How to retrieve the max value of a function output-CodePudding

I have a function f(x). I want to calculate x where f(x) = max. How can I do that in a script?

Given: x is a positive number, f(x) can be positive or negative. I want to start with x = 1. If f(1) is already negative I'm not interested anymore. With increasing x, also f(x) returns increasing values, until a peak is reached, and then f(x) decreases. x at the peak is what I am interested in.

EDIT: Ok what I tried so far:

I tried starting with x = 1, then x *=2. If f(x) is smaller then the last result, I set back x to x/4.

Example: f(16) = 9, f(32) = 11, f(64) = 10. The peak can be between x=16 and x=64. So my new starting point is f(16). From there on, I want to continue in a similar way, but I cant find an algorithm.

Here is what I got so far:

let x = 1
let lasty = 0
let holder = 1

while (iteration   < 20) {   
    
    let y = myFunction(x)

    if(y < lasty ) {
        x = x / 4   
        holder = 1         
    }          
    
    x  = holder * 2  
    holder  = 1     

    lasty = y

}

EDIT2: My improved version which works quite good but for sure not perfect:

let x = 1
let lasty = 0  
let iteration = 0 
let previousX = 1
let lastX = 1
let step = 2
let maxY = -Infinity
let bestX = 0

let randomInput = Math.random

while (iteration   < 20) {    

    let y = myFunction(x, randomInput) //added randomInput to show the function does not rely on x alone
    
    if (y < 0 && iteration == 1) break  

    if(y > maxY) {
        maxY = y
        bestX = x
    }

    if (y < lasty) {
        x = previousX
        step *= 0.8
        lasty = 0
    } else {
        previousX = lastX
        lastX = x
        x = x * step 
        lasty = y
    }
}

if(bestX > 0) {
    console.log(`Got best x: ${bestX}`)
}

EDIT3: Added random additional parameter to emphasise the needed approach

EDIT4: I should also mention that the probability of f(x) = max is the highest when 0 < x < 100000

CodePudding user response：

Assuming you want to maximise y, You can just store the x and y values where xy is highest:

let highestX = 1; // this is just the corresponding x value for the highest y
let highestY = -Infinity;

let x = 1
let lasty = 0
let holder = 1

while (iteration   < 20) {   
    
    let y = myFunction(x);

    // code for storing the highest y and corresponding x
    if (y > highestY) {
        highestY = y;
        highestX = x;
    }

    if(y < lasty ) {
        x = x / 4   
        holder = 1         
    }          
    
    x  = holder * 2  
    holder  = 1     

    lasty = y

}

console.log('f(x) is maximised when x =', highestX);

CodePudding user response：

It could be solved using recursive function calls.

// array of arguments
const args = [...Array(16).keys()];
// sample function
const sampleFunc = (x) => Math.sin(x);
// recursive function
function getElementWithFuncMaximum(arr, func, index = 0, currValue = 0) {
  const currFuncValue = func(arr[index]);
  return currFuncValue >= currValue 
    ? getElementWithFuncMaximum(arr, func, index   1, currFuncValue)
    : arr[index - 1];
}
console.log(getElementWithFuncMaximum(args, sampleFunc));