sgeqrt3()

recursive subroutine sgeqrt3	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldt, * )	T,
		integer	LDT,
		integer	INFO
	)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

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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

[in]	M	M is INTEGER The number of rows of the matrix A. M >= N.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	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.
[in]	LDT	LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N).
[out]	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.

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).