NAG Library Routine Document

e02bdf (dim1_spline_integ)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{ncap7}$ – IntegerInput

On entry: $\stackrel{-}{n}+7$, where $\stackrel{-}{n}$ is the number of intervals of the spline (which is one greater than the number of interior knots, i.e., the knots strictly within the range $a$ to $b$) over which the spline is defined.

Constraint: $\mathbf{ncap7}\ge 8$.

2:     $\mathbf{lamda}\left(\mathbf{ncap7}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{lamda}\left(\mathit{j}\right)$ must be set to the value of the $\mathit{j}$th member of the complete set of knots, ${\lambda }_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,\stackrel{-}{n}+7$.

Constraint: the $\mathbf{lamda}\left(j\right)$ must be in nondecreasing order with $$\begin{gathered} \mathbf{lamda}\left(\mathbf{ncap7}-3\right)> \\ \mathbf{lamda}\left(4\right) \end{gathered}$$ and satisfy $\mathbf{lamda}\left(1\right)=\mathbf{lamda}\left(2\right)=\mathbf{lamda}\left(3\right)=\mathbf{lamda}\left(4\right)$ and $$\begin{gathered} \mathbf{lamda}\left(\mathbf{ncap7}-3\right)=\mathbf{lamda}\left(\mathbf{ncap7}-2\right)= \\ \mathbf{lamda}\left(\mathbf{ncap7}-1\right)=\mathbf{lamda}\left(\mathbf{ncap7}\right) \end{gathered}$$.

3:     $\mathbf{c}\left(\mathbf{ncap7}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the coefficient $c_{\mathit{i}}$ of the B-spline $N_{\mathit{i}}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\stackrel{-}{n}+3$. The remaining elements of the array are not referenced.

4:     $\mathbf{dint}$ – Real (Kind=nag_wp)Output

On exit: the value of the definite integral of $s\left(x\right)$ between the limits $x=a$ and $x=b$, where $a={\lambda }_4$ and $b={\lambda }_{\stackrel{-}{n}+4}$.

5:     $\mathbf{ifail}$ – 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, $\mathbf{ncap7}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ncap7}\ge 8$.

$\mathbf{ifail}=2$

On entry, $J=〈\mathit{\text{value}}〉$, $\mathbf{lamda}\left(J\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(J-1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(J\right)\ge \mathbf{lamda}\left(J-1\right)$.

On entry, $\mathbf{lamda}\left(1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(2\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(1\right)=\mathbf{lamda}\left(2\right)$.

On entry, $\mathbf{lamda}\left(2\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(3\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(2\right)=\mathbf{lamda}\left(3\right)$.

On entry, $\mathbf{lamda}\left(3\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(4\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(3\right)=\mathbf{lamda}\left(4\right)$.

On entry, $\mathbf{lamda}\left(4\right)=〈\mathit{\text{value}}〉$, $\mathrm{NCAP4}=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(\mathrm{NCAP4}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(4\right)<\mathbf{lamda}\left(\mathrm{NCAP4}\right)$.

On entry, $\mathbf{ncap7}=〈\mathit{\text{value}}〉$, $\mathbf{lamda}\left(\mathbf{ncap7}-1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(\mathbf{ncap7}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(\mathbf{ncap7}-1\right)=\mathbf{lamda}\left(\mathbf{ncap7}\right)$.

On entry, $\mathbf{ncap7}=〈\mathit{\text{value}}〉$, $\mathbf{lamda}\left(\mathbf{ncap7}-2\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(\mathbf{ncap7}-1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(\mathbf{ncap7}-2\right)=\mathbf{lamda}\left(\mathbf{ncap7}-1\right)$.

On entry, $\mathbf{ncap7}=〈\mathit{\text{value}}〉$, $\mathbf{lamda}\left(\mathbf{ncap7}-3\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(\mathbf{ncap7}-3\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(\mathbf{ncap7}-3\right)=\mathbf{lamda}\left(\mathbf{ncap7}-2\right)$.

$\mathbf{ifail}=-99$

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 (e02bdfe.f90)

10.2

Program Data

Program Data (e02bdfe.d)

10.3

Program Results

Program Results (e02bdfe.r)