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**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 .See the LUPDT Example section for an example of the LUPDT call.

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