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

 

 Input:



  x                      n x p matrix 

                         

                         

  pvt                    p x 1 vector. The vector of 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, 21.9.2000

