.TH "hfrk" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hfrk \- hfrk: Hermitian rank-k update, RFP format .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchfrk\fP (transr, uplo, trans, n, k, alpha, a, lda, beta, c)" .br .RI "\fBCHFRK\fP performs a Hermitian rank-k operation for matrix in RFP format\&. " .ti -1c .RI "subroutine \fBdsfrk\fP (transr, uplo, trans, n, k, alpha, a, lda, beta, c)" .br .RI "\fBDSFRK\fP performs a symmetric rank-k operation for matrix in RFP format\&. " .ti -1c .RI "subroutine \fBssfrk\fP (transr, uplo, trans, n, k, alpha, a, lda, beta, c)" .br .RI "\fBSSFRK\fP performs a symmetric rank-k operation for matrix in RFP format\&. " .ti -1c .RI "subroutine \fBzhfrk\fP (transr, uplo, trans, n, k, alpha, a, lda, beta, c)" .br .RI "\fBZHFRK\fP performs a Hermitian rank-k operation for matrix in RFP format\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "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)" .PP \fBCHFRK\fP performs a Hermitian rank-k operation for matrix in RFP format\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSR\fP .PP .nf TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'C': The Conjugate-transpose Form of RFP A is stored\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fITRANS\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. Unchanged on exit\&. .fi .PP .br \fIK\fP .PP .nf 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\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. Unchanged on exit\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf 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\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. Unchanged on exit\&. .fi .PP .br \fIC\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBDSFRK\fP performs a symmetric rank-k operation for matrix in RFP format\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSR\fP .PP .nf TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'T': The Transpose Form of RFP A is stored\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fITRANS\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. Unchanged on exit\&. .fi .PP .br \fIK\fP .PP .nf 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\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha\&. Unchanged on exit\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf 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\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION On entry, BETA specifies the scalar beta\&. Unchanged on exit\&. .fi .PP .br \fIC\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBSSFRK\fP performs a symmetric rank-k operation for matrix in RFP format\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSR\fP .PP .nf TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'T': The Transpose Form of RFP A is stored\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fITRANS\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. Unchanged on exit\&. .fi .PP .br \fIK\fP .PP .nf 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\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. Unchanged on exit\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf 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\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. Unchanged on exit\&. .fi .PP .br \fIC\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBZHFRK\fP performs a Hermitian rank-k operation for matrix in RFP format\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSR\fP .PP .nf TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'C': The Conjugate-transpose Form of RFP A is stored\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fITRANS\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. Unchanged on exit\&. .fi .PP .br \fIK\fP .PP .nf 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\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha\&. Unchanged on exit\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf 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\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION On entry, BETA specifies the scalar beta\&. Unchanged on exit\&. .fi .PP .br \fIC\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.