Provided by: liblapack-doc_3.12.1-6build1_all 
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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Version 3.12.0 Thu Aug 28 2025 19:20:45 larf(3)