nag_file_print_matrix_real_packed (x04cc) prints a double triangular matrix stored in packed form. It is an easy-to-use driver for nag_file_print_matrix_real_packed_comp (x04cd). The function uses default values for the format in which numbers are printed, for labelling the rows and columns, and for output record length. The matrix must be packed by column.

nag_file_print_matrix_real_packed (x04cc) will choose a format code such that numbers will be printed with an

F 8.4

, an

F 11.4

or a

1 PE 13.4

format . The

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

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 PE 13.4

code is chosen.

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).

References

None.

Parameters

Compulsory Input Parameters

1: $uplo$ – string (length ≥ 1)

Indicates the type of the matrix to be printed

$uplo ='L'$: The matrix is lower triangular. In this case, the packed array a holds the matrix elements in the following order: $(1, 1), (2, 1), \dots, (n, 1), (2, 2), (3, 2), \dots, (n, 2)$ , etc.
$uplo ='U'$: The matrix is upper triangular. In this case, the packed array a holds the matrix elements in the following order: $(1, 1), (1, 2), (2, 2), (1, 3), (2, 3), (3, 3), (1, 4)$ , etc.

Constraint:

uplo ='L'

'U'

2: $diag$ – string (length ≥ 1)

Indicates whether the diagonal elements of the matrix are to be printed.

$diag ='B'$: The diagonal elements of the matrix are not referenced and not printed.
$diag ='U'$: The diagonal elements of the matrix are not referenced, but are assumed all to be unity, and are printed as such.
$diag ='N'$: The diagonal elements of the matrix are referenced and printed.

Constraint:

diag ='B'

'U'

'N'

3: $n$ – int64int32nag_int scalar

The order of the matrix to be printed.

If n is less than

1

, nag_file_print_matrix_real_packed (x04cc) will exit immediately after printing title; no row or column labels are printed.

4: $a (:)$ – double array

The dimension of the array a must be at least

\max (1, n \times (n + 1) / 2)

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 $uplo ='U'$ , the upper triangle of $A$ must be stored with element $A_{i j}$ in $a (i + j (j - 1) / 2)$ for $i \leq j$ ;
if $uplo ='L'$ , the lower triangle of $A$ must be stored with element $A_{i j}$ in $a (i + (2 n - j) (j - 1) / 2)$ for $i \geq j$ .

diag ='U'

, the diagonal elements of

A

are assumed to be

1

, and are not referenced; the same storage scheme is used whether

diag ='N'

or ‘U’.

5: $title$ – string

A title to be printed above the matrix.

title =' '

, 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.

Optional Input Parameters

None.

Output Parameters

1: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,

uplo \neq'L'

'U'

$ifail = 2$

On entry,

diag \neq'N'

'U'

'B'

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

A call to nag_file_print_matrix_real_packed (x04cc) is equivalent to a call to nag_file_print_matrix_real_packed_comp (x04cd) with the following argument values:


ncols = 80
indent = 0
labrow = 'I'
labcol = 'I'
form = ' '

Example

The example program calls nag_file_print_matrix_real_packed (x04cc) twice, first to print a

4

4

lower triangular matrix, and then to print a

5

5

upper triangular matrix.

Open in the MATLAB editor: x04cc_example

function x04cc_example


fprintf('x04cc example results\n\n');

nmax = 5;
la = (nmax*(nmax+1))/2;
a = [1:la];

% First matrix : 4x4 unit lower triangular 
mtitle = 'Example 1:';
n = int64(nmax-1);
uplo   = 'Lower';
diag   = 'Unit';
[ifail] = x04cc( ...
                 uplo, diag, n, a, mtitle);

fprintf('\n');
% Second matrix : 5x5 non-unit upper triangular 
mtitle = 'Example 2:';
n = int64(nmax);
uplo   = 'Upper';
diag   = 'Non-unit';
[ifail] = x04cc( ...
                 uplo, diag, n, a, mtitle);

x04cc example results

 Example 1:
             1          2          3          4
 1      1.0000
 2      2.0000     1.0000
 3      3.0000     6.0000     1.0000
 4      4.0000     7.0000     9.0000     1.0000

 Example 2:
             1          2          3          4          5
 1      1.0000     2.0000     4.0000     7.0000    11.0000
 2                 3.0000     5.0000     8.0000    12.0000
 3                            6.0000     9.0000    13.0000
 4                                      10.0000    14.0000
 5                                                 15.0000

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox