Python sympy.gamma() Examples

The following are 4 code examples of sympy.gamma(). You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may also want to check out all available functions/classes of the module sympy , or try the search function .
Example #1
Source File: test_tools.py    From quadpy with GNU General Public License v3.0 6 votes vote down vote up 
def test_integrate():
    moments = quadpy.tools.integrate(lambda x: [x ** k for k in range(5)], -1, +1)
    assert (moments == [2, 0, sympy.S(2) / 3, 0, sympy.S(2) / 5]).all()

    moments = quadpy.tools.integrate(
        lambda x: orthopy.line_segment.tree_legendre(x, 4, "monic", symbolic=True),
        -1,
        +1,
    )
    assert (moments == [2, 0, 0, 0, 0]).all()

    # Example from Gautschi's "How to and how not to" article
    moments = quadpy.tools.integrate(
        lambda x: [x ** k * sympy.exp(-(x ** 3) / 3) for k in range(5)], 0, sympy.oo
    )
    S = numpy.vectorize(sympy.S)
    gamma = numpy.vectorize(sympy.gamma)
    n = numpy.arange(5)
    reference = 3 ** (S(n - 2) / 3) * gamma(S(n + 1) / 3)
    assert numpy.all([sympy.simplify(m - r) == 0 for m, r in zip(moments, reference)])
Example #2
Source File: theanocode.py    From Computable with MIT License 5 votes vote down vote up 
def _print_factorial(self, expr, **kwargs):
        return self._print(sympy.gamma(expr.args[0] + 1), **kwargs)
Example #3
Source File: test_sympy_conv.py    From symengine.py with MIT License 5 votes vote down vote up 
def test_gamma():
    x = Symbol("x")
    e1 = sympy.gamma(sympy.Symbol("x"))
    e2 = gamma(x)
    assert sympify(e1) == e2
    assert e1 == e2._sympy_()
Example #4
Source File: test_tools.py    From quadpy with GNU General Public License v3.0 4 votes vote down vote up 
def test_gautschi_how_to_and_how_not_to():
    """Test Gautschi's famous example from

    W. Gautschi,
    How and how not to check Gaussian quadrature formulae,
    BIT Numerical Mathematics,
    June 1983, Volume 23, Issue 2, pp 209–216,
    <https://doi.org/10.1007/BF02218441>.
    """
    points = numpy.array(
        [
            1.457697817613696e-02,
            8.102669876765460e-02,
            2.081434595902250e-01,
            3.944841255669402e-01,
            6.315647839882239e-01,
            9.076033998613676e-01,
            1.210676808760832,
            1.530983977242980,
            1.861844587312434,
            2.199712165681546,
            2.543839804028289,
            2.896173043105410,
            3.262066731177372,
            3.653371887506584,
            4.102376773975577,
        ]
    )
    weights = numpy.array(
        [
            3.805398607861561e-2,
            9.622028412880550e-2,
            1.572176160500219e-1,
            2.091895332583340e-1,
            2.377990401332924e-1,
            2.271382574940649e-1,
            1.732845807252921e-1,
            9.869554247686019e-2,
            3.893631493517167e-2,
            9.812496327697071e-3,
            1.439191418328875e-3,
            1.088910025516801e-4,
            3.546866719463253e-6,
            3.590718819809800e-8,
            5.112611678291437e-11,
        ]
    )

    # weight function exp(-t**3/3)
    n = len(points)
    moments = numpy.array(
        [3.0 ** ((k - 2) / 3.0) * math.gamma((k + 1) / 3.0) for k in range(2 * n)]
    )

    alpha, beta = quadpy.tools.coefficients_from_gauss(points, weights)
    # alpha, beta = quadpy.tools.chebyshev(moments)

    errors_alpha, errors_beta = quadpy.tools.check_coefficients(moments, alpha, beta)

    assert numpy.max(errors_alpha) > 1.0e-2
    assert numpy.max(errors_beta) > 1.0e-2