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Diffstat (limited to 'gsl-1.9/diff/diff.c')
| -rw-r--r-- | gsl-1.9/diff/diff.c | 180 |
1 files changed, 180 insertions, 0 deletions
diff --git a/gsl-1.9/diff/diff.c b/gsl-1.9/diff/diff.c new file mode 100644 index 0000000..83aae18 --- /dev/null +++ b/gsl-1.9/diff/diff.c @@ -0,0 +1,180 @@ +/* diff/diff.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 David Morrison + * + * 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 2 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 <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_diff.h> + +int +gsl_diff_backward (const gsl_function * f, + double x, double *result, double *abserr) +{ + /* Construct a divided difference table with a fairly large step + size to get a very rough estimate of f''. Use this to estimate + the step size which will minimize the error in calculating f'. */ + + int i, k; + double h = GSL_SQRT_DBL_EPSILON; + double a[3], d[3], a2; + + /* Algorithm based on description on pg. 204 of Conte and de Boor + (CdB) - coefficients of Newton form of polynomial of degree 2. */ + + for (i = 0; i < 3; i++) + { + a[i] = x + (i - 2.0) * h; + d[i] = GSL_FN_EVAL (f, a[i]); + } + + for (k = 1; k < 4; k++) + { + for (i = 0; i < 3 - k; i++) + { + d[i] = (d[i + 1] - d[i]) / (a[i + k] - a[i]); + } + } + + /* Adapt procedure described on pg. 282 of CdB to find best value of + step size. */ + + a2 = fabs (d[0] + d[1] + d[2]); + + if (a2 < 100.0 * GSL_SQRT_DBL_EPSILON) + { + a2 = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + h = sqrt (GSL_SQRT_DBL_EPSILON / (2.0 * a2)); + + if (h > 100.0 * GSL_SQRT_DBL_EPSILON) + { + h = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + *result = (GSL_FN_EVAL (f, x) - GSL_FN_EVAL (f, x - h)) / h; + *abserr = fabs (10.0 * a2 * h); + + return GSL_SUCCESS; +} + +int +gsl_diff_forward (const gsl_function * f, + double x, double *result, double *abserr) +{ + /* Construct a divided difference table with a fairly large step + size to get a very rough estimate of f''. Use this to estimate + the step size which will minimize the error in calculating f'. */ + + int i, k; + double h = GSL_SQRT_DBL_EPSILON; + double a[3], d[3], a2; + + /* Algorithm based on description on pg. 204 of Conte and de Boor + (CdB) - coefficients of Newton form of polynomial of degree 2. */ + + for (i = 0; i < 3; i++) + { + a[i] = x + i * h; + d[i] = GSL_FN_EVAL (f, a[i]); + } + + for (k = 1; k < 4; k++) + { + for (i = 0; i < 3 - k; i++) + { + d[i] = (d[i + 1] - d[i]) / (a[i + k] - a[i]); + } + } + + /* Adapt procedure described on pg. 282 of CdB to find best value of + step size. */ + + a2 = fabs (d[0] + d[1] + d[2]); + + if (a2 < 100.0 * GSL_SQRT_DBL_EPSILON) + { + a2 = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + h = sqrt (GSL_SQRT_DBL_EPSILON / (2.0 * a2)); + + if (h > 100.0 * GSL_SQRT_DBL_EPSILON) + { + h = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + *result = (GSL_FN_EVAL (f, x + h) - GSL_FN_EVAL (f, x)) / h; + *abserr = fabs (10.0 * a2 * h); + + return GSL_SUCCESS; +} + +int +gsl_diff_central (const gsl_function * f, + double x, double *result, double *abserr) +{ + /* Construct a divided difference table with a fairly large step + size to get a very rough estimate of f'''. Use this to estimate + the step size which will minimize the error in calculating f'. */ + + int i, k; + double h = GSL_SQRT_DBL_EPSILON; + double a[4], d[4], a3; + + /* Algorithm based on description on pg. 204 of Conte and de Boor + (CdB) - coefficients of Newton form of polynomial of degree 3. */ + + for (i = 0; i < 4; i++) + { + a[i] = x + (i - 2.0) * h; + d[i] = GSL_FN_EVAL (f, a[i]); + } + + for (k = 1; k < 5; k++) + { + for (i = 0; i < 4 - k; i++) + { + d[i] = (d[i + 1] - d[i]) / (a[i + k] - a[i]); + } + } + + /* Adapt procedure described on pg. 282 of CdB to find best + value of step size. */ + + a3 = fabs (d[0] + d[1] + d[2] + d[3]); + + if (a3 < 100.0 * GSL_SQRT_DBL_EPSILON) + { + a3 = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + h = pow (GSL_SQRT_DBL_EPSILON / (2.0 * a3), 1.0 / 3.0); + + if (h > 100.0 * GSL_SQRT_DBL_EPSILON) + { + h = 100.0 * GSL_SQRT_DBL_EPSILON; + } + + *result = (GSL_FN_EVAL (f, x + h) - GSL_FN_EVAL (f, x - h)) / (2.0 * h); + *abserr = fabs (100.0 * a3 * h * h); + + return GSL_SUCCESS; +} |