NAG Library Function Document

nag_dsyrk (f16ypc)

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 3.2.1.3 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:    $\mathbf{uplo}$ – 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.

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

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

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

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

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

4:    $\mathbf{n}$ – IntegerInput

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

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

5:    $\mathbf{k}$ – IntegerInput

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

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

6:    $\mathbf{alpha}$ – doubleInput

On entry: the scalar $\alpha$.

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

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

9:    $\mathbf{beta}$ – doubleInput

On entry: the scalar $\beta$.

10:  $\mathbf{c}\left[\mathit{dim}\right]$ – doubleInput/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 $C$.

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

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

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

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction 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 $\mathbf{trans}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

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 $\mathbf{trans}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f16ypce.c)

10.2  Program Data

Program Data (f16ypce.d)

10.3  Program Results

Program Results (f16ypce.r)