Introduction to Matlab Part II 1Daniel Baur / Introduction to Matlab Part II Daniel Baur / Michael Sokolov ETH Zurich, Institut für Chemie- und Bioingenieurwissenschaften ETH Hönggerberg / HCI F128 / F123 – Zürich

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

Review of matrices  Creating matrices A = [1 2 3; 4 5 6; 7 8 9];  Direct: A = [1 2 3; 4 5 6; 7 8 9]; B = zeros(3,2);  Matrix of zeros: B = zeros(3,2); C = ones(3,2);  Matrix of ones: C = ones(3,2); R = rand(3,2);  Random matrix: R = rand(3,2); RD = randn(2,3);  Normally distributed: RD = randn(2,3);  Matrix characteristics [nRows, nColumns] = size(A); nColumns = size(A,2);  Size [nRows, nColumns] = size(A); nColumns = size(A,2); maxDim = length(A);  Largest dimension maxDim = length(A); nElements = numel(A);  Number of elements nElements = numel(A);  Creating vectors v = ones(3,1);  Single argument calls create a square matrix, therefore use commands like v = ones(3,1); to create vectors 3Daniel Baur / Introduction to Matlab Part II

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

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  D*C Not commutative!  A^2 Element-by-element operations  A.^2  E = 2.^A;  E = 2.^A; E i,j = 2^A i,j  sqrt(A) Functions using matrices  sqrtm(A)  sqrtm(A)^2  inv(A) 5Daniel Baur / Introduction to Matlab Part II

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 = A\b; 6Daniel Baur / Introduction to Matlab Part II Do not use x = inv(A)*b!

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  Function m-file: Starts with the function key-word, accepts inputs and gives outputs. All variables are local. classdef  Class m-file: Contains the classdef key-word, used in object oriented programming. 7Daniel Baur / Introduction to Matlab Part II

Example of a Script  Problem definition  v = 1e-17*ones(100,1); sum(v)  v1 = [v;1]; sum(v1)-1  v2 = [1;v]; sum(v2)-1  Create the «mysum» script  (In Matlab:) File  New  M-File  clear all; close all;  v = 1e-17*ones(100,1);  v1 = [v;1];  s = sum(v1);  s-1  (In Editor:) File  Save As...  mysum.m  Check the directory path! 8Daniel Baur / Introduction to Matlab Part II Avoid reserved words and built-in function names

 You should see  How to run the script?  From the command window (check the path!)  From the editor (press Run button or use Debug  Run or press F5) Example of a Script (Continued) 9Daniel Baur / Introduction to Matlab Part II The editor has found unusual syntax or even a syntax error here! Mouse-over to see what is the issue. The editor has found unusual syntax or even a syntax error here! Mouse-over to see what is the issue.

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: 10Daniel Baur / Introduction to Matlab Part I In the context of if and while, both kinds of operators short-circuit.

Relational and logical operators (continued)  Example of element-by-element comparison: isequal(A,B)  Compare entire matrices with isequal(A,B) 11Daniel Baur / Introduction to Matlab Part I All numbers other than 0 evaluate to TRUE

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

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

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

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 15Daniel Baur / Introduction to Matlab Part II It is good practice to limit the number of iterations (eg. while n < nmax)

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

Exercise help rand 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 G i,j = 2+2*C i,j 2 / F j,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 17Daniel Baur / Introduction to Matlab Part II

Solutions (one Possibility) 18Daniel Baur / Introduction to Matlab Part II

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

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

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

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 22Daniel Baur / Introduction to Matlab Part II

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; 23Daniel Baur / Introduction to Matlab Part II

Data type «struct» 24Daniel Baur / Introduction to Matlab Part II comp(1).name = 'water'.MW = density= 1.Antoine= [8.07; 1730; 233]; comp(2).name = 'ethanol'.MW = density= Antoine= [8.20; 1643; 230]; comp(3).name =....MW =....density=....Antoine=... comp(1,n)struct

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

Possible Solution 26Daniel Baur / Introduction to Matlab Part II