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.diag == (A, B, 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 isinstance(block_collapse(X.inverse() * 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():
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.diag == (A, B, 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 isinstance(block_collapse(X.inverse() * 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_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_matmul():
assert bc_matmul(H*b1*b2*G) == BlockMatrix([[(H*G*G + H*H*H)*G]])
assert bc_matmul(H*G) == H*G
