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ckpts/universal/global_step120/zero/4.mlp.dense_h_to_4h_swiglu.weight/exp_avg.pt

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ckpts/universal/global_step120/zero/4.mlp.dense_h_to_4h_swiglu.weight/fp32.pt

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ckpts/universal/global_step120/zero/5.mlp.dense_4h_to_h.weight/exp_avg.pt

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ckpts/universal/global_step120/zero/7.mlp.dense_h_to_4h.weight/exp_avg_sq.pt

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ckpts/universal/global_step120/zero/7.mlp.dense_h_to_4h.weight/fp32.pt

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+version https://git-lfs.github.com/spec/v1
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venv/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)]])

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_derivatives.py

@@ -0,0 +1,477 @@
+"""
+Some examples have been taken from:
+
+http://www.math.uwaterloo.ca/~hwolkowi//matrixcookbook.pdf
+"""
+from sympy import KroneckerProduct
+from sympy.combinatorics import Permutation
+from sympy.concrete.summations import Sum
+from sympy.core.numbers import Rational
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.expressions.determinant import Determinant
+from sympy.matrices.expressions.diagonal import DiagMatrix
+from sympy.matrices.expressions.hadamard import (HadamardPower, HadamardProduct, hadamard_product)
+from sympy.matrices.expressions.inverse import Inverse
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.special import OneMatrix
+from sympy.matrices.expressions.trace import Trace
+from sympy.matrices.expressions.matadd import MatAdd
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.matrices.expressions.special import (Identity, ZeroMatrix)
+from sympy.tensor.array.array_derivatives import ArrayDerivative
+from sympy.matrices.expressions import hadamard_power
+from sympy.tensor.array.expressions.array_expressions import ArrayAdd, ArrayTensorProduct, PermuteDims
+
+i, j, k = symbols("i j k")
+m, n = symbols("m n")
+
+X = MatrixSymbol("X", k, k)
+x = MatrixSymbol("x", k, 1)
+y = MatrixSymbol("y", k, 1)
+
+A = MatrixSymbol("A", k, k)
+B = MatrixSymbol("B", k, k)
+C = MatrixSymbol("C", k, k)
+D = MatrixSymbol("D", k, k)
+
+a = MatrixSymbol("a", k, 1)
+b = MatrixSymbol("b", k, 1)
+c = MatrixSymbol("c", k, 1)
+d = MatrixSymbol("d", k, 1)
+
+
+KDelta = lambda i, j: KroneckerDelta(i, j, (0, k-1))
+
+
+def _check_derivative_with_explicit_matrix(expr, x, diffexpr, dim=2):
+    # TODO: this is commented because it slows down the tests.
+    return
+
+    expr = expr.xreplace({k: dim})
+    x = x.xreplace({k: dim})
+    diffexpr = diffexpr.xreplace({k: dim})
+
+    expr = expr.as_explicit()
+    x = x.as_explicit()
+    diffexpr = diffexpr.as_explicit()
+
+    assert expr.diff(x).reshape(*diffexpr.shape).tomatrix() == diffexpr
+
+
+def test_matrix_derivative_by_scalar():
+    assert A.diff(i) == ZeroMatrix(k, k)
+    assert (A*(X + B)*c).diff(i) == ZeroMatrix(k, 1)
+    assert x.diff(i) == ZeroMatrix(k, 1)
+    assert (x.T*y).diff(i) == ZeroMatrix(1, 1)
+    assert (x*x.T).diff(i) == ZeroMatrix(k, k)
+    assert (x + y).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_power(x, 2).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_power(x, i).diff(i).dummy_eq(
+        HadamardProduct(x.applyfunc(log), HadamardPower(x, i)))
+    assert hadamard_product(x, y).diff(i) == ZeroMatrix(k, 1)
+    assert hadamard_product(i*OneMatrix(k, 1), x, y).diff(i) == hadamard_product(x, y)
+    assert (i*x).diff(i) == x
+    assert (sin(i)*A*B*x).diff(i) == cos(i)*A*B*x
+    assert x.applyfunc(sin).diff(i) == ZeroMatrix(k, 1)
+    assert Trace(i**2*X).diff(i) == 2*i*Trace(X)
+
+    mu = symbols("mu")
+    expr = (2*mu*x)
+    assert expr.diff(x) == 2*mu*Identity(k)
+
+
+def test_one_matrix():
+    assert MatMul(x.T, OneMatrix(k, 1)).diff(x) == OneMatrix(k, 1)
+
+
+def test_matrix_derivative_non_matrix_result():
+    # This is a 4-dimensional array:
+    I = Identity(k)
+    AdA = PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2))
+    assert A.diff(A) == AdA
+    assert A.T.diff(A) == PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2, 3))
+    assert (2*A).diff(A) == PermuteDims(ArrayTensorProduct(2*I, I), Permutation(3)(1, 2))
+    assert MatAdd(A, A).diff(A) == ArrayAdd(AdA, AdA)
+    assert (A + B).diff(A) == AdA
+
+
+def test_matrix_derivative_trivial_cases():
+    # Cookbook example 33:
+    # TODO: find a way to represent a four-dimensional zero-array:
+    assert X.diff(A) == ArrayDerivative(X, A)
+
+
+def test_matrix_derivative_with_inverse():
+
+    # Cookbook example 61:
+    expr = a.T*Inverse(X)*b
+    assert expr.diff(X) == -Inverse(X).T*a*b.T*Inverse(X).T
+
+    # Cookbook example 62:
+    expr = Determinant(Inverse(X))
+    # Not implemented yet:
+    # assert expr.diff(X) == -Determinant(X.inv())*(X.inv()).T
+
+    # Cookbook example 63:
+    expr = Trace(A*Inverse(X)*B)
+    assert expr.diff(X) == -(X**(-1)*B*A*X**(-1)).T
+
+    # Cookbook example 64:
+    expr = Trace(Inverse(X + A))
+    assert expr.diff(X) == -(Inverse(X + A)).T**2
+
+
+def test_matrix_derivative_vectors_and_scalars():
+
+    assert x.diff(x) == Identity(k)
+    assert x[i, 0].diff(x[m, 0]).doit() == KDelta(m, i)
+
+    assert x.T.diff(x) == Identity(k)
+
+    # Cookbook example 69:
+    expr = x.T*a
+    assert expr.diff(x) == a
+    assert expr[0, 0].diff(x[m, 0]).doit() == a[m, 0]
+    expr = a.T*x
+    assert expr.diff(x) == a
+
+    # Cookbook example 70:
+    expr = a.T*X*b
+    assert expr.diff(X) == a*b.T
+
+    # Cookbook example 71:
+    expr = a.T*X.T*b
+    assert expr.diff(X) == b*a.T
+
+    # Cookbook example 72:
+    expr = a.T*X*a
+    assert expr.diff(X) == a*a.T
+    expr = a.T*X.T*a
+    assert expr.diff(X) == a*a.T
+
+    # Cookbook example 77:
+    expr = b.T*X.T*X*c
+    assert expr.diff(X) == X*b*c.T + X*c*b.T
+
+    # Cookbook example 78:
+    expr = (B*x + b).T*C*(D*x + d)
+    assert expr.diff(x) == B.T*C*(D*x + d) + D.T*C.T*(B*x + b)
+
+    # Cookbook example 81:
+    expr = x.T*B*x
+    assert expr.diff(x) == B*x + B.T*x
+
+    # Cookbook example 82:
+    expr = b.T*X.T*D*X*c
+    assert expr.diff(X) == D.T*X*b*c.T + D*X*c*b.T
+
+    # Cookbook example 83:
+    expr = (X*b + c).T*D*(X*b + c)
+    assert expr.diff(X) == D*(X*b + c)*b.T + D.T*(X*b + c)*b.T
+    assert str(expr[0, 0].diff(X[m, n]).doit()) == \
+        'b[n, 0]*Sum((c[_i_1, 0] + Sum(X[_i_1, _i_3]*b[_i_3, 0], (_i_3, 0, k - 1)))*D[_i_1, m], (_i_1, 0, k - 1)) + Sum((c[_i_2, 0] + Sum(X[_i_2, _i_4]*b[_i_4, 0], (_i_4, 0, k - 1)))*D[m, _i_2]*b[n, 0], (_i_2, 0, k - 1))'
+
+    # See https://github.com/sympy/sympy/issues/16504#issuecomment-1018339957
+    expr = x*x.T*x
+    I = Identity(k)
+    assert expr.diff(x) == KroneckerProduct(I, x.T*x) + 2*x*x.T
+
+
+def test_matrix_derivatives_of_traces():
+
+    expr = Trace(A)*A
+    I = Identity(k)
+    assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2)))
+    assert expr[i, j].diff(A[m, n]).doit() == (
+        KDelta(i, m)*KDelta(j, n)*Trace(A) +
+        KDelta(m, n)*A[i, j]
+    )
+
+    ## First order:
+
+    # Cookbook example 99:
+    expr = Trace(X)
+    assert expr.diff(X) == Identity(k)
+    assert expr.rewrite(Sum).diff(X[m, n]).doit() == KDelta(m, n)
+
+    # Cookbook example 100:
+    expr = Trace(X*A)
+    assert expr.diff(X) == A.T
+    assert expr.rewrite(Sum).diff(X[m, n]).doit() == A[n, m]
+
+    # Cookbook example 101:
+    expr = Trace(A*X*B)
+    assert expr.diff(X) == A.T*B.T
+    assert expr.rewrite(Sum).diff(X[m, n]).doit().dummy_eq((A.T*B.T)[m, n])
+
+    # Cookbook example 102:
+    expr = Trace(A*X.T*B)
+    assert expr.diff(X) == B*A
+
+    # Cookbook example 103:
+    expr = Trace(X.T*A)
+    assert expr.diff(X) == A
+
+    # Cookbook example 104:
+    expr = Trace(A*X.T)
+    assert expr.diff(X) == A
+
+    # Cookbook example 105:
+    # TODO: TensorProduct is not supported
+    #expr = Trace(TensorProduct(A, X))
+    #assert expr.diff(X) == Trace(A)*Identity(k)
+
+    ## Second order:
+
+    # Cookbook example 106:
+    expr = Trace(X**2)
+    assert expr.diff(X) == 2*X.T
+
+    # Cookbook example 107:
+    expr = Trace(X**2*B)
+    assert expr.diff(X) == (X*B + B*X).T
+    expr = Trace(MatMul(X, X, B))
+    assert expr.diff(X) == (X*B + B*X).T
+
+    # Cookbook example 108:
+    expr = Trace(X.T*B*X)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 109:
+    expr = Trace(B*X*X.T)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 110:
+    expr = Trace(X*X.T*B)
+    assert expr.diff(X) == B*X + B.T*X
+
+    # Cookbook example 111:
+    expr = Trace(X*B*X.T)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 112:
+    expr = Trace(B*X.T*X)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 113:
+    expr = Trace(X.T*X*B)
+    assert expr.diff(X) == X*B.T + X*B
+
+    # Cookbook example 114:
+    expr = Trace(A*X*B*X)
+    assert expr.diff(X) == A.T*X.T*B.T + B.T*X.T*A.T
+
+    # Cookbook example 115:
+    expr = Trace(X.T*X)
+    assert expr.diff(X) == 2*X
+    expr = Trace(X*X.T)
+    assert expr.diff(X) == 2*X
+
+    # Cookbook example 116:
+    expr = Trace(B.T*X.T*C*X*B)
+    assert expr.diff(X) == C.T*X*B*B.T + C*X*B*B.T
+
+    # Cookbook example 117:
+    expr = Trace(X.T*B*X*C)
+    assert expr.diff(X) == B*X*C + B.T*X*C.T
+
+    # Cookbook example 118:
+    expr = Trace(A*X*B*X.T*C)
+    assert expr.diff(X) == A.T*C.T*X*B.T + C*A*X*B
+
+    # Cookbook example 119:
+    expr = Trace((A*X*B + C)*(A*X*B + C).T)
+    assert expr.diff(X) == 2*A.T*(A*X*B + C)*B.T
+
+    # Cookbook example 120:
+    # TODO: no support for TensorProduct.
+    # expr = Trace(TensorProduct(X, X))
+    # expr = Trace(X)*Trace(X)
+    # expr.diff(X) == 2*Trace(X)*Identity(k)
+
+    # Higher Order
+
+    # Cookbook example 121:
+    expr = Trace(X**k)
+    #assert expr.diff(X) == k*(X**(k-1)).T
+
+    # Cookbook example 122:
+    expr = Trace(A*X**k)
+    #assert expr.diff(X) == # Needs indices
+
+    # Cookbook example 123:
+    expr = Trace(B.T*X.T*C*X*X.T*C*X*B)
+    assert expr.diff(X) == C*X*X.T*C*X*B*B.T + C.T*X*B*B.T*X.T*C.T*X + C*X*B*B.T*X.T*C*X + C.T*X*X.T*C.T*X*B*B.T
+
+    # Other
+
+    # Cookbook example 124:
+    expr = Trace(A*X**(-1)*B)
+    assert expr.diff(X) == -Inverse(X).T*A.T*B.T*Inverse(X).T
+
+    # Cookbook example 125:
+    expr = Trace(Inverse(X.T*C*X)*A)
+    # Warning: result in the cookbook is equivalent if B and C are symmetric:
+    assert expr.diff(X) == - X.inv().T*A.T*X.inv()*C.inv().T*X.inv().T - X.inv().T*A*X.inv()*C.inv()*X.inv().T
+
+    # Cookbook example 126:
+    expr = Trace((X.T*C*X).inv()*(X.T*B*X))
+    assert expr.diff(X) == -2*C*X*(X.T*C*X).inv()*X.T*B*X*(X.T*C*X).inv() + 2*B*X*(X.T*C*X).inv()
+
+    # Cookbook example 127:
+    expr = Trace((A + X.T*C*X).inv()*(X.T*B*X))
+    # Warning: result in the cookbook is equivalent if B and C are symmetric:
+    assert expr.diff(X) == B*X*Inverse(A + X.T*C*X) - C*X*Inverse(A + X.T*C*X)*X.T*B*X*Inverse(A + X.T*C*X) - C.T*X*Inverse(A.T + (C*X).T*X)*X.T*B.T*X*Inverse(A.T + (C*X).T*X) + B.T*X*Inverse(A.T + (C*X).T*X)
+
+
+def test_derivatives_of_complicated_matrix_expr():
+    expr = a.T*(A*X*(X.T*B + X*A) + B.T*X.T*(a*b.T*(X*D*X.T + X*(X.T*B + A*X)*D*B - X.T*C.T*A)*B + B*(X*D.T + B*A*X*A.T - 3*X*D))*B + 42*X*B*X.T*A.T*(X + X.T))*b
+    result = (B*(B*A*X*A.T - 3*X*D + X*D.T) + a*b.T*(X*(A*X + X.T*B)*D*B + X*D*X.T - X.T*C.T*A)*B)*B*b*a.T*B.T + B**2*b*a.T*B.T*X.T*a*b.T*X*D + 42*A*X*B.T*X.T*a*b.T + B*D*B**3*b*a.T*B.T*X.T*a*b.T*X + B*b*a.T*A*X + a*b.T*(42*X + 42*X.T)*A*X*B.T + b*a.T*X*B*a*b.T*B.T**2*X*D.T + b*a.T*X*B*a*b.T*B.T**3*D.T*(B.T*X + X.T*A.T) + 42*b*a.T*X*B*X.T*A.T + A.T*(42*X + 42*X.T)*b*a.T*X*B + A.T*B.T**2*X*B*a*b.T*B.T*A + A.T*a*b.T*(A.T*X.T + B.T*X) + A.T*X.T*b*a.T*X*B*a*b.T*B.T**3*D.T + B.T*X*B*a*b.T*B.T*D - 3*B.T*X*B*a*b.T*B.T*D.T - C.T*A*B**2*b*a.T*B.T*X.T*a*b.T + X.T*A.T*a*b.T*A.T
+    assert expr.diff(X) == result
+
+
+def test_mixed_deriv_mixed_expressions():
+
+    expr = 3*Trace(A)
+    assert expr.diff(A) == 3*Identity(k)
+
+    expr = k
+    deriv = expr.diff(A)
+    assert isinstance(deriv, ZeroMatrix)
+    assert deriv == ZeroMatrix(k, k)
+
+    expr = Trace(A)**2
+    assert expr.diff(A) == (2*Trace(A))*Identity(k)
+
+    expr = Trace(A)*A
+    I = Identity(k)
+    assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2)))
+
+    expr = Trace(Trace(A)*A)
+    assert expr.diff(A) == (2*Trace(A))*Identity(k)
+
+    expr = Trace(Trace(Trace(A)*A)*A)
+    assert expr.diff(A) == (3*Trace(A)**2)*Identity(k)
+
+
+def test_derivatives_matrix_norms():
+
+    expr = x.T*y
+    assert expr.diff(x) == y
+    assert expr[0, 0].diff(x[m, 0]).doit() == y[m, 0]
+
+    expr = (x.T*y)**S.Half
+    assert expr.diff(x) == y/(2*sqrt(x.T*y))
+
+    expr = (x.T*x)**S.Half
+    assert expr.diff(x) == x*(x.T*x)**Rational(-1, 2)
+
+    expr = (c.T*a*x.T*b)**S.Half
+    assert expr.diff(x) == b*a.T*c/sqrt(c.T*a*x.T*b)/2
+
+    expr = (c.T*a*x.T*b)**Rational(1, 3)
+    assert expr.diff(x) == b*a.T*c*(c.T*a*x.T*b)**Rational(-2, 3)/3
+
+    expr = (a.T*X*b)**S.Half
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T
+
+    expr = d.T*x*(a.T*X*b)**S.Half*y.T*c
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*x.T*d*y.T*c*b.T
+
+
+def test_derivatives_elementwise_applyfunc():
+
+    expr = x.applyfunc(tan)
+    assert expr.diff(x).dummy_eq(
+        DiagMatrix(x.applyfunc(lambda x: tan(x)**2 + 1)))
+    assert expr[i, 0].diff(x[m, 0]).doit() == (tan(x[i, 0])**2 + 1)*KDelta(i, m)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = (i**2*x).applyfunc(sin)
+    assert expr.diff(i).dummy_eq(
+        HadamardProduct((2*i)*x, (i**2*x).applyfunc(cos)))
+    assert expr[i, 0].diff(i).doit() == 2*i*x[i, 0]*cos(i**2*x[i, 0])
+    _check_derivative_with_explicit_matrix(expr, i, expr.diff(i))
+
+    expr = (log(i)*A*B).applyfunc(sin)
+    assert expr.diff(i).dummy_eq(
+        HadamardProduct(A*B/i, (log(i)*A*B).applyfunc(cos)))
+    _check_derivative_with_explicit_matrix(expr, i, expr.diff(i))
+
+    expr = A*x.applyfunc(exp)
+    # TODO: restore this result (currently returning the transpose):
+    #  assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(exp))*A.T)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = x.T*A*x + k*y.applyfunc(sin).T*x
+    assert expr.diff(x).dummy_eq(A.T*x + A*x + k*y.applyfunc(sin))
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = x.applyfunc(sin).T*y
+    # TODO: restore (currently returning the transpose):
+    #  assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(cos))*y)
+    _check_derivative_with_explicit_matrix(expr, x, expr.diff(x))
+
+    expr = (a.T * X * b).applyfunc(sin)
+    assert expr.diff(X).dummy_eq(a*(a.T*X*b).applyfunc(cos)*b.T)
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * X.applyfunc(sin) * b
+    assert expr.diff(X).dummy_eq(
+        DiagMatrix(a)*X.applyfunc(cos)*DiagMatrix(b))
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * (A*X*B).applyfunc(sin) * b
+    assert expr.diff(X).dummy_eq(
+        A.T*DiagMatrix(a)*(A*X*B).applyfunc(cos)*DiagMatrix(b)*B.T)
+    _check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T * (A*X*b).applyfunc(sin) * b.T
+    # TODO: not implemented
+    #assert expr.diff(X) == ...
+    #_check_derivative_with_explicit_matrix(expr, X, expr.diff(X))
+
+    expr = a.T*A*X.applyfunc(sin)*B*b
+    assert expr.diff(X).dummy_eq(
+        HadamardProduct(A.T * a * b.T * B.T, X.applyfunc(cos)))
+
+    expr = a.T * (A*X.applyfunc(sin)*B).applyfunc(log) * b
+    # TODO: wrong
+    # assert expr.diff(X) == A.T*DiagMatrix(a)*(A*X.applyfunc(sin)*B).applyfunc(Lambda(k, 1/k))*DiagMatrix(b)*B.T
+
+    expr = a.T * (X.applyfunc(sin)).applyfunc(log) * b
+    # TODO: wrong
+    # assert expr.diff(X) == DiagMatrix(a)*X.applyfunc(sin).applyfunc(Lambda(k, 1/k))*DiagMatrix(b)
+
+
+def test_derivatives_of_hadamard_expressions():
+
+    # Hadamard Product
+
+    expr = hadamard_product(a, x, b)
+    assert expr.diff(x) == DiagMatrix(hadamard_product(b, a))
+
+    expr = a.T*hadamard_product(A, X, B)*b
+    assert expr.diff(X) == HadamardProduct(a*b.T, A, B)
+
+    # Hadamard Power
+
+    expr = hadamard_power(x, 2)
+    assert expr.diff(x).doit() == 2*DiagMatrix(x)
+
+    expr = hadamard_power(x.T, 2)
+    assert expr.diff(x).doit() == 2*DiagMatrix(x)
+
+    expr = hadamard_power(x, S.Half)
+    assert expr.diff(x) == S.Half*DiagMatrix(hadamard_power(x, Rational(-1, 2)))
+
+    expr = hadamard_power(a.T*X*b, 2)
+    assert expr.diff(X) == 2*a*a.T*X*b*b.T
+
+    expr = hadamard_power(a.T*X*b, S.Half)
+    assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_determinant.py

@@ -0,0 +1,62 @@
+from sympy.core import S, symbols
+from sympy.matrices import eye, ones, Matrix, ShapeError
+from sympy.matrices.expressions import (
+    Identity, MatrixExpr, MatrixSymbol, Determinant,
+    det, per, ZeroMatrix, Transpose,
+    Permanent
+)
+from sympy.matrices.expressions.special import OneMatrix
+from sympy.testing.pytest import raises
+from sympy.assumptions.ask import Q
+from sympy.assumptions.refine import refine
+
+n = symbols('n', integer=True)
+A = MatrixSymbol('A', n, n)
+B = MatrixSymbol('B', n, n)
+C = MatrixSymbol('C', 3, 4)
+
+
+def test_det():
+    assert isinstance(Determinant(A), Determinant)
+    assert not isinstance(Determinant(A), MatrixExpr)
+    raises(ShapeError, lambda: Determinant(C))
+    assert det(eye(3)) == 1
+    assert det(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 17
+    _ = A / det(A)  # Make sure this is possible
+
+    raises(TypeError, lambda: Determinant(S.One))
+
+    assert Determinant(A).arg is A
+
+def test_eval_determinant():
+    assert det(Identity(n)) == 1
+    assert det(ZeroMatrix(n, n)) == 0
+    assert det(OneMatrix(n, n)) == Determinant(OneMatrix(n, n))
+    assert det(OneMatrix(1, 1)) == 1
+    assert det(OneMatrix(2, 2)) == 0
+    assert det(Transpose(A)) == det(A)
+
+
+def test_refine():
+    assert refine(det(A), Q.orthogonal(A)) == 1
+    assert refine(det(A), Q.singular(A)) == 0
+    assert refine(det(A), Q.unit_triangular(A)) == 1
+    assert refine(det(A), Q.normal(A)) == det(A)
+
+
+def test_commutative():
+    det_a = Determinant(A)
+    det_b = Determinant(B)
+    assert det_a.is_commutative
+    assert det_b.is_commutative
+    assert det_a * det_b == det_b * det_a
+
+def test_permanent():
+    assert isinstance(Permanent(A), Permanent)
+    assert not isinstance(Permanent(A), MatrixExpr)
+    assert isinstance(Permanent(C), Permanent)
+    assert Permanent(ones(3, 3)).doit() == 6
+    _ = C / per(C)
+    assert per(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 103
+    raises(TypeError, lambda: Permanent(S.One))
+    assert Permanent(A).arg is A

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_diagonal.py

@@ -0,0 +1,156 @@
+from sympy.matrices.expressions import MatrixSymbol
+from sympy.matrices.expressions.diagonal import DiagonalMatrix, DiagonalOf, DiagMatrix, diagonalize_vector
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.symbol import Symbol
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions.matmul import MatMul
+from sympy.matrices.expressions.special import Identity
+from sympy.testing.pytest import raises
+
+
+n = Symbol('n')
+m = Symbol('m')
+
+
+def test_DiagonalMatrix():
+    x = MatrixSymbol('x', n, m)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length is None
+    assert D.shape == (n, m)
+
+    x = MatrixSymbol('x', n, n)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == n
+    assert D.shape == (n, n)
+    assert D[1, 2] == 0
+    assert D[1, 1] == x[1, 1]
+    i = Symbol('i')
+    j = Symbol('j')
+    x = MatrixSymbol('x', 3, 3)
+    ij = DiagonalMatrix(x)[i, j]
+    assert ij != 0
+    assert ij.subs({i:0, j:0}) == x[0, 0]
+    assert ij.subs({i:0, j:1}) == 0
+    assert ij.subs({i:1, j:1}) == x[1, 1]
+    assert ask(Q.diagonal(D))  # affirm that D is diagonal
+
+    x = MatrixSymbol('x', n, 3)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == 3
+    assert D.shape == (n, 3)
+    assert D[2, m] == KroneckerDelta(2, m)*x[2, m]
+    assert D[3, m] == 0
+    raises(IndexError, lambda: D[m, 3])
+
+    x = MatrixSymbol('x', 3, n)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length == 3
+    assert D.shape == (3, n)
+    assert D[m, 2] == KroneckerDelta(m, 2)*x[m, 2]
+    assert D[m, 3] == 0
+    raises(IndexError, lambda: D[3, m])
+
+    x = MatrixSymbol('x', n, m)
+    D = DiagonalMatrix(x)
+    assert D.diagonal_length is None
+    assert D.shape == (n, m)
+    assert D[m, 4] != 0
+
+    x = MatrixSymbol('x', 3, 4)
+    assert [DiagonalMatrix(x)[i] for i in range(12)] == [
+        x[0, 0], 0, 0, 0, 0, x[1, 1], 0, 0, 0, 0, x[2, 2], 0]
+
+    # shape is retained, issue 12427
+    assert (
+        DiagonalMatrix(MatrixSymbol('x', 3, 4))*
+        DiagonalMatrix(MatrixSymbol('x', 4, 2))).shape == (3, 2)
+
+
+def test_DiagonalOf():
+    x = MatrixSymbol('x', n, n)
+    d = DiagonalOf(x)
+    assert d.shape == (n, 1)
+    assert d.diagonal_length == n
+    assert d[2, 0] == d[2] == x[2, 2]
+
+    x = MatrixSymbol('x', n, m)
+    d = DiagonalOf(x)
+    assert d.shape == (None, 1)
+    assert d.diagonal_length is None
+    assert d[2, 0] == d[2] == x[2, 2]
+
+    d = DiagonalOf(MatrixSymbol('x', 4, 3))
+    assert d.shape == (3, 1)
+    d = DiagonalOf(MatrixSymbol('x', n, 3))
+    assert d.shape == (3, 1)
+    d = DiagonalOf(MatrixSymbol('x', 3, n))
+    assert d.shape == (3, 1)
+    x = MatrixSymbol('x', n, m)
+    assert [DiagonalOf(x)[i] for i in range(4)] ==[
+        x[0, 0], x[1, 1], x[2, 2], x[3, 3]]
+
+
+def test_DiagMatrix():
+    x = MatrixSymbol('x', n, 1)
+    d = DiagMatrix(x)
+    assert d.shape == (n, n)
+    assert d[0, 1] == 0
+    assert d[0, 0] == x[0, 0]
+
+    a = MatrixSymbol('a', 1, 1)
+    d = diagonalize_vector(a)
+    assert isinstance(d, MatrixSymbol)
+    assert a == d
+    assert diagonalize_vector(Identity(3)) == Identity(3)
+    assert DiagMatrix(Identity(3)).doit() == Identity(3)
+    assert isinstance(DiagMatrix(Identity(3)), DiagMatrix)
+
+    # A diagonal matrix is equal to its transpose:
+    assert DiagMatrix(x).T == DiagMatrix(x)
+    assert diagonalize_vector(x.T) == DiagMatrix(x)
+
+    dx = DiagMatrix(x)
+    assert dx[0, 0] == x[0, 0]
+    assert dx[1, 1] == x[1, 0]
+    assert dx[0, 1] == 0
+    assert dx[0, m] == x[0, 0]*KroneckerDelta(0, m)
+
+    z = MatrixSymbol('z', 1, n)
+    dz = DiagMatrix(z)
+    assert dz[0, 0] == z[0, 0]
+    assert dz[1, 1] == z[0, 1]
+    assert dz[0, 1] == 0
+    assert dz[0, m] == z[0, m]*KroneckerDelta(0, m)
+
+    v = MatrixSymbol('v', 3, 1)
+    dv = DiagMatrix(v)
+    assert dv.as_explicit() == Matrix([
+        [v[0, 0], 0, 0],
+        [0, v[1, 0], 0],
+        [0, 0, v[2, 0]],
+    ])
+
+    v = MatrixSymbol('v', 1, 3)
+    dv = DiagMatrix(v)
+    assert dv.as_explicit() == Matrix([
+        [v[0, 0], 0, 0],
+        [0, v[0, 1], 0],
+        [0, 0, v[0, 2]],
+    ])
+
+    dv = DiagMatrix(3*v)
+    assert dv.args == (3*v,)
+    assert dv.doit() == 3*DiagMatrix(v)
+    assert isinstance(dv.doit(), MatMul)
+
+    a = MatrixSymbol("a", 3, 1).as_explicit()
+    expr = DiagMatrix(a)
+    result = Matrix([
+        [a[0, 0], 0, 0],
+        [0, a[1, 0], 0],
+        [0, 0, a[2, 0]],
+    ])
+    assert expr.doit() == result
+    expr = DiagMatrix(a.T)
+    assert expr.doit() == result

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py

@@ -0,0 +1,35 @@
+from sympy.core.expr import unchanged
+from sympy.core.mul import Mul
+from sympy.matrices import Matrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.matrices.expressions.dotproduct import DotProduct
+from sympy.testing.pytest import raises
+
+
+A = Matrix(3, 1, [1, 2, 3])
+B = Matrix(3, 1, [1, 3, 5])
+C = Matrix(4, 1, [1, 2, 4, 5])
+D = Matrix(2, 2, [1, 2, 3, 4])
+
+def test_docproduct():
+    assert DotProduct(A, B).doit() == 22
+    assert DotProduct(A.T, B).doit() == 22
+    assert DotProduct(A, B.T).doit() == 22
+    assert DotProduct(A.T, B.T).doit() == 22
+
+    raises(TypeError, lambda: DotProduct(1, A))
+    raises(TypeError, lambda: DotProduct(A, 1))
+    raises(TypeError, lambda: DotProduct(A, D))
+    raises(TypeError, lambda: DotProduct(D, A))
+
+    raises(TypeError, lambda: DotProduct(B, C).doit())
+
+def test_dotproduct_symbolic():
+    A = MatrixSymbol('A', 3, 1)
+    B = MatrixSymbol('B', 3, 1)
+
+    dot = DotProduct(A, B)
+    assert dot.is_scalar == True
+    assert unchanged(Mul, 2, dot)
+    # XXX Fix forced evaluation for arithmetics with matrix expressions
+    assert dot * A == (A[0, 0]*B[0, 0] + A[1, 0]*B[1, 0] + A[2, 0]*B[2, 0])*A

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_factorizations.py

@@ -0,0 +1,29 @@
+from sympy.matrices.expressions.factorizations import lu, LofCholesky, qr, svd
+from sympy.assumptions.ask import (Q, ask)
+from sympy.core.symbol import Symbol
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+
+n = Symbol('n')
+X = MatrixSymbol('X', n, n)
+
+def test_LU():
+    L, U = lu(X)
+    assert L.shape == U.shape == X.shape
+    assert ask(Q.lower_triangular(L))
+    assert ask(Q.upper_triangular(U))
+
+def test_Cholesky():
+    LofCholesky(X)
+
+def test_QR():
+    Q_, R = qr(X)
+    assert Q_.shape == R.shape == X.shape
+    assert ask(Q.orthogonal(Q_))
+    assert ask(Q.upper_triangular(R))
+
+def test_svd():
+    U, S, V = svd(X)
+    assert U.shape == S.shape == V.shape == X.shape
+    assert ask(Q.orthogonal(U))
+    assert ask(Q.orthogonal(V))
+    assert ask(Q.diagonal(S))

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py

@@ -0,0 +1,56 @@
+from sympy.core import symbols, Lambda
+from sympy.functions import KroneckerDelta
+from sympy.matrices import Matrix
+from sympy.matrices.expressions import FunctionMatrix, MatrixExpr, Identity
+from sympy.testing.pytest import raises, warns
+from sympy.utilities.exceptions import SymPyDeprecationWarning
+
+
+def test_funcmatrix_creation():
+    i, j, k = symbols('i j k')
+    assert FunctionMatrix(2, 2, Lambda((i, j), 0))
+    assert FunctionMatrix(0, 0, Lambda((i, j), 0))
+
+    raises(ValueError, lambda: FunctionMatrix(-1, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2.0, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2j, 0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, -1, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, 2.0, Lambda((i, j), 0)))
+    raises(ValueError, lambda: FunctionMatrix(0, 2j, Lambda((i, j), 0)))
+
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda(i, 0)))
+    with warns(SymPyDeprecationWarning, test_stacklevel=False):
+        # This raises a deprecation warning from sympify()
+        raises(ValueError, lambda: FunctionMatrix(2, 2, lambda i, j: 0))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i,), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i, j, k), 0)))
+    raises(ValueError, lambda: FunctionMatrix(2, 2, i+j))
+    assert FunctionMatrix(2, 2, "lambda i, j: 0") == \
+        FunctionMatrix(2, 2, Lambda((i, j), 0))
+
+    m = FunctionMatrix(2, 2, KroneckerDelta)
+    assert m.as_explicit() == Identity(2).as_explicit()
+    assert m.args[2].dummy_eq(Lambda((i, j), KroneckerDelta(i, j)))
+
+    n = symbols('n')
+    assert FunctionMatrix(n, n, Lambda((i, j), 0))
+    n = symbols('n', integer=False)
+    raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0)))
+    n = symbols('n', negative=True)
+    raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0)))
+
+
+def test_funcmatrix():
+    i, j = symbols('i,j')
+    X = FunctionMatrix(3, 3, Lambda((i, j), i - j))
+    assert X[1, 1] == 0
+    assert X[1, 2] == -1
+    assert X.shape == (3, 3)
+    assert X.rows == X.cols == 3
+    assert Matrix(X) == Matrix(3, 3, lambda i, j: i - j)
+    assert isinstance(X*X + X, MatrixExpr)
+
+
+def test_replace_issue():
+    X = FunctionMatrix(3, 3, KroneckerDelta)
+    assert X.replace(lambda x: True, lambda x: x) == X

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_indexing.py

@@ -0,0 +1,299 @@
+from sympy.concrete.summations import Sum
+from sympy.core.symbol import symbols, Symbol, Dummy
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import eye
+from sympy.matrices.expressions.blockmatrix import BlockMatrix
+from sympy.matrices.expressions.hadamard import HadamardPower
+from sympy.matrices.expressions.matexpr import (MatrixSymbol,
+    MatrixExpr, MatrixElement)
+from sympy.matrices.expressions.matpow import MatPow
+from sympy.matrices.expressions.special import (ZeroMatrix, Identity,
+    OneMatrix)
+from sympy.matrices.expressions.trace import Trace, trace
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+from sympy.testing.pytest import XFAIL, raises
+
+k, l, m, n = symbols('k l m n', integer=True)
+i, j = symbols('i j', integer=True)
+
+W = MatrixSymbol('W', k, l)
+X = MatrixSymbol('X', l, m)
+Y = MatrixSymbol('Y', l, m)
+Z = MatrixSymbol('Z', m, n)
+
+X1 = MatrixSymbol('X1', m, m)
+X2 = MatrixSymbol('X2', m, m)
+X3 = MatrixSymbol('X3', m, m)
+X4 = MatrixSymbol('X4', m, m)
+
+A = MatrixSymbol('A', 2, 2)
+B = MatrixSymbol('B', 2, 2)
+x = MatrixSymbol('x', 1, 2)
+y = MatrixSymbol('x', 2, 1)
+
+
+def test_symbolic_indexing():
+    x12 = X[1, 2]
+    assert all(s in str(x12) for s in ['1', '2', X.name])
+    # We don't care about the exact form of this.  We do want to make sure
+    # that all of these features are present
+
+
+def test_add_index():
+    assert (X + Y)[i, j] == X[i, j] + Y[i, j]
+
+
+def test_mul_index():
+    assert (A*y)[0, 0] == A[0, 0]*y[0, 0] + A[0, 1]*y[1, 0]
+    assert (A*B).as_mutable() == (A.as_mutable() * B.as_mutable())
+    X = MatrixSymbol('X', n, m)
+    Y = MatrixSymbol('Y', m, k)
+
+    result = (X*Y)[4,2]
+    expected = Sum(X[4, i]*Y[i, 2], (i, 0, m - 1))
+    assert result.args[0].dummy_eq(expected.args[0], i)
+    assert result.args[1][1:] == expected.args[1][1:]
+
+
+def test_pow_index():
+    Q = MatPow(A, 2)
+    assert Q[0, 0] == A[0, 0]**2 + A[0, 1]*A[1, 0]
+    n = symbols("n")
+    Q2 = A**n
+    assert Q2[0, 0] == 2*(
+            -sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] +
+            4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2
+        )**n * \
+        A[0, 1]*A[1, 0]/(
+            (sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] +
+                  A[1, 1]**2) + A[0, 0] - A[1, 1])*
+            sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2)
+        ) - 2*(
+            sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] +
+            4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2
+        )**n * A[0, 1]*A[1, 0]/(
+            (-sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] +
+            A[1, 1]**2) + A[0, 0] - A[1, 1])*
+            sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2)
+        )
+
+
+def test_transpose_index():
+    assert X.T[i, j] == X[j, i]
+
+
+def test_Identity_index():
+    I = Identity(3)
+    assert I[0, 0] == I[1, 1] == I[2, 2] == 1
+    assert I[1, 0] == I[0, 1] == I[2, 1] == 0
+    assert I[i, 0].delta_range == (0, 2)
+    raises(IndexError, lambda: I[3, 3])
+
+
+def test_block_index():
+    I = Identity(3)
+    Z = ZeroMatrix(3, 3)
+    B = BlockMatrix([[I, I], [I, I]])
+    e3 = ImmutableMatrix(eye(3))
+    BB = BlockMatrix([[e3, e3], [e3, e3]])
+    assert B[0, 0] == B[3, 0] == B[0, 3] == B[3, 3] == 1
+    assert B[4, 3] == B[5, 1] == 0
+
+    BB = BlockMatrix([[e3, e3], [e3, e3]])
+    assert B.as_explicit() == BB.as_explicit()
+
+    BI = BlockMatrix([[I, Z], [Z, I]])
+
+    assert BI.as_explicit().equals(eye(6))
+
+
+def test_block_index_symbolic():
+    # Note that these matrices may be zero-sized and indices may be negative, which causes
+    # all naive simplifications given in the comments to be invalid
+    A1 = MatrixSymbol('A1', n, k)
+    A2 = MatrixSymbol('A2', n, l)
+    A3 = MatrixSymbol('A3', m, k)
+    A4 = MatrixSymbol('A4', m, l)
+    A = BlockMatrix([[A1, A2], [A3, A4]])
+    assert A[0, 0] == MatrixElement(A, 0, 0)  # Cannot be A1[0, 0]
+    assert A[n - 1, k - 1] == A1[n - 1, k - 1]
+    assert A[n, k] == A4[0, 0]
+    assert A[n + m - 1, 0] == MatrixElement(A, n + m - 1, 0)  # Cannot be A3[m - 1, 0]
+    assert A[0, k + l - 1] == MatrixElement(A, 0, k + l - 1)  # Cannot be A2[0, l - 1]
+    assert A[n + m - 1, k + l - 1] == MatrixElement(A, n + m - 1, k + l - 1)  # Cannot be A4[m - 1, l - 1]
+    assert A[i, j] == MatrixElement(A, i, j)
+    assert A[n + i, k + j] == MatrixElement(A, n + i, k + j)  # Cannot be A4[i, j]
+    assert A[n - i - 1, k - j - 1] == MatrixElement(A, n - i - 1, k - j - 1)  # Cannot be A1[n - i - 1, k - j - 1]
+
+
+def test_block_index_symbolic_nonzero():
+    # All invalid simplifications from test_block_index_symbolic() that become valid if all
+    # matrices have nonzero size and all indices are nonnegative
+    k, l, m, n = symbols('k l m n', integer=True, positive=True)
+    i, j = symbols('i j', integer=True, nonnegative=True)
+    A1 = MatrixSymbol('A1', n, k)
+    A2 = MatrixSymbol('A2', n, l)
+    A3 = MatrixSymbol('A3', m, k)
+    A4 = MatrixSymbol('A4', m, l)
+    A = BlockMatrix([[A1, A2], [A3, A4]])
+    assert A[0, 0] == A1[0, 0]
+    assert A[n + m - 1, 0] == A3[m - 1, 0]
+    assert A[0, k + l - 1] == A2[0, l - 1]
+    assert A[n + m - 1, k + l - 1] == A4[m - 1, l - 1]
+    assert A[i, j] == MatrixElement(A, i, j)
+    assert A[n + i, k + j] == A4[i, j]
+    assert A[n - i - 1, k - j - 1] == A1[n - i - 1, k - j - 1]
+    assert A[2 * n, 2 * k] == A4[n, k]
+
+
+def test_block_index_large():
+    n, m, k = symbols('n m k', integer=True, positive=True)
+    i = symbols('i', integer=True, nonnegative=True)
+    A1 = MatrixSymbol('A1', n, n)
+    A2 = MatrixSymbol('A2', n, m)
+    A3 = MatrixSymbol('A3', n, k)
+    A4 = MatrixSymbol('A4', m, n)
+    A5 = MatrixSymbol('A5', m, m)
+    A6 = MatrixSymbol('A6', m, k)
+    A7 = MatrixSymbol('A7', k, n)
+    A8 = MatrixSymbol('A8', k, m)
+    A9 = MatrixSymbol('A9', k, k)
+    A = BlockMatrix([[A1, A2, A3], [A4, A5, A6], [A7, A8, A9]])
+    assert A[n + i, n + i] == MatrixElement(A, n + i, n + i)
+
+
+@XFAIL
+def test_block_index_symbolic_fail():
+    # To make this work, symbolic matrix dimensions would need to be somehow assumed nonnegative
+    # even if the symbols aren't specified as such.  Then 2 * n < n would correctly evaluate to
+    # False in BlockMatrix._entry()
+    A1 = MatrixSymbol('A1', n, 1)
+    A2 = MatrixSymbol('A2', m, 1)
+    A = BlockMatrix([[A1], [A2]])
+    assert A[2 * n, 0] == A2[n, 0]
+
+
+def test_slicing():
+    A.as_explicit()[0, :]  # does not raise an error
+
+
+def test_errors():
+    raises(IndexError, lambda: Identity(2)[1, 2, 3, 4, 5])
+    raises(IndexError, lambda: Identity(2)[[1, 2, 3, 4, 5]])
+
+
+def test_matrix_expression_to_indices():
+    i, j = symbols("i, j")
+    i1, i2, i3 = symbols("i_1:4")
+
+    def replace_dummies(expr):
+        repl = {i: Symbol(i.name) for i in expr.atoms(Dummy)}
+        return expr.xreplace(repl)
+
+    expr = W*X*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = Z.T*X.T*W.T
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[j, i2]*X[i2, i1]*Z[i1, i], (i1, 0, m-1), (i2, 0, l-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j), i) == expr
+
+    expr = W*X*Z + W*Y*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\
+        Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = 2*W*X*Z + 3*W*Y*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+        2*Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\
+        3*Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = W*(X + Y)*Z
+    assert replace_dummies(expr._entry(i, j)) == \
+            Sum(W[i, i1]*(X[i1, i2] + Y[i1, i2])*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr
+
+    expr = A*B**2*A
+    #assert replace_dummies(expr._entry(i, j)) == \
+    #        Sum(A[i, i1]*B[i1, i2]*B[i2, i3]*A[i3, j], (i1, 0, 1), (i2, 0, 1), (i3, 0, 1))
+
+    # Check that different dummies are used in sub-multiplications:
+    expr = (X1*X2 + X2*X1)*X3
+    assert replace_dummies(expr._entry(i, j)) == \
+           Sum((Sum(X1[i, i2] * X2[i2, i1], (i2, 0, m - 1)) + Sum(X1[i3, i1] * X2[i, i3], (i3, 0, m - 1))) * X3[
+               i1, j], (i1, 0, m - 1))
+
+
+def test_matrix_expression_from_index_summation():
+    from sympy.abc import a,b,c,d
+    A = MatrixSymbol("A", k, k)
+    B = MatrixSymbol("B", k, k)
+    C = MatrixSymbol("C", k, k)
+    w1 = MatrixSymbol("w1", k, 1)
+
+    i0, i1, i2, i3, i4 = symbols("i0:5", cls=Dummy)
+
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr, a) == W*X*Z
+    expr = Sum(W.T[b,a]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1))
+    assert MatrixExpr.from_index_summation(expr, a) == W*X*Z
+    expr = Sum(A[b, a]*B[b, c]*C[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B*C
+    expr = Sum(A[b, a]*B[c, b]*C[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C
+    expr = Sum(C[c, d]*A[b, a]*B[c, b], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C
+    expr = Sum(A[a, b] + B[a, b], (a, 0, k-1), (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == OneMatrix(1, k)*A*OneMatrix(k, 1) + OneMatrix(1, k)*B*OneMatrix(k, 1)
+    expr = Sum(A[a, b]**2, (a, 0, k - 1), (b, 0, k - 1))
+    assert MatrixExpr.from_index_summation(expr, a) == Trace(A * A.T)
+    expr = Sum(A[a, b]**3, (a, 0, k - 1), (b, 0, k - 1))
+    assert MatrixExpr.from_index_summation(expr, a) == Trace(HadamardPower(A.T, 2) * A)
+    expr = Sum((A[a, b] + B[a, b])*C[b, c], (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == (A+B)*C
+    expr = Sum((A[a, b] + B[b, a])*C[b, c], (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == (A+B.T)*C
+    expr = Sum(A[a, b]*A[b, c]*A[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A**3
+    expr = Sum(A[a, b]*A[b, c]*B[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A**2*B
+
+    # Parse the trace of a matrix:
+
+    expr = Sum(A[a, a], (a, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, None) == trace(A)
+    expr = Sum(A[a, a]*B[b, c]*C[c, d], (a, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, b) == trace(A)*B*C
+
+    # Check wrong sum ranges (should raise an exception):
+
+    ## Case 1: 0 to m instead of 0 to m-1
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m))
+    raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a))
+    ## Case 2: 1 to m-1 instead of 0 to m-1
+    expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 1, m-1))
+    raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a))
+
+    # Parse nested sums:
+    expr = Sum(A[a, b]*Sum(B[b, c]*C[c, d], (c, 0, k-1)), (b, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A*B*C
+
+    # Test Kronecker delta:
+    expr = Sum(A[a, b]*KroneckerDelta(b, c)*B[c, d], (b, 0, k-1), (c, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, a) == A*B
+
+    expr = Sum(KroneckerDelta(i1, m)*KroneckerDelta(i2, n)*A[i, i1]*A[j, i2], (i1, 0, k-1), (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, m) == ArrayTensorProduct(A.T, A)
+
+    # Test numbered indices:
+    expr = Sum(A[i1, i2]*w1[i2, 0], (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*w1, i1, 0)
+
+    expr = Sum(A[i1, i2]*B[i2, 0], (i2, 0, k-1))
+    assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*B, i1, 0)

venv/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))

venv/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)]

venv/lib/python3.10/site-packages/sympy/matrices/expressions/tests/test_matadd.py

@@ -0,0 +1,58 @@
+from sympy.matrices.expressions import MatrixSymbol, MatAdd, MatPow, MatMul
+from sympy.matrices.expressions.special import GenericZeroMatrix, ZeroMatrix
+from sympy.matrices.common import ShapeError
+from sympy.matrices import eye, ImmutableMatrix
+from sympy.core import Add, Basic, S
+from sympy.core.add import add
+from sympy.testing.pytest import XFAIL, raises
+
+X = MatrixSymbol('X', 2, 2)
+Y = MatrixSymbol('Y', 2, 2)
+
+def test_evaluate():
+    assert MatAdd(X, X, evaluate=True) == add(X, X, evaluate=True) == MatAdd(X, X).doit()
+
+def test_sort_key():
+    assert MatAdd(Y, X).doit().args == add(Y, X).doit().args == (X, Y)
+
+
+def test_matadd_sympify():
+    assert isinstance(MatAdd(eye(1), eye(1)).args[0], Basic)
+    assert isinstance(add(eye(1), eye(1)).args[0], Basic)
+
+
+def test_matadd_of_matrices():
+    assert MatAdd(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2))
+    assert add(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2))
+
+
+def test_doit_args():
+    A = ImmutableMatrix([[1, 2], [3, 4]])
+    B = ImmutableMatrix([[2, 3], [4, 5]])
+    assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2
+    assert MatAdd(A, MatMul(A, B)).doit() == A + A*B
+    assert (MatAdd(A, X, MatMul(A, B), Y, MatAdd(2*A, B)).doit() ==
+    add(A, X, MatMul(A, B), Y, add(2*A, B)).doit() ==
+    MatAdd(3*A + A*B + B, X, Y))
+
+
+def test_generic_identity():
+    assert MatAdd.identity == GenericZeroMatrix()
+    assert MatAdd.identity != S.Zero
+
+
+def test_zero_matrix_add():
+    assert Add(ZeroMatrix(2, 2), ZeroMatrix(2, 2)) == ZeroMatrix(2, 2)
+
+@XFAIL
+def test_matrix_Add_with_scalar():
+    raises(TypeError, lambda: Add(0, ZeroMatrix(2, 2)))
+
+
+def test_shape_error():
+    A = MatrixSymbol('A', 2, 3)
+    B = MatrixSymbol('B', 3, 3)
+    raises(ShapeError, lambda: MatAdd(A, B))
+
+    A = MatrixSymbol('A', 3, 2)
+    raises(ShapeError, lambda: MatAdd(A, B))