Man page - larf(3)

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Manual

larf

NAME
SYNOPSIS
Functions
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)
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)
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)
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)
subroutine slarf (character side, integer m, integer n, real, dimension( *) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc,real, dimension( * ) work)
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)
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)
Author

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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