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- testing 3.12.0-4
- unstable 3.12.1-2
- experimental 3.12.1-1
| larz(3) | LAPACK | 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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Further Details:
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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Further Details:
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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Further Details:
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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Further Details:
Author¶
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| Tue Jan 14 2025 16:19:47 | Version 3.12.0 |