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



NAME
       ZUNGTR

SYNOPSIS
       SUBROUTINE ZUNGTR (UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            ZUNGTR generates a complex unitary matrix Q which is defined as the
            product of n-1 elementary reflectors of order N, as returned by
            ZHETRD:

            if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

            if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).




ARGUMENTS
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U': Upper triangle of A contains elementary reflectors
                            from ZHETRD;
                     = 'L': Lower triangle of A contains elementary reflectors
                            from ZHETRD.

           N         (input)
                     N is INTEGER
                     The order of the matrix Q. 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 ZHETRD.
                     On exit, the N-by-N unitary matrix Q.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= 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 ZHETRD.

           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 >= N-1.
                     For optimum performance LWORK >= (N-1)*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                      ZUNGTR(3)