Language Reference: LUPDT Call

LUPDT Call

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

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 $\text{[math]}$ lower triangular matrix $\text{[math]}$ that is updated or downdated by using the $\text{[math]}$ rows in $\text{[math]}$ .
bup: is an $\text{[math]}$ matrix $\text{[math]}$ of right-hand sides that is updated or downdated by using the $\text{[math]}$ rows in $\text{[math]}$ . If b is not specified, bup is not accessible.
sup: is a $\text{[math]}$ vector of square roots of residual sum of squares that is updated or downdated by using the $\text{[math]}$ rows in $\text{[math]}$ . If ssq is not specified, sup is not accessible.

The input arguments to the LUPDT subroutine are as follows:

L: specifies an $\text{[math]}$ lower triangular matrix $\text{[math]}$ to be updated or downdated by $\text{[math]}$ row vectors $\text{[math]}$ stored in the $\text{[math]}$ matrix $\text{[math]}$ . Only the lower triangle of L is used; the upper triangle can contain any information.
z: is a $\text{[math]}$ matrix $\text{[math]}$ used rowwise to update or downdate the matrix $\text{[math]}$ .
b: specifies an optional $\text{[math]}$ matrix $\text{[math]}$ 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 $\text{[math]}$ matrix $\text{[math]}$ used rowwise to update or downdate the right-hand-side matrix b.
ssq: specifies an optional $\text{[math]}$ 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 $\text{[math]}$ . See the example in the documentation for the RZLIND call.