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NAG Library Routine Document

F06YRF (DSYR2K)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1 Purpose

F06YRF (DSYR2K) performs one of the symmetric rank-

2 k

update operations

C \leftarrow α A B^{T} + α B A^{T} + β C or C \leftarrow α A^{T} B + α B^{T} A + β C,

where

A

and

B

are real matrices,

C

is an

n

n

real symmetric matrix, and

α

and

β

are real scalars.

2 Specification

SUBROUTINE F06YRF (

UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

INTEGER	N, K, LDA, LDB, LDC
REAL (KIND=nag_wp)	ALPHA, A(LDA,), B(LDB,), BETA, C(LDC,*)
CHARACTER(1)	UPLO, TRANS

The routine may be called by 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: $N$ – INTEGERInput

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: $K$ – INTEGERInput

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) arrayInput

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

k

TRANS ='N'

, or

k

n

TRANS ='T'

'C'

7: $LDA$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06YRF (DSYR2K) 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) arrayInput

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

k

TRANS ='N'

, or

k

n

TRANS ='T'

'C'

9: $LDB$ – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F06YRF (DSYR2K) 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) arrayInput/Output

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

\max (1, N)

On entry: the

n

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: $LDC$ – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F06YRF (DSYR2K) is called.

Constraint:

LDC \geq \max (1, N)

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

F06YRF (DSYR2K) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

F06YRF (DSYR2K) 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.