Implementation and test of the Javascript (Nodejs) algorithm for automatically finding function credits using Monte Carlo

Javascript is used to implement the function integration algorithm.

The calculation result shows that the algorithm accuracy is greatly affected by the random number generator.

 

 

[Javascript]
// Monte carro calculates the definite integral of a given function
// Specify a function
Function f1 (x, xmin, xmax)
{
If (x> = xmin & x <= xmax)
Return x * Math. sqrt (1 + x * x)-1;
}
 
Function f2 (x, xmin, xmax)
{
If (x> = xmin & x <= xmax)
Return x * Math. log (1 + x );
}
 
Function f3 (x, xmin, xmax)
{
If (x> = xmin & x <= xmax)
Return Math. sqrt (1-x * x );
}
 
Function f4 (x, xmin, xmax)
{
If (x> = xmin & x <= xmax)
Return Math. cos (x)-0.9;
}
 
 
// Obtain the upper and lower limits of the function-the accuracy is greatly affected-if y> 0 is used for credits, the base limit is 0. If y is <0, the upper limit is 0; if y crosses the X axis, the default limit is not modified.
Function getLimit (func, xmin, xmax)
{
// Boundary Limit
Var t1 = func (xmin, xmin, xmax), t2 = func (xmax, xmin, xmax );
Var limit = {y0: Math. min (t1, t2), y1: Math. max (t1, t2 )};
Var delta = 1e-3, lastX, lastY;
For (var x = xmin, I = 0; x <= xmax; x + = delta, I ++)
{
Y = func (x, xmin, xmax );
If (y <limit. y0)
Limit. y0 = y;
If (y> limit. y1)
Limit. y1 = y;
If (I = 0)
{
LastX = x;
LastY = y;
}
Else
{
Var tx = (lastX + x)/2;
Var ty = func (tx, xmin, xmax );
If (Math. abs (lastY)> Math. abs (y ))
{
If (Math. abs (lastY) <Math. abs (ty ))
{
LastX = tx;
LastY = ty;
If (ty <0 & limit. y0> ty)
Limit. y0 = ty;
Else if (ty> = 0 & limit. y1 <= ty)
Limit. y1 = ty;
}
}
If (Math. abs (lastY) <Math. abs (y ))
{
If (Math. abs (y) <Math. abs (ty ))
{
LastX = tx;
LastY = ty;
If (ty <0 & limit. y0> ty)
Limit. y0 = ty;
Else if (ty> = 0 & limit. y1 <= ty)
Limit. y1 = ty;
}
}
}
}
If (limit. y0> 0)
Limit. y0 = 0;
If (limit. y1 <0)
Limit. y1 = 0;
Return limit;
}
 
// Points
Function cumulate (func, N, xmin, xmax)
{
Var limit = getLimit (func, xmin, xmax );
// Console. log ('limit = ', Limit. y0, limit. y1 );
Var x, yr, y;
Var cntA = 0, cntB = 0;
For (var I = 0; I <N; I ++)
{
X = xmin + (xmax-xmin) * Math. random ();
Yr = limit. y0 + (limit. y1-limit. y0) * Math. random ();
Y = func (x, xmin, xmax );
If (y> = 0 & yr> = 0 & yr <= y)
CntA ++;
Else
If (y <= 0 & yr <= 0 & yr> = y)
CntB ++;
}
// Console. log ('counts = ', cntA, cntB );
Return (cntA-cntB) * (xmax-xmin) * (limit. y1-limit. y0)/N;
}
 
// Test
Var t1, t2;
Var rst;
Var N = 1e7;
Var fs = [f1, f2, f3, f4];
Var ans = [-0.593682861167513, 0.25, Math. PI/4,-0.058529015192103493347497678369701];
For (var I = 0; I <4; I ++)
{
T1 = new Date ();
Rst = cumulate (fs [I], N, 0, 1 );
T2 = new Date ();
Console. log ('[', I, '] =', ans [I]. toFixed (15), rst. toFixed (15), t2-t1, 'ms ');
}