table of contents
her(3) | Library Functions Manual | her(3) |
NAME¶
her - {he,sy}r: Hermitian/symmetric rank-1 update
SYNOPSIS¶
Functions¶
subroutine CHER (uplo, n, alpha, x, incx, a, lda)
CHER subroutine DSYR (uplo, n, alpha, x, incx, a, lda)
DSYR subroutine SSYR (uplo, n, alpha, x, incx, a, lda)
SSYR subroutine ZHER (uplo, n, alpha, x, incx, a, lda)
ZHER subroutine CSYR (uplo, n, alpha, x, incx, a, lda)
CSYR performs the symmetric rank-1 update of a complex symmetric
matrix. subroutine ZSYR (uplo, n, alpha, x, incx, a, lda)
ZSYR performs the symmetric rank-1 update of a complex symmetric
matrix.
Detailed Description¶
Function Documentation¶
subroutine CHER (character uplo, integer n, real alpha, complex, dimension(*) x, integer incx, complex, dimension(lda,*) a, integer lda)¶
CHER
Purpose:
!> !> CHER performs the hermitian rank 1 operation !> !> A := alpha*x*x**H + A, !> !> where alpha is a real scalar, x is an n element vector and A is an !> n by n hermitian matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !>
ALPHA
!> ALPHA is REAL !> On entry, ALPHA specifies the scalar alpha. !>
X
!> X is COMPLEX array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !>
A
!> A is COMPLEX array, dimension ( LDA, N ) !> Before entry with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the hermitian matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the hermitian matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !> 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. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, n ). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 2 Blas routine. !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !>
Definition at line 134 of file cher.f.
subroutine CSYR (character uplo, integer n, complex alpha, complex, dimension( * ) x, integer incx, complex, dimension( lda, * ) a, integer lda)¶
CSYR performs the symmetric rank-1 update of a complex symmetric matrix.
Purpose:
!> !> CSYR performs the symmetric rank 1 operation !> !> A := alpha*x*x**H + A, !> !> where alpha is a complex scalar, x is an n element vector and A is an !> n by n symmetric matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> !> Unchanged on exit. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !>
ALPHA
!> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !>
X
!> X is COMPLEX array, dimension at least !> ( 1 + ( N - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the N- !> element vector x. !> Unchanged on exit. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !>
A
!> A is COMPLEX array, dimension ( LDA, N ) !> Before entry, with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the symmetric matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry, with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the symmetric matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, N ). !> Unchanged on exit. !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 134 of file csyr.f.
subroutine DSYR (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(lda,*) a, integer lda)¶
DSYR
Purpose:
!> !> DSYR performs the symmetric rank 1 operation !> !> A := alpha*x*x**T + A, !> !> where alpha is a real scalar, x is an n element vector and A is an !> n by n symmetric matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !>
ALPHA
!> ALPHA is DOUBLE PRECISION. !> On entry, ALPHA specifies the scalar alpha. !>
X
!> X is DOUBLE PRECISION array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !>
A
!> A is DOUBLE PRECISION array, dimension ( LDA, N ) !> Before entry with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the symmetric matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the symmetric matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, n ). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 2 Blas routine. !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !>
Definition at line 131 of file dsyr.f.
subroutine SSYR (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(lda,*) a, integer lda)¶
SSYR
Purpose:
!> !> SSYR performs the symmetric rank 1 operation !> !> A := alpha*x*x**T + A, !> !> where alpha is a real scalar, x is an n element vector and A is an !> n by n symmetric matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !>
ALPHA
!> ALPHA is REAL !> On entry, ALPHA specifies the scalar alpha. !>
X
!> X is REAL array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !>
A
!> A is REAL array, dimension ( LDA, N ) !> Before entry with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the symmetric matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the symmetric matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, n ). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 2 Blas routine. !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !>
Definition at line 131 of file ssyr.f.
subroutine ZHER (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*) a, integer lda)¶
ZHER
Purpose:
!> !> ZHER performs the hermitian rank 1 operation !> !> A := alpha*x*x**H + A, !> !> where alpha is a real scalar, x is an n element vector and A is an !> n by n hermitian matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !>
ALPHA
!> ALPHA is DOUBLE PRECISION. !> On entry, ALPHA specifies the scalar alpha. !>
X
!> X is COMPLEX*16 array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !>
A
!> A is COMPLEX*16 array, dimension ( LDA, N ) !> Before entry with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the hermitian matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the hermitian matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !> 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. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, n ). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 2 Blas routine. !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !>
Definition at line 134 of file zher.f.
subroutine ZSYR (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16, dimension( lda, * ) a, integer lda)¶
ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.
Purpose:
!> !> ZSYR performs the symmetric rank 1 operation !> !> A := alpha*x*x**H + A, !> !> where alpha is a complex scalar, x is an n element vector and A is an !> n by n symmetric matrix. !>
Parameters
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> !> Unchanged on exit. !>
N
!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !>
ALPHA
!> ALPHA is COMPLEX*16 !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !>
X
!> X is COMPLEX*16 array, dimension at least !> ( 1 + ( N - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the N- !> element vector x. !> Unchanged on exit. !>
INCX
!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !>
A
!> A is COMPLEX*16 array, dimension ( LDA, N ) !> Before entry, with UPLO = 'U' or 'u', the leading n by n !> upper triangular part of the array A must contain the upper !> triangular part of the symmetric matrix and the strictly !> lower triangular part of A is not referenced. On exit, the !> upper triangular part of the array A is overwritten by the !> upper triangular part of the updated matrix. !> Before entry, with UPLO = 'L' or 'l', the leading n by n !> lower triangular part of the array A must contain the lower !> triangular part of the symmetric matrix and the strictly !> upper triangular part of A is not referenced. On exit, the !> lower triangular part of the array A is overwritten by the !> lower triangular part of the updated matrix. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, N ). !> Unchanged on exit. !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 134 of file zsyr.f.
Author¶
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