{smcl}
{* 25jun2007}{...}
{cmd:help mata MCatnode()}
{cmd:help mata MCatwt()}
{cmd:help mata tlMCatnode()}
{cmd:help mata tlMCatwt()}
{cmd:help mata intres()}
{hline}
{* index rpn Monte Carlo integration with stratified antithetic sampling mata}{...}
{* index MCatnode()}{...}
{* index MCatwt()}{...}
{* index tlMCatnode()}{...}
{* index tlMCatwt()}{...}
{* index intres()}{...}

{title:Title}

{p 4 4 2} {bf:Functions for Monte Carlo integration with stratified antithetic sampling with rpnfcn()}


{title:Syntax}

{p 16 12 2}
{bf:{ul:Command name}}{space 5} {ul:Argument}

{p 16 12 2}
{cmd:&MCatnode()}{space 6} {it:&ab}

{p 16 12 2}
{cmd:&MCatwt()}{space 8} {it:&ab}

{p 16 12 2}
{cmd:&tlMCatnode()}{space 4} {it:&a}

{p 16 12 2}
{cmd:&tlMCatwt()}{space 6} NULL

{p 16 12 2}
{cmd:&intres()}{space 8} NULL


{title:Description}

{p 4 4 2} These functions are to be used with {cmd:rpnfcn()}. The
functions {cmd:&MCatnode()}, {cmd:&MCatwt()}, {cmd:&tlMCatnode()}, and
{cmd:&tlMCatwt()} compute nodes and weights for numerical integration
based on Monte Carlo with stratified antithetic sampling. The function
{cmd:&intres()} computes the result by summing the evaluated nodes
multiplied with the weights. 

{title:Remarks}

{p 4 4 2} {cmd:&MCatnode()} and {cmd:&tlMCatnode()} use the argument
vector {it:ab} and {it:a}, respectively, to set up the nodes based on
the matrix of uniformly distributed random variables presumed to be in
the current top element of the stack in {cmd:rpnfcn()}. The number of
columns of the matrix of uniformly distributed random variables equals
the number of strata used in the integration, thus precision is
improved when the number of columns is increased. {it:ab} must be a
matrix with two columns specifying the lower and upper boundary of the
integration interval, respectively, while {it:a} must be a column
vector specifying the lower boundary for the indefinite integral.



{title:Source code}

{p 4 4 2}
{view rpnint.mata, adopath asis:rpnint.mata}

{title:Author}

{p 4 4 2}{browse "http://www.almen.dk/hstovring":Henrik Støvring},
Research Unit of General Practice, University of Southern Denmark.
Please email
{browse "mailto:hstovring@health.sdu.dk":hstovring@health.sdu.dk}
if you have comments, questions or observe any problems.


{title:Also see}

{p 4 13 2}
Manual:  {hi:[M] Mata Reference Manual}

{p 4 13 2}
Online:  help for 
{bf:{help mata:[M-0] mata}},
{bf:{help mf_rpnfcn: Evaluation of algorithm matrix using RPN}},
{bf:{help mf_rpnbinop:RPN stack manipulation functions}}, 
{bf:{help mf_rpnbinop:RPN binary operators}}, 
{bf:{help mf_rpndist:RPN distribution functions}},
{p_end}