137 lines
4.5 KiB
Python
137 lines
4.5 KiB
Python
|
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))])
|