nag_ode_bvp_ps_lin_grid_vals (d02uwc) (PDF version)
d02 Chapter Contents
d02 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_ode_bvp_ps_lin_grid_vals (d02uwc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ode_bvp_ps_lin_grid_vals (d02uwc) interpolates from a set of function values on a supplied grid onto a set of values for a uniform grid on the same range. The interpolation is performed using barycentric Lagrange interpolation. nag_ode_bvp_ps_lin_grid_vals (d02uwc) is primarily a utility function to map a set of function values specified on a Chebyshev Gauss–Lobatto grid onto a uniform grid.

2  Specification

#include <nag.h>
#include <nagd02.h>
void  nag_ode_bvp_ps_lin_grid_vals (Integer n, Integer nip, const double x[], const double f[], double xip[], double fip[], NagError *fail)

3  Description

nag_ode_bvp_ps_lin_grid_vals (d02uwc) interpolates from a set of n+1 function values, fxi, on a supplied grid, xi, for i=0,1,,n, onto a set of m values, f^x^j, on a uniform grid, x^j, for j=1,2,,m. The image x^ has the same range as x, so that x^j = xmin + j-1 / m-1 × xmax - xmin , for j=1,2,,m. The interpolation is performed using barycentric Lagrange interpolation as described in Berrut and Trefethen (2004).
nag_ode_bvp_ps_lin_grid_vals (d02uwc) is primarily a utility function to map a set of function values specified on a Chebyshev Gauss–Lobatto grid computed by nag_ode_bvp_ps_lin_cgl_grid (d02ucc) onto an evenly-spaced grid with the same range as the original grid.

4  References

Berrut J P and Trefethen L N (2004) Barycentric lagrange interpolation SIAM Rev. 46(3) 501–517

5  Arguments

1:     nIntegerInput
On entry: n, where the number of grid points for the input data is n+1.
Constraint: n>0 and n is even.
2:     nipIntegerInput
On entry: the number, m, of grid points in the uniform mesh x^ onto which function values are interpolated. If nip=1 then on successful exit from nag_ode_bvp_ps_lin_grid_vals (d02uwc), fip[0] will contain the value fxn.
Constraint: nip>0.
3:     x[n+1]const doubleInput
On entry: the grid points, xi, for i=0,1,,n, at which the function is specified.
Usually this should be the array of Chebyshev Gauss–Lobatto points returned in nag_ode_bvp_ps_lin_cgl_grid (d02ucc).
4:     f[n+1]const doubleInput
On entry: the function values, fxi, for i=0,1,,n.
5:     xip[nip]doubleOutput
On exit: the evenly-spaced grid points, x^j, for j=1,2,,m.
6:     fip[nip]doubleOutput
On exit: the set of interpolated values f^x^j, for j=1,2,,m. Here f^x^jfx=x^j.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n>0.
On entry, n=value.
Constraint: n is even.
On entry, nip=value.
Constraint: nip>0.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

nag_ode_bvp_ps_lin_grid_vals (d02uwc) is intended, primarily, for use with Chebyshev Gauss–Lobatto input grids. For such input grids and for well-behaved functions (no discontinuities, peaks or cusps), the accuracy should be a small multiple of machine precision.

8  Further Comments

None.

9  Example

This example interpolates the function x+cos5x, as specified on a 65-point Gauss–Lobatto grid on -1,1, onto a coarse uniform grid.

9.1  Program Text

Program Text (d02uwce.c)

9.2  Program Data

Program Data (d02uwce.d)

9.3  Program Results

Program Results (d02uwce.r)


nag_ode_bvp_ps_lin_grid_vals (d02uwc) (PDF version)
d02 Chapter Contents
d02 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012