zungbr (l)  Linux Man Pages
zungbr: generates one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form
NAME
ZUNGBR  generates one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal formSYNOPSIS
 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( * )
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 = aqQaq, A is assumed to have been an MbyK 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(m1) and ZUNGBR returns Q as an MbyM matrix.
If VECT = aqPaq, A is assumed to have been a KbyN 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(n1) . . . G(2) G(1) and ZUNGBR returns P**H as an NbyN 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:
= aqQaq: generate Q;
= aqPaq: 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 = aqQaq, M >= N >= min(M,K); if VECT = aqPaq, N >= M >= min(N,K).
 K (input) INTEGER
 If VECT = aqQaq, the number of columns in the original MbyK matrix reduced by ZGEBRD. If VECT = aqPaq, the number of rows in the original KbyN matrix reduced by ZGEBRD. K >= 0.
 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 MbyN 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 = aqQaq (min(N,K)) if VECT = aqPaq 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 (workspace/output) COMPLEX*16 array, dimension (MAX(1,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. 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 (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value