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larf(3) LAPACK 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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