ZGEQRT3(3)     LAPACK routine of NEC Numeric Library Collection     ZGEQRT3(3)



NAME
       ZGEQRT3

SYNOPSIS
       RECURSIVE SUBROUTINE ZGEQRT3 (M, N, A, LDA, T, LDT, INFO)



PURPOSE
            ZGEQRT3 RECURSIVEly computes a QR factorization of a complex M-by-N
            matrix A, using the compact WY representation of Q.





ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= N.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           A         (input/output)
                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the complex M-by-N matrix A.  On exit, the elements on
                     and above the diagonal contain the N-by-N upper triangular matrix R;
                     the elements below the diagonal are the columns of V.  See below for
                     further details.

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

           T         (output)
                     T is COMPLEX*16 array, dimension (LDT,N)
                     The N-by-N upper triangular factor of the block reflector.
                     The elements on and above the diagonal contain the block
                     reflector T; the elements below the diagonal are not used.
                     See below for further details.

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

           INFO      (output)
                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value






FURTHER DETAILS
             The matrix V stores the elementary reflectors H(i) in the i-th column
             below the diagonal. For example, if M=5 and N=3, the matrix V is

                          V = (  1       )
                              ( v1  1    )
                              ( v1 v2  1 )
                              ( v1 v2 v3 )
                              ( v1 v2 v3 )

             where the vi's represent the vectors which define H(i), which are returned
             in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
             block reflector H is then given by

                          H = I - V * T * V**H

             where V**H is the conjugate transpose of V.

             For details of the algorithm, see Elmroth and Gustavson (cited above).



LAPACK routine                  31 October 2017                     ZGEQRT3(3)