masatomix · December 15, 2018 12:20
diff --git a/file0.txt b/file0.txt
 \left(
 \begin{array}{c}
 \cos\theta\\
 \sin\theta
 \end{array}
 \right) 
diff --git a/file1.txt b/file1.txt
 \boldsymbol{a}\cdot\boldsymbol{b}  := \|\boldsymbol{a}\|\|\boldsymbol{b}\|\ \cos\theta
diff --git a/file10.txt b/file10.txt
 \begin{align}
 \cos\theta &= \frac{\boldsymbol{a}\cdot\boldsymbol{b}}{\|\boldsymbol{a}\|\|\boldsymbol{b}\|}\\
 &= \frac{\sum_{i=1}^{n} a_ib_i}{\sqrt{\sum_{i=1}^{n} a_i^2} \cdot \sqrt{\sum_{i=1}^{n} b_i^2}}
 \end{align}
diff --git a/file11.txt b/file11.txt
 \boldsymbol{x} = 
 \left(
 \begin{array}{c}
 x_1 -m_x\\
 x_2 -m_x\\
 \vdots\\
 x_n -m_x\\
 \end{array}
 \right) 
 ,
 \boldsymbol{y} = 
 \left(
 \begin{array}{c}
 y_1 -m_y\\
 y_2 -m_y\\
 \vdots\\
 y_n -m_y\\
 \end{array}
 \right) 
diff --git a/file12.txt b/file12.txt
 \begin{align}
 r_{xy} :&= \frac{\boldsymbol{x}\cdot\boldsymbol{y}}{\|\boldsymbol{x}\|\|\boldsymbol{y}\|}\\
 &=\frac{\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\sum_{i=1}^{n} (y_i -m_y)^2}}\\
 &= (\boldsymbol{x}と\boldsymbol{y}のなす角\theta の \cos\theta )

 \end{align}
diff --git a/file13.txt b/file13.txt
 m_x:= \frac{1}{n} \sum_{i=1}^{n}x_i \\
 m_y:= \frac{1}{n} \sum_{i=1}^{n}y_i 
diff --git a/file14.txt b/file14.txt
 \begin{align}
 r_{xy} 
 &=\frac{\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\sum_{i=1}^{n} (y_i -m_y)^2}}\\
 &=\frac{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\frac{1}{n}\sum_{i=1}^{n} (y_i -m_y)^2}}\\
 &=\frac{S_{xy}}{S_xS_y}
 \end{align}
diff --git a/file15.txt b/file15.txt
 \begin{align}

 S_{xy}&:=\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)\\
 S_x&:=\sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)^2}\\
 S_y&:=\sqrt{\frac{1}{n}\sum_{i=1}^{n} (y_i -m_y)^2}

 \end{align}
diff --git a/file16.txt b/file16.txt
 $ head weight.csv 
 key,体重,体脂肪率,BMI
 2017-12-10,58.5750,14.2425,23.4000
 2017-12-11,58.6333,14.1255,23.4333
 2017-12-12,58.3250,14.4700,23.3500
 2017-12-13,58.4000,14.8275,23.3500
 2017-12-14,57.2000,14.1450,22.9000
 2017-12-15,57.9500,13.6900,23.2000
 2017-12-16,58.0000,14.3400,23.2000
 2017-12-17,58.6167,14.0995,23.4333
 2017-12-18,58.7500,14.0150,23.4500
 .....
diff --git a/file17.txt b/file17.txt
 $ sw_vers
 ProductName:    Mac OS X
 ProductVersion: 10.14.1 (Mojaveです)
 BuildVersion:   18B75
diff --git a/file18.txt b/file18.txt
 $ python3 -m venv ./venv
 $ source ./venv/bin/activate
 (venv) $ which python3
 /xxx/venv/bin/python3
 (venv) $  python3 --version
 Python 3.7.1
 (venv) $ 
diff --git a/file19.txt b/file19.txt
 (venv) $ cat requirement.txt
 matplotlib==3.0.2
 numpy==1.15.4
 pandas==0.23.4
 PyQt5==5.11.3
 (venv) $ pip install -r requirement.txt
 ... 割愛
 (venv) $ cat weight.py
diff --git a/file2.txt b/file2.txt
 \begin{align}
 \boldsymbol{a}\cdot\boldsymbol{b} &= \|\boldsymbol{a}\|\|\boldsymbol{b}\|\ \cos\theta\\
 &=\|\boldsymbol{a}\|\times( \|\boldsymbol{b}\|\ \cos\theta)\\
 \end{align}
diff --git a/file20.txt b/file20.txt
 # !/usr/bin/env python
 # -*- coding: utf-8 -*-

 import matplotlib.pyplot as plt
 import numpy as np
 import pandas as pd
 import sys


 def main(args):
    # データ読み込み
    df = pd.read_csv('./weight.csv', index_col='key')
    print(df.head(10))
    print(df.shape)

    # データ列取り出し
    data1 = df['体重']
    data2 = df['体脂肪率']
    data3 = df['BMI']


    # 平均
    mean1 = np.mean(data1)  # mx
    mean2 = np.mean(data2)  # my

    # 分散と、共分散
    v1 = np.var(data1, ddof=0)  # 1/n * Σ (X-mx)^2
    v2 = np.var(data2, ddof=0)  # 1/n * Σ (Y-my)^2
    cov = np.cov(data1, data2, ddof=0)[1, 0]  # 1/n * Σ (X-mx)*(Y-my)
    # 共分散は共分散行列で返ってくるので、[1,0],[0,1] をとればいい

    # 標準偏差
    std_dev1 = np.sqrt(v1)
    std_dev2 = np.sqrt(v2)

    # 相関係数
    cor = np.corrcoef(data1, data2)[1, 0]
    cor2 = cov / (std_dev1 * std_dev2)  # もしくは計算で。

    print('--- 体重と体脂肪率 ----')
    print(f'　　平均: {mean1:.3f}, {mean2:.3f}')
    print(f'標準偏差: {std_dev1:.3f}, {std_dev2:.3f}')
    print(f'　　分散: {v1:.3f}, {v2:.3f}')
    print(f'　共分散: {cov:.10f}')
    print(f'相関係数: {cor:.10f}')
    print(f'相関係数: {cor2:.10f}')

    print('-------')

    # ちなみに体重とBMIの相関係数
    cor3 = np.corrcoef(data1, data3)[1, 0]
    print(f'体重とBMIの相関係数: {cor3:.10f}')

    plot(df)


 def plot(df):
    xorg = df['体重']
    yorg = df['BMI']

    mx = np.mean(xorg)
    my = np.mean(yorg)

    fig = plt.figure()

    ax1 = fig.add_subplot(2, 1, 1)
    ax2 = fig.add_subplot(2, 1, 2)

    ax1.scatter(xorg, yorg, label='体重とBMI', s=5)
    ax1.scatter(mx, my, label='平均')

    ax1.set_xlabel('体重')
    ax1.set_ylabel('BMI')
    ax1.grid(True)  # グリッド線

    plot_poly_1d(ax1, xorg, yorg)
    ax1.legend(loc='upper left')

    yorg2 = df['体脂肪率']
    my2 = np.mean(yorg2)
    ax2.scatter(xorg, yorg2, label='体重と体脂肪率', s=5)
    ax2.scatter(mx, my2, label='平均')

    ax2.set_xlabel('体重')
    ax2.set_ylabel('体脂肪率')
    ax2.grid(True)  # グリッド線

    plot_poly_1d(ax2, xorg, yorg2)
    ax2.legend(loc='lower left')

    plt.tight_layout()  # タイトルの被りを防ぐ

    # グラフに情報を表示
    plt.show()


 # 線形回帰直線
 def plot_poly_1d(ax, xorg, yorg):
    # y = ax + b のa ,b を配列で返す
    poly_fit = np.polyfit(xorg, yorg, 1)

    # 関数を作成
    poly_1d = np.poly1d(poly_fit)

    xs = np.linspace(xorg.min(), xorg.max())
    ys = poly_1d(xs)

    ax.plot(xs, ys, label=f'{poly_fit[1]:.2f}+{poly_fit[0]:.2f}x')


 if __name__ == "__main__":
    main(sys.argv)


diff --git a/file21.txt b/file21.txt
 (venv) $ python3 weight.py
                 体重     体脂肪率      BMI
 key                                  
 2017-12-10  58.5750  14.2425  23.4000
 2017-12-11  58.6333  14.1255  23.4333
 2017-12-12  58.3250  14.4700  23.3500
 2017-12-13  58.4000  14.8275  23.3500
 2017-12-14  57.2000  14.1450  22.9000
 2017-12-15  57.9500  13.6900  23.2000
 2017-12-16  58.0000  14.3400  23.2000
 2017-12-17  58.6167  14.0995  23.4333
 2017-12-18  58.7500  14.0150  23.4500
 2017-12-19  58.5875  14.2555  23.4250
 (356, 3)
 --- 体重と体脂肪率 ----
 　　平均: 59.935, 14.514
 標準偏差: 0.835, 0.478
 　　分散: 0.698, 0.229
 　共分散: -0.0193105736
 相関係数: -0.0483200035
 相関係数: -0.0483200035
 -------
 体重とBMIの相関係数: 0.9980663360
diff --git a/file3.txt b/file3.txt
 \boldsymbol{a}\cdot(\boldsymbol{b}+\boldsymbol{c}) = 
 \boldsymbol{a}\cdot\boldsymbol{b}+\boldsymbol{a}\cdot\boldsymbol{c}
diff --git a/file4.txt b/file4.txt
 \begin{align}
 \boldsymbol{a}\cdot(\boldsymbol{b}+\boldsymbol{c}) &=\boldsymbol{a}\cdot\boldsymbol{d}\\
 &=\|\boldsymbol{a}\|\times( \boldsymbol{d}を\boldsymbol{a}へ射影したときの長さ)\\
 &=\|\boldsymbol{a}\|\times( \boldsymbol{b}を\boldsymbol{a}へ射影したときの長さ +\boldsymbol{c}を\boldsymbol{a}へ射影したときの長さ )\\
 &=\|\boldsymbol{a}\|\times( \boldsymbol{b}を\boldsymbol{a}へ射影したときの長さ) +\|\boldsymbol{a}\|\times(\boldsymbol{c}を\boldsymbol{a}へ射影したときの長さ )\\
 &=\boldsymbol{a}\cdot\boldsymbol{b}+\boldsymbol{a}\cdot\boldsymbol{c}\\
 (Q.E.D.)
 \end{align}
diff --git a/file5.txt b/file5.txt
 \boldsymbol{a} = 
 \left(
 \begin{array}{c}
 a_1\\
 a_2
 \end{array}
 \right) 
 ,
 \boldsymbol{b} = 
 \left(
 \begin{array}{c}
 b_1\\
 b_2
 \end{array}
 \right) 
diff --git a/file6.txt b/file6.txt
 \boldsymbol{e_1} = 
 \left(
 \begin{array}{c}
 1\\
 0
 \end{array}
 \right) 
 ,
 \boldsymbol{e_2} = 
 \left(
 \begin{array}{c}
 0\\
 1
 \end{array}
 \right) 
diff --git a/file7.txt b/file7.txt
 \begin{align}
 \boldsymbol{a}\cdot\boldsymbol{b} &=(a_1\boldsymbol{e_1}+a_2\boldsymbol{e_2})\cdot(b_1\boldsymbol{e_1} +b_2\boldsymbol{e_2})\\
 &=a_1 b_1 \boldsymbol{e_1}\cdot\boldsymbol{e_1}+a_2b_2\boldsymbol{e_2}\cdot\boldsymbol{e_2}\\
 &\qquad + a_1 b_2 \boldsymbol{e_1}\cdot\boldsymbol{e_2}+a_2 b_1 \boldsymbol{e_2}\cdot\boldsymbol{e_1}\\
 &= a_1b_1 + a_2b_2\\
 &=\|\boldsymbol{a}\|\|\boldsymbol{b}\|\ \cos\theta
 \end{align}
diff --git a/file8.txt b/file8.txt
 \boldsymbol{a} = 
 \left(
 \begin{array}{c}
 a_1\\
 a_2\\
 \vdots\\
 a_n\\
 \end{array}
 \right) 
 ,
 \boldsymbol{b} = 
 \left(
 \begin{array}{c}
 b_1\\
 b_2\\
 \vdots\\
 b_n\\
 \end{array}
 \right) 
diff --git a/file9.txt b/file9.txt
 \begin{align}
 \boldsymbol{a}\cdot\boldsymbol{b} &=\|\boldsymbol{a}\|\|\boldsymbol{b}\|\ \cos\theta\\
 &= a_1b_1 + a_2b_2 ... +a_nb_n\\
 &= \sum_{i=1}^{n} a_ib_i
 \end{align}
	\left(
	\begin{array}{c}
	\cos\theta\\
	\sin\theta
	\end{array}
	\right)
	\begin{align}
	\cos\theta &= \frac{\boldsymbol{a}\cdot\boldsymbol{b}}{\\|\boldsymbol{a}\\|\\|\boldsymbol{b}\\|}\\
	&= \frac{\sum_{i=1}^{n} a_ib_i}{\sqrt{\sum_{i=1}^{n} a_i^2} \cdot \sqrt{\sum_{i=1}^{n} b_i^2}}
	\end{align}
	\boldsymbol{x} =
	\left(
	\begin{array}{c}
	x_1 -m_x\\
	x_2 -m_x\\
	\vdots\\
	x_n -m_x\\
	\end{array}
	\right)
	,
	\boldsymbol{y} =
	\left(
	\begin{array}{c}
	y_1 -m_y\\
	y_2 -m_y\\
	\vdots\\
	y_n -m_y\\
	\end{array}
	\right)
	\begin{align}
	r_{xy} :&= \frac{\boldsymbol{x}\cdot\boldsymbol{y}}{\\|\boldsymbol{x}\\|\\|\boldsymbol{y}\\|}\\
	&=\frac{\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\sum_{i=1}^{n} (y_i -m_y)^2}}\\
	&= (\boldsymbol{x}と\boldsymbol{y}のなす角\theta の \cos\theta )

	\end{align}
	m_x:= \frac{1}{n} \sum_{i=1}^{n}x_i \\
	m_y:= \frac{1}{n} \sum_{i=1}^{n}y_i
	\begin{align}
	r_{xy}
	&=\frac{\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\sum_{i=1}^{n} (y_i -m_y)^2}}\\
	&=\frac{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)}{\sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)^2} \cdot \sqrt{\frac{1}{n}\sum_{i=1}^{n} (y_i -m_y)^2}}\\
	&=\frac{S_{xy}}{S_xS_y}
	\end{align}
	\begin{align}

	S_{xy}&:=\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)(y_i -m_y)\\
	S_x&:=\sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i -m_x)^2}\\
	S_y&:=\sqrt{\frac{1}{n}\sum_{i=1}^{n} (y_i -m_y)^2}

	\end{align}
	$ head weight.csv
	key,体重,体脂肪率,BMI
	2017-12-10,58.5750,14.2425,23.4000
	2017-12-11,58.6333,14.1255,23.4333
	2017-12-12,58.3250,14.4700,23.3500
	2017-12-13,58.4000,14.8275,23.3500
	2017-12-14,57.2000,14.1450,22.9000
	2017-12-15,57.9500,13.6900,23.2000
	2017-12-16,58.0000,14.3400,23.2000
	2017-12-17,58.6167,14.0995,23.4333
	2017-12-18,58.7500,14.0150,23.4500
	.....
	$ sw_vers
	ProductName: Mac OS X
	ProductVersion: 10.14.1 (Mojaveです)
	BuildVersion: 18B75
	$ python3 -m venv ./venv
	$ source ./venv/bin/activate
	(venv) $ which python3
	/xxx/venv/bin/python3
	(venv) $ python3 --version
	Python 3.7.1
	(venv) $