least squares poly regression

Regression class
1. least squares regression of nth order
3. output polynomial coefficients
2. plot result

Author: StephenGemin

matrix/__init__.py

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+from . import matrix_operation

regression/__init__.py

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+"""
+    References
+    ------------
+    https://en.wikipedia.org/wiki/Polynomial_regression
+"""
+
+import numpy as np
+from scipy import linalg
+import matplotlib.pyplot as plt
+from matplotlib import style
+style.use('seaborn')
+
+# from matrix import matrix_operation as mat_op
+
+
+class Regression:
+    """
+    Class that contains functions for linear and polynomial regression
+    Both regression cases are offered with:
+        1. traditional (least squares)
+        2. gradient descent
+    """
+    def __init__(self, x, y):
+        self.x = np.sort(np.asarray(x))
+        self.y = y
+        self.beta = None
+        self.coeffs = None
+        self.poly_eqn = None
+
+    def the_algorithm_ls_reg(self, order=1):
+        """
+        :param order: nth order polynomial
+        :type order: int
+        :return: ndarray
+
+
+        _____________________________________________
+        Still under development
+        Plan to incorporate this with the matrix operations already committed to the repo
+        _____________________________________________
+        """
+        pass
+
+    def ls_reg(self, order=1):
+        """
+        :param order: nth order polynomial
+        :type order: int
+        :return: self : object;
+        Output is in increasing order of x.  Ex. Cx**0 + Bx**1 + Ax**2
+
+        Regression model according to the equation below:
+        y = ß0 + ß1(xi) + ß2(xi)**2 + ... + ßm(xi)**m   -->  (i == 1, 2, ..., n)
+
+        Calculated according to the equation below, written in vector form
+        ß =  (X.T • X)**-1 • X.T • y
+
+        Nomenclature:
+        ß -- coefficient (paramater) vector
+        X -- design matrix
+        X.T -- transposed design matrix
+        y -- response vector
+        """
+
+        self.coeffs = self._create_coeffs(order)
+        print(self.x)
+        print(self.coeffs)
+        beta = np.matmul(np.matmul(linalg.pinv(np.matmul(np.transpose(self.coeffs), self.coeffs)),
+                                   np.transpose(self.coeffs)), self.y)
+        self.beta = beta
+        return self
+
+    def _create_coeffs(self, order):
+        coeffs = np.zeros((self.x.shape[0], order + 1))
+        for i in np.arange(0, order + 1):
+            coeffs[:, i] = self.x ** i
+        return coeffs
+
+    def plot_prediction(self):
+        """
+        Plot regression prediction
+        :return: matplotlib figure
+        """
+
+        # Following taken from https://github.com/pickus91/Polynomial-Regression-From-Scratch.git
+        pred_line = self.beta[0]
+        label_holder = []
+        for i in range(self.beta.shape[0]-1, 0, -1):
+            pred_line += self.beta[i] * self.x ** i
+            label_holder.append('%.*f' % (2, self.beta[i]) + r'$x^' + str(i) + '$')
+        label_holder.append('%.*f' % (2, self.beta[0]))
+
+        plt.figure()
+        plt.scatter(self.x, self.y)
+        plt.plot(self.x, pred_line, label=''.join(label_holder))
+        plt.title(f'Poly Fit: Order {self.beta.shape[0]-1}')
+        plt.xlabel('x')
+        plt.ylabel('y')
+        plt.legend(loc='best', frameon=True, fancybox=True, facecolor='white', shadow=True)
+        plt.show()
+
+    def __str__(self):
+        build_string = f'{self.__class__.__name__} analysis with the following inputs: \n\n\tx : \n{self.x} \n\tx-type : {type(self.x)}'
+        build_string += f'\n\n\ty : \n{self.y} \n\ty-type : {type(self.y)}'
+        build_string += f'\n\n\tOutput : \n{self.beta}'
+        return build_string
+
+    def __repr__(self):
+        return f'{self.__class__.__name__} analysis with inputs \n\tx shape: {self.x.shape}\n\ty shape: {self.y.shape}'
+
+
+if __name__ == '__main__':
+    np.random.seed(0)
+    num_points = 30
+    x = 2 - 3 * np.random.normal(0, 1, num_points)
+    y = x - 2 * (x ** 2) + 0.5 * (x ** 3) + np.random.normal(-3, 3, num_points)
+
+    reg = Regression(x, y)
+    print(reg.ls_reg(order=4))
+    reg.plot_prediction()