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NAG Toolbox: nag_file_print_matrix_complex_gen_comp (x04db)
Purpose
nag_file_print_matrix_complex_gen_comp (x04db) prints a complex matrix stored in a twodimensional array.
Syntax
[
ifail] = x04db(
matrix,
diag,
a,
usefrm,
form,
title,
labrow,
labcol,
ncols,
indent, 'm',
m, 'n',
n, 'rlabs',
rlabs, 'clabs',
clabs)
[
ifail] = nag_file_print_matrix_complex_gen_comp(
matrix,
diag,
a,
usefrm,
form,
title,
labrow,
labcol,
ncols,
indent, 'm',
m, 'n',
n, 'rlabs',
rlabs, 'clabs',
clabs)
Description
nag_file_print_matrix_complex_gen_comp (x04db) prints a complex matrix, or part of it, using a format specifier supplied by you.
The matrix is output to the unit defined by
nag_file_set_unit_advisory (x04ab).
References
None.
Parameters
Compulsory Input Parameters
 1:
$\mathrm{matrix}$ – string (length ≥ 1)

Indicates the part of the matrix to be printed.
 ${\mathbf{matrix}}=\text{'G'}$
 The whole of the rectangular matrix.
 ${\mathbf{matrix}}=\text{'L'}$
 The lower triangle of the matrix, or the lower trapezium if the matrix has more rows than columns.
 ${\mathbf{matrix}}=\text{'U'}$
 The upper triangle of the matrix, or the upper trapezium if the matrix has more columns than rows.
Constraint:
${\mathbf{matrix}}=\text{'G'}$, $\text{'L'}$ or $\text{'U'}$.
 2:
$\mathrm{diag}$ – string (length ≥ 1)

Unless
${\mathbf{matrix}}=\text{'G'}$,
diag must specify 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.
If
${\mathbf{matrix}}=\text{'G'}$, then
diag need not be set.
Constraint:
if ${\mathbf{matrix}}\ne \text{'G'}$, ${\mathbf{diag}}=\text{'B'}$, $\text{'U'}$ or $\text{'N'}$.
 3:
$\mathrm{a}\left(\mathit{lda},:\right)$ – complex array

The first dimension of the array
a must be at least
$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
The second dimension of the array
a must be at least
$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The matrix to be printed. Only the elements that will be referred to, as specified by arguments
matrix and
diag, need be set.
 4:
$\mathrm{usefrm}$ – string (length ≥ 1)

Indicates how the value of
form is to be used to print matrix elements, except in MATLAB mode where
usefrm is ignored.
 ${\mathbf{usefrm}}=\text{'A'}$
 The format code in form is assumed to contain a single real editdescriptor which is to be used to print the real and imaginary parts of each complex number one above the other. Each row of the matrix is separated by a blank line, and any row labels are attached only to the real parts. This option means that about twice as many columns can be fitted into ncols characters than if any other usefrm option is used. A typical value of form for this usefrm option might be $\text{'E13.4'}$, $\text{'*'}$ or $\text{''}$.
 ${\mathbf{usefrm}}=\text{'B'}$
 The format code in form is assumed to contain a single editdescriptor such as $\text{'E13.4'}$, $\text{'*'}$ or $\text{''}$ which is used to print the real and imaginary parts of each complex number separated by a comma, and surrounded by brackets. Thus a matrix element printed with this usefrm option might look like this: $\left(12.345,11.323\right)$.
 ${\mathbf{usefrm}}=\text{'D'}$
 The format code in form is used unaltered to print a complex number. This usefrm option allows you flexibility to specify exactly how the number is printed. With this option for usefrm and a suitable value for form it is possible, for example, to print a complex number in the form $\left(0.123+3.214i\right)$ or $\left(\text{0.123e\u221202},\text{0.234e\u221201}\right)$. See Example for an example illustrating this option.
Constraint:
${\mathbf{usefrm}}=\text{'A'}$, $\text{'B'}$ or $\text{'D'}$.
 5:
$\mathrm{form}$ – string

Describes the Fortran format code that is used in conjunction with
usefrm for printing the elements of the matrix
a. The format code may be any allowed on the system, whether it is standard Fortran or not. It may or may not be enclosed in brackets.
In addition, there are the following special codes which force
nag_file_print_matrix_complex_gen_comp (x04db) to choose its own format code:
 ${\mathbf{form}}=\text{''}$
 nag_file_print_matrix_complex_gen_comp (x04db) will choose a format code such that numbers will be printed with an F8.4, an F11.4 or a 1PE13.4 format. The F8.4 code is chosen if the sizes of the real and imaginary parts of all the matrix elements to be printed lie between $0.001$ and $1.0$. The F11.4 code is chosen if the sizes of all the numbers to be printed lie between $0.001$ and $9999.9999$. Otherwise the 1PE13.4 code is chosen.
 ${\mathbf{form}}=\text{'*'}$
 nag_file_print_matrix_complex_gen_comp (x04db) will choose a format code such that numbers will be printed to as many significant digits as are necessary to distinguish between neighbouring machine numbers. Thus any two numbers that are stored with different internal representations should look different on output. Whether they do in fact look different will depend on the runtime library of the Fortran compiler in use.
By preceding the desired format code by the string ‘MATLAB’,
nag_file_print_matrix_complex_gen_comp (x04db) will print the matrix such that it can be input into MATLAB, and
title will be used as the name of the matrix.
More complicated values of
form, to print a complex number in a desired form, may be used. See the description of argument
usefrm for more details.
Examples of valid values for
form are
$\text{'(F11.4)'}$,
$\text{'1P,2E13.5'}$,
$\text{'MATLABF11.4'}$,
$\text{'MATLAB*'}$.
Constraint:
the character length of the format specifier in
form must be
$\text{}\le 80$.
 6:
$\mathrm{title}$ – string

A title to be printed above the matrix, or name of the matrix.
If ${\mathbf{title}}=\text{''}$, no title (and no blank line) will be printed.
If
title contains more than
ncols characters, the contents of
title will be wrapped onto more than one line, with the break after
ncols characters.
Any trailing blank characters in
title are ignored.
If printing in MATLAB mode,
title will be used as the name of the matrix.
 7:
$\mathrm{labrow}$ – string (length ≥ 1)

Indicates the type of labelling to be applied to the rows of the matrix, except in MATLAB mode where
labrow is ignored.
 ${\mathbf{labrow}}=\text{'N'}$
 Prints no row labels.
 ${\mathbf{labrow}}=\text{'I'}$
 Prints integer row labels.
 ${\mathbf{labrow}}=\text{'C'}$
 Prints character labels, which must be supplied in array rlabs.
Constraint:
${\mathbf{labrow}}=\text{'N'}$, $\text{'I'}$ or $\text{'C'}$.
 8:
$\mathrm{labcol}$ – string (length ≥ 1)

Indicates the type of labelling to be applied to the columns of the matrix, except in MATLAB mode where
labcol is ignored.
 ${\mathbf{labcol}}=\text{'N'}$
 Prints no column labels.
 ${\mathbf{labcol}}=\text{'I'}$
 Prints integer column labels.
 ${\mathbf{labcol}}=\text{'C'}$
 Prints character labels, which must be supplied in array clabs.
Constraint:
${\mathbf{labcol}}=\text{'N'}$, $\text{'I'}$ or $\text{'C'}$.
 9:
$\mathrm{ncols}$ – int64int32nag_int scalar

The maximum output record length. If the number of columns of the matrix is too large to be accommodated in
ncols characters, the matrix will be printed in parts, containing the largest possible number of matrix columns, and each part separated by a blank line.
ncols must be large enough to hold at least one column of the matrix using the format specifier in
form. If a value less than 0 or greater than
$132$ is supplied for
ncols, then the value
$80$ is used instead.
 10:
$\mathrm{indent}$ – int64int32nag_int scalar

The number of columns by which the matrix (and any title and labels) should be indented. The effective value of
ncols is reduced by
indent columns. If a value less than
$0$ or greater than
ncols is supplied for
indent, the value
$0$ is used instead.
Optional Input Parameters
 1:
$\mathrm{m}$ – int64int32nag_int scalar
 2:
$\mathrm{n}$ – int64int32nag_int scalar

Default:
the first dimension of the array
a and the second dimension of the array
a.
The number of rows and columns of the matrix, respectively, to be printed.
If either
m or
n is less than
$1$,
nag_file_print_matrix_complex_gen_comp (x04db) will exit immediately after printing
title; no row or column labels are printed.
 3:
$\mathrm{rlabs}\left(:\right)$ – cell array of strings

The dimension of the array
rlabs
must be at least
${\mathbf{m}}$ if
${\mathbf{labrow}}=\text{'C'}$, and at least
$1$ otherwise
If
${\mathbf{labrow}}=\text{'C'}$,
rlabs must contain labels for the rows of the matrix, except in MATLAB mode where
rlabs is ignored.
Labels are rightjustified when output, in a field which is as wide as necessary to hold the longest row label. Note that this field width is subtracted from the number of usable columns,
ncols.
 4:
$\mathrm{clabs}\left(:\right)$ – cell array of strings

The dimension of the array
clabs
must be at least
${\mathbf{n}}$ if
${\mathbf{labcol}}=\text{'C'}$, and at least
$1$ otherwise
If
${\mathbf{labcol}}=\text{'C'}$,
clabs must contain labels for the columns of the matrix, except in MATLAB mode where
clabs is ignored.
Labels are rightjustified when output. Any label that is too long for the column width, which is determined by
form, is truncated.
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,  ${\mathbf{matrix}}\ne \text{'G'}$, $\text{'L'}$ or $\text{'U'}$. 
 ${\mathbf{ifail}}=2$

On entry,  ${\mathbf{matrix}}=\text{'L'}$ or $\text{'U'}$, but ${\mathbf{diag}}\ne \text{'N'}$, $\text{'U'}$ or $\text{'B'}$. 
 ${\mathbf{ifail}}=3$

On entry,  $\mathit{lda}<{\mathbf{m}}$. 
 ${\mathbf{ifail}}=4$

On entry,  ${\mathbf{usefrm}}\ne \text{'A'}$, $\text{'B'}$ or $\text{'D'}$. 
 ${\mathbf{ifail}}=5$

On entry,  the format specifier in form is more than $80$ characters long. 
 ${\mathbf{ifail}}=6$

The format specifier in
form cannot be used to output a number. The specifier probably has too wide a field width or contains an illegal edit descriptor.
 ${\mathbf{ifail}}=7$

On entry,  either labrow or ${\mathbf{labcol}}\ne \text{'N'}$, $\text{'I'}$ or $\text{'C'}$. 
 ${\mathbf{ifail}}=8$

The quantity ${\mathbf{ncols}}{\mathbf{indent}}\mathit{labwid}$ (where $\mathit{labwid}$ is the width needed for the row labels) is not large enough to hold at least one column of the matrix.
 ${\mathbf{ifail}}=99$
An unexpected error has been triggered by this routine. Please
contact
NAG.
 ${\mathbf{ifail}}=399$
Your licence key may have expired or may not have been installed correctly.
 ${\mathbf{ifail}}=999$
Dynamic memory allocation failed.
Accuracy
Not applicable.
Example
The example program calls nag_file_print_matrix_complex_gen_comp (x04db) three times, first to print a $3$ by $4$ rectangular matrix, next to print a $4$ by $4$ upper triangular matrix, and then to print a $3$ by $4$ lower triangular matrix; various options for labelling and formatting are illustrated.
Open in the MATLAB editor:
x04db_example
function x04db_example
fprintf('x04db example results\n\n');
nmax = 4;
b = zeros(nmax,nmax);
for j = 1:nmax
b(j,:) = [1:nmax] + 10*j;
end
a = b  i*b;
mtitle = 'Example 1:';
matrix = 'General';
diag = ' ';
usefrm = 'Bracketed';
format = ' ';
labrow = 'Integer';
labcol = labrow;
ncols = int64(80);
indent = int64(0);
[ifail] = x04db( ...
matrix, diag, a, usefrm, format, mtitle, ...
labrow, labcol, ncols, indent);
fprintf('\n');
mtitle = 'Example 2:';
matrix = 'Upper';
diag = 'Nonunit';
usefrm = 'Above';
format = 'F8.2';
labrow = 'Character';
labcol = labrow;
rlabs = {'Uno '; 'Due '; 'Tre '; 'Quattro'};
clabs = {'Un '; 'Deux '; 'Trois '; 'Quatre '};
[ifail] = x04db( ...
matrix, diag, a, usefrm, format, mtitle, labrow, ...
labcol, ncols, indent, 'rlabs', rlabs, 'clabs', clabs);
fprintf('\n Example 3:\n');
mtitle = 'A';
matrix = 'Lower';
diag = 'Unit';
usefrm = ' ';
format = 'MATLABF8.2';
labrow = 'No labels';
labcol = labrow;
[ifail] = x04db( ...
matrix, diag, a(1:3,1:3), usefrm, format, mtitle, labrow, ...
labcol, ncols, indent, 'rlabs', rlabs, 'clabs', clabs);
x04db example results
Example 1:
1 2
1 ( 11.0000, 11.0000) ( 12.0000, 12.0000)
2 ( 21.0000, 21.0000) ( 22.0000, 22.0000)
3 ( 31.0000, 31.0000) ( 32.0000, 32.0000)
4 ( 41.0000, 41.0000) ( 42.0000, 42.0000)
3 4
1 ( 13.0000, 13.0000) ( 14.0000, 14.0000)
2 ( 23.0000, 23.0000) ( 24.0000, 24.0000)
3 ( 33.0000, 33.0000) ( 34.0000, 34.0000)
4 ( 43.0000, 43.0000) ( 44.0000, 44.0000)
Example 2:
Un Deux Trois Quatre
Uno 11.00 12.00 13.00 14.00
11.00 12.00 13.00 14.00
Due 22.00 23.00 24.00
22.00 23.00 24.00
Tre 33.00 34.00
33.00 34.00
Quattro 44.00
44.00
Example 3:
A = [
( 1.00 +0.00i) ( 0.00 +0.00i) ( 0.00 +0.00i);
( 21.00 21.00i) ( 1.00 +0.00i) ( 0.00 +0.00i);
( 31.00 31.00i) ( 32.00 32.00i) ( 1.00 +0.00i);
];
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, 64bit version, 64bit version)
© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2015