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Matlab

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1Introduction to MatlabTodd WittmanJune 16, 2008What is Matlab? Matlab (Matrix Laboratory) is a programming language optimized for linear algebra operations. It is very useful for numerical computation and is commonly used by mathematicians. After you program in Matlab, you probably won't want to go back to C++.2Basic Arithmetic If we type a calculation, when we press ENTER the result appears as ans.2+3ans =5 Pressing the up arrow repeats the last input. In addition to basic + - * / there are basic mathematical functionsexp(2) sin(pi) asin(2) There may be round-off errors. Watch out for the values Inf and NaN.Variables To assign a value to a variable, just type it. We don't need to declare variables first: x=2 Matlab is weakly typed, which means the variable type is flexible.x=2 x=2.3 x=2+4i x='hello' To see what variables are available type: who To delete a variable x: clear x If you type just clear, all variables will be deleted.3Vectors & Matrices We enclose vector values in square brackets.v = [2 3 4 5 6] We can look up a value at a position: v(2) The colon operator takes on a range of valuesv = 2:6 More generally we set start:step:end (default step=1) Ex Make a vector of even integers 2 through 100evens = 2:2:100Matrices To make a 2D matrix, the semi-colon skips to the next row:A = [2 3 4; 5 6 7] We look up values by row,column: A(2,3) = 7; You can look up sections with the colon: A(1:2,2:3) Special matricesrand(10,20) eye(3) zeros(4,5) ones(3,2) As matrices get large, you can supress output with a semi-colon at the end.R = rand(20,20); We can display matrix values graphically with imagesc.4Matrix Operations Matrix multiplication: A*B A^3 Component-wise operations: A.*B A.^3 Inverse: inv(A) Transpose: A' Look up matrix size: size(A) Eignenvalues: [v,d] = eig(A); Linear solver Ax=b: x = linsolve(A,b); Vectorize a matrix: A(:) Change matrix size: reshape(A,[r,c]);Basic Flow Controlwhile i > 0...endfor i = 1:10...endif x >0...elseif x<0...else...end5Basic Plotting The plot function takes two vectors as input. The first goes on the horizontal axis (x) and the second is the vertical (y). Ex Plot a sine wave.x=0:0.1:2*pi;y=sin(x);plot(x,y,'r')axis([0,2*pi,-1,1])title('A sine wave') You can reset the axis and tick marks manually too. You can add text to the plot:xlabel ylabel title legend gtextLoading & Saving Data You can navigate directories by pressing the ... button at top. Check current position: pwd ls imread - Read an image into a matrix. You may have to convert between uint8 and double formats. textread - Read a text file. xlsread - Read an Excel file. We can save data to a .mat filesave my_data x y zload my_data6m Files We can create programs with extension .m We essentially define new functions for Matlab to use. The first line is:[out1, out2] = function_name (in1, in2) Comments are denoted by the % sign. Ex Write a function that computes the average band of a 3-band color image.Symbolic Variables To do symbolic computation, we create symbolic variables with syms. Then we can do symbolic integration and differentiation.syms x;diff(3*x^2+6*x-4)ans =6*x+6int(exp(2*x))ans =1/2*exp(2*x)7The Matlab Help Matlab has awesome Help documentation. It usually provides examples of how to use functions. If you need to do a standard math calculation, there is probably a Matlab calculation that will do it for you.Watch the Video For a summary of what we've covered, watch the Youtube video by Stuart McGarrity.http://www.youtube.com/watch?v=MdrShPzHeYg Mathworks also has some video demos


Matlab

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