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. |