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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				 Tue Sep 25 2012			     sgeqrt3.f(3)
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