Introduction to Matlab Part II Tommaso Marcato Michael

Introduction to Matlab Part II Tommaso Marcato/ Michael Sokolov ETH Zurich, Institut für Chemie- und Bioingenieurwissenschaften ETH Hönggerberg / HCI E 120 / F 137 – Zürich E-Mail: tommaso. marcato@chem. ethz. ch michael. sokolov@chem. ethz. ch https: //shihlab. ethz. ch/education/Snm/matlab-introduction Tommaso Marcato / Introduction to Matlab Part II 1

Review of vectors § Vector handling § Row vector: § Column vector: § Vector with defined spacing: § Vector with even spacing: § Transpose: a a b c d e f = = = = [1 2 3]; [1, 2, 3]; [1; 2; 3]; 0: 5: 100; (or 0: 100) linspace(0, 100, 21); logspace(0, 3, 25); e'; Tommaso Marcato / Introduction to Matlab Part II 2

Review of matrices § Creating matrices § § § Direct: Matrix of zeros: Matrix of ones: Random matrix: Normally distributed: A = [1 2 3; 4 5 6; 7 8 9]; B = zeros(3, 2); C = ones(3, 2); R = rand(3, 2); RD = randn(2, 3); § Matrix characteristics § Size § Largest dimension § Number of elements [n. Rows, n. Columns] = size(A); n. Columns = size(A, 2); max. Dim = length(A); n. Elements = numel(A); § Creating vectors § Single argument calls create a square matrix, therefore use commands like v = ones(3, 1); to create vectors Tommaso Marcato / Introduction to Matlab Part II 3

Review of accessing elements § Vectors (a = (1: 5). ^2; ) (1: 5). ^2; § § § Single element: Multiple elemets: Range of elements: Last element: All elements: a(3); a([1, 3]); a(2: 4); a(end); a(: ) always returns a column vector. § Matrices (A = a'*a; ) a'*a; § § § Single element: Submatrix: Entire row / column Multiple rows / columns Last element of row / column All elements as column vector A(1, 3); A(2: 3, 2: 3); A(2, : ); A(: , 3); A([2, 3], [1, 3, 5]); A(2, end); A(end, 3); b = A(: ); Tommaso Marcato / Introduction to Matlab Part II 4

Review of matrix operations Create a Matrix § A = rand(3); Operations with constants § B = 2*A § C = 2+A Matrix addition; Transpose § D = A+C § D = D' Deleting rows / columns § C(3, : ) = []; § D(: , 2) = []; Matrix multiplication § C*D § D*C Not commutative! § A^2 Element-by-element operations § A. ^2 § E = 2. ^A; Ei, j = 2^Ai, j § sqrt(A) Functions using matrices § sqrtm(A)^2 § inv(A) Tommaso Marcato / Introduction to Matlab Part II 5

Review of matrix operations (continued) § Matrix properties § § sum(A, dim); det(A); inv(A); eigs(A); § More creation options and reshaping § B = [ones(4); diag(1: 4); eye(4)]; § B = reshape(B, 24, 6); § C = repmat(B, 1, 3); § Solution of linear algebraic systems § A = rand(3); § b = rand(3, 1); § x = Ab; Do not use x = inv(A)*b! Tommaso Marcato / Introduction to Matlab Part II 6

M-Files § What is an m-file? § An m-file is a collection of commands. It is equivalent to programs, functions, subroutines, modules, etc. in other programming languages. It can even contain entire class definitions. § What can I use it for? § Creating a permanent record of what you are doing § Experimenting on an algorithm § Writing utilities and whole programs § What types of m-files are there? § Script m-file: No input and output. Operates on workspace variables. § Function m-file: Starts with the function key-word, accepts inputs and gives outputs. All variables are local. § Class m-file: Contains the classdef key-word, used in object oriented programming. Tommaso Marcato / Introduction to Matlab Part II 7

Example of a Script § Problem definition § § § v = 1 e-17*ones(100, 1); sum(v) v 1 = [v; 1]; sum(v 1)-1 v 2 = [1; v]; sum(v 2)-1 § Create the «mysum» script § § § (In Matlab: ) File New M-File clear all; close all; v = 1 e-17*ones(100, 1); v 1 = [v; 1]; s = sum(v 1); s-1 Avoid reserved words and built-in function names § (In Editor: ) File Save As. . . mysum. m § Check the directory path! Tommaso Marcato / Introduction to Matlab Part II 8

Example of a Script (Continued) § You should see The editor has found unusual syntax or even a syntax error here! Mouse-over to see what is the issue. § How to run the script? § From the command window (check the path!) § From the editor (press Run button or use Debug Run or press F 5) Tommaso Marcato / Introduction to Matlab Part II 9

Relational and logical operators § Relational operators are straight forward in Matlab: § <, >, <=, >=, ==, ~= § The NOT operator is the tilde symbol «~» § For the logical operators AND and OR, two kinds exist: § &&, || § &, | Operators with short-circuiting (scalars only) Operators for element-by-element comparisons § Logical operators return logical types § Example of how short-circuitung operators work: In the context of if and while, both kinds of operators short-circuit. Tommaso Marcato / Introduction to Matlab Part II 10

Relational and logical operators (continued) § Example of element-by-element comparison: All numbers other than § Compare entire matrices with isequal(A, B) Tommaso Marcato / Introduction to Matlab Part II 11

Relational and logical Operators (continued) § There a some more operators that you can use: § § § any(A, dim); all(A, dim); xor(A, B); isnumeric(A); isfinite(A); True if at least one element is ≠ 0 True if all elements are ≠ 0 True if one is = 0 and the other is ≠ 0 True if A is a numerical type True for each element if it is neither Na. N nor inf § Indexing is possible through logical variable types (try it!) § A(A<0); All elements < 0 § A(isfinite(A)); All elements except Na. N and inf § A(A == B); All elements that are equal to their counterpart § You can even edit elements directly this way Tommaso Marcato / Introduction to Matlab Part II 12

For-loops in Matlab § General form of for-loops: § Example: If Matlab gets stuck in a loop (or any other calculation), use ctrl+c to terminate the program. Tommaso Marcato / Introduction to Matlab Part II 13

Examples with for-loops § Try these: Loops are almost always slower than matrix / vector calculations! Tommaso Marcato / Introduction to Matlab Part II 14

While-loops in Matlab § General form of while-loops: § while expression statements; end § The statements are executed as long as the expression is true (or ≠ 0) § The statements are executed an indefinite number of times It is good practice to limit the number of iterations (eg. while n < nmax) Tommaso Marcato / Introduction to Matlab Part II 15

Examples of loops § Try the following: Vectorize your operations and use built-in functions. If you must use a loop, preallocate your variables. Tommaso Marcato / Introduction to Matlab Part II 16

Exercise 1. Create the matrix A(5, 5) with random elements between -2 and 2 (type help rand to figure out how the function works) 2. Set all negative elements of A to 1. 5 (use logical indexing!) 3. Create a matrix B consisting of the 2 nd and 3 rd column of A 4. Create a matrix C consisting of the 1 st and 4 th row of A 5. Calculate D = A∙B∙C. What is the size of D? 6. Add D+A = E. Multiply the transpose of E with B to create F. 7. Create the matrix G so that Gi, j = 2+2*Ci, j 2 / Fj, i 8. Create an equally spaced row vector b with 5 elements from 3 to 38 9. Find the solution of the linear system A∙x = b’ 10. Find the solution of y∙A = b 11. Compute the 2 -norm of x 12. Find the vector v representing the 2 -norm of each column of A 13. Find the values of the series Tommaso Marcato / Introduction to Matlab Part II 17

Solutions (one Possibility) Tommaso Marcato / Introduction to Matlab Part II 18

Controlling program flow § The if block has the following structure § if expression statements; else statements; end § Example The elseif and else clauses are optional. Tommaso Marcato / Introduction to Matlab Part II 19

Controlling program flow (Continued) § The switch block does multiple comparisons at once § switch variable case expression statements; . . . otherwise statements; end § Example Message identifier Error message Tommaso Marcato / Introduction to Matlab Part II 20

Controlling program flow (Continued) § Other commands for controlling program flow are: § § § break; continue; return; Exits the current loop Immediately goes to the next iteration Terminates the entire program / function Tommaso Marcato / Introduction to Matlab Part II 21

Controlling program flow (Continued) § The try block checks for errors occuring during execution § try statements; catch err statements; end § If an error occurs in the try block, the catch block is executed immediately instead of continuing § Example Tommaso Marcato / Introduction to Matlab Part II 22

Data type «struct» § What is a struct? § Structs are arrays with a property called «fields» . Fields hold different kinds of data and are accessed by dots. Structs are very useful for bundling different kinds of information. § Example (try it out!) comp(1). name = 'water'; comp(1). Mw = 18. 02; comp(1). density = 1; comp(2). name = 'ethanol'; comp(2). Mw = 46. 06; comp(2). density = 0. 789; Tommaso Marcato / Introduction to Matlab Part II 23

Data type «struct» comp(1) comp(2) comp(3) . name = 'water' . name = 'ethanol' . name =. . MW = 18. 02 . MW = 46. 06 . MW =. . density = 1 . density = 0. 789 . density =. . Antoine = [ 8. 07; 1730; 233]; . Antoine = [ 8. 20; 1643; 230]; . Antoine =. . . comp (1, n) struct Tommaso Marcato / Introduction to Matlab Part II 24

Exercise § Create a new m-file called quadratic_roots. m § Implement the following algorithm § If b > 0 § Elseif b < 0 § Else Tommaso Marcato / Introduction to Matlab Part II 25

Possible Solution Tommaso Marcato / Introduction to Matlab Part II 26