graphically display amplitudes vs heights of a matrix of vectors in matlab

To graphically display the amplitudes vs heights of a matrix of vectors in MATLAB, you can use the quiver function.

The quiver function allows you to plot vectors in a 2D or 3D space. In this case, we will use it to plot the vector amplitudes at specific heights. Here's a step-by-step guide:

1. Define your matrix of vectors. Let's call it vectors. Each row of the matrix represents a vector, and the columns represent its components.

   main.m
   vectors = [1, 2, 3; 4, 5, 6; 7, 8, 9];
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2. Compute the amplitudes of each vector. You can use the vecnorm function to calculate the magnitude (amplitude) of each vector.

   main.m
   amplitudes = vecnorm(vectors, 2, 2);
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   Here, 2 specifies the Euclidean norm (magnitude) of each vector, and 2 indicates that the norm should be calculated along rows.

3. Define the heights at which you want to plot the vectors. Let's say we have a height vector heights that corresponds to each row of the matrix.

   main.m
   heights = [1, 2, 3];
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4. Plot the vectors using the quiver function. The quiver function takes the x-coordinates, y-coordinates, and magnitudes (amplitudes) of the vectors.

   main.m
   quiver(zeros(size(vectors, 1), 1), heights, vectors(:, 1), vectors(:, 2), amplitudes);
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   In this example, zeros(size(vectors, 1), 1) generates the x-coordinates for the vectors, heights provides the y-coordinates, vectors(:, 1) and vectors(:, 2) represent the x and y components of the vectors, and amplitudes assigns a magnitude-dependent color to each vector.

5. Customize the plot as per your needs (labels, titles, axis limits, etc.).

   main.m
   xlabel('X');
   ylabel('Height');
   title('Amplitudes vs Heights');
   xlim([min(vectors(:, 1)) - 1, max(vectors(:, 1)) + 1]);
   ylim([min(heights) - 1, max(heights) + 1]);
   colorbar;
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   Here, I've added x and y labels, a title, set the x-axis and y-axis limits, and added a colorbar for the magnitude representation.

That's it! You now have a graphical display of the amplitudes vs heights of your matrix of vectors in MATLAB.