Mapping a range of values to another

Question

I am looking for ideas on how to translate one range values to another in Python. I am working on hardware project and am reading data from a sensor that can return a range of values, I am then using that data to drive an actuator that requires a different range of values.

For example lets say that the sensor returns values in the range 1 to 512, and the actuator is driven by values in the range 5 to 10. I would like a function that I can pass a value and the two ranges and get back the value mapped to the second range. If such a function was named translate it could be used like this:

sensor_value = 256
actuator_value = translate(sensor_value, 1, 512, 5, 10)

In this example I would expect the output actuator_value to be 7.5 since the sensor_value is in the middle of the possible input range.

Answer 1

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.

Answer 2

def translate(sensor_val, in_from, in_to, out_from, out_to):
    out_range = out_to - out_from
    in_range = in_to - in_from
    in_val = sensor_val - in_from
    val=(float(in_val)/in_range)*out_range
    out_val = out_from+val
    return out_val

Answer 3

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

Answer 4

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]