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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_file_print_matrix_complex_band (x04de)

## Purpose

nag_file_print_matrix_complex_band (x04de) is an easy-to-use function to print a complex band matrix stored in a packed two-dimensional array.

## Syntax

[ifail] = x04de(m, n, kl, ku, a, title)
[ifail] = nag_file_print_matrix_complex_band(m, n, kl, ku, a, title)

## Description

nag_file_print_matrix_complex_band (x04de) prints a complex band matrix stored in a packed two-dimensional array. It is an easy-to-use driver for nag_file_print_matrix_complex_band_comp (x04df). The function uses default values for the format in which numbers are printed, for labelling the rows and columns, and for output record length.
nag_file_print_matrix_complex_band (x04de) 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 nag_file_set_unit_advisory (x04ab).

None.

## Parameters

### Compulsory Input Parameters

1:     $\mathrm{m}$int64int32nag_int scalar
2:     $\mathrm{n}$int64int32nag_int scalar
The number of rows and columns of the band matrix, respectively, to be printed.
If either m or n is less than $1$, nag_file_print_matrix_complex_band (x04de) will exit immediately after printing title; no row or column labels are printed.
3:     $\mathrm{kl}$int64int32nag_int scalar
The number of subdiagonals of the band matrix $A$.
Constraint: ${\mathbf{kl}}\ge 0$.
4:     $\mathrm{ku}$int64int32nag_int scalar
The number of superdiagonals of the band matrix $A$.
Constraint: ${\mathbf{ku}}\ge 0$.
5:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex array
The first dimension of the array a must be at least ${\mathbf{kl}}+{\mathbf{ku}}+1$.
The second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{m}}+{\mathbf{ku}},{\mathbf{n}}\right)\right)$.
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:     $\mathrm{title}$ – string
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.

None.

### Output Parameters

1:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

## Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{kl}}<0$.
${\mathbf{ifail}}=2$
 On entry, ${\mathbf{ku}}<0$.
${\mathbf{ifail}}=3$
 On entry, $\mathit{lda}<{\mathbf{kl}}+{\mathbf{ku}}+1$.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

## Accuracy

Not applicable.

A call to nag_file_print_matrix_complex_band (x04de) is equivalent to a call to nag_file_print_matrix_complex_band_comp (x04df) with the following argument values:
```
ncols = 80
indent = 0
labrow = 'I'
labcol = 'I'
form = ' '
usefrm = 'A' ```

## Example

This example program calls nag_file_print_matrix_complex_band (x04de) to print a $5$ by $5$ band matrix with one sub-diagonal and one super-diagonal.
```function x04de_example

fprintf('x04de example results\n\n');

nmax = 5;
b = zeros(nmax,nmax);
for j = 1:nmax
b(j,:) = [1:nmax] + 10*j;
end

a = b - i*b;

% 5x5 tridiagonal matrix
m = int64(nmax);
n = m;
kl = int64(1);
ku = kl;

mtitle = 'Band Matrix:';
[ifail] = x04de( ...
m, n, kl, ku, a, mtitle);

```
```x04de example results

Band Matrix:
1          2          3          4          5
1     21.0000    12.0000
-21.0000   -12.0000

2     31.0000    22.0000    13.0000
-31.0000   -22.0000   -13.0000

3                32.0000    23.0000    14.0000
-32.0000   -23.0000   -14.0000

4                           33.0000    24.0000    15.0000
-33.0000   -24.0000   -15.0000

5                                      34.0000    25.0000
-34.0000   -25.0000
```