larfy(3)

NAME
larfy - larfy: apply Householder reflector symmetrically (2-sided)

SYNOPSIS

  Functions

subroutine clarfy (uplo, n, v, incv, tau, c, ldc, work)
CLARFY
subroutine dlarfy (uplo, n, v, incv, tau, c, ldc, work)
DLARFY
subroutine slarfy (uplo, n, v, incv, tau, c, ldc, work)
SLARFY
subroutine zlarfy (uplo, n, v, incv, tau, c, ldc, work)
ZLARFY

Detailed Description

Function Documentation

  subroutine clarfy (character uplo, integer n, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)

CLARFY

Purpose:

    !>
    !> CLARFY applies an elementary reflector, or Householder matrix, H,
    !> to an n x n Hermitian matrix C, from both the left and the right.
    !>
    !> H is represented in the form
    !>
    !>    H = I - tau * v * v'
    !>
    !> where  tau  is a scalar and  v  is a vector.
    !>
    !> If  tau  is  zero, then  H  is taken to be the unit matrix.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          Hermitian matrix C is stored.
    !>          = 'U':  Upper triangle
    !>          = 'L':  Lower triangle
    !>

    N

    !>          N is INTEGER
    !>          The number of rows and columns of the matrix C.  N >= 0.
    !>

    V

    !>          V is COMPLEX array, dimension
    !>                  (1 + (N-1)*abs(INCV))
    !>          The vector v as described above.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between successive elements of v.  INCV must
    !>          not be zero.
    !>

    TAU

    !>          TAU is COMPLEX
    !>          The value tau as described above.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC, N)
    !>          On entry, the matrix C.
    !>          On exit, C is overwritten by H * C * H'.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C.  LDC >= max( 1, N ).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dlarfy (character uplo, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARFY

Purpose:

    !>
    !> DLARFY applies an elementary reflector, or Householder matrix, H,
    !> to an n x n symmetric matrix C, from both the left and the right.
    !>
    !> H is represented in the form
    !>
    !>    H = I - tau * v * v'
    !>
    !> where  tau  is a scalar and  v  is a vector.
    !>
    !> If  tau  is  zero, then  H  is taken to be the unit matrix.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix C is stored.
    !>          = 'U':  Upper triangle
    !>          = 'L':  Lower triangle
    !>

    N

    !>          N is INTEGER
    !>          The number of rows and columns of the matrix C.  N >= 0.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension
    !>                  (1 + (N-1)*abs(INCV))
    !>          The vector v as described above.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between successive elements of v.  INCV must
    !>          not be zero.
    !>

    TAU

    !>          TAU is DOUBLE PRECISION
    !>          The value tau as described above.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC, N)
    !>          On entry, the matrix C.
    !>          On exit, C is overwritten by H * C * H'.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C.  LDC >= max( 1, N ).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine slarfy (character uplo, integer n, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARFY

Purpose:

    !>
    !> SLARFY applies an elementary reflector, or Householder matrix, H,
    !> to an n x n symmetric matrix C, from both the left and the right.
    !>
    !> H is represented in the form
    !>
    !>    H = I - tau * v * v'
    !>
    !> where  tau  is a scalar and  v  is a vector.
    !>
    !> If  tau  is  zero, then  H  is taken to be the unit matrix.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix C is stored.
    !>          = 'U':  Upper triangle
    !>          = 'L':  Lower triangle
    !>

    N

    !>          N is INTEGER
    !>          The number of rows and columns of the matrix C.  N >= 0.
    !>

    V

    !>          V is REAL array, dimension
    !>                  (1 + (N-1)*abs(INCV))
    !>          The vector v as described above.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between successive elements of v.  INCV must
    !>          not be zero.
    !>

    TAU

    !>          TAU is REAL
    !>          The value tau as described above.
    !>

    C

    !>          C is REAL array, dimension (LDC, N)
    !>          On entry, the matrix C.
    !>          On exit, C is overwritten by H * C * H'.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C.  LDC >= max( 1, N ).
    !>

    WORK

    !>          WORK is REAL array, dimension (N)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zlarfy (character uplo, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

ZLARFY

Purpose:

    !>
    !> ZLARFY applies an elementary reflector, or Householder matrix, H,
    !> to an n x n Hermitian matrix C, from both the left and the right.
    !>
    !> H is represented in the form
    !>
    !>    H = I - tau * v * v'
    !>
    !> where  tau  is a scalar and  v  is a vector.
    !>
    !> If  tau  is  zero, then  H  is taken to be the unit matrix.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          Hermitian matrix C is stored.
    !>          = 'U':  Upper triangle
    !>          = 'L':  Lower triangle
    !>

    N

    !>          N is INTEGER
    !>          The number of rows and columns of the matrix C.  N >= 0.
    !>

    V

    !>          V is COMPLEX*16 array, dimension
    !>                  (1 + (N-1)*abs(INCV))
    !>          The vector v as described above.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between successive elements of v.  INCV must
    !>          not be zero.
    !>

    TAU

    !>          TAU is COMPLEX*16
    !>          The value tau as described above.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC, N)
    !>          On entry, the matrix C.
    !>          On exit, C is overwritten by H * C * H'.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C.  LDC >= max( 1, N ).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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