[Help-gsl] b-spline evaluation

[Iryna Feuerstein]

Hello,

I've tried to construct b-splines and evaluate them on the uniform 
knots. I become always the same error on the margins of the interval, 
over which the b-splines where constructed.

Here my code:

#include <iostream>
#include <gsl/gsl_bspline.h>

int main()
{
    // allocate workspace for 5 cubic b-spline functions
    gsl_bspline_workspace * w = gsl_bspline_alloc(4, 5);
    // construct five uniform knots {0, 1, 2, 3, 4}
    gsl_bspline_knots_uniform(0, 4, w);
    // allocate vector to save the b-spline values
    // the size of the vector is in this case 7
    gsl_vector * values = gsl_vector_alloc(gsl_bspline_ncoeffs(w));

    // evaluate all of the created b-splines at the point x = 0
    gsl_bspline_eval(0, values, w);
    std::cout << "x = 0, values: ";
    for (std::size_t i = 0; i < values->size; i++)
        std::cout << gsl_vector_get(values, i) << " ";
    std::cout << std::endl;

    // evaluate all of the created b-splines at the point x = 1
    gsl_bspline_eval(1, values, w);
    std::cout << "x = 1, values: ";
    for (std::size_t i = 0; i < values->size; i++)
        std::cout << gsl_vector_get(values, i) << " ";
    std::cout << std::endl;

    // evaluate all of the created b-splines at the point x = 2
    gsl_bspline_eval(2, values, w);
    std::cout << "x = 2, values: ";
    for (std::size_t i = 0; i < values->size; i++)
        std::cout << gsl_vector_get(values, i) << " ";
    std::cout << std::endl;

    // evaluate all of the created b-splines at the point x = 3
    gsl_bspline_eval(3, values, w);
    std::cout << "x = 3, values: ";
    for (std::size_t i = 0; i < values->size; i++)
        std::cout << gsl_vector_get(values, i) << " ";
    std::cout << std::endl;

    // evaluate all of the created b-splines at the point x = 4
    gsl_bspline_eval(4, values, w);
    std::cout << "x = 4, values: ";
    for (std::size_t i = 0; i < values->size; i++)
        std::cout << gsl_vector_get(values, i) << " ";
    std::cout << std::endl;
}

The output of the program should be:
x = 0, values: 0,166667  0,666667  0,166667  0  0  0  0
x = 1, values: 0  0,166667  0,666667  0,166667  0  0  0
x = 2, values: 0  0  0,166667  0,666667  0,166667  0  0
x = 3, values: 0  0  0  0,166667  0,666667  0,166667  0
x = 4, values: 0  0  0  0  0,166667  0,666667  0,166667

But I get:
x = 0, values: 1  0        0                0                
0                 0       0
x = 1, values: 0  0,25  0,583333  0,166667  0                 0       0
x = 2, values: 0  0        0,166667  0,666667  0,166667  0       0
x = 3, values: 0  0        0                0,166667  0,583333  0,25  0
x = 4, values: 0  0        0                0                 
0                0        1

By construction of a workspace with more b-splines (over larger 
intervals), I get the same error. The values at both first and last 
knots are not calculated properly. Does anybody know the reason of this 
mistake?

Best regards,
Iryna.