852 lines
28 KiB
Python
852 lines
28 KiB
Python
# -*- encoding:utf-8 -*-
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from __future__ import print_function
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from __future__ import division
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import warnings
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import matplotlib.pyplot as plt
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import numpy as np
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import pandas as pd
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import seaborn as sns
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# noinspection PyUnresolvedReferences
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import abu_local_env
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import abupy
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from abupy import ABuSymbolPd
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from abupy import six, xrange
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from abc import ABCMeta, abstractmethod
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warnings.filterwarnings('ignore')
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sns.set_context(rc={'figure.figsize': (14, 7)})
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# 使用沙盒数据，目的是和书中一样的数据环境
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abupy.env.enable_example_env_ipython()
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tsla_close = ABuSymbolPd.make_kl_df('usTSLA').close
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# x序列: 0，1，2, ...len(tsla_close)
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x = np.arange(0, tsla_close.shape[0])
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# 收盘价格序列
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y = tsla_close.values
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"""
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第六章 量化工具——数学：你一生的追求到底能带来多少幸福
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abu量化系统github地址：https://github.com/bbfamily/abu (您的star是我的动力！)
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abu量化文档教程ipython notebook：https://github.com/bbfamily/abu/tree/master/abupy_lecture
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"""
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def sample_611_1(show=True):
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"""
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6.1.1 线性回归
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:return:
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"""
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import statsmodels.api as sm
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from statsmodels import regression
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def regress_y(_y):
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_y = _y
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# x序列: 0，1，2, ...len(y)
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_x = np.arange(0, len(_y))
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_x = sm.add_constant(_x)
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# 使用OLS做拟合
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_model = regression.linear_model.OLS(_y, _x).fit()
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return _model
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model = regress_y(y)
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b = model.params[0]
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k = model.params[1]
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# y = kx + b
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y_fit = k * x + b
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if show:
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plt.plot(x, y)
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plt.plot(x, y_fit, 'r')
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plt.show()
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# summary模型拟合概述，表6-1所示
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print(model.summary())
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return y_fit
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# noinspection PyPep8Naming
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def sample_611_2():
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"""
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6.1.1 线性回归
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:return:
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"""
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y_fit = sample_611_1(show=False)
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MAE = sum(np.abs(y - y_fit)) / len(y)
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print('偏差绝对值之和(MAE)={}'.format(MAE))
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MSE = sum(np.square(y - y_fit)) / len(y)
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print('偏差绝对值之和(MSE)={}'.format(MSE))
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RMSE = np.sqrt(sum(np.square(y - y_fit)) / len(y))
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print('偏差绝对值之和(RMSE)={}'.format(RMSE))
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from sklearn import metrics
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print('sklearn偏差绝对值之和(MAE)={}'.format(metrics.mean_absolute_error(y, y_fit)))
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print('sklearn偏差平方(MSE)={}'.format(metrics.mean_squared_error(y, y_fit)))
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print('sklearn偏差平方和开平方(RMSE)={}'.format(np.sqrt(metrics.mean_squared_error(y, y_fit))))
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# noinspection PyCallingNonCallable
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def sample_612():
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"""
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6.1.2 多项式回归
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:return:
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"""
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import itertools
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# 生成9个subplots 3*3
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_, axs = plt.subplots(nrows=3, ncols=3, figsize=(15, 15))
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# 将 3 * 3转换成一个线性list
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axs_list = list(itertools.chain.from_iterable(axs))
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# 1-9次多项式回归
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poly = np.arange(1, 10, 1)
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for p_cnt, ax in zip(poly, axs_list):
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# 使用polynomial.Chebyshev.fit进行多项式拟合
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p = np.polynomial.Chebyshev.fit(x, y, p_cnt)
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# 使用p直接对x序列代人即得到拟合结果序列
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y_fit = p(x)
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# 度量mse值
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from sklearn import metrics
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mse = metrics.mean_squared_error(y, y_fit)
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# 使用拟合次数和mse误差大小设置标题
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ax.set_title('{} poly MSE={}'.format(p_cnt, mse))
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ax.plot(x, y, '', x, y_fit, 'r.')
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plt.show()
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def sample_613():
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"""
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6.1.3 插值
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:return:
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"""
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from scipy.interpolate import interp1d, splrep, splev
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# 示例两种插值计算方式
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_, axs = plt.subplots(nrows=1, ncols=2, figsize=(14, 5))
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# 线性插值
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linear_interp = interp1d(x, y)
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# axs[0]左边的
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axs[0].set_title('interp1d')
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# 在相同坐标系下，同样的x，插值的y值使r.绘制（红色点）
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axs[0].plot(x, y, '', x, linear_interp(x), 'r.')
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# B-spline插值
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splrep_interp = splrep(x, y)
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# axs[1]右边的
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axs[1].set_title('splrep')
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# #在相同坐标系下，同样的x，插值的y值使g.绘制（绿色点）
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axs[1].plot(x, y, '', x, splev(x, splrep_interp), 'g.')
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plt.show()
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"""
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6.2 蒙特卡洛方法与凸优化
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6.2.1 你一生的追求到底能带来多少幸福
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"""
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# 每个人平均寿命期望是75年，约75*365=27375天
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K_INIT_LIVING_DAYS = 27375
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class Person(object):
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"""
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人类
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"""
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def __init__(self):
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# 初始化人平均能活的寿命
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self.living = K_INIT_LIVING_DAYS
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# 初始化幸福指数
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self.happiness = 0
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# 初始化财富值
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self.wealth = 0
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# 初始化名望权利
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self.fame = 0
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# 活着的第几天
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self.living_day = 0
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def live_one_day(self, seek):
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"""
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每天只能进行一个seek，这个seek决定了你今天追求的是什么，得到了什么
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seek的类型属于下面将编写的BaseSeekDay
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:param seek:
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:return:
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"""
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# 调用每个独特的BaseSeekDay类都会实现的do_seek_day，得到今天的收获
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consume_living, happiness, wealth, fame = seek.do_seek_day()
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# 每天要减去生命消耗，有些seek前面还会增加生命
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self.living -= consume_living
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# seek得到的幸福指数积累
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self.happiness += happiness
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# seek得到的财富积累
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self.wealth += wealth
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# seek得到的名望权力积累
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self.fame += fame
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# 活完这一天了
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self.living_day += 1
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class BaseSeekDay(six.with_metaclass(ABCMeta, object)):
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def __init__(self):
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# 每个追求每天消耗生命的常数
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self.living_consume = 0
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# 每个追求每天幸福指数常数
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self.happiness_base = 0
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# 每个追求每天财富积累常数
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self.wealth_base = 0
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# 每个追求每天名望权利积累常数
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self.fame_base = 0
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# 每个追求每天消耗生命的可变因素序列
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self.living_factor = [0]
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# 每个追求每天幸福指数的可变因素序列
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self.happiness_factor = [0]
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# 每个追求每天财富积累的可变因素序列
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self.wealth_factor = [0]
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# 每个追求每天名望权利的可变因素序列
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self.fame_factor = [0]
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# 追求了多少天了这一生
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self.do_seek_day_cnt = 0
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# 子类进行常数及可变因素序列设置
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self._init_self()
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@abstractmethod
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def _init_self(self, *args, **kwargs):
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# 子类必须实现，设置自己的生命消耗的常数，幸福指数常数等常数设置
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pass
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@abstractmethod
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def _gen_living_days(self, *args, **kwargs):
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# 子类必须实现，设置自己的可变因素序列
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pass
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def do_seek_day(self):
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"""
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每一天的追求具体seek
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:return:
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"""
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# 生命消耗=living_consume:消耗常数 * happiness_factor:可变序列
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if self.do_seek_day_cnt >= len(self.living_factor):
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# 超出len(self.living_factor), 就取最后一个living_factor[-1]
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consume_living = \
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self.living_factor[-1] * self.living_consume
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else:
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# 每个类自定义这个追求的消耗生命常数，以及living_factor，比如
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# HealthSeekDay追求健康，living_factor序列的值即由负值->正值
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# 每个子类living_factor会有自己特点的变化速度及序列长度，导致每个
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# 追求对生命的消耗随着追求的次数变化不一
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consume_living = self.living_factor[self.do_seek_day_cnt] \
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* self.living_consume
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# 幸福指数=happiness_base:幸福常数 * happiness_factor:可变序列
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if self.do_seek_day_cnt >= len(self.happiness_factor):
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# 超出len(self.happiness_factor), 就取最后一个
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# 由于happiness_factor值由:n—>0 所以happiness_factor[-1]=0
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# 即随着追求一个事物的次数过多后会变的没有幸福感
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happiness = self.happiness_factor[
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-1] * self.happiness_base
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else:
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# 每个类自定义这个追求的幸福指数常数，以及happiness_factor
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# happiness_factor子类的定义一般是从高－>低变化
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happiness = self.happiness_factor[
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self.do_seek_day_cnt] * self.happiness_base
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# 财富积累=wealth_base:积累常数 * wealth_factor:可变序列
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if self.do_seek_day_cnt >= len(self.wealth_factor):
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# 超出len(self.wealth_factor), 就取最后一个
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wealth = self.wealth_factor[-1] * self.wealth_base
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else:
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# 每个类自定义这个追求的财富指数常数，以及wealth_factor
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wealth = self.wealth_factor[
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self.do_seek_day_cnt] * self.wealth_base
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# 权利积累=fame_base:积累常数 * fame_factor:可变序列
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if self.do_seek_day_cnt >= len(self.fame_factor):
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# 超出len(self.fame_factor), 就取最后一个
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fame = self.fame_factor[-1] * self.fame_base
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else:
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# 每个类自定义这个追求的名望权利指数常数，以及fame_factor
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fame = self.fame_factor[
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self.do_seek_day_cnt] * self.fame_base
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# 追求了多少天了这一生 + 1
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self.do_seek_day_cnt += 1
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# 返回这个追求这一天对生命的消耗，得到的幸福，财富，名望权利
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return consume_living, happiness, wealth, fame
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def regular_mm(group):
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# 最小-最大规范化
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return (group - group.min()) / (group.max() - group.min())
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"""
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HealthSeekDay
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"""
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class HealthSeekDay(BaseSeekDay):
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"""
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HealthSeekDay追求健康长寿的一天:
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形象：健身，旅游，娱乐，做感兴趣的事情。
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抽象：追求健康长寿。
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"""
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def _init_self(self):
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# 每天对生命消耗的常数＝1，即代表1天
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self.living_consume = 1
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# 每天幸福指数常数＝1
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self.happiness_base = 1
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# 设定可变因素序列
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self._gen_living_days()
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def _gen_living_days(self):
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# 只生成12000个序列，因为下面的happiness_factor序列值由1－>0
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# 所以大于12000次的追求都将只是单纯消耗生命，并不增加幸福指数
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# 即随着做一件事情的次数越来越多，幸福感越来越低，直到完全体会不到幸福
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days = np.arange(1, 12000)
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# 基础函数选用sqrt, 影响序列变化速度
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living_days = np.sqrt(days)
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"""
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对生命消耗可变因素序列值由-1->1, 也就是这个追求一开始的时候对生命
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的消耗为负增长，延长了生命，随着追求的次数不断增多对生命的消耗转为正
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数因为即使一个人天天锻炼身体，天天吃营养品，也还是会有自然死亡的那
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一天
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"""
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# *2-1的目的:regular_mm在0-1之间,HealthSeekDay要结果在－1，1之间
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self.living_factor = regular_mm(living_days) * 2 - 1
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# 结果在1-0之间 [::-1]: 将0->1转换到1->0
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self.happiness_factor = regular_mm(days)[::-1]
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def sample_621_1():
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"""
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6.2.1_1 你一生的故事：HealthSeekDay
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:return:
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"""
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# 初始化我
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me = Person()
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# 初始化追求健康长寿快乐
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seek_health = HealthSeekDay()
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while me.living > 0:
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# 只要还活着，就追求健康长寿快乐
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me.live_one_day(seek_health)
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print('只追求健康长寿快乐活了{}年，幸福指数{},积累财富{},名望权力{}'.format
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(round(me.living_day / 365, 2), round(me.happiness, 2),
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me.wealth, me.fame))
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plt.plot(seek_health.living_factor * seek_health.living_consume)
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plt.plot(seek_health.happiness_factor * seek_health.happiness_base)
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plt.legend(['living_factor', 'happiness_factor'], loc='best')
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plt.show()
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"""
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StockSeekDay
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"""
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class StockSeekDay(BaseSeekDay):
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"""
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StockSeekDay追求财富金钱的一天:
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形象：做股票投资赚钱的事情。
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抽象：追求财富金钱
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"""
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def _init_self(self, show=False):
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# 每天对生命消耗的常数＝2，即代表2天
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self.living_consume = 2
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# 每天幸福指数常数＝0.5
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self.happiness_base = 0.5
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# 财富积累常数＝10，默认＝0
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self.wealth_base = 10
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# 设定可变因素序列
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self._gen_living_days()
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def _gen_living_days(self):
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# 只生成10000个序列
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days = np.arange(1, 10000)
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# 针对生命消耗living_factor的基础函数还是sqrt
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living_days = np.sqrt(days)
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# 由于不需要像HealthSeekDay从负数开始，所以直接regular_mm 即:0->1
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self.living_factor = regular_mm(living_days)
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# 针对幸福感可变序列使用了np.power4，即变化速度比sqrt快
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happiness_days = np.power(days, 4)
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# 幸福指数可变因素会快速递减由1->0
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self.happiness_factor = regular_mm(happiness_days)[::-1]
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"""
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这里简单设定wealth_factor=living_factor
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living_factor(0-1), 导致wealth_factor(0-1), 即财富积累越到
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后面越有效率，速度越快，头一个100万最难赚
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"""
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self.wealth_factor = self.living_factor
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def sample_621_2():
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"""
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6.2.1_2 你一生的故事：StockSeekDay
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:return:
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"""
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# 初始化我
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me = Person()
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# 初始化追求财富金钱
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seek_stock = StockSeekDay()
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while me.living > 0:
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# 只要还活着，就追求财富金钱
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me.live_one_day(seek_stock)
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print('只追求财富金钱活了{}年，幸福指数{}, 积累财富{}, 名望权力{}'.format
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(round(me.living_day / 365, 2), round(me.happiness, 2),
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round(me.wealth, 2), me.fame))
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plt.plot(seek_stock.living_factor * seek_stock.living_consume)
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plt.plot(seek_stock.happiness_factor * seek_stock.happiness_base)
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plt.legend(['living_factor', 'happiness_factor'], loc='best')
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plt.show()
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"""
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FameSeekDay
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"""
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class FameSeekDay(BaseSeekDay):
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"""
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FameTask追求名望权力的一天:
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追求名望权力
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"""
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def _init_self(self):
|
||
# 每天对生命消耗的常数＝3，即代表3天
|
||
self.living_consume = 3
|
||
# 每天幸福指数常数＝0.6
|
||
self.happiness_base = 0.6
|
||
# 名望权利积累常数＝10，默认＝0
|
||
self.fame_base = 10
|
||
# 设定可变因素序列
|
||
self._gen_living_days()
|
||
|
||
def _gen_living_days(self):
|
||
# 只生成12000个序列
|
||
days = np.arange(1, 12000)
|
||
# 针对生命消耗living_factor的基础函数还是sqrt
|
||
living_days = np.sqrt(days)
|
||
# 由于不需要像HealthSeekDay从负数开始，所以直接regular_mm 即:0->1
|
||
self.living_factor = regular_mm(living_days)
|
||
|
||
# 针对幸福感可变序列使用了np.power2
|
||
# 即变化速度比StockSeekDay慢但比HealthSeekDay快
|
||
happiness_days = np.power(days, 2)
|
||
# 幸福指数可变因素递减由1->0
|
||
self.happiness_factor = regular_mm(happiness_days)[::-1]
|
||
|
||
# 这里简单设定fame_factor=living_factor
|
||
self.fame_factor = self.living_factor
|
||
|
||
|
||
def sample_621_3():
|
||
"""
|
||
6.2.1_3 你一生的故事：FameSeekDay
|
||
:return:
|
||
"""
|
||
# 初始化我
|
||
me = Person()
|
||
# 初始化追求名望权力
|
||
seek_fame = FameSeekDay()
|
||
while me.living > 0:
|
||
# 只要还活着，就追求名望权力
|
||
me.live_one_day(seek_fame)
|
||
|
||
print('只追求名望权力活了{}年，幸福指数{}, 积累财富{}, 名望权力{}'.format
|
||
(round(me.living_day / 365, 2), round(me.happiness, 2),
|
||
round(me.wealth, 2), round(me.fame, 2)))
|
||
|
||
plt.plot(seek_fame.living_factor * seek_fame.living_consume)
|
||
plt.plot(seek_fame.happiness_factor * seek_fame.happiness_base)
|
||
plt.legend(['living_factor', 'happiness_factor'], loc='best')
|
||
plt.show()
|
||
|
||
|
||
"""
|
||
6.2.2 使用蒙特卡洛方法计算怎样度过一生最幸福
|
||
"""
|
||
|
||
|
||
def my_life(weights):
|
||
"""
|
||
追求健康长寿快乐的权重:weights[0]
|
||
追求财富金钱的权重:weights[1]
|
||
追求名望权力的权重:weights[2]
|
||
"""
|
||
# 追求健康长寿快乐
|
||
seek_health = HealthSeekDay()
|
||
# 追求财富金钱
|
||
seek_stock = StockSeekDay()
|
||
# 追求名望权力
|
||
seek_fame = FameSeekDay()
|
||
|
||
# 放在一个list中对对应下面np.random.choice中的index[0, 1, 2]
|
||
seek_list = [seek_health, seek_stock, seek_fame]
|
||
|
||
# 初始化我
|
||
me = Person()
|
||
# 加权随机抽取序列。80000天肯定够了, 80000天快220年了。。。
|
||
seek_choice = np.random.choice([0, 1, 2], 80000, p=weights)
|
||
|
||
while me.living > 0:
|
||
# 追求从加权随机抽取序列已经初始化好的
|
||
seek_ind = seek_choice[me.living_day]
|
||
seek = seek_list[seek_ind]
|
||
# 只要还活着，就追求
|
||
me.live_one_day(seek)
|
||
return round(me.living_day / 365, 2), round(me.happiness, 2), round(me.wealth, 2), round(me.fame, 2)
|
||
|
||
|
||
def sample_622():
|
||
"""
|
||
6.2.2 使用蒙特卡洛方法计算怎样度过一生最幸福
|
||
:return:
|
||
"""
|
||
living_day, happiness, wealth, fame = my_life([0.4, 0.3, 0.3])
|
||
print('活了{}年，幸福指数{}, 积累财富{}, 名望权力{}'.format(
|
||
living_day, happiness, wealth, fame))
|
||
|
||
from abupy import AbuProgress
|
||
progress = AbuProgress(2000, 0, label='my_life...')
|
||
|
||
result = []
|
||
for pos, _ in enumerate(xrange(2000)):
|
||
# 2000次随机权重分配
|
||
weights = np.random.random(3)
|
||
weights /= np.sum(weights)
|
||
# result中：tuple[0]权重weights,，tuple[1]my_life返回的结果
|
||
result.append((weights, my_life(weights)))
|
||
progress.show(a_progress=pos + 1)
|
||
|
||
# result中tuple[1]=my_life返回的结果, my_life[1]=幸福指数，so->x[1][1]
|
||
sorted_scores = sorted(result, key=lambda p_x: p_x[1][1], reverse=True)
|
||
# 将最优权重sorted_scores[0][0]代入my_life得到结果
|
||
living_day, happiness, wealth, fame = my_life(sorted_scores[0][0])
|
||
|
||
print('活了{}年，幸福指数{}, 积累财富{}, 名望权力{}'.format
|
||
(living_day, happiness, wealth, fame))
|
||
|
||
print('人生最优权重：追求健康{:.3f},追求财富{:.3f},追求名望{:.3f}'.format(
|
||
sorted_scores[0][0][0], sorted_scores[0][0][1],
|
||
sorted_scores[0][0][2]))
|
||
|
||
# noinspection PyUnresolvedReferences
|
||
from mpl_toolkits.mplot3d import Axes3D
|
||
"""
|
||
result中: tuple[0]权重weights, tuple[1]my_life返回的结果
|
||
r[0][0]: 追求健康长寿快乐的权重
|
||
r[0][1]: 追求财富金钱的权重
|
||
r[0][2]: 追求名望权力的权重
|
||
r[1][1]: my_life[1]=幸福指数
|
||
"""
|
||
result_show = np.array(
|
||
[[r[0][0], r[0][1], r[0][2], r[1][1]] for r in result])
|
||
|
||
fig = plt.figure(figsize=(9, 6))
|
||
ax = fig.gca(projection='3d')
|
||
ax.view_init(30, 60)
|
||
"""
|
||
x:追求健康长寿快乐的权重, y:追求财富金钱的权重
|
||
z:追求名望权力的权重, c:color 幸福指数, 颜色越深越幸福
|
||
"""
|
||
ax.scatter3D(result_show[:, 0], result_show[:, 1], result_show[:, 2],
|
||
c=result_show[:, 3], cmap='spring')
|
||
ax.set_xlabel('health')
|
||
ax.set_ylabel('stock')
|
||
ax.set_zlabel('fame')
|
||
plt.show()
|
||
|
||
# 幸福指数
|
||
happiness_result = result_show[:, 3]
|
||
# 使用qcut分10份
|
||
print('pd.qcut(happiness_result, 10).value_counts():\n', pd.qcut(happiness_result, 10).value_counts())
|
||
|
||
|
||
"""
|
||
6.2.3 凸优化基础概念
|
||
"""
|
||
|
||
|
||
# noinspection PyTypeChecker
|
||
def sample_623():
|
||
"""
|
||
6.2.3 趋势骨架图
|
||
:return:
|
||
"""
|
||
import scipy.optimize as sco
|
||
from scipy.interpolate import interp1d
|
||
|
||
# 继续使用TSLA收盘价格序列
|
||
# interp1d线性插值函数
|
||
linear_interp = interp1d(x, y)
|
||
# 绘制插值
|
||
plt.plot(linear_interp(x))
|
||
|
||
# fminbound寻找给定范围内的最小值：在linear_inter中寻找全局最优范围1－504
|
||
global_min_pos = sco.fminbound(linear_interp, 1, 504)
|
||
# 绘制全局最优点，全局最小值点，r<：红色三角
|
||
plt.plot(global_min_pos, linear_interp(global_min_pos), 'r<')
|
||
|
||
# 每个单位都先画一个点，由两个点连成一条直线形成股价骨架图
|
||
last_postion = None
|
||
# 步长50，每50个单位求一次局部最小
|
||
for find_min_pos in np.arange(50, len(x), 50):
|
||
# fmin_bfgs寻找给定值的局部最小值
|
||
local_min_pos = sco.fmin_bfgs(linear_interp, find_min_pos, disp=0)
|
||
# 形成最小点位置信息(x, y)
|
||
draw_postion = (local_min_pos, linear_interp(local_min_pos))
|
||
# 第一个50单位last_postion＝none, 之后都有值
|
||
if last_postion is not None:
|
||
# 将两两临近局部最小值相连，两个点连成一条直线
|
||
plt.plot([last_postion[0][0], draw_postion[0][0]],
|
||
[last_postion[1][0], draw_postion[1][0]], 'o-')
|
||
# 将这个步长单位内的最小值点赋予last_postion
|
||
last_postion = draw_postion
|
||
plt.show()
|
||
|
||
|
||
def sample_624():
|
||
"""
|
||
6.2.4 全局最优求解怎样度过一生最幸福
|
||
:return:
|
||
"""
|
||
import scipy.optimize as sco
|
||
|
||
def minimize_happiness_global(weights):
|
||
if np.sum(weights) != 1:
|
||
# 过滤权重和不等于1的权重组合
|
||
return 0
|
||
# 最优都是寻找最小值，所以要得到幸福指数最大的权重，
|
||
# 返回-my_life，这样最小的结果其实是幸福指数最大的权重配比
|
||
return -my_life(weights)[1]
|
||
|
||
opt_global = sco.brute(minimize_happiness_global,
|
||
((0, 1.1, 0.1), (0, 1.1, 0.1), (0, 1.1, 0.1)))
|
||
print(opt_global)
|
||
|
||
living_day, happiness, wealth, fame = my_life(opt_global)
|
||
print('活了{}年，幸福指数{}, 积累财富{}, 名望权力{}'.format
|
||
(living_day, happiness, wealth, fame))
|
||
|
||
|
||
# noinspection PyTypeChecker
|
||
def sample_625():
|
||
"""
|
||
6.2.5 非凸函数计算怎样度过一生最幸福
|
||
:return:
|
||
"""
|
||
import scipy.optimize as sco
|
||
|
||
method = 'SLSQP'
|
||
# 提供一个函数来规范参数,np.sum(weights) = 1 -> np.sum(weights) - 1 = 0
|
||
constraints = ({'type': 'eq', 'fun': lambda p_x: np.sum(p_x) - 1})
|
||
# 参数的范围选定
|
||
bounds = tuple((0, 0.9) for _ in xrange(3))
|
||
print('bounds:', bounds)
|
||
|
||
def minimize_happiness_local(weights):
|
||
# print(weights)
|
||
return -my_life(weights)[1]
|
||
|
||
# 初始化猜测最优参数，这里使用brute计算出的全局最优参数作为guess
|
||
guess = [0.5, 0.2, 0.3]
|
||
opt_local = sco.minimize(minimize_happiness_local, guess,
|
||
method=method, bounds=bounds,
|
||
constraints=constraints)
|
||
print('opt_local:', opt_local)
|
||
|
||
|
||
# noinspection PyShadowingNames
|
||
def sample_626():
|
||
"""
|
||
6.2.6 标准凸函数求最优
|
||
:return:
|
||
"""
|
||
import scipy.optimize as sco
|
||
|
||
fig = plt.figure()
|
||
from mpl_toolkits.mplot3d import Axes3D
|
||
ax = Axes3D(fig)
|
||
x = np.arange(-10, 10, 0.5)
|
||
y = np.arange(-10, 10, 0.5)
|
||
x_grid, y_grid = np.meshgrid(x, y)
|
||
# z^2 = x^2 + y^2
|
||
z_grid = x_grid ** 2 + y_grid ** 2
|
||
|
||
ax.plot_surface(x_grid, y_grid, z_grid, rstride=1, cstride=1,
|
||
cmap='hot')
|
||
plt.show()
|
||
|
||
def convex_func(xy):
|
||
return xy[0] ** 2 + xy[1] ** 2
|
||
|
||
bounds = ((-10, 10), (-10, 10))
|
||
guess = [5, 5]
|
||
for method in ['SLSQP', 'TNC', 'L-BFGS-B']:
|
||
# 打印start
|
||
print(method + ' start')
|
||
# noinspection PyTypeChecker
|
||
ret = sco.minimize(convex_func, guess, method=method,
|
||
bounds=bounds)
|
||
print(ret)
|
||
# 这里通过np.allclose判定结果是不是（0， 0）
|
||
print('result is (0, 0): {}'.format(
|
||
np.allclose(ret['x'], [0., 0.], atol=0.001)))
|
||
# 打印end
|
||
print(method + ' end')
|
||
|
||
|
||
"""
|
||
6.3 线性代数
|
||
"""
|
||
|
||
# 获取多支股票数据组成panel
|
||
my_stock_df = ABuSymbolPd.make_kl_df(
|
||
['usBIDU', 'usGOOG', 'usFB', 'usAAPL', 'us.IXIC'], n_folds=2)
|
||
# 变换轴向，形成新的切面
|
||
my_stock_df = my_stock_df.swapaxes('items', 'minor')
|
||
my_stock_df_close = my_stock_df['close'].dropna(axis=0)
|
||
|
||
|
||
def regular_std(group):
|
||
# z-score规范化也称零-均值规范化
|
||
return (group - group.mean()) / group.std()
|
||
|
||
|
||
def sample_630():
|
||
"""
|
||
获取多支股票数据组成panel
|
||
:return:
|
||
"""
|
||
print('my_stock_df_close.tail():\n', my_stock_df_close.tail())
|
||
|
||
my_stock_df_close_std = regular_std(my_stock_df_close)
|
||
my_stock_df_close_std.plot()
|
||
plt.show()
|
||
|
||
|
||
def sample_631():
|
||
"""
|
||
6.3.1 矩阵基础知识
|
||
:return:
|
||
"""
|
||
from scipy import linalg
|
||
|
||
# dataframe转换matrix通过as_matrix
|
||
cs_matrix = my_stock_df_close.as_matrix()
|
||
# cs_matrix本身有5列数据(5支股票)，要变成方阵即保留5行数据0:5
|
||
cs_matrix = cs_matrix[0:5, :]
|
||
print('cs_matrix.shape:', cs_matrix.shape)
|
||
print('cs_matrix:\n', cs_matrix)
|
||
|
||
eye5 = np.eye(5)
|
||
print(eye5)
|
||
|
||
cs_matrix_inv = linalg.inv(cs_matrix)
|
||
print('逆矩阵: cs_matrix_inv')
|
||
print(cs_matrix_inv)
|
||
# 上面打印cs_matrix_inv输出上并非绝对标准单位矩阵，是对角线值元素接近与1，非对
|
||
# 角线元素接近与0的矩阵，需要使用np.allclose来确认结果
|
||
print('相乘后的结果是单位矩阵：{}'.format(
|
||
np.allclose(np.dot(cs_matrix, cs_matrix_inv), eye5)))
|
||
|
||
|
||
def sample_632():
|
||
"""
|
||
6.3.2 特征值和特征向量
|
||
:return:
|
||
"""
|
||
from scipy import mat, linalg
|
||
|
||
a = mat('[1.5 -0.5; -0.5 1.5]')
|
||
u, d = linalg.eig(a)
|
||
print('特征值向量：{}'.format(u))
|
||
print('特征向量（列向量）矩阵：{}'.format(d))
|
||
|
||
|
||
def sample_634():
|
||
"""
|
||
6.3.4 PCA和SVD使用实例
|
||
:return:
|
||
"""
|
||
from sklearn.decomposition import PCA
|
||
|
||
my_stock_df_close_std = regular_std(my_stock_df_close)
|
||
# n_components=1只保留一个维度
|
||
pca = PCA(n_components=1)
|
||
# 稍后会有展示fit_transform的实现，以及关键核心代码抽取
|
||
my_stock_df_trans_pca = \
|
||
pca.fit_transform(my_stock_df_close_std.as_matrix())
|
||
|
||
plt.plot(my_stock_df_trans_pca)
|
||
plt.show()
|
||
|
||
# 可视化维度和主成分关系，参数空
|
||
pca = PCA()
|
||
# 直接使用fit，不用fit_transform
|
||
pca.fit(my_stock_df_close_std)
|
||
|
||
# x:保留的维度 y:保留的维度下的方差比总和即保留了多少主成分
|
||
plt.plot(np.arange(1, len(pca.explained_variance_ratio_) + 1),
|
||
np.cumsum(pca.explained_variance_ratio_))
|
||
plt.xlabel('component')
|
||
plt.ylabel('explained variance')
|
||
plt.show()
|
||
|
||
# 0.95即保留95%主成分
|
||
pca = PCA(0.95)
|
||
# 稍后会有展示fit_transform的实现，以及关键核心代码抽取
|
||
my_stock_df_trans_pca = \
|
||
pca.fit_transform(my_stock_df_close_std.as_matrix())
|
||
plt.plot(my_stock_df_trans_pca)
|
||
plt.show()
|
||
|
||
# noinspection PyPep8Naming
|
||
def my_pca(n_components=1):
|
||
from scipy import linalg
|
||
|
||
# svd奇异值分解
|
||
U, S, V = linalg.svd(my_stock_df_close_std.as_matrix(),
|
||
full_matrices=False)
|
||
# 通过n_components进行降维
|
||
U = U[:, :n_components]
|
||
U *= S[:n_components]
|
||
# 绘制降维后的矩阵
|
||
plt.plot(U)
|
||
|
||
# 输出如图6－19所示
|
||
my_pca(n_components=3)
|
||
plt.show()
|
||
|
||
|
||
if __name__ == "__main__":
|
||
sample_611_1()
|
||
# sample_611_2()
|
||
# sample_612()
|
||
# sample_613()
|
||
# sample_621_1()
|
||
# sample_621_2()
|
||
# sample_621_3()
|
||
# sample_622()
|
||
# sample_623()
|
||
# sample_624()
|
||
# sample_625()
|
||
# sample_626()
|
||
# sample_630()
|
||
# sample_631()
|
||
# sample_632()
|
||
# sample_634()
|