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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 F8.4$\mathrm{F}8.4$, an F11.4$\mathrm{F}11.4$ or a 1PE13.4$1\mathrm{PE}13.4$ format. The F8.4$\mathrm{F}8.4$ code is chosen if the sizes of all the matrix elements to be printed lie between 0.001$0.001$ and 1.0$1.0$. The F11.4$\mathrm{F}11.4$ code is chosen if the sizes of all the matrix elements to be printed lie between 0.001$0.001$ and 9999.9999$9999.9999$. Otherwise the 1PE13.4$1\mathrm{PE}13.4$ 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$80$.
The matrix is output to the unit defined by nag_file_set_unit_advisory (x04ab).

None.

Parameters

Compulsory Input Parameters

1:     m – int64int32nag_int scalar
2:     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$1$, nag_file_print_matrix_complex_band (x04de) will exit immediately after printing title; no row or column labels are printed.
3:     kl – int64int32nag_int scalar
The number of subdiagonals of the band matrix A$A$.
Constraint: kl0${\mathbf{kl}}\ge 0$.
4:     ku – int64int32nag_int scalar
The number of superdiagonals of the band matrix A$A$.
Constraint: ku0${\mathbf{ku}}\ge 0$.
5:     a(lda, : $:$) – complex array
The first dimension of the array a must be at least kl + ku + 1${\mathbf{kl}}+{\mathbf{ku}}+1$
The second dimension of the array must be at least max (1,min (m + ku,n))$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{m}}+{\mathbf{ku}},{\mathbf{n}}\right)\right)$
The band matrix to be printed.
The matrix is stored in rows 1$1$ to kl + ku + 1${k}_{l}+{k}_{u}+1$, more precisely, the element Aij${A}_{ij}$ must be stored in
 a(ku + 1 + i − j,j)  for ​max (1,j − ku) ≤ i ≤ min (m,j + kl).$aku+1+i-jj for ​max(1,j-ku)≤i≤min(m,j+kl).$
6:     title – string
A title to be printed above the matrix.
If title = ' ', no title (and no blank line) will be printed.
If title contains more than 80$80$ characters, the contents of title will be wrapped onto more than one line, with the break after 80$80$ characters.
Any trailing blank characters in title are ignored.

None.

lda

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
 On entry, kl < 0${\mathbf{kl}}<0$.
ifail = 2${\mathbf{ifail}}=2$
 On entry, ku < 0${\mathbf{ku}}<0$.
ifail = 3${\mathbf{ifail}}=3$
 On entry, lda < kl + ku + 1$\mathit{lda}<{\mathbf{kl}}+{\mathbf{ku}}+1$.

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

```function nag_file_print_matrix_complex_band_example
m = int64(5);
n = int64(5);
kl = int64(1);
ku = int64(1);
a = [ 11 - 11i,  12 - 12i,  13 - 13i,  14 - 14i,  15 - 15i;
21 - 21i,  22 - 22i,  23 - 23i,  24 - 24i,  25 - 25i;
31 - 31i,  32 - 32i,  33 - 33i,  34 - 34i,  35 - 35i];
title = 'Band Matrix:';
[ifail] = nag_file_print_matrix_complex_band(m, n, kl, ku, a, title)
```
```
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

ifail =

0

```
```function x04de_example
m = int64(5);
n = int64(5);
kl = int64(1);
ku = int64(1);
a = [ 11 - 11i,  12 - 12i,  13 - 13i,  14 - 14i,  15 - 15i;
21 - 21i,  22 - 22i,  23 - 23i,  24 - 24i,  25 - 25i;
31 - 31i,  32 - 32i,  33 - 33i,  34 - 34i,  35 - 35i];
title = 'Band Matrix:';
[ifail] = x04de(m, n, kl, ku, a, title)
```
```
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

ifail =

0

```