NAG Toolbox: nag_matop_ztpttr (f01vd)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{uplo}$ – 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 $\text{'L'}$.

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

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

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

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

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

More precisely,

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

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: f01vd_example

function f01vd_example


fprintf('f01vd example results\n\n');

uplo = 'u';
n = int64(4);
ap = [1.1 + 1.1i;
      1.2 + 1.2i;
      2.2 + 2.2i;
      1.3 + 1.3i;
      2.3 + 2.3i;
      3.3 + 3.3i;
      1.4 + 1.4i;
      2.4 + 2.4i;
      3.4 + 3.4i;
      4.4 + 4.4i];
% Print the packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ap, 'b', 'f5.2', 'Packed matrix ap:', 'i', ...
                'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = f01vd(uplo, n, ap);
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04db(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
                'i', int64(80), int64(0));

f01vd example results


 Packed matrix 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)

 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)