LUPDT Call

Language Reference

provides updating and downdating for rank deficient linear least squares solutions, complete orthogonal factorization, and Moore-Penrose inverses

CALL LUPDT( lup, bup, sup, l, z<, b, y<, ssq>>);

The LUPDT subroutine returns the following values:

lup: is an n ×n lower triangular matrix L that is updated or downdated by using the q rows in Z.
bup: is an n ×p 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 inputs to the LUPDT subroutine are as follows:

l: specifies an n ×n lower triangular matrix L to be updated or downdated by q row vectors z stored in the q ×n matrix Z. Only the lower triangle of l is used; the upper triangle may contain any information.
z: is a q ×n matrix Z used rowwise to update or downdate the matrix L.
b: specifies an optional n ×p matrix B 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 q ×p matrix Y used rowwise to update or downdate the right-hand-side matrix B.
ssq: specifies an optional p ×1 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 ${\tilde{L}\tilde{L}^' = LL^' + ZZ^'}$ .See the LUPDT Example section for an example of the LUPDT call.