NAG Library Routine Document

Integer, Intent (In)	::	n, k, lda
Real (Kind=nag_wp), Intent (In)	::	alpha, a(lda,*), beta
Real (Kind=nag_wp), Intent (Inout)	::	c(n*(n+1)/2)
Character (1), Intent (In)	::	transr, uplo, trans

C Header Interface

#include <nagmk26.h>

void	f06wcf_ (const char transr, const char uplo, const char trans, const Integer n, const Integer k, const double alpha, const double a[], const Integer lda, const double beta, double c[], const Charlen length_transr, const Charlen length_uplo, const Charlen length_trans)

The routine may be called by its LAPACK name dsfrk.

3

Description

f06wcf (dsfrk) performs one of the symmetric rank-

k

update operations

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

where

A

is a real matrix,

C

is an

n

n

real symmetric matrix stored in Rectangular Full Packed (RFP) format, and

α

and

β

are real scalars. The RFP storage format is described in Section 3.3.3 in the F07 Chapter Introduction.

n = 0

or if

β = 1.0

and either

k = 0

α = 0.0

then f06wcf (dsfrk) returns immediately. If

β = 0.0

and either

k = 0

α = 0.0

then

C

is set to the zero matrix.

4

References

Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

5

Arguments

1: $transr$ – Character(1)Input

On entry: specifies whether the RFP representation of

C

is normal or transposed.

$transr ='N'$: The matrix $C$ is stored in normal RFP format.
$transr ='T'$: The matrix $C$ is stored in transposed RFP format.

Constraint:

transr ='N'

'T'

2: $uplo$ – Character(1)Input

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

C

is stored in RFP format.

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

Constraint:

uplo ='U'

'L'

3: $trans$ – Character(1)Input

On entry: specifies the operation to be performed.

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

Constraint:

trans ='N'

'T'

4: $n$ – IntegerInput

On entry:

n

, the order of the matrix

C

Constraint:

n \geq 0

5: $k$ – IntegerInput

On entry:

k

, the number of columns of

A

trans ='N'

, or the number of rows of

A

trans ='T'

Constraint:

k \geq 0

6: $alpha$ – Real (Kind=nag_wp)Input

On entry: the scalar

α

7: $a (lda *)$ – 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'

On entry: the matrix

A

;

A

n

k

trans ='N'

, or

k

n

trans ='T'

. If

alpha = 0.0

, a is not referenced.

8: $lda$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06wcf (dsfrk) is called.

Constraints:

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

9: $beta$ – Real (Kind=nag_wp)Input

On entry: the scalar

β

10: $c (n \times (n + 1) / 2)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: the upper or lower triangular part (as specified by uplo) of the

n

n

symmetric matrix

C

, stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction.

On exit: the updated matrix

C

, that is its upper or lower triangular part stored in RFP format.

6

Error Indicators and Warnings

None.

7

Accuracy

Not applicable.

8

Parallelism and Performance

f06wcf (dsfrk) 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.

9

Further Comments

None.

10

Example

This example reads in the lower triangular part of a symmetric matrix

C

which it converts to RFP format. It also reads in

α

β

and a

6

4

matrix

A

and then performs the symmetric rank-

4

update

C \leftarrow α A A^{T} + β C

NAG Library Routine Document

f06wcf (dsfrk)

▸▿ 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

10.1 Program Text

10.2 Program Data

10.3 Program Results

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

10.1

Program Text

10.2

Program Data

10.3

Program Results