her2(3)

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

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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.
    !>

    Y

    !>          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

    !>          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

    !>          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.
    !>

    Y

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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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