NAG Library Function Document

nag_dsptrd (f08gec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – 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 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

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

2:    $\mathbf{uplo}$ – Nag_UploTypeInput

On entry: indicates whether the upper or lower triangular part of $A$ is stored.

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

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

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

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{ap}\left[\mathit{dim}\right]$ – doubleInput/Output

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 upper or lower triangle of the $n$ by $n$ symmetric 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 $i\ge j$.

On exit: ap is overwritten by the tridiagonal matrix $T$ and details of the orthogonal matrix $Q$.

5:    $\mathbf{d}\left[\mathbf{n}\right]$ – doubleOutput

On exit: the diagonal elements of the tridiagonal matrix $T$.

6:    $\mathbf{e}\left[\mathbf{n}-1\right]$ – doubleOutput

On exit: the off-diagonal elements of the tridiagonal matrix $T$.

7:    $\mathbf{tau}\left[\mathbf{n}-1\right]$ – doubleOutput

On exit: further details of the orthogonal matrix $Q$.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

nag_dopgtr(order,uplo,n,ap,tau,&q,pdq,&fail)

nag_dopmtr(order,Nag_LeftSide,uplo,Nag_NoTrans,n,p,ap,tau,&c,
  pdc,&fail)

10

Example

10.1

Program Text

Program Text (f08gece.c)

10.2

Program Data

Program Data (f08gece.d)

10.3

Program Results

Program Results (f08gece.r)