Spaces:
Running
Running
File size: 5,366 Bytes
6a86ad5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 |
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)]
|