# NAG Library Routine Document

## 1Purpose

x04def is an easy-to-use routine to print a complex band matrix stored in a packed two-dimensional array.

## 2Specification

Fortran Interface
 Subroutine x04def ( m, n, kl, ku, a, lda,
 Integer, Intent (In) :: m, n, kl, ku, lda Integer, Intent (Inout) :: ifail Complex (Kind=nag_wp), Intent (In) :: a(lda,*) Character (*), Intent (In) :: title
C Header Interface
#include <nagmk26.h>
 void x04def_ (const Integer *m, const Integer *n, const Integer *kl, const Integer *ku, const Complex a[], const Integer *lda, const char *title, Integer *ifail, const Charlen length_title)

## 3Description

x04def prints a complex band matrix stored in a packed two-dimensional array. It is an easy-to-use driver for x04dff. The routine uses default values for the format in which numbers are printed, for labelling the rows and columns, and for output record length.
x04def will choose a format code such that numbers will be printed with an $\mathrm{F}8.4$, an $\mathrm{F}11.4$ or a $1\mathrm{PE}13.4$ format. The $\mathrm{F}8.4$ code is chosen if the sizes of all the matrix elements to be printed lie between $0.001$ and $1.0$. The $\mathrm{F}11.4$ code is chosen if the sizes of all the matrix elements to be printed lie between $0.001$ and $9999.9999$. Otherwise the $1\mathrm{PE}13.4$ code is chosen. The chosen code is used to print each complex element of the matrix with the real part above the imaginary part.
The matrix is printed with integer row and column labels, and with a maximum record length of $80$.
The matrix is output to the unit defined by x04abf.

None.

## 5Arguments

1:     $\mathbf{m}$ – IntegerInput
2:     $\mathbf{n}$ – IntegerInput
On entry: the number of rows and columns of the band matrix, respectively, to be printed.
If either m or n is less than $1$, x04def will exit immediately after printing title; no row or column labels are printed.
3:     $\mathbf{kl}$ – IntegerInput
On entry: the number of subdiagonals of the band matrix $A$.
Constraint: ${\mathbf{kl}}\ge 0$.
4:     $\mathbf{ku}$ – IntegerInput
On entry: the number of superdiagonals of the band matrix $A$.
Constraint: ${\mathbf{ku}}\ge 0$.
5:     $\mathbf{a}\left({\mathbf{lda}},*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{m}}+{\mathbf{ku}},{\mathbf{n}}\right)\right)$.
On entry: the band matrix to be printed.
The matrix is stored in rows $1$ to ${k}_{l}+{k}_{u}+1$, more precisely, the element ${A}_{ij}$ must be stored in
 $aku+1+i-jj for ​max1,j-ku≤i≤minm,j+kl.$
6:     $\mathbf{lda}$ – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which x04def is called.
Constraint: ${\mathbf{lda}}\ge {\mathbf{kl}}+{\mathbf{ku}}+1$.
7:     $\mathbf{title}$ – Character(*)Input
On entry: a title to be printed above the matrix.
If , 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.
8:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, . 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  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  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).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{kl}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{kl}}\ge 0$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{ku}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{ku}}\ge 0$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{lda}}<{\mathbf{kl}}+{\mathbf{ku}}+1$: ${\mathbf{lda}}=〈\mathit{\text{value}}〉$, ${\mathbf{kl}}=〈\mathit{\text{value}}〉$, ${\mathbf{ku}}=〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=-99$
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.

Not applicable.

## 8Parallelism and Performance

x04def is not threaded in any implementation.

## 9Further Comments

A call to x04def is equivalent to a call to x04dff with the following argument values:
```
NCOLS = 80
INDENT = 0
LABROW = 'I'
LABCOL = 'I'
FORM = ' '
USEFRM = 'A' ```

## 10Example

This example program calls x04def to print a $5$ by $5$ band matrix with one subdiagonal and one superdiagonal.

### 10.1Program Text

Program Text (x04defe.f90)

None.

### 10.3Program Results

Program Results (x04defe.r)