NAG Toolbox: nag_file_print_matrix_complex_packed_comp (x04dd)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{uplo}$ – string (length ≥ 1)

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:     $\mathrm{diag}$ – string (length ≥ 1)

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:     $\mathrm{n}$ – int64int32nag_int scalar

The number of rows and columns of the matrix to be printed.

If n is less than $1$, nag_file_print_matrix_complex_packed_comp (x04dd) will exit immediately after printing title; no row or column labels are printed.

4:     $\mathrm{a}\left(:\right)$ – complex array

The dimension of the array a must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$

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:     $\mathrm{usefrm}$ – 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 edit-descriptor 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 edit-descriptor 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 $\left(\text{0.123e−02},\text{0.234e−01}\right)$. See Example for an example illustrating this option.

Constraint: $\mathbf{usefrm}=\text{'A'}$, $\text{'B'}$ or $\text{'D'}$.

6:     $\mathrm{form}$ – 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_packed_comp (x04dd) to choose its own format code:

$\mathbf{form}=\text{' '}$

nag_file_print_matrix_complex_packed_comp (x04dd) 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_packed_comp (x04dd) 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 run-time library of the Fortran compiler in use.

By preceding the desired format code by the string ‘MATLAB’, nag_file_print_matrix_complex_packed_comp (x04dd) 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 $\le 80$.

7:     $\mathrm{title}$ – 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.

8:     $\mathrm{labrow}$ – 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 $\text{'C'}$.

9:     $\mathrm{rlabs}\left(:\right)$ – cell array of strings

The dimension of the array rlabs must be at least $\mathbf{n}$ 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 right-justified 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.

10:   $\mathrm{labcol}$ – 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 $\text{'C'}$.

11:   $\mathrm{clabs}\left(:\right)$ – 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 right-justified when output. Any label that is too long for the column width, which is determined by form, is truncated.

12:   $\mathrm{ncols}$ – 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.

13:   $\mathrm{indent}$ – 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

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

   $\mathbf{ifail}=1$

On entry,

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

   $\mathbf{ifail}=2$

On entry,

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

   $\mathbf{ifail}=3$

On entry,

$\mathbf{usefrm}\ne \text{'A'}$, $\text{'B'}$ or $\text{'D'}$.

   $\mathbf{ifail}=4$

On entry,

the format specifier in form is more than $80$ characters long.

   $\mathbf{ifail}=5$

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.

   $\mathbf{ifail}=6$

On entry,

either labrow or $\mathbf{labcol}\ne \text{'N'}$, $\text{'I'}$ or $\text{'C'}$.

   $\mathbf{ifail}=7$

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

Further Comments

Example

Open in the MATLAB editor: x04dd_example

function x04dd_example


fprintf('x04dd example results\n\n');

nmax = 4;
la = (nmax*(nmax+1))/2;
a = [1:la] - i*[1:la];

% First matrix : 4x4 non-unit lower triangular 
n = int64(nmax);
mtitle = 'Example 1:';
uplo   = 'Lower';
diag   = 'Non-unit';

% Bracketed representation of complex numbers and Default formatting
usefrm = 'Bracketed';
format = ' ';

% Integer labels
labrow = 'Integer';
labcol = labrow;
rlabs = {'       '};
clabs = {'       '};

% 80 colunms wide, no indent
ncols  = int64(80);
indent = int64(0);

[ifail] = x04dd( ...
                 uplo, diag, n, a, usefrm, format, mtitle, labrow, rlabs, ...
                 labcol, clabs, ncols, indent);

fprintf('\n');
% Second matrix : 4x4 Unit upper triangular 
mtitle = 'Example 2:';
n = int64(nmax);
uplo   = 'Upper';
diag   = 'Unit';

% Define formatting of complex numbers
usefrm = 'Direct';
format = 'SS,F7.1,SP,F6.1,''i''';

% Character labels
labrow = 'Character';
labcol = labrow;
rlabs  = {'Uno    '; 'Due    '; 'Tre    '; 'Quattro'};
clabs  = {'Un     '; 'Deux   '; 'Trois  '; 'Quatre '};

[ifail] = x04dd( ...
                 uplo, diag, n, a, usefrm, format, mtitle, labrow, rlabs, ...
                 labcol, clabs, ncols, indent);

fprintf('\n Example 3:\n');
% Third matrix: Upper triangular non-unit matrix 
mtitle = 'A';
diag   = 'Non-unit';
usefrm = ' ';
format = 'MATLABF8.2';
labrow = 'No labels';
labcol = labrow;

[ifail] = x04dd( ...
                 uplo, diag, n, a, usefrm, format, mtitle, labrow, rlabs, ...
                 labcol, clabs, ncols, indent);

x04dd example results

 Example 1:
                            1                         2
 1  (     1.0000,    -1.0000)
 2  (     2.0000,    -2.0000) (     5.0000,    -5.0000)
 3  (     3.0000,    -3.0000) (     6.0000,    -6.0000)
 4  (     4.0000,    -4.0000) (     7.0000,    -7.0000)

                            3                         4
 1
 2
 3  (     8.0000,    -8.0000)
 4  (     9.0000,    -9.0000) (    10.0000,   -10.0000)

 Example 2:
                     Un          Deux         Trois        Quatre
     Uno     1.0  +0.0i    2.0  -2.0i    4.0  -4.0i    7.0  -7.0i
     Due                   1.0  +0.0i    5.0  -5.0i    8.0  -8.0i
     Tre                                 1.0  +0.0i    9.0  -9.0i
 Quattro                                               1.0  +0.0i

 Example 3:
 A = [
   (    1.00   -1.00i) (    2.00   -2.00i) (    4.00   -4.00i) ...
   (    7.00   -7.00i);
   (    0.00   +0.00i) (    3.00   -3.00i) (    5.00   -5.00i) ...
   (    8.00   -8.00i);
   (    0.00   +0.00i) (    0.00   +0.00i) (    6.00   -6.00i) ...
   (    9.00   -9.00i);
   (    0.00   +0.00i) (    0.00   +0.00i) (    0.00   +0.00i) ...
   (   10.00  -10.00i);
     ];