# How to find the indexes of the minimum or maximum value(s) in a matrix using python ?

Daidalos October 08, 2019

Examples of how to find the indexes of the minimum or maximum value(s) in a matrix using python and the numpy function called where:

Let's consider the following 2D matrix:

>>> import numpy as np
>>> A = np.random.randint(100, size=(4, 4))
>>> A
array([[73, 37,  6, 21],
       [16, 53, 77, 44],
       [98, 95,  3, 29],
       [77, 67, 87, 86]])


### Find min and max values

First, to find the minimum value, a solution is to use the numpy function min()

>>> vmin = A.min()
>>> vmin
3


and for the maximum value, the max() function

>>> vmax = A.max()
>>> vmax
98


### Find corresponding indexes

Now, it is possible to retrieve the indexes using the numpy function where.

minimum value indexes

>>> np.where(A == vmin)
(array([2]), array([2]))


maximum value indexes:

>>> np.where(A == vmax)
(array([2]), array([0]))


Note: another example with a matrix with several minimum:

>>> import numpy as np
>>> A = np.random.randint(5, size=(10,))
>>> A
array([4, 0, 4, 0, 2, 0, 2, 3, 2, 4])
>>> vmin = A.min()
>>> vmin
0
>>> np.where(A == vmin)
(array([1, 3, 5]),)


### Example of how to plot the min on a matplotlib imshow figure

from pylab import figure, cm

import matplotlib.pyplot as plt
import numpy as np

def f(x1,x2):
    return x1 * np.exp(-(x1**2+x2**2))

x1_min = -2.0
x1_max = 2.0
x2_min = -2.0
x2_max = 2.0

x1, x2 = np.meshgrid(np.arange(x1_min,x1_max, 0.1), np.arange(x2_min,x2_max, 0.1))

y = f(x1,x2)

#----- find min value

vmin = y.min()

#----- find min value indexes

min_indexes = np.where(y == vmin)

min1 = x1[ min_indexes[0] , min_indexes[1] ][0]
min2 = x2[ min_indexes[0] , min_indexes[1] ][0]

#----- plot

plt.imshow(y,extent=[x1_min,x1_max,x2_min,x2_max], cmap=cm.jet, origin='lower')

plt.colorbar()

plt.scatter(min1,min2,color='r',marker='x')

plt.savefig("plot_minimum_imshow.png")

#plt.show()


### References

How to find the minimum value in a numpy matrix? stackoverflow
numpy.where docs.scipy.org
Sorting, searching, and counting docs.scipy.org

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