def test_doit_args():
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix([[2, 3], [4, 5]])
assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2
assert MatAdd(A, MatMul(A, B)).doit() == A + A * B
assert (MatAdd(A, X, MatMul(A, B), Y,
MatAdd(2 * A, B)).doit() == MatAdd(3 * A + A * B + B, X, Y))
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_as_explicit_nonsquare():
A = ImmutableMatrix([[1, 2, 3], [4, 5, 6]])
assert MatPow(A, 1).as_explicit() == A
pytest.raises(ShapeError, lambda: MatPow(A, 0).as_explicit())
pytest.raises(ShapeError, lambda: MatPow(A, 2).as_explicit())
pytest.raises(ShapeError, lambda: MatPow(A, -1).as_explicit())
pytest.raises(ValueError, lambda: MatPow(A, pi).as_explicit())
def test_doit_nonsquare():
X = ImmutableMatrix([[1, 2, 3], [4, 5, 6]])
assert MatPow(X, 1).doit() == X
pytest.raises(ShapeError, lambda: MatPow(X, 0).doit())
pytest.raises(ShapeError, lambda: MatPow(X, 2).doit())
pytest.raises(ShapeError, lambda: MatPow(X, -1).doit())
pytest.raises(ShapeError, lambda: MatPow(X, pi).doit())
def test_Trace_MatAdd_doit():
# See issue #9028
X = ImmutableMatrix([[1, 2, 3]] * 3)
Y = MatrixSymbol('Y', 3, 3)
q = MatAdd(X, 2 * X, Y, -3 * Y)
assert Trace(q).arg == q
assert Trace(q).doit() == 18 - 2 * Trace(Y)
def test_classof():
A = Matrix(3, 3, range(9))
B = ImmutableMatrix(3, 3, range(9))
C = MatrixSymbol('C', 3, 3)
assert classof(A, A) == Matrix
assert classof(B, B) == ImmutableMatrix
assert classof(A, B) == ImmutableMatrix
assert classof(B, A) == ImmutableMatrix
pytest.raises(TypeError, lambda: classof(A, C))
def test_doit_with_MatrixBase():
X = ImmutableMatrix([[1, 2], [3, 4]])
assert MatPow(X, 0).doit() == ImmutableMatrix(Identity(2))
assert MatPow(X, 1).doit() == X
assert MatPow(X, 2).doit() == X**2
assert MatPow(X, -1).doit() == X.inv()
assert MatPow(X, -2).doit() == (X.inv())**2
# less expensive than testing on a 2x2
assert MatPow(ImmutableMatrix([4]), Rational(1, 2)).doit() == ImmutableMatrix([2])
def test_as_explicit():
A = ImmutableMatrix([[1, 2], [3, 4]])
assert MatPow(A, 0).as_explicit() == ImmutableMatrix(Identity(2))
assert MatPow(A, 1).as_explicit() == A
assert MatPow(A, 2).as_explicit() == A**2
assert MatPow(A, -1).as_explicit() == A.inv()
assert MatPow(A, -2).as_explicit() == (A.inv())**2
# less expensive than testing on a 2x2
A = ImmutableMatrix([4])
assert MatPow(A, Rational(1, 2)).as_explicit() == A**Rational(1, 2)
def test_matmul_simplify():
A = MatrixSymbol('A', 1, 1)
assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
MatMul(A, ImmutableMatrix([[1]]))
def test_MatrixElement_doit():
u = MatrixSymbol('u', 2, 1)
v = ImmutableMatrix([3, 5])
assert u[0, 0].subs(u, v).doit() == v[0, 0]
assert u[0, 0].subs(u, v).doit(deep=False) == v[0, 0]
def test_trace_constant_factor():
# Issue 9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A)
assert trace(2 * A) == 2 * Trace(A)
X = ImmutableMatrix([[1, 2], [3, 4]])
assert trace(MatMul(2, X)) == 10
def test_dense_conversion():
X = MatrixSymbol('X', 2, 2)
assert ImmutableMatrix(X) == ImmutableMatrix(2, 2, lambda i, j: X[i, j])
assert Matrix(X) == Matrix(2, 2, lambda i, j: X[i, j])
Matrix, ImmutableMatrix, MatrixExpr
Here we test the extent to which they cooperate
"""
import pytest
from diofant import symbols
from diofant.matrices import (Matrix, MatrixSymbol, eye, Identity,
ImmutableMatrix)
from diofant.matrices.expressions import MatrixExpr, MatAdd
from diofant.matrices.matrices import classof
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)
a, b, c = symbols('a,b,c')
def test_IM_MM():
assert isinstance(MM + IM, ImmutableMatrix)
assert isinstance(IM + MM, ImmutableMatrix)
assert isinstance(2 * IM + MM, ImmutableMatrix)
assert MM.equals(IM)
def test_ME_MM():
assert isinstance(Identity(3) + MM, MatrixExpr)
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_matadd_of_matrices():
assert MatAdd(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2))
def test_collapse_MatrixBase():
A = Matrix([[1, 1], [1, 1]])
B = Matrix([[1, 2], [3, 4]])
assert MatMul(A, B).doit() == ImmutableMatrix([[4, 6], [4, 6]])
def test_doit_drills_down():
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[2, 3], [4, 5]])
assert MatMul(X, MatPow(Y, 2)).doit() == X*Y**2
assert MatMul(C, Transpose(D*C)).doit().args == (C, C.T, D.T)
def test_doit_nested_MatrixExpr():
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[2, 3], [4, 5]])
assert MatPow(MatMul(X, Y), 2).doit() == (X*Y)**2
assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2
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