# 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. Built-in Variables and Functions 4. Input/Output Data Files 5. Basic Graphics 6. Functions 7. Decisions 8. Loops (for loops and while loops) 1

2 Built-in Variables and Functions Built-in variables: Variable Meaning ans value of an expression when that expression is not assigned to a variable eps floating-point precision i, j unit imaginary numbers, i=j=sqrt(-1) pi π, realmax largest positive floating-point number realmin smallest positive floating-point 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 built-in variables, it is not a good idea to do so, because they are used by the built-in functions. Built-in 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 n-th 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 built-in 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 function-name (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 x-y curve >> plot(x,y, o ) % x-y curve with open circle at each data point >> plot(x,y, yo ) % x-y curve with yellow open circle at each data point >> plot(x,y, r-- ) % x-y 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 User-defined Matlab functions work just like the built-in functions. The syntax of a userdefined Matlab function is: function [outputparameterlist] = functionname (inputparameterlist) % helpcomments statements outputparameter = value; return where inputparameterlist and outputparameterlist are comma-separated 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 M-file 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 element-wise 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 element-wise 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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