/************************************************************************** * Desc: Vector functions * Author: Andrew Howard * Date: 10 Dec 2002 * CVS: $Id: pf_vector.c,v 1.3.2.1 2003/04/18 19:01:18 inspectorg Exp $ *************************************************************************/#include <math.h>#include <gsl/gsl_matrix.h>#include <gsl/gsl_eigen.h>#include <gsl/gsl_linalg.h>#include "pf_vector.h"// Return a zero vectorpf_vector_t pf_vector_zero(){  pf_vector_t c;  c.v[0] = 0.0;  c.v[1] = 0.0;  c.v[2] = 0.0;    return c;}// Check for NAN or INF in any componentint pf_vector_finite(pf_vector_t a){  int i;    for (i = 0; i < 3; i++)    if (!finite(a.v[i]))      return 0;    return 1;}// Print a vectorvoid pf_vector_fprintf(pf_vector_t a, FILE *file, const char *fmt){  int i;  for (i = 0; i < 3; i++)  {    fprintf(file, fmt, a.v[i]);    fprintf(file, " ");  }  fprintf(file, "\n");  return;     }// Simple vector additionpf_vector_t pf_vector_add(pf_vector_t a, pf_vector_t b){  pf_vector_t c;  c.v[0] = a.v[0] + b.v[0];  c.v[1] = a.v[1] + b.v[1];  c.v[2] = a.v[2] + b.v[2];    return c;}// Simple vector subtractionpf_vector_t pf_vector_sub(pf_vector_t a, pf_vector_t b){  pf_vector_t c;  c.v[0] = a.v[0] - b.v[0];  c.v[1] = a.v[1] - b.v[1];  c.v[2] = a.v[2] - b.v[2];    return c;}// Transform from local to global coords (a + b)pf_vector_t pf_vector_coord_add(pf_vector_t a, pf_vector_t b){  pf_vector_t c;  c.v[0] = b.v[0] + a.v[0] * cos(b.v[2]) - a.v[1] * sin(b.v[2]);  c.v[1] = b.v[1] + a.v[0] * sin(b.v[2]) + a.v[1] * cos(b.v[2]);  c.v[2] = b.v[2] + a.v[2];    return c;}// Transform from global to local coords (a - b)pf_vector_t pf_vector_coord_sub(pf_vector_t a, pf_vector_t b){  pf_vector_t c;  c.v[0] = +(a.v[0] - b.v[0]) * cos(b.v[2]) + (a.v[1] - b.v[1]) * sin(b.v[2]);  c.v[1] = -(a.v[0] - b.v[0]) * sin(b.v[2]) + (a.v[1] - b.v[1]) * cos(b.v[2]);  c.v[2] = a.v[2] - b.v[2];    return c;}// Return a zero matrixpf_matrix_t pf_matrix_zero(){  int i, j;  pf_matrix_t c;  for (i = 0; i < 3; i++)    for (j = 0; j < 3; j++)      c.m[i][j] = 0.0;          return c;}// Check for NAN or INF in any componentint pf_matrix_finite(pf_matrix_t a){  int i, j;    for (i = 0; i < 3; i++)    for (j = 0; j < 3; j++)      if (!finite(a.m[i][j]))        return 0;    return 1;}// Print a matrixvoid pf_matrix_fprintf(pf_matrix_t a, FILE *file, const char *fmt){  int i, j;  for (i = 0; i < 3; i++)  {    for (j = 0; j < 3; j++)    {      fprintf(file, fmt, a.m[i][j]);      fprintf(file, " ");    }    fprintf(file, "\n");  }  return;     }// Compute the matrix inversepf_matrix_t pf_matrix_inverse(pf_matrix_t a, double *det){  double lndet;  int signum;  gsl_permutation *p;  gsl_matrix_view A, Ai;  pf_matrix_t ai;  A = gsl_matrix_view_array((double*) a.m, 3, 3);  Ai = gsl_matrix_view_array((double*) ai.m, 3, 3);    // Do LU decomposition  p = gsl_permutation_alloc(3);  gsl_linalg_LU_decomp(&A.matrix, p, &signum);  // Check for underflow  lndet = gsl_linalg_LU_lndet(&A.matrix);  if (lndet < -1000)  {    //printf("underflow in matrix inverse lndet = %f", lndet);    gsl_matrix_set_zero(&Ai.matrix);  }  else  {    // Compute inverse    gsl_linalg_LU_invert(&A.matrix, p, &Ai.matrix);  }  gsl_permutation_free(p);  if (det)    *det = exp(lndet);  return ai;}// Decompose a covariance matrix [a] into a rotation matrix [r] and a diagonal// matrix [d] such that a = r d r^T.void pf_matrix_unitary(pf_matrix_t *r, pf_matrix_t *d, pf_matrix_t a){  int i, j;  gsl_matrix *aa;  gsl_vector *eval;  gsl_matrix *evec;  gsl_eigen_symmv_workspace *w;  aa = gsl_matrix_alloc(3, 3);  eval = gsl_vector_alloc(3);  evec = gsl_matrix_alloc(3, 3);  for (i = 0; i < 3; i++)    for (j = 0; j < 3; j++)      gsl_matrix_set(aa, i, j, a.m[i][j]);  // Compute eigenvectors/values  w = gsl_eigen_symmv_alloc(3);  gsl_eigen_symmv(aa, eval, evec, w);  gsl_eigen_symmv_free(w);  *d = pf_matrix_zero();  for (i = 0; i < 3; i++)  {    d->m[i][i] = gsl_vector_get(eval, i);    for (j = 0; j < 3; j++)      r->m[i][j] = gsl_matrix_get(evec, i, j);  }    gsl_matrix_free(evec);  gsl_vector_free(eval);  gsl_matrix_free(aa);    return;}