cgeqp3 man page on Scientific

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CGEQP3(1)		 LAPACK routine (version 3.2)		     CGEQP3(1)

NAME
       CGEQP3 - computes a QR factorization with column pivoting of a matrix A

SYNOPSIS
       SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   INTEGER	  JPVT( * )

	   REAL		  RWORK( * )

	   COMPLEX	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       CGEQP3  computes a QR factorization with column pivoting of a matrix A:
       A*P = Q*R  using Level 3 BLAS.

ARGUMENTS
       M       (input) INTEGER
	       The number of rows of the matrix A. M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input/output) COMPLEX 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  unitary matrix Q as a product of min(M,N)
	       elementary reflectors.

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

       JPVT    (input/output) 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     (output) COMPLEX array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

       WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
	       On exit, if INFO=0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The  dimension  of  the	array WORK. LWORK >= N+1.  For optimal
	       performance LWORK >= ( N+1 )*NB, where NB is the optimal block‐
	       size.   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.

       RWORK   (workspace) REAL array, dimension (2*N)

       INFO    (output) INTEGER
	       = 0: successful exit.
	       < 0: if INFO = -i, the i-th argument had an illegal value.

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'
       where tau is a real/complex 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).
       Based on contributions by
	 G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
	 X. Sun, Computer Science Dept., Duke University, USA

 LAPACK routine (version 3.2)	 November 2008			     CGEQP3(1)
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