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her

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cher (character uplo, integer n, real alpha, complex,dimension(*) x, integer incx, complex, dimension(lda,*) a, integer lda)
subroutine csyr (character uplo, integer n, complex alpha, complex,dimension( * ) x, integer incx, complex, dimension( lda, * ) a, integerlda)
subroutine dsyr (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) x, integer incx, double precision,dimension(lda,*) a, integer lda)
subroutine ssyr (character uplo, integer n, real alpha, real, dimension(*)x, integer incx, real, dimension(lda,*) a, integer lda)
subroutine zher (character uplo, integer n, double precision alpha,complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*)a, integer lda)
subroutine zsyr (character uplo, integer n, complex*16 alpha, complex*16,dimension( * ) x, integer incx, complex*16, dimension( lda, * ) a,integer lda)
Author

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

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 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 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 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 Tennessee

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.

subroutine csyr (character uplo, integer n, complex alpha, complex,dimension( * ) x, integer incx, complex, dimension( lda, * ) a, integerlda)

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

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 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 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 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsyr (character uplo, integer n, double precision alpha, doubleprecision, 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

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 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 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 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 Tennessee

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.

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

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 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 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 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 Tennessee

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.

subroutine zher (character uplo, integer n, double precision alpha,complex16, dimension() x, integer incx, complex16, 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

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 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 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 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 Tennessee

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.

subroutine zsyr (character uplo, integer n, complex16 alpha, complex16,dimension( * ) x, integer incx, complex16, 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

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 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 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 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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