table of contents
larfx(3) | Library Functions Manual | 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.
Definition at line 118 of file clarfx.f.
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.
Definition at line 119 of file dlarfx.f.
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.
Definition at line 119 of file slarfx.f.
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.
Definition at line 118 of file zlarfx.f.
Author¶
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