zgeqrt3.f(3)							      LAPACK							      zgeqrt3.f(3)

NAME

       zgeqrt3.f -

SYNOPSIS

   Functions/Subroutines
       recursive subroutine zgeqrt3 (M, N, A, LDA, T, LDT, INFO)
	   ZGEQRT3

Function/Subroutine Documentation
   recursive subroutine zgeqrt3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT,
       integerINFO)
       ZGEQRT3

       Purpose:

	    ZGEQRT3 recursively computes a QR factorization of a complex 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 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

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

	   T

		     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

		     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:
	   November 2011

       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).

       Definition at line 133 of file zgeqrt3.f.

Author
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Version 3.4.1							  Sun May 26 2013						      zgeqrt3.f(3)