我试图将一个范围的数字转换为另一个,保持比率。数学不是我的强项。

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).


当前回答

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

或者更容易读懂:

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

或者如果你想保护旧范围为0的情况(OldMin = OldMax):

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

注意,在这种情况下,我们被迫任意选择一个可能的新范围值。根据上下文,明智的选择可能是:NewMin(见示例),NewMax或(NewMin + NewMax) / 2

其他回答

使用Numpy和interp函数,你可以将你的值从旧范围转换为新范围:

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

你也可以尝试映射一个值列表:

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

我在一个用js解决的问题中使用了这个解决方案,所以我想我将分享翻译。谢谢你的解释和解决方案。

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;
}

列出理解一行的解决方案

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

完整版

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

在由PenguinTD提供的清单中,我不明白为什么范围是颠倒的,它不需要颠倒范围就能工作。线性范围转换基于线性方程Y=Xm+n,其中m和n是从给定的范围推导出来的。与其将范围称为min和max,不如将它们称为1和2。所以公式是:

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

当X=x1时Y=y1,当X=x2时Y=y2。X1, x2, y1和y2可以取任意正值或负值。在宏中定义表达式使其更有用,它可以与任何参数名称一起使用。

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

在所有实参都是整数值的情况下,浮点强制转换将确保浮点除法。 根据应用程序的不同,可能不需要检查x1=x2和y1==y2的范围。

实际上,在某些情况下,上述答案会失效。 如错误的输入值,错误的输入范围,负输入/输出范围。

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