LearningFromData/gradient_descent.py at master · monkey0105/LearningFromData · GitHub

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# -*- coding: utf-8 -*-
# __author__ = 'wangjz'

"""
Learning From Data
HW #5

Consider the nonlinear error surface E(u, v) = (uev − 2ve−u
)
2
. We start at the point
(u, v) = (1, 1) and minimize this error using gradient descent in the uv space. Use
η = 0.1 (learning rate, not step size).

How many iterations (among the given choices) does it take for the error E(u, v)
to fall below 10−14 for the first time? In your programs, make sure to use double
precision to get the needed accuracy

w(t + 1) = w(t) − η ∇Ein(w(t))

"""

from math import e


def e_func(u, v):
    x = u * pow(e, v) - 2 * v * pow(e, -u)
    return x * x


def partial_u(u, v):
    """计算u偏导"""
    fir = 2 * (u * pow(e, v) - 2 * v * pow(e, -u))
    sec = (pow(e, v) + 2 * v * pow(e, -u))

    return fir * sec


def partial_v(u, v):
    """计算v偏导"""
    fir = 2 * (u * pow(e, v) - 2 * v * pow(e, -u))
    sec = (u * pow(e, v) - 2 * pow(e, -u))

    return fir * sec

glb_u, glb_v = 1.0, 1.0
eta = 0.1
goal = pow(10, -14)
cnt = 15

while cnt > 0:
    cnt -= 1
    glb_u -= eta * partial_u(glb_u, glb_v)
    glb_v -= eta * partial_v(glb_u, glb_v)

print e_func(glb_u, glb_v)