1 / 14

Matlab

Matlab. Gradient. [FX,FY,FZ,...] = GRADIENT(F,...). Distance between grid points in X,Y,Z,… direction. [FX,FY,FZ,…] is numerical gradient of matrix F. FX corresponds to dF/dx, the differences in the x (column) direction. y. (1,5). (2,5). (3,5). (4,5). (5,5). (1,4). (2,4). (3,4).

baruch
Download Presentation

Matlab

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Matlab Gradient [FX,FY,FZ,...] = GRADIENT(F,...) Distance between grid points in X,Y,Z,… direction [FX,FY,FZ,…] is numerical gradient of matrix F FX corresponds to dF/dx, the differences in the x (column) direction

  2. y (1,5) (2,5) (3,5) (4,5) (5,5) (1,4) (2,4) (3,4) (4,4) (5,4) (1,3) (2,3) (3,3) (4,3) (5,3) x (1,2) (2,2) (3,2) (4,2) (5,2) (1,1) (2,1) (3,1) (4,1) (5,1) Example [x,y] = meshgrid(-2:.2:2, -2:.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(z),hold on, quiver(px,py), hold off [x,y] = meshgrid(-2:1:2, -2:1:2) Create a mesh on the domain of the function z. Examples: x(4,5)=1 y(4,5)=2 x(2,2)=-1 y(2,5)=2

  3. y (1,5) (2,5) (3,5) (4,5) (5,5) (1,4) (2,4) (3,4) (4,4) (5,4) (1,3) (2,3) (3,3) (4,3) (5,3) x (1,2) (2,2) (3,2) (4,2) (5,2) (1,1) (2,1) (3,1) (4,1) (5,1) [x,y] = meshgrid(-2:.2:2, -2:.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(z),hold on, quiver(px,py), hold off z=x.*exp(-x.^2-y.^2) Element by element operation X(4,5)=1 Y(4,5)=2 Z(4,5)=1*exp(-1^2-2^2)=exp(-5)=0.0067 -0.0007 -0.0067 0 0.0067 0.0007 -0.0135 -0.1353 0 0.1353 0.0135 -0.0366 -0.3679 0 0.3679 0.0366 -0.0135 -0.1353 0 0.1353 0.0135 -0.0007 -0.0067 0 0.0067 0.0007

  4. y (1,5) (2,5) (3,5) (4,5) (5,5) (1,4) (2,4) (3,4) (4,4) (5,4) (1,3) (2,3) (3,3) (4,3) (5,3) x (1,2) (2,2) (3,2) (4,2) (5,2) (1,1) (2,1) (3,1) (4,1) (5,1) -0.0007 -0.0067 0 0.0067 0.0007 -0.0135 -0.1353 0 0.1353 0.0135 -0.0366 -0.3679 0 0.3679 0.0366 -0.0135 -0.1353 0 0.1353 0.0135 -0.0007 -0.0067 0 0.0067 0.0007 [x,y] = meshgrid(-2:.2:2, -2:.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(z),hold on, quiver(px,py), hold off [px,py]=gradient(z,1,1) px = -0.0061 0.0003 0.0067 0.0003 -0.0061 -0.1219 0.0067 0.1353 0.0067 -0.1219 -0.3312 0.0183 0.3679 0.0183 -0.3312 -0.1219 0.0067 0.1353 0.0067 -0.1219 -0.0061 0.0003 0.0067 0.0003 -0.0061 py = -0.0128 -0.1286 0 0.1286 0.0128 -0.0180 -0.1806 0 0.1806 0.0180 0 0 0 0 0 0.0180 0.1806 0 -0.1806 -0.0180 0.0128 0.1286 0 -0.1286 -0.0128

  5. CONTOUR(Z) is a contour plot of matrix Z treating the values in Z as heights above a plane. A contour plot are the level curves of Z for some values V. The values V are chosen automatically. [x,y] = meshgrid(-2:.2:2, -2:.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(z),hold on, quiver(px,py), hold off px = -0.0061 0.0003 0.0067 0.0003 -0.0061 -0.1219 0.0067 0.1353 0.0067 -0.1219 -0.3312 0.0183 0.3679 0.0183 -0.3312 -0.1219 0.0067 0.1353 0.0067 -0.1219 -0.0061 0.0003 0.0067 0.0003 -0.0061 py = -0.0128 -0.1286 0 0.1286 0.0128 -0.0180 -0.1806 0 0.1806 0.0180 0 0 0 0 0 0.0180 0.1806 0 -0.1806 -0.0180 0.0128 0.1286 0 -0.1286 -0.0128 z = x .* exp(-x.^2 - y.^2);

  6. [x,y] = meshgrid(-2:.2:2, -2:.2:2); z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(z),hold on, quiver(px,py), hold off HOLD ON holds the current plot and all axis properties so that subsequent graphing commands add to the existing graph. HOLD OFF returns to the default mode whereby PLOT commands erase the previous plots and reset all axis properties before drawing new plots.

  7. Matlab Divergence: DIV = DIVERGENCE(X,Y,Z,U,V,W) computes the divergence of a 3-D vector field U,V,W. The arrays X,Y,Z define the coordinates for U,V,W and must be monotonic and 3-D plaid (as if produced by MESHGRID). Example: load wind div = divergence(x,y,z,u,v,w); slice(x,y,z,div,[90 134],[59],[0]); shading interp daspect([1 1 1]) camlight

  8. load wind div = divergence(x,y,z,u,v,w); slice(x,y,z,div,[90 134],[59],[0]); shading interp daspect([1 1 1]) camlight Slice at (90,59,0) Wind is an array of (41,35,15). Origin: (70.2,17.5,0) End: (134.3, 60, 16) z y x

  9. load wind div = divergence(x,y,z,u,v,w); slice(x,y,z,div,[90 134],[59],[0]); shading interp daspect([1 1 1]) camlight

  10. load wind div = divergence(x,y,z,u,v,w); slice(x,y,z,div,[90 134],[59],[0]); shading interp daspect([1 1 1]) camlight

  11. load wind div = divergence(x,y,z,u,v,w); slice(x,y,z,div,[90 134],[59],[0]); shading interp daspect([1 1 1]) camlight

  12. Curl: [CURLX, CURLY, CURLZ, CAV] = CURL(X,Y,Z,U,V,W) computes the curl and angular velocity perpendicular to the flow (in radians per time unit) of a 3D vector field U,V,W. The arrays X,Y,Z define the coordinates for U,V,W and must be monotonic and 3D plaid (as if produced by MESHGRID). Ω Angular Velocity:

  13. Example: load wind cav = curl(x,y,z,u,v,w); slice(x,y,z,cav,[90 134],[59],[0]); shading interp daspect([1 1 1]); axis tight colormap hot(16) camlight

  14. Laplacien L = DEL2(U), when U is a matrix, is a discrete approximation of 0.25*del^2 u = (d^2u/dx^2 + d^2/dy^2)/4. The matrix L is the same size as U, with each element equal to the difference between an element of U and the average of its four neighbors.

More Related