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Diffstat (limited to '.venv/lib/python3.12/site-packages/numpy/polynomial/tests/test_hermite.py')
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diff --git a/.venv/lib/python3.12/site-packages/numpy/polynomial/tests/test_hermite.py b/.venv/lib/python3.12/site-packages/numpy/polynomial/tests/test_hermite.py new file mode 100644 index 00000000..53ee0844 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/numpy/polynomial/tests/test_hermite.py @@ -0,0 +1,555 @@ +"""Tests for hermite module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.hermite as herm +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + +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: + + 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: + x = np.linspace(-3, 3, 100) + + def test_hermadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={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 = f"At i={i}, j={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 = f"At i={i}, j={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 = f"At i={i}, j={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) + + def test_hermpow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(herm.hermmul, [c]*j, np.array([1])) + res = herm.hermpow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # 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 = f"At i={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) + + 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: + + def test_hermint(self): + # check exceptions + assert_raises(TypeError, 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(TypeError, 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)) + + 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: + + def test_hermder(self): + # check exceptions + assert_raises(TypeError, herm.hermder, [0], .5) + assert_raises(ValueError, herm.hermder, [0], -1) + + # check that zeroth derivative 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: + # 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: + + 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) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, herm.hermcompanion, []) + assert_raises(ValueError, herm.hermcompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(herm.hermcompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(herm.hermcompanion([1, 2])[0, 0] == -.25) + + +class TestGauss: + + 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: + + 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) |