NAG FL Interface
e02bdf (dim1_​spline_​integ)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{ncap7}$ – Integer Input

On entry: $\overline{n}+7$, where $\overline{n}$ 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) array Input

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 $\mathit{j}=1,2,\dots ,\overline{n}+7$.

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) array Input

On entry: the coefficient $c_{\mathit{i}}$ of the B-spline $N_{\mathit{i}}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\overline{n}+3$. 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 $b={\lambda }_{\overline{n}+4}$.

5: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results