Convert a number range to another range, maintaining ratio

I'm trying to convert one range of numbers to another, maintaining ratio. Maths is not my strong point.

I have an image file where point values may range from -16000.00 to 16000.00 though the typical range may be much less. What I want to do is compress these values into the integer range 0-100, where 0 is the value of the smallest point, and 100 is the value of the largest. All points in between should keep a relative ratio even though some precision is being lost I'd like to do this in python but even a general algorithm should suffice. I'd prefer an algorithm where the min/max or either range can be adjusted (ie, the second range could be -50 to 800 instead of 0 to 100).

NewValue = (((OldValue - OldMin) * (NewMax - NewMin)) / (OldMax - OldMin)) + NewMin

Or a little more readable:

OldRange = (OldMax - OldMin)  
NewRange = (NewMax - NewMin)  
NewValue = (((OldValue - OldMin) * NewRange) / OldRange) + NewMin

Or if you want to protect for the case where the old range is 0 (OldMin = OldMax):

OldRange = (OldMax - OldMin)
if (OldRange == 0)
    NewValue = NewMin
else
{
    NewRange = (NewMax - NewMin)  
    NewValue = (((OldValue - OldMin) * NewRange) / OldRange) + NewMin
}

Note that in this case we're forced to pick one of the possible new range values arbitrarily. Depending on context, sensible choices could be: NewMin (see sample), NewMax or (NewMin + NewMax) / 2

That's a simple linear conversion.

new_value = ( (old_value - old_min) / (old_max - old_min) ) * (new_max - new_min) + new_min

So converting 10000 on the scale of -16000 to 16000 to a new scale of 0 to 100 yields:

old_value = 10000
old_min = -16000
old_max = 16000
new_min = 0
new_max = 100

new_value = ( ( 10000 - -16000 ) / (16000 - -16000) ) * (100 - 0) + 0
          = 81.25

Actually there are some cases that above answers would break. Such as wrongly input value, wrongly input range, negative input/output ranges.

def remap( x, oMin, oMax, nMin, nMax ):

    #range check
    if oMin == oMax:
        print "Warning: Zero input range"
        return None

    if nMin == nMax:
        print "Warning: Zero output range"
        return None
	
    #check reversed input range
    reverseInput = False
    oldMin = min( oMin, oMax )
    oldMax = max( oMin, oMax )
    if not oldMin == oMin:
        reverseInput = True
	
    #check reversed output range
    reverseOutput = False	
    newMin = min( nMin, nMax )
    newMax = max( nMin, nMax )
    if not newMin == nMin :
        reverseOutput = True

    portion = (x-oldMin)*(newMax-newMin)/(oldMax-oldMin)
    if reverseInput:
        portion = (oldMax-x)*(newMax-newMin)/(oldMax-oldMin)

    result = portion + newMin
    if reverseOutput:
        result = newMax - portion
	
    return result

#test cases
print remap( 25.0, 0.0, 100.0, 1.0, -1.0 ), "==", 0.5
print remap( 25.0, 100.0, -100.0, -1.0, 1.0 ), "==", -0.25
print remap( -125.0, -100.0, -200.0, 1.0, -1.0 ), "==", 0.5
print remap( -125.0, -200.0, -100.0, -1.0, 1.0 ), "==", 0.5
#even when value is out of bound
print remap( -20.0, 0.0, 100.0, 0.0, 1.0 ), "==", -0.2

There is a condition, when all of the values that you are checking are the same, where @jerryjvl's code would return NaN.

if (OldMin != OldMax && NewMin != NewMax):
    return (((OldValue - OldMin) * (NewMax - NewMin)) / (OldMax - OldMin)) + NewMin
else:
    return (NewMax + NewMin) / 2

I didn't dig up the BNF for this, but the Arduino documentation had a great example of the function and it's breakdown. I was able to use this in Python by simply adding a def renaming to remap (cause map is a built-in) and removing the type casts and curly braces (ie just remove all the 'long's).

Original

long map(long x, long in_min, long in_max, long out_min, long out_max)
{
  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}

Python

def remap(x, in_min, in_max, out_min, out_max):
  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min

https://www.arduino.cc/en/reference/map

Here's some short Python functions for your copy and paste ease, including a function to scale an entire list.

def scale_number(unscaled, to_min, to_max, from_min, from_max):
    return (to_max-to_min)*(unscaled-from_min)/(from_max-from_min)+to_min

def scale_list(l, to_min, to_max):
    return [scale_number(i, to_min, to_max, min(l), max(l)) for i in l]

Which can be used like so:

scale_list([1,3,4,5], 0, 100)

>[0.0, 50.0, 75.0, 100.0]

In my case I wanted to scale a logarithmic curve, like so:

scale_list([math.log(i+1) for i in range(5)], 0, 50)

> [0.0, 21.533827903669653, 34.130309724299266, 43.06765580733931, 50.0]

Added KOTLIN version with Mathematical Explanation

Consider we have a scale between (OMin, Omax) and we we have a value X in this range

We want to convert it to scale (NMin, NMax)

We know X and we need to find Y, the ratio must be same:

 => (Y-NMin)/(NMax-NMin) = (X-OMin)/(OMax-OMin)  
      
 =>  (Y-NMin)/NewRange = (X-OMin)/OldRange 

 =>   Y = ((X-OMin)*NewRange)/oldRange)+NMin  Answer
   

Pragmatically we can write this rquation like this:

 private fun  convertScale(oldValueToConvert:Int): Float {
       // Old Scale 50-100
       val oldScaleMin = 50
       val oldScaleMax = 100
       val oldScaleRange= (oldScaleMax - oldScaleMin)

       //new Scale 0-1
       val newScaleMin = 0.0f
       val newScaleMax = 1.0f
       val newScaleRange=  (newScaleMax - newScaleMin)
     
       return ((oldValueToConvert - oldScaleMin)* newScaleRange/ oldScaleRange) + newScaleMin
    }

JAVA

/**
     * 
     * @param x
     * @param inMin
     * @param inMax
     * @param outMin
     * @param outMax
     * @return
     */
        private long normalize(long x, long inMin, long inMax, long outMin, long outMax) {
          long outRange = outMax - outMin;
          long inRange  = inMax - inMin;
          return (x - inMin) *outRange / inRange + outMin;
        }

Usage:

float brightness = normalize(progress, 0, 10, 0,255);

I used this solution in a problem I was solving in js, so I thought I would share the translation. Thanks for the explanation and solution.

function remap( x, oMin, oMax, nMin, nMax ){
//range check
if (oMin == oMax){
    console.log("Warning: Zero input range");
    return None;
};

if (nMin == nMax){
    console.log("Warning: Zero output range");
    return None
}

//check reversed input range
var reverseInput = false;
oldMin = Math.min( oMin, oMax );
oldMax = Math.max( oMin, oMax );
if (oldMin != oMin){
    reverseInput = true;
}

//check reversed output range
var reverseOutput = false;  
newMin = Math.min( nMin, nMax )
newMax = Math.max( nMin, nMax )
if (newMin != nMin){
    reverseOutput = true;
};

var portion = (x-oldMin)*(newMax-newMin)/(oldMax-oldMin)
if (reverseInput){
    portion = (oldMax-x)*(newMax-newMin)/(oldMax-oldMin);
};

var result = portion + newMin
if (reverseOutput){
    result = newMax - portion;
}

return result;
}

In the listing provided by PenguinTD, I do not understand why the ranges are reversed, it works without having to reverse the ranges. Linear range conversion is based upon the linear equation Y=Xm+n, where m and n are derived from the given ranges. Rather than refer to the ranges as min and max, it would be better to refer to them as 1 and 2. So the formula would be:

Y = (((X - x1) * (y2 - y1)) / (x2 - x1)) + y1

Where Y=y1 when X=x1, and Y=y2 when X=x2. x1, x2, y1 & y2 can be given any positive or negative value. Defining the expression in a macro makes it more useful,it can then be used with any argument names.

#define RangeConv(X, x1, x2, y1, y2) (((float)((X - x1) * (y2 - y1)) / (x2 - x1)) + y1)

The float cast would ensure floating point division in the case where all the arguments are integer values. Depending on the application it may not be necessary to check the ranges x1=x2 and y1==y2.

I personally use the helper class which supports generics (Swift 3, 4.x compatible)

struct Rescale<Type : BinaryFloatingPoint> {
    typealias RescaleDomain = (lowerBound: Type, upperBound: Type)

    var fromDomain: RescaleDomain
    var toDomain: RescaleDomain

    init(from: RescaleDomain, to: RescaleDomain) {
        self.fromDomain = from
        self.toDomain = to
    }

    func interpolate(_ x: Type ) -> Type {
        return self.toDomain.lowerBound * (1 - x) + self.toDomain.upperBound * x;
    }

    func uninterpolate(_ x: Type) -> Type {
        let b = (self.fromDomain.upperBound - self.fromDomain.lowerBound) != 0 ? self.fromDomain.upperBound - self.fromDomain.lowerBound : 1 / self.fromDomain.upperBound;
        return (x - self.fromDomain.lowerBound) / b
    }

    func rescale(_ x: Type )  -> Type {
        return interpolate( uninterpolate(x) )
    }
}

Ex:

   let rescaler = Rescale<Float>(from: (-1, 1), to: (0, 100))
    
   print(rescaler.rescale(0)) // OUTPUT: 50

C++ Variant

I found PenguinTD's Solution usefull, so i ported it to C++ if anyone needs it:

> float remap(float x, float oMin, float oMax, float nMin, float nMax ){ > > //range check > if( oMin == oMax) { > //std::cout<< "Warning: Zero input range"; > return -1; } > > if( nMin == nMax){ > //std::cout<<"Warning: Zero output range"; > return -1; } > > //check reversed input range > bool reverseInput = false; > float oldMin = min( oMin, oMax ); > float oldMax = max( oMin, oMax ); > if (oldMin == oMin) > reverseInput = true; > > //check reversed output range > bool reverseOutput = false;
> float newMin = min( nMin, nMax ); > float newMax = max( nMin, nMax ); > if (newMin == nMin) > reverseOutput = true; > > float portion = (x-oldMin)(newMax-newMin)/(oldMax-oldMin); > if (reverseInput) > portion = (oldMax-x)(newMax-newMin)/(oldMax-oldMin); > > float result = portion + newMin; > if (reverseOutput) > result = newMax - portion; > > return result; }

PHP Port

Found PenguinTD's solution helpful so I ported it to PHP. Help yourself!

/**
* =====================================
*              Remap Range            
* =====================================
* - Convert one range to another. (including value)
*
* @param    int $intValue   The value in the old range you wish to convert
* @param    int $oMin       The minimum of the old range
* @param    int $oMax       The maximum of the old range
* @param    int $nMin       The minimum of the new range
* @param    int $nMax       The maximum of the new range
*
* @return   float $fResult  The old value converted to the new range
*/
function remapRange($intValue, $oMin, $oMax, $nMin, $nMax) {
    // Range check
    if ($oMin == $oMax) {
        echo 'Warning: Zero input range';
        return false;
    }

    if ($nMin == $nMax) {
        echo 'Warning: Zero output range';
        return false;
    }

    // Check reversed input range
    $bReverseInput = false;
    $intOldMin = min($oMin, $oMax);
    $intOldMax = max($oMin, $oMax);
    if ($intOldMin != $oMin) {
        $bReverseInput = true;
    }

    // Check reversed output range
    $bReverseOutput = false;
    $intNewMin = min($nMin, $nMax);
    $intNewMax = max($nMin, $nMax);
    if ($intNewMin != $nMin) {
        $bReverseOutput = true;
    }

    $fRatio = ($intValue - $intOldMin) * ($intNewMax - $intNewMin) / ($intOldMax - $intOldMin);
    if ($bReverseInput) {
        $fRatio = ($intOldMax - $intValue) * ($intNewMax - $intNewMin) / ($intOldMax - $intOldMin);
    }

    $fResult = $fRatio + $intNewMin;
    if ($bReverseOutput) {
        $fResult = $intNewMax - $fRatio;
    }

    return $fResult;
}

Here is a Javascript version that returns a function that does the rescaling for predetermined source and destination ranges, minimizing the amount of computation that has to be done each time.

// This function returns a function bound to the 
// min/max source & target ranges given.
// oMin, oMax = source
// nMin, nMax = dest.
function makeRangeMapper(oMin, oMax, nMin, nMax ){
	//range check
	if (oMin == oMax){
		console.log("Warning: Zero input range");
		return undefined;
	};

	if (nMin == nMax){
		console.log("Warning: Zero output range");
		return undefined
	}

	//check reversed input range
	var reverseInput = false;
	let oldMin = Math.min( oMin, oMax );
	let oldMax = Math.max( oMin, oMax );
	if (oldMin != oMin){
	    reverseInput = true;
	}

	//check reversed output range
	var reverseOutput = false;  
	let newMin = Math.min( nMin, nMax )
	let newMax = Math.max( nMin, nMax )
	if (newMin != nMin){
	    reverseOutput = true;
	}

	// Hot-rod the most common case.
	if (!reverseInput && !reverseOutput) {
		let dNew = newMax-newMin;
		let dOld = oldMax-oldMin;
 		return (x)=>{
			return ((x-oldMin)* dNew / dOld) + newMin;
		}
	}

	return (x)=>{
		let portion;
		if (reverseInput){
			portion = (oldMax-x)*(newMax-newMin)/(oldMax-oldMin);
		} else {
			portion = (x-oldMin)*(newMax-newMin)/(oldMax-oldMin)
		}
		let result;
		if (reverseOutput){
			result = newMax - portion;
		} else {
			result = portion + newMin;
		}
		
		return result;
	}	
}

Here is an example of using this function to scale 0-1 into -0x80000000, 0x7FFFFFFF

let normTo32Fn = makeRangeMapper(0, 1, -0x80000000, 0x7FFFFFFF);
let fs = normTo32Fn(0.5);
let fs2 = normTo32Fn(0);

List comprehension one liner solution

color_array_new = [int((((x - min(node_sizes)) * 99) / (max(node_sizes) - min(node_sizes))) + 1) for x in node_sizes]

Longer version

def colour_specter(waste_amount):
color_array = []
OldRange = max(waste_amount) - min(waste_amount)
NewRange = 99
for number_value in waste_amount:
    NewValue = int((((number_value - min(waste_amount)) * NewRange) / OldRange) + 1)
    color_array.append(NewValue)
print(color_array)
return color_array

Java Version

Always works no matter what you feed it!

I left everything expanded out so that it's easier to follow for learning. Rounding at the end, of course, is optional.

	private long remap(long p, long Amin, long Amax, long Bmin, long Bmax ) {

	double deltaA = Amax - Amin;
	double deltaB = Bmax - Bmin;
	double scale  = deltaB / deltaA;
	double negA   = -1 * Amin;
	double offset = (negA * scale) + Bmin;
	double q      = (p * scale) + offset;
	return Math.round(q);

}

I wrote a function to do this in R. The method is the same as above, but I needed to do this a bunch of times in R, so I thought I'd share in case it helps anybody.

convertRange <- function(
  oldValue,
  oldRange = c(-16000.00, 16000.00), 
  newRange = c(0, 100),
  returnInt = TRUE # the poster asked for an integer, so this is an option
){
  oldMin <- oldRange[1]
  oldMax <- oldRange[2]
  newMin <- newRange[1]
  newMax <- newRange[2]
  newValue = (((oldValue - oldMin)* (newMax - newMin)) / (oldMax - oldMin)) + newMin
  
  if(returnInt){
   return(round(newValue))
  } else {
   return(newValue)
  }
}

Short-cut/simplified proposal

 NewRange/OldRange = Handy multiplicand or HM
 Convert OldValue in OldRange to NewValue in NewRange = 
 (OldValue - OldMin x HM) + NewMin

wayne

This example converts a songs current position into an angle range of 20 - 40.

    /// <summary>
    /// This test converts Current songtime to an angle in a range. 
    /// </summary>
    [Fact]
    public void ConvertRangeTests()
    {            
       //Convert a songs time to an angle of a range 20 - 40
        var result = ConvertAndGetCurrentValueOfRange(
            TimeSpan.Zero, TimeSpan.FromMinutes(5.4),
            20, 40, 
            2.7
            );

        Assert.True(result == 30);
    }

    /// <summary>
    /// Gets the current value from the mixValue maxValue range.        
    /// </summary>
    /// <param name="startTime">Start of the song</param>
    /// <param name="duration"></param>
    /// <param name="minValue"></param>
    /// <param name="maxValue"></param>
    /// <param name="value">Current time</param>
    /// <returns></returns>
    public double ConvertAndGetCurrentValueOfRange(
                TimeSpan startTime,
                TimeSpan duration,
                double minValue,
                double maxValue,
                double value)
	{
		var timeRange = duration - startTime;
		var newRange = maxValue - minValue;
		var ratio = newRange / timeRange.TotalMinutes;
		var newValue = value * ratio;
        var currentValue= newValue + minValue;
		return currentValue;
	}

Using Numpy and interp function, you can convert your value from old range to new range:

>>> import numpy as np
>>> np.interp(0, [-16000,16000], [0,100])
50.0

You can also try it to map a list of values:

>>> np.interp([-16000,0,12000] ,[-16000,16000], [0,100])
array([ 0. , 50. , 87.5])