Provided by: liblapack-doc_3.12.0-3build1_all 
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
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 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, 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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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
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 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
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 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, 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
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 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, 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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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