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RedHat 9 (Linux i386) - man page for dgelsx (redhat section l)

DGELSX(l)					)					DGELSX(l)

NAME
       DGELSX - routine is deprecated and has been replaced by routine DGELSY

SYNOPSIS
       SUBROUTINE DGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, INFO )

	   INTEGER	  INFO, LDA, LDB, M, N, NRHS, RANK

	   DOUBLE	  PRECISION RCOND

	   INTEGER	  JPVT( * )

	   DOUBLE	  PRECISION A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
       This  routine  is deprecated and has been replaced by routine DGELSY.  DGELSX computes the
       minimum-norm solution to a real linear least squares problem:
	   minimize || A * X - B ||
       using a complete orthogonal factorization of A.	A is an M-by-N matrix which may be  rank-
       deficient.

       Several	right hand side vectors b and solution vectors x can be handled in a single call;
       they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS
       solution matrix X.

       The routine first computes a QR factorization with column pivoting:
	   A * P = Q * [ R11 R12 ]
		       [  0  R22 ]
       with R11 defined as the largest leading submatrix whose estimated condition number is less
       than 1/RCOND.  The order of R11, RANK, is the effective rank of A.

       Then, R22 is considered to be negligible, and R12 is annihilated by orthogonal transforma-
       tions from the right, arriving at the complete orthogonal factorization:
	  A * P = Q * [ T11 0 ] * Z
		      [  0  0 ]
       The minimum-norm solution is then
	  X = P * Z' [ inv(T11)*Q1'*B ]
		     [	      0       ]
       where Q1 consists of the first RANK columns of Q.

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.

       NRHS    (input) INTEGER
	       The  number  of right hand sides, i.e., the number of columns of matrices B and X.
	       NRHS >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, A has been overwritten by details of  its
	       complete orthogonal factorization.

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

       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       On entry, the M-by-NRHS right hand side matrix B.  On exit, the N-by-NRHS solution
	       matrix X.  If m >= n and RANK = n, the residual sum-of-squares for the solution in
	       the i-th column is given by the sum of squares of elements N+1:M in that column.

       LDB     (input) INTEGER
	       The leading dimension of the array B. LDB >= max(1,M,N).

       JPVT    (input/output) INTEGER array, dimension (N)
	       On  entry, if JPVT(i) .ne. 0, the i-th column of A is an initial column, otherwise
	       it is a free column.  Before the QR factorization of A, all  initial  columns  are
	       permuted  to the leading positions; only the remaining free columns are moved as a
	       result of column pivoting during the factorization.  On exit, if JPVT(i) = k, then
	       the i-th column of A*P was the k-th column of A.

       RCOND   (input) DOUBLE PRECISION
	       RCOND  is used to determine the effective rank of A, which is defined as the order
	       of the largest leading triangular submatrix R11 in the QR factorization with  piv-
	       oting of A, whose estimated condition number < 1/RCOND.

       RANK    (output) INTEGER
	       The  effective  rank of A, i.e., the order of the submatrix R11.  This is the same
	       as the order of the submatrix T11 in the complete orthogonal factorization of A.

       WORK    (workspace) DOUBLE PRECISION array, dimension
	       (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),

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

LAPACK version 3.0			   15 June 2000 				DGELSX(l)


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