int leastsq(float **a, int m, int n, float *b) {
int i,j;
float *d, *c;
printf("leastsq(%d x %d)\n",m,n);
for(i = 0; i < m; i++) {
printf("[ ");
for(j = 0; j < n; j++) {
printf(" %2.4f", a[i][j]);
}
printf(" ]");
printf(" = %g\n", b[i]);
}
c = malloc(sizeof(float)*n);
assert(c != NULL);
d = malloc(sizeof(float)*n);
assert(d != NULL);
if (qrdcmp(a,m,n,c,d))
return -1;
qrsolv(a,n,c,d,b);
free(c);
free(d);
}
int main(void)
{
int i,j,k,l,m,n,sing;
float con,**a,*c,*d,**q,**qt,**r,**x;
char dummy[MAXSTR];
FILE *fp;
a=matrix(1,NP,1,NP);
c=vector(1,NP);
d=vector(1,NP);
q=matrix(1,NP,1,NP);
qt=matrix(1,NP,1,NP);
r=matrix(1,NP,1,NP);
x=matrix(1,NP,1,NP);
if ((fp = fopen("matrx1.dat","r")) == NULL)
nrerror("Data file matrx1.dat not found\n");
while (!feof(fp)) {
fgets(dummy,MAXSTR,fp);
fgets(dummy,MAXSTR,fp);
fscanf(fp,"%d %d ",&n,&m);
fgets(dummy,MAXSTR,fp);
for (k=1;k<=n;k++)
for (l=1;l<=n;l++) fscanf(fp,"%f ",&a[k][l]);
fgets(dummy,MAXSTR,fp);
for (l=1;l<=m;l++)
for (k=1;k<=n;k++) fscanf(fp,"%f ",&x[k][l]);
/* Print out a-matrix for comparison with product of
Q and R decomposition matrices */
printf("Original matrix:\n");
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) printf("%12.6f",a[k][l]);
printf("\n");
}
/* Perform the decomposition */
qrdcmp(a,n,c,d,&sing);
if (sing) fprintf(stderr,"Singularity in QR decomposition.\n");
/* find the Q and R matrices */
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) {
if (l > k) {
r[k][l]=a[k][l];
q[k][l]=0.0;
} else if (l < k) {
r[k][l]=q[k][l]=0.0;
} else {
r[k][l]=d[k];
q[k][l]=1.0;
}
}
}
for (i=n-1;i>=1;i--) {
for (con=0.0,k=i;k<=n;k++) con += a[k][i]*a[k][i];
con /= 2.0;
for (k=i;k<=n;k++) {
for (l=i;l<=n;l++) {
qt[k][l]=0.0;
for (j=i;j<=n;j++) {
qt[k][l] += q[j][l]*a[k][i]*a[j][i]/con;
}
}
}
for (k=i;k<=n;k++)
for (l=i;l<=n;l++) q[k][l] -= qt[k][l];
}
/* compute product of Q and R matrices for comparison
with original matrix. */
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) {
x[k][l]=0.0;
for (j=1;j<=n;j++)
x[k][l] += q[k][j]*r[j][l];
}
}
printf("\nProduct of Q and R matrices:\n");
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) printf("%12.6f",x[k][l]);
printf("\n");
}
printf("\nQ matrix of the decomposition:\n");
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) printf("%12.6f",q[k][l]);
printf("\n");
}
printf("\nR matrix of the decomposition:\n");
for (k=1;k<=n;k++) {
for (l=1;l<=n;l++) printf("%12.6f",r[k][l]);
printf("\n");
}
printf("\n***********************************\n");
printf("press return for next problem:\n");
(void) getchar();
}
fclose(fp);
free_matrix(x,1,NP,1,NP);
free_matrix(r,1,NP,1,NP);
free_matrix(qt,1,NP,1,NP);
free_matrix(q,1,NP,1,NP);
free_vector(d,1,NP);
free_vector(c,1,NP);
free_matrix(a,1,NP,1,NP);
return 0;
}
