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dgeqp3.f(3)				      LAPACK				      dgeqp3.f(3)

       dgeqp3.f -

       subroutine dgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)

Function/Subroutine Documentation
   subroutine dgeqp3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
       integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision,
       dimension( * )WORK, integerLWORK, integerINFO)


	    DGEQP3 computes a QR factorization with column pivoting of a
	    matrix A:  A*P = Q*R  using Level 3 BLAS.


		     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 DOUBLE PRECISION 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 trapezoidal 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


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


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


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


		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
		     On exit, if INFO=0, WORK(1) returns the optimal LWORK.


		     The dimension of the array WORK. LWORK >= 3*N+1.
		     For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
		     is the optimal blocksize.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.


		     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.

	   September 2012

       Further Details:

	     The matrix Q is represented as a product of elementary reflectors

		Q = H(1) H(2) . . . H(k), where k = min(m,n).

	     Each H(i) has the form

		H(i) = I - tau * v * v**T

	     where tau is a real scalar, and v is a real/complex 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), and tau in TAU(i).

	   G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer
	   Science Dept., Duke University, USA

       Definition at line 152 of file dgeqp3.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dgeqp3.f(3)
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