A Short Introduction to Matlab

Transcription

1 A Short Introduction to Matlab Duke University

2 Overview basic matrix operations built in functions user defined functions I/O graphics looping

3 Overview basic matrix operations built in functions user defined functions I/O graphics looping

4 Overview basic matrix operations built in functions user defined functions I/O graphics looping

5 Overview basic matrix operations built in functions user defined functions I/O graphics looping

6 Overview basic matrix operations built in functions user defined functions I/O graphics looping

7 Overview basic matrix operations built in functions user defined functions I/O graphics looping

8 Overview basic matrix operations built in functions user defined functions I/O graphics looping

9 Basic Operations Matlab is a Matrix language. It allows operations such as C=A*B; to compute the matrix product C = AB where A and B are appropriately dimensioned matrices. It has a number of built in functions that simplify our lives, such as inv() which computes a matrix inverse, randn(n, m) which computes an n m matrix of random N(0, 1) numbers, and normcdf () which computes the cumulative normal distribution function, to mention a few.

10 Basic Operations Matlab is a Matrix language. It allows operations such as C=A*B; to compute the matrix product C = AB where A and B are appropriately dimensioned matrices. It has a number of built in functions that simplify our lives, such as inv() which computes a matrix inverse, randn(n, m) which computes an n m matrix of random N(0, 1) numbers, and normcdf () which computes the cumulative normal distribution function, to mention a few.

11 An example (ex1) y=randn(100,1); x=[ones(100,1) randn(100,2)]; b=inv(x *x)*x *y; e=y-x*b; se=sqrt(diag(var(e)*inv(x *x))); t=b./se; disp( coefficients ) disp(b ) disp( st. errors ) disp(se ) disp( t-values ) disp(t )

12 Built in functions This example uses a number of built in functions to compute regression coefficients. These functions are randn ones inv sqrt diag var disp Full overview: see help or manuals.

13 Writing your own functions You can write your own function (or mapping) as follows function [return1,return2,..] =functionname(arg1,arg2,..,) (code) Example: (Black & Scholes) function [C,P]=BS(S,X,r,q,T,sigma) d1=(log(s./x)+(r-q+.5*sigma. 2 ). T )./(sigma sqrt(t )) d2=d1-sigma*sqrt(t) C=S*exp(-q*T).*normcdf(d1)-X.*exp(-r*T)*normcdf(d2) P=X*exp(-r*T)*normcdf(-d2)-S*exp(-q*T)*normcdf(-d1);

14 User defined functions are stored in separate files with filenames identical to the function name, with the.m extension. You can now call BS with numerical values, say [c,p]=bs(1,1,.05,0,.5,.15); which assigns the values and to c and p. This function calls another function normcdf which gives the normal cdf, function p=normcdf(x); p=.5*erf(x/sqrt(2))+.5; where erf is another built-in function (error function), erf (x) = x 2 π e u2 du. (1)

15 Working with data Need to get (large amounts of) data into matlab. Load function This function allows you to read basic numerical matrices stored in matlab or ascii (text) format. load x.txt loads the ascii file x.txt into memory. The date are stored in x variable name.

16 textread function This function allows combinations of text and numerical values to be read. Ex. Suppose a text file contains C :33: N C :33: P C :33: M C :33: M C :33: M C :33: M..

17 Then the statement [SYMBOL, DATE, TIME, PRICE,EX] = textread( C.txt, will read the various column in the data file. The second argument to this function is a formatting string. It tells the function to expect data of type string (character data), integer, string, floating point, and string again.

18 Then the statement [SYMBOL, DATE, TIME, PRICE,EX] = textread( C.txt, will read the various column in the data file. The second argument to this function is a formatting string. It tells the function to expect data of type string (character data), integer, string, floating point, and string again.

19 Graphics Matlab can produce production quality graphics. The simple command plot(x,y) plots y against x drawing lines between the data-points, while the command scatter(x,y) In dealing with time-series data, I plot a daily (say) time series recorded over a couple of years with time on the x-axis in the following way:

20 load GEmonth; x=month; p=log(x(:,7)); tstart=2001; tend= (3/12); T=length(x); dt=(tend-tstart)/t; ti=[tstart:dt:tend]; ti=ti(1:end-1); plot(ti,p)

21 Multiple plots It is sometimes useful to construct plot matrices. The code subplot(2,1,1) plot(ti,p) subplot(2,1,2) plot(ti,x(:,8)) gives a 2 1 plot.

22 Loops Looping is one of the most important ways to construct code. We use loops whenever we need to access element by element data, as for example when constructing a recursion. A loop is a statement that will be repeatedly executed until a condition is met. The most common loop is a for loop A simple example is for i=1:10 disp(x(i,:)) end which prints rows 1-10 of x to screen.

23 Loops Looping is one of the most important ways to construct code. We use loops whenever we need to access element by element data, as for example when constructing a recursion. A loop is a statement that will be repeatedly executed until a condition is met. The most common loop is a for loop A simple example is for i=1:10 disp(x(i,:)) end which prints rows 1-10 of x to screen.

24 Loops Looping is one of the most important ways to construct code. We use loops whenever we need to access element by element data, as for example when constructing a recursion. A loop is a statement that will be repeatedly executed until a condition is met. The most common loop is a for loop A simple example is for i=1:10 disp(x(i,:)) end which prints rows 1-10 of x to screen.

25 Another loop construction is a while loop: i=1; while i<10 disp(x(i,1:5)) i=i+1; end

26 Two things to notice: if i 10 when initiating the code, it will not execute because the condition i < 10 is not met. The statement i = i + 1 is not an equation (without solution). Rather, it is a common trick in which the variable i is incremented so that for each iteration, it increases by one. If we "forget" to increase i inside the loop, the program will never finish. This is an example of an infinite loop, and we will have to kill the program to figure out the error.

27 Two things to notice: if i 10 when initiating the code, it will not execute because the condition i < 10 is not met. The statement i = i + 1 is not an equation (without solution). Rather, it is a common trick in which the variable i is incremented so that for each iteration, it increases by one. If we "forget" to increase i inside the loop, the program will never finish. This is an example of an infinite loop, and we will have to kill the program to figure out the error.

28 Nested loops are sometimes necessary to access arrays with multiple indices. For example for i=1:n for j=1:m m(i,j)=...something end end assigns values to m(i, j). In matlab we can also work with higher dimensional arrays (tensors), which can be indexed x(i, j, k, l) (say).

29 Matlab Debugger To find mistakes (bugs) in a program, it is useful to debug the program. There are two very useful ways to control execution of a program through the debugger You can insert a breakpoint in the program. A breakpoint stops execution, allowing you to examine the state of the various variables at that point. Line by line excecution. After inserting a breakpoint somewhere in the code, you can execute the code line by line by hitting the F10 button. This allows you to stop, look at the values of the local variables, manipulate variables on the command line, etc. If the code calls local user defined or built in functions, you can access that code when stepping through (line by line) by hitting the F11 (step in) button, and shift+f11 (step out) button(s). This allows you to look at code in the functions as well as in the main program.

30 Matlab Debugger To find mistakes (bugs) in a program, it is useful to debug the program. There are two very useful ways to control execution of a program through the debugger You can insert a breakpoint in the program. A breakpoint stops execution, allowing you to examine the state of the various variables at that point. Line by line excecution. After inserting a breakpoint somewhere in the code, you can execute the code line by line by hitting the F10 button. This allows you to stop, look at the values of the local variables, manipulate variables on the command line, etc. If the code calls local user defined or built in functions, you can access that code when stepping through (line by line) by hitting the F11 (step in) button, and shift+f11 (step out) button(s). This allows you to look at code in the functions as well as in the main program.

31 Matlab Debugger To find mistakes (bugs) in a program, it is useful to debug the program. There are two very useful ways to control execution of a program through the debugger You can insert a breakpoint in the program. A breakpoint stops execution, allowing you to examine the state of the various variables at that point. Line by line excecution. After inserting a breakpoint somewhere in the code, you can execute the code line by line by hitting the F10 button. This allows you to stop, look at the values of the local variables, manipulate variables on the command line, etc. If the code calls local user defined or built in functions, you can access that code when stepping through (line by line) by hitting the F11 (step in) button, and shift+f11 (step out) button(s). This allows you to look at code in the functions as well as in the main program.

32 Matlab Profiler The profiler allows you to time the execution of various blocks of code. This allows you to identify bottlenecks in the code, which can then be re-written or tuned to boost performance.