larfx(3)

NAME
larfx - larfx: apply Householder reflector, unrolled

SYNOPSIS

  Functions

subroutine clarfx (side, m, n, v, tau, c, ldc, work)
CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.
subroutine dlarfx (side, m, n, v, tau, c, ldc, work)
DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.
subroutine slarfx (side, m, n, v, tau, c, ldc, work)
SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.
subroutine zlarfx (side, m, n, v, tau, c, ldc, work)
ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Detailed Description

Function Documentation

  subroutine clarfx (character side, integer m, integer n, complex, dimension( * ) v, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)

CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:

    !>
    !> CLARFX 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
    !>
    !> This version uses inline code if H has order < 11.
    !>

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 (M) if SIDE = 'L'
    !>                                        or (N) if SIDE = 'R'
    !>          The vector v in the representation of H.
    !>

    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'
    !>          WORK is not referenced if H has order < 11.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dlarfx (character side, integer m, integer n, double precision, dimension( * ) v, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:

    !>
    !> DLARFX 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
    !>
    !> This version uses inline code if H has order < 11.
    !>

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 (M) if SIDE = 'L'
    !>                                     or (N) if SIDE = 'R'
    !>          The vector v in the representation of H.
    !>

    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 >= (1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension
    !>                      (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>          WORK is not referenced if H has order < 11.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine slarfx (character side, integer m, integer n, real, dimension( * ) v, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:

    !>
    !> SLARFX 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
    !>
    !> This version uses inline code if H has order < 11.
    !>

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 (M) if SIDE = 'L'
    !>                                     or (N) if SIDE = 'R'
    !>          The vector v in the representation of H.
    !>

    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 >= (1,M).
    !>

    WORK

    !>          WORK is REAL array, dimension
    !>                      (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>          WORK is not referenced if H has order < 11.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zlarfx (character side, integer m, integer n, complex*16, dimension( * ) v, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

Purpose:

    !>
    !> ZLARFX 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
    !>
    !> This version uses inline code if H has order < 11.
    !>

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 (M) if SIDE = 'L'
    !>                                        or (N) if SIDE = 'R'
    !>          The vector v in the representation of H.
    !>

    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'
    !>          WORK is not referenced if H has order < 11.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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