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Mini Shell
Mini Shell
from sympy import MatrixSymbol, symbols, Identity, sin, cos
from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
from sympy.tensor.array.expressions.array_expressions import ArraySymbol, ArrayTensorProduct, \
PermuteDims, ArrayDiagonal, ArrayElementwiseApplyFunc, ArrayContraction
from sympy.tensor.array.expressions.arrayexpr_derivatives import array_derive
k = symbols("k")
I = Identity(k)
X = MatrixSymbol("X", k, k)
x = MatrixSymbol("x", k, 1)
A = MatrixSymbol("A", k, k)
B = MatrixSymbol("B", k, k)
C = MatrixSymbol("C", k, k)
D = MatrixSymbol("D", k, k)
A1 = ArraySymbol("A", 3, 2, k)
def test_arrayexpr_derivatives1():
res = array_derive(X, X)
assert res == PermuteDims(ArrayTensorProduct(I, I), [0, 2, 1, 3])
cg = ArrayTensorProduct(A, X, B)
res = array_derive(cg, X)
assert res == PermuteDims(
ArrayTensorProduct(I, A, I, B),
[0, 4, 2, 3, 1, 5, 6, 7])
cg = ArrayContraction(X, (0, 1))
res = array_derive(cg, X)
assert res == ArrayContraction(ArrayTensorProduct(I, I), (1, 3))
cg = ArrayDiagonal(X, (0, 1))
res = array_derive(cg, X)
assert res == ArrayDiagonal(ArrayTensorProduct(I, I), (1, 3))
cg = ElementwiseApplyFunction(sin, X)
res = array_derive(cg, X)
assert res.dummy_eq(ArrayDiagonal(
ArrayTensorProduct(
ElementwiseApplyFunction(cos, X),
I,
I
), (0, 3), (1, 5)))
cg = ArrayElementwiseApplyFunc(sin, X)
res = array_derive(cg, X)
assert res.dummy_eq(ArrayDiagonal(
ArrayTensorProduct(
I,
I,
ArrayElementwiseApplyFunc(cos, X)
), (1, 4), (3, 5)))
res = array_derive(A1, A1)
assert res == PermuteDims(
ArrayTensorProduct(Identity(3), Identity(2), Identity(k)),
[0, 2, 4, 1, 3, 5]
)
cg = ArrayElementwiseApplyFunc(sin, A1)
res = array_derive(cg, A1)
assert res.dummy_eq(ArrayDiagonal(
ArrayTensorProduct(
Identity(3), Identity(2), Identity(k),
ArrayElementwiseApplyFunc(cos, A1)
), (1, 6), (3, 7), (5, 8)
))
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