NAG Library Function Document

nag_zsyr2k (f16zwc)

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: specifies whether the upper or lower triangular part of $C$ is stored.

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

The upper triangular part of $C$ is stored.

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

The lower triangular part of $C$ is stored.

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

3:    $\mathbf{trans}$ – Nag_TransTypeInput

On entry: specifies the operation to be performed.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

$C\leftarrow \alpha A{B}^{\mathrm{T}}+\alpha B{A}^{\mathrm{T}}+\beta C$.

$\mathbf{trans}=\mathrm{Nag\_Trans}$

$C\leftarrow \alpha A^{\mathrm{T}}B+\alpha B^{\mathrm{T}}A+\beta C$.

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_Trans}$.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $C$; the number of rows of $A$ and $B$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or the number of columns of $A$ and $B$ otherwise.

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

5:    $\mathbf{k}$ – IntegerInput

On entry: $k$, the number of columns of $A$ and $B$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or the number of rows of $A$ and $B$ otherwise.

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

6:    $\mathbf{alpha}$ – ComplexInput

On entry: the scalar $\alpha$.

7:    $\mathbf{a}\left[\mathit{dim}\right]$ – const ComplexInput

Note: the dimension, dim, of the array a must be at least

• $\max \left(1,\mathbf{pda}\times \mathbf{k}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pda}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$;
• $\max \left(1,\mathbf{pda}\times \mathbf{n}\right)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{k}\times \mathbf{pda}\right)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

On entry: the matrix $A$; $A$ is $n$ by $k$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or $k$ by $n$ otherwise.

8:    $\mathbf{pda}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

9:    $\mathbf{b}\left[\mathit{dim}\right]$ – const ComplexInput

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{k}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdb}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$;
• $\max \left(1,\mathbf{pdb}\times \mathbf{n}\right)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{k}\times \mathbf{pdb}\right)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $B_{ij}$ is stored in $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $B_{ij}$ is stored in $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$.

On entry: the matrix $B$; $B$ is $n$ by $k$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or $k$ by $n$ otherwise.

10:  $\mathbf{pdb}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{k}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{k}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

11:  $\mathbf{beta}$ – ComplexInput

On entry: the scalar $\beta$.

12:  $\mathbf{c}\left[\mathit{dim}\right]$ – ComplexInput/Output

Note: the dimension, dim, of the array c must be at least $\max \left(1,\mathbf{pdc}\times \mathbf{n}\right)$.

On entry: the $n$ by $n$ symmetric matrix $C$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $C_{ij}$ is stored in $\mathbf{c}\left[\left(j-1\right)\times \mathbf{pdc}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $C_{ij}$ is stored in $\mathbf{c}\left[\left(i-1\right)\times \mathbf{pdc}+j-1\right]$.

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangular part of $C$ must be stored and the elements of the array below the diagonal are not referenced.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangular part of $C$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the updated matrix $C$.

13:  $\mathbf{pdc}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) of the matrix $C$ in the array c.

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

14:  $\mathbf{fail}$ – 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_ENUM_INT_2

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_Trans}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT

On entry, $\mathbf{k}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\ge 0$.

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

NE_INT_2

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \max \left(1,\mathbf{n}\right)$.

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_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

10

Example

10.1

Program Text

Program Text (f16zwce.c)

10.2

Program Data

Program Data (f16zwce.d)

10.3

Program Results

Program Results (f16zwce.r)