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

    !>          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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