ungr2(3) Library Functions Manual ungr2(3)

ungr2 - {un,or}gr2: step in ungrq


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).

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.

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.

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.

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.

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