Integer, Intent (In)	::	n, k, lda, ldb, ldc
Real (Kind=nag_wp), Intent (In)	::	alpha, a(lda,), b(ldb,), beta
Real (Kind=nag_wp), Intent (Inout)	::	c(ldc,*)
Character (1), Intent (In)	::	uplo, trans

C Header Interface

#include <nag.h>

void	f06yrf_ (const char uplo, const char trans, const Integer n, const Integer k, const double alpha, const double a[], const Integer lda, const double b[], const Integer ldb, const double beta, double c[], const Integer *ldc, const Charlen length_uplo, const Charlen length_trans)

The routine may be called by the names f06yrf, nagf_blas_dsyr2k or its BLAS name dsyr2k.

3 Description

None.

4 References

None.

5 Arguments

1: $uplo$ – Character(1) Input

On entry: specifies whether the upper or lower triangular part of

C

is stored.

$uplo ='U'$: The upper triangular part of $C$ is stored.
$uplo ='L'$: The lower triangular part of $C$ is stored.

Constraint:

uplo ='U'

'L'

2: $trans$ – Character(1) Input

On entry: specifies the operation to be performed.

$trans ='N'$: $C \leftarrow α A B^{T} + α B A^{T} + β C$ .
$trans ='T'$ or $'C'$: $C \leftarrow α A^{T} B + α B^{T} A + β C$ .

Constraint:

trans ='N'

'T'

'C'

3: $n$ – Integer Input

On entry:

n

, the order of the matrix

C

; the number of rows of

A

and

B

trans ='N'

, or the number of columns of

A

and

B

trans ='T'

'C'

Constraint:

n \geq 0

4: $k$ – Integer Input

On entry:

k

, the number of columns of

A

and

B

trans ='N'

, or the number of rows of

A

and

B

trans ='T'

'C'

Constraint:

k \geq 0

5: $alpha$ – Real (Kind=nag_wp) Input

On entry: the scalar

α

6: $a (lda, *)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array a must be at least

\max (1, k)

trans ='N'

and at least

\max (1, n)

trans ='T'

'C'

On entry: the matrix

A

;

A

n \times k

trans ='N'

, or

k \times n

trans ='T'

'C'

7: $lda$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f06yrf is called.

Constraints:

if $trans ='N'$ , $lda \geq \max (1, n)$ ;
if $trans ='T'$ or $'C'$ , $lda \geq \max (1, k)$ .

8: $b (ldb, *)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array b must be at least

\max (1, k)

trans ='N'

and at least

\max (1, n)

trans ='T'

'C'

On entry: the matrix

B

;

B

n \times k

trans ='N'

, or

k \times n

trans ='T'

'C'

9: $ldb$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f06yrf is called.

Constraints:

if $trans ='N'$ , $ldb \geq \max (1, n)$ ;
if $trans ='T'$ or $'C'$ , $ldb \geq \max (1, k)$ .

10: $beta$ – Real (Kind=nag_wp) Input

On entry: the scalar

β

11: $c (ldc, *)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array c must be at least

\max (1, n)

On entry: the

n \times n

symmetric matrix

C

If $uplo ='U'$ , the upper triangular part of $C$ must be stored and the elements of the array below the diagonal are not referenced.
If $uplo ='L'$ , 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

12: $ldc$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f06yrf is called.

Constraint:

ldc \geq \max (1, n)

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f06yrf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

f06yrf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.