Plot gradient vector in ContourPlot

  • #1
Lambda96
196
68
TL;DR Summary
Plot gradient vector in ContourPlot
Hi,

I have made the following ContourPlot in mathematica and now I wanted to ##\vec{r}_1= \left(\begin{array}{c} -1 \\ 1 \end{array}\right)##, ##\vec{r}_2= \left(\begin{array}{c} 0 \\ \sqrt{2} \end{array}\right)## and ##\vec{r}_3= \left(\begin{array}{c} 1 \\ 1 \end{array}\right)## insert the gradient into the ContourPlot.

Bildschirmfoto 2023-12-11 um 15.33.19.png


Is this possible and if so, how?
 
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  • #3
Thank you Orodruin for your help 👍

Since I want to have the vectors at certain points in the ContourPlot, I used ListVectorPlot[{{x1,y1},{vx1,vy1}},...}].

Unfortunately, Mathematica then plots a vector field

Bildschirmfoto 2023-12-12 um 12.35.57.png
 
  • #4
Check out the VectorPoints option
 

FAQ: Plot gradient vector in ContourPlot

1. How do I plot a gradient vector field on a ContourPlot?

To plot a gradient vector field on a ContourPlot, you can use the `quiver` function in combination with `contour`. First, calculate the gradient of your function, then use `quiver` to plot the vectors and `contour` to plot the contours. For example, in Python with matplotlib, you might use:

import numpy as npimport matplotlib.pyplot as pltx = np.linspace(-5, 5, 100)y = np.linspace(-5, 5, 100)X, Y = np.meshgrid(x, y)Z = X**2 + Y**2 # Example function# Calculate gradientsU, V = np.gradient(Z)# Plot contour and gradientplt.contour(X, Y, Z)plt.quiver(X, Y, U, V)plt.show()

2. How can I adjust the density of the gradient vectors in the plot?

You can adjust the density of the gradient vectors by changing the step size in your meshgrid or by using the `quiver` function's `scale` parameter. For instance, to reduce the density, you can create a coarser grid:

x = np.linspace(-5, 5, 20) # Fewer pointsy = np.linspace(-5, 5, 20)X, Y = np.meshgrid(x, y)Z = X**2 + Y**2U, V = np.gradient(Z)plt.contour(X, Y, Z)plt.quiver(X, Y, U, V)plt.show()

3. How can I normalize the gradient vectors for better visualization?

To normalize the gradient vectors, you can divide each vector by its magnitude. This ensures that all vectors have the same length, making the direction of the gradient more apparent:

magnitude = np.sqrt(U**2 + V**2)U_normalized = U / magnitudeV_normalized = V / magnitudeplt.contour(X, Y, Z)plt.quiver(X, Y, U_normalized, V_normalized)plt.show()

4. Can I color the gradient vectors based on their magnitude?

Yes, you can color the gradient vectors based on their magnitude by passing a color array to the `quiver` function using the `C` parameter. Here's how you can do it:

magnitude = np.sqrt(U**2 + V**2)plt.contour(X, Y, Z)plt.quiver(X, Y, U, V, magnitude)plt.colorbar

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