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
assert (block_collapse(X + Identity(m + n)) == BlockMatrix(
[[A + Identity(n), B], [C, D + Identity(m)]]))
X + Identity(m + n)
assert (X + MatrixSymbol('Q', n + m, n + m)).is_MatAdd
assert (X * MatrixSymbol('Q', n + m, n + m)).is_MatMul
assert block_collapse(Y.inverse()) == A.inverse()
assert block_collapse(X.inverse()) == BlockMatrix(
[[(-B * D.inverse() * C + A).inverse(),
-A.inverse() * B * (D + -C * A.inverse() * B).inverse()],
[
-(D - C * A.inverse() * B).inverse() * C * A.inverse(),
(D - C * A.inverse() * B).inverse()
]])
assert isinstance(X.inverse(), Inverse)
assert not X.is_Identity
Z = BlockMatrix([[Identity(n), B], [C, D]])
assert not Z.is_Identity
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_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_BlockMatrix():
n, m = symbols('n m', integer=True)
X = MatrixSymbol('X', n, n)
Y = MatrixSymbol('Y', m, m)
Z = MatrixSymbol('Z', n, m)
B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]])
assert str(B) == "Matrix([\n[X, Z],\n[0, Y]])"
def test_reblock_2x2():
B = BlockMatrix([[MatrixSymbol(f'A_{i:d}{j:d}', 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_block_plus_ident():
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, m)
C = MatrixSymbol('C', m, n)
D = MatrixSymbol('D', m, m)
E = MatrixSymbol('E', n, n)
X = BlockMatrix([[A, B], [C, D]])
assert bc_block_plus_ident(X+Identity(m+n)) == \
BlockDiagMatrix(Identity(n), Identity(m)) + X
assert bc_block_plus_ident(A + Identity(n)) == A + Identity(n)
assert bc_block_plus_ident(A + E) == A + E
def test_blockcut():
A = MatrixSymbol('A', n, m)
B = blockcut(A, (n / 2, n / 2), (m / 2, m / 2))
assert A[i, j] == B[i, j]
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_bc_transpose():
assert bc_transpose(Transpose(BlockMatrix([[A, B], [C, D]]))) == \
BlockMatrix([[A.T, C.T], [B.T, D.T]])
assert BlockMatrix([[A, B], [C,
D]]).transpose() == BlockMatrix([[A.T, C.T],
[B.T, D.T]])
def test_bc_matadd():
assert bc_matadd(BlockMatrix([[G, H]]) + BlockMatrix([[H, H]])) == \
BlockMatrix([[G+H, H+H]])
assert bc_matadd(A + B) == A + B
def test_deblock():
B = BlockMatrix([[MatrixSymbol(f'A_{i:d}{j:d}', n, n) for j in range(4)]
for i in range(4)])
assert deblock(reblock_2x2(B)) == B
def test_bc_matmul():
assert bc_matmul(H * b1 * b2 * G) == BlockMatrix([[
(H * G * G + H * H * H) * G
]])
assert bc_matmul(H * G) == H * G
def test_BlockMatrix_Determinant():
A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
X = BlockMatrix([[A, B], [C, D]])
assert isinstance(det(X), Expr)
def test_BlockMatrix_equals():
A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD']
X = BlockMatrix([[A, B], [C, D]])
assert X.equals(X) is True
assert X.equals(Matrix([1, 2])) is False
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)
transpose)
from diofant.matrices.expressions.blockmatrix import (bc_block_plus_ident,
bc_dist, bc_matadd,
bc_matmul, bc_transpose,
deblock, reblock_2x2)
__all__ = ()
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
]])
assert bc_matmul(H * G) == H * G
def test_bc_matadd():
assert bc_matadd(BlockMatrix([[G, H]]) + BlockMatrix([[H, H]])) == \
BlockMatrix([[G+H, H+H]])
assert bc_matadd(A + B) == A + B
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