int
test_cspline_sin(void)
{
cspline * c = cspline_new(9, 1024);
mfp_block * in = mfp_block_new(1024);
mfp_block * out = mfp_block_new(1024);
int x;
int fail = 0;
cspline_init(c, 0.0, 2.0*M_PI, sin_coeffs);
for(x = 0; x < 1024; x++) {
in->data[x] = (float)x * 2.0*M_PI/1024.0;
}
cspline_block_eval(c, in, out);
for(x = 0; x < 1024; x++) {
if (fabs(out->data[x] - sin(in->data[x])) > 0.01) {
fail = 1;
printf("index=%d x=%f expected=%f got=%f\n", x, in->data[x], sin(in->data[x]), out->data[x]);
}
}
if (fail)
return 0;
return 1;
}
int
benchmark_cspline_sin(void)
{
struct timeval start, end;
float naive, fast;
cspline * c = cspline_new(9, 1024);
mfp_block * in = mfp_block_new(1024);
mfp_block * out = mfp_block_new(1024);
int x;
int fail = 0;
cspline_init(c, 0.0, 2.0*M_PI, sin_coeffs);
for(x = 0; x < 1024; x++) {
in->data[x] = (float)x * 2.0*M_PI/1024.0;
}
gettimeofday(&start, NULL);
for(x = 0; x < 1024; x++) {
cspline_block_eval(c, in, out);
}
gettimeofday(&end, NULL);
fast = (end.tv_sec + end.tv_usec/1000000.0) - (start.tv_sec + start.tv_usec / 1000000.0);
gettimeofday(&start, NULL);
for(x = 0; x < 1024; x++) {
naive_block_sin(in, out);
}
gettimeofday(&end, NULL);
naive = (end.tv_sec + end.tv_usec/1000000.0) - (start.tv_sec + start.tv_usec / 1000000.0);
printf("\n Naive: %f, fast: %f\n", naive, fast);
return 1;
}
int
test_cspline_create(void)
{
cspline * c = cspline_new(4, 8);
mfp_block * in = mfp_block_new(8);
mfp_block * out = mfp_block_new(8);
int i;
int fail = 0;
float coeff_1[] = { 1.0, 0.0, 0.0, 0.0,
2.0, 0.0, 0.0, 0.0,
3.0, 0.0, 0.0, 0.0,
4.0, 0.0, 0.0, 0.0 };
float answers_1[] = { 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0 };
float coeff_2[] = { 0.0, 1.0, 0.0, 0.0,
0.0, 2.0, 0.0, 0.0,
0.0, 3.0, 0.0, 0.0,
0.0, 4.0, 0.0, 0.0 };
float answers_2[] = { 0.0, 0.25, 1.0, 1.50, 3.0, 3.75, 6.0, 7.0 };
if((c == NULL) || (c->num_segments != 4))
return 0;
cspline_init(c, 0.0, 2.0, coeff_1);
for (i=0; i<8; i++) {
in->data[i] = (float)i / 4.0;
}
cspline_block_eval(c, in, out);
for (i=0; i<8; i++) {
if (out->data[i] != answers_1[i]) {
printf("err %d %f %f\n", i, out->data[i], answers_1[i]);
fail = 1;
}
}
cspline_init(c, 0.0, 2.0, coeff_2);
for (i=0; i<8; i++) {
in->data[i] = (float)i / 4.0;
}
cspline_block_eval(c, in, out);
for (i=0; i<8; i++) {
if (out->data[i] != answers_2[i]) {
printf("err (2) %d %f %f\n", i, out->data[i], answers_1[i]);
fail = 1;
}
}
if (fail)
return 0;
return 1;
}
int main(int argc, char *argv[]){
// Number of points to be fitted with a given spline
int dim = 10;
// Number of points for the fitted graph
int steps = 100;
// Allocate memory for a vector x with all the x-coordinates
double *x1 = malloc(dim*sizeof(double));
double *x2 = malloc(dim*sizeof(double));
// Allocate memory for a vector y with all the y-coordinates
double *y1 = malloc(dim*sizeof(double));
double *y2 = malloc(dim*sizeof(double));
// Allocation for the points (z,s) for the interpolant
double z,s;
// Allocation of step variables
double x0, xn, h;
/*
* A. (6 points) Linear and quadratic splines
*/
// Input n points for the interpolation
printf("# x y (points)\n");
for(int i = 0; i < dim; i++){
x1[i] = i + 0.5*sin(i);
y1[i] = i + cos(i*i);
printf(" %2.6f %2.6f \n",x1[i],y1[i]);
}
// Calculate m points for the interpolants
x0 = x1[0];
xn = x1[dim-1];
h = (xn - x0)/steps;
// Linear spline interpolation
s=0;
z=0;
printf("\n\n"); //New block (Gnuplot)
printf("# x y (liner spline interpolation)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = linterp(z,x1,y1,dim);
printf(" %2.6f %2.6f \n", z, s);
}
// Quadratic spline interpolation
s=0;
z=0;
qspline *qs = qspline_new(dim,x1,y1);
printf("\n\n"); //New block (Gnuplot)
printf("# x y (quadratic spline interpolation)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = qspline_get(qs,z);
printf(" %2.6f %2.6f \n", z, s);
}
/*
* B. (3 points) derivatives and integrals with quadratic spline
*/
//Input for the derivatives and integrals
fprintf(stderr, "# x y (points)\n");
for(int i = 0 ;i<dim; i++){
x2[i] = i*2*PI/(dim-1);
y2[i] = sin(x2[i]);
fprintf(stderr," %2.6f %2.6f \n", x2[i], y2[i]);
}
x0 = x2[0];
xn = x2[dim-1];
h = (xn - x0)/steps;
// Quadratic spline interpolation
s=0;
z=0;
qs = qspline_new(dim,x2,y2);
fprintf(stderr, "\n\n"); //New block (Gnuplot)
fprintf(stderr, "# x y (quadratic spline interpolation)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = qspline_get(qs, z);
fprintf(stderr, " %2.6f %2.6f \n", z, s);
}
// Derivative of the quadratic spline interpolation
fprintf(stderr, "\n\n"); //New block (Gnuplot)
fprintf(stderr, "# x y (derivative of the quadratic spline)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = qspline_deriv(qs, z);
fprintf(stderr," %2.6f %2.6f \n", z, s);
}
// Integration the quadratic spline interpolation
fprintf(stderr, "\n\n"); //New block (Gnuplot)
fprintf(stderr, "# x y (integration of the quadratic spline)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = qspline_int(qs, z);
fprintf(stderr," %2.6f %2.6f \n", z, s);
}
/*
* C. (1 point) Derivatives and integrals with cubic spline
*/
// Cubic spline interpolation with x and y values from A.
s=0;
z=0;
x0 = x1[0];
xn = x1[dim-1];
h = (xn - x0)/steps;
cspline* cs = cspline_new(dim,x1,y1);
fprintf(stdout, "\n\n"); //New block (Gnuplot)
fprintf(stdout, "# x y (cubic spline interpolation)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = cspline_get(cs, z);
fprintf(stdout," %2.6f %2.6f \n", z, s);
}
// Derivative of the cubic spline interpolation with x,y values from B.
s=0;
z=0;
x0 = x2[0];
xn = x2[dim-1];
h = (xn - x0)/steps;
cs = cspline_new(dim,x2,y2);
fprintf(stderr, "\n\n"); //New block (Gnuplot)
fprintf(stderr, "# x y (derivative of the cubic spline)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = cspline_deriv(cs, z);
fprintf(stderr," %2.6f %2.6f \n", z, s);
}
// Integration of the cubic spline interpolation with x,y values from B.
fprintf(stderr, "\n\n"); //New block (Gnuplot)
fprintf(stderr, "# x y (derivative of the cubic spline)\n");
for(int i = 0; i < steps; i++){
z = x0 + h*i;
s = cspline_int(cs, z);
fprintf(stderr," %2.6f %2.6f \n", z, s);
}
// Free memory
qspline_free(qs);
cspline_free(cs);
free(x1);
free(x2);
free(y1);
free(y2);
fclose(stdout);
fclose(stderr);
return 0;
}
