Python中曲线的极值点

Question

我从一个位移传感器那里获取了一些数据，某次迭代的变化值看起来是这样的：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。（其他的迭代也有类似的模式。）

我对曲线的最高点和最低点很感兴趣。我从一个初始位置开始，然后在循环中返回到这个位置（我计算了这些值的部分和，以得到总位移或线）。部分和看起来是这样的：[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]。我对107和-1（下一个曲线的最低点）很感兴趣。

但是我还没想出怎么写代码来处理多个曲线（迭代）。你能帮我吗？

Answer 1

你可以使用这个函数来获取绝对极值：

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

在这里，我对这个函数进行了调整，使它能够找到局部极值：

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

你可以在这个基础上进一步优化这个函数。例如，这个函数可以跳过前面的值，直到满足 min_threshold < value < max_threshold 的条件，以找到一个周期的开始；而在最后，如果没有完整的周期结束，它还可以返回最后一个极值。

最后，这里有一个函数，它可以处理像你示例数据中的点元组。

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))