<filename>tests/test_sampling.py
import unittest
import pdb

import numpy as np

from UncertainSCI.families import JacobiPolynomials
from UncertainSCI.distributions import BetaDistribution, TensorialDistribution

from UncertainSCI.pce import PolynomialChaosExpansion

class SamplingTestCase(unittest.TestCase):
    """
    Testing Sampling constructions.
    """

    def setUp(self):
        self.longMessage = True

    def test_gq(self):
        """
        Tests construction of a bivariate Gauss quadrature rule.
        """

        a1 = 10*np.random.rand(1)[0]
        b1 = 10*np.random.rand(1)[0]
        a2 = 10*np.random.rand(1)[0]
        b2 = 10*np.random.rand(1)[0]

        M1 = 1 + int(np.ceil(30*np.random.random()))
        M2 = 1 + int(np.ceil(30*np.random.random()))

        bounds1 = np.sort(np.random.randn(2))
        bounds2 = np.sort(np.random.randn(2))

        # First "manually" create Gauss quadrature grid
        J1 = JacobiPolynomials(alpha=b1-1, beta=a1-1)
        J2 = JacobiPolynomials(alpha=b2-1, beta=a2-1)

        x1, w1 = J1.gauss_quadrature(M1)
        x1 = (x1+1)/2 * (bounds1[1] - bounds1[0]) + bounds1[0]
        x2, w2 = J2.gauss_quadrature(M2)
        x2 = (x2+1)/2 * (bounds2[1] - bounds2[0]) + bounds2[0]

        X = np.meshgrid(x1, x2)
        x = np.vstack([X[0].flatten(), X[1].flatten()]).T
        W = np.meshgrid(w1, w2)
        w = W[0].flatten() * W[1].flatten()

        p1 = BetaDistribution(alpha=a1, beta=b1, bounds=bounds1)
        p2 = BetaDistribution(alpha=a2, beta=b2, bounds=bounds2)

        # order is irrelevant
        pce = PolynomialChaosExpansion(order=3, distribution=[p1, p2], sampling='gq', M=[M1, M2])
        pce.generate_samples()

        xerr = np.linalg.norm(pce.samples - x)
        werr = np.linalg.norm(pce.weights - w)

        msg = 'Failed for (M1, alpha1, beta1)=({0:d}, '\
              '{1:1.6f}, {2:1.6f}), (M2, alpha2, beta2)=({3:d}, '\
              '{4:1.6f}, {5:1.6f})'.format(M1, a1, b1, M2, a2, b2)

        delta = 1e-10
        self.assertAlmostEqual(xerr, 0, delta=delta, msg=msg)
        self.assertAlmostEqual(werr, 0, delta=delta, msg=msg)


if __name__ == "__main__":

    unittest.main(verbosity=2)

<filename>tests/test_sampling.py
import unittest
import pdb

import numpy as np

from UncertainSCI.families import JacobiPolynomials
from UncertainSCI.distributions import BetaDistribution, TensorialDistribution

from UncertainSCI.pce import PolynomialChaosExpansion

class SamplingTestCase(unittest.TestCase):
    """
    Testing Sampling constructions.
    """

    def setUp(self):
        self.longMessage = True

    def test_gq(self):
        """
        Tests construction of a bivariate Gauss quadrature rule.
        """

        a1 = 10*np.random.rand(1)[0]
        b1 = 10*np.random.rand(1)[0]
        a2 = 10*np.random.rand(1)[0]
        b2 = 10*np.random.rand(1)[0]

        M1 = 1 + int(np.ceil(30*np.random.random()))
        M2 = 1 + int(np.ceil(30*np.random.random()))

        bounds1 = np.sort(np.random.randn(2))
        bounds2 = np.sort(np.random.randn(2))

        # First "manually" create Gauss quadrature grid
        J1 = JacobiPolynomials(alpha=b1-1, beta=a1-1)
        J2 = JacobiPolynomials(alpha=b2-1, beta=a2-1)

        x1, w1 = J1.gauss_quadrature(M1)
        x1 = (x1+1)/2 * (bounds1[1] - bounds1[0]) + bounds1[0]
        x2, w2 = J2.gauss_quadrature(M2)
        x2 = (x2+1)/2 * (bounds2[1] - bounds2[0]) + bounds2[0]

        X = np.meshgrid(x1, x2)
        x = np.vstack([X[0].flatten(), X[1].flatten()]).T
        W = np.meshgrid(w1, w2)
        w = W[0].flatten() * W[1].flatten()

        p1 = BetaDistribution(alpha=a1, beta=b1, bounds=bounds1)
        p2 = BetaDistribution(alpha=a2, beta=b2, bounds=bounds2)

        # order is irrelevant
        pce = PolynomialChaosExpansion(order=3, distribution=[p1, p2], sampling='gq', M=[M1, M2])
        pce.generate_samples()

        xerr = np.linalg.norm(pce.samples - x)
        werr = np.linalg.norm(pce.weights - w)

        msg = 'Failed for (M1, alpha1, beta1)=({0:d}, '\
              '{1:1.6f}, {2:1.6f}), (M2, alpha2, beta2)=({3:d}, '\
              '{4:1.6f}, {5:1.6f})'.format(M1, a1, b1, M2, a2, b2)

        delta = 1e-10
        self.assertAlmostEqual(xerr, 0, delta=delta, msg=msg)
        self.assertAlmostEqual(werr, 0, delta=delta, msg=msg)


if __name__ == "__main__":

    unittest.main(verbosity=2)

Testing Sampling constructions. Tests construction of a bivariate Gauss quadrature rule. # First "manually" create Gauss quadrature grid # order is irrelevant