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Gradient &

Mathematical Modeling and Simulation Using MATLAB. Gradient &. Prof. Muhammad Saeed. Gradient I: x =-2:0.2:2; y = x .* exp(-x.^2); px = gradient(y,.2); quiver(x,px). Gradient II: [x,y] = meshgrid(-2:0.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2);

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Gradient &

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  1. Mathematical Modeling and Simulation Using MATLAB Gradient& Prof. Muhammad Saeed

  2. Gradient I: • x =-2:0.2:2; • y = x .* exp(-x.^2); • px = gradient(y,.2); • quiver(x,px)

  3. Gradient II: • [x,y] = meshgrid(-2:0.2:2); • z = x .* exp(-x.^2 - y.^2); • [px,py] = gradient(z,.2,.2); • contour(x,y,z), hold on, quiver(x,y,px,py), hold off

  4. Gradient II: • [x,y] = meshgrid(-2:0.2:2); • u = x .* exp(-x.^2 - y.^2); • [gx,gy] = gradient(u,.2,.2); • contour(x,y,u), hold on, quiver(x,y,gx,gy), hold off

  5. [x,y] = meshgrid(-4:4,-3:3); u = x.*x+y.*y; V = 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 v = 4*del2(u)

  6. [x,y,z] = meshgrid(-3:3,-3:3,-3:3); u = x.*x + y.*y + z.*z; v = 6*del2(u)

  7. v(:,:,1) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,2) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,5) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,6) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,3) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,4) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 v(:,:,7) = 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  8. End

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