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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 

!>          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 Tennessee

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 

!>          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 Tennessee

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 

!>          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 Tennessee

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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file zungr2.f.

Author

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