NAG Library Routine Document

d01tdf  (dim1_gauss_wrec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of Gauss points required. The resulting quadrature rule will be exact for all polynomials of degree $2n-1$.

Constraint: $\mathbf{n}>0$.

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

On entry: a contains the coefficients $a\left(j\right)$.

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

On entry: b contains the coefficients $b\left(j\right)$.

On exit: elements of b are altered to make the underlying eigenvalue problem symmetric.

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

On entry: c contains the coefficients $c\left(j\right)$.

On exit: elements of c are altered to make the underlying eigenvalue problem symmetric.

5:     $\mathbf{muzero}$ – Real (Kind=nag_wp)Input

On entry: muzero contains the definite integral of the weight function for the interval of interest.

6:     $\mathbf{weight}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{weight}\left(j\right)$ contains the weight corresponding to the $j$th abscissa.

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

On exit: $\mathbf{abscis}\left(j\right)$ the $j$th abscissa.

8:     $\mathbf{ifail}$ – 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

$\mathbf{ifail}=1$

The number of weights and abscissae requested (n) is less than $1$: $\mathbf{n}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=4$

Unexpected failure in eigenvalue computation. Please contact NAG.

$\mathbf{ifail}=5$

The algorithm failed to converge. The $i$th diagonal was not zero: $i=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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 (d01tdfe.f90)

10.2

Program Data

10.3

Program Results

Program Results (d01tdfe.r)