Numerical integration: Difference between revisions

=={{header|Stata}}==

<lang>mata

function integrate(f,a,b,n,u,v) {

s = 0

h = (b-a)/n

m = length(u)

for (i=0; i<n; i++) {

x = a+i*h

for (j=1; j<=m; j++) s = s+v[j]*(*f)(x+h*u[j])

}

return(s*h)

}

function log_(x) {

return(log(x))

}

function id(x) {

return(x)

}

function cube(x) {

return(x*x*x)

}

function inv(x) {

return(1/x)

}

function test(f,a,b,n) {

return(integrate(f,a,b,n,(0,1),(1,0)),

integrate(f,a,b,n,(0,1),(0,1)),

integrate(f,a,b,n,(0.5),(1)),

integrate(f,a,b,n,(0,1),(0.5,0.5)),

integrate(f,a,b,n,(0,1/2,1),(1/6,4/6,1/6)))

}

test(&cube(),0,1,100)

test(&inv(),1,100,1000)

test(&id(),0,5000,5000000)

test(&id(),0,6000,6000000)

end</lang>

'''Output'''

<pre> 1 2 3 4 5

+--------------------------------------------------------+

1 | .245025 .255025 .2499875 .250025 .25 |

+--------------------------------------------------------+

1 2 3 4 5

+-----------------------------------------------------------------------+

1 | 4.654991058 4.556981058 4.604762549 4.605986058 4.605170385 |

+-----------------------------------------------------------------------+

1 2 3 4 5

+------------------------------------------------------------------+

1 | 12499997.5 12500002.5 12500000 12500000 12500000 |

+------------------------------------------------------------------+

1 2 3 4 5

+--------------------------------------------------------+

1 | 17999997 18000003 18000000 18000000 18000000 |

+--------------------------------------------------------+</pre>