2.1.17.5.3 ocmath_1d_spline_evaluate

Description

Evaluates a cubic spline from its B-spline representation.

Syntax

int ocmath_1d_spline_evaluate( double dX, double * pY, ocmath_Spline * spline )

Parameters

dX

[input]the value of the independent variable (abscissa) x

pY

[output]pointer to the value of the dependent variable (ordinate) y

spline

[input] pointer to the structure ocmath_Spline, usually returned by function ocmath_1d_spline_fit

Return

NE_NOERROR (code 0) --- success

NE_INT_ARG_LT (error code 11) --- spline->n < 8

NE_ABSCI_OUTSIDE_KNOT_INTVL (error code 247) --- dX not satisfy spline->lamda[3] <= dX <= spline->lamda[spline->n - 4]

Examples

EX1

//Evaluate at 9 equally-spaced points in the interval [1.0, 9.0] the cubic spline with
//(augmented) knots 1.0, 1.0, 1.0, 1.0, 3.0, 6.0, 8.0, 9.0, 9.0, 9.0, 9.0 and normalised
//cubic B-spline coefficients 1.0, 2.0, 4.0, 7.0, 6.0, 4.0, 3.0.
void ocmath_1d_spline_evaluate_ex1()
{
    double a, b,ncap7;
    int m =9;
    int ncap = 4;
    int r;
    double lamda[11] = {1.00, 1.00, 1.00, 1.00, 3.00, 6.00, 8.00, 9.00, 9.00, 9.00, 9.00};
    double c[11] = {1.00, 2.00, 4.00, 7.00, 6.00, 4.00, 3.00};
    double s;
    double x;
    int i, j;
    ocmath_Spline spline;
    ncap7 = ncap +7;
    spline.n = ncap7;
    spline.lamda = lamda;
    spline.c = c;
    a = spline.lamda[3];
    printf("a = %f\n",a);
    b = spline.lamda[ncap+3];
    printf("b = %f\n",b);
    printf("Augmented set of knots stored in spline.lamda:\n");
    for(j = 0; j < ncap7-1; j++)
        printf("%10.4f",lamda[j]);
    printf("\nB-spline coefficients stored in spline.c\n\n");
    for(j = 0; j< ncap+3; j++)
        printf("%10.4f",c[j]);
    printf("\n x Value of cubic spline\n\n");
    for (r=1; r<=m; ++r)
    {
        x = 1.0*((m-r) * a + (r-1) * b) /(m-1);
        s= 0;
         ocmath_1d_spline_evaluate(x, &s, &spline);
        printf("%10.4f%15.4f\n",x,s);
    }
}
//The output:
//a = 1.000000
//b = 9.000000
//Augmented set of knots stored in spline.lamda:
//    1.0000    1.0000    1.0000    1.0000    3.0000    6.0000    8.0000    9.0000    9.0000    9.0000
//B-spline coefficients stored in spline.c
//     1.0000    2.0000    4.0000    7.0000    6.0000    4.0000    3.0000
//x Value of cubic spline

//       1.0000         1.0000
//    2.0000         2.3779
//    3.0000         3.6229
//    4.0000         4.8327
//    5.0000         5.8273
//    6.0000         6.3571
//    7.0000         6.1905
//    8.0000         5.1667
//    9.0000         3.0000

Remark

See Also

ocmath_2d_spline_eval

Header to Include

origin.h

Reference

nag_1d_spline_evaluate(e02bbc)nag_1d_spline_evaluate(e02bbc), NAG Manual