zungbr.f - Man Page

subroutine zungbr (vect, m, n, k, a, lda, tau, work, lwork, info)
ZUNGBR

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.

Definition at line 156 of file zungbr.f.