lsfg.c File Reference

Computes generalized least squares fits using a function passed by the caller. More...

#include "matlib.h"
#include "mdb.h"

Go to the source code of this file.

Functions
int	p_merror (char *message)
long	lsfg (double *xd, double *yd, double *sy, long n_pts, long n_terms, int32_t *order, double *coef, double *s_coef, double *chi, double *diff, double(*fn)(double x, long ord))
	Computes generalized least squares fits using a function passed by the caller.

Detailed Description

Computes generalized least squares fits using a function passed by the caller.

This file contains the implementation of the lsfg() function, which performs generalized least squares fitting using user-provided basis functions. It also declares the p_merror() function for handling matrix errors.

Michael Borland, 1986.

Definition in file lsfg.c.

Function Documentation

lsfg()

long lsfg	(	double *	xd,
		double *	yd,
		double *	sy,
		long	n_pts,
		long	n_terms,
		int32_t *	order,
		double *	coef,
		double *	s_coef,
		double *	chi,
		double *	diff,
		double(*	fn )(double x, long ord) )

Computes generalized least squares fits using a function passed by the caller.

Parameters

xd	Array of x-data points.
yd	Array of y-data points.
sy	Array of standard deviations for y-data points. If NULL, an unweighted fit is performed.
n_pts	Number of data points.
n_terms	Number of terms in the fit.
order	Array specifying the order for each term.
coef	Output array to store the coefficients of the fit.
s_coef	Output array to store the standard deviations of the coefficients.
chi	Output pointer to store the reduced chi-squared value.
diff	Output array to store the differences between observed and fitted y-values.
fn	Function pointer to the basis function.

Returns

Returns 1 on success, 0 on failure.

Definition at line 30 of file lsfg.c.

  {
  long i, j, unweighted;
  double xp, *x_i, x0;
  static MATRIX *X, *Y, *Yp, *C, *C_1, *Xt, *A, *Ca, *XtC, *XtCX, *T, *Tt, *TC;
 
  if (n_pts < n_terms) {
    printf("error: insufficient data for requested order of fit\n");
    printf("(%ld data points, %ld terms in fit)\n", n_pts, n_terms);
    exit(1);
  }
 
  unweighted = 1;
  if (sy)
    for (i = 1; i < n_pts; i++)
      if (sy[i] != sy[0]) {
        unweighted = 0;
        break;
      }
 
  /* allocate matrices */
  m_alloc(&X, n_pts, n_terms);
  m_alloc(&Y, n_pts, 1);
  m_alloc(&Yp, n_pts, 1);
  m_alloc(&Xt, n_terms, n_pts);
  if (!unweighted) {
    m_alloc(&C, n_pts, n_pts);
    m_alloc(&C_1, n_pts, n_pts);
    m_zero(C);
    m_zero(C_1);
  }
  m_alloc(&A, n_terms, 1);
  m_alloc(&Ca, n_terms, n_terms);
  m_alloc(&XtC, n_terms, n_pts);
  m_alloc(&XtCX, n_terms, n_terms);
  m_alloc(&T, n_terms, n_pts);
  m_alloc(&Tt, n_pts, n_terms);
  m_alloc(&TC, n_terms, n_pts);
 
  /* Compute X, Y, C, C_1.  X[i][j] = F(xd[i]), order[j]). Y[i][0] = yd[i].  
   * C   = delta(i,j)*sy[i]^2  (covariance matrix of yd)            
   * C_1 = INV(C)                                                        
   */
  for (i = 0; i < n_pts; i++) {
    x_i = X->a[i];
    Y->a[i][0] = yd[i];
    if (!unweighted) {
      C->a[i][i] = sqr(sy[i]);
      C_1->a[i][i] = 1 / C->a[i][i];
    }
    x0 = xd[i];
    for (j = 0; j < n_terms; j++)
      x_i[j] = (*fn)(x0, order[j]);
  }
 
  /* Compute A, the matrix of coefficients.
   * Weighted least-squares solution is A = INV(Xt.INV(C).X).Xt.INV(C).y 
   * Unweighted solution is A = INV(Xt.X).Xt.y 
   */
  if (unweighted) {
    /* eliminating 2 matrix operations makes this much faster than a weighted fit
       * if there are many data points.
       */
    if (!m_trans(Xt, X))
      return (p_merror("transposing X"));
    if (!m_mult(XtCX, Xt, X))
      return (p_merror("multiplying Xt.X"));
    if (!m_invert(XtCX, XtCX))
      return (p_merror("inverting XtCX"));
    if (!m_mult(T, XtCX, Xt))
      return (p_merror("multiplying XtX.Xt"));
    if (!m_mult(A, T, Y))
      return (p_merror("multiplying T.Y"));
 
    /* Compute covariance matrix of A, Ca = (T.Tt)*C[0][0] */
    if (!m_trans(Tt, T))
      return (p_merror("computing transpose of T"));
    if (!m_mult(Ca, T, Tt))
      return (p_merror("multiplying T.Tt"));
    if (!m_scmul(Ca, Ca, sy ? sqr(sy[0]) : 1))
      return (p_merror("multiplying T.Tt by scalar"));
  } else {
    if (!m_trans(Xt, X))
      return (p_merror("transposing X"));
    if (!m_mult(XtC, Xt, C_1))
      return (p_merror("multiplying Xt.C_1"));
    if (!m_mult(XtCX, XtC, X))
      return (p_merror("multiplying XtC.X"));
    if (!m_invert(XtCX, XtCX))
      return (p_merror("inverting XtCX"));
    if (!m_mult(T, XtCX, XtC))
      return (p_merror("multiplying XtCX.XtC"));
    if (!m_mult(A, T, Y))
      return (p_merror("multiplying T.Y"));
 
    /* Compute covariance matrix of A, Ca = T.C.Tt */
    if (!m_mult(TC, T, C))
      return (p_merror("multiplying T.C"));
    if (!m_trans(Tt, T))
      return (p_merror("computing transpose of T"));
    if (!m_mult(Ca, TC, Tt))
      return (p_merror("multiplying TC.Tt"));
  }
 
  for (i = 0; i < n_terms; i++) {
    coef[i] = A->a[i][0];
    s_coef[i] = sqrt(Ca->a[i][i]);
  }
 
  /* Compute Yp = X.A, use to compute chi-squared */
  if (!m_mult(Yp, X, A))
    return (p_merror("multiplying X.A"));
  *chi = 0;
  for (i = 0; i < n_pts; i++) {
    xp = (Yp->a[i][0] - yd[i]);
    if (diff != NULL)
      diff[i] = xp;
    xp /= sy ? sy[i] : 1;
    *chi += xp * xp;
  }
  if (n_pts != n_terms)
    *chi /= (n_pts - n_terms);
 
  /* de-allocate matrices */
  m_free(&X);
  m_free(&Y);
  m_free(&Yp);
  m_free(&Xt);
  if (!unweighted) {
    m_free(&C);
    m_free(&C_1);
  }
  m_free(&A);
  m_free(&Ca);
  m_free(&XtC);
  m_free(&XtCX);
  m_free(&T);
  m_free(&Tt);
  m_free(&TC);
 
  return (1);
}