table of contents
| ungr2(3) | LAPACK | ungr2(3) |
NAME¶
ungr2 - {un,or}gr2: step in ungrq
SYNOPSIS¶
Functions¶
subroutine cungr2 (m, n, k, a, lda, tau, work, info)
CUNGR2 generates all or part of the unitary matrix Q from an RQ
factorization determined by cgerqf (unblocked algorithm). subroutine
dorgr2 (m, n, k, a, lda, tau, work, info)
DORGR2 generates all or part of the orthogonal matrix Q from an RQ
factorization determined by sgerqf (unblocked algorithm). subroutine
sorgr2 (m, n, k, a, lda, tau, work, info)
SORGR2 generates all or part of the orthogonal matrix Q from an RQ
factorization determined by sgerqf (unblocked algorithm). subroutine
zungr2 (m, n, k, a, lda, tau, work, info)
ZUNGR2 generates all or part of the unitary matrix Q from an RQ
factorization determined by cgerqf (unblocked algorithm).
Detailed Description¶
Function Documentation¶
subroutine cungr2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)¶
CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).
Purpose:
CUNGR2 generates an m by n complex matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n
Q = H(1)**H H(2)**H . . . H(k)**H
as returned by CGERQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGERQF in the last k rows of its array argument
A.
On exit, the m-by-n matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGERQF.
WORK
WORK is COMPLEX array, dimension (M)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dorgr2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)¶
DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).
Purpose:
DORGR2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n
Q = H(1) H(2) . . . H(k)
as returned by DGERQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGERQF in the last k rows of its array argument
A.
On exit, the m by n matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGERQF.
WORK
WORK is DOUBLE PRECISION array, dimension (M)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sorgr2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)¶
SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).
Purpose:
SORGR2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n
Q = H(1) H(2) . . . H(k)
as returned by SGERQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGERQF in the last k rows of its array argument
A.
On exit, the m by n matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGERQF.
WORK
WORK is REAL array, dimension (M)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zungr2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)¶
ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).
Purpose:
ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n
Q = H(1)**H H(2)**H . . . H(k)**H
as returned by ZGERQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGERQF in the last k rows of its array argument
A.
On exit, the m-by-n matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGERQF.
WORK
WORK is COMPLEX*16 array, dimension (M)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
Generated automatically by Doxygen for LAPACK from the source code.
| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |