l + n, k + m)
+    assert X.blockshape == (2, 2)
+    assert transpose(X) == BlockMatrix(Matrix([[A.T, C.T], [B.T, D.T]]))
+    assert transpose(X).shape == X.shape[::-1]
+
+    # Test that BlockMatrices and MatrixSymbols can still mix
+    assert (X*M).is_MatMul
+    assert X._blockmul(M).is_MatMul
+    assert (X*M).shape == (n + l, p)
+    assert (X + N).is_MatAdd
+    assert X._blockadd(N).is_MatAdd
+    assert (X + N).shape == X.shape
+
+    E = MatrixSymbol('E', m, 1)
+    F = MatrixSymbol('F', k, 1)
+
+    Y = BlockMatrix(Matrix([[E], [F]]))
+
+    assert (X*Y).shape == (l + n, 1)
+    assert block_collapse(X*Y).blocks[0, 0] == A*E + B*F
+    assert block_collapse(X*Y).blocks[1, 0] == C*E + D*F
+
+    # block_collapse passes down into container objects, transposes, and inverse
+    assert block_collapse(transpose(X*Y)) == transpose(block_collapse(X*Y))
+    assert block_collapse(Tuple(X*Y, 2*X)) == (
+        block_collapse(X*Y), block_collapse(2*X))
+
+    # Make sure that MatrixSymbols will enter 1x1 BlockMatrix if it simplifies
+    Ab = BlockMatrix([[A]])
+    Z = MatrixSymbol('Z', *A.shape)
+    assert block_collapse(Ab + Z) == A + Z
+
+def test_block_collapse_explicit_matrices():
+    A = Matrix([[1, 2], [3, 4]])
+    assert block_collapse(BlockMatrix([[A]])) == A
+
+    A = ImmutableSparseMatrix([[1, 2], [3, 4]])
+    assert block_collapse(BlockMatrix([[A]])) == A
+
+def test_issue_17624():
+    a = MatrixSymbol("a", 2, 2)
+    z = ZeroMatrix(2, 2)
+    b = BlockMatrix([[a, z], [z, z]])
+    assert block_collapse(b * b) == BlockMatrix([[a**2, z], [z, z]])
+    assert block_collapse(b * b * b) == BlockMatrix([[a**3, z], [z, z]])
+
+def test_issue_18618():
+    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    assert A == Matrix(BlockDiagMatrix(A))
+
+def test_BlockMatrix_trace():
+    A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
+    X = BlockMatrix([[A, B], [C, D]])
+    assert trace(X) == trace(A) + trace(D)
+    assert trace(BlockMatrix([ZeroMatrix(n, n)])) == 0
+
+def test_BlockMatrix_Determinant():
+    A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
+    X = BlockMatrix([[A, B], [C, D]])
+    from sympy.assumptions.ask import Q
+    from sympy.assumptions.assume import assuming
+    with assuming(Q.invertible(A)):
+        assert det(X) == det(A) * det(X.schur('A'))
+
+    assert isinstance(det(X), Expr)
+    assert det(BlockMatrix([A])) == det(A)
+    assert det(BlockMatrix([ZeroMatrix(n, n)])) == 0
+
+def test_squareBlockMatrix():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    Y = BlockMatrix([[A]])
+
+    assert X.is_square
+
+    Q = X + Identity(m + n)
+    assert (block_collapse(Q) ==
+        BlockMatrix([[A + Identity(n), B], [C, D + Identity(m)]]))
+
+    assert (X + MatrixSymbol('Q', n + m, n + m)).is_MatAdd
+    assert (X * MatrixSymbol('Q', n + m, n + m)).is_MatMul
+
+    assert block_collapse(Y.I) == A.I
+
+    assert isinstance(X.inverse(), Inverse)
+
+    assert not X.is_Identity
+
+    Z = BlockMatrix([[Identity(n), B], [C, D]])
+    assert not Z.is_Identity
+
+
+def test_BlockMatrix_2x2_inverse_symbolic():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, k - m)
+    C = MatrixSymbol('C', k - n, m)
+    D = MatrixSymbol('D', k - n, k - m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert X.is_square and X.shape == (k, k)
+    assert isinstance(block_collapse(X.I), Inverse)  # Can't invert when none of the blocks is square
+
+    # test code path where only A is invertible
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = ZeroMatrix(m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [A.I + A.I * B * X.schur('A').I * C * A.I, -A.I * B * X.schur('A').I],
+        [-X.schur('A').I * C * A.I, X.schur('A').I],
+    ])
+
+    # test code path where only B is invertible
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, n)
+    C = ZeroMatrix(m, m)
+    D = MatrixSymbol('D', m, n)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [-X.schur('B').I * D * B.I, X.schur('B').I],
+        [B.I + B.I * A * X.schur('B').I * D * B.I, -B.I * A * X.schur('B').I],
+    ])
+
+    # test code path where only C is invertible
+    A = MatrixSymbol('A', n, m)
+    B = ZeroMatrix(n, n)
+    C = MatrixSymbol('C', m, m)
+    D = MatrixSymbol('D', m, n)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [-C.I * D * X.schur('C').I, C.I + C.I * D * X.schur('C').I * A * C.I],
+        [X.schur('C').I, -X.schur('C').I * A * C.I],
+    ])
+
+    # test code path where only D is invertible
+    A = ZeroMatrix(n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+    assert block_collapse(X.inverse()) == BlockMatrix([
+        [X.schur('D').I, -X.schur('D').I * B * D.I],
+        [-D.I * C * X.schur('D').I, D.I + D.I * C * X.schur('D').I * B * D.I],
+    ])
+
+
+def test_BlockMatrix_2x2_inverse_numeric():
+    """Test 2x2 block matrix inversion numerically for all 4 formulas"""
+    M = Matrix([[1, 2], [3, 4]])
+    # rank deficient matrices that have full rank when two of them combined
+    D1 = Matrix([[1, 2], [2, 4]])
+    D2 = Matrix([[1, 3], [3, 9]])
+    D3 = Matrix([[1, 4], [4, 16]])
+    assert D1.rank() == D2.rank() == D3.rank() == 1
+    assert (D1 + D2).rank() == (D2 + D3).rank() == (D3 + D1).rank() == 2
+
+    # Only A is invertible
+    K = BlockMatrix([[M, D1], [D2, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only B is invertible
+    K = BlockMatrix([[D1, M], [D2, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only C is invertible
+    K = BlockMatrix([[D1, D2], [M, D3]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+    # Only D is invertible
+    K = BlockMatrix([[D1, D2], [D3, M]])
+    assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
+
+
+@slow
+def test_BlockMatrix_3x3_symbolic():
+    # Only test one of these, instead of all permutations, because it's slow
+    rowblocksizes = (n, m, k)
+    colblocksizes = (m, k, n)
+    K = BlockMatrix([
+        [MatrixSymbol('M%s%s' % (rows, cols), rows, cols) for cols in colblocksizes]
+        for rows in rowblocksizes
+    ])
+    collapse = block_collapse(K.I)
+    assert isinstance(collapse, BlockMatrix)
+
+
+def test_BlockDiagMatrix():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    C = MatrixSymbol('C', l, l)
+    M = MatrixSymbol('M', n + m + l, n + m + l)
+
+    X = BlockDiagMatrix(A, B, C)
+    Y = BlockDiagMatrix(A, 2*B, 3*C)
+
+    assert X.blocks[1, 1] == B
+    assert X.shape == (n + m + l, n + m + l)
+    assert all(X.blocks[i, j].is_ZeroMatrix if i != j else X.blocks[i, j] in [A, B, C]
+            for i in range(3) for j in range(3))
+    assert X.__class__(*X.args) == X
+    assert X.get_diag_blocks() == (A, B, C)
+
+    assert isinstance(block_collapse(X.I * X), Identity)
+
+    assert bc_matmul(X*X) == BlockDiagMatrix(A*A, B*B, C*C)
+    assert block_collapse(X*X) == BlockDiagMatrix(A*A, B*B, C*C)
+    #XXX: should be == ??
+    assert block_collapse(X + X).equals(BlockDiagMatrix(2*A, 2*B, 2*C))
+    assert block_collapse(X*Y) == BlockDiagMatrix(A*A, 2*B*B, 3*C*C)
+    assert block_collapse(X + Y) == BlockDiagMatrix(2*A, 3*B, 4*C)
+
+    # Ensure that BlockDiagMatrices can still interact with normal MatrixExprs
+    assert (X*(2*M)).is_MatMul
+    assert (X + (2*M)).is_MatAdd
+
+    assert (X._blockmul(M)).is_MatMul
+    assert (X._blockadd(M)).is_MatAdd
+
+def test_BlockDiagMatrix_nonsquare():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', k, l)
+    X = BlockDiagMatrix(A, B)
+    assert X.shape == (n + k, m + l)
+    assert X.shape == (n + k, m + l)
+    assert X.rowblocksizes == [n, k]
+    assert X.colblocksizes == [m, l]
+    C = MatrixSymbol('C', n, m)
+    D = MatrixSymbol('D', k, l)
+    Y = BlockDiagMatrix(C, D)
+    assert block_collapse(X + Y) == BlockDiagMatrix(A + C, B + D)
+    assert block_collapse(X * Y.T) == BlockDiagMatrix(A * C.T, B * D.T)
+    raises(NonInvertibleMatrixError, lambda: BlockDiagMatrix(A, C.T).inverse())
+
+def test_BlockDiagMatrix_determinant():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', m, m)
+    assert det(BlockDiagMatrix()) == 1
+    assert det(BlockDiagMatrix(A)) == det(A)
+    assert det(BlockDiagMatrix(A, B)) == det(A) * det(B)
+
+    # non-square blocks
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', n, m)
+    assert det(BlockDiagMatrix(C, D)) == 0
+
+def test_BlockDiagMatrix_trace():
+    assert trace(BlockDiagMatrix()) == 0
+    assert trace(BlockDiagMatrix(ZeroMatrix(n, n))) == 0
+    A = MatrixSymbol('A', n, n)
+    assert trace(BlockDiagMatrix(A)) == trace(A)
+    B = MatrixSymbol('B', m, m)
+    assert trace(BlockDiagMatrix(A, B)) == trace(A) + trace(B)
+
+    # non-square blocks
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', n, m)
+    assert isinstance(trace(BlockDiagMatrix(C, D)), Trace)
+
+def test_BlockDiagMatrix_transpose():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', k, l)
+    assert transpose(BlockDiagMatrix()) == BlockDiagMatrix()
+    assert transpose(BlockDiagMatrix(A)) == BlockDiagMatrix(A.T)
+    assert transpose(BlockDiagMatrix(A, B)) == BlockDiagMatrix(A.T, B.T)
+
+def test_issue_2460():
+    bdm1 = BlockDiagMatrix(Matrix([i]), Matrix([j]))
+    bdm2 = BlockDiagMatrix(Matrix([k]), Matrix([l]))
+    assert block_collapse(bdm1 + bdm2) == BlockDiagMatrix(Matrix([i + k]), Matrix([j + l]))
+
+def test_blockcut():
+    A = MatrixSymbol('A', n, m)
+    B = blockcut(A, (n/2, n/2), (m/2, m/2))
+    assert B == BlockMatrix([[A[:n/2, :m/2], A[:n/2, m/2:]],
+                             [A[n/2:, :m/2], A[n/2:, m/2:]]])
+
+    M = ImmutableMatrix(4, 4, range(16))
+    B = blockcut(M, (2, 2), (2, 2))
+    assert M == ImmutableMatrix(B)
+
+    B = blockcut(M, (1, 3), (2, 2))
+    assert ImmutableMatrix(B.blocks[0, 1]) == ImmutableMatrix([[2, 3]])
+
+def test_reblock_2x2():
+    B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), 2, 2)
+                            for j in range(3)]
+                            for i in range(3)])
+    assert B.blocks.shape == (3, 3)
+
+    BB = reblock_2x2(B)
+    assert BB.blocks.shape == (2, 2)
+
+    assert B.shape == BB.shape
+    assert B.as_explicit() == BB.as_explicit()
+
+def test_deblock():
+    B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), n, n)
+                    for j in range(4)]
+                    for i in range(4)])
+
+    assert deblock(reblock_2x2(B)) == B
+
+def test_block_collapse_type():
+    bm1 = BlockDiagMatrix(ImmutableMatrix([1]), ImmutableMatrix([2]))
+    bm2 = BlockDiagMatrix(ImmutableMatrix([3]), ImmutableMatrix([4]))
+
+    assert bm1.T.__class__ == BlockDiagMatrix
+    assert block_collapse(bm1 - bm2).__class__ == BlockDiagMatrix
+    assert block_collapse(Inverse(bm1)).__class__ == BlockDiagMatrix
+    assert block_collapse(Transpose(bm1)).__class__ == BlockDiagMatrix
+    assert bc_transpose(Transpose(bm1)).__class__ == BlockDiagMatrix
+    assert bc_inverse(Inverse(bm1)).__class__ == BlockDiagMatrix
+
+def test_invalid_block_matrix():
+    raises(ValueError, lambda: BlockMatrix([
+        [Identity(2), Identity(5)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [Identity(n), Identity(m)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [ZeroMatrix(n, n), ZeroMatrix(n, n)],
+        [ZeroMatrix(n, n - 1), ZeroMatrix(n, n + 1)],
+    ]))
+    raises(ValueError, lambda: BlockMatrix([
+        [ZeroMatrix(n - 1, n), ZeroMatrix(n, n)],
+        [ZeroMatrix(n + 1, n), ZeroMatrix(n, n)],
+    ]))
+
+def test_block_lu_decomposition():
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, m)
+    C = MatrixSymbol('C', m, n)
+    D = MatrixSymbol('D', m, m)
+    X = BlockMatrix([[A, B], [C, D]])
+
+    #LDU decomposition
+    L, D, U = X.LDUdecomposition()
+    assert block_collapse(L*D*U) == X
+
+    #UDL decomposition
+    U, D, L = X.UDLdecomposition()
+    assert block_collapse(U*D*L) == X
+
+    #LU decomposition
+    L, U = X.LUdecomposition()
+    assert block_collapse(L*U) == X
+
+def test_issue_21866():
+    n  = 10
+    I  = Identity(n)
+    O  = ZeroMatrix(n, n)
+    A  = BlockMatrix([[  I,  O,  O,  O ],
+                      [  O,  I,  O,  O ],
+                      [  O,  O,  I,  O ],
+                      [  I,  O,  O,  I ]])
+    Ainv = block_collapse(A.inv())
+    AinvT = BlockMatrix([[  I,  O,  O,  O ],
+                      [  O,  I,  O,  O ],
+                      [  O,  O,  I,  O ],
+                      [  -I,  O,  O,  I ]])
+    assert Ainv == AinvT
+
+
+def test_adjoint_and_special_matrices():
+    A = Identity(3)
+    B = OneMatrix(3, 2)
+    C = ZeroMatrix(2, 3)
+    D = Identity(2)
+    X = BlockMatrix([[A, B], [C, D]])
+    X2 = BlockMatrix([[A, S.ImaginaryUnit*B], [C, D]])
+    assert X.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [OneMatrix(2, 3), D]])
+    assert re(X) == X
+    assert X2.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [-S.ImaginaryUnit*OneMatrix(2, 3), D]])
+    assert im(X2) == BlockMatrix([[ZeroMatrix(3, 3), OneMatrix(3, 2)], [ZeroMatrix(2, 3), ZeroMatrix(2, 2)]])

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_inverse.py

@@ -0,0 +1,62 @@
+from sympy.core import symbols, S
+from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix
+from sympy.matrices.common import NonInvertibleMatrixError, NonSquareMatrixError
+from sympy.matrices import eye, Identity
+from sympy.testing.pytest import raises
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+
+n, m, l = symbols('n m l', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+
+
+def test_inverse():
+    assert Inverse(C).args == (C, S.NegativeOne)
+    assert Inverse(C).shape == (n, n)
+    assert Inverse(A*E).shape == (n, n)
+    assert Inverse(E*A).shape == (m, m)
+    assert Inverse(C).inverse() == C
+    assert Inverse(Inverse(C)).doit() == C
+    assert isinstance(Inverse(Inverse(C)), Inverse)
+
+    assert Inverse(*Inverse(E*A).args) == Inverse(E*A)
+
+    assert C.inverse().inverse() == C
+
+    assert C.inverse()*C == Identity(C.rows)
+
+    assert Identity(n).inverse() == Identity(n)
+    assert (3*Identity(n)).inverse() == Identity(n)/3
+
+    # Simplifies Muls if possible (i.e. submatrices are square)
+    assert (C*D).inverse() == D.I*C.I
+    # But still works when not possible
+    assert isinstance((A*E).inverse(), Inverse)
+    assert Inverse(C*D).doit(inv_expand=False) == Inverse(C*D)
+
+    assert Inverse(eye(3)).doit() == eye(3)
+    assert Inverse(eye(3)).doit(deep=False) == eye(3)
+
+    assert OneMatrix(1, 1).I == Identity(1)
+    assert isinstance(OneMatrix(n, n).I, Inverse)
+
+def test_inverse_non_invertible():
+    raises(NonInvertibleMatrixError, lambda: ZeroMatrix(n, n).I)
+    raises(NonInvertibleMatrixError, lambda: OneMatrix(2, 2).I)
+
+def test_refine():
+    assert refine(C.I, Q.orthogonal(C)) == C.T
+
+
+def test_inverse_matpow_canonicalization():
+    A = MatrixSymbol('A', 3, 3)
+    assert Inverse(MatPow(A, 3)).doit() == MatPow(Inverse(A), 3).doit()
+
+
+def test_nonsquare_error():
+    A = MatrixSymbol('A', 3, 4)
+    raises(NonSquareMatrixError, lambda: Inverse(A))

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_kronecker.py

@@ -0,0 +1,150 @@
+from sympy.core.mod import Mod
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.integers import floor
+from sympy.matrices.dense import (Matrix, eye)
+from sympy.matrices import MatrixSymbol, Identity
+from sympy.matrices.expressions import det, trace
+
+from sympy.matrices.expressions.kronecker import (KroneckerProduct,
+                                                  kronecker_product,
+                                                  combine_kronecker)
+
+
+mat1 = Matrix([[1, 2 * I], [1 + I, 3]])
+mat2 = Matrix([[2 * I, 3], [4 * I, 2]])
+
+i, j, k, n, m, o, p, x = symbols('i,j,k,n,m,o,p,x')
+Z = MatrixSymbol('Z', n, n)
+W = MatrixSymbol('W', m, m)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', n, m)
+C = MatrixSymbol('C', m, k)
+
+
+def test_KroneckerProduct():
+    assert isinstance(KroneckerProduct(A, B), KroneckerProduct)
+    assert KroneckerProduct(A, B).subs(A, C) == KroneckerProduct(C, B)
+    assert KroneckerProduct(A, C).shape == (n*m, m*k)
+    assert (KroneckerProduct(A, C) + KroneckerProduct(-A, C)).is_ZeroMatrix
+    assert (KroneckerProduct(W, Z) * KroneckerProduct(W.I, Z.I)).is_Identity
+
+
+def test_KroneckerProduct_identity():
+    assert KroneckerProduct(Identity(m), Identity(n)) == Identity(m*n)
+    assert KroneckerProduct(eye(2), eye(3)) == eye(6)
+
+
+def test_KroneckerProduct_explicit():
+    X = MatrixSymbol('X', 2, 2)
+    Y = MatrixSymbol('Y', 2, 2)
+    kp = KroneckerProduct(X, Y)
+    assert kp.shape == (4, 4)
+    assert kp.as_explicit() == Matrix(
+        [
+            [X[0, 0]*Y[0, 0], X[0, 0]*Y[0, 1], X[0, 1]*Y[0, 0], X[0, 1]*Y[0, 1]],
+            [X[0, 0]*Y[1, 0], X[0, 0]*Y[1, 1], X[0, 1]*Y[1, 0], X[0, 1]*Y[1, 1]],
+            [X[1, 0]*Y[0, 0], X[1, 0]*Y[0, 1], X[1, 1]*Y[0, 0], X[1, 1]*Y[0, 1]],
+            [X[1, 0]*Y[1, 0], X[1, 0]*Y[1, 1], X[1, 1]*Y[1, 0], X[1, 1]*Y[1, 1]]
+        ]
+    )
+
+
+def test_tensor_product_adjoint():
+    assert KroneckerProduct(I*A, B).adjoint() == \
+        -I*KroneckerProduct(A.adjoint(), B.adjoint())
+    assert KroneckerProduct(mat1, mat2).adjoint() == \
+        kronecker_product(mat1.adjoint(), mat2.adjoint())
+
+
+def test_tensor_product_conjugate():
+    assert KroneckerProduct(I*A, B).conjugate() == \
+        -I*KroneckerProduct(A.conjugate(), B.conjugate())
+    assert KroneckerProduct(mat1, mat2).conjugate() == \
+        kronecker_product(mat1.conjugate(), mat2.conjugate())
+
+
+def test_tensor_product_transpose():
+    assert KroneckerProduct(I*A, B).transpose() == \
+        I*KroneckerProduct(A.transpose(), B.transpose())
+    assert KroneckerProduct(mat1, mat2).transpose() == \
+        kronecker_product(mat1.transpose(), mat2.transpose())
+
+
+def test_KroneckerProduct_is_associative():
+    assert kronecker_product(A, kronecker_product(
+        B, C)) == kronecker_product(kronecker_product(A, B), C)
+    assert kronecker_product(A, kronecker_product(
+        B, C)) == KroneckerProduct(A, B, C)
+
+
+def test_KroneckerProduct_is_bilinear():
+    assert kronecker_product(x*A, B) == x*kronecker_product(A, B)
+    assert kronecker_product(A, x*B) == x*kronecker_product(A, B)
+
+
+def test_KroneckerProduct_determinant():
+    kp = kronecker_product(W, Z)
+    assert det(kp) == det(W)**n * det(Z)**m
+
+
+def test_KroneckerProduct_trace():
+    kp = kronecker_product(W, Z)
+    assert trace(kp) == trace(W)*trace(Z)
+
+
+def test_KroneckerProduct_isnt_commutative():
+    assert KroneckerProduct(A, B) != KroneckerProduct(B, A)
+    assert KroneckerProduct(A, B).is_commutative is False
+
+
+def test_KroneckerProduct_extracts_commutative_part():
+    assert kronecker_product(x * A, 2 * B) == x * \
+        2 * KroneckerProduct(A, B)
+
+
+def test_KroneckerProduct_inverse():
+    kp = kronecker_product(W, Z)
+    assert kp.inverse() == kronecker_product(W.inverse(), Z.inverse())
+
+
+def test_KroneckerProduct_combine_add():
+    kp1 = kronecker_product(A, B)
+    kp2 = kronecker_product(C, W)
+    assert combine_kronecker(kp1*kp2) == kronecker_product(A*C, B*W)
+
+
+def test_KroneckerProduct_combine_mul():
+    X = MatrixSymbol('X', m, n)
+    Y = MatrixSymbol('Y', m, n)
+    kp1 = kronecker_product(A, X)
+    kp2 = kronecker_product(B, Y)
+    assert combine_kronecker(kp1+kp2) == kronecker_product(A+B, X+Y)
+
+
+def test_KroneckerProduct_combine_pow():
+    X = MatrixSymbol('X', n, n)
+    Y = MatrixSymbol('Y', n, n)
+    assert combine_kronecker(KroneckerProduct(
+        X, Y)**x) == KroneckerProduct(X**x, Y**x)
+    assert combine_kronecker(x * KroneckerProduct(X, Y)
+                             ** 2) == x * KroneckerProduct(X**2, Y**2)
+    assert combine_kronecker(
+        x * (KroneckerProduct(X, Y)**2) * KroneckerProduct(A, B)) == x * KroneckerProduct(X**2 * A, Y**2 * B)
+    # cannot simplify because of non-square arguments to kronecker product:
+    assert combine_kronecker(KroneckerProduct(A, B.T) ** m) == KroneckerProduct(A, B.T) ** m
+
+
+def test_KroneckerProduct_expand():
+    X = MatrixSymbol('X', n, n)
+    Y = MatrixSymbol('Y', n, n)
+
+    assert KroneckerProduct(X + Y, Y + Z).expand(kroneckerproduct=True) == \
+        KroneckerProduct(X, Y) + KroneckerProduct(X, Z) + \
+        KroneckerProduct(Y, Y) + KroneckerProduct(Y, Z)
+
+def test_KroneckerProduct_entry():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', o, p)
+
+    assert KroneckerProduct(A, B)._entry(i, j) == A[Mod(floor(i/o), n), Mod(floor(j/p), m)]*B[Mod(i, o), Mod(j, p)]

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_matexpr.py

@@ -0,0 +1,567 @@
+from sympy.concrete.summations import Sum
+from sympy.core.exprtools import gcd_terms
+from sympy.core.function import (diff, expand)
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Dummy, Symbol, Str)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import zeros
+from sympy.polys.polytools import factor
+
+from sympy.core import (S, symbols, Add, Mul, SympifyError, Rational,
+                    Function)
+from sympy.functions import sin, cos, tan, sqrt, cbrt, exp
+from sympy.simplify import simplify
+from sympy.matrices import (ImmutableMatrix, Inverse, MatAdd, MatMul,
+        MatPow, Matrix, MatrixExpr, MatrixSymbol,
+        SparseMatrix, Transpose, Adjoint, MatrixSet)
+from sympy.matrices.common import NonSquareMatrixError
+from sympy.matrices.expressions.determinant import Determinant, det
+from sympy.matrices.expressions.matexpr import MatrixElement
+from sympy.matrices.expressions.special import ZeroMatrix, Identity
+from sympy.testing.pytest import raises, XFAIL
+
+
+n, m, l, k, p = symbols('n m l k p', integer=True)
+x = symbols('x')
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+w = MatrixSymbol('w', n, 1)
+
+
+def test_matrix_symbol_creation():
+    assert MatrixSymbol('A', 2, 2)
+    assert MatrixSymbol('A', 0, 0)
+    raises(ValueError, lambda: MatrixSymbol('A', -1, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2.0, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2j, 2))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, -1))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, 2.0))
+    raises(ValueError, lambda: MatrixSymbol('A', 2, 2j))
+
+    n = symbols('n')
+    assert MatrixSymbol('A', n, n)
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: MatrixSymbol('A', n, n))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: MatrixSymbol('A', n, n))
+
+
+def test_matexpr_properties():
+    assert A.shape == (n, m)
+    assert (A * B).shape == (n, l)
+    assert A[0, 1].indices == (0, 1)
+    assert A[0, 0].symbol == A
+    assert A[0, 0].symbol.name == 'A'
+
+
+def test_matexpr():
+    assert (x*A).shape == A.shape
+    assert (x*A).__class__ == MatMul
+    assert 2*A - A - A == ZeroMatrix(*A.shape)
+    assert (A*B).shape == (n, l)
+
+
+def test_matexpr_subs():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    C = MatrixSymbol('C', m, l)
+
+    assert A.subs(n, m).shape == (m, m)
+    assert (A*B).subs(B, C) == A*C
+    assert (A*B).subs(l, n).is_square
+
+    W = MatrixSymbol("W", 3, 3)
+    X = MatrixSymbol("X", 2, 2)
+    Y = MatrixSymbol("Y", 1, 2)
+    Z = MatrixSymbol("Z", n, 2)
+    # no restrictions on Symbol replacement
+    assert X.subs(X, Y) == Y
+    # it might be better to just change the name
+    y = Str('y')
+    assert X.subs(Str("X"), y).args == (y, 2, 2)
+    # it's ok to introduce a wider matrix
+    assert X[1, 1].subs(X, W) == W[1, 1]
+    # but for a given MatrixExpression, only change
+    # name if indexing on the new shape is valid.
+    # Here, X is 2,2; Y is 1,2 and Y[1, 1] is out
+    # of range so an error is raised
+    raises(IndexError, lambda: X[1, 1].subs(X, Y))
+    # here, [0, 1] is in range so the subs succeeds
+    assert X[0, 1].subs(X, Y) == Y[0, 1]
+    # and here the size of n will accept any index
+    # in the first position
+    assert W[2, 1].subs(W, Z) == Z[2, 1]
+    # but not in the second position
+    raises(IndexError, lambda: W[2, 2].subs(W, Z))
+    # any matrix should raise if invalid
+    raises(IndexError, lambda: W[2, 2].subs(W, zeros(2)))
+
+    A = SparseMatrix([[1, 2], [3, 4]])
+    B = Matrix([[1, 2], [3, 4]])
+    C, D = MatrixSymbol('C', 2, 2), MatrixSymbol('D', 2, 2)
+
+    assert (C*D).subs({C: A, D: B}) == MatMul(A, B)
+
+
+def test_addition():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', n, m)
+
+    assert isinstance(A + B, MatAdd)
+    assert (A + B).shape == A.shape
+    assert isinstance(A - A + 2*B, MatMul)
+
+    raises(TypeError, lambda: A + 1)
+    raises(TypeError, lambda: 5 + A)
+    raises(TypeError, lambda: 5 - A)
+
+    assert A + ZeroMatrix(n, m) - A == ZeroMatrix(n, m)
+    raises(TypeError, lambda: ZeroMatrix(n, m) + S.Zero)
+
+
+def test_multiplication():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    C = MatrixSymbol('C', n, n)
+
+    assert (2*A*B).shape == (n, l)
+    assert (A*0*B) == ZeroMatrix(n, l)
+    assert (2*A).shape == A.shape
+
+    assert A * ZeroMatrix(m, m) * B == ZeroMatrix(n, l)
+
+    assert C * Identity(n) * C.I == Identity(n)
+
+    assert B/2 == S.Half*B
+    raises(NotImplementedError, lambda: 2/B)
+
+    A = MatrixSymbol('A', n, n)
+    B = MatrixSymbol('B', n, n)
+    assert Identity(n) * (A + B) == A + B
+
+    assert A**2*A == A**3
+    assert A**2*(A.I)**3 == A.I
+    assert A**3*(A.I)**2 == A
+
+
+def test_MatPow():
+    A = MatrixSymbol('A', n, n)
+
+    AA = MatPow(A, 2)
+    assert AA.exp == 2
+    assert AA.base == A
+    assert (A**n).exp == n
+
+    assert A**0 == Identity(n)
+    assert A**1 == A
+    assert A**2 == AA
+    assert A**-1 == Inverse(A)
+    assert (A**-1)**-1 == A
+    assert (A**2)**3 == A**6
+    assert A**S.Half == sqrt(A)
+    assert A**Rational(1, 3) == cbrt(A)
+    raises(NonSquareMatrixError, lambda: MatrixSymbol('B', 3, 2)**2)
+
+
+def test_MatrixSymbol():
+    n, m, t = symbols('n,m,t')
+    X = MatrixSymbol('X', n, m)
+    assert X.shape == (n, m)
+    raises(TypeError, lambda: MatrixSymbol('X', n, m)(t))  # issue 5855
+    assert X.doit() == X
+
+
+def test_dense_conversion():
+    X = MatrixSymbol('X', 2, 2)
+    assert ImmutableMatrix(X) == ImmutableMatrix(2, 2, lambda i, j: X[i, j])
+    assert Matrix(X) == Matrix(2, 2, lambda i, j: X[i, j])
+
+
+def test_free_symbols():
+    assert (C*D).free_symbols == {C, D}
+
+
+def test_zero_matmul():
+    assert isinstance(S.Zero * MatrixSymbol('X', 2, 2), MatrixExpr)
+
+
+def test_matadd_simplify():
+    A = MatrixSymbol('A', 1, 1)
+    assert simplify(MatAdd(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
+        MatAdd(A, Matrix([[1]]))
+
+
+def test_matmul_simplify():
+    A = MatrixSymbol('A', 1, 1)
+    assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
+        MatMul(A, Matrix([[1]]))
+
+
+def test_invariants():
+    A = MatrixSymbol('A', n, m)
+    B = MatrixSymbol('B', m, l)
+    X = MatrixSymbol('X', n, n)
+    objs = [Identity(n), ZeroMatrix(m, n), A, MatMul(A, B), MatAdd(A, A),
+            Transpose(A), Adjoint(A), Inverse(X), MatPow(X, 2), MatPow(X, -1),
+            MatPow(X, 0)]
+    for obj in objs:
+        assert obj == obj.__class__(*obj.args)
+
+
+def test_matexpr_indexing():
+    A = MatrixSymbol('A', n, m)
+    A[1, 2]
+    A[l, k]
+    A[l + 1, k + 1]
+    A = MatrixSymbol('A', 2, 1)
+    for i in range(-2, 2):
+        for j in range(-1, 1):
+            A[i, j]
+
+
+def test_single_indexing():
+    A = MatrixSymbol('A', 2, 3)
+    assert A[1] == A[0, 1]
+    assert A[int(1)] == A[0, 1]
+    assert A[3] == A[1, 0]
+    assert list(A[:2, :2]) == [A[0, 0], A[0, 1], A[1, 0], A[1, 1]]
+    raises(IndexError, lambda: A[6])
+    raises(IndexError, lambda: A[n])
+    B = MatrixSymbol('B', n, m)
+    raises(IndexError, lambda: B[1])
+    B = MatrixSymbol('B', n, 3)
+    assert B[3] == B[1, 0]
+
+
+def test_MatrixElement_commutative():
+    assert A[0, 1]*A[1, 0] == A[1, 0]*A[0, 1]
+
+
+def test_MatrixSymbol_determinant():
+    A = MatrixSymbol('A', 4, 4)
+    assert A.as_explicit().det() == A[0, 0]*A[1, 1]*A[2, 2]*A[3, 3] - \
+        A[0, 0]*A[1, 1]*A[2, 3]*A[3, 2] - A[0, 0]*A[1, 2]*A[2, 1]*A[3, 3] + \
+        A[0, 0]*A[1, 2]*A[2, 3]*A[3, 1] + A[0, 0]*A[1, 3]*A[2, 1]*A[3, 2] - \
+        A[0, 0]*A[1, 3]*A[2, 2]*A[3, 1] - A[0, 1]*A[1, 0]*A[2, 2]*A[3, 3] + \
+        A[0, 1]*A[1, 0]*A[2, 3]*A[3, 2] + A[0, 1]*A[1, 2]*A[2, 0]*A[3, 3] - \
+        A[0, 1]*A[1, 2]*A[2, 3]*A[3, 0] - A[0, 1]*A[1, 3]*A[2, 0]*A[3, 2] + \
+        A[0, 1]*A[1, 3]*A[2, 2]*A[3, 0] + A[0, 2]*A[1, 0]*A[2, 1]*A[3, 3] - \
+        A[0, 2]*A[1, 0]*A[2, 3]*A[3, 1] - A[0, 2]*A[1, 1]*A[2, 0]*A[3, 3] + \
+        A[0, 2]*A[1, 1]*A[2, 3]*A[3, 0] + A[0, 2]*A[1, 3]*A[2, 0]*A[3, 1] - \
+        A[0, 2]*A[1, 3]*A[2, 1]*A[3, 0] - A[0, 3]*A[1, 0]*A[2, 1]*A[3, 2] + \
+        A[0, 3]*A[1, 0]*A[2, 2]*A[3, 1] + A[0, 3]*A[1, 1]*A[2, 0]*A[3, 2] - \
+        A[0, 3]*A[1, 1]*A[2, 2]*A[3, 0] - A[0, 3]*A[1, 2]*A[2, 0]*A[3, 1] + \
+        A[0, 3]*A[1, 2]*A[2, 1]*A[3, 0]
+
+    B = MatrixSymbol('B', 4, 4)
+    assert Determinant(A + B).doit() == det(A + B) == (A + B).det()
+
+
+def test_MatrixElement_diff():
+    assert (A[3, 0]*A[0, 0]).diff(A[0, 0]) == A[3, 0]
+
+
+def test_MatrixElement_doit():
+    u = MatrixSymbol('u', 2, 1)
+    v = ImmutableMatrix([3, 5])
+    assert u[0, 0].subs(u, v).doit() == v[0, 0]
+
+
+def test_identity_powers():
+    M = Identity(n)
+    assert MatPow(M, 3).doit() == M**3
+    assert M**n == M
+    assert MatPow(M, 0).doit() == M**2
+    assert M**-2 == M
+    assert MatPow(M, -2).doit() == M**0
+    N = Identity(3)
+    assert MatPow(N, 2).doit() == N**n
+    assert MatPow(N, 3).doit() == N
+    assert MatPow(N, -2).doit() == N**4
+    assert MatPow(N, 2).doit() == N**0
+
+
+def test_Zero_power():
+    z1 = ZeroMatrix(n, n)
+    assert z1**4 == z1
+    raises(ValueError, lambda:z1**-2)
+    assert z1**0 == Identity(n)
+    assert MatPow(z1, 2).doit() == z1**2
+    raises(ValueError, lambda:MatPow(z1, -2).doit())
+    z2 = ZeroMatrix(3, 3)
+    assert MatPow(z2, 4).doit() == z2**4
+    raises(ValueError, lambda:z2**-3)
+    assert z2**3 == MatPow(z2, 3).doit()
+    assert z2**0 == Identity(3)
+    raises(ValueError, lambda:MatPow(z2, -1).doit())
+
+
+def test_matrixelement_diff():
+    dexpr = diff((D*w)[k,0], w[p,0])
+
+    assert w[k, p].diff(w[k, p]) == 1
+    assert w[k, p].diff(w[0, 0]) == KroneckerDelta(0, k, (0, n-1))*KroneckerDelta(0, p, (0, 0))
+    _i_1 = Dummy("_i_1")
+    assert dexpr.dummy_eq(Sum(KroneckerDelta(_i_1, p, (0, n-1))*D[k, _i_1], (_i_1, 0, n - 1)))
+    assert dexpr.doit() == D[k, p]
+
+
+def test_MatrixElement_with_values():
+    x, y, z, w = symbols("x y z w")
+    M = Matrix([[x, y], [z, w]])
+    i, j = symbols("i, j")
+    Mij = M[i, j]
+    assert isinstance(Mij, MatrixElement)
+    Ms = SparseMatrix([[2, 3], [4, 5]])
+    msij = Ms[i, j]
+    assert isinstance(msij, MatrixElement)
+    for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]:
+        assert Mij.subs({i: oi, j: oj}) == M[oi, oj]
+        assert msij.subs({i: oi, j: oj}) == Ms[oi, oj]
+    A = MatrixSymbol("A", 2, 2)
+    assert A[0, 0].subs(A, M) == x
+    assert A[i, j].subs(A, M) == M[i, j]
+    assert M[i, j].subs(M, A) == A[i, j]
+
+    assert isinstance(M[3*i - 2, j], MatrixElement)
+    assert M[3*i - 2, j].subs({i: 1, j: 0}) == M[1, 0]
+    assert isinstance(M[i, 0], MatrixElement)
+    assert M[i, 0].subs(i, 0) == M[0, 0]
+    assert M[0, i].subs(i, 1) == M[0, 1]
+
+    assert M[i, j].diff(x) == Matrix([[1, 0], [0, 0]])[i, j]
+
+    raises(ValueError, lambda: M[i, 2])
+    raises(ValueError, lambda: M[i, -1])
+    raises(ValueError, lambda: M[2, i])
+    raises(ValueError, lambda: M[-1, i])
+
+
+def test_inv():
+    B = MatrixSymbol('B', 3, 3)
+    assert B.inv() == B**-1
+
+    # https://github.com/sympy/sympy/issues/19162
+    X = MatrixSymbol('X', 1, 1).as_explicit()
+    assert X.inv() == Matrix([[1/X[0, 0]]])
+
+    X = MatrixSymbol('X', 2, 2).as_explicit()
+    detX = X[0, 0]*X[1, 1] - X[0, 1]*X[1, 0]
+    invX = Matrix([[ X[1, 1], -X[0, 1]],
+                   [-X[1, 0],  X[0, 0]]]) / detX
+    assert X.inv() == invX
+
+
+@XFAIL
+def test_factor_expand():
+    A = MatrixSymbol("A", n, n)
+    B = MatrixSymbol("B", n, n)
+    expr1 = (A + B)*(C + D)
+    expr2 = A*C + B*C + A*D + B*D
+    assert expr1 != expr2
+    assert expand(expr1) == expr2
+    assert factor(expr2) == expr1
+
+    expr = B**(-1)*(A**(-1)*B**(-1) - A**(-1)*C*B**(-1))**(-1)*A**(-1)
+    I = Identity(n)
+    # Ideally we get the first, but we at least don't want a wrong answer
+    assert factor(expr) in [I - C, B**-1*(A**-1*(I - C)*B**-1)**-1*A**-1]
+
+
+def test_issue_2749():
+    A = MatrixSymbol("A", 5, 2)
+    assert (A.T * A).I.as_explicit() == Matrix([[(A.T * A).I[0, 0], (A.T * A).I[0, 1]], \
+    [(A.T * A).I[1, 0], (A.T * A).I[1, 1]]])
+
+
+def test_issue_2750():
+    x = MatrixSymbol('x', 1, 1)
+    assert (x.T*x).as_explicit()**-1 == Matrix([[x[0, 0]**(-2)]])
+
+
+def test_issue_7842():
+    A = MatrixSymbol('A', 3, 1)
+    B = MatrixSymbol('B', 2, 1)
+    assert Eq(A, B) == False
+    assert Eq(A[1,0], B[1, 0]).func is Eq
+    A = ZeroMatrix(2, 3)
+    B = ZeroMatrix(2, 3)
+    assert Eq(A, B) == True
+
+
+def test_issue_21195():
+    t = symbols('t')
+    x = Function('x')(t)
+    dx = x.diff(t)
+    exp1 = cos(x) + cos(x)*dx
+    exp2 = sin(x) + tan(x)*(dx.diff(t))
+    exp3 = sin(x)*sin(t)*(dx.diff(t)).diff(t)
+    A = Matrix([[exp1], [exp2], [exp3]])
+    B = Matrix([[exp1.diff(x)], [exp2.diff(x)], [exp3.diff(x)]])
+    assert A.diff(x) == B
+
+
+def test_MatMul_postprocessor():
+    z = zeros(2)
+    z1 = ZeroMatrix(2, 2)
+    assert Mul(0, z) == Mul(z, 0) in [z, z1]
+
+    M = Matrix([[1, 2], [3, 4]])
+    Mx = Matrix([[x, 2*x], [3*x, 4*x]])
+    assert Mul(x, M) == Mul(M, x) == Mx
+
+    A = MatrixSymbol("A", 2, 2)
+    assert Mul(A, M) == MatMul(A, M)
+    assert Mul(M, A) == MatMul(M, A)
+    # Scalars should be absorbed into constant matrices
+    a = Mul(x, M, A)
+    b = Mul(M, x, A)
+    c = Mul(M, A, x)
+    assert a == b == c == MatMul(Mx, A)
+    a = Mul(x, A, M)
+    b = Mul(A, x, M)
+    c = Mul(A, M, x)
+    assert a == b == c == MatMul(A, Mx)
+    assert Mul(M, M) == M**2
+    assert Mul(A, M, M) == MatMul(A, M**2)
+    assert Mul(M, M, A) == MatMul(M**2, A)
+    assert Mul(M, A, M) == MatMul(M, A, M)
+
+    assert Mul(A, x, M, M, x) == MatMul(A, Mx**2)
+
+
+@XFAIL
+def test_MatAdd_postprocessor_xfail():
+    # This is difficult to get working because of the way that Add processes
+    # its args.
+    z = zeros(2)
+    assert Add(z, S.NaN) == Add(S.NaN, z)
+
+
+def test_MatAdd_postprocessor():
+    # Some of these are nonsensical, but we do not raise errors for Add
+    # because that breaks algorithms that want to replace matrices with dummy
+    # symbols.
+
+    z = zeros(2)
+
+    assert Add(0, z) == Add(z, 0) == z
+
+    a = Add(S.Infinity, z)
+    assert a == Add(z, S.Infinity)
+    assert isinstance(a, Add)
+    assert a.args == (S.Infinity, z)
+
+    a = Add(S.ComplexInfinity, z)
+    assert a == Add(z, S.ComplexInfinity)
+    assert isinstance(a, Add)
+    assert a.args == (S.ComplexInfinity, z)
+
+    a = Add(z, S.NaN)
+    # assert a == Add(S.NaN, z) # See the XFAIL above
+    assert isinstance(a, Add)
+    assert a.args == (S.NaN, z)
+
+    M = Matrix([[1, 2], [3, 4]])
+    a = Add(x, M)
+    assert a == Add(M, x)
+    assert isinstance(a, Add)
+    assert a.args == (x, M)
+
+    A = MatrixSymbol("A", 2, 2)
+    assert Add(A, M) == Add(M, A) == A + M
+
+    # Scalars should be absorbed into constant matrices (producing an error)
+    a = Add(x, M, A)
+    assert a == Add(M, x, A) == Add(M, A, x) == Add(x, A, M) == Add(A, x, M) == Add(A, M, x)
+    assert isinstance(a, Add)
+    assert a.args == (x, A + M)
+
+    assert Add(M, M) == 2*M
+    assert Add(M, A, M) == Add(M, M, A) == Add(A, M, M) == A + 2*M
+
+    a = Add(A, x, M, M, x)
+    assert isinstance(a, Add)
+    assert a.args == (2*x, A + 2*M)
+
+
+def test_simplify_matrix_expressions():
+    # Various simplification functions
+    assert type(gcd_terms(C*D + D*C)) == MatAdd
+    a = gcd_terms(2*C*D + 4*D*C)
+    assert type(a) == MatAdd
+    assert a.args == (2*C*D, 4*D*C)
+
+
+def test_exp():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 2, 2)
+    expr1 = exp(A)*exp(B)
+    expr2 = exp(B)*exp(A)
+    assert expr1 != expr2
+    assert expr1 - expr2 != 0
+    assert not isinstance(expr1, exp)
+    assert not isinstance(expr2, exp)
+
+
+def test_invalid_args():
+    raises(SympifyError, lambda: MatrixSymbol(1, 2, 'A'))
+
+
+def test_matrixsymbol_from_symbol():
+    # The label should be preserved during doit and subs
+    A_label = Symbol('A', complex=True)
+    A = MatrixSymbol(A_label, 2, 2)
+
+    A_1 = A.doit()
+    A_2 = A.subs(2, 3)
+    assert A_1.args == A.args
+    assert A_2.args[0] == A.args[0]
+
+
+def test_as_explicit():
+    Z = MatrixSymbol('Z', 2, 3)
+    assert Z.as_explicit() == ImmutableMatrix([
+        [Z[0, 0], Z[0, 1], Z[0, 2]],
+        [Z[1, 0], Z[1, 1], Z[1, 2]],
+    ])
+    raises(ValueError, lambda: A.as_explicit())
+
+
+def test_MatrixSet():
+    M = MatrixSet(2, 2, set=S.Reals)
+    assert M.shape == (2, 2)
+    assert M.set == S.Reals
+    X = Matrix([[1, 2], [3, 4]])
+    assert X in M
+    X = ZeroMatrix(2, 2)
+    assert X in M
+    raises(TypeError, lambda: A in M)
+    raises(TypeError, lambda: 1 in M)
+    M = MatrixSet(n, m, set=S.Reals)
+    assert A in M
+    raises(TypeError, lambda: C in M)
+    raises(TypeError, lambda: X in M)
+    M = MatrixSet(2, 2, set={1, 2, 3})
+    X = Matrix([[1, 2], [3, 4]])
+    Y = Matrix([[1, 2]])
+    assert (X in M) == S.false
+    assert (Y in M) == S.false
+    raises(ValueError, lambda: MatrixSet(2, -2, S.Reals))
+    raises(ValueError, lambda: MatrixSet(2.4, -1, S.Reals))
+    raises(TypeError, lambda: MatrixSet(2, 2, (1, 2, 3)))
+
+
+def test_matrixsymbol_solving():
+    A = MatrixSymbol('A', 2, 2)
+    B = MatrixSymbol('B', 2, 2)
+    Z = ZeroMatrix(2, 2)
+    assert -(-A + B) - A + B == Z
+    assert (-(-A + B) - A + B).simplify() == Z
+    assert (-(-A + B) - A + B).expand() == Z
+    assert (-(-A + B) - A + B - Z).simplify() == Z
+    assert (-(-A + B) - A + B - Z).expand() == Z
+    assert (A*(A + B) + B*(A.T + B.T)).expand() == A**2 + A*B + B*A.T + B*B.T

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_matpow.py

@@ -0,0 +1,217 @@
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.simplify.powsimp import powsimp
+from sympy.testing.pytest import raises
+from sympy.core.expr import unchanged
+from sympy.core import symbols, S
+from sympy.matrices import Identity, MatrixSymbol, ImmutableMatrix, ZeroMatrix, OneMatrix, Matrix
+from sympy.matrices.common import NonSquareMatrixError
+from sympy.matrices.expressions import MatPow, MatAdd, MatMul
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matexpr import MatrixElement
+
+n, m, l, k = symbols('n m l k', integer=True)
+A = MatrixSymbol('A', n, m)
+B = MatrixSymbol('B', m, l)
+C = MatrixSymbol('C', n, n)
+D = MatrixSymbol('D', n, n)
+E = MatrixSymbol('E', m, n)
+
+
+def test_entry_matrix():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(X, 0)[0, 0] == 1
+    assert MatPow(X, 0)[0, 1] == 0
+    assert MatPow(X, 1)[0, 0] == 1
+    assert MatPow(X, 1)[0, 1] == 2
+    assert MatPow(X, 2)[0, 0] == 7
+
+
+def test_entry_symbol():
+    from sympy.concrete import Sum
+    assert MatPow(C, 0)[0, 0] == 1
+    assert MatPow(C, 0)[0, 1] == 0
+    assert MatPow(C, 1)[0, 0] == C[0, 0]
+    assert isinstance(MatPow(C, 2)[0, 0], Sum)
+    assert isinstance(MatPow(C, n)[0, 0], MatrixElement)
+
+
+def test_as_explicit_symbol():
+    X = MatrixSymbol('X', 2, 2)
+    assert MatPow(X, 0).as_explicit() == ImmutableMatrix(Identity(2))
+    assert MatPow(X, 1).as_explicit() == X.as_explicit()
+    assert MatPow(X, 2).as_explicit() == (X.as_explicit())**2
+    assert MatPow(X, n).as_explicit() == ImmutableMatrix([
+        [(X ** n)[0, 0], (X ** n)[0, 1]],
+        [(X ** n)[1, 0], (X ** n)[1, 1]],
+    ])
+
+    a = MatrixSymbol("a", 3, 1)
+    b = MatrixSymbol("b", 3, 1)
+    c = MatrixSymbol("c", 3, 1)
+
+    expr = (a.T*b)**S.Half
+    assert expr.as_explicit() == Matrix([[sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])]])
+
+    expr = c*(a.T*b)**S.Half
+    m = sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])
+    assert expr.as_explicit() == Matrix([[c[0, 0]*m], [c[1, 0]*m], [c[2, 0]*m]])
+
+    expr = (a*b.T)**S.Half
+    denom = sqrt(a[0, 0]*b[0, 0] + a[1, 0]*b[1, 0] + a[2, 0]*b[2, 0])
+    expected = (a*b.T).as_explicit()/denom
+    assert expr.as_explicit() == expected
+
+    expr = X**-1
+    det = X[0, 0]*X[1, 1] - X[1, 0]*X[0, 1]
+    expected = Matrix([[X[1, 1], -X[0, 1]], [-X[1, 0], X[0, 0]]])/det
+    assert expr.as_explicit() == expected
+
+    expr = X**m
+    assert expr.as_explicit() == X.as_explicit()**m
+
+
+def test_as_explicit_matrix():
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(A, 0).as_explicit() == ImmutableMatrix(Identity(2))
+    assert MatPow(A, 1).as_explicit() == A
+    assert MatPow(A, 2).as_explicit() == A**2
+    assert MatPow(A, -1).as_explicit() == A.inv()
+    assert MatPow(A, -2).as_explicit() == (A.inv())**2
+    # less expensive than testing on a 2x2
+    A = ImmutableMatrix([4])
+    assert MatPow(A, S.Half).as_explicit() == A**S.Half
+
+
+def test_doit_symbol():
+    assert MatPow(C, 0).doit() == Identity(n)
+    assert MatPow(C, 1).doit() == C
+    assert MatPow(C, -1).doit() == C.I
+    for r in [2, S.Half, S.Pi, n]:
+        assert MatPow(C, r).doit() == MatPow(C, r)
+
+
+def test_doit_matrix():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    assert MatPow(X, 0).doit() == ImmutableMatrix(Identity(2))
+    assert MatPow(X, 1).doit() == X
+    assert MatPow(X, 2).doit() == X**2
+    assert MatPow(X, -1).doit() == X.inv()
+    assert MatPow(X, -2).doit() == (X.inv())**2
+    # less expensive than testing on a 2x2
+    assert MatPow(ImmutableMatrix([4]), S.Half).doit() == ImmutableMatrix([2])
+    X = ImmutableMatrix([[0, 2], [0, 4]]) # det() == 0
+    raises(ValueError, lambda: MatPow(X,-1).doit())
+    raises(ValueError, lambda: MatPow(X,-2).doit())
+
+
+def test_nonsquare():
+    A = MatrixSymbol('A', 2, 3)
+    B = ImmutableMatrix([[1, 2, 3], [4, 5, 6]])
+    for r in [-1, 0, 1, 2, S.Half, S.Pi, n]:
+        raises(NonSquareMatrixError, lambda: MatPow(A, r))
+        raises(NonSquareMatrixError, lambda: MatPow(B, r))
+
+
+def test_doit_equals_pow(): #17179
+    X = ImmutableMatrix ([[1,0],[0,1]])
+    assert MatPow(X, n).doit() == X**n == X
+
+
+def test_doit_nested_MatrixExpr():
+    X = ImmutableMatrix([[1, 2], [3, 4]])
+    Y = ImmutableMatrix([[2, 3], [4, 5]])
+    assert MatPow(MatMul(X, Y), 2).doit() == (X*Y)**2
+    assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2
+
+
+def test_identity_power():
+    k = Identity(n)
+    assert MatPow(k, 4).doit() == k
+    assert MatPow(k, n).doit() == k
+    assert MatPow(k, -3).doit() == k
+    assert MatPow(k, 0).doit() == k
+    l = Identity(3)
+    assert MatPow(l, n).doit() == l
+    assert MatPow(l, -1).doit() == l
+    assert MatPow(l, 0).doit() == l
+
+
+def test_zero_power():
+    z1 = ZeroMatrix(n, n)
+    assert MatPow(z1, 3).doit() == z1
+    raises(ValueError, lambda:MatPow(z1, -1).doit())
+    assert MatPow(z1, 0).doit() == Identity(n)
+    assert MatPow(z1, n).doit() == z1
+    raises(ValueError, lambda:MatPow(z1, -2).doit())
+    z2 = ZeroMatrix(4, 4)
+    assert MatPow(z2, n).doit() == z2
+    raises(ValueError, lambda:MatPow(z2, -3).doit())
+    assert MatPow(z2, 2).doit() == z2
+    assert MatPow(z2, 0).doit() == Identity(4)
+    raises(ValueError, lambda:MatPow(z2, -1).doit())
+
+
+def test_OneMatrix_power():
+    o = OneMatrix(3, 3)
+    assert o ** 0 == Identity(3)
+    assert o ** 1 == o
+    assert o * o == o ** 2 == 3 * o
+    assert o * o * o == o ** 3 == 9 * o
+
+    o = OneMatrix(n, n)
+    assert o * o == o ** 2 == n * o
+    # powsimp necessary as n ** (n - 2) * n does not produce n ** (n - 1)
+    assert powsimp(o ** (n - 1) * o) == o ** n == n ** (n - 1) * o
+
+
+def test_transpose_power():
+    from sympy.matrices.expressions.transpose import Transpose as TP
+
+    assert (C*D).T**5 == ((C*D)**5).T == (D.T * C.T)**5
+    assert ((C*D).T**5).T == (C*D)**5
+
+    assert (C.T.I.T)**7 == C**-7
+    assert (C.T**l).T**k == C**(l*k)
+
+    assert ((E.T * A.T)**5).T == (A*E)**5
+    assert ((A*E).T**5).T**7 == (A*E)**35
+    assert TP(TP(C**2 * D**3)**5).doit() == (C**2 * D**3)**5
+
+    assert ((D*C)**-5).T**-5 == ((D*C)**25).T
+    assert (((D*C)**l).T**k).T == (D*C)**(l*k)
+
+
+def test_Inverse():
+    assert Inverse(MatPow(C, 0)).doit() == Identity(n)
+    assert Inverse(MatPow(C, 1)).doit() == Inverse(C)
+    assert Inverse(MatPow(C, 2)).doit() == MatPow(C, -2)
+    assert Inverse(MatPow(C, -1)).doit() == C
+
+    assert MatPow(Inverse(C), 0).doit() == Identity(n)
+    assert MatPow(Inverse(C), 1).doit() == Inverse(C)
+    assert MatPow(Inverse(C), 2).doit() == MatPow(C, -2)
+    assert MatPow(Inverse(C), -1).doit() == C
+
+
+def test_combine_powers():
+    assert (C ** 1) ** 1 == C
+    assert (C ** 2) ** 3 == MatPow(C, 6)
+    assert (C ** -2) ** -3 == MatPow(C, 6)
+    assert (C ** -1) ** -1 == C
+    assert (((C ** 2) ** 3) ** 4) ** 5 == MatPow(C, 120)
+    assert (C ** n) ** n == C ** (n ** 2)
+
+
+def test_unchanged():
+    assert unchanged(MatPow, C, 0)
+    assert unchanged(MatPow, C, 1)
+    assert unchanged(MatPow, Inverse(C), -1)
+    assert unchanged(Inverse, MatPow(C, -1), -1)
+    assert unchanged(MatPow, MatPow(C, -1), -1)
+    assert unchanged(MatPow, MatPow(C, 1), 1)
+
+
+def test_no_exponentiation():
+    # if this passes, Pow.as_numer_denom should recognize
+    # MatAdd as exponent
+    raises(NotImplementedError, lambda: 3**(-2*C))

env-llmeval/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_slice.py

@@ -0,0 +1,65 @@
+from sympy.matrices.expressions.slice import MatrixSlice
+from sympy.matrices.expressions import MatrixSymbol
+from sympy.abc import a, b, c, d, k, l, m, n
+from sympy.testing.pytest import raises, XFAIL
+from sympy.functions.elementary.integers import floor
+from sympy.assumptions import assuming, Q
+
+
+X = MatrixSymbol('X', n, m)
+Y = MatrixSymbol('Y', m, k)
+
+def test_shape():
+    B = MatrixSlice(X, (a, b), (c, d))
+    assert B.shape == (b - a, d - c)
+
+def test_entry():
+    B = MatrixSlice(X, (a, b), (c, d))
+    assert B[0,0] == X[a, c]
+    assert B[k,l] == X[a+k, c+l]
+    raises(IndexError, lambda : MatrixSlice(X, 1, (2, 5))[1, 0])
+
+    assert X[1::2, :][1, 3] == X[1+2, 3]
+    assert X[:, 1::2][3, 1] == X[3, 1+2]
+
+def test_on_diag():
+    assert not MatrixSlice(X, (a, b), (c, d)).on_diag
+    assert MatrixSlice(X, (a, b), (a, b)).on_diag
+
+def test_inputs():
+    assert MatrixSlice(X, 1, (2, 5)) == MatrixSlice(X, (1, 2), (2, 5))
+    assert MatrixSlice(X, 1, (2, 5)).shape == (1, 3)
+
+def test_slicing():
+    assert X[1:5, 2:4] == MatrixSlice(X, (1, 5), (2, 4))
+    assert X[1, 2:4] == MatrixSlice(X, 1, (2, 4))
+    assert X[1:5, :].shape == (4, X.shape[1])
+    assert X[:, 1:5].shape == (X.shape[0], 4)
+
+    assert X[::2, ::2].shape == (floor(n/2), floor(m/2))
+    assert X[2, :] == MatrixSlice(X, 2, (0, m))
+    assert X[k, :] == MatrixSlice(X, k, (0, m))
+
+def test_exceptions():
+    X = MatrixSymbol('x', 10, 20)
+    raises(IndexError, lambda: X[0:12, 2])
+    raises(IndexError, lambda: X[0:9, 22])
+    raises(IndexError, lambda: X[-1:5, 2])
+
+@XFAIL
+def test_symmetry():
+    X = MatrixSymbol('x', 10, 10)
+    Y = X[:5, 5:]
+    with assuming(Q.symmetric(X)):
+        assert Y.T == X[5:, :5]
+
+def test_slice_of_slice():
+    X = MatrixSymbol('x', 10, 10)
+    assert X[2, :][:, 3][0, 0] == X[2, 3]
+    assert X[:5, :5][:4, :4] == X[:4, :4]
+    assert X[1:5, 2:6][1:3, 2] == X[2:4, 4]
+    assert X[1:9:2, 2:6][1:3, 2] == X[3:7:2, 4]
+
+def test_negative_index():
+    X = MatrixSymbol('x', 10, 10)
+    assert X[-1, :] == X[9, :]