NAG FL Interface
x04cdf (print_​matrix_​real_​packed_​comp)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – Character(1) Input

On entry: 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: $\mathbf{diag}$ – Character(1) Input

On entry: 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: $\mathbf{n}$ – Integer Input

On entry: the order of the matrix to be printed.

If n is less than $1$, x04cdf will exit immediately after printing title; no row or column labels are printed.

4: $\mathbf{a}\left(*\right)$ – Real (Kind=nag_wp) array Input

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

On entry: 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: $\mathbf{form}$ – Character(*) Input

On entry: describes the Fortran format code 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 x04cdf to choose its own format code:

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

x04cdf 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 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 matrix elements to be printed lie between $0.001$ and $9999.9999$. Otherwise the 1PE13.4 code is chosen.

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

x04cdf 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’, x04cdf will print the matrix such that it can be input into MATLAB, and title will be used as the name of the matrix.

Examples of valid values for form are $\text{'}\mathrm{F11.4}\text{'}$, $\text{'}\mathrm{1PE13.5}\text{'}$, $\text{'}\mathrm{G14.5}\text{'}$, $\text{'}\mathrm{MATLABF11.4}\text{'}$, $\text{'}\mathrm{MATLAB*}\text{'}$.

Constraint: the character length of the format specifier in form must be $\le 80$.

6: $\mathbf{title}$ – Character(*) Input

On entry: 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: $\mathbf{labrow}$ – Character(1) Input

On entry: 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: $\mathbf{rlabs}\left(*\right)$ – Character(*) array Input

Note: the dimension of the array rlabs must be at least $\mathbf{n}$ if $\mathbf{labrow}=\text{'C'}$, and at least $1$ otherwise.

On entry: 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.

9: $\mathbf{labcol}$ – Character(1) Input

On entry: 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 $\text{'C'}$.

10: $\mathbf{clabs}\left(*\right)$ – Character(*) array Input

Note: the dimension of the array clabs must be at least $\mathbf{n}$ if $\mathbf{labcol}=\text{'C'}$, and at least $1$ otherwise.

On entry: 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.

11: $\mathbf{ncols}$ – Integer Input

On entry: 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.

12: $\mathbf{indent}$ – Integer Input

On entry: 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.

13: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, uplo is not valid: $\mathbf{uplo}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

On entry, diag is not valid: $\mathbf{diag}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=3$

The string $〈\mathit{\text{value}}〉$ has not been recognized as a valid format.

$\mathbf{ifail}=4$

The string $〈\mathit{\text{value}}〉$ has not been recognized as a valid format.

$\mathbf{ifail}=5$

On entry, either labrow or labcol is not valid: $\mathbf{labrow}=〈\mathit{\text{value}}〉$, $\mathbf{labcol}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=6$

On entry, $\mathbf{ncols}-\mathbf{indent}$ is not wide enough to hold at least one matrix column: $\mathbf{ncols}=〈\mathit{\text{value}}〉$, $\mathbf{indent}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results