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/*--------------------------------------------------------------------
* The GMT-system: 09/21/99 @(#)trend1d.c 2.43
*
* Copyright (c) 1991-1999 by P. Wessel and W. H. F. Smith
* See COPYING file for copying and redistribution conditions.
*
* 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; version 2 of the License.
*
* 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.
*
* Contact info: www.soest.hawaii.edu/gmt
*--------------------------------------------------------------------*/
/*
* trend1d [<xy[w]file>] -F<output_flags> -N[f]<n_m_parameters>[r]
* [-C<condition_#>] [-I[<confid>]] [-V] [-W]
*
* where:
* [<xy[w]file>] is an ascii file with x y in first 2 columns [or
* x y w in first 3 columns]. Default reads from GMT_stdin.
* -F<output_flags> is a string of at least one, up to five, in
* and order, from the set {x y m r w}. x,y = input,
* m = model, r = residual = y-m, and w= weight used.
* -N[f]<n_m_parameters>[r]
* If iterative Robust fitting desired, use append r.
* To fit a Fourier model, use -Nf.
* Number of terms in the model is <n_m_parameters>.
* Example: Robust quadratic polynomial: -N2r.
* [-C<condition_#>] Cut off eigenvalue spectrum; use only eigen-
* values such that (lambda_max / lambda[i]) < condition_#.
* [-I[<confid>]] Iteratively Increment the number of model parameters,
* searching for the significant model size, up to a maximum
* set by <n_m_parameters>. We start with a 1 parameter
* model and then iteratively increase the number of
* model parameters, m, while m <= <n_m_parameters> &&
* reduction in variance from i to i+1 is significant
* at the <confid> level according to F test. If user sets
* -I without giving <confid> then <confid> = 0.95.
* [-V] Verbose operation.
* [-W] Weighted data are input. Read 3 cols and use 3rd as weight.
*
*
* Read GMT_stdin or file of x y pairs, or weighted pairs as x,y w data. Fit
* a regression model y = f(x) + e, where e are error misfits and f(x) has
* some user-prescribed functional form. Presently available models are
* polynomials and Fourier series. The user may choose the number of terms
* in the model to fit, whether to seek iterative refinement robust w.r.t.
* outliers, and whether to seek automatic discovery of the significant
* number of model parameters.
*
*
* In trend1d I chose to construct the polynomial model using Chebyshev
* Polynomials so that the user may easily compare the sizes of the
* coefficients (and compare with a Fourier series as well). Tn(x)
* is an n-degree polynomial with n zero-crossings in [-1,1] and n+1
* extrema, at which the value of Tn(x) is +/- 1. It is this property
* which makes it easy to compare the size of the coefficients.
*
* During model fitting the data x coordinate is normalized into the domain
* [-1, 1] for Chebyshev Polynomial fitting, or into the domain [-pi, pi]
* for Fourier series fitting. Before writing out the data the coordinate
* is rescaled to match the original input values.
*
* An n degree polynomial can be written with terms of the form a0 + a1*x
* + a2*x*x + ... But it can also be written using other polynomial
* basis functions, such as a0*P0 + a1*P1 + a2*P2..., the Legendre
* polynomials, and a0*T0 + a1*T1 + a2*T2..., the Chebyshev polynomials.
* (The domain of the x values has to be in [-1, 1] in order to use P or T.)
* It is well known that the ordinary polynomial basis 1, x, x*x, ... gives
* terribly ill- conditioned matrices. The Ps and Ts do much better.
* This is because the ordinary basis is far from orthogonal. The Ps
* are orthogonal on [-1,1] and the Ts are orthogonal on [-1,1] under a
* simple weight function.
* Because the Ps have ordinary orthogonality on [-1,1], I expected them
* to be the best basis for a regression model; best meaning that they
* would lead to the most balanced G'G (matrix of normal equations) with
* the smallest condition number and the most nearly diagonal model
* parameter covariance matrix ((G'G)inverse). It turns out, however, that
* the G'G obtained from the Ts is very similar and usually has a smaller
* condition number than the Ps G'G. Both of these are vastly superior to
* the usual polynomials 1, x, x*x. In a test with 1000 equally spaced
* data and 8 model parameters, the Chebyshev system had a condition # = 10.6,
* Legendre = 14.8, and traditional = 54722.7. For 1000 randomly spaced data
* and 8 model parameters, the results were C = 13.1, L = 15.6, and P = 54916.6.
* As the number of model parameters approaches the number of data, the
* situation still holds, although all matrices get ill-conditioned; for 8
* random data and 8 model parameters, C = 1.8e+05, L = 2.6e+05, P = 1.1e+08.
* I expected the Legendre polynomials to have a covariance matrix more nearly
* diagonal than that of the Chebyshev polynomials, but on this criterion also
* the Chebyshev turned out to do better. Only as ndata -> n_model_parameters
* does the Legendre covariance matrix do better than the Chebyshev. So for
* all these reasons I use Chebyshev polynomials.
*
* Author: W. H. F. Smith
* Date: 25 February 1991-1999.
* Revised: 11 June, 1991-1999 for v2.0 of GMT-SYSTEM.
* 13-JUN-1998, for GMT 3.1 (PW)
*/
#include "gmt.h"
#define N_OUTPUT_CHOICES 5
#define POLYNOMIAL 0
#define FOURIER 1
struct DATA {
double x;
double y;
double m;
double r;
double w;
} *data;
main(int argc, char **argv)
{
void read_data(struct DATA **data, int *n_data, double *xmin, double *xmax, int weighted_input, double **work, FILE *fp);
void write_output(struct DATA *data, int n_data, char *output_choice, int n_outputs), transform_x(struct DATA *data, int n_data, int model_type, double xmin, double xmax);
void untransform_x(struct DATA *data, int n_data, int model_type, double xmin, double xmax);
void recompute_weights(struct DATA *data, int n_data, double *work, double *scale);
void allocate_array_space(int np, double **gtg, double **v, double **gtd, double **lambda, double **workb, double **workz, double **c_model, double **o_model, double **w_model);
void free_the_memory(double *gtg, double *v, double *gtd, double *lambda, double *workb, double *workz, double *c_model, double *o_model, double *w_model, struct DATA *data, double *work);
void calc_m_and_r(struct DATA *data, int n_data, double *model, int n_model, int m_type, double *grow);
void move_model_a_to_b(double *model_a, double *model_b, int n_model, double *chisq_a, double *chisq_b);
void load_gtg_and_gtd(struct DATA *data, int n_data, double *gtg, double *gtd, double *grow, int n_model, int mp, int m_type);
void solve_system(double *gtg, double *gtd, double *model, int n_model, int mp, double *lambda, double *v, double *b, double *z, double c_no, int *ir);
int i, j, n_data, n_outputs, n_model, n_model_max, model_type, np, significant, rank, n_req;
BOOLEAN error = FALSE, weighted_input = FALSE, weighted_output = FALSE, robust = FALSE, increment = FALSE;
double c_no = 1.0e06; /* Condition number for matrix solution */
double confid = 0.51; /* Confidence interval for significance test */
double *gtg, *v, *gtd, *lambda, *workb, *workz, *c_model, *o_model, *w_model, *work; /* Arrays */
double xmin, xmax, c_chisq, o_chisq, w_chisq, scale = 1.0, prob;
double get_chisq(struct DATA *data, int n_data, int n_model);
char output_choice[N_OUTPUT_CHOICES], format[BUFSIZ];
FILE *fp = NULL;
argc = GMT_begin (argc, argv);
model_type = POLYNOMIAL;
n_outputs = 0;
n_model_max = 0;
for (i = 0; i < N_OUTPUT_CHOICES; i++) output_choice[i] = 0;
for (i = 1; i < argc; i++) {
if (argv[i][0] == '-') {
switch (argv[i][1]) {
/* Common parameters */
case 'H':
case 'V':
case ':':
case '\0':
error += GMT_get_common_args (argv[i], 0, 0, 0, 0);
break;
/* Supplemental parameters */
case 'b':
error += GMT_io_selection (&argv[i][2]);
break;
case 'F':
j = 2;
while (argv[i][j]) {
switch (argv[i][j]) {
case 'x':
output_choice[j-2] = 'x';
break;
case 'y':
output_choice[j-2] = 'y';
break;
case 'm':
output_choice[j-2] = 'm';
break;
case 'r':
output_choice[j-2] = 'r';
break;
case 'w':
output_choice[j-2] = 'w';
weighted_output = TRUE;
break;
default:
error = TRUE;
fprintf (stderr, "%s: GMT SYNTAX ERROR -F option. Unrecognized output choice %c\n", GMT_program, argv[i][j]);
}
n_outputs++;
j++;
}
break;
case 'C':
c_no = atof(&argv[i][2]);
break;
case 'I':
increment = TRUE;
confid = (argv[i][2]) ? atof(&argv[i][2]) : 0.51;
break;
case 'N':
if (argv[i][strlen (argv[i]) - 1] == 'r') robust = TRUE;
j = 2;
if (argv[i][j] == 'F' || argv[i][j] == 'f') {
model_type = FOURIER;
j++;
}
else if (argv[i][j] == 'P' || argv[i][j] == 'p') {
model_type = POLYNOMIAL;
j++;
}
if (argv[i][j])
n_model_max = atoi(&argv[i][j]);
else {
error = TRUE;
fprintf (stderr, "%s: GMT SYNTAX ERROR -N option. No model specified\n", GMT_program);
}
break;
case 'W':
weighted_input = TRUE;
break;
default:
error = TRUE;
GMT_default_error (argv[i][1]);
break;
}
}
else {
if ((fp = GMT_fopen(argv[i], GMT_io.r_mode)) == NULL) {
fprintf (stderr, "%s: Could not open file %s\n", GMT_program, argv[i]);
error = TRUE;
}
}
}
if (argc == 1 || GMT_quick) {
fprintf(stderr,"trend1d %s - Fit a [weighted] [robust] polynomial [or Fourier] model for y = f(x) to ascii xy[w]\n\n", GMT_VERSION);
fprintf(stderr,"usage: trend1d -F<xymrw> -N[f]<n_model>[r] [<xy[w]file>] [-C<condition_#>]\n");
fprintf(stderr,"\t[-H[<nrec>]] [-I[<confidence>]] [-V] [-W] [-:] [-bi[s][<n>]] [-bo[s]]\n\n");
if (GMT_quick) exit (EXIT_FAILURE);
fprintf(stderr,"\t-F Choose at least 1, up to 5, any order, of xymrw for ascii output to stdout.\n");
fprintf(stderr,"\t x=x, y=y, m=model, r=residual=y-m, w=weight. w determined iteratively if robust fit used.\n");
fprintf(stderr,"\t-N fit a Polynomial [Default] or Fourier (-Nf) model with <n_model> terms.\n");
fprintf(stderr,"\t Append r for robust model. E.g., robust quadratic = -N3r.\n");
fprintf (stderr, "\n\tOPTIONS:\n");
fprintf(stderr,"\t[<xy[w]file>] name of ascii file, first 2 cols = x y [3 cols = x y w]. [Default reads stdin].\n");
fprintf(stderr,"\t-C Truncate eigenvalue spectrum so matrix has <condition_#>. [Default = 1.0e06].\n");
GMT_explain_option ('H');
fprintf(stderr,"\t-I Iteratively Increase # model parameters, to a max of <n_model> so long as the\n");
fprintf(stderr,"\t reduction in variance is significant at the <confidence> level.\n");
fprintf(stderr,"\t Give -I without a number to default to 0.51 confidence level.\n");
GMT_explain_option ('V');
fprintf(stderr,"\t-W Weighted input given, weights in 3rd column. [Default is unweighted].\n");
GMT_explain_option (':');
GMT_explain_option ('i');
GMT_explain_option ('n');
fprintf(stderr,"\t Default is 2 (or 3 if -W is set) input columns.\n");
GMT_explain_option ('o');
exit (EXIT_FAILURE);
}
if (c_no <= 1.0) {
fprintf (stderr, "%s: GMT SYNTAX ERROR -C option. Condition number must be larger than unity\n", GMT_program);
error++;
}
if (confid < 0.0 || confid > 1.0) {
fprintf (stderr, "%s: GMT SYNTAX ERROR -C option. Give 0 < confidence level < 1.0\n", GMT_program);
error++;
}
if (n_outputs > N_OUTPUT_CHOICES) {
fprintf (stderr, "%s: GMT SYNTAX ERROR -F option. Too many output columns specified (%d)\n", GMT_program, n_outputs);
error++;
}
if (n_model_max <= 0.0) {
fprintf (stderr, "%s: GMT SYNTAX ERROR -N option. A positive number of terms must be specified\n", GMT_program);
error++;
}
if (GMT_io.binary[0] && gmtdefs.io_header) {
fprintf (stderr, "%s: GMT SYNTAX ERROR. Binary input data cannot have header -H\n", GMT_program);
error++;
}
n_req = (weighted_input) ? 3 : 2;
if (GMT_io.binary[0] && GMT_io.ncol[0] == 0) GMT_io.ncol[0] = n_req;
if (GMT_io.binary[0] && GMT_io.ncol[0] < n_req) {
fprintf (stderr, "%s: GMT SYNTAX ERROR. Binary input data (-bi) must have at least %d columns\n", GMT_program, n_req);
error++;
}
if (error) exit (EXIT_FAILURE);
GMT_put_history (argc, argv); /* Update .gmtcommands */
if (GMT_io.binary[0] && gmtdefs.verbose) {
char *type[2] = {"double", "single"};
fprintf (stderr, "%s: Expects %d-column %s-precision binary data\n", GMT_program, GMT_io.ncol[0], type[GMT_io.single_precision[0]]);
}
#ifdef SET_IO_MODE
GMT_setmode (1);
#endif
np = n_model_max; /* Row dimension for matrices gtg and v */
allocate_array_space(np, >g, &v, >d, &lambda, &workb, &workz, &c_model, &o_model, &w_model);
read_data(&data, &n_data, &xmin, &xmax, weighted_input, &work, fp);
if (xmin == xmax) {
fprintf(stderr,"%s: Fatal error in input data. X min = X max.\n", GMT_program);
exit (EXIT_FAILURE);
}
if (n_data == 0) {
fprintf(stderr,"%s: Fatal error. Could not read any data.\n", GMT_program);
exit (EXIT_FAILURE);
}
if (n_data < n_model_max) fprintf(stderr,"%s: Warning. Ill-posed problem. n_data < n_model_max.\n", GMT_program);
transform_x(data, n_data, model_type, xmin, xmax); /* Set domain to [-1, 1] or [-pi, pi] */
if (gmtdefs.verbose) {
sprintf(format,"%%s: Read %%d data with X values from %s to %s\n\0", gmtdefs.d_format, gmtdefs.d_format);
fprintf(stderr, format, GMT_program, n_data, xmin, xmax);
fprintf(stderr,"N_model\tRank\tChi_Squared\tSignificance\n");
}
sprintf (format, "%%d\t%%d\t%s\t%s\n\0", gmtdefs.d_format, gmtdefs.d_format);
if (increment) {
n_model = 1;
/* Fit first model */
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, 1.0);
if (robust) {
do {
recompute_weights(data, n_data, work, &scale);
move_model_a_to_b(c_model, w_model, n_model, &c_chisq, &w_chisq);
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
significant = GMT_sig_f(c_chisq, n_data-n_model, w_chisq, n_data-n_model, confid, &prob);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, prob);
} while (significant);
/* Go back to previous model only if w_chisq < c_chisq */
if (w_chisq < c_chisq) {
move_model_a_to_b(w_model, c_model, n_model, &w_chisq, &c_chisq);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
if (weighted_output && n_model == n_model_max) recompute_weights(data, n_data, work, &scale);
}
}
/* First [robust] model has been found */
significant = TRUE;
while(n_model < n_model_max && significant) {
move_model_a_to_b(c_model, o_model, n_model, &c_chisq, &o_chisq);
n_model++;
/* Fit next model */
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, 1.00);
if (robust) {
do {
recompute_weights(data, n_data, work, &scale);
move_model_a_to_b(c_model, w_model, n_model, &c_chisq, &w_chisq);
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
significant = GMT_sig_f(c_chisq, n_data-n_model, w_chisq, n_data-n_model, confid, &prob);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, prob);
} while (significant);
/* Go back to previous model only if w_chisq < c_chisq */
if (w_chisq < c_chisq) {
move_model_a_to_b(w_model, c_model, n_model, &w_chisq, &c_chisq);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
if (weighted_output && n_model == n_model_max) recompute_weights(data, n_data, work, &scale);
}
}
/* Next [robust] model has been found */
significant = GMT_sig_f(c_chisq, n_data-n_model, o_chisq, n_data-n_model-1, confid, &prob);
}
if (!(significant) ) { /* Go back to previous [robust] model, stored in o_model */
n_model--;
rank--;
move_model_a_to_b(o_model, c_model, n_model, &o_chisq, &c_chisq);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
if (robust && weighted_output) recompute_weights(data, n_data, work, &scale);
}
}
else {
n_model = n_model_max;
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, 1.00);
if (robust) {
do {
recompute_weights(data, n_data, work, &scale);
move_model_a_to_b(c_model, w_model, n_model, &c_chisq, &w_chisq);
load_gtg_and_gtd(data, n_data, gtg, gtd, workb, n_model, np, model_type);
solve_system(gtg, gtd, c_model, n_model, np, lambda, v, workb, workz, c_no, &rank);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
c_chisq = get_chisq(data, n_data, n_model);
significant = GMT_sig_f(c_chisq, n_data-n_model, w_chisq, n_data-n_model, confid, &prob);
if (gmtdefs.verbose) fprintf(stderr, format, n_model, rank, c_chisq, prob);
} while (significant);
/* Go back to previous model only if w_chisq < c_chisq */
if (w_chisq < c_chisq) {
move_model_a_to_b(w_model, c_model, n_model, &w_chisq, &c_chisq);
calc_m_and_r(data, n_data, c_model, n_model, model_type, workb);
if (weighted_output && n_model == n_model_max) recompute_weights(data, n_data, work, &scale);
}
}
}
if (gmtdefs.verbose) {
sprintf (format, "%%s: Final model stats: N model parameters %%d. Rank %%d. Chi-Squared: %s\n\0", gmtdefs.d_format);
fprintf(stderr, format, GMT_program, n_model, rank, c_chisq);
fprintf(stderr,"Model Coefficients:");
sprintf (format, "%s\t\0", gmtdefs.d_format);
for (i = 0; i < n_model; i++) fprintf (stderr, format, c_model[i]);
fprintf(stderr,"\n");
}
untransform_x(data, n_data, model_type, xmin, xmax);
write_output(data, n_data, output_choice, n_outputs);
free_the_memory(gtg, v, gtd, lambda, workb, workz, c_model, o_model, w_model, data, work);
GMT_end (argc, argv);
}
void read_data(struct DATA **data, int *n_data, double *xmin, double *xmax, int weighted_input, double **work, FILE *fp)
{
int i, ix, iy, n_alloc = GMT_CHUNK, n_expected_fields, n_fields;
double *in;
char buffer[BUFSIZ];
if (fp == NULL) {
fp = GMT_stdin;
#ifdef SET_IO_MODE
GMT_setmode (0);
#endif
}
(*data) = (struct DATA *) GMT_memory (VNULL, (size_t)n_alloc, sizeof(struct DATA), GMT_program);
ix = (gmtdefs.xy_toggle) ? 1 : 0; iy = 1 - ix; /* Set up which columns have x and y */
if (gmtdefs.io_header) for (i = 0; i < gmtdefs.n_header_recs; i++) fgets (buffer, BUFSIZ, fp);
i = 0;
n_expected_fields = (GMT_io.binary[0]) ? GMT_io.ncol[0] : BUFSIZ;
while ((n_fields = GMT_input (fp, &n_expected_fields, &in)) >= 0 && !(GMT_io.status & GMT_IO_EOF)) {
if (GMT_io.status & GMT_IO_MISMATCH) {
fprintf (stderr, "%s: Mismatch between actual (%d) and expected (%d) fields near line %d\n", GMT_program, n_fields, n_expected_fields, i);
exit (EXIT_FAILURE);
}
(*data)[i].x = in[ix];
(*data)[i].y = in[iy];
(*data)[i].w = (weighted_input) ? in[2] : 1.0;
if (i) {
if (*xmin > (*data)[i].x) *xmin = (*data)[i].x;
if (*xmax < (*data)[i].x) *xmax = (*data)[i].x;
}
else {
*xmin = (*data)[i].x;
*xmax = (*data)[i].x;
}
i++;
if (i == n_alloc) {
n_alloc += GMT_CHUNK;
*data = (struct DATA *) GMT_memory ((void *)*data, (size_t)n_alloc, sizeof(struct DATA), GMT_program);
}
}
if (fp != GMT_stdin) GMT_fclose(fp);
*data = (struct DATA *) GMT_memory ((void *)*data, (size_t)i, sizeof(struct DATA), GMT_program);
*work = (double *) GMT_memory (VNULL, (size_t)i, sizeof(double), GMT_program);
*n_data = i;
}
void allocate_array_space(int np, double **gtg, double **v, double **gtd, double **lambda, double **workb, double **workz, double **c_model, double **o_model, double **w_model)
{
*gtg = (double *) GMT_memory (VNULL, (size_t)(np*np), sizeof(double), GMT_program);
*v = (double *) GMT_memory (VNULL, (size_t)(np*np), sizeof(double), GMT_program);
*gtd = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*lambda = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*workb = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*workz = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*c_model = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*o_model = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
*w_model = (double *) GMT_memory (VNULL, (size_t)np, sizeof(double), GMT_program);
}
void write_output(struct DATA *data, int n_data, char *output_choice, int n_outputs)
{
int i, j;
double out[5];
for (i = 0; i < n_data; i++) {
for (j = 0; j < n_outputs; j++) {
switch (output_choice[j]) {
case 'x':
out[j] = data[i].x;
break;
case 'y':
out[j] = data[i].y;
break;
case 'm':
out[j] = data[i].m;
break;
case 'r':
out[j] = data[i].r;
break;
case 'w':
out[j] = data[i].w;
break;
}
}
GMT_output (GMT_stdout, n_outputs, out);
}
}
void free_the_memory(double *gtg, double *v, double *gtd, double *lambda, double *workb, double *workz, double *c_model, double *o_model, double *w_model, struct DATA *data, double *work)
{
GMT_free ((void *)work);
GMT_free ((void *)data);
GMT_free ((void *)w_model);
GMT_free ((void *)o_model);
GMT_free ((void *)c_model);
GMT_free ((void *)workz);
GMT_free ((void *)workb);
GMT_free ((void *)lambda);
GMT_free ((void *)gtd);
GMT_free ((void *)v);
GMT_free ((void *)gtg);
}
void transform_x(struct DATA *data, int n_data, int model_type, double xmin, double xmax)
{
int i;
double offset, scale;
offset = 0.5 * (xmin + xmax); /* Mid Range */
scale = 2.0 / (xmax - xmin); /* 1 / (1/2 Range) */
if (model_type == FOURIER) { /* Set Range to 1 period */
scale *= M_PI;
}
for (i = 0; i < n_data; i++) {
data[i].x = (data[i].x - offset) * scale;
}
}
void untransform_x(struct DATA *data, int n_data, int model_type, double xmin, double xmax)
{
int i;
double offset, scale;
offset = 0.5 * (xmin + xmax); /* Mid Range */
scale = 0.5 * (xmax - xmin); /* 1/2 Range */
if (model_type == FOURIER) {
scale /= M_PI;
}
for (i = 0; i < n_data; i++) {
data[i].x = (data[i].x * scale) + offset;
}
}
double get_chisq(struct DATA *data, int n_data, int n_model)
{
int i, nu;
double chi = 0.0;
for (i = 0; i < n_data; i++) { /* Weight is already squared */
if (data[i].w == 1.0) {
chi += (data[i].r * data[i].r);
}
else {
chi += (data[i].r * data[i].r * data[i].w);
}
}
nu = n_data - n_model;
if (nu > 1) return(chi/nu);
return(chi);
}
void recompute_weights(struct DATA *data, int n_data, double *work, double *scale)
{
int i;
double k, ksq, rr;
/* First find median { fabs(data[].r) },
estimate scale from this,
and compute chisq based on this. */
for (i = 0; i < n_data; i++) {
work[i] = fabs(data[i].r);
}
qsort((void *)work, (size_t)n_data, sizeof(double), GMT_comp_double_asc);
if (n_data%2) {
*scale = 1.4826 * work[n_data/2];
}
else {
*scale = 0.7413 * (work[n_data/2 - 1] + work[n_data/2]);
}
k = 1.5 * (*scale); /* Huber[1964] weight; 95% efficient for Normal data */
ksq = k * k;
for (i = 0; i < n_data; i++) {
rr = fabs(data[i].r);
if (rr <= k) {
data[i].w = 1.0;
}
else {
data[i].w = (2*k/rr) - (ksq/(rr*rr) ); /* This is really w-squared */
}
}
}
void load_g_row(double x, int n, double *gr, int m)
/* Current data position, appropriately normalized. */
/* Number of model parameters, and elements of gr[] */
/* Elements of row of G matrix. */
/* Parameter indicating model type */
{
/* Routine computes the elements gr[j] in the ith row of the
G matrix (Menke notation), where x is the ith datum's
abcissa. */
int j, k;
if (n) {
gr[0] = 1.0;
switch (m) {
case POLYNOMIAL:
/* Create Chebyshev polynomials */
if (n > 1) gr[1] = x;
for (j = 2; j < n; j++) {
gr[j] = 2 * x * gr[j-1] - gr[j-2];
}
break;
case FOURIER:
for (j = 1; j < n; j++) {
k = (j + 1)/2;
if (k > 1) {
if (j%2) {
gr[j] = cos(k*x);
}
else {
gr[j] = sin(k*x);
}
}
else {
if (j%2) {
gr[j] = cos(x);
}
else {
gr[j] = sin(x);
}
}
}
break;
}
}
}
void calc_m_and_r(struct DATA *data, int n_data, double *model, int n_model, int m_type, double *grow)
{
/* model[n_model] holds solved coefficients of m_type model.
grow[n_model] is a vector for a row of G matrix. */
int i, j;
for (i = 0; i < n_data; i++) {
load_g_row(data[i].x, n_model, grow, m_type);
data[i].m = 0.0;
for (j = 0; j < n_model; j++) {
data[i].m += model[j]*grow[j];
}
data[i].r = data[i].y - data[i].m;
}
}
void move_model_a_to_b(double *model_a, double *model_b, int n_model, double *chisq_a, double *chisq_b)
{
int i;
for(i = 0; i< n_model; i++) {
model_b[i] = model_a[i];
}
*chisq_b = *chisq_a;
}
void load_gtg_and_gtd(struct DATA *data, int n_data, double *gtg, double *gtd, double *grow, int n_model, int mp, int m_type)
/* mp is row dimension of gtg */
{
int i, j, k;
double wy;
/* First zero the contents for summing: */
for (j = 0; j < n_model; j++) {
for (k = 0; k < n_model; k++) {
gtg[j + k*mp] = 0.0;
}
gtd[j] = 0.0;
}
/* Sum over all data */
for (i = 0; i < n_data; i++) {
load_g_row(data[i].x, n_model, grow, m_type);
if (data[i].w != 1.0) {
wy = data[i].w * data[i].y;
for (j = 0; j < n_model; j++) {
for (k = 0; k < n_model; k++) {
gtg[j + k*mp] += (data[i].w * grow[j] * grow[k]);
}
gtd[j] += (wy * grow[j]);
}
}
else {
for (j = 0; j < n_model; j++) {
for (k = 0; k < n_model; k++) {
gtg[j + k*mp] += (grow[j] * grow[k]);
}
gtd[j] += (data[i].y * grow[j]);
}
}
}
}
void solve_system(double *gtg, double *gtd, double *model, int n_model, int mp, double *lambda, double *v, double *b, double *z, double c_no, int *ir)
{
int i, j, k, rank = 0, n, m, nrots;
double c_test, temp_inverse_ij;
if (n_model == 1) {
model[0] = gtd[0] / gtg[0];
*ir = 1;
}
else {
n = n_model;
m = mp;
if(GMT_jacobi(gtg, &n, &m, lambda, v, b, z, &nrots)) {
fprintf(stderr,"%s: Warning: Matrix Solver Convergence Failure.\n", GMT_program);
}
c_test = fabs(lambda[0])/c_no;
while(rank < n_model && lambda[rank] > 0.0 && lambda[rank] > c_test) rank++;
for (i = 0; i < n_model; i++) {
model[i] = 0.0;
for (j = 0; j < n_model; j++) {
temp_inverse_ij = 0.0;
for (k = 0; k < rank; k++) {
temp_inverse_ij += (v[i + k*mp] * v[j + k*mp] / lambda[k]);
}
model[i] += (temp_inverse_ij * gtd[j]);
}
}
*ir = rank;
}
}
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