NAG CL Interface
e01bgc (dim1_monotonic_deriv)

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NAG Library Manual, Mark 30

Interfaces: FL CL CPP AD PY MB

NAG CL Interface Introduction

E01 (Interp) Chapter Contents

E01 (Interp) Chapter Introduction

e01bg: FL CL CPP AD PY MB

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

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Short (a00aac)
Long (impl_details)
Full (nag_info_impl_details)

1 Purpose

e01bgc evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points.

2 Specification

#include <nag.h>

void	e01bgc (Integer n, const double x[], const double f[], const double d[], Integer m, const double px[], double pf[], double pd[], NagError *fail)

The function may be called by the names: e01bgc, nag_interp_dim1_monotonic_deriv or nag_monotonic_deriv.

3 Description

e01bgc evaluates a piecewise cubic Hermite interpolant, as computed by the NAG function e01bec, at the points

px [i]

, for

i = 0, 1, \dots, m - 1

. The first derivatives at the points are also computed. If any point lies outside the interval from

x [0]

x [n - 1]

, values of the interpolant and its derivative are extrapolated from the nearest extreme cubic, and a warning is returned.

If values of the interpolant only, and not of its derivative, are required, e01bfc should be used.

The function is derived from routine PCHFD in Fritsch (1982).

4 References

Fritsch F N (1982) PCHIP final specifications Report UCID-30194 Lawrence Livermore National Laboratory

5 Arguments

1: $n$ – Integer Input: On entry: n must be unchanged from the previous call of e01bec.
2: $x [n]$ – const double Input
3: $f [n]$ – const double Input
4: $d [n]$ – const double Input: On entry: x, f and d must be unchanged from the previous call of e01bec.
5: $m$ – Integer Input: On entry: $m$ , the number of points at which the interpolant is to be evaluated.

Constraint: $m \geq 1$ .
6: $px [m]$ – const double Input: On entry: the $m$ values of $x$ at which the interpolant is to be evaluated.
7: $pf [m]$ – double Output: On exit: $pf [i]$ contains the value of the interpolant evaluated at the point $px [i]$ , for $i = 0, 1, \dots, m - 1$ .
8: $pd [m]$ – double Output: On exit: $pd [i]$ contains the first derivative of the interpolant evaluated at the point $px [i]$ , for $i = 0, 1, \dots, m - 1$ .
9: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_INT_ARG_LT: On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 1$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 2$ .
NE_NOT_MONOTONIC: On entry, $x [r - 1] \geq x [r]$ for $r = ⟨ value ⟩$ : $x [r - 1] = ⟨ value ⟩$ , $x [r] = ⟨ value ⟩$ .
The values of $x [r]$ , for $r = 0, 1, \dots, n - 1$ , are not in strictly increasing order.
NW_EXTRAPOLATE: Warning – some points in array px lie outside the range $x [0] \dots x [n - 1]$ . Values at these points are unreliable as they have been computed by extrapolation.

7 Accuracy

The computational errors in the arrays pf and pd should be negligible in most practical situations.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

e01bgc is not threaded in any implementation.

9 Further Comments

The time taken by e01bgc is approximately proportional to the number of evaluation points,

m

. The evaluation will be most efficient if the elements of px are in nondecreasing order (or, more generally, if they are grouped in increasing order of the intervals

[x [r - 1], x [r]]

). A single call of e01bgc with

m > 1

is more efficient than several calls with

m = 1

10 Example

This example program reads in values of n, x, f and d and calls e01bgc to compute the values of the interpolant and its derivative at equally spaced points.

NAG CL Interfacee01bgc (dim1_​monotonic_​deriv)