introduction to matlab part ii 1daniel baur / introduction to matlab part ii daniel baur / michael...

1Daniel Baur / Introduction to Matlab Part II

Introduction to Matlab

Part II

Daniel Baur / Michael Sokolov

ETH Zurich, Institut für Chemie- und Bioingenieurwissenschaften

ETH Hönggerberg / HCI F128 / F123 – Zürich

E-Mail: daniel.baur@chem.ethz.ch

michael.sokolov@chem.ethz.ch

http://www.morbidelli-group.ethz.ch/education/snm/Matlab

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Review of vectors

Vector handling Row vector: a = [1 2 3];

a = [1, 2, 3]; Column vector: b = [1; 2; 3]; Vector with defined spacing: c = 0:5:100; (or 0:100) Vector with even spacing: d = linspace(0, 100, 21);

e = logspace(0, 3, 25);

Transpose: f = e';

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Review of matrices

Creating matrices Direct: A = [1 2 3; 4 5 6; 7 8 9]; Matrix of zeros: B = zeros(3,2); Matrix of ones: C = ones(3,2); Random matrix: R = rand(3,2); Normally distributed: RD = randn(2,3);

Matrix characteristics Size [nRows, nColumns] = size(A);

nColumns = size(A,2); Largest dimension maxDim = length(A); Number of elements nElements = numel(A);

Creating vectors Single argument calls create a square matrix, therefore use

commands like v = ones(3,1); to create vectors

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Review of accessing elements

Vectors (a = (1:5).^2;) Single element: a(3); Multiple elemets: a([1, 3]); Range of elements: a(2:4); Last element: a(end); All elements: a(:);

Matrices (A = a'*a;) Single element: A(1,3); Submatrix: A(2:3,2:3); Entire row / column A(2,:); A(:,3); Multiple rows / columns A([2, 3],[1, 3, 5]); Last element of row / column A(2,end); A(end,3); All elements as column vector b = A(:);

a(:) always returns a

column vector.

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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) sqrtm(A)^2 inv(A)

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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;

Do not use

x = inv(A)*b!

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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.

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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!

Avoid reserved words and

built-in function names

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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)

The editor has found unusual syntax

or even a syntax error here!

Mouse-over to see what is the issue.

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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.

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Relational and logical operators (continued)

Example of element-by-element comparison:

Compare entire matrices with isequal(A,B)

All numbers other

than

0 evaluate to TRUE

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Relational and logical Operators (continued)

There are a some more operators that you can use: any(A,dim); True if at least one element is ≠ 0 all(A,dim); True if all elements are ≠ 0 xor(A,B); True if one is = 0 and the other is ≠ 0 isnumeric(A); True if A is a numerical type 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); All elements < 0 A(isfinite(A)); All elements except NaN and inf A(A == B); All elements that are equal to their

counterpart

You can even edit elements directlythis way

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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.

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Examples with for-loops

Try these:

Loops are almost always slower

than matrix / vector calculations!

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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)

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Examples of loops

Try the following:

Vectorize your operations

and use built-in functions.

If you must use a loop,

preallocate your variables.

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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 2nd and 3rd column of A4. Create a matrix C consisting of the 1st and 4th row of A5. 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 = b11. Compute the 2-norm of x12. Find the vector v representing the 2-norm of each column of A13. Find the values of the series

20 10, i i is s s v

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Solutions (one Possibility)

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Controlling program flow

The if block has the following structure if expression

statements;elseif expression

statements;else

statements;end

Example

The elseif and else

clauses are optional.

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Controlling program flow (Continued)

The switch block does multiple comparisons at once switch variable

case expressionstatements;

case expressionstatements;

...otherwise

statements;end

ExampleMessage identifier

Error message

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Controlling program flow (Continued)

Other commands for controlling program flow are: break; Exits the current loop continue; Immediately goes to the next iteration return; Terminates the entire program / function

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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

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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;

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Data type «struct»

comp(1)

.name = 'water'

.MW = 18.02

.density = 1

.Antoine = [

8.07;

1730;

233];

comp(2)

.name =

'ethanol'.MW = 46.06

.density = 0.789

.Antoine = [

8.20;

1643;

230];

comp(3)

.name = ...

.MW = ...

.density = ...

.Antoine = ...

comp (1,n) struct

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Exercise

Create a new m-file called quadratic_roots.m Implement the following algorithm

If b > 0

Elseif b < 0

Else

2

2 12

4;

2

b b ac cx x

a ax

2

1 21

4;

2

b b ac cx x

a ax

1/2

1 2

cx x

a

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Possible Solution