# dsfrk.f - Man Page

SRC/dsfrk.f

## Synopsis

### Functions/Subroutines

subroutine **dsfrk** (transr, uplo, trans, n, k, alpha, a, lda, beta, c)**DSFRK** performs a symmetric rank-k operation for matrix in RFP format.

## Function/Subroutine Documentation

### subroutine dsfrk (character transr, character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension( lda, * ) a, integer lda, double precision beta, double precision, dimension( * ) c)

**DSFRK** performs a symmetric rank-k operation for matrix in RFP format.

**Purpose:**

Level 3 BLAS like routine for C in RFP Format. DSFRK performs one of the symmetric rank--k operations C := alpha*A*A**T + beta*C, or C := alpha*A**T*A + beta*C, where alpha and beta are real scalars, C is an n--by--n symmetric matrix and A is an n--by--k matrix in the first case and a k--by--n matrix in the second case.

**Parameters***TRANSR*TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'T': The Transpose Form of RFP A is stored.

*UPLO*UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit.

*TRANS*TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit.

*K*K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit.

*ALPHA*ALPHA is DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is DOUBLE PRECISION array, dimension (LDA,ka) where KA is K when TRANS = 'N' or 'n', and is N otherwise. Before entry with TRANS = 'N' or 'n', the leading N--by--K part of the array A must contain the matrix A, otherwise the leading K--by--N part of the array A must contain the matrix A. Unchanged on exit.

*LDA*LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit.

*BETA*BETA is DOUBLE PRECISION On entry, BETA specifies the scalar beta. Unchanged on exit.

*C*C is DOUBLE PRECISION array, dimension (NT) NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP Format. RFP Format is described by TRANSR, UPLO and N.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **164** of file **dsfrk.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsfrk(3) is an alias of dsfrk.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK