ZUNGHR(3)      LAPACK routine of NEC Numeric Library Collection      ZUNGHR(3)



NAME
       ZUNGHR

SYNOPSIS
       SUBROUTINE ZUNGHR (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            ZUNGHR generates a complex unitary matrix Q which is defined as the
            product of IHI-ILO elementary reflectors of order N, as returned by
            ZGEHRD:

            Q = H(ilo) H(ilo+1) . . . H(ihi-1).




ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the matrix Q. N >= 0.

           ILO       (input)
                     ILO is INTEGER

           IHI       (input)
                     IHI is INTEGER

                     ILO and IHI must have the same values as in the previous call
                     of ZGEHRD. Q is equal to the unit matrix except in the
                     submatrix Q(ilo+1:ihi,ilo+1:ihi).
                     1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

           A         (input/output)
                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the vectors which define the elementary reflectors,
                     as returned by ZGEHRD.
                     On exit, the N-by-N unitary matrix Q.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= max(1,N).

           TAU       (input)
                     TAU is COMPLEX*16 array, dimension (N-1)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by ZGEHRD.

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK. LWORK >= IHI-ILO.
                     For optimum performance LWORK >= (IHI-ILO)*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)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value



LAPACK routine                  31 October 2017                      ZUNGHR(3)