# hfrk - Man Page

hfrk: Hermitian rank-k update, RFP format

## Synopsis

### Functions

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

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

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

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

## Detailed Description

## Function Documentation

### subroutine chfrk (character transr, character uplo, character trans, integer n, integer k, real alpha, complex, dimension( lda, * ) a, integer lda, real beta, complex, dimension( * ) c)

**CHFRK** performs a Hermitian rank-k operation for matrix in RFP format.

**Purpose:**

Level 3 BLAS like routine for C in RFP Format. CHFRK performs one of the Hermitian rank--k operations C := alpha*A*A**H + beta*C, or C := alpha*A**H*A + beta*C, where alpha and beta are real scalars, C is an n--by--n Hermitian 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; = 'C': The Conjugate-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**H + beta*C. TRANS = 'C' or 'c' C := alpha*A**H*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 = 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit.

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

*A*A is COMPLEX 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 REAL On entry, BETA specifies the scalar beta. Unchanged on exit.

*C*C is COMPLEX array, dimension (N*(N+1)/2) On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **166** of file **chfrk.f**.

### 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**.

### subroutine ssfrk (character transr, character uplo, character trans, integer n, integer k, real alpha, real, dimension( lda, * ) a, integer lda, real beta, real, dimension( * ) c)

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

**Purpose:**

Level 3 BLAS like routine for C in RFP Format. SSFRK 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 REAL On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is REAL 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 REAL On entry, BETA specifies the scalar beta. Unchanged on exit.

*C*C is REAL 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 **ssfrk.f**.

### subroutine zhfrk (character transr, character uplo, character trans, integer n, integer k, double precision alpha, complex*16, dimension( lda, * ) a, integer lda, double precision beta, complex*16, dimension( * ) c)

**ZHFRK** performs a Hermitian rank-k operation for matrix in RFP format.

**Purpose:**

Level 3 BLAS like routine for C in RFP Format. ZHFRK performs one of the Hermitian rank--k operations C := alpha*A*A**H + beta*C, or C := alpha*A**H*A + beta*C, where alpha and beta are real scalars, C is an n--by--n Hermitian 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; = 'C': The Conjugate-transpose Form of RFP A is stored.

*UPLO**TRANS*TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. Unchanged on exit.

*N**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 = 'C' or 'c', 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 COMPLEX*16 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**BETA*BETA is DOUBLE PRECISION On entry, BETA specifies the scalar beta. Unchanged on exit.

*C*C is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **166** of file **zhfrk.f**.

## Author

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