NAG Library Routine Document

F07GTF (ZPPEQU)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: indicates whether the upper or lower triangular part of $A$ is stored in the array AP, as follows:

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

The upper triangle of $A$ is stored.

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

The lower triangle of $A$ is stored.

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

2:     N – INTEGERInput

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

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

3:     AP($*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the dimension of the array AP must be at least $\max \left(1,\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$.

On entry: the $n$ by $n$ Hermitian 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 $i\ge j$.

Only the elements of AP corresponding to the diagonal elements $A$ are referenced.

4:     S(N) – REAL (KIND=nag_wp) arrayOutput

On exit: if $\mathbf{INFO}=\mathbf{0}$, S contains the diagonal elements of the scaling matrix $S$.

5:     SCOND – REAL (KIND=nag_wp)Output

On exit: if $\mathbf{INFO}=\mathbf{0}$, SCOND contains the ratio of the smallest value of S to the largest value of S. If $\mathbf{SCOND}\ge 0.1$ and AMAX is neither too large nor too small, it is not worth scaling by $S$.

6:     AMAX – REAL (KIND=nag_wp)Output

On exit: $\max \left|a_{ij}\right|$. If AMAX is very close to overflow or underflow, the matrix $A$ should be scaled.

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

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the $i$th diagonal element of $A$ is not positive (and hence $A$ cannot be positive definite).

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07gtfe.f90)

9.2  Program Data

Program Data (f07gtfe.d)

9.3  Program Results

Program Results (f07gtfe.r)