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

Source: Internet
Author: User

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 ');
}

Related Article

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.