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bspline_impl.c
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bspline_impl.c
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#include <stdlib.h>
/* function prototypes */
double *bspline(double *, double *, int, double *, int, int, int, int, int);
double bspline_quad(double *, int, int, int, int, int, int);
double *bspline_prod(double *, int, double *, int, int, int, int, int, int);
void bspline_gram(double *, double *, int, int, int, int);
void invband_compute(double *, double *, int, int);
double *bspline(double *output, double *x, int nx,
double *knots, int nknots,
int m, int d, int lower, int upper){
int nbasis;
int index, i, j, k;
double *result, *b, *b0, *b1;
double *f0, *f1;
double denom;
nbasis = upper - lower;
result = output;
f0 = (double *) malloc(sizeof(double) * nx);
f1 = (double *) malloc(sizeof(double) * nx);
if (m == 1) {
for(i=0; i<nbasis; i++) {
index = i + lower;
if(index < nknots - 1) {
if ((knots[index] != knots[index+1]) && (d <= 0)) {
for (k=0; k<nx; k++) {
*result = (double) (x[k] >= knots[index]) * (x[k] < knots[index+1]);
result++;
}
}
else {
for (k=0; k<nx; k++) {
*result = 0.;
result++;
}
}
}
else {
for (k=0; k<nx; k++) {
*result = 0.;
result++;
}
}
}
}
else {
b = (double *) malloc(sizeof(double) * (nbasis+1) * nx);
bspline(b, x, nx, knots, nknots, m-1, d-1, lower, upper+1);
for(i=0; i<nbasis; i++) {
b0 = b + nx*i;
b1 = b + nx*(i+1);
index = i+lower;
if ((knots[index] != knots[index+m-1]) && (index+m-1 < nknots)) {
denom = knots[index+m-1] - knots[index];
if (d <= 0) {
for (k=0; k<nx; k++) {
f0[k] = (x[k] - knots[index]) / denom;
}
}
else {
for (k=0; k<nx; k++) {
f0[k] = (m-1) / (knots[index+m-1] - knots[index]);
}
}
}
else {
for (k=0; k<nx; k++) {
f0[k] = 0.;
}
}
index = i+lower+1;
if ((knots[index] != knots[index+m-1]) && (index+m-1 < nknots)) {
denom = knots[index+m-1] - knots[index];
if (d <= 0) {
for (k=0; k<nx; k++) {
f1[k] = (knots[index+m-1] - x[k]) / denom;
}
}
else {
for (k=0; k<nx; k++) {
f1[k] = -(m-1) / (knots[index+m-1] - knots[index]);
}
}
}
else {
for (k=0; k<nx; k++) {
f1[k] = 0.;
}
}
for (k=0; k<nx; k++) {
*result = f0[k]*(*b0) + f1[k]*(*b1);
b0++; b1++; result++;
}
}
free(b);
}
free(f0); free(f1);
result = result - nx * nbasis;
return(result);
}
double bspline_quad(double *knots, int nknots,
int m, int l, int r, int dl, int dr)
/* This is based on scipy.integrate.fixed_quad */
{
double *y;
double qx[18]={-0.9915651684209309, -0.95582394957139838,
-0.89260246649755604, -0.80370495897252303, -0.69168704306035333,
-0.55977083107394743, -0.41175116146284346, -0.25188622569150576,
-0.084775013041735417, 0.084775013041735306, 0.25188622569150554,
0.41175116146284246, 0.55977083107394743, 0.69168704306035189,
0.80370495897252314, 0.89260246649755637, 0.95582394957139616,
0.9915651684209319};
double qw[18]={0.021616013526480963, 0.049714548894972385,
0.076425730254889301, 0.10094204410628659, 0.12255520671147889,
0.14064291467065104, 0.15468467512626605, 0.16427648374583206,
0.16914238296314324, 0.16914238296314299, 0.16427648374583295,
0.1546846751262658, 0.14064291467065093, 0.12255520671147752,
0.10094204410628753, 0.076425730254888483, 0.049714548894967854,
0.021616013526484387};
double x[18];
int nq=18;
int k, kk;
int lower, upper;
double result, a, b, partial;
result = 0;
/* TO DO: figure out knot span more efficiently */
lower = l - m - 1;
if (lower < 0) { lower = 0;}
upper = lower + 2 * m + 4;
if (upper > nknots - 1) { upper = nknots-1; }
for (k=lower; k<upper; k++) {
partial = 0.;
a = knots[k]; b=knots[k+1];
for (kk=0; kk<nq; kk++) {
x[kk] = (b - a) * (qx[kk] + 1) / 2. + a;
}
y = bspline_prod(x, nq, knots, nknots, m, l, r, dl, dr);
for (kk=0; kk<nq; kk++) {
partial += y[kk] * qw[kk];
}
free(y); /* bspline_prod malloc's memory, but does not free it */
result += (b - a) * partial / 2.;
}
return(result);
}
double *bspline_prod(double *x, int nx, double *knots, int nknots,
int m, int l, int r, int dl, int dr){
double *result, *bl, *br;
int k;
if (abs(r - l) <= m) {
result = (double *) malloc(sizeof(double) * nx);
bl = (double *) malloc(sizeof(double) * nx);
br = (double *) malloc(sizeof(double) * nx);
bl = bspline(bl, x, nx, knots, nknots, m, dl, l, l+1);
br = bspline(br, x, nx, knots, nknots, m, dr, r, r+1);
for (k=0; k<nx; k++) {
result[k] = bl[k] * br[k];
}
free(bl); free(br);
}
else {
for (k=0; k<nx; k++) {
result[k] = 0.;
}
}
return(result);
}
void bspline_gram(double *output, double *knots, int nknots,
int m, int dl, int dr){
/* Presumes that the first m and last m knots are to be ignored, i.e.
the interior knots are knots[(m+1):-(m+1)] and the boundary knots are
knots[m] and knots[-m]. In this setting the first basis element of interest
is the 1st not the 0th. Should maybe be fixed? */
double *result;
int l, r, i, j;
int nbasis;
nbasis = nknots - m;
result = output;
for (i=0; i<nbasis; i++) {
for (j=0; j<m; j++) {
l = i;
r = l+j;
*result = bspline_quad(knots, nknots, m, l, r, dl, dr);
result++;
}
}
}
void invband_compute(double *dataptr, double *L, int n, int m) {
/* Note: m is number of bands not including the diagonal so L is of size (m+1)xn */
int i,j,k;
int idx, idy;
double *data, *odata;
double diag;
data = dataptr;
for (i=0; i<n; i++) {
diag = L[i];
data[i] = 1.0 / (diag*diag) ;
for (j=0; j<=m; j++) {
L[j*n+i] /= diag;
if (j > 0) { data[j*n+i] = 0;}
}
}
for (i=n-1; i>=0; i--) {
for (j=1; j <= (m<n-1-i ? m:n-1-i); j++) {
for (k=1; k<=(n-1-i<m ? n-1-i:m); k++) {
idx = (j<k ? k-j:j-k); idy = (j<k ? i+j:i+k);
data[j*n+i] -= L[k*n+i] * data[idx*n+idy];
}
}
for (k=1; k<=(n-1-i<m ? n-1-i:m); k++) {
data[i] -= L[k*n+i] * data[k*n+i];
}
}
return;
}