nag_monotonic_intg (e01bhc) (PDF version)
e01 Chapter Contents
e01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_monotonic_intg (e01bhc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_monotonic_intg (e01bhc) evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval a,b .

2  Specification

#include <nag.h>
#include <nage01.h>
void  nag_monotonic_intg (Integer n, const double x[], const double f[], const double d[], double a, double b, double *integral, NagError *fail)

3  Description

nag_monotonic_intg (e01bhc) evaluates the definite integral of a piecewise cubic Hermite interpolant, as computed by nag_monotonic_interpolant (e01bec), over the interval a,b .
If either a  or b  lies outside the interval from x[0]  to x[n-1] , computation of the integral involves extrapolation and a warning is returned.
The function is derived from routine PCHIA in Fritsch (1982).

4  References

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

5  Arguments

1:     nIntegerInput
On entry: n must be unchanged from the previous call of nag_monotonic_interpolant (e01bec).
2:     x[n]const doubleInput
3:     f[n]const doubleInput
4:     d[n]const doubleInput
On entry: x, f and d must be unchanged from the previous call of nag_monotonic_interpolant (e01bec).
5:     adoubleInput
6:     bdoubleInput
On entry: the interval a,b  over which integration is to be performed.
7:     integraldouble *Output
On exit: the value of the definite integral of the interpolant over the interval a,b .
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_INT_ARG_LT
On entry, n=value.
Constraint: n2.
NE_NOT_MONOTONIC
On entry, x[r-1] x[r]  for r=value  : x[r-1] = value, x[r] = value.
The values of x[r] , for r=0,1,,n - 1, are not in strictly increasing order.
NW_INTERVAL_EXTRAPOLATE
On entry, limits a, b must not be outside interval x[0],x[n-1] , a=value , b=value , x[0] = value, x[value] = value. Extrapolation was performed to compute the integral. The value returned is therefore unreliable.

7  Accuracy

The computational error in the value returned for integral should be negligible in most practical situations.

8  Further Comments

The time taken by nag_monotonic_intg (e01bhc) is approximately proportional to the number of data points included within the interval a,b .

9  Example

This example program reads in values of n, x, f and d. It then reads in pairs of values for a and b, and evaluates the definite integral of the interpolant over the interval a,b  until end-of-file is reached.

9.1  Program Text

Program Text (e01bhce.c)

9.2  Program Data

Program Data (e01bhce.d)

9.3  Program Results

Program Results (e01bhce.r)


nag_monotonic_intg (e01bhc) (PDF version)
e01 Chapter Contents
e01 Chapter Introduction
NAG C Library Manual

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