EVOLUTION-MANAGER

Edit File: test_hermite.py

"""Tests for hermite module.

"""
from __future__ import division

import numpy as np
import numpy.polynomial.hermite as herm
from numpy.polynomial.polynomial import polyval
from numpy.testing import (
        TestCase, assert_almost_equal, assert_raises,
        assert_equal, assert_, run_module_suite)

H0 = np.array([   1])
H1 = np.array([0,     2])
H2 = np.array([  -2, 0,      4])
H3 = np.array([0,   -12, 0,      8])
H4 = np.array([  12, 0,    -48, 0,    16])
H5 = np.array([0,   120, 0,   -160, 0,    32])
H6 = np.array([-120, 0,    720, 0,  -480, 0,    64])
H7 = np.array([0, -1680, 0,   3360, 0, -1344, 0,   128])
H8 = np.array([1680, 0, -13440, 0, 13440, 0, -3584, 0, 256])
H9 = np.array([0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512])

Hlist = [H0, H1, H2, H3, H4, H5, H6, H7, H8, H9]

def trim(x) :
    return herm.hermtrim(x, tol=1e-6)

class TestConstants(TestCase) :

def test_hermdomain(self) :
        assert_equal(herm.hermdomain, [-1, 1])

def test_hermzero(self) :
        assert_equal(herm.hermzero, [0])

def test_hermone(self) :
        assert_equal(herm.hermone, [1])

def test_hermx(self) :
        assert_equal(herm.hermx, [0, .5])

class TestArithmetic(TestCase) :
    x = np.linspace(-3, 3, 100)

def test_hermadd(self) :
        for i in range(5) :
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i,j)
                tgt = np.zeros(max(i,j) + 1)
                tgt[i] += 1
                tgt[j] += 1
                res = herm.hermadd([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

def test_hermsub(self) :
        for i in range(5) :
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i,j)
                tgt = np.zeros(max(i,j) + 1)
                tgt[i] += 1
                tgt[j] -= 1
                res = herm.hermsub([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

def test_hermmulx(self):
        assert_equal(herm.hermmulx([0]), [0])
        assert_equal(herm.hermmulx([1]), [0,.5])
        for i in range(1, 5):
            ser = [0]*i + [1]
            tgt = [0]*(i - 1) + [i, 0, .5]
            assert_equal(herm.hermmulx(ser), tgt)

def test_hermmul(self) :
        # check values of result
        for i in range(5) :
            pol1 = [0]*i + [1]
            val1 = herm.hermval(self.x, pol1)
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i,j)
                pol2 = [0]*j + [1]
                val2 = herm.hermval(self.x, pol2)
                pol3 = herm.hermmul(pol1, pol2)
                val3 = herm.hermval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                assert_almost_equal(val3, val1*val2, err_msg=msg)

def test_hermdiv(self) :
        for i in range(5) :
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i,j)
                ci = [0]*i + [1]
                cj = [0]*j + [1]
                tgt = herm.hermadd(ci, cj)
                quo, rem = herm.hermdiv(tgt, ci)
                res = herm.hermadd(herm.hermmul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)

class TestEvaluation(TestCase) :
    # coefficients of 1 + 2*x + 3*x**2
    c1d = np.array([2.5, 1., .75])
    c2d = np.einsum('i,j->ij', c1d, c1d)
    c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)

# some random values in [-1, 1)
    x = np.random.random((3, 5))*2 - 1
    y = polyval(x, [1., 2., 3.])

def test_hermval(self) :
        #check empty input
        assert_equal(herm.hermval([], [1]).size, 0)

#check normal input)
        x = np.linspace(-1,1)
        y = [polyval(x, c) for c in Hlist]
        for i in range(10) :
            msg = "At i=%d" % i
            ser = np.zeros
            tgt = y[i]
            res = herm.hermval(x, [0]*i + [1])
            assert_almost_equal(res, tgt, err_msg=msg)

#check that shape is preserved
        for i in range(3) :
            dims = [2]*i
            x = np.zeros(dims)
            assert_equal(herm.hermval(x, [1]).shape, dims)
            assert_equal(herm.hermval(x, [1,0]).shape, dims)
            assert_equal(herm.hermval(x, [1,0,0]).shape, dims)

def test_hermval2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

#test exceptions
        assert_raises(ValueError, herm.hermval2d, x1, x2[:2], self.c2d)

#test values
        tgt = y1*y2
        res = herm.hermval2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

#test shape
        z = np.ones((2,3))
        res = herm.hermval2d(z, z, self.c2d)
        assert_(res.shape == (2,3))

def test_hermval3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

#test exceptions
        assert_raises(ValueError, herm.hermval3d, x1, x2, x3[:2], self.c3d)

#test values
        tgt = y1*y2*y3
        res = herm.hermval3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

#test shape
        z = np.ones((2,3))
        res = herm.hermval3d(z, z, z, self.c3d)
        assert_(res.shape == (2,3))

def test_hermgrid2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

#test values
        tgt = np.einsum('i,j->ij', y1, y2)
        res = herm.hermgrid2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

#test shape
        z = np.ones((2,3))
        res = herm.hermgrid2d(z, z, self.c2d)
        assert_(res.shape == (2, 3)*2)

def test_hermgrid3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

#test values
        tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
        res = herm.hermgrid3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

#test shape
        z = np.ones((2,3))
        res = herm.hermgrid3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3)*3)

class TestIntegral(TestCase) :

def test_hermint(self) :
        # check exceptions
        assert_raises(ValueError, herm.hermint, [0], .5)
        assert_raises(ValueError, herm.hermint, [0], -1)
        assert_raises(ValueError, herm.hermint, [0], 1, [0,0])

# test integration of zero polynomial
        for i in range(2, 5):
            k = [0]*(i - 2) + [1]
            res = herm.hermint([0], m=i, k=k)
            assert_almost_equal(res, [0, .5])

# check single integration with integration constant
        for i in range(5) :
            scl = i + 1
            pol = [0]*i + [1]
            tgt = [i] + [0]*i + [1/scl]
            hermpol = herm.poly2herm(pol)
            hermint = herm.hermint(hermpol, m=1, k=[i])
            res = herm.herm2poly(hermint)
            assert_almost_equal(trim(res), trim(tgt))

# check single integration with integration constant and lbnd
        for i in range(5) :
            scl = i + 1
            pol = [0]*i + [1]
            hermpol = herm.poly2herm(pol)
            hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(herm.hermval(-1, hermint), i)

# check single integration with integration constant and scaling
        for i in range(5) :
            scl = i + 1
            pol = [0]*i + [1]
            tgt = [i] + [0]*i + [2/scl]
            hermpol = herm.poly2herm(pol)
            hermint = herm.hermint(hermpol, m=1, k=[i], scl=2)
            res = herm.herm2poly(hermint)
            assert_almost_equal(trim(res), trim(tgt))

# check multiple integrations with default k
        for i in range(5) :
            for j in range(2,5) :
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j) :
                    tgt = herm.hermint(tgt, m=1)
                res = herm.hermint(pol, m=j)
                assert_almost_equal(trim(res), trim(tgt))

# check multiple integrations with defined k
        for i in range(5) :
            for j in range(2,5) :
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j) :
                    tgt = herm.hermint(tgt, m=1, k=[k])
                res = herm.hermint(pol, m=j, k=range(j))
                assert_almost_equal(trim(res), trim(tgt))

# check multiple integrations with lbnd
        for i in range(5) :
            for j in range(2,5) :
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j) :
                    tgt = herm.hermint(tgt, m=1, k=[k], lbnd=-1)
                res = herm.hermint(pol, m=j, k=range(j), lbnd=-1)
                assert_almost_equal(trim(res), trim(tgt))

# check multiple integrations with scaling
        for i in range(5) :
            for j in range(2,5) :
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j) :
                    tgt = herm.hermint(tgt, m=1, k=[k], scl=2)
                res = herm.hermint(pol, m=j, k=range(j), scl=2)
                assert_almost_equal(trim(res), trim(tgt))

def test_hermint_axis(self):
        # check that axis keyword works
        c2d = np.random.random((3, 4))

tgt = np.vstack([herm.hermint(c) for c in c2d.T]).T
        res = herm.hermint(c2d, axis=0)
        assert_almost_equal(res, tgt)

tgt = np.vstack([herm.hermint(c) for c in c2d])
        res = herm.hermint(c2d, axis=1)
        assert_almost_equal(res, tgt)

tgt = np.vstack([herm.hermint(c, k=3) for c in c2d])
        res = herm.hermint(c2d, k=3, axis=1)
        assert_almost_equal(res, tgt)

class TestDerivative(TestCase) :

def test_hermder(self) :
        # check exceptions
        assert_raises(ValueError, herm.hermder, [0], .5)
        assert_raises(ValueError, herm.hermder, [0], -1)

# check that zeroth deriviative does nothing
        for i in range(5) :
            tgt = [0]*i + [1]
            res = herm.hermder(tgt, m=0)
            assert_equal(trim(res), trim(tgt))

# check that derivation is the inverse of integration
        for i in range(5) :
            for j in range(2,5) :
                tgt = [0]*i + [1]
                res = herm.hermder(herm.hermint(tgt, m=j), m=j)
                assert_almost_equal(trim(res), trim(tgt))

# check derivation with scaling
        for i in range(5) :
            for j in range(2,5) :
                tgt = [0]*i + [1]
                res = herm.hermder(herm.hermint(tgt, m=j, scl=2), m=j, scl=.5)
                assert_almost_equal(trim(res), trim(tgt))

def test_hermder_axis(self):
        # check that axis keyword works
        c2d = np.random.random((3, 4))

tgt = np.vstack([herm.hermder(c) for c in c2d.T]).T
        res = herm.hermder(c2d, axis=0)
        assert_almost_equal(res, tgt)

tgt = np.vstack([herm.hermder(c) for c in c2d])
        res = herm.hermder(c2d, axis=1)
        assert_almost_equal(res, tgt)

class TestVander(TestCase):
    # some random values in [-1, 1)
    x = np.random.random((3, 5))*2 - 1

def test_hermvander(self) :
        # check for 1d x
        x = np.arange(3)
        v = herm.hermvander(x, 3)
        assert_(v.shape == (3, 4))
        for i in range(4) :
            coef = [0]*i + [1]
            assert_almost_equal(v[..., i], herm.hermval(x, coef))

# check for 2d x
        x = np.array([[1, 2], [3, 4], [5, 6]])
        v = herm.hermvander(x, 3)
        assert_(v.shape == (3, 2, 4))
        for i in range(4) :
            coef = [0]*i + [1]
            assert_almost_equal(v[..., i], herm.hermval(x, coef))

def test_hermvander2d(self) :
        # also tests hermval2d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3))
        van = herm.hermvander2d(x1, x2, [1, 2])
        tgt = herm.hermval2d(x1, x2, c)
        res = np.dot(van, c.flat)
        assert_almost_equal(res, tgt)

# check shape
        van = herm.hermvander2d([x1], [x2], [1, 2])
        assert_(van.shape == (1, 5, 6))

def test_hermvander3d(self) :
        # also tests hermval3d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3, 4))
        van = herm.hermvander3d(x1, x2, x3, [1, 2, 3])
        tgt = herm.hermval3d(x1, x2, x3, c)
        res = np.dot(van, c.flat)
        assert_almost_equal(res, tgt)

# check shape
        van = herm.hermvander3d([x1], [x2], [x3], [1, 2, 3])
        assert_(van.shape == (1, 5, 24))

class TestFitting(TestCase):

def test_hermfit(self) :
        def f(x) :
            return x*(x - 1)*(x - 2)

# Test exceptions
        assert_raises(ValueError, herm.hermfit, [1],    [1],     -1)
        assert_raises(TypeError,  herm.hermfit, [[1]],  [1],      0)
        assert_raises(TypeError,  herm.hermfit, [],     [1],      0)
        assert_raises(TypeError,  herm.hermfit, [1],    [[[1]]],  0)
        assert_raises(TypeError,  herm.hermfit, [1, 2], [1],      0)
        assert_raises(TypeError,  herm.hermfit, [1],    [1, 2],   0)
        assert_raises(TypeError,  herm.hermfit, [1],    [1],   0, w=[[1]])
        assert_raises(TypeError,  herm.hermfit, [1],    [1],   0, w=[1,1])

# Test fit
        x = np.linspace(0,2)
        y = f(x)
        #
        coef3 = herm.hermfit(x, y, 3)
        assert_equal(len(coef3), 4)
        assert_almost_equal(herm.hermval(x, coef3), y)
        #
        coef4 = herm.hermfit(x, y, 4)
        assert_equal(len(coef4), 5)
        assert_almost_equal(herm.hermval(x, coef4), y)
        #
        coef2d = herm.hermfit(x, np.array([y,y]).T, 3)
        assert_almost_equal(coef2d, np.array([coef3,coef3]).T)
        # test weighting
        w = np.zeros_like(x)
        yw = y.copy()
        w[1::2] = 1
        y[0::2] = 0
        wcoef3 = herm.hermfit(x, yw, 3, w=w)
        assert_almost_equal(wcoef3, coef3)
        #
        wcoef2d = herm.hermfit(x, np.array([yw,yw]).T, 3, w=w)
        assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T)
        # test scaling with complex values x points whose square
        # is zero when summed.
        x = [1, 1j, -1, -1j]
        assert_almost_equal(herm.hermfit(x, x, 1), [0, .5])

class TestGauss(TestCase):

def test_100(self):
        x, w = herm.hermgauss(100)

# test orthogonality. Note that the results need to be normalized,
        # otherwise the huge values that can arise from fast growing
        # functions like Laguerre can be very confusing.
        v = herm.hermvander(x, 99)
        vv = np.dot(v.T * w, v)
        vd = 1/np.sqrt(vv.diagonal())
        vv = vd[:,None] * vv * vd
        assert_almost_equal(vv, np.eye(100))

# check that the integral of 1 is correct
        tgt = np.sqrt(np.pi)
        assert_almost_equal(w.sum(), tgt)

class TestMisc(TestCase) :

def test_hermfromroots(self) :
        res = herm.hermfromroots([])
        assert_almost_equal(trim(res), [1])
        for i in range(1,5) :
            roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2])
            pol = herm.hermfromroots(roots)
            res = herm.hermval(roots, pol)
            tgt = 0
            assert_(len(pol) == i + 1)
            assert_almost_equal(herm.herm2poly(pol)[-1], 1)
            assert_almost_equal(res, tgt)

def test_hermroots(self) :
        assert_almost_equal(herm.hermroots([1]), [])
        assert_almost_equal(herm.hermroots([1, 1]), [-.5])
        for i in range(2,5) :
            tgt = np.linspace(-1, 1, i)
            res = herm.hermroots(herm.hermfromroots(tgt))
            assert_almost_equal(trim(res), trim(tgt))

def test_hermtrim(self) :
        coef = [2, -1, 1, 0]

# Test exceptions
        assert_raises(ValueError, herm.hermtrim, coef, -1)

# Test results
        assert_equal(herm.hermtrim(coef), coef[:-1])
        assert_equal(herm.hermtrim(coef, 1), coef[:-3])
        assert_equal(herm.hermtrim(coef, 2), [0])

def test_hermline(self) :
        assert_equal(herm.hermline(3,4), [3, 2])

def test_herm2poly(self) :
        for i in range(10) :
            assert_almost_equal(herm.herm2poly([0]*i + [1]), Hlist[i])

def test_poly2herm(self) :
        for i in range(10) :
            assert_almost_equal(herm.poly2herm(Hlist[i]), [0]*i + [1])

def test_weight(self):
        x = np.linspace(-5, 5, 11)
        tgt = np.exp(-x**2)
        res = herm.hermweight(x)
        assert_almost_equal(res, tgt)

if __name__ == "__main__":
    run_module_suite()