zungbr.f(3)

NAME
zungbr.f -

SYNOPSIS

  Functions/Subroutines
subroutine zungbr (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGBR

Function/Subroutine Documentation

  subroutine zungbr (characterVECT, integerM, integerN, integerK, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, integerINFO)

ZUNGBR

Purpose:

     ZUNGBR generates one of the complex unitary matrices Q or P**H
     determined by ZGEBRD when reducing a complex matrix A to bidiagonal
     form: A = Q * B * P**H.  Q and P**H are defined as products of
     elementary reflectors H(i) or G(i) respectively.
     If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
     is of order M:
     if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
     columns of Q, where m >= n >= k;
     if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
     M-by-M matrix.
     If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
     is of order N:
     if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
     rows of P**H, where n >= m >= k;
     if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
     an N-by-N matrix.

Parameters:
    VECT

              VECT is CHARACTER*1
              Specifies whether the matrix Q or the matrix P**H is
              required, as defined in the transformation applied by ZGEBRD:
              = 'Q':  generate Q;
              = 'P':  generate P**H.

    M

              M is INTEGER
              The number of rows of the matrix Q or P**H to be returned.
              M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q or P**H to be returned.
              N >= 0.
              If VECT = 'Q', M >= N >= min(M,K);
              if VECT = 'P', N >= M >= min(N,K).

    K

              K is INTEGER
              If VECT = 'Q', the number of columns in the original M-by-K
              matrix reduced by ZGEBRD.
              If VECT = 'P', the number of rows in the original K-by-N
              matrix reduced by ZGEBRD.
              K >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by ZGEBRD.
              On exit, the M-by-N matrix Q or P**H.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= M.

    TAU

              TAU is COMPLEX*16 array, dimension
                                    (min(M,K)) if VECT = 'Q'
                                    (min(N,K)) if VECT = 'P'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i) or G(i), which determines Q or P**H, as
              returned by ZGEBRD in its array argument TAUQ or TAUP.

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,min(M,N)).
              For optimum performance LWORK >= min(M,N)*NB, where NB
              is the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    April 2012

Definition at line 158 of file zungbr.f.

Author

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