{smcl}
{* 25jun2007}{...}
{cmd:help mata MCatnode()}
{cmd:help mata MCatwt()}
{cmd:help mata tlMCatnode()}
{cmd:help mata tlMCatwt()}
{cmd:help mata intres()}{right:(SJ7-4: pr0034)}
{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 setup 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, whereas {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 or questions or observe any problems.


{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-0] mata}

{p 4 13 2}
Online:  
{bf:{help mata:[M-0] mata}},
{bf:{help mf_rpnfcn}},
{bf:{help mf_rpnbinop}}, 
{bf:{help mf_rpnbinop}}, 
{bf:{help mf_rpndist}}
{p_end}