Language Reference
LUPDT Call
CALL LUPDT (lup, bup, sup, L, z <, b> <, y> <, ssq> ) ;
This subroutine is supported by the IML procedure and the iml action.
The LUPDT subroutine provides updating and downdating for rank deficient linear least squares solutions, complete orthogonal factorization, and Moore-Penrose inverses.
The LUPDT subroutine returns the following values:
- lup
is an
lower triangular matrix L that is updated or downdated by using the q rows in Z. - bup
is an
matrix B of right-hand sides that is updated or downdated by using the q rows in Y. If b is not specified, bup is not accessible. - sup
is a p vector of square roots of residual sum of squares that is updated or downdated by using the q rows in Y. If ssq is not specified, sup is not accessible.
The input arguments to the LUPDT subroutine are as follows:
- L
specifies an
lower triangular matrix 
to be updated or downdated by q row vectors z stored in the 
matrix Z. Only the lower triangle of L is used; the upper triangle can contain any information. - z
is a
matrix Z used rowwise to update or downdate the matrix L. - b
specifies an optional
matrix 
of right-hand sides that have to be updated or downdated simultaneously with L. If b is specified, the argument y must be specified. - y
specifies an optional
matrix Y used rowwise to update or downdate the right-hand-side matrix b. - ssq
specifies an optional
vector that, if b is specified, specifies the square root of the error sum of squares that should be updated or downdated simultaneously with L and b.
The relevant formula for the LUPDT call is 
. See the section Complete QR Decomposition with LUPDT in the documentation for the RZLIND call.