Introduction to MATLAB (2.29 Spring 06)


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1 Introduction to MATLAB (2.29 Spring 06) 1. Assignment of Variables (i.e. scalars, vectors, matrices) 2. Mathematical Operations 3. Builtin Variables and Functions 4. Input/Output Data Files 5. Basic Graphics 6. Functions 7. Decisions 8. Loops (for loops and while loops) 1
2 Builtin Variables and Functions Builtin variables: Variable Meaning ans value of an expression when that expression is not assigned to a variable eps floatingpoint precision i, j unit imaginary numbers, i=j=sqrt(1) pi π, realmax largest positive floatingpoint number realmin smallest positive floatingpoint number Inf, the result of evaluation 1/0 NaN not a number (i.e. the result of evaluating 0/0) * Although you can assign the values of these builtin variables, it is not a good idea to do so, because they are used by the builtin functions. Builtin functions: Trigonometric: sin  Sine. sind  Sine of argument in degrees. sinh  Hyperbolic sine. asin  Inverse sine. asind  Inverse sine, result in degrees. asinh  Inverse hyperbolic sine. cos  Cosine. cosd  Cosine of argument in degrees. cosh  Hyperbolic cosine. acos  Inverse cosine. acosd  Inverse cosine, result in degrees. acosh  Inverse hyperbolic cosine. tan  Tangent. tand  Tangent of argument in degrees. tanh  Hyperbolic tangent. atan  Inverse tangent. atand  Inverse tangent, result in degrees. atan2  Four quadrant inverse tangent. Exponential: exp  Exponential. log  Natural logarithm. log10  Common (base 10) logarithm. log2  Base 2 logarithm and dissect floating point number. reallog  Natural logarithm of real number. 2
3 realsqrt sqrt nthroot  Square root of number greater than or equal to zero.  Square root.  Real nth root of real numbers. Complex: abs  Absolute value. angle  Phase angle. complex  Construct complex data from real and imaginary parts. conj  Complex conjugate. imag  Complex imaginary part. real  Complex real part. * To find more builtin elementary mathematical functions, use the help command: >> help elfun ** To find the meaning of a specific function and how to use it, use the help command: >> help functionname (e.g. help sind) 3
4 Input/Output Data Files Export data to a file using save command: save filename save filename variable1 variable2 save filename variable1 variable2 ascii >> % for example >> clear >> x=[0:10]; y=10*x; >> save xyfile1 %save all variables in xyfile1.mat file >> save xyfile2 x y %save x and y in xyfile2.mat file >> save xyfile3 x y ascii %save x and y in xyfile3 file in ascii format >> >> xy=[x y ] >> save xyfile4 xy ascii >> type xyfile4 Equivalently to a function form: save( filename, ariable1, variable2 ) >> % for example >> clear >> x=[0:10]; y=10*x; >> save( xyfile5, x, y ) % xyfile5.mat is identical to xyfile2.mat Import data from a file into Matlab using load command: load filename load filename matrixvariable %filename must be in a binary mat file %filename contains only columns of numbers %corresponding to a matrix The syntax of the function form of load : D=load( filename ) If filename is a mat file, the D variable created by this function is a Matlab structure. >> D=load( xyfile2 ) >> D = x: [ ] y: [ ] If filename is a plain text file, the D variable will be a matrix containing all of the data in filename. >> D=load( xyfile3 ) D =
5 Graphics Line plots: Single line: plot(xdata,ydata,symbol) Two lines: plot(xdata1,ydata1,symbol1,xdata2,ydata2,symbol2) Multiple lines: plot(xdata1,ydata1,symbol1,xdata2,ydata2,symbol2, ) symbol is a string constructed from the characters of color and symbol (or line) type. >> clear >> x=[0:20]; y=x.^2; >> plot(x,y) % solid line of xy curve >> plot(x,y, o ) % xy curve with open circle at each data point >> plot(x,y, yo ) % xy curve with yellow open circle at each data point >> plot(x,y, r ) % xy curve with data points connected by red dash line >> plot(x,y, r,x,y, yo ) % two curves in one figure >> plot(x,y, r,x,y, yo,x,2*y, r*,x,3*y,  ) %four curves >> xlabel( time (seconds) ) >> ylable( position (meters) ) >> title( position vs. time ) >> legend( curve1, curve2, curve3, curve4 ) Surface plots Contour plots 5
6 Functions Userdefined Matlab functions work just like the builtin functions. The syntax of a userdefined Matlab function is: function [outputparameterlist] = functionname (inputparameterlist) % helpcomments statements outputparameter = value; return where inputparameterlist and outputparameterlist are commaseparated list of variables used to pass data into and out of the function, statements are Matlab statements that compute the value that is assigned to outputparamter. The function Mfile should be saved as functionname.m. functionname must also be the same as the name of the file (without the.m ). % for example % sumprod.m function [s,p]=sumprod(x,y) % sumpord computes the sum and elementwise product of x and y s=x+y; p=x.* y; return Primary function vs. subfunctions % for example  use of subfunctions % sumprod2.m function [s,p]=sumprod2(x,y) % sumpord2 computes the sum and elementwise product of x and y s=sum2(x,y) p=prod2(x,y) return function s2=sum2(x,y) s2=x+y function p2=prod2(x,y) p2=x.* y 6
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