NAG Toolbox: nag_matop_ztfttr (f01vh)

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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex array

The first dimension of the array a will be $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array a will be $\mathbf{n}$.

The triangular matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$, $a$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, $a$ is lower triangular and the elements of the array above the diagonal are not referenced.

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

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

Error Indicators and Warnings

   $\mathbf{info}<0$

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

Accuracy

Further Comments

Example

Open in the MATLAB editor: f01vh_example

function f01vh_example


fprintf('f01vh 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 packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ar, 'b', 'f5.2', 'RFP Packed Array ar:', 'i', ...
                'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = f01vh(transr, uplo, n, ar);
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04db(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
                'i', int64(80), int64(0));

f01vh 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)

 Unpacked matrix a:
                1             2             3             4
 1  ( 1.10, 1.10) ( 1.20, 1.20) ( 1.30, 1.30) ( 1.40, 1.40)
 2                ( 2.20, 2.20) ( 2.30, 2.30) ( 2.40, 2.40)
 3                              ( 3.30, 3.30) ( 3.40, 3.40)
 4                                            ( 4.40, 4.40)