根据其他变量为一个变量生成方程-解网

问：

我有一个特定的数据集，其中有 3 个不同的函数和 3 个不同的变量：

x = 1
strLen_x = int(3**x + 0.25*(-3*(-1)**x + 3**x + 6)) # Function 1
y = 2
strLen_y = 2*y # Function 2
z = 3
strLen_z = 3*(z + 1 + (z//4)) # Function 3
# Expecting Function 4 in terms of 1, 2, and 3

最终输出，即......变量只不过是依赖于 3 个不同变量的变量。我试图想出一个通用方程，其中是所有 3 个变量（）。strLen_x, y, and zstrLen_xyzx, y, z

下面是具有不同值的输出的表。注意：所有变量都是正整数。x, y, zy > 1

这里，是要获得的最终值。Output

python-3.x 函数数学序列

# see https://stackoverflow.com/questions/75650950/generate-equation-for-one-variable-in-terms-of-others

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler, PolynomialFeatures

def mse(y_test, predictions):
    return np.mean((y_test-predictions)**2)

if __name__ == "__main__":
    df = pd.read_csv('../resources/strlen.csv')

    cols = df.select_dtypes(np.number).columns

    X = df[['x', 'y', 'z']].to_numpy()
    y = df[['len']].to_numpy()

    scaler = StandardScaler()
    X_scaled = scaler.fit_transform(X)
    y_scaled = scaler.fit_transform(y)

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1234)

    reg = linear_model.LinearRegression()
    reg.fit(X_train, y_train)
    predictions = reg.predict(X_test)
    err = mse(y_test, predictions)
    print("Error       : ", err)
    print("Intercept   : ", reg.intercept_ )
    print("Coefficients: ", reg.coef_)

    y_pred_line = reg.predict(X)
    cmap = plt.get_cmap('viridis')
    fig = plt.figure(figsize=(8, 6))

    sns.scatterplot(data=df, x='x', y='len', hue='y', style='z')
    sns.lineplot(data=df, x='x', y='len')

    x_line = np.linspace(df.iloc[:, 0:3].min(axis=0), df.iloc[:, 0:3].max(axis=0), num=11)
    y_line = np.array(reg.intercept_[0] + np.matrix(x_line) * np.matrix(reg.coef_.transpose()))

    print('x_line: ', x_line, ' shape: ', x_line.shape)
    print('y_line: ', y_line, ' shape: ', y_line.shape)
    m1 = plt.plot(x_line[:, 0], y_line, color='red')

    plt.show()

这是我用你的数据创建的.csv：

x,y,z,len
12,6,6,12
12,4,12,16
36,4,6,10
36,4,24,60
36,4,6,10
36,8,9,160
102,6,6,102
306,4,9,80
306,4,24,240
306,8,24,7680
306,8,27,8960
306,10,21,19535
306,10,27,27345
912,10,21,97660
912,10,24,117190
912,10,36,175785

在代码中修复文件的路径并运行它。

这是数据图。红线是线性拟合结果：

我使用了一个完整的二阶多项式：.y = a0 + a1*x + a2*y + a3*z + a4*x^2 + a5*x*y + a6*x*z + a7*y^2 + a8*y*z + a9*z*z

您可以通过打印来查看系数。reg.coef_

根据其他变量为一个变量生成方程

Generate equation for one variable in terms of others

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