NAG Library Function Document

nag_monotonic_intg (e01bhc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: n must be unchanged from the previous call of nag_monotonic_interpolant (e01bec).

2:    $\mathbf{x}\left[\mathbf{n}\right]$ – const doubleInput

3:    $\mathbf{f}\left[\mathbf{n}\right]$ – const doubleInput

4:    $\mathbf{d}\left[\mathbf{n}\right]$ – const doubleInput

On entry: x, f and d must be unchanged from the previous call of nag_monotonic_interpolant (e01bec).

5:    $\mathbf{a}$ – doubleInput

6:    $\mathbf{b}$ – doubleInput

On entry: the interval $\left[a,b\right]$ over which integration is to be performed.

7:    $\mathbf{integral}$ – double *Output

On exit: the value of the definite integral of the interpolant over the interval $\left[a,b\right]$.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_INT_ARG_LT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

NE_NOT_MONOTONIC

On entry, $\mathbf{x}\left[r-1\right]\ge \mathbf{x}\left[r\right]$ for $r=〈\mathit{\text{value}}〉$ : $\mathbf{x}\left[r-1\right]=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[r\right]=〈\mathit{\text{value}}〉$.
The values of $\mathbf{x}\left[\mathit{r}\right]$, for $\mathit{r}=0,1,\dots ,n-1$, are not in strictly increasing order.

NW_INTERVAL_EXTRAPOLATE

On entry, limits a, b must not be outside interval $\left[\mathbf{x}\left[0\right],\mathbf{x}\left[n-1\right]\right]$, $\mathbf{a}=〈\mathit{\text{value}}〉$, $\mathbf{b}=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[0\right]=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$. Extrapolation was performed to compute the integral. The value returned is therefore unreliable.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e01bhce.c)

10.2

Program Data

Program Data (e01bhce.d)

10.3

Program Results

Program Results (e01bhce.r)