image-handler/image-handler10.0/venv/lib/site-packages/sympy/matrices/tests/test_immutable.py

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))])