SYNOPSIS
 SUBROUTINE DGELS(
 TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO )
 CHARACTER TRANS
 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
DGELS solves overdetermined or underdetermined real linear systems involving an MbyN matrix A, or its transpose, using a QR or LQ factorization 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 MbyNRHS right hand side matrix B and the NbyNRHS solution matrix X.
ARGUMENTS
 TRANS (input) CHARACTER*1

= 'N': the linear system involves A;
= 'T': the linear system involves A**T.  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 the matrices B and X. NRHS >=0.
 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 On entry, the MbyN 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 factorization as returned by DGELQF.
 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 matrix B of right hand side vectors, stored columnwise; B is MbyNRHS if TRANS = 'N', or NbyNRHS if TRANS = 'T'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise: if TRANS = '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 column; if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors; if TRANS = 'T' and m >= n, rows 1 to M of B contain the minimum norm solution vectors; if TRANS = '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) INTEGER
 The leading dimension of the array B. LDB >= MAX(1,M,N).
 WORK (workspace/output) DOUBLE PRECISION 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 >= max( 1, MN + max( MN, NRHS ) ). For optimal performance, LWORK >= max( 1, MN + max( MN, NRHS )*NB ). where MN = min(M,N) and NB is the optimum 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.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the ith diagonal element of the triangular factor of A is zero, so that A does not have full rank; the least squares solution could not be computed.