 Usage:  {y,aux,jpvt} = qr(x,{pvt})  
 
 Input:

  x                      n x p matrix 
                         
  pvt                    p x 1 vector. The vector integers that control the selection 
                         of the pivot columns. The k-th column of x 
                         is placed in one of three classes according to the 
                         value of jpvt[k]: if pvt[k]> 0, then k-th column is an initial 
                         column, if pvt[k]= 0, then k-th column is a free column, 
                         if pvt[k] < 0, then k-th column is a final column. 
                         Before the decomposition is computed, initial columns 
                         are moved to the beginning of the matrix x and final 
                         columns to the end. Both initial and final columns 
                         are frozen in place during the computation and only 
                         free columns are moved. At the k-th stage of the 
                         reduction, if k-th column is occupied by a free column 
                         it is interchanged with the free column of largest 
                         reduced l_2-norm. 
                         
 Output:

  y                      n x p matrix. y contains in its upper triangle the upper 
                         triangular matrix R of the QR factorization. 
                         Below its diagonal x contains information from 
                         which the orthogonal part of the decomposition 
                         can be recovered. 
                         
                         
  aux                    p x 1 vector. aux contains further information required to recover 
                         the orthogonal part of the decomposition. 
                         
  jpvt                   n x 1 vector. jpvt contains the index of the column of y 
                         that has been interchanged into the k-th column of the 
                         original matrix, if pivoting was requested. 
                         
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(C) MD*TECH Method and Data Technologies, 17.8.2000
