NAG Library Function Document

nag_zppequ (f07gtc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:     uplo – Nag_UploTypeInput

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

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

The upper triangle of $A$ is stored.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

The lower triangle of $A$ is stored.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

3:     n – IntegerInput

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

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

4:     ap[$\mathit{dim}$] – const ComplexInput

Note: the dimension, dim, 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 rows or columns.

The storage of elements $A_{ij}$ depends on the order and uplo arguments as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(j-1\right)\times j/2+i-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(2n-j\right)\times \left(j-1\right)/2+i-1\right]$, for $i\ge j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(2n-i\right)\times \left(i-1\right)/2+j-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{ap}\left[\left(i-1\right)\times i/2+j-1\right]$, for $i\ge j$.

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

5:     s[n] – doubleOutput

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, s contains the diagonal elements of the scaling matrix $S$.

6:     scond – double *Output

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, 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 $S$.

7:     amax – double *Output

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

8:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_MAT_NOT_POS_DEF

The $⟨\mathit{\text{value}}⟩$th diagonal element of $A$ is not positive (and hence $A$ cannot be positive definite).

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f07gtce.c)

10.2  Program Data

Program Data (f07gtce.d)

10.3  Program Results

Program Results (f07gtce.r)