plotting Graph in 3D help

Question

Fareeha 2024-7-4

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评论： Umar 2024-7-30

采纳的回答： Umar

在 MATLAB Online 中打开

basic()

function basic

K=0.2; n=0.3; lam=0.1;

%Defining parameters

sol1 = bvpinit(linspace(0,6,300),[0 0 0 0 0]);

sol = bvp4c(@bvp2D, @bc2D, sol1);

x = sol.x;

y = sol.y;

%%% Plotting of the velocity

figure (1)

plot(x, y(2, :) ,'linewidth', 1.5);

hold on

xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)

ylabel('f^{\prime}(\eta)', 'fontweight', 'bold', 'fontsize', 16)

%% Residual of the boundary conditions

function residual = bc2D(y0, yinf)

residual=[y0(1); y0(2) - 1; y0(4)+n*y0(3); yinf(2)-lam; yinf(4)];

end

%% System of First Order ODEs

function yvector = bvp2D(~,y)

yy1 =(1/(1+K))*(-y(1)*y(3)+y(2)^2-K*y(5)-lam^2);

yy2 =(2/(2+K))*(-y(1)*y(5)+y(2)*y(4)+K*(2*y(4)+y(3)));

yvector = [y(2);y(3);yy1; y(5); yy2];

end

i want to plot this graph in 3D, how can I?

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Answer 1

Umar 2024-7-4

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编辑：Walter Roberson 2024-7-29

Hi Fareeha,

You asked, i want to plot this graph in 3D, how can I?

In order to do that, you can use plot3 function to achieve your goal. For more information on this function, please refer to

https://www.mathworks.com/help/matlab/ref/plot3.html#

Let me know if this answers your question.

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Umar 2024-7-4

编辑：Walter Roberson 2024-7-4

在 MATLAB Online 中打开

Hi Fareeha,

To answer your question about z in your example code, it will be set to zeros to plot the data in 3D space.

% Plotting the velocity in 3D
figure(1)
% Plotting in 3D
plot3(x, y(2, :), zeros(size(x)), 'linewidth', 1.5);
Unrecognized function or variable 'x'.
hold on
xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
ylabel('f^{\prime}(\eta)', 'fontweight', 'bold', 'fontsize', 16)
zlabel('Z-axis Label') % Adding Z-axis label

Also, in the provided function basic, which involves solving a boundary value problem using bvp4c, the primary focus seems to be on plotting the velocity profile rather than generating contour plots.

Here is a full version of your code by graphing plot in 3D.

function basic
K = 0.2;
n = 0.3;
lam = 0.1;
% Defining parameters
sol1 = bvpinit(linspace(0, 6, 300), [0 0 0 0 0]);
sol = bvp4c(@bvp2D, @bc2D, sol1);
x = sol.x;
y = sol.y;
% Plotting the velocity in 3D
figure(1)
% Plotting in 3D
plot3(x, y(2, :), zeros(size(x)), 'linewidth', 1.5);
hold on
xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
ylabel('f^{\prime}(\eta)', 'fontweight', 'bold', 'fontsize', 16)
zlabel('Z-axis Label') % Adding Z-axis label
% Residual of the boundary conditions
function residual = bc2D(y0, yinf)
     residual = [y0(1); y0(2) - 1; y0(4) + n * y0(3); yinf(2) - lam; yinf(4)];
 end
% System of First Order ODEs
function yvector = bvp2D(~, y)
    yy1 = (1 / (1 + K)) * (-y(1) * y(3) + y(2)^2 - K * y(5) - lam^2);
    yy2 = (2 / (2 + K)) * (-y(1) * y(5) + y(2) * y(4) + K * (2 * y(4) + y(3)));
    yvector = [y(2); y(3); yy1; y(5); yy2];
end
end

In the updated code snippet, the plot3 function is used to create a 3D plot of the velocity by enhanceing visualization by adding a third dimension to the plot. In this case, the velocity data is plotted in 3D space, providing a more comprehensive view of the results. Additionally, a Z-axis label is added to the plot for clarity. The rest of the code remains the same, defining parameters, handling boundary conditions, and solving the system of first-order ODEs as before. Your bc2D function still calculates the residual of the boundary conditions, while the bvp2D function defines the system of ODEs to be solved using the bvp4c solver.

Hope this will help resolve your problem.

Umar 2024-7-5

编辑：Walter Roberson 2024-7-29

在 MATLAB Online 中打开

Hi Fareeha,

To modify the existing code for generating a contour plot, we need to adjust the plotting section and include the necessary commands to create a contour plot. Below is the updated code with modifications for generating a contour plot:

function basic
K = 0.2; n = 0.3; lam = 0.1;
% Defining parameters
sol1 = bvpinit(linspace(0, 6, 300), [0 0 0 0 0]); sol = bvp4c(@bvp2D, @bc2D, sol1); x = sol.x; y = sol.y;
% Plotting the velocity in 3D 
figure(1)
% Plotting in 3D
plot3(x, y(2, :), zeros(size(x)), 'linewidth', 1.5); hold on
xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16) 
ylabel('f^{\prime}(\eta)', 'fontweight', 'bold', 'fontsize', 16)
zlabel('Z-axis Label') % Adding Z-axis label
% Generating Contour Plot
figure(2)
contourf(x, y(2, :), 'LineWidth', 1.5); % Creating a filled contour plot 
colorbar; % Adding a color bar for reference 
xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16) 
ylabel('f^{\prime}(\eta)', 'fontweight', 'bold', 'fontsize', 16) 
title('Contour Plot') % Adding a title to the plot
% Residual of the boundary conditions 
    function residual = bc2D(y0, yinf)
        residual = [y0(1); y0(2) - 1; y0(4) + n * y0(3); yinf(2) - lam; yinf(4)]; 
    end
% System of First Order ODEs 
    function yvector = bvp2D(~, y) 
        yy1 = (1 / (1 + K)) * (-y(1) * y(3) + y(2)^2 - K * y(5) - lam^2); yy2 = (2 / (2 + K)) * (-y(1) * y(5) + y(2) * y(4) + K * (2 * y(4) + y(3))); yvector = [y(2); y(3); yy1; y(5); yy2]; 
    end
end

In this updated code, a new figure (Figure 2) is created to display the contour plot using the contourf function. The contourf function generates a filled contour plot based on the values of x and y(2, :). Additionally, a color bar is added to provide a reference for the contour levels.

By incorporating these modifications, the code will now produce a contour plot alongside the existing 3D plot, offering a visual representation of the data in a different format.

Umar 2024-7-6

Hi Fareeha,

To fix the error, ensure that the input matrix Z passed to the contourf function is at least a 2x2 matrix. Here's an example to demonstrate how to fix the error:

% Create sample data

x = 1:5; y = 1:5; [X, Y] = meshgrid(x, y);

% Example data, replace with your own data

Z = peaks(5);

% Plot the contour

contourf(X, Y, Z, 'LineWidth', 1.5);

Please see attached plot.

In this example, X and Y are 2D matrices created using meshgrid, and Z is a sample 5x5 matrix. By ensuring that Z is a valid 2D matrix, the error should be resolved when calling contourf.

Let me know if you need further assistance or help.

Fareeha 2024-7-7

编辑：Fareeha 2024-7-7

Screenshot 2024-07-07 at 8.47.01 PM.png

@Umar thank you, i have just used z=peak(); in my code and able to generate contour.. I am attaching figure for reference.. can you tell how to check whether i am getting right figure?

can i use Z=peak(); in my code?

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Answer 2

Umar 2024-7-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2134516-plotting-graph-in-3d-help#answer_1482251

Hi Fareeha,

In response to your first question, to confirm if you are getting the right figure after using the "z=peak();" function in your code, you can employ various methods. One common approach is to visually inspect the output or result generated by the function to see if it aligns with your expectations. This could involve plotting or displaying the figure to ensure it matches what you anticipate. Furthermore, you can compare the output obtained from "z=peak();" with known values or expected outcomes to validate its accuracy. By verifying against established benchmarks or test cases, you can assess if the figure produced by the function is correct. Also, bear in mind that in MATLAB, the function z=peak(); is typically used to generate a sample data matrix that can be visualized as a contour plot. When you use this function, it creates a 49x49 matrix with peak values that form a peak in the center. If you want to generate the correct contour plot using this data, you do not necessarily have to modify your code. However, it is important to ensure that you are using the correct variable name when accessing the data matrix. In this case, if you initially used z=peak(); to store the data matrix, you should continue to reference it as z in your code.

Regarding your second query about using "Z=peak();" instead of "z=peak();", it typically depends on the programming language or environment you are working in. In some languages, variable names are case-sensitive, meaning that "z" and "Z" would be treated as distinct variables. Therefore, using "Z=peak();" might create a new variable "Z" rather than updating the existing variable "z". To ensure consistency and prevent potential errors, it is advisable to stick to a consistent naming convention for variables within your code. If you intend to update the original variable "z" with a new value from "peak();", it is recommended to use the same case for consistency.

Hope this answers all your questions.

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Umar 2024-7-27

编辑：Walter Roberson 2024-7-29

在 MATLAB Online 中打开

Hi Fareeha,

To modify the existing code to include streamlines, obtain the solution sol using bvp4c by extracting the velocity components u and v from sol.y to create a meshgrid for streamlines. Here is code snippet to show how to do it,

u = sol.y(3, :); % Extract u component
v = sol.y(2, :); % Extract v component
[X, Y] = meshgrid(x, y(1, :)); % Create meshgrid for streamlines

Next, plot the streamlines using the streamline function. Adjust the density of streamlines by specifying the starting points and the streamline spacing.

figure(2);
streamline(X, Y, reshape(u, size(X)), reshape(v, size(X)), [start_x1, start_x2, ...], [start_y1, start_y2, ...]);
    xlabel('x', 'fontweight', 'bold', 'fontsize', 16);
    ylabel('y', 'fontweight', 'bold', 'fontsize', 16);
    title('Streamlines', 'fontweight', 'bold', 'fontsize', 16);

For more information on this function, please refer to

https://www.mathworks.com/help/matlab/ref/streamline.html

Make sure to replace [start_x1, start_x2, ...] and [start_y1, start_y2, ...] with the desired starting points for streamlines and specifying multiple starting points to visualize a variety of streamlines.

I hope this answers your question. Good luck!

Fareeha 2024-7-30

@Umar i tried it and now i got this error:

Error using stream2 (line 46)

U,V must all be size 2x2 or greater.

Error in streamline (line 62)

verts = stream2(x,y,u,v,sx,sy,options);

Error in contour_plot_Magnetic_C (line 34)

streamline(X, Y, reshaped_u, reshaped_v, 0, 0);

i am using streamline function neither verts nor stream2.. then why i am getting this errror?

Umar 2024-7-30

@Fareeha,

Could you please share your code snippet that is causing these errors. Thx

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plotting Graph in 3D help

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