Ubuntu Manpage: her2 - {he,sy}r2: Hermitian/symmetric rank-2 update

Provided by: liblapack-doc_3.12.0-3build1.1_all

NAME

       her2 - {he,sy}r2: Hermitian/symmetric rank-2 update

SYNOPSIS

   Functions
       subroutine cher2 (uplo, n, alpha, x, incx, y, incy, a, lda)
           CHER2
       subroutine dsyr2 (uplo, n, alpha, x, incx, y, incy, a, lda)
           DSYR2
       subroutine ssyr2 (uplo, n, alpha, x, incx, y, incy, a, lda)
           SSYR2
       subroutine zher2 (uplo, n, alpha, x, incx, y, incy, a, lda)
           ZHER2

Detailed Description

Function Documentation

subroutine cher2 (character uplo, integer n, complex alpha, complex, dimension(*) x, integer
incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)
CHER2

Purpose:

CHER2 performs the hermitian rank 2 operation

A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors 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 COMPLEX
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.

Y is COMPLEX array, dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY 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 dsyr2 (character uplo, integer n, double precision alpha, double precision,
dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double
precision, dimension(lda,*) a, integer lda)
DSYR2

Purpose:

DSYR2 performs the symmetric rank 2 operation

A := alpha*x*y**T + alpha*y*x**T + A,

where alpha is a scalar, x and y are n element vectors 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.

Y is DOUBLE PRECISION array, dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY 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 ssyr2 (character uplo, integer n, real alpha, real, dimension(*) x, integer incx,
real, dimension(*) y, integer incy, real, dimension(lda,*) a, integer lda)
SSYR2

Purpose:

SSYR2 performs the symmetric rank 2 operation

A := alpha*x*y**T + alpha*y*x**T + A,

where alpha is a scalar, x and y are n element vectors 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.

Y is REAL array, dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY 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 zher2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x,
integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a,
integer lda)
ZHER2

Purpose:

ZHER2 performs the hermitian rank 2 operation

A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors 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 COMPLEX*16
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.

Y is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY 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.

Author

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