NAG Library Routine Document

X04DCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: indicates the type of the matrix to be printed

$\mathbf{UPLO}=\text{'L'}$

The matrix is lower triangular. In this case, the packed array A holds the matrix elements in the following order: $\left(1,1\right),\left(2,1\right),\dots ,\left(\mathbf{N},1\right),\left(2,2\right),\left(3,2\right),\dots ,\left(\mathbf{N},2\right)$, etc.

$\mathbf{UPLO}=\text{'U'}$

The matrix is upper triangular. In this case, the packed array A holds the matrix elements in the following order: $\left(1,1\right),\left(1,2\right),\left(2,2\right),\left(1,3\right),\left(2,3\right),\left(3,3\right),\left(1,4\right)$, etc.

Constraint: $\mathbf{UPLO}=\text{'L'}$ or $\text{'U'}$.

2:     DIAG – CHARACTER(1)Input

On entry: indicates whether the diagonal elements of the matrix are to be printed.

$\mathbf{DIAG}=\text{'B'}$

The diagonal elements of the matrix are not referenced and not printed.

$\mathbf{DIAG}=\text{'U'}$

The diagonal elements of the matrix are not referenced, but are assumed all to be unity, and are printed as such.

$\mathbf{DIAG}=\text{'N'}$

The diagonal elements of the matrix are referenced and printed.

Constraint: $\mathbf{DIAG}=\text{'B'}$, $\text{'U'}$ or $\text{'N'}$.

3:     N – INTEGERInput

On entry: the order of the matrix to be printed.

If N is less than $1$, X04DCF will exit immediately after printing TITLE; no row or column labels are printed.

4:     A($*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the dimension of the array A must be at least $\max \left(1,\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$.

On entry: the matrix to be printed. Note that A must have space for the diagonal elements of the matrix, even if these are not stored.

More precisely,

• if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{A}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{A}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

If $\mathbf{DIAG}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{DIAG}=\text{'N'}$ or ‘U’.

5:     TITLE – CHARACTER(*)Input

On entry: a title to be printed above the matrix.

If $\mathbf{TITLE}=\text{' '}$, no title (and no blank line) will be printed.

If TITLE contains more than $80$ characters, the contents of TITLE will be wrapped onto more than one line, with the break after $80$ characters.

Any trailing blank characters in TITLE are ignored.

6:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,

$\mathbf{UPLO}\ne \text{'L'}$ or $\text{'U'}$.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{DIAG}\ne \text{'N'}$, $\text{'U'}$ or $\text{'B'}$.

7  Accuracy

8  Further Comments

NCOLS = 80
INDENT = 0
LABROW = 'I'
LABCOL = 'I'
FORM = ' '
USEFRM = 'A' 

9  Example

9.1  Program Text

Program Text (x04dcfe.f90)

9.2  Program Data

9.3  Program Results

Program Results (x04dcfe.r)