def test_equality():
a, b, c = Identity(3), eye(3), ImmutableMatrix(eye(3))
for x in [a, b, c]:
for y in [a, b, c]:
assert x.equals(y)
def test_Identity_doit():
Inn = Identity(Add(n, n, evaluate=False))
assert isinstance(Inn.rows, Add)
assert Inn.doit() == Identity(2*n)
assert isinstance(Inn.doit().rows, Mul)
import pytest
from diofant import (Identity, ImmutableMatrix, MatAdd, Matrix, MatrixExpr,
MatrixSymbol, eye)
from diofant.abc import a
from diofant.matrices.matrices import classof
__all__ = ()
SM = MatrixSymbol('X', 3, 3)
MM = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
IM = ImmutableMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
meye = eye(3)
imeye = ImmutableMatrix(eye(3))
ideye = Identity(3)
def test_IM_MM():
assert isinstance(MM + IM, ImmutableMatrix)
assert isinstance(IM + MM, ImmutableMatrix)
assert isinstance(2 * IM + MM, ImmutableMatrix)
assert MM.equals(IM)
assert MM.equals(2) is False
def test_ME_MM():
assert isinstance(Identity(3) + MM, MatrixExpr)
assert isinstance(SM + MM, MatAdd)
assert isinstance(MM + SM, MatAdd)
assert (Identity(3) + MM)[1, 1] == 6
def test_ME_MM():
assert isinstance(Identity(3) + MM, MatrixExpr)
assert isinstance(SM + MM, MatAdd)
assert isinstance(MM + SM, MatAdd)
assert (Identity(3) + MM)[1, 1] == 6
def test_remove_ids():
assert remove_ids(MatMul(A, Identity(m), B, evaluate=False)) == \
MatMul(A, B, evaluate=False)
assert null_safe(remove_ids)(MatMul(Identity(n), evaluate=False)) == \
MatMul(Identity(n), evaluate=False)
def test_xxinv():
assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
MatMul(Identity(n), D, evaluate=False)
def test_doit_square_MatrixSymbol_symsize():
assert MatPow(C, 0).doit() == Identity(n)
assert MatPow(C, 0).doit(deep=False) == Identity(n)
assert MatPow(C, 1).doit() == C
for r in [2, -1, pi]:
assert MatPow(C, r).doit() == MatPow(C, r)
def test_as_explicit_symbol():
X = MatrixSymbol('X', 2, 2)
assert MatPow(X, 0).as_explicit() == ImmutableMatrix(Identity(2))
assert MatPow(X, 1).as_explicit() == X.as_explicit()
assert MatPow(X, 2).as_explicit() == (X.as_explicit())**2
def test_eval_determinant():
assert det(Matrix()) == 1
assert det(Identity(n)) == 1
assert det(ZeroMatrix(n, n)) == 0
assert det(Transpose(A)) == det(A)
def test_errors():
pytest.raises(IndexError, lambda: Identity(2)[1, 2, 3, 4, 5])
pytest.raises(IndexError, lambda: Identity(2)[[1, 2, 3, 4, 5]])
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
pytest.raises(IndexError, lambda: I[3, 3])