NAG Library Routine Document

F01VDF (ZTPTTR)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: 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:     N – INTEGERInput

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{N}\ge 1$.

3:     AP($\mathbf{N}\times \left(\mathbf{N}+1\right)/2$) – COMPLEX (KIND=nag_wp) arrayInput

On entry: 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 $i\ge j$.

4:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayOutput

Note: the second dimension of the array A must be at least $\mathbf{N}$.

On exit: 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.

5:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F01VDF (ZTPTTR) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

6:     INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  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.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01vdfe.f90)

9.2  Program Data

Program Data (f01vdfe.d)

9.3  Program Results

Program Results (f01vdfe.r)