Exemplo n.º 1
0
 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)
Exemplo n.º 2
0
    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))
Exemplo n.º 3
0
 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)
Exemplo n.º 4
0
    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
            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)
Exemplo n.º 5
0
    def test_hermfit(self):
        def f(x):
            return x * (x - 1) * (x - 2)

        def f2(x):
            return x**4 + x**2 + 1

        # 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])
        assert_raises(ValueError, herm.hermfit, [1], [1], [
            -1,
        ])
        assert_raises(ValueError, herm.hermfit, [1], [1], [2, -1, 6])
        assert_raises(TypeError, herm.hermfit, [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)
        coef3 = herm.hermfit(x, y, [0, 1, 2, 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)
        coef4 = herm.hermfit(x, y, [0, 1, 2, 3, 4])
        assert_equal(len(coef4), 5)
        assert_almost_equal(herm.hermval(x, coef4), y)
        # check things still work if deg is not in strict increasing
        coef4 = herm.hermfit(x, y, [2, 3, 4, 1, 0])
        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)
        coef2d = herm.hermfit(x, np.array([y, y]).T, [0, 1, 2, 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)
        wcoef3 = herm.hermfit(x, yw, [0, 1, 2, 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)
        wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, [0, 1, 2, 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])
        assert_almost_equal(herm.hermfit(x, x, [0, 1]), [0, .5])
        # test fitting only even Legendre polynomials
        x = np.linspace(-1, 1)
        y = f2(x)
        coef1 = herm.hermfit(x, y, 4)
        assert_almost_equal(herm.hermval(x, coef1), y)
        coef2 = herm.hermfit(x, y, [0, 2, 4])
        assert_almost_equal(herm.hermval(x, coef2), y)
        assert_almost_equal(coef1, coef2)
Exemplo n.º 6
0
    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])
        assert_raises(ValueError, herm.hermint, [0], lbnd=[0])
        assert_raises(ValueError, herm.hermint, [0], scl=[0])
        assert_raises(ValueError, herm.hermint, [0], axis=.5)

        # 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=list(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=list(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=list(range(j)), scl=2)
                assert_almost_equal(trim(res), trim(tgt))