larfy(3)                   Library Functions Manual                   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.

       Definition at line 107 of file clarfy.f.

   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.

       Definition at line 107 of file dlarfy.f.

   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.

       Definition at line 107 of file slarfy.f.

   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.

       Definition at line 107 of file zlarfy.f.

Author
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LAPACK                          Version 3.12.0                        larfy(3)