NAME

       dgeqrt3.f -

SYNOPSIS

   Functions/Subroutines
       recursive subroutine dgeqrt3 (M, N, A, LDA, T, LDT, INFO)
           DGEQRT3 recursively computes a QR factorization of a general real or complex matrix
           using the compact WY representation of Q.

Function/Subroutine Documentation

   recursive subroutine dgeqrt3 (integerM, integerN, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( ldt, * )T, integerLDT, integerINFO)
       DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using
       the compact WY representation of Q.

       Purpose:

            DGEQRT3 recursively computes a QR factorization of a real M-by-N
            matrix A, using the compact WY representation of Q.

            Based on the algorithm of Elmroth and Gustavson,
            IBM J. Res. Develop. Vol 44 No. 4 July 2000.

       Parameters:
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= N.

           N

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

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the real 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

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

           T

                     T is DOUBLE PRECISION 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

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

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       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**T

             where V**T is the transpose of V.

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

       Definition at line 133 of file dgeqrt3.f.

Author

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