table of contents
| larfx(3) | LAPACK | 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 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 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 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 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 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 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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