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sgeqpf.f(3)				      LAPACK				      sgeqpf.f(3)

       sgeqpf.f -

       subroutine sgeqpf (M, N, A, LDA, JPVT, TAU, WORK, INFO)

Function/Subroutine Documentation
   subroutine sgeqpf (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer,
       dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)


	    This routine is deprecated and has been replaced by routine SGEQP3.

	    SGEQPF computes a QR factorization with column pivoting of a
	    real M-by-N matrix A: A*P = Q*R.


		     M is INTEGER
		     The number of rows of the matrix A. M >= 0.


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


		     A is REAL array, dimension (LDA,N)
		     On entry, the M-by-N matrix A.
		     On exit, the upper triangle of the array contains the
		     min(M,N)-by-N upper triangular matrix R; the elements
		     below the diagonal, together with the array TAU,
		     represent the orthogonal matrix Q as a product of
		     min(m,n) elementary reflectors.


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


		     JPVT is INTEGER array, dimension (N)
		     On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
		     to the front of A*P (a leading column); if JPVT(i) = 0,
		     the i-th column of A is a free column.
		     On exit, if JPVT(i) = k, then the i-th column of A*P
		     was the k-th column of A.


		     TAU is REAL array, dimension (min(M,N))
		     The scalar factors of the elementary reflectors.


		     WORK is REAL array, dimension (3*N)


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

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Further Details:

	     The matrix Q is represented as a product of elementary reflectors

		Q = H(1) H(2) . . . H(n)

	     Each H(i) has the form

		H = I - tau * v * v**T

	     where tau is a real scalar, and v is a real vector with
	     v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).

	     The matrix P is represented in jpvt as follows: If
		jpvt(j) = i
	     then the jth column of P is the ith canonical unit vector.

	     Partial column norm updating strategy modified by
	       Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
	       University of Zagreb, Croatia.
	     -- April 2011							--
	     For more details see LAPACK Working Note 176.

       Definition at line 143 of file sgeqpf.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      sgeqpf.f(3)
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