Mapping a range of values to another

One solution would be:

def translate(value, leftMin, leftMax, rightMin, rightMax):
    # Figure out how 'wide' each range is
    leftSpan = leftMax - leftMin
    rightSpan = rightMax - rightMin

    # Convert the left range into a 0-1 range (float)
    valueScaled = float(value - leftMin) / float(leftSpan)

    # Convert the 0-1 range into a value in the right range.
    return rightMin + (valueScaled * rightSpan)

You could possibly use algebra to make it more efficient, at the expense of readability.

Using scipy.interpolate.interp1d

You can also use scipy.interpolate package to do such conversions (if you don't mind dependency on SciPy):

>>> from scipy.interpolate import interp1d
>>> m = interp1d([1,512],[5,10])
>>> m(256)
array(7.4951076320939336)

or to convert it back to normal float from 0-rank scipy array:

>>> float(m(256))
7.4951076320939336

You can do also multiple conversions in one command easily:

>>> m([100,200,300])
array([ 5.96868885,  6.94716243,  7.92563601])

As a bonus, you can do non-uniform mappings from one range to another, for intance if you want to map [1,128] to [1,10], [128,256] to [10,90] and [256,512] to [90,100] you can do it like this:

>>> m = interp1d([1,128,256,512],[1,10,90,100])
>>> float(m(400))
95.625

interp1d creates piecewise linear interpolation objects (which are callable just like functions).

Using numpy.interp

As noted by ~unutbu, numpy.interp is also an option (with less dependencies):

>>> from numpy import interp
>>> interp(256,[1,512],[5,10])
7.4951076320939336

I was looking for the same thing in python to map angles 0-300deg to raw dynamixel values 0-1023, or 1023-0 depending on the actuator orientations.

I ended up going very simple.

Variables:

x:input value; 
a,b:input range
c,d:output range
y:return value

Function:

def mapFromTo(x,a,b,c,d):
   y=(x-a)/(b-a)*(d-c)+c
   return y

Usage:

dyn111.goal_position=mapFromTo(pos111,0,300,0,1024)

This would actually be a good case for creating a closure, that is write a function that returns a function. Since you probably have many of these values, there is little value in calculating and recalculating these value spans and factors for every value, nor for that matter, in passing those min/max limits around all the time.

Instead, try this:

def make_interpolater(left_min, left_max, right_min, right_max): 
    # Figure out how 'wide' each range is  
    leftSpan = left_max - left_min  
    rightSpan = right_max - right_min  

    # Compute the scale factor between left and right values 
    scaleFactor = float(rightSpan) / float(leftSpan) 

    # create interpolation function using pre-calculated scaleFactor
    def interp_fn(value):
        return right_min + (value-left_min)*scaleFactor

    return interp_fn

Now you can write your processor as:

# create function for doing interpolation of the desired
# ranges
scaler = make_interpolater(1, 512, 5, 10)

# receive list of raw values from sensor, assign to data_list

# now convert to scaled values using map 
scaled_data = map(scaler, data_list)

# or a list comprehension, if you prefer
scaled_data = [scaler(x) for x in data_list]