def test_fftw_inverse():
c = FFTW(y)
with assuming(Q.complex(y)):
f = build(c, [y], [DFT(y)], modname='fftw2', filename='tmp/fftw2.f90')
c = IFFTW(y)
with assuming(Q.complex(y)):
fi = build(c, [y], [DFT(y).T], modname='ifftw', filename='tmp/ifftw.f90')
x = np.random.random_sample((8,)) + 1j * np.random.random_sample((8,))
expected = x
f(x)
fi(x)
assert np.allclose(expected, x)
def test_pow1():
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**Rational(1, 3)) != x
assert refine((x**3)**Rational(1, 3), Q.real(x)) != x
assert refine((x**3)**Rational(1, 3), Q.positive(x)) == x
assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x)
assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x)
# powers of (-1)
assert refine((-1)**(x + y), Q.even(x)) == (-1)**y
assert refine((-1)**(x + y + z), Q.odd(x) & Q.odd(z)) == (-1)**y
assert refine((-1)**(x + y + 1), Q.odd(x)) == (-1)**y
assert refine((-1)**(x + y + 2), Q.odd(x)) == (-1)**(y + 1)
assert refine((-1)**(x + 3)) == (-1)**(x + 1)
# continuation
assert refine((-1)**((-1)**x/2 - S.Half), Q.integer(x)) == (-1)**x
assert refine((-1)**((-1)**x/2 + S.Half), Q.integer(x)) == (-1)**(x + 1)
assert refine((-1)**((-1)**x/2 + 5*S.Half), Q.integer(x)) == (-1)**(x + 1)
def test_pow():
assert refine((-1) ** x, Q.even(x)) == 1
assert refine((-1) ** x, Q.odd(x)) == -1
assert refine((-2) ** x, Q.even(x)) == 2 ** x
# nested powers
assert refine(sqrt(x ** 2)) != Abs(x)
assert refine(sqrt(x ** 2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x ** 2), Q.real(x)) == Abs(x)
assert refine(sqrt(x ** 2), Q.positive(x)) == x
assert refine((x ** 3) ** (S(1) / 3)) != x
assert refine((x ** 3) ** (S(1) / 3), Q.real(x)) != x
assert refine((x ** 3) ** (S(1) / 3), Q.positive(x)) == x
assert refine(sqrt(1 / x), Q.real(x)) != 1 / sqrt(x)
assert refine(sqrt(1 / x), Q.positive(x)) == 1 / sqrt(x)
# powers of (-1)
assert refine((-1) ** (x + y), Q.even(x)) == (-1) ** y
assert refine((-1) ** (x + y + z), Q.odd(x) & Q.odd(z)) == (-1) ** y
assert refine((-1) ** (x + y + 1), Q.odd(x)) == (-1) ** y
assert refine((-1) ** (x + y + 2), Q.odd(x)) == (-1) ** (y + 1)
assert refine((-1) ** (x + 3)) == (-1) ** (x + 1)
assert refine((-1) ** ((-1) ** x / 2 - S.Half), Q.integer(x)) == (-1) ** x
assert refine((-1) ** ((-1) ** x / 2 + S.Half), Q.integer(x)) == (-1) ** (x + 1)
assert refine((-1) ** ((-1) ** x / 2 + 5 * S.Half), Q.integer(x)) == (-1) ** (x + 1)
assert refine((-1) ** ((-1) ** x / 2 - 7 * S.Half), Q.integer(x)) == (-1) ** (x + 1)
assert refine((-1) ** ((-1) ** x / 2 - 9 * S.Half), Q.integer(x)) == (-1) ** x
# powers of Abs
assert refine(Abs(x) ** 2, Q.real(x)) == x ** 2
assert refine(Abs(x) ** 3, Q.real(x)) == Abs(x) ** 3
assert refine(Abs(x) ** 2) == Abs(x) ** 2
def test_pow():
x, y, z = symbols('x,y,z')
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**(S(1)/3)) != x
assert refine((x**3)**(S(1)/3), Q.real(x)) != x
assert refine((x**3)**(S(1)/3), Q.positive(x)) == x
assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x)
assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x)
# powers of (-1)
assert refine((-1)**(x+y), Q.even(x)) == (-1)**y
assert refine((-1)**(x+y+z), Q.odd(x) & Q.odd(z))==(-1)**y
assert refine((-1)**(x+y+1), Q.odd(x))==(-1)**y
assert refine((-1)**(x+y+2), Q.odd(x))==(-1)**(y+1)
assert refine((-1)**(x+3)) == (-1)**(x+1)
def test_pow():
x, y, z = symbols('x,y,z')
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**(S(1) / 3)) != x
assert refine((x**3)**(S(1) / 3), Q.real(x)) != x
assert refine((x**3)**(S(1) / 3), Q.positive(x)) == x
assert refine(sqrt(1 / x), Q.real(x)) != 1 / sqrt(x)
assert refine(sqrt(1 / x), Q.positive(x)) == 1 / sqrt(x)
# powers of (-1)
assert refine((-1)**(x + y), Q.even(x)) == (-1)**y
assert refine((-1)**(x + y + z), Q.odd(x) & Q.odd(z)) == (-1)**y
assert refine((-1)**(x + y + 1), Q.odd(x)) == (-1)**y
assert refine((-1)**(x + y + 2), Q.odd(x)) == (-1)**(y + 1)
assert refine((-1)**(x + 3)) == (-1)**(x + 1)
def test_matrix_element_sets():
X = MatrixSymbol('X', 4, 4)
assert ask(Q.real(X[1, 2]), Q.real_elements(X))
assert ask(Q.integer(X[1, 2]), Q.integer_elements(X))
assert ask(Q.complex(X[1, 2]), Q.complex_elements(X))
assert ask(Q.integer_elements(Identity(3)))
assert ask(Q.integer_elements(ZeroMatrix(3, 3)))
from sympy.matrices.expressions.fourier import DFT
assert ask(Q.complex_elements(DFT(3)))
def test_matrix_element_sets():
X = MatrixSymbol('X', 4, 4)
assert ask(Q.real(X[1, 2]), Q.real_elements(X))
assert ask(Q.integer(X[1, 2]), Q.integer_elements(X))
assert ask(Q.complex(X[1, 2]), Q.complex_elements(X))
assert ask(Q.integer_elements(Identity(3)))
assert ask(Q.integer_elements(ZeroMatrix(3, 3)))
from sympy.matrices.expressions.fourier import DFT
assert ask(Q.complex_elements(DFT(3)))
def dtype_of(expr, *assumptions):
if hasattr(expr, 'fortran_type'):
return expr.fortran_type()
with assuming(*assumptions):
if ask(Q.integer(expr) | Q.integer_elements(expr)) or expr.is_integer:
result = 'integer'
elif ask(Q.real(expr) | Q.real_elements(expr)) or expr.is_real:
result = 'real(kind=8)'
elif ask(Q.complex(expr) | Q.complex_elements(expr)) or expr.is_complex:
result = 'complex(kind=8)'
else:
raise TypeError('Could not infer type of %s'%str(expr))
return result
def test_pow1():
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**(S(1)/3)) != x
assert refine((x**3)**(S(1)/3), Q.real(x)) != x
assert refine((x**3)**(S(1)/3), Q.positive(x)) == x
assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x)
assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x)
def test_pow1():
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**(S(1)/3)) != x
assert refine((x**3)**(S(1)/3), Q.real(x)) != x
assert refine((x**3)**(S(1)/3), Q.positive(x)) == x
assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x)
assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x)
def test_pow():
assert refine((-1)**x, Q.even(x)) == 1
assert refine((-1)**x, Q.odd(x)) == -1
assert refine((-2)**x, Q.even(x)) == 2**x
# nested powers
assert refine(sqrt(x**2)) != Abs(x)
assert refine(sqrt(x**2), Q.complex(x)) != Abs(x)
assert refine(sqrt(x**2), Q.real(x)) == Abs(x)
assert refine(sqrt(x**2), Q.positive(x)) == x
assert refine((x**3)**(S(1) / 3)) != x
assert refine((x**3)**(S(1) / 3), Q.real(x)) != x
assert refine((x**3)**(S(1) / 3), Q.positive(x)) == x
assert refine(sqrt(1 / x), Q.real(x)) != 1 / sqrt(x)
assert refine(sqrt(1 / x), Q.positive(x)) == 1 / sqrt(x)
# powers of (-1)
assert refine((-1)**(x + y), Q.even(x)) == (-1)**y
assert refine((-1)**(x + y + z), Q.odd(x) & Q.odd(z)) == (-1)**y
assert refine((-1)**(x + y + 1), Q.odd(x)) == (-1)**y
assert refine((-1)**(x + y + 2), Q.odd(x)) == (-1)**(y + 1)
assert refine((-1)**(x + 3)) == (-1)**(x + 1)
assert refine((-1)**((-1)**x / 2 - S.Half), Q.integer(x)) == (-1)**x
assert refine((-1)**((-1)**x / 2 + S.Half), Q.integer(x)) == (-1)**(x + 1)
assert refine((-1)**((-1)**x / 2 + 5 * S.Half),
Q.integer(x)) == (-1)**(x + 1)
assert refine((-1)**((-1)**x / 2 - 7 * S.Half),
Q.integer(x)) == (-1)**(x + 1)
assert refine((-1)**((-1)**x / 2 - 9 * S.Half), Q.integer(x)) == (-1)**x
# powers of Abs
assert refine(Abs(x)**2, Q.real(x)) == x**2
assert refine(Abs(x)**3, Q.real(x)) == Abs(x)**3
assert refine(Abs(x)**2) == Abs(x)**2