hpr2(3)

NAME
hpr2 - {hp,sp}r2: Hermitian/symmetric rank-2 update

SYNOPSIS

  Functions
subroutine chpr2 (uplo, n, alpha, x, incx, y, incy, ap)
CHPR2
subroutine dspr2 (uplo, n, alpha, x, incx, y, incy, ap)
DSPR2
subroutine sspr2 (uplo, n, alpha, x, incx, y, incy, ap)
SSPR2
subroutine zhpr2 (uplo, n, alpha, x, incx, y, incy, ap)
ZHPR2

Detailed Description

Function Documentation

  subroutine chpr2 (character uplo, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(*) ap)

CHPR2

Purpose:

    !>
    !> CHPR2  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, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    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.
    !>

    AP

    !>          AP is COMPLEX array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the upper triangular part of the
    !>           updated matrix.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on. On exit, the array
    !>           AP 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.
    !>

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.
    !>

Definition at line 144 of file chpr2.f.

  subroutine dspr2 (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(*) ap)

DSPR2

Purpose:

    !>
    !> DSPR2  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, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the upper triangular part of the
    !>           updated matrix.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the lower triangular part of the
    !>           updated matrix.
    !>

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.
    !>

Definition at line 141 of file dspr2.f.

  subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(*) ap)

SSPR2

Purpose:

    !>
    !> SSPR2  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, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    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.
    !>

    AP

    !>          AP is REAL array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the upper triangular part of the
    !>           updated matrix.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the lower triangular part of the
    !>           updated matrix.
    !>

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.
    !>

Definition at line 141 of file sspr2.f.

  subroutine zhpr2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(*) ap)

ZHPR2

Purpose:

    !>
    !> ZHPR2  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, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on. On exit, the array
    !>           AP is overwritten by the upper triangular part of the
    !>           updated matrix.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on. On exit, the array
    !>           AP 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.
    !>

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.
    !>

Definition at line 144 of file zhpr2.f.

Author

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