
NAMEzungbr.f SYNOPSISFunctions/Subroutinessubroutine zungbr (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO) Function/Subroutine Documentationsubroutine 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 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 = 'P', 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. VECT
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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 MbyK matrix reduced by ZGEBRD. If VECT = 'P', the number of rows in the original KbyN 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 MbyN 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 ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
Definition at line 158 of file zungbr.f.
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