NAG Library Routine Document

e01bgf (dim1_monotonic_deriv)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

2:     $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

3:     $\mathbf{f}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

4:     $\mathbf{d}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: n, x, f and d must be unchanged from the previous call of e01bef.

5:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of points at which the interpolant is to be evaluated.

Constraint: $\mathbf{m}\ge 1$.

6:     $\mathbf{px}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the $m$ values of $x$ at which the interpolant is to be evaluated.

7:     $\mathbf{pf}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{pf}\left(\mathit{i}\right)$ contains the value of the interpolant evaluated at the point $\mathbf{px}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,m$.

8:     $\mathbf{pd}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{pd}\left(\mathit{i}\right)$ contains the first derivative of the interpolant evaluated at the point $\mathbf{px}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,m$.

9:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

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

$\mathbf{ifail}=2$

On entry, $r=〈\mathit{\text{value}}〉$, $\mathbf{x}\left(r-1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left(r\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left(r-1\right)<\mathbf{x}\left(r\right)$ for all $r$.

$\mathbf{ifail}=3$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

$\mathbf{ifail}=4$

Warning – some points in array px lie outside the range $\mathbf{x}\left(1\right)\cdots \mathbf{x}\left(\mathbf{n}\right)$. Values at these points are unreliable because computed by extrapolation.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e01bgfe.f90)

10.2

Program Data

Program Data (e01bgfe.d)

10.3

Program Results

Program Results (e01bgfe.r)