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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