Numpy Meshgrid function (original) (raw)

The numpy.meshgrid function is used to create a rectangular grid out of two given one-dimensional arrays representing the Cartesian indexing or Matrix indexing. Meshgrid function is somewhat inspired from MATLAB. Consider the below figure with X-axis ranging from -4 to 4 and Y-axis ranging from -5 to 5. So there are a total of (9 * 11) = 99 points marked in the figure each with a X-coordinate and a Y-coordinate. For any line parallel to the X-axis, the X-coordinates of the marked points respectively are -4, -3, -2, -1, 0, 1, 2, 3, 4. On the other hand, for any line parallel to the Y-axis, the Y-coordinates of the marked points from bottom to top are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. The numpy.meshgrid function returns two 2-Dimensional arrays representing the X and Y coordinates of all the points. Examples:

Input : x = [-4, -3, -2, -1, 0, 1, 2, 3, 4] y = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5] Output : x_1 = array([[-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.], [-4., -3., -2., -1., 0., 1., 2., 3., 4.]])

y_1 = array([[-5., -5., -5., -5., -5., -5., -5., -5., -5.], [-4., -4., -4., -4., -4., -4., -4., -4., -4.], [-3., -3., -3., -3., -3., -3., -3., -3., -3.], [-2., -2., -2., -2., -2., -2., -2., -2., -2.], [-1., -1., -1., -1., -1., -1., -1., -1., -1.], [ 0., 0., 0., 0., 0., 0., 0., 0., 0.], [ 1., 1., 1., 1., 1., 1., 1., 1., 1.], [ 2., 2., 2., 2., 2., 2., 2., 2., 2.], [ 3., 3., 3., 3., 3., 3., 3., 3., 3.], [ 4., 4., 4., 4., 4., 4., 4., 4., 4.], [ 5., 5., 5., 5., 5., 5., 5., 5., 5.]])

Input : x = [0, 1, 2, 3, 4, 5] y = [2, 3, 4, 5, 6, 7, 8]

Output : x_1 = array([[0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.], [0., 1., 2., 3., 4., 5.]])

y_1 = array([[2., 2., 2., 2., 2., 2.], [3., 3., 3., 3., 3., 3.], [4., 4., 4., 4., 4., 4.], [5., 5., 5., 5., 5., 5.], [6., 6., 6., 6., 6., 6.], [7., 7., 7., 7., 7., 7.], [8., 8., 8., 8., 8., 8.]]

Below is the code:

Python3 1== `

Sample code for generation of first example

import numpy as np

from matplotlib import pyplot as plt

pyplot imported for plotting graphs

x = np.linspace(-4, 4, 9)

numpy.linspace creates an array of

9 linearly placed elements between

-4 and 4, both inclusive

y = np.linspace(-5, 5, 11)

The meshgrid function returns

two 2-dimensional arrays

x_1, y_1 = np.meshgrid(x, y)

print("x_1 = ") print(x_1) print("y_1 = ") print(y_1)

`

Output:

x_1 = [[-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.] [-4. -3. -2. -1. 0. 1. 2. 3. 4.]] y_1 = [[-5. -5. -5. -5. -5. -5. -5. -5. -5.] [-4. -4. -4. -4. -4. -4. -4. -4. -4.] [-3. -3. -3. -3. -3. -3. -3. -3. -3.] [-2. -2. -2. -2. -2. -2. -2. -2. -2.] [-1. -1. -1. -1. -1. -1. -1. -1. -1.] [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] [ 1. 1. 1. 1. 1. 1. 1. 1. 1.] [ 2. 2. 2. 2. 2. 2. 2. 2. 2.] [ 3. 3. 3. 3. 3. 3. 3. 3. 3.] [ 4. 4. 4. 4. 4. 4. 4. 4. 4.] [ 5. 5. 5. 5. 5. 5. 5. 5. 5.]]

The output of coordinates by meshgrid can also be used for plotting functions within the given coordinate range. An Ellipse: x_1^2+4y_1^2 = 0 Python3‘∗∗∗∗ellipse=xx∗2+4∗yy2∗∗∗∗plt.contourf(x1,y1,ellipse,cmap=′jet′)∗∗∗∗plt.colorbar()∗∗∗∗plt.show()∗∗∗∗‘Output:![](https://media.geeksforgeeks.org/wp−content/uploads/20190326234845/klklm.png)RandomData:Python3‘∗∗∗∗randomdata=np.random.random((11,9))∗∗∗∗plt.contourf(x1,y1,randomdata,cmap=′jet′)∗∗∗∗plt.colorbar()∗∗∗∗plt.show()∗∗∗∗‘Output:![](https://media.geeksforgeeks.org/wp−content/uploads/20190326234945/sdcasdv.png)ASinefunction:Python3 `

ellipse = xx * 2 + 4 * yy2 plt.contourf(x_1, y_1, ellipse, cmap = 'jet')

plt.colorbar() plt.show()

Output: ![](https://media.geeksforgeeks.org/wp-content/uploads/20190326234845/klklm.png) Random Data: Python3

random_data = np.random.random((11, 9)) plt.contourf(x_1, y_1, random_data, cmap = 'jet')

plt.colorbar() plt.show()

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style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">//</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ia</span><span class="mord">.</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ee</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ee</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord mathnormal">s</span><span class="mord">.</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord">/</span><span class="mord mathnormal">wp</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">co</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord">/</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.01968em;">pl</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">d</span><span class="mord mathnormal">s</span><span class="mord">/20190326234945/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">d</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord">.</span><span class="mord mathnormal">p</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">in</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">u</span><span class="mord mathnormal">n</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span></span></span></span></span>\\dfrac{\\sin(x\_1^2+y\_1^2)}{x\_1^2+y\_1^2} Python3

sine = (np.sin(x_12 + y_12))/(x_12 + y_12) plt.contourf(x_1, y_1, sine, cmap = 'jet')

plt.colorbar() plt.show()

** Output: ![](https://media.geeksforgeeks.org/wp-content/uploads/20190326235153/jnjn-300x205.png)** We observe that x\_1 is a row repeated matrix whereas y\_1 is a column repeated matrix. One row of x\_1 and one column of y\_1 is enough to determine the positions of all the points as the other values will get repeated over and over. So we can edit above code as follows:x_1, y_1 = np.meshgrid(x, y, sparse = True)`This will produce the following output:

x_1 = [[-4. -3. -2. -1. 0. 1. 2. 3. 4.]] y_1 = [[-5.] [-4.] [-3.] [-2.] [-1.] [ 0.] [ 1.] [ 2.] [ 3.] [ 4.] [ 5.]]

The shape of x_1 changed from (11, 9) to (1, 9) and that of y_1 changed from (11, 9) to (11, 1) The indexing of Matrix is however different. Actually, it is the exact opposite of Cartesian indexing.For the matrix shown above, for a given row Y-coordinate increases as 0, 1, 2, 3 from left to right whereas for a given column X-coordinate increases from top to bottom as 0, 1, 2. The two 2-dimensional arrays returned from Matrix indexing will be the transpose of the arrays generated by the previous program. The following code can be used for obtaining Matrix indexing:

Python3 1== `

Sample code for generation of Matrix indexing

import numpy as np

x = np.linspace(-4, 4, 9)

numpy.linspace creates an array

of 9 linearly placed elements between

-4 and 4, both inclusive

y = np.linspace(-5, 5, 11)

The meshgrid function returns

two 2-dimensional arrays

x_1, y_1 = np.meshgrid(x, y)

x_2, y_2 = np.meshgrid(x, y, indexing = 'ij')

The following 2 lines check if x_2 and y_2 are the

transposes of x_1 and y_1 respectively

print("x_2 = ") print(x_2) print("y_2 = ") print(y_2)

np.all is Boolean and operator;

returns true if all holds true.

print(np.all(x_2 == x_1.T)) print(np.all(y_2 == y_1.T))

`

Output:

x_2 = [[-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.] [-3. -3. -3. -3. -3. -3. -3. -3. -3. -3. -3.] [-2. -2. -2. -2. -2. -2. -2. -2. -2. -2. -2.] [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.] [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [ 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.] [ 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3.] [ 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.]] y_2 = [[-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.]]

True

True

The sparse = True can also be added in the meshgrid function of Matrix indexing. In this case, the shape of x_2 will change from (9, 11) to (9, 1) and that of y_2 will change from (9, 11) to (1, 11).