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sgeqrt3.f(3)                        LAPACK                        sgeqrt3.f(3)

NAME
       sgeqrt3.f -

SYNOPSIS
   Functions/Subroutines
       recursive subroutine sgeqrt3 (M, N, A, LDA, T, LDT, INFO)
           SGEQRT3 recursively computes a QR factorization of a general real
           or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation
   recursive subroutine sgeqrt3 (integerM, integerN, real, dimension( lda, *
       )A, integerLDA, real, dimension( ldt, * )T, integerLDT, integerINFO)
       SGEQRT3 recursively computes a QR factorization of a general real or
       complex matrix using the compact WY representation of Q.

       Purpose:

            SGEQRT3 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 REAL 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 REAL 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 sgeqrt3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                   Sat Nov 16 2013                   sgeqrt3.f(3)