# Plotting a decision boundary separating 2 classes using Matplotlib’s pyplot

Your question is more complicated than a simple plot : you need to draw the contour which will maximize the inter-class distance. Fortunately it’s a well-studied field, particularly for SVM machine learning.

The easiest method is to download the `scikit-learn` module, which provides a lot of cool methods to draw boundaries: `scikit-learn`: Support Vector Machines

Code :

``````# -*- coding: utf-8 -*-

import numpy as np
import matplotlib
from matplotlib import pyplot as plt
import scipy
from sklearn import svm

mu_vec1 = np.array([0,0])
cov_mat1 = np.array([[2,0],[0,2]])
x1_samples = np.random.multivariate_normal(mu_vec1, cov_mat1, 100)
mu_vec1 = mu_vec1.reshape(1,2).T # to 1-col vector

mu_vec2 = np.array([1,2])
cov_mat2 = np.array([[1,0],[0,1]])
x2_samples = np.random.multivariate_normal(mu_vec2, cov_mat2, 100)
mu_vec2 = mu_vec2.reshape(1,2).T

fig = plt.figure()

plt.scatter(x1_samples[:,0],x1_samples[:,1], marker="+")
plt.scatter(x2_samples[:,0],x2_samples[:,1], c="green", marker="o")

X = np.concatenate((x1_samples,x2_samples), axis = 0)
Y = np.array([0]*100 + [1]*100)

C = 1.0  # SVM regularization parameter
clf = svm.SVC(kernel="linear",  gamma=0.7, C=C )
clf.fit(X, Y)
``````

## Linear Plot

``````w = clf.coef_[0]
a = -w[0] / w[1]
xx = np.linspace(-5, 5)
yy = a * xx - (clf.intercept_[0]) / w[1]

plt.plot(xx, yy, 'k-')
``````

## MultiLinear Plot

``````C = 1.0  # SVM regularization parameter
clf = svm.SVC(kernel="rbf",  gamma=0.7, C=C )
clf.fit(X, Y)

h = .02  # step size in the mesh
# create a mesh to plot in
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))

# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])

# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contour(xx, yy, Z, cmap=plt.cm.Paired)
``````

## Implementation

If you want to implement it yourself, you need to solve the following quadratic equation:

The Wikipedia article

Unfortunately, for non-linear boundaries like the one you draw, it’s a difficult problem relying on a kernel trick but there isn’t a clear cut solution.