CGELSX man page on IRIX

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CGELSX(3F)							    CGELSX(3F)

NAME
     CGELSX - compute the minimum-norm solution to a complex linear least
     squares problem

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

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

	 REAL		RCOND

	 INTEGER	JPVT( * )

	 REAL		RWORK( * )

	 COMPLEX	A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
     CGELSX computes the minimum-norm solution to a complex 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
     unitary transformations 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.

									Page 1

CGELSX(3F)							    CGELSX(3F)

     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) COMPLEX 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) COMPLEX 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) REAL
	     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 pivoting 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) COMPLEX array, dimension
	     (min(M,N) + max( N, 2*min(M,N)+NRHS )),

     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

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