NAG FL Interface
d02uwf (bvp_​ps_​lin_​grid_​vals)

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1 Purpose

d02uwf 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. d02uwf is primarily a utility routine to map a set of function values specified on a Chebyshev Gauss–Lobatto grid onto a uniform grid.

2 Specification

Fortran Interface
Subroutine d02uwf ( n, nip, x, f, xip, fip, ifail)
Integer, Intent (In) :: n, nip
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x(n+1), f(n+1)
Real (Kind=nag_wp), Intent (Out) :: xip(nip), fip(nip)
C Header Interface
#include <nag.h>
void  d02uwf_ (const Integer *n, const Integer *nip, const double x[], const double f[], double xip[], double fip[], Integer *ifail)
The routine may be called by the names d02uwf or nagf_ode_bvp_ps_lin_grid_vals.

3 Description

d02uwf interpolates from a set of n+1 function values, f(xi), 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).
d02uwf is primarily a utility routine to map a set of function values specified on a Chebyshev Gauss–Lobatto grid computed by d02ucf 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: n Integer Input
On entry: n, where the number of grid points for the input data is n+1.
Constraint: n>0 and n is even.
2: nip Integer Input
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 d02uwf, fip(1) will contain the value f(xn).
Constraint: nip>0.
3: x(n+1) Real (Kind=nag_wp) array Input
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 d02ucf.
4: f(n+1) Real (Kind=nag_wp) array Input
On entry: the function values, f(xi), for i=0,1,,n.
5: xip(nip) Real (Kind=nag_wp) array Output
On exit: the evenly-spaced grid points, x^j, for j=1,2,,m.
6: fip(nip) Real (Kind=nag_wp) array Output
On exit: the set of interpolated values f^(x^j), for j=1,2,,m. Here f^(x^j)f(x=x^j).
7: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
ifail=1
On entry, n=value.
Constraint: n>0.
On entry, n=value.
Constraint: n is even.
ifail=2
On entry, nip=value.
Constraint: nip>0.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

d02uwf 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 Parallelism and Performance

d02uwf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example interpolates the function x+cos(5x), as specified on a 65-point Gauss–Lobatto grid on [−1,1], onto a coarse uniform grid.

10.1 Program Text

Program Text (d02uwfe.f90)

10.2 Program Data

Program Data (d02uwfe.d)

10.3 Program Results

Program Results (d02uwfe.r)