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Numerical Operations

Introduction to Matlab:. Numerical Operations. Numerical Interpolation. S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn. Interpolation Topics. 1D Interpolation Interp1 Command Spline Command 2D Interpolation Interp2 Command. 1-D Interpolation.

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Numerical Operations

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  1. Introduction to Matlab: Numerical Operations Numerical Interpolation S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn

  2. Interpolation Topics • 1D Interpolation • Interp1 Command • Spline Command • 2D Interpolation • Interp2 Command

  3. 1-D Interpolation • The command interp1 is used for One Dimensional Interpolation • Given xdata and ydata • Want to estimate the values of the function: xi=[xi(1) xi(2) … ]’ % values of x

  4. interp1 Command yi=interp1(xdata,ydata,xi,method) • Where the method of interpolation can be: • ‘linear’ for linear interpolation • ‘spline’ for Spline Interpolation • ‘cubic’ for Cubic Interpolation

  5. A Coarse Sine Wave » xdata=[0:pi/4:2*pi]'; » ydata=sin(xdata); » plot(xdata,ydata); » title('Course Sine Wave'); » xlabel('xdata'); » ylabel('ydata');

  6. Interpolated Sine Wave » xi=[0:pi/64:2*pi]'; » yi=interp1(xdata, ydata,xi,'spline'); » plot(xi,yi) » title('Interpolated Sine Wave'); » xlabel('xi'); » ylabel('yi');

  7. Good Fit & Error • Check For Error • Check for Good Fit » plot(xi,sin(xi),'r',xi,yi,'x'); » plot(xi,(yi-sin(xi)));

  8. Spline • Use spline for a cubic spline interpolation method » yi=spline(xdata,ydata,xi); » plot(xi,yi); » title('Cubic Spline Interpolation'); » xlabel('xi'); » ylabel('yi');

  9. 2-D Interpolation • Consider the following sheet of metal with the following temperatures at different points: • We will estimate the temperatures on a finer scale

  10. Plot Original Mesh • Set up Matrices in Matlab » z=[82 81 80 82 84 79 63 61 65 81 84 84 82 85 86]; » xdata =[1:5]; » ydata=[1:3]'; • Plot the Original Mesh » mesh(xdata,ydata,z); » title('Original Metal Temps'); » zlabel('temp');

  11. Original Mesh • Course • Concave

  12. Finer 2-D Interpolation • Estimate Temperature Surface to a finer scale using the interp2 command » xi=[1:0.1:5]; » yi=[1:0.2:3]'; » zi=interp2(xdata,ydata,z,xi,yi,'cubic'); % or ‘linear’ or ‘spline’ » mesh(xi,yi,zi); » title('2D Interp Metal Temps'); » zlabel('temp');

  13. 2-D Interpolated Mesh • Smooth • Concave

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