Purpose
 =======
 
       LA_GELS computes the minimum-norm least squares solution to one 
 or more real or complex linear systems of the form A*x = b, A^T*x = b
 or A^H*x = b using a QR or LQ factorization of A. Matrix A is 
 rectangular assumed to be of full rank. The vectors b and correspon-
 ding solution vectors x are the columns of matrices denoted B and X,
 respectively.
 
 ==========
 
       SUBROUTINE LA_GELS( A, B, TRANS=trans, INFO=info )
           <type>(<wp>), INTENT( INOUT ) :: A(:,:), <rhs>
 	   CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: TRANS
 	   INTEGER, INTENT(OUT), OPTIONAL :: INFO
       where
          <type> ::= REAL | COMPLEX
 	  <wp>   ::= KIND(1.0) | KIND(1.0D0)
          <rhs>  ::= B(:,:) | B(:)
 
 Arguments
 =========
 
 A        (input/output) REAL or COMPLEX rectangular array, shape (:,:).
          On entry, the matrix A.
 	  On exit, if size(A,1) >= size(A,2), A is overwritten by
 	  details of its QR factorization. If size(A,1) < size(A,2), A 
 	  is overwritten by details of its LQ factorization.
 B        (input/output) REAL or COMPLEX array, shape (:,:) with 
          size(B,1) = max(size(A,1), size(A,2)) or shape (:) with 
 	  size(B) = max(size(A,1); size(A,2)).
 	  On entry, the matrix B.
 	  On exit, the solution matrix X. There are four cases:
 	   1. If TRANS = 'N' and size(A,1) >= size(A,2), then rows 1 
 	      to size(A,2) of B contain, columnwise, the least squares
 	      solution vector(s); the residual sum of squares for the 
 	      solution vector in a column of B is given by the sum of
 	      squares of elements in rows size(A,2)+1 to size(A,1) of
 	      that column.
 	   2. If TRANS = 'N' and size(A,1) < size(A,2), then rows 1 
 	      to size(A,2) of B contain, columnwise, the minimum norm 
 	      solution vector(s).
 	   3. If TRANS = 'T' or TRANS = 'C', and size(A,1)>=size(A,2),
 	      then rows 1 to size(A,1) of B contain, columnwise, the 
 	      minimum norm solution vector(s).
 	   4. If TRANS = 'T' or TRANS = 'C', and size(A,1) < size(A,2),
 	      then rows 1 to size(A,1) of B contain, columnwise, the 
 	      least squares solution vector(s); the residual sum of 
 	      squares for the solution vector in a column of B is given
 	      by the sum of squares of elements in rows size(A,1)+1 to 
 	      size(A,2) of that column.
 TRANS    Optional (input) CHARACTER(LEN=1).
          Specifies the form of the system of equations:
 	   = 'N': Ax = b (No transpose)
           = 'T': A^T*x = b (Transpose)
 	   = 'C': A^H*x = b (Conjugate transpose)
 	  Default value: 'N'.
 INFO     Optional (output) INTEGER
           = 0: successful exit.
 	   < 0: if INFO = -i, the i-th argument had an illegal value.
 	  If INFO is not present and an error occurs, then the program
 	  is terminated with an error message.