NAG Toolbox: nag_matop_ztfttp (f01vm)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

$\mathbf{transr}=\text{'N'}$

The RFP representation of the matrix $A$ is stored.

$\mathbf{transr}=\text{'C'}$

The conjugate transpose of the RFP representation of the matrix $A$ is stored.

Constraint: $\mathbf{transr}=\text{'N'}$ or $\text{'C'}$.

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

Specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\text{'U'}$

$A$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

3:     $\mathrm{n}$ – int64int32nag_int scalar

$n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

4:     $\mathrm{ar}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – complex array

The upper or lower $n$ by $n$ triangular matrix $A$ (as specified by uplo) in either normal or transposed RFP format (as specified by transr). The storage format is described in Rectangular Full Packed (RFP) Storage in the F07 Chapter Introduction.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{ap}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – complex array

The $n$ by $n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{uplo}=\text{'U'}$, the upper triangle of $A$ is stored with element $A_{ij}$ in $\mathbf{ap}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the lower triangle of $A$ is stored with element $A_{ij}$ in $\mathbf{ap}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

2:     $\mathrm{info}$ – int64int32nag_int scalar

$\mathbf{info}=0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $-999<\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

   $\mathbf{info}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f01vm_example

function f01vm_example


fprintf('f01vm example results\n\n');

transr = 'n';
uplo   = 'u';
n      = int64(4);
ar = [1.3 + 1.3i;
      2.3 + 2.3i;
      3.3 + 3.3i;
      1.1 - 1.1i;
      1.2 - 1.2i;
      1.4 + 1.4i;
      2.4 + 2.4i;
      3.4 + 3.4i;
      4.4 + 4.4i;
      2.2 - 2.2i];
% Print the Rectangular Full Packed array
fprintf('\n');
[ifail] = x04db('g', 'x', ar, 'b', 'f5.2', 'RFP Packed Array ar:', 'i', ...
                'n', int64(80), int64(0));
% Convert to packed vector form
[ap, info] = f01vm(transr, uplo, n, ar);
% Print the packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ap, 'b', 'f5.2', 'Packed Array ap:', 'i', ...
                'n', int64(80), int64(0));

f01vm example results


 RFP Packed Array ar:
  1  ( 1.30, 1.30)
  2  ( 2.30, 2.30)
  3  ( 3.30, 3.30)
  4  ( 1.10,-1.10)
  5  ( 1.20,-1.20)
  6  ( 1.40, 1.40)
  7  ( 2.40, 2.40)
  8  ( 3.40, 3.40)
  9  ( 4.40, 4.40)
 10  ( 2.20,-2.20)

 Packed Array ap:
  1  ( 1.10, 1.10)
  2  ( 1.20, 1.20)
  3  ( 2.20, 2.20)
  4  ( 1.30, 1.30)
  5  ( 2.30, 2.30)
  6  ( 3.30, 3.30)
  7  ( 1.40, 1.40)
  8  ( 2.40, 2.40)
  9  ( 3.40, 3.40)
 10  ( 4.40, 4.40)