x04cc is an easy-to-use method to print a real triangular matrix stored in a packed one-dimensional array.

Syntax

C#
public static void x04cc( string uplo, string diag, int n, double[] a, string title, out int ifail )

Visual Basic
Public Shared Sub x04cc ( _ uplo As String, _ diag As String, _ n As Integer, _ a As Double(), _ title As String, _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void x04cc( String^ uplo, String^ diag, int n, array<double>^ a, String^ title, [OutAttribute] int% ifail )

F#
static member x04cc : uplo : string * diag : string * n : int * a : float[] * title : string * ifail : int byref -> unit

Parameters

uplo

Type: System..::..String

On entry: 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"

diag

Type: System..::..String

On entry: 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"

n: Type: System..::..Int32
On entry: the order of the matrix to be printed.
If n is less than $1$ , x04cc will exit immediately after printing title; no row or column labels are printed.

a

Type: array<System..::..Double>[]()[][]

An array of size [dim1]

Note: the dimension of the array a must be at least

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

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 $uplo = "U"$ , 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’.

title: Type: System..::..String
On entry: a title to be printed above the matrix.
If $title =' '$ , no title (and no blank line) will be printed.

If title contains more than $80$ 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.

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

x04cc prints a real triangular matrix stored in packed form. It is an easy-to-use driver for (X04CDF not in this release). The method 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.

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 (X04ABF not in this release).

References

None.

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$

On entry,

uplo \neq "L"

"U"

$ifail = 2$

On entry,

diag \neq "N"

"U"

"B"

$ifail = -9000$: An error occured, see message report.
$ifail = -6000$: Invalid Parameters $〈value〉$
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

Not applicable.

Parallelism and Performance

None.

Further Comments

A call to x04cc is equivalent to a call to (X04CDF not in this release) with the following argument values:

Example

The example program calls x04cc twice, first to print a

4

4

lower triangular matrix, and then to print a

5

5

upper triangular matrix.

Example program (C#): x04cce.cs

Example program results: x04cce.r