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dgels(3P)		    Sun Performance Library		     dgels(3P)

NAME
       dgels  -	 solve	overdetermined	or underdetermined real linear systems
       involving an M-by-N matrix A, or its transpose, using a QR or  LQ  fac‐
       torization of A

SYNOPSIS
       SUBROUTINE DGELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
	     INFO)

       CHARACTER * 1 TRANSA
       INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO
       DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)

       SUBROUTINE DGELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
	     INFO)

       CHARACTER * 1 TRANSA
       INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO
       DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)

   F95 INTERFACE
       SUBROUTINE GELS([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB], [WORK],
	      LDWORK, [INFO])

       CHARACTER(LEN=1) :: TRANSA
       INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: A, B

       SUBROUTINE GELS_64([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB],
	      [WORK], LDWORK, [INFO])

       CHARACTER(LEN=1) :: TRANSA
       INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: A, B

   C INTERFACE
       #include <sunperf.h>

       void  dgels  (char  transa, int m, int n, int nrhs, double* a, int lda,
		 double* b, int ldb, int* info);

       void dgels_64 (char transa, long m, long n, long nrhs, double* a,  long
		 lda, double* b, long ldb, long* info);

PURPOSE
       dgels  solves  overdetermined  or  underdetermined  real linear systems
       involving an M-by-N matrix A, or its transpose, using a QR or  LQ  fac‐
       torization of A.	 It is assumed that A has full rank.

       The following options are provided:

       1. If TRANS = 'N' and m >= n:  find the least squares solution of
	  an overdetermined system, i.e., solve the least squares problem
		       minimize || B - A*X ||.

       2. If TRANS = 'N' and m < n:  find the minimum norm solution of
	  an underdetermined system A * X = B.

       3. If TRANS = 'T' and m >= n:  find the minimum norm solution of
	  an undetermined system A**T * X = B.

       4. If TRANS = 'T' and m < n:  find the least squares solution of
	  an overdetermined system, i.e., solve the least squares problem
		       minimize || B - A**T * X ||.

       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.

ARGUMENTS
       TRANSA (input)
		 = 'N': the linear system involves A;
		 = 'T': the linear system involves A**T.

		 TRANSA is defaulted to 'N' for F95 INTERFACE.

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

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

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

       A (input/output)
		 On entry, the M-by-N matrix A.	 On exit, if  M	 >=  N,	 A  is
		 overwritten by details of its QR factorization as returned by
		 DGEQRF; if M <	 N, A is overwritten by details of its LQ fac‐
		 torization as returned by DGELQF.

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

       B (input/output)
		 On  entry,  the  matrix  B of right hand side vectors, stored
		 columnwise; B is M-by-NRHS if TRANSA = 'N', or	 N-by-NRHS  if
		 TRANSA = 'T'.	On exit, B is overwritten by the solution vec‐
		 tors, stored columnwise: if TRANSA = 'N' and m >= n,  rows  1
		 to  n	of  B  contain the least squares solution vectors; the
		 residual sum of squares for the solution in  each  column  is
		 given by the sum of squares of elements N+1 to M in that col‐
		 umn; if TRANSA = 'N' and m < n, rows 1 to N of B contain  the
		 minimum  norm	solution  vectors; if TRANSA = 'T' and m >= n,
		 rows 1 to M of B contain the minimum norm  solution  vectors;
		 if TRANSA = 'T' and m < n, rows 1 to M of B contain the least
		 squares solution vectors; the residual sum of squares for the
		 solution  in  each  column  is given by the sum of squares of
		 elements M+1 to N in that column.

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

       WORK (workspace)
		 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.

       LDWORK (input)
		 The dimension of the array WORK.  LDWORK >= max( 1, MN + max(
		 MN,  NRHS ) ).	 For optimal performance, LDWORK >= max( 1, MN
		 + max( MN, NRHS )*NB ).  where MN = min(M,N) and  NB  is  the
		 optimum block size.

		 If  LDWORK  = -1, then a workspace query is assumed; the rou‐
		 tine 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 LDWORK is issued by XERBLA.

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

				  6 Mar 2009			     dgels(3P)
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