Maxima and Minima Point of a Curve in Python

Question

I have a captured a data from a displacement sensor, the delta values for one iteration look like this. 0, 1, 2, 4, 7, 9, 14, 24, 14, 10, 9, 7, 3 2, 1, 0, 0, 0, 0, -1, -3, -5, -7, -9, -14, -24, -14, -9, -8, -6, -4, -3, -1, 0, 0, 0. (other iterations are also have same pattern.)

I am interested in the maxima and minima points of a curves. I start with a initial position and come back to this position for a loops for line(I've take the partial sum of the values to get the total displacement or line). The partial sum look like this [0, 1, 3, 7, 14, 23, 37, 61, 75, 85, 94, 101, 104, 106, 107, 107, 107, 107, 107, 106, 103, 98, 91, 82, 68, 44, 30, 21, 13, 7, 3, 0, -1, -1, -1, -1]. I am interested in 107 and -1 (the next curve minima)

But I am not figure out the code for say n no. of curve (iteration). Can you help me with this?

Answer 1

You can use this function for getting the absolute extrema:

def extrema(value, deltas):
    max_value = min_value = value
    for delta in deltas:
        value += delta
        if value < min_value:
            min_value = value
        elif value > max_value:
            max_value = value
    return min_value, max_value

Here I have adapted the function to yield local extrema:

def extrema(value, deltas):
    values = [value]
    for delta in deltas:
        value += delta
        values.append(value)
    average = sum(values)/len(values)
    threshold = (max(values) - min(values))/6
    min_threshold = average - threshold
    max_threshold = average + threshold
    min_value = max_value = None
    for value in values:
        if value < min_threshold:
            if min_value is None or value < min_value:
                min_value = value
        elif value > max_threshold:
            if max_value is None or value > max_value:
                max_value = value
        elif min_value is not None and max_value is not None:
            yield min_value, max_value
            max_value = min_value = None

You can fine-tune the function from here. For instance, the function could skip the first values until min_threshold < value < max_threshold to find the start of a cycle, and at the end it could yield the last extremum if it did not end with a full cycle.

Lastly, here is a function that works with point tuples as in your example data.

class Point(object):

    __slots__ = ('x', 'y')

    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    def __repr__(self):
        return str((self.x, self.y))

    def __iadd__(self, other):
        self.x += other.x
        self.y += other.y
        return self

    def __isub__(self, other):
        self.x -= other.x
        self.y -= other.y
        return self

    def __idiv__(self, number):
        self.x /= number
        self.y /= number
        return self

    def abs(self):
        return abs(self.x) + abs(self.y)

    def copy(self):
        return Point(self.x, self.y)


def extrema(moves, jitter=0.1, threshold=1000, sample=16):
    point = Point()
    minpoint = Point()
    maxpoint = Point()
    average = Point()
    average /= 1.0
    turned = False
    for move in moves:
        point += move
        x = point.x
        if x < minpoint.x:
            minpoint.x = x
        elif x > maxpoint.x:
            maxpoint.x = x
        y = point.y
        if y < minpoint.y:
            minpoint.y = y
        elif y > maxpoint.y:
            maxpoint.y = y
        delta = move.copy()
        delta -= average
        delta /= sample
        average += delta
        if average.abs() < jitter:
            if point.abs() > threshold:
                turned = True
            elif turned:
                yield minpoint, maxpoint
                point = Point() # reset (calibrate)
                minpoint = Point()
                maxpoint = Point()
                turned = False


# read data from file
moves = [Point(*map(int, move.split(',')))
    for move in open('data.txt').read().split(';') if move]

# generate extrema
print list(extrema(moves))