larf(3)                    Library Functions Manual                    larf(3)

NAME
       larf - larf: apply Householder reflector

SYNOPSIS
   Functions
       subroutine clarf (side, m, n, v, incv, tau, c, ldc, work)
           CLARF applies an elementary reflector to a general rectangular
           matrix.
       subroutine dlarf (side, m, n, v, incv, tau, c, ldc, work)
           DLARF applies an elementary reflector to a general rectangular
           matrix.
       subroutine dlarf1f (side, m, n, v, incv, tau, c, ldc, work)
           DLARF1F applies an elementary reflector to a general rectangular
       subroutine dlarf1l (side, m, n, v, incv, tau, c, ldc, work)
           DLARF1L applies an elementary reflector to a general rectangular
       subroutine slarf (side, m, n, v, incv, tau, c, ldc, work)
           SLARF applies an elementary reflector to a general rectangular
           matrix.
       subroutine zlarf (side, m, n, v, incv, tau, c, ldc, work)
           ZLARF applies an elementary reflector to a general rectangular
           matrix.
       subroutine zlarf1f (side, m, n, v, incv, tau, c, ldc, work)
           ZLARF1F applies an elementary reflector to a general rectangular

Detailed Description
Function Documentation
   subroutine clarf (character side, integer m, integer n, complex, dimension(
       * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c,
       integer ldc, complex, dimension( * ) work)
       CLARF applies an elementary reflector to a general rectangular matrix.

       Purpose:


           !>
           !> CLARF applies a complex elementary reflector H to a complex M-by-N
           !> matrix C, from either the left or the right. H is represented in the
           !> form
           !>
           !>       H = I - tau * v * v**H
           !>
           !> where tau is a complex scalar and v is a complex vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>
           !> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
           !> tau.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is COMPLEX array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is COMPLEX
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is COMPLEX array, dimension (LDC,N)
           !>          On entry, the M-by-N matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is COMPLEX array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 127 of file clarf.f.

   subroutine dlarf (character side, integer m, integer n, double precision,
       dimension( * ) v, integer incv, double precision tau, double precision,
       dimension( ldc, * ) c, integer ldc, double precision, dimension( * )
       work)
       DLARF applies an elementary reflector to a general rectangular matrix.

       Purpose:


           !>
           !> DLARF applies a real elementary reflector H to a real m by n matrix
           !> C, from either the left or the right. H is represented in the form
           !>
           !>       H = I - tau * v * v**T
           !>
           !> where tau is a real scalar and v is a real vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is DOUBLE PRECISION array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is DOUBLE PRECISION
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is DOUBLE PRECISION array, dimension (LDC,N)
           !>          On entry, the m by n matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 123 of file dlarf.f.

   subroutine dlarf1f (character side, integer m, integer n, double precision,
       dimension( * ) v, integer incv, double precision tau, double precision,
       dimension( ldc, * ) c, integer ldc, double precision, dimension( * )
       work)
       DLARF1F applies an elementary reflector to a general rectangular

       Purpose:


           !>
           !> DLARF1F applies a real elementary reflector H to a real m by n matrix
           !> C, from either the left or the right. H is represented in the form
           !>
           !>       H = I - tau * v * v**T
           !>
           !> where tau is a real scalar and v is a real vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is DOUBLE PRECISION array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0. V(1) is not referenced or modified.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is DOUBLE PRECISION
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is DOUBLE PRECISION array, dimension (LDC,N)
           !>          On entry, the m by n matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 158 of file dlarf1f.f.

   subroutine dlarf1l (character side, integer m, integer n, double precision,
       dimension( * ) v, integer incv, double precision tau, double precision,
       dimension( ldc, * ) c, integer ldc, double precision, dimension( * )
       work)
       DLARF1L applies an elementary reflector to a general rectangular

       Purpose:


           !>
           !> DLARF1L applies a real elementary reflector H to a real m by n matrix
           !> C, from either the left or the right. H is represented in the form
           !>
           !>       H = I - tau * v * v**T
           !>
           !> where tau is a real scalar and v is a real vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is DOUBLE PRECISION array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is DOUBLE PRECISION
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is DOUBLE PRECISION array, dimension (LDC,N)
           !>          On entry, the m by n matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 125 of file dlarf1l.f.

   subroutine slarf (character side, integer m, integer n, real, dimension( *
       ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc,
       real, dimension( * ) work)
       SLARF applies an elementary reflector to a general rectangular matrix.

       Purpose:


           !>
           !> SLARF applies a real elementary reflector H to a real m by n matrix
           !> C, from either the left or the right. H is represented in the form
           !>
           !>       H = I - tau * v * v**T
           !>
           !> where tau is a real scalar and v is a real vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is REAL array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is REAL
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is REAL array, dimension (LDC,N)
           !>          On entry, the m by n matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is REAL array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 123 of file slarf.f.

   subroutine zlarf (character side, integer m, integer n, complex*16,
       dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension(
       ldc, * ) c, integer ldc, complex*16, dimension( * ) work)
       ZLARF applies an elementary reflector to a general rectangular matrix.

       Purpose:


           !>
           !> ZLARF applies a complex elementary reflector H to a complex M-by-N
           !> matrix C, from either the left or the right. H is represented in the
           !> form
           !>
           !>       H = I - tau * v * v**H
           !>
           !> where tau is a complex scalar and v is a complex vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>
           !> To apply H**H, supply conjg(tau) instead
           !> tau.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>          = 'R': form  C * H
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is COMPLEX*16 array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is COMPLEX*16
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is COMPLEX*16 array, dimension (LDC,N)
           !>          On entry, the M-by-N matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is COMPLEX*16 array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 127 of file zlarf.f.

   subroutine zlarf1f (character side, integer m, integer n, complex*16,
       dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension(
       ldc, * ) c, integer ldc, complex*16, dimension( * ) work)
       ZLARF1F applies an elementary reflector to a general rectangular

       Purpose:


           !>
           !> ZLARF1F applies a complex elementary reflector H to a real m by n matrix
           !> C, from either the left or the right. H is represented in the form
           !>
           !>       H = I - tau * v * v**H
           !>
           !> where tau is a complex scalar and v is a complex vector.
           !>
           !> If tau = 0, then H is taken to be the unit matrix.
           !>
           !> To apply H**H, supply conjg(tau) instead
           !> tau.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': form  H * C
           !>
           !> \param[in] M
           !> \verbatim
           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           V

           !>          V is COMPLEX*16 array, dimension
           !>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
           !>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
           !>          The vector v in the representation of H. V is not used if
           !>          TAU = 0. V(1) is not referenced or modified.
           !>

           INCV

           !>          INCV is INTEGER
           !>          The increment between elements of v. INCV <> 0.
           !>

           TAU

           !>          TAU is COMPLEX*16
           !>          The value tau in the representation of H.
           !>

           C

           !>          C is COMPLEX*16 array, dimension (LDC,N)
           !>          On entry, the m by n matrix C.
           !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
           !>          or C * H if SIDE = 'R'.
           !>

           LDC

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

           WORK

           !>          WORK is COMPLEX*16 array, dimension
           !>                         (N) if SIDE = 'L'
           !>                      or (M) if SIDE = 'R'
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 158 of file zlarf1f.f.

Author
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LAPACK                          Version 3.12.0                         larf(3)