table of contents
larz(3) | Library Functions Manual | larz(3) |
NAME¶
larz - larz: apply reflector
SYNOPSIS¶
Functions¶
subroutine CLARZ (side, m, n, l, v, incv, tau, c, ldc,
work)
CLARZ applies an elementary reflector (as returned by stzrzf) to a
general matrix. subroutine DLARZ (side, m, n, l, v, incv, tau, c,
ldc, work)
DLARZ applies an elementary reflector (as returned by stzrzf) to a
general matrix. subroutine SLARZ (side, m, n, l, v, incv, tau, c,
ldc, work)
SLARZ applies an elementary reflector (as returned by stzrzf) to a
general matrix. subroutine ZLARZ (side, m, n, l, v, incv, tau, c,
ldc, work)
ZLARZ applies an elementary reflector (as returned by stzrzf) to a
general matrix.
Detailed Description¶
Function Documentation¶
subroutine CLARZ (character side, integer m, integer n, integer l, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)¶
CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Purpose:
!> !> CLARZ 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. !> !> H is a product of k elementary reflectors as returned by CTZRZF. !>
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. !>
L
!> L is INTEGER !> The number of entries of the vector V containing !> the meaningful part of the Householder vectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !>
V
!> V is COMPLEX array, dimension (1+(L-1)*abs(INCV)) !> The vector v in the representation of H as returned by !> CTZRZF. 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Further Details:
!>
Definition at line 146 of file clarz.f.
subroutine DLARZ (character side, integer m, integer n, integer l, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)¶
DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Purpose:
!> !> DLARZ 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. !> !> !> H is a product of k elementary reflectors as returned by DTZRZF. !>
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. !>
L
!> L is INTEGER !> The number of entries of the vector V containing !> the meaningful part of the Householder vectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !>
V
!> V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV)) !> The vector v in the representation of H as returned by !> DTZRZF. 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Further Details:
!>
Definition at line 144 of file dlarz.f.
subroutine SLARZ (character side, integer m, integer n, integer l, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)¶
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Purpose:
!> !> SLARZ 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. !> !> !> H is a product of k elementary reflectors as returned by STZRZF. !>
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. !>
L
!> L is INTEGER !> The number of entries of the vector V containing !> the meaningful part of the Householder vectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !>
V
!> V is REAL array, dimension (1+(L-1)*abs(INCV)) !> The vector v in the representation of H as returned by !> STZRZF. 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Further Details:
!>
Definition at line 144 of file slarz.f.
subroutine ZLARZ (character side, integer m, integer n, integer l, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)¶
ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Purpose:
!> !> ZLARZ 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. !> !> H is a product of k elementary reflectors as returned by ZTZRZF. !>
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. !>
L
!> L is INTEGER !> The number of entries of the vector V containing !> the meaningful part of the Householder vectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !>
V
!> V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV)) !> The vector v in the representation of H as returned by !> ZTZRZF. 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Further Details:
!>
Definition at line 146 of file zlarz.f.
Author¶
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