MATLAB BASICS. Macro II. February 25, T.A.: Lucila Berniell. Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

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1 MATLAB BASICS Macro II T.A.: Lucila Berniell February 25, 2010 Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

2 MATLAB windows Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

3 Numbers, vectors and matrices Numbers: MATLAB uses conventional decimal notation. Precision: roughly 16 significant decimal digits and a finite range of roughly to Inf, Inf and NaN (Not-a-Number). Vectors: x=[2 3 4] is a row vector, while y=x is a column vector (Note: is the transpose operator). Matrices: x=[2 3 4; 1 3 5] Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

4 Basic operations Basic arithmetic operations: a and b can be scalars, vectors or matrices (of course, if conformable!): addition (a+b), subtraction (a-b), multiplication (a*b), division (a/b), and exponentiation (a 2 ). transpose (a ) Element-by-element arithmetic operations:.*,.ˆ, etc... For instance: [1 2 3].*[4 5 6]=[ ]. Other element-by-element operations: exp, log, sqrt, cos, sin, tan, arccos, arcsin, arctan, and abs. Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

5 Manipulating vectors and matrices A number of ways to create or modify vectors or matrices: By enumeration: x=[2 3 4; 1 3 5]. Matrices with ones and zeros: a=zeros(m,n) (or a=ones(m,n)) creates a matrix of zeros (or ones) with m rows and n columns. Replacing one element: x(1,1)=log(5) puts log(5) in the position (1,1) of matrix x. Replacing one row (column): x(:,1)=log(5) puts log(5) in every position in the first column of matrix x. y=linspace(a,b,n) generates a row vector y of n points linearly spaced between them and including a and b. Another way to create a similar vector is: c=d:j:e (where c+j<e and j is the jump ). Useful commands for manipulating matrices: size(a) gives the dimensions of A. length(x) is equivalent to max(size(x)). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

6 Relations and Logical operators Relations: <, <=, >,>=, ==, =. Logical vectors: Let a=[ ], then c=(a < 0) is a logical vector that takes the value 1 in those positions in vector a for which the statement (a < 0) is true (c=[ ]). Logical operators: or (, also ), and (&, also &&) and not ( ). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

7 Looping: the for loop The for loop: for k = index vector (for instance, 1:1:10 or just 1:10) commands end The commands between for and end are executed for all values stored in the index vector. The for loops can be nested. Example of a simple for loop: for k = 1:5 A(k)=1/k; end Then, A=[ ]. Remark: too many loops is not a good idea (vectorization should be used whenever possible. Write k=1:1:5; A=k.ˆ (-1) instead of the loop above). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

8 while-loop and if-statement while loop: When you don t know the number of repetitions a priori. iter=0 while expression commands iter=iter+1; end Remark: iter (or whatever you want to name this counter) will tell you how many iterations have been performed (useful in while loops). if-statement: if expression commands (evaluated if expression is true) else commands (evaluated if expression is false) end elseif-statement: if there are several alternatives. Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

9 Max-min operators If A is a vector, max(a) returns the largest element in A. If A is a matrix, max(a) treats the columns of A as vectors (returning a row vector containing the maximum element from each column). C = max(a,b) returns an array the same size as A and B with the largest elements taken from A or B. The dimensions of A and B must match, or they may be scalar. C = max(a,[],dim) returns the largest elements along the dimension of A specified by scalar dim. For example, max(a,[],1) produces the maximum values along the first dimension of A. (Note: [] is the empty matrix) A = max(a,[],1) = [10 9 7] and max(a,[],2) = [8 7 10] Min operator: let C=max(A), then C=min(-A). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

10 Plots: 2-D plots plot(y) plots the columns of Y versus their index. Let Y=log(3:1:55): Let X=linspace(100,1000,max(size(Y))).ˆ5 (Y and X have the same dim). plot(x,y) gives: Editing Plots (labels, references, color, etc.): in the toolbar in the pop-up window (click on Edit/Figure Properties...) Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

11 Plots: 3-D plots Surface plots: surf(z) creates a 3-D shaded surface from the components in matrix Z, using x = 1:n and y = 1:m, where [m,n] = size(z). Height, Z, is a single-valued function and it specifies the color data as well as surface height. Let Z=magic(10) (a 10x10 matrix), surf(z) gives: Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

12 Plots: 3-D plots surf(x,y,z) creates a shaded surface using Z for the color data as well as surface height and X and Y are vectors (or matrices) defining the x and y components of a surface. If X and Y are vectors, length(x) = n and length(y) = m, where [m,n] = size(z). Let X=1:20, Y=1:10, and Z be defined by Z = logx + 5logY, or for i=x for j=y Z(j,i)=log(i)+5*log(j); end end Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

13 Saving your code and your results Saving your code (what you are writing in the Editor window): save a text file, but with extension.m. Saving your results (objects in the Workspace and graphs): many different ways to do it. So far just use: Command save followed by the name you choose ( results for instance) saves all the object in the Workspace. To load stored results just type load results, and all objects are back into the Workspace. For Graphs: the saving options in the toolbar in the pop-up window. Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

14 Miscellaneous Suppress output to the screen: adding a ; after the statement. Commenting your code: use % at the beginning of the line containing your comment. clear all cleans the Workspace and clc cleans the Command window. Interrupting a running program: Crtl+c. Long command lines: use... (three periods) followed by an Enter. It is always more efficient to initialize matrices that you will use for looping (i.e., do not allow matrices to grow inside a loop). You can initialize these matrices as zeros(m,n). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15

15 Help! If you don t know how to do something in MATLAB, you have some options: call the guy who knows, or use the MATLAB help (type help + command in the command window). Macro II (PhD - uc3m) MatLab Basics 02/25/ / 15