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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 

!>          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.

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.

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.

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.

Author

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