def test_Matrix_printing():
# Test returning a Matrix
mat = Matrix([x * y, Piecewise((2 + x, y > 0), (y, True)), sin(z)])
A = MatrixSymbol('A', 3, 1)
assert fcode(mat, A) == (' A(1, 1) = x*y\n'
' if (y > 0) then\n'
' A(2, 1) = x + 2\n'
' else\n'
' A(2, 1) = y\n'
' end if\n'
' A(3, 1) = sin(z)')
# Test using MatrixElements in expressions
expr = Piecewise((2 * A[2, 0], x > 0),
(A[2, 0], True)) + sin(A[1, 0]) + A[0, 0]
assert fcode(expr, standard=95) == (
' merge(2*A(3, 1), A(3, 1), x > 0) + sin(A(2, 1)) + A(1, 1)')
# Test using MatrixElements in a Matrix
q = MatrixSymbol('q', 5, 1)
M = MatrixSymbol('M', 3, 3)
m = Matrix([[sin(q[1, 0]), 0, cos(q[2, 0])],
[q[1, 0] + q[2, 0], q[3, 0], 5],
[2 * q[4, 0] / q[1, 0],
sqrt(q[0, 0]) + 4, 0]])
assert fcode(m, M) == (' M(1, 1) = sin(q(2, 1))\n'
' M(2, 1) = q(2, 1) + q(3, 1)\n'
' M(3, 1) = 2*q(5, 1)*1.0/q(2, 1)\n'
' M(1, 2) = 0\n'
' M(2, 2) = q(4, 1)\n'
' M(3, 2) = 4 + sqrt(q(1, 1))\n'
' M(1, 3) = cos(q(3, 1))\n'
' M(2, 3) = 5\n'
' M(3, 3) = 0')
def test_fcode_precedence():
assert fcode(And(x < y, y < x + 1), source_format='free') == \
'x < y .and. y < x + 1'
assert fcode(Or(x < y, y < x + 1), source_format='free') == \
'x < y .or. y < x + 1'
assert fcode(Xor(x < y, y < x + 1, evaluate=False),
source_format='free') == 'x < y .neqv. y < x + 1'
assert fcode(Equivalent(x < y, y < x + 1), source_format='free') == \
'x < y .eqv. y < x + 1'
def test_line_wrapping():
assert fcode(((x + y)**10).expand(), assign_to='var') == (
' var = x**10 + 10*x**9*y + 45*x**8*y**2 + 120*x**7*y**3 + 210*x**6*\n'
' @ y**4 + 252*x**5*y**5 + 210*x**4*y**6 + 120*x**3*y**7 + 45*x**2*y\n'
' @ **8 + 10*x*y**9 + y**10')
e = [x**i for i in range(11)]
assert fcode(Add(*e)) == (
' x**10 + x**9 + x**8 + x**7 + x**6 + x**5 + x**4 + x**3 + x**2 + x\n'
' @ + 1')
def test_user_functions():
assert fcode(sin(x), user_functions={'sin': 'zsin'}) == ' zsin(x)'
assert fcode(gamma(x), user_functions={'gamma':
'mygamma'}) == ' mygamma(x)'
g = Function('g')
assert fcode(g(x), user_functions={'g': 'great'}) == ' great(x)'
n = symbols('n', integer=True)
assert fcode(factorial(n), user_functions={'factorial':
'fct'}) == ' fct(n)'
def test_not_fortran():
g = Function('g')
assert fcode(gamma(
x)) == 'C Not supported in Fortran:\nC gamma\n gamma(x)'
assert fcode(
Integral(sin(x))
) == 'C Not supported in Fortran:\nC Integral\n Integral(sin(x), x)'
assert fcode(
g(x)) == 'C Not supported in Fortran:\nC g\n g(x)'
def test_inline_function():
g = implemented_function('g', Lambda(x, 2 * x))
assert fcode(g(x)) == ' 2*x'
g = implemented_function('g', Lambda(x, 2 * pi / x))
assert fcode(g(x)) == (' parameter (pi = 3.14159265358979d0)\n'
' 2*pi/x')
A = IndexedBase('A')
i = Idx('i', symbols('n', integer=True))
g = implemented_function('g', Lambda(x, x * (1 + x) * (2 + x)))
assert fcode(
g(A[i]),
assign_to=A[i]) == (' do i = 1, n\n'
' A(i) = (A(i) + 1)*(A(i) + 2)*A(i)\n'
' end do')
def test_fcode_complex():
assert fcode(I) == ' cmplx(0,1)'
x = symbols('x')
assert fcode(4 * I) == ' cmplx(0,4)'
assert fcode(3 + 4 * I) == ' cmplx(3,4)'
assert fcode(3 + 4 * I + x) == ' cmplx(3,4) + x'
assert fcode(I * x) == ' cmplx(0,1)*x'
assert fcode(3 + 4 * I - x) == ' cmplx(3,4) - x'
x = symbols('x', imaginary=True)
assert fcode(5 * x) == ' 5*x'
assert fcode(I * x) == ' cmplx(0,1)*x'
assert fcode(3 + x) == ' x + 3'
def test_free_form_continuation_line():
result = fcode(((cos(x) + sin(y))**(7)).expand(), source_format='free')
expected = (
'sin(y)**7 + 7*sin(y)**6*cos(x) + 21*sin(y)**5*cos(x)**2 + 35*sin(y)**4* &\n'
' cos(x)**3 + 35*sin(y)**3*cos(x)**4 + 21*sin(y)**2*cos(x)**5 + 7* &\n'
' sin(y)*cos(x)**6 + cos(x)**7')
assert result == expected
def test_loops():
n, m = symbols('n,m', integer=True)
A = IndexedBase('A')
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
expected = ('do i = 1, m\n'
' y(i) = 0\n'
'end do\n'
'do i = 1, m\n'
' do j = 1, n\n'
' y(i) = %(rhs)s\n'
' end do\n'
'end do')
code = fcode(A[i, j] * x[j], assign_to=y[i], source_format='free')
assert (code == expected % {
'rhs': 'y(i) + A(i, j)*x(j)'
} or code == expected % {
'rhs': 'y(i) + x(j)*A(i, j)'
} or code == expected % {
'rhs': 'x(j)*A(i, j) + y(i)'
} or code == expected % {
'rhs': 'A(i, j)*x(j) + y(i)'
})
def test_fcode_Indexed_without_looking_for_contraction():
len_y = 5
y = IndexedBase('y', shape=(len_y, ))
x = IndexedBase('x', shape=(len_y, ))
Dy = IndexedBase('Dy', shape=(len_y - 1, ))
i = Idx('i', len_y - 1)
e = Eq(Dy[i], (y[i + 1] - y[i]) / (x[i + 1] - x[i]))
code0 = fcode(e.rhs, assign_to=e.lhs, contract=False)
assert code0.endswith('Dy(i) = (y(i + 1) - y(i))/(x(i + 1) - x(i))')
def test_fcode_functions_with_integers():
assert fcode(x * log(10)) == ' x*2.30258509299405d0'
assert fcode(x * log(10)) == ' x*2.30258509299405d0'
assert fcode(x * log(Integer(10))) == ' x*2.30258509299405d0'
assert fcode(log(Integer(10))) == ' 2.30258509299405d0'
assert fcode(exp(10)) == ' parameter (E = 2.71828182845905d0)\n E**10'
assert fcode(x * log(log(10))) == ' x*0.834032445247956d0'
assert fcode(x * log(log(Integer(10)))) == ' x*0.834032445247956d0'
def test_fcode_Relational():
assert fcode(Relational(x, y, '=='), source_format='free') == 'Eq(x, y)'
assert fcode(Relational(x, y, '!='), source_format='free') == 'Ne(x, y)'
assert fcode(Relational(x, y, '>='), source_format='free') == 'x >= y'
assert fcode(Relational(x, y, '<='), source_format='free') == 'x <= y'
assert fcode(Relational(x, y, '>'), source_format='free') == 'x > y'
assert fcode(Relational(x, y, '<'), source_format='free') == 'x < y'
def test_fcode_Rational():
assert fcode(Rational(3, 7)) == ' 3.0d0/7.0d0'
assert fcode(Rational(18, 9)) == ' 2'
assert fcode(Rational(3, -7)) == ' -3.0d0/7.0d0'
assert fcode(Rational(-3, -7)) == ' 3.0d0/7.0d0'
assert fcode(x + Rational(3, 7)) == ' x + 3.0d0/7.0d0'
assert fcode(Rational(3, 7) * x) == ' (3.0d0/7.0d0)*x'
def test_dummy_loops():
i, m = symbols('i m', integer=True, cls=Dummy)
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx(i, m)
expected = (
'do i_%(icount)i = 1, m_%(mcount)i\n'
' y(i_%(icount)i) = x(i_%(icount)i)\n'
'end do'
) % {'icount': i.label.dummy_index, 'mcount': m.dummy_index}
code = fcode(x[i], assign_to=y[i], source_format='free')
assert code == expected
def test_fcode_Piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
# Check that inline conditional (merge) fails if standard isn't 95+
pytest.raises(NotImplementedError, lambda: fcode(expr))
code = fcode(expr, standard=95)
expected = ' merge(x, x**2, x < 1)'
assert code == expected
assert fcode(Piecewise((x, x < 1), (x**2, True)),
assign_to='var') == (' if (x < 1) then\n'
' var = x\n'
' else\n'
' var = x**2\n'
' end if')
a = cos(x) / x
b = sin(x) / x
for i in range(10):
a = diff(a, x)
b = diff(b, x)
expected = (
' if (x < 0) then\n'
' weird_name = -cos(x)/x + 10*sin(x)/x**2 + 90*cos(x)/x**3 - 720*\n'
' @ sin(x)/x**4 - 5040*cos(x)/x**5 + 30240*sin(x)/x**6 + 151200*cos(x\n'
' @ )/x**7 - 604800*sin(x)/x**8 - 1814400*cos(x)/x**9 + 3628800*sin(x\n'
' @ )/x**10 + 3628800*cos(x)/x**11\n'
' else\n'
' weird_name = -sin(x)/x - 10*cos(x)/x**2 + 90*sin(x)/x**3 + 720*\n'
' @ cos(x)/x**4 - 5040*sin(x)/x**5 - 30240*cos(x)/x**6 + 151200*sin(x\n'
' @ )/x**7 + 604800*cos(x)/x**8 - 1814400*sin(x)/x**9 - 3628800*cos(x\n'
' @ )/x**10 + 3628800*sin(x)/x**11\n'
' end if')
code = fcode(Piecewise((a, x < 0), (b, True)), assign_to='weird_name')
assert code == expected
code = fcode(Piecewise((x, x < 1), (x**2, x > 1), (sin(x), True)),
standard=95)
expected = ' merge(x, merge(x**2, sin(x), x > 1), x < 1)'
assert code == expected
# Check that Piecewise without a True (default) condition error
expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
pytest.raises(ValueError, lambda: fcode(expr))
assert (fcode(Piecewise((0, x < -1), (1, And(x >= -1, x < 0)), (-1, True)),
assign_to='var') == ' if (x < -1) then\n'
' var = 0\n'
' else if (x >= -1 .and. x < 0) then\n'
' var = 1\n'
' else\n'
' var = -1\n'
' end if')
def test_fcode_Xlogical():
# binary Xor
assert fcode(Xor(x, y, evaluate=False), source_format='free') == \
'x .neqv. y'
assert fcode(Xor(x, Not(y), evaluate=False), source_format='free') == \
'x .neqv. .not. y'
assert fcode(Xor(Not(x), y, evaluate=False), source_format='free') == \
'y .neqv. .not. x'
assert fcode(Xor(Not(x), Not(y), evaluate=False),
source_format='free') == '.not. x .neqv. .not. y'
assert fcode(Not(Xor(x, y, evaluate=False), evaluate=False),
source_format='free') == '.not. (x .neqv. y)'
# binary Equivalent
assert fcode(Equivalent(x, y), source_format='free') == 'x .eqv. y'
assert fcode(Equivalent(x, Not(y)), source_format='free') == \
'x .eqv. .not. y'
assert fcode(Equivalent(Not(x), y), source_format='free') == \
'y .eqv. .not. x'
assert fcode(Equivalent(Not(x), Not(y)), source_format='free') == \
'.not. x .eqv. .not. y'
assert fcode(Not(Equivalent(x, y), evaluate=False),
source_format='free') == '.not. (x .eqv. y)'
# mixed And/Equivalent
assert fcode(Equivalent(And(y, z), x), source_format='free') == \
'x .eqv. y .and. z'
assert fcode(Equivalent(And(z, x), y), source_format='free') == \
'y .eqv. x .and. z'
assert fcode(Equivalent(And(x, y), z), source_format='free') == \
'z .eqv. x .and. y'
assert fcode(And(Equivalent(y, z), x), source_format='free') == \
'x .and. (y .eqv. z)'
assert fcode(And(Equivalent(z, x), y), source_format='free') == \
'y .and. (x .eqv. z)'
assert fcode(And(Equivalent(x, y), z), source_format='free') == \
'z .and. (x .eqv. y)'
# mixed Or/Equivalent
assert fcode(Equivalent(Or(y, z), x), source_format='free') == \
'x .eqv. y .or. z'
assert fcode(Equivalent(Or(z, x), y), source_format='free') == \
'y .eqv. x .or. z'
assert fcode(Equivalent(Or(x, y), z), source_format='free') == \
'z .eqv. x .or. y'
assert fcode(Or(Equivalent(y, z), x), source_format='free') == \
'x .or. (y .eqv. z)'
assert fcode(Or(Equivalent(z, x), y), source_format='free') == \
'y .or. (x .eqv. z)'
assert fcode(Or(Equivalent(x, y), z), source_format='free') == \
'z .or. (x .eqv. y)'
# mixed Xor/Equivalent
assert fcode(Equivalent(Xor(y, z, evaluate=False), x),
source_format='free') == 'x .eqv. (y .neqv. z)'
assert fcode(Equivalent(Xor(z, x, evaluate=False), y),
source_format='free') == 'y .eqv. (x .neqv. z)'
assert fcode(Equivalent(Xor(x, y, evaluate=False), z),
source_format='free') == 'z .eqv. (x .neqv. y)'
assert fcode(Xor(Equivalent(y, z), x, evaluate=False),
source_format='free') == 'x .neqv. (y .eqv. z)'
assert fcode(Xor(Equivalent(z, x), y, evaluate=False),
source_format='free') == 'y .neqv. (x .eqv. z)'
assert fcode(Xor(Equivalent(x, y), z, evaluate=False),
source_format='free') == 'z .neqv. (x .eqv. y)'
# mixed And/Xor
assert fcode(Xor(And(y, z), x, evaluate=False), source_format='free') == \
'x .neqv. y .and. z'
assert fcode(Xor(And(z, x), y, evaluate=False), source_format='free') == \
'y .neqv. x .and. z'
assert fcode(Xor(And(x, y), z, evaluate=False), source_format='free') == \
'z .neqv. x .and. y'
assert fcode(And(Xor(y, z, evaluate=False), x), source_format='free') == \
'x .and. (y .neqv. z)'
assert fcode(And(Xor(z, x, evaluate=False), y), source_format='free') == \
'y .and. (x .neqv. z)'
assert fcode(And(Xor(x, y, evaluate=False), z), source_format='free') == \
'z .and. (x .neqv. y)'
# mixed Or/Xor
assert fcode(Xor(Or(y, z), x, evaluate=False), source_format='free') == \
'x .neqv. y .or. z'
assert fcode(Xor(Or(z, x), y, evaluate=False), source_format='free') == \
'y .neqv. x .or. z'
assert fcode(Xor(Or(x, y), z, evaluate=False), source_format='free') == \
'z .neqv. x .or. y'
assert fcode(Or(Xor(y, z, evaluate=False), x), source_format='free') == \
'x .or. (y .neqv. z)'
assert fcode(Or(Xor(z, x, evaluate=False), y), source_format='free') == \
'y .or. (x .neqv. z)'
assert fcode(Or(Xor(x, y, evaluate=False), z), source_format='free') == \
'z .or. (x .neqv. y)'
# trinary Xor
assert fcode(Xor(x, y, z, evaluate=False), source_format='free') == \
'x .neqv. y .neqv. z'
assert fcode(Xor(x, y, Not(z), evaluate=False), source_format='free') == \
'x .neqv. y .neqv. .not. z'
assert fcode(Xor(x, Not(y), z, evaluate=False), source_format='free') == \
'x .neqv. z .neqv. .not. y'
assert fcode(Xor(Not(x), y, z, evaluate=False), source_format='free') == \
'y .neqv. z .neqv. .not. x'
def test_fcode_Float():
assert fcode(Float(42.0)) == ' 42.0000000000000d0'
assert fcode(Float(-1e20)) == ' -1.00000000000000d+20'
def test_implicit():
assert fcode(sin(x)) == ' sin(x)'
assert fcode(atan2(x, y)) == ' atan2(x, y)'
assert fcode(conjugate(x)) == ' conjg(x)'
def test_fcode_Integer():
assert fcode(Integer(67)) == ' 67'
assert fcode(Integer(-1)) == ' -1'
def test_printmethod():
class MyFunction(Function):
def _fcode(self, printer):
return 'myf(%s)' % printer._print(self.args[0])
assert fcode(MyFunction(x)) == ' myf(x)'
def test_assign_to():
assert fcode(sin(x), assign_to='s') == ' s = sin(x)'
def test_free_form_code_line():
assert fcode(cos(x) + sin(y), source_format='free') == 'sin(y) + cos(x)'
def test_settings():
pytest.raises(TypeError, lambda: fcode(Integer(4), method='garbage'))
def test_fcode_Logical():
# unary Not
assert fcode(Not(x), source_format='free') == '.not. x'
# binary And
assert fcode(And(x, y), source_format='free') == 'x .and. y'
assert fcode(And(x, Not(y)), source_format='free') == 'x .and. .not. y'
assert fcode(And(Not(x), y), source_format='free') == 'y .and. .not. x'
assert fcode(And(Not(x), Not(y)), source_format='free') == \
'.not. x .and. .not. y'
assert fcode(Not(And(x, y), evaluate=False), source_format='free') == \
'.not. (x .and. y)'
# binary Or
assert fcode(Or(x, y), source_format='free') == 'x .or. y'
assert fcode(Or(x, Not(y)), source_format='free') == 'x .or. .not. y'
assert fcode(Or(Not(x), y), source_format='free') == 'y .or. .not. x'
assert fcode(Or(Not(x), Not(y)), source_format='free') == \
'.not. x .or. .not. y'
assert fcode(Not(Or(x, y), evaluate=False), source_format='free') == \
'.not. (x .or. y)'
# mixed And/Or
assert fcode(And(Or(y, z), x),
source_format='free') == 'x .and. (y .or. z)'
assert fcode(And(Or(z, x), y),
source_format='free') == 'y .and. (x .or. z)'
assert fcode(And(Or(x, y), z),
source_format='free') == 'z .and. (x .or. y)'
assert fcode(Or(And(y, z), x), source_format='free') == 'x .or. y .and. z'
assert fcode(Or(And(z, x), y), source_format='free') == 'y .or. x .and. z'
assert fcode(Or(And(x, y), z), source_format='free') == 'z .or. x .and. y'
# trinary And
assert fcode(And(x, y, z), source_format='free') == 'x .and. y .and. z'
assert fcode(And(x, y, Not(z)), source_format='free') == \
'x .and. y .and. .not. z'
assert fcode(And(x, Not(y), z), source_format='free') == \
'x .and. z .and. .not. y'
assert fcode(And(Not(x), y, z), source_format='free') == \
'y .and. z .and. .not. x'
assert fcode(Not(And(x, y, z), evaluate=False), source_format='free') == \
'.not. (x .and. y .and. z)'
# trinary Or
assert fcode(Or(x, y, z), source_format='free') == 'x .or. y .or. z'
assert fcode(Or(x, y, Not(z)), source_format='free') == \
'x .or. y .or. .not. z'
assert fcode(Or(x, Not(y), z), source_format='free') == \
'x .or. z .or. .not. y'
assert fcode(Or(Not(x), y, z), source_format='free') == \
'y .or. z .or. .not. x'
assert fcode(Not(Or(x, y, z), evaluate=False), source_format='free') == \
'.not. (x .or. y .or. z)'
def test_args():
pytest.raises(ValueError, lambda: fcode(x, source_format='spam'))
pytest.raises(ValueError, lambda: fcode(x, standard='eggs'))
def test_fcode_functions():
assert fcode(sin(x)**cos(y)) == ' sin(x)**cos(y)'
def test_fcode_NumberSymbol():
p = FCodePrinter()
assert fcode(
Catalan
) == ' parameter (Catalan = 0.915965594177219d0)\n Catalan'
assert fcode(
EulerGamma
) == ' parameter (EulerGamma = 0.577215664901533d0)\n EulerGamma'
assert fcode(E) == ' parameter (E = 2.71828182845905d0)\n E'
assert fcode(
GoldenRatio
) == ' parameter (GoldenRatio = 1.61803398874989d0)\n GoldenRatio'
assert fcode(pi) == ' parameter (pi = 3.14159265358979d0)\n pi'
assert fcode(pi,
precision=5) == ' parameter (pi = 3.1416d0)\n pi'
assert fcode(Catalan,
human=False) == ({(Catalan, p._print(Catalan.evalf(15)))},
set(), ' Catalan')
assert fcode(EulerGamma, human=False) == ({
(EulerGamma, p._print(EulerGamma.evalf(15)))
}, set(), ' EulerGamma')
assert fcode(E, human=False) == ({(E, p._print(E.evalf(15)))}, set(),
' E')
assert fcode(GoldenRatio, human=False) == ({
(GoldenRatio, p._print(GoldenRatio.evalf(15)))
}, set(), ' GoldenRatio')
assert fcode(pi, human=False) == ({(pi, p._print(pi.evalf(15)))}, set(),
' pi')
assert fcode(pi,
precision=5, human=False) == ({(pi, p._print(pi.evalf(5)))},
set(), ' pi')
def test_fcode_Pow():
n = symbols('n', integer=True)
assert fcode(x**3) == ' x**3'
assert fcode(x**(y**3)) == ' x**(y**3)'
assert fcode(1/(sin(x)*3.5)**(x - y**x)/(x**2 + y)) == \
' (3.5d0*sin(x))**(-x + y**x)/(x**2 + y)'
assert fcode(sqrt(x)) == ' sqrt(x)'
assert fcode(sqrt(n)) == ' sqrt(dble(n))'
assert fcode(x**0.5) == ' sqrt(x)'
assert fcode(sqrt(x)) == ' sqrt(x)'
assert fcode(sqrt(10)) == ' sqrt(10.0d0)'
assert fcode(x**-1.0) == ' 1.0/x'
assert fcode(x**-2.0, 'y',
source_format='free') == 'y = x**(-2.0d0)' # 2823
assert fcode(x**Rational(3, 7)) == ' x**(3.0d0/7.0d0)'
