NAG Toolbox: nag_matop_dtrttf (f01ve)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

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

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

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

$\mathbf{transr}=\text{'T'}$

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

Constraint: $\mathbf{transr}=\text{'N'}$ or $\text{'T'}$.

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

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

The second dimension of the array a must be at least $\mathbf{n}$.

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.

Optional Input Parameters

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

Default: the first dimension of the array a.

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

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

Output Parameters

1:     $\mathrm{ar}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – double 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.

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: f01ve_example

function f01ve_example


fprintf('f01ve example results\n\n');

uplo   = 'u';
transr = 'n';
a = [1.1, 1.2, 1.3, 1.4;
     0.0, 2.2, 2.3, 2.4;
     0.0, 0.0, 3.3, 3.4;
     0.0, 0.0, 0.0, 4.4];
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04cb(uplo, 'n', a, 'f5.2', 'Unpacked matrix a:', 'i', ...
                {''}, 'i', {''}, int64(80), int64(0));
% Convert to Rectangular Full Packed form
[ar, info] = f01ve(transr, uplo, a);
% Print the Rectangular Full Packed array
fprintf('\n');
[ifail] = x04cb('g', 'x', ar, 'f5.2', 'RFP Packed Array ar:', 'i', ...
                {''}, 'n', {''}, int64(80), int64(0));

n = int64(size(a,1));
k = int64(n/2);
q = n - k;
if transr=='N' || transr=='n'
  lar1 = 2*k + 1;
  lar2 = q;
else
  lar1 = q;
  lar2 = 2*k + 1;
end

ar = reshape(ar,lar1,lar2);

fprintf('\n');
[ifail] = x04cb('g', 'x', ar, 'f5.2', ... 
                'RFP Packed Array ar (graphical representation):', 'i', ...
                {''}, 'i', {''}, int64(80), int64(0), 'm', lar1, 'n', lar2);

f01ve example results


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

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

 RFP Packed Array ar (graphical representation):
       1    2
 1  1.30 1.40
 2  2.30 2.40
 3  3.30 3.40
 4  1.10 4.40
 5  1.20 2.20