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([[1, 2], [2, 1]])
assert X.T == X
assert X.is_symmetric
assert type(X.cholesky()) == ImmutableMatrix
L, D = X.LDLdecomposition()
assert (type(L), type(D)) == (ImmutableMatrix, ImmutableMatrix)
assert X.is_diagonalizable()
assert X.berkowitz_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.minorMatrix(0, 0)) == ImmutableMatrix
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, A).doit(deep=False) == 2 * A
assert (MatAdd(A, X, MatMul(A, B), Y,
MatAdd(2 * A, B)).doit() == MatAdd(X, Y, 3 * A + A * B + B))
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_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: y - 1, y: x - 1}, simultaneous=True) == \
ImmutableMatrix([[1 - y, (x - 1)*(y - 1)], [2 - x - y, (x - 1)**2]])
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_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_Equality():
assert Equality(IM, IM) is true
assert Unequality(IM, IM) is false
assert Equality(IM, IM.subs({1: 2})) is false
assert Unequality(IM, IM.subs({1: 2})) is true
assert Equality(IM, 2) is false
assert Unequality(IM, 2) is true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is false
assert Unequality(M, IM) is true
assert Equality(M, M.subs({x: 2})).subs({x: 2}) is true
assert Unequality(M, M.subs({x: 2})).subs({x: 2}) is false
assert Equality(M, M.subs({x: 2})).subs({x: 3}) is false
assert Unequality(M, M.subs({x: 2})).subs({x: 3}) is true
def test_Trace_MatAdd_doit():
# See issue sympy/sympy#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_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_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_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_block_index():
I = Identity(3)
Z = ZeroMatrix(3, 3)
B = BlockMatrix([[I, I], [I, I]])
e3 = ImmutableMatrix(eye(3))
BB = BlockMatrix([[e3, e3], [e3, e3]])
assert B[0, 0] == B[3, 0] == B[0, 3] == B[3, 3] == 1
assert B[4, 3] == B[5, 1] == 0
BB = BlockMatrix([[e3, e3], [e3, e3]])
assert B.as_explicit() == BB.as_explicit()
BI = BlockMatrix([[I, Z], [Z, I]])
assert BI.as_explicit().equals(eye(6))
def test_Equality():
assert Equality(IM, IM) is true
assert Unequality(IM, IM) is false
assert Equality(IM, IM.subs({1: 2})) is false
assert Unequality(IM, IM.subs({1: 2})) is true
assert Equality(IM, 2) is false
assert Unequality(IM, 2) is true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is false
assert Unequality(M, IM) is true
assert Equality(M, M.subs({x: 2})).subs({x: 2}) is true
assert Unequality(M, M.subs({x: 2})).subs({x: 2}) is false
assert Equality(M, M.subs({x: 2})).subs({x: 3}) is false
assert Unequality(M, M.subs({x: 2})).subs({x: 3}) is true
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_as_immutable():
X = Matrix([[1, 2], [3, 4]])
assert sympify(X) == X.as_immutable() == ImmutableMatrix([[1, 2], [3, 4]])
X = SparseMatrix(5, 5, {})
assert sympify(X) == X.as_immutable() == ImmutableSparseMatrix(
[[0 for i in range(5)] for i in range(5)])
def test_slicing():
assert IM[1, :] == ImmutableMatrix([[4, 5, 6]])
assert IM[:2, :2] == ImmutableMatrix([[1, 2], [4, 5]])
def test_deterimant():
assert ImmutableMatrix(4, 4, lambda i, j: i + j).det() == 0
import pytest
from diofant import (Equality, ImmutableMatrix, ImmutableSparseMatrix, Matrix,
SparseMatrix, Unequality, eye, false, sympify, true,
zeros)
from diofant.abc import x, y
__all__ = ()
IM = ImmutableMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
ieye = ImmutableMatrix(eye(3))
def test_immutable_creation():
assert IM.shape == (3, 3)
assert IM[1, 2] == 6
assert IM[2, 2] == 9
def test_immutability():
with pytest.raises(TypeError):
IM[2, 2] = 5
ISM = SparseMatrix(IM).as_immutable()
with pytest.raises(TypeError):
ISM[2, 2] = 5
def test_slicing():
assert IM[1, :] == ImmutableMatrix([[4, 5, 6]])
assert IM[:2, :2] == ImmutableMatrix([[1, 2], [4, 5]])
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_matadd_of_matrices():
assert MatAdd(eye(2), 4 * eye(2),
eye(2)).doit() == ImmutableMatrix(6 * eye(2))
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_trace_constant_factor():
# Issue sympy/sympy#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_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_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([[1, 2], [2, 1]])
assert X.T == X
assert X.is_symmetric
assert type(X.cholesky()) == ImmutableMatrix
L, D = X.LDLdecomposition()
assert (type(L), type(D)) == (ImmutableMatrix, ImmutableMatrix)
assert X.is_diagonalizable()
assert X.berkowitz_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.minorMatrix(0, 0)) == ImmutableMatrix
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_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])
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_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