table of contents
| ungr2(3) | Library Functions Manual | 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.
Definition at line 113 of file cungr2.f.
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.
Definition at line 113 of file dorgr2.f.
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.
Definition at line 113 of file sorgr2.f.
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.
Definition at line 113 of file zungr2.f.
Author¶
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