table of contents
| ungl2(3) | LAPACK | ungl2(3) |
NAME¶
ungl2 - {un,or}gl2: generate explicit Q, level 2, step in unglq
SYNOPSIS¶
Functions¶
subroutine cungl2 (m, n, k, a, lda, tau, work, info)
CUNGL2 generates all or part of the unitary matrix Q from an LQ
factorization determined by cgelqf (unblocked algorithm). subroutine
dorgl2 (m, n, k, a, lda, tau, work, info)
DORGL2 subroutine sorgl2 (m, n, k, a, lda, tau, work, info)
SORGL2 subroutine zungl2 (m, n, k, a, lda, tau, work, info)
ZUNGL2 generates all or part of the unitary matrix Q from an LQ
factorization determined by cgelqf (unblocked algorithm).
Detailed Description¶
Function Documentation¶
subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)¶
CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
Purpose:
CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF.
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 i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by CGELQF in the first 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 CGELQF.
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 dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)¶
DORGL2
Purpose:
DORGL2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k) . . . H(2) H(1)
as returned by DGELQF.
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 i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by DGELQF in the first 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 DGELQF.
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 sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)¶
SORGL2
Purpose:
SORGL2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k) . . . H(2) H(1)
as returned by SGELQF.
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 i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by SGELQF in the first 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 SGELQF.
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 zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)¶
ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
Purpose:
ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by ZGELQF.
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 i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by ZGELQF in the first 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 ZGELQF.
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¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |