/* poly/test.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ #include #include #include #include #include #include #include /* sort by Re(z) then by Im(z) */ static int cmp_cplx(const double *a, const double *b) { double r = a[0] - b[0]; if (r == 0.0) { double t = a[1] - b[1]; return t < 0.0 ? -1 : t > 0.0 ? 1 : 0; } else if (r < 0.0) return -1; else return 1; } int main (void) { const double eps = 100.0 * GSL_DBL_EPSILON; gsl_ieee_env_setup (); /* Polynomial evaluation */ { double x, y; double c[3] = { 1.0, 0.5, 0.3 }; x = 0.5; y = gsl_poly_eval (c, 3, x); gsl_test_rel (y, 1 + 0.5 * x + 0.3 * x * x, eps, "gsl_poly_eval({1, 0.5, 0.3}, 0.5)"); } { double x, y; double d[11] = { 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1 }; x = 1.0; y = gsl_poly_eval (d, 11, x); gsl_test_rel (y, 1.0, eps, "gsl_poly_eval({1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1}, 1.0)"); } { gsl_complex x, y; double c[1] = {0.3}; GSL_SET_REAL (&x, 0.75); GSL_SET_IMAG (&x, 1.2); y = gsl_poly_complex_eval (c, 1, x); gsl_test_rel (GSL_REAL (y), 0.3, eps, "y.real, gsl_poly_complex_eval ({0.3}, 0.75 + 1.2i)"); gsl_test_rel (GSL_IMAG (y), 0.0, eps, "y.imag, gsl_poly_complex_eval ({0.3}, 0.75 + 1.2i)"); } { gsl_complex x, y; double c[4] = {2.1, -1.34, 0.76, 0.45}; GSL_SET_REAL (&x, 0.49); GSL_SET_IMAG (&x, 0.95); y = gsl_poly_complex_eval (c, 4, x); gsl_test_rel (GSL_REAL (y), 0.3959143, eps, "y.real, gsl_poly_complex_eval ({2.1, -1.34, 0.76, 0.45}, 0.49 + 0.95i)"); gsl_test_rel (GSL_IMAG (y), -0.6433305, eps, "y.imag, gsl_poly_complex_eval ({2.1, -1.34, 0.76, 0.45}, 0.49 + 0.95i)"); } { gsl_complex x, y; gsl_complex c[1]; GSL_SET_REAL (&c[0], 0.674); GSL_SET_IMAG (&c[0], -1.423); GSL_SET_REAL (&x, -1.44); GSL_SET_IMAG (&x, 9.55); y = gsl_complex_poly_complex_eval (c, 1, x); gsl_test_rel (GSL_REAL (y), 0.674, eps, "y.real, gsl_complex_poly_complex_eval ({0.674 - 1.423i}, -1.44 + 9.55i)"); gsl_test_rel (GSL_IMAG (y), -1.423, eps, "y.imag, gsl_complex_poly_complex_eval ({0.674 - 1.423i}, -1.44 + 9.55i)"); } { gsl_complex x, y; gsl_complex c[4]; GSL_SET_REAL (&c[0], -2.31); GSL_SET_IMAG (&c[0], 0.44); GSL_SET_REAL (&c[1], 4.21); GSL_SET_IMAG (&c[1], -3.19); GSL_SET_REAL (&c[2], 0.93); GSL_SET_IMAG (&c[2], 1.04); GSL_SET_REAL (&c[3], -0.42); GSL_SET_IMAG (&c[3], 0.68); GSL_SET_REAL (&x, 0.49); GSL_SET_IMAG (&x, 0.95); y = gsl_complex_poly_complex_eval (c, 4, x); gsl_test_rel (GSL_REAL (y), 1.82462012, eps, "y.real, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i)"); gsl_test_rel (GSL_IMAG (y), 2.30389412, eps, "y.imag, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i)"); } /* Quadratic */ { double x0, x1; int n = gsl_poly_solve_quadratic (4.0, -20.0, 26.0, &x0, &x1); gsl_test (n != 0, "gsl_poly_solve_quadratic, no roots, (2x - 5)^2 = -1"); } { double x0, x1; int n = gsl_poly_solve_quadratic (4.0, -20.0, 25.0, &x0, &x1); gsl_test (n != 2, "gsl_poly_solve_quadratic, one root, (2x - 5)^2 = 0"); gsl_test_rel (x0, 2.5, 1e-9, "x0, (2x - 5)^2 = 0"); gsl_test_rel (x1, 2.5, 1e-9, "x1, (2x - 5)^2 = 0"); gsl_test (x0 != x1, "x0 == x1, (2x - 5)^2 = 0"); } { double x0, x1; int n = gsl_poly_solve_quadratic (4.0, -20.0, 21.0, &x0, &x1); gsl_test (n != 2, "gsl_poly_solve_quadratic, two roots, (2x - 5)^2 = 4"); gsl_test_rel (x0, 1.5, 1e-9, "x0, (2x - 5)^2 = 4"); gsl_test_rel (x1, 3.5, 1e-9, "x1, (2x - 5)^2 = 4"); } { double x0, x1; int n = gsl_poly_solve_quadratic (4.0, 7.0, 0.0, &x0, &x1); gsl_test (n != 2, "gsl_poly_solve_quadratic, two roots, x(4x + 7) = 0"); gsl_test_rel (x0, -1.75, 1e-9, "x0, x(4x + 7) = 0"); gsl_test_rel (x1, 0.0, 1e-9, "x1, x(4x + 7) = 0"); } { double x0, x1; int n = gsl_poly_solve_quadratic (5.0, 0.0, -20.0, &x0, &x1); gsl_test (n != 2, "gsl_poly_solve_quadratic, two roots b = 0, 5 x^2 = 20"); gsl_test_rel (x0, -2.0, 1e-9, "x0, 5 x^2 = 20"); gsl_test_rel (x1, 2.0, 1e-9, "x1, 5 x^2 = 20"); } { double x0, x1; int n = gsl_poly_solve_quadratic (0.0, 3.0, -21.0, &x0, &x1); gsl_test (n != 1, "gsl_poly_solve_quadratic, one root (linear) 3 x - 21 = 0"); gsl_test_rel (x0, 7.0, 1e-9, "x0, 3x - 21 = 0"); } { double x0, x1; int n = gsl_poly_solve_quadratic (0.0, 0.0, 1.0, &x0, &x1); gsl_test (n != 0, "gsl_poly_solve_quadratic, no roots 1 = 0"); } /* Cubic */ { double x0, x1, x2; int n = gsl_poly_solve_cubic (0.0, 0.0, -27.0, &x0, &x1, &x2); gsl_test (n != 1, "gsl_poly_solve_cubic, one root, x^3 = 27"); gsl_test_rel (x0, 3.0, 1e-9, "x0, x^3 = 27"); } { double x0, x1, x2; int n = gsl_poly_solve_cubic (-51.0, 867.0, -4913.0, &x0, &x1, &x2); gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x-17)^3=0"); gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)^3=0"); gsl_test_rel (x1, 17.0, 1e-9, "x1, (x-17)^3=0"); gsl_test_rel (x2, 17.0, 1e-9, "x2, (x-17)^3=0"); } { double x0, x1, x2; int n = gsl_poly_solve_cubic (-57.0, 1071.0, -6647.0, &x0, &x1, &x2); gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x-17)(x-17)(x-23)=0"); gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)(x-17)(x-23)=0"); gsl_test_rel (x1, 17.0, 1e-9, "x1, (x-17)(x-17)(x-23)=0"); gsl_test_rel (x2, 23.0, 1e-9, "x2, (x-17)(x-17)(x-23)=0"); } { double x0, x1, x2; int n = gsl_poly_solve_cubic (-11.0, -493.0, +6647.0, &x0, &x1, &x2); gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x+23)(x-17)(x-17)=0"); gsl_test_rel (x0, -23.0, 1e-9, "x0, (x+23)(x-17)(x-17)=0"); gsl_test_rel (x1, 17.0, 1e-9, "x1, (x+23)(x-17)(x-17)=0"); gsl_test_rel (x2, 17.0, 1e-9, "x2, (x+23)(x-17)(x-17)=0"); } { double x0, x1, x2; int n = gsl_poly_solve_cubic (-143.0, 5087.0, -50065.0, &x0, &x1, &x2); gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x-17)(x-31)(x-95)=0"); gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)(x-31)(x-95)=0"); gsl_test_rel (x1, 31.0, 1e-9, "x1, (x-17)(x-31)(x-95)=0"); gsl_test_rel (x2, 95.0, 1e-9, "x2, (x-17)(x-31)(x-95)=0"); } { double x0, x1, x2; int n = gsl_poly_solve_cubic (-109.0, 803.0, 50065.0, &x0, &x1, &x2); gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x+17)(x-31)(x-95)=0"); gsl_test_rel (x0, -17.0, 1e-9, "x0, (x+17)(x-31)(x-95)=0"); gsl_test_rel (x1, 31.0, 1e-9, "x1, (x+17)(x-31)(x-95)=0"); gsl_test_rel (x2, 95.0, 1e-9, "x2, (x+17)(x-31)(x-95)=0"); } /* Quadratic with complex roots */ { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 26.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, 2 roots (2x - 5)^2 = -1"); gsl_test_rel (GSL_REAL (z0), 2.5, 1e-9, "z0.real, (2x - 5)^2 = -1"); gsl_test_rel (GSL_IMAG (z0), -0.5, 1e-9, "z0.imag, (2x - 5)^2 = -1"); gsl_test_rel (GSL_REAL (z1), 2.5, 1e-9, "z1.real, (2x - 5)^2 = -1"); gsl_test_rel (GSL_IMAG (z1), 0.5, 1e-9, "z1.imag, (2x - 5)^2 = -1"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 25.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, one root, (2x - 5)^2 = 0"); gsl_test_rel (GSL_REAL (z0), 2.5, 1e-9, "z0.real, (2x - 5)^2 = 0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag (2x - 5)^2 = 0"); gsl_test_rel (GSL_REAL (z1), 2.5, 1e-9, "z1.real, (2x - 5)^2 = 0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag (2x - 5)^2 = 0"); gsl_test (GSL_REAL (z0) != GSL_REAL (z1), "z0.real == z1.real, (2x - 5)^2 = 0"); gsl_test (GSL_IMAG (z0) != GSL_IMAG (z1), "z0.imag == z1.imag, (2x - 5)^2 = 0"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 21.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, two roots, (2x - 5)^2 = 4"); gsl_test_rel (GSL_REAL (z0), 1.5, 1e-9, "z0.real, (2x - 5)^2 = 4"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (2x - 5)^2 = 4"); gsl_test_rel (GSL_REAL (z1), 3.5, 1e-9, "z1.real, (2x - 5)^2 = 4"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (2x - 5)^2 = 4"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (4.0, 7.0, 0.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, two roots, x(4x + 7) = 0"); gsl_test_rel (GSL_REAL (z0), -1.75, 1e-9, "z0.real, x(4x + 7) = 0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, x(4x + 7) = 0"); gsl_test_rel (GSL_REAL (z1), 0.0, 1e-9, "z1.real, x(4x + 7) = 0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, x(4x + 7) = 0"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (5.0, 0.0, -20.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, two roots b = 0, 5 x^2 = 20"); gsl_test_rel (GSL_REAL (z0), -2.0, 1e-9, "z0.real, 5 x^2 = 20"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, 5 x^2 = 20"); gsl_test_rel (GSL_REAL (z1), 2.0, 1e-9, "z1.real, 5 x^2 = 20"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, 5 x^2 = 20"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (5.0, 0.0, 20.0, &z0, &z1); gsl_test (n != 2, "gsl_poly_complex_solve_quadratic, two roots b = 0, 5 x^2 = -20"); gsl_test_rel (GSL_REAL (z0), 0.0, 1e-9, "z0.real, 5 x^2 = -20"); gsl_test_rel (GSL_IMAG (z0), -2.0, 1e-9, "z0.imag, 5 x^2 = -20"); gsl_test_rel (GSL_REAL (z1), 0.0, 1e-9, "z1.real, 5 x^2 = -20"); gsl_test_rel (GSL_IMAG (z1), 2.0, 1e-9, "z1.imag, 5 x^2 = -20"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (0.0, 3.0, -21.0, &z0, &z1); gsl_test (n != 1, "gsl_poly_complex_solve_quadratic, one root (linear) 3 x - 21 = 0"); gsl_test_rel (GSL_REAL (z0), 7.0, 1e-9, "z0.real, 3x - 21 = 0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, 3x - 21 = 0"); } { gsl_complex z0, z1; int n = gsl_poly_complex_solve_quadratic (0.0, 0.0, 1.0, &z0, &z1); gsl_test (n != 0, "gsl_poly_complex_solve_quadratic, no roots 1 = 0"); } /* Cubic with complex roots */ { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (0.0, 0.0, -27.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three root, x^3 = 27"); gsl_test_rel (GSL_REAL (z0), -1.5, 1e-9, "z0.real, x^3 = 27"); gsl_test_rel (GSL_IMAG (z0), -1.5 * sqrt (3.0), 1e-9, "z0.imag, x^3 = 27"); gsl_test_rel (GSL_REAL (z1), -1.5, 1e-9, "z1.real, x^3 = 27"); gsl_test_rel (GSL_IMAG (z1), 1.5 * sqrt (3.0), 1e-9, "z1.imag, x^3 = 27"); gsl_test_rel (GSL_REAL (z2), 3.0, 1e-9, "z2.real, x^3 = 27"); gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, x^3 = 27"); } { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (-1.0, 1.0, 39.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three root, (x+3)(x^2-4x+13) = 0"); gsl_test_rel (GSL_REAL (z0), -3.0, 1e-9, "z0.real, (x+3)(x^2+1) = 0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x+3)(x^2+1) = 0"); gsl_test_rel (GSL_REAL (z1), 2.0, 1e-9, "z1.real, (x+3)(x^2+1) = 0"); gsl_test_rel (GSL_IMAG (z1), -3.0, 1e-9, "z1.imag, (x+3)(x^2+1) = 0"); gsl_test_rel (GSL_REAL (z2), 2.0, 1e-9, "z2.real, (x+3)(x^2+1) = 0"); gsl_test_rel (GSL_IMAG (z2), 3.0, 1e-9, "z2.imag, (x+3)(x^2+1) = 0"); } { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (-51.0, 867.0, -4913.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three roots, (x-17)^3=0"); gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)^3=0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)^3=0"); gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x-17)^3=0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)^3=0"); gsl_test_rel (GSL_REAL (z2), 17.0, 1e-9, "z2.real, (x-17)^3=0"); gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)^3=0"); } { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (-57.0, 1071.0, -6647.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three roots, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_REAL (z2), 23.0, 1e-9, "z2.real, (x-17)(x-17)(x-23)=0"); gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)(x-17)(x-23)=0"); } { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (-11.0, -493.0, +6647.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three roots, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_REAL (z0), -23.0, 1e-9, "z0.real, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_REAL (z2), 17.0, 1e-9, "z2.real, (x+23)(x-17)(x-17)=0"); gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x+23)(x-17)(x-17)=0"); } { gsl_complex z0, z1, z2; int n = gsl_poly_complex_solve_cubic (-143.0, 5087.0, -50065.0, &z0, &z1, &z2); gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three roots, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_REAL (z1), 31.0, 1e-9, "z1.real, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_REAL (z2), 95.0, 1e-9, "z2.real, (x-17)(x-31)(x-95)=0"); gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)(x-31)(x-95)=0"); } { /* Wilkinson polynomial: y = (x-1)(x-2)(x-3)(x-4)(x-5) */ double a[6] = { -120, 274, -225, 85, -15, 1 }; double z[6*2]; gsl_poly_complex_workspace *w = gsl_poly_complex_workspace_alloc (6); int status = gsl_poly_complex_solve (a, 6, w, z); gsl_poly_complex_workspace_free (w); gsl_test (status, "gsl_poly_complex_solve, 5th-order Wilkinson polynomial"); gsl_test_rel (z[0], 1.0, 1e-9, "z0.real, 5th-order polynomial"); gsl_test_rel (z[1], 0.0, 1e-9, "z0.imag, 5th-order polynomial"); gsl_test_rel (z[2], 2.0, 1e-9, "z1.real, 5th-order polynomial"); gsl_test_rel (z[3], 0.0, 1e-9, "z1.imag, 5th-order polynomial"); gsl_test_rel (z[4], 3.0, 1e-9, "z2.real, 5th-order polynomial"); gsl_test_rel (z[5], 0.0, 1e-9, "z2.imag, 5th-order polynomial"); gsl_test_rel (z[6], 4.0, 1e-9, "z3.real, 5th-order polynomial"); gsl_test_rel (z[7], 0.0, 1e-9, "z3.imag, 5th-order polynomial"); gsl_test_rel (z[8], 5.0, 1e-9, "z4.real, 5th-order polynomial"); gsl_test_rel (z[9], 0.0, 1e-9, "z4.imag, 5th-order polynomial"); } { /* : 8-th order polynomial y = x^8 + x^4 + 1 */ double a[9] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 }; double z[8*2]; double C = 0.5; double S = sqrt (3.0) / 2.0; gsl_poly_complex_workspace *w = gsl_poly_complex_workspace_alloc (9); int status = gsl_poly_complex_solve (a, 9, w, z); gsl_poly_complex_workspace_free (w); gsl_test (status, "gsl_poly_complex_solve, 8th-order polynomial"); gsl_test_rel (z[0], -S, 1e-9, "z0.real, 8th-order polynomial"); gsl_test_rel (z[1], C, 1e-9, "z0.imag, 8th-order polynomial"); gsl_test_rel (z[2], -S, 1e-9, "z1.real, 8th-order polynomial"); gsl_test_rel (z[3], -C, 1e-9, "z1.imag, 8th-order polynomial"); gsl_test_rel (z[4], -C, 1e-9, "z2.real, 8th-order polynomial"); gsl_test_rel (z[5], S, 1e-9, "z2.imag, 8th-order polynomial"); gsl_test_rel (z[6], -C, 1e-9, "z3.real, 8th-order polynomial"); gsl_test_rel (z[7], -S, 1e-9, "z3.imag, 8th-order polynomial"); gsl_test_rel (z[8], C, 1e-9, "z4.real, 8th-order polynomial"); gsl_test_rel (z[9], S, 1e-9, "z4.imag, 8th-order polynomial"); gsl_test_rel (z[10], C, 1e-9, "z5.real, 8th-order polynomial"); gsl_test_rel (z[11], -S, 1e-9, "z5.imag, 8th-order polynomial"); gsl_test_rel (z[12], S, 1e-9, "z6.real, 8th-order polynomial"); gsl_test_rel (z[13], C, 1e-9, "z6.imag, 8th-order polynomial"); gsl_test_rel (z[14], S, 1e-9, "z7.real, 8th-order polynomial"); gsl_test_rel (z[15], -C, 1e-9, "z7.imag, 8th-order polynomial"); } { /* 15-th order polynomial y = (x + 1) * (x^10 + x^9 + 2 * x^7 + 4 * x^2 + 4 * x + 8) * (x - 1)^2 * (x - 2)^2 Problem reported by Munagala Ramanath (bug #39055) */ double a[16] = { 32, -48, -8, 28, -8, 16, -16, 12, -16, 6, 10, -17, 10, 2, -4, 1 }; double z[16*2]; double expected[16*2] = { -1.6078107423472359, 0.00000000000000000, -1.3066982484920768, 0.00000000000000000, -1.0000000000000000, 0.00000000000000000, -0.65893856175240950, -0.83459757287426684, -0.65893856175240950, 0.83459757287426684, -0.070891117403341281, -1.1359249087587791, -0.070891117403341281, 1.1359249087587791, 0.57284747839410854, -1.1987808988289705, 0.57284747839410854, 1.1987808988289705, 1.0000000000000000, 0.00000000000000000, 1.0000000000000000, 0.00000000000000000, 1.1142366961812986, -0.48083981203389980, 1.1142366961812986, 0.48083981203389980, 2.0000000000000000, 0.00000000000000000, 2.0000000000000000, 0.00000000000000000 }; int i; gsl_poly_complex_workspace *w = gsl_poly_complex_workspace_alloc (16); int status = gsl_poly_complex_solve (a, 16, w, z); gsl_poly_complex_workspace_free (w); gsl_test (status, "gsl_poly_complex_solve, 15th-order polynomial"); gsl_heapsort(z, 15, 2 * sizeof(double), (gsl_comparison_fn_t) &cmp_cplx); for (i = 0; i<15; i++) { gsl_test_rel (z[2*i], expected[2*i], 1e-7, "z%d.real, 15th-order polynomial", i); gsl_test_rel (z[2*i+1], expected[2*i+1], 1e-7, "z%d.imag, 15th-order polynomial", i); } } { int i; double xa[7] = {0.16, 0.97, 1.94, 2.74, 3.58, 3.73, 4.70 }; double ya[7] = {0.73, 1.11, 1.49, 1.84, 2.30, 2.41, 3.07 }; double dd_expected[7] = { 7.30000000000000e-01, 4.69135802469136e-01, -4.34737219941284e-02, 2.68681098870099e-02, -3.22937056934996e-03, 6.12763259971375e-03, -6.45402453527083e-03 }; double dd[7], coeff[7], work[7]; gsl_poly_dd_init (dd, xa, ya, 7); for (i = 0; i < 7; i++) { gsl_test_rel (dd[i], dd_expected[i], 1e-10, "divided difference dd[%d]", i); } for (i = 0; i < 7; i++) { double y = gsl_poly_dd_eval(dd, xa, 7, xa[i]); gsl_test_rel (y, ya[i], 1e-10, "divided difference y[%d]", i); } gsl_poly_dd_taylor (coeff, 1.5, dd, xa, 7, work); for (i = 0; i < 7; i++) { double y = gsl_poly_eval(coeff, 7, xa[i] - 1.5); gsl_test_rel (y, ya[i], 1e-10, "taylor expansion about 1.5 y[%d]", i); } } { size_t i; double xa[3] = { 1.3, 1.6, 1.9 }; double ya[3] = { 0.6200860, 0.4554022, 0.2818186 }; double dya[3] = { -0.5220232, -0.5698959, -0.5811571 }; double dd_expected[6] = { 6.200860000000e-01, -5.220232000000e-01, -8.974266666667e-02, 6.636555555556e-02, 2.666666666662e-03, -2.774691357989e-03 }; double dd[6], za[6], coeff[6], work[6]; gsl_poly_dd_hermite_init(dd, za, xa, ya, dya, 3); for (i = 0; i < 6; i++) { gsl_test_rel (dd[i], dd_expected[i], 1e-10, "hermite divided difference dd[%d]", i); } for (i = 0; i < 3; i++) { double y = gsl_poly_dd_eval(dd, za, 6, xa[i]); gsl_test_rel (y, ya[i], 1e-10, "hermite divided difference y[%d]", i); } for (i = 0; i < 3; i++) { gsl_poly_dd_taylor(coeff, xa[i], dd, za, 6, work); gsl_test_rel (coeff[1], dya[i], 1e-10, "hermite divided difference dy/dx[%d]", i); } } { double c[6] = { +1.0, -2.0, +3.0, -4.0, +5.0, -6.0 }; double dc[6]; double x; x = -0.5; gsl_poly_eval_derivs(c, 6, x, dc, 6); gsl_test_rel (dc[0], c[0] + c[1]*x + c[2]*x*x + c[3]*x*x*x + c[4]*x*x*x*x + c[5]*x*x*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6}, 3.75)"); gsl_test_rel (dc[1], c[1] + 2.0*c[2]*x + 3.0*c[3]*x*x + 4.0*c[4]*x*x*x + 5.0*c[5]*x*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 1, -12.375)"); gsl_test_rel (dc[2], 2.0*c[2] + 3.0*2.0*c[3]*x + 4.0*3.0*c[4]*x*x + 5.0*4.0*c[5]*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 2, +48.0)"); gsl_test_rel (dc[3], 3.0*2.0*c[3] + 4.0*3.0*2.0*c[4]*x + 5.0*4.0*3.0*c[5]*x*x , eps,"gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 3, -174.0)"); gsl_test_rel (dc[4], 4.0*3.0*2.0*c[4] + 5.0*4.0*3.0*2.0*c[5]*x, eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 4, +480.0)"); gsl_test_rel (dc[5], 5.0*4.0*3.0*2.0*c[5] , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 5, -720.0)"); } /* now summarize the results */ exit (gsl_test_summary ()); }