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crh_LinearRegression.py

+# -*- coding: utf-8 -*-
+"""
+Created on Wed Nov 17 20:17:16 2021
+
+Provides functions for calculating the coeffs (m,c) of the 
+linear regression y=mx+c for a given set of point-data [x,y]
+
+flag: plot
+
+@author: hoefert
+"""
+
+## https://www.mathematik.de/algebra/74-erste-hilfe/algebra/matrizen/2432-anwendungen-der-matrizenrechnung
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def linearRegression(x, y, plot = False):
+    # creating the LES A'A ( m c)' = A'y 
+    # with A = (x , 1)
+            
+    # creating LES (over determined)
+    n = len(x)
+    A= np.ones((n,2))
+    A[:,0] = np.transpose(x)
+    b = np.transpose(y)
+    
+    M = np.matmul(A.T,A)
+    
+    bTrans = np.matmul(A.T,b)
+    [m,c] = np.linalg.solve(M,bTrans)
+    
+    if plot:
+        plotLinearRegression(x, y, m, c)
+    
+    return m,c
+
+
+def logLinearRegression(x, y, plot = False):
+    
+    xLog = np.log10(x)
+    yLog = np.log10(y)
+    
+    m,c = linearRegression(xLog,yLog)
+    
+    if plot:
+        plotLog10LinearRegression(x, y, m, c)
+    
+    return m,c
+
+
+def plotLinearRegression(x,y,m,c):
+    xLin = np.linspace(min(x),max(x),100)
+    yLin = xLin*m+c
+    plt.plot(x,y,'o')
+    plt.plot(xLin,yLin,linewidth=2)
+    plt.grid('both')
+    plt.show()
+
+    
+def plotLog10LinearRegression(x,y,m,c, plotLog  = False):
+    plt.plot(x,y,'o')
+    xLin = np.linspace(min(x),max(x),100)
+    yLin = 10**c*xLin**m
+    plt.plot(xLin,yLin,linewidth=2)
+    if plotLog:
+        plt.xscale('log')
+        plt.yscale('log')
+    plt.grid('both')
+    plt.show()
+    
+
+