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# Gradient & - PowerPoint PPT Presentation

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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Presentation Transcript

Using

MATLAB

• x =-2:0.2:2;

• y = x .* exp(-x.^2);

• px = gradient(y,.2);

• quiver(x,px)

• [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

• [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

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)

u = x.*x + y.*y + z.*z;

v = 6*del2(u)

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