.TH ZUNGQR 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZUNGQR - an M-by-N complex matrix Q with orthonormal columns, .SH SYNOPSIS .TP 19 SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) .TP 19 .ti +4 INTEGER INFO, K, LDA, LWORK, M, N .TP 19 .ti +4 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) .SH PURPOSE ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M .br Q = H(1) H(2) . . . H(k) .br as returned by ZGEQRF. .br .SH ARGUMENTS .TP 8 M (input) INTEGER The number of rows of the matrix Q. M >= 0. .TP 8 N (input) INTEGER The number of columns of the matrix Q. M >= N >= 0. .TP 8 K (input) INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. .TP 8 A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q. .TP 8 LDA (input) INTEGER The first dimension of the array A. LDA >= max(1,M). .TP 8 TAU (input) COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQRF. .TP 8 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. .TP 8 LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument has an illegal value