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NAME ZUNGBR - generate one of the matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form SYNOPSIS SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) CHARACTER VECT INTEGER INFO, K, LDA, LWORK, M, N COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK ) PURPOSE ZUNGBR generates one of the 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. ARGUMENTS VECT (input) 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 (input) INTEGER The number of rows of the matrix Q or P**H to be returned. M >= 0. N (input) 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 (input) INTEGER K >= 0. 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. A (input/output) 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 (input) INTEGER The leading dimension of the array A. LDA >= M. TAU (input) 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 elemen- tary reflector H(i) or G(i), which determines Q or P**H, as returned by ZGEBRD in its array argument TAUQ or TAUP. WORK (workspace) COMPLEX*16 array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) 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. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value