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.

  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.

  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.

  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.

  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.

  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.

  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.

Author

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