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from itertools import product
from sympy.core.relational import (Equality, Unequality)
from sympy.core.singleton import S
from sympy.core.sympify import sympify
from sympy.integrals.integrals import integrate
from sympy.matrices.dense import (Matrix, eye, zeros)
from sympy.matrices.immutable import ImmutableMatrix
from sympy.matrices import SparseMatrix
from sympy.matrices.immutable import \
ImmutableDenseMatrix, ImmutableSparseMatrix
from sympy.abc import x, y
from sympy.testing.pytest import raises
IM = ImmutableDenseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
ISM = ImmutableSparseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
ieye = ImmutableDenseMatrix(eye(3))
def test_creation():
assert IM.shape == ISM.shape == (3, 3)
assert IM[1, 2] == ISM[1, 2] == 6
assert IM[2, 2] == ISM[2, 2] == 9
def test_immutability():
with raises(TypeError):
IM[2, 2] = 5
with raises(TypeError):
ISM[2, 2] = 5
def test_slicing():
assert IM[1, :] == ImmutableDenseMatrix([[4, 5, 6]])
assert IM[:2, :2] == ImmutableDenseMatrix([[1, 2], [4, 5]])
assert ISM[1, :] == ImmutableSparseMatrix([[4, 5, 6]])
assert ISM[:2, :2] == ImmutableSparseMatrix([[1, 2], [4, 5]])
def test_subs():
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix([[1, 2], [x, 4]])
C = ImmutableMatrix([[-x, x*y], [-(x + y), y**2]])
assert B.subs(x, 3) == A
assert (x*B).subs(x, 3) == 3*A
assert (x*eye(2) + B).subs(x, 3) == 3*eye(2) + A
assert C.subs([[x, -1], [y, -2]]) == A
assert C.subs([(x, -1), (y, -2)]) == A
assert C.subs({x: -1, y: -2}) == A
assert C.subs({x: y - 1, y: x - 1}, simultaneous=True) == \
ImmutableMatrix([[1 - y, (x - 1)*(y - 1)], [2 - x - y, (x - 1)**2]])
def test_as_immutable():
data = [[1, 2], [3, 4]]
X = Matrix(data)
assert sympify(X) == X.as_immutable() == ImmutableMatrix(data)
data = {(0, 0): 1, (0, 1): 2, (1, 0): 3, (1, 1): 4}
X = SparseMatrix(2, 2, data)
assert sympify(X) == X.as_immutable() == ImmutableSparseMatrix(2, 2, data)
def test_function_return_types():
# Lets ensure that decompositions of immutable matrices remain immutable
# I.e. do MatrixBase methods return the correct class?
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[1], [0]])
q, r = X.QRdecomposition()
assert (type(q), type(r)) == (ImmutableMatrix, ImmutableMatrix)
assert type(X.LUsolve(Y)) == ImmutableMatrix
assert type(X.QRsolve(Y)) == ImmutableMatrix
X = ImmutableMatrix([[5, 2], [2, 7]])
assert X.T == X
assert X.is_symmetric
assert type(X.cholesky()) == ImmutableMatrix
L, D = X.LDLdecomposition()
assert (type(L), type(D)) == (ImmutableMatrix, ImmutableMatrix)
X = ImmutableMatrix([[1, 2], [2, 1]])
assert X.is_diagonalizable()
assert X.det() == -3
assert X.norm(2) == 3
assert type(X.eigenvects()[0][2][0]) == ImmutableMatrix
assert type(zeros(3, 3).as_immutable().nullspace()[0]) == ImmutableMatrix
X = ImmutableMatrix([[1, 0], [2, 1]])
assert type(X.lower_triangular_solve(Y)) == ImmutableMatrix
assert type(X.T.upper_triangular_solve(Y)) == ImmutableMatrix
assert type(X.minor_submatrix(0, 0)) == ImmutableMatrix
# issue 6279
# https://github.com/sympy/sympy/issues/6279
# Test that Immutable _op_ Immutable => Immutable and not MatExpr
def test_immutable_evaluation():
X = ImmutableMatrix(eye(3))
A = ImmutableMatrix(3, 3, range(9))
assert isinstance(X + A, ImmutableMatrix)
assert isinstance(X * A, ImmutableMatrix)
assert isinstance(X * 2, ImmutableMatrix)
assert isinstance(2 * X, ImmutableMatrix)
assert isinstance(A**2, ImmutableMatrix)
def test_deterimant():
assert ImmutableMatrix(4, 4, lambda i, j: i + j).det() == 0
def test_Equality():
assert Equality(IM, IM) is S.true
assert Unequality(IM, IM) is S.false
assert Equality(IM, IM.subs(1, 2)) is S.false
assert Unequality(IM, IM.subs(1, 2)) is S.true
assert Equality(IM, 2) is S.false
assert Unequality(IM, 2) is S.true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is S.false
assert Unequality(M, IM) is S.true
assert Equality(M, M.subs(x, 2)).subs(x, 2) is S.true
assert Unequality(M, M.subs(x, 2)).subs(x, 2) is S.false
assert Equality(M, M.subs(x, 2)).subs(x, 3) is S.false
assert Unequality(M, M.subs(x, 2)).subs(x, 3) is S.true
def test_integrate():
intIM = integrate(IM, x)
assert intIM.shape == IM.shape
assert all(intIM[i, j] == (1 + j + 3*i)*x for i, j in
product(range(3), range(3)))
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