Programming Basics for Logistics Algorithms: Lecture 4

Tatiana Polishchuk

Associate Professor, 

Linköping University, KTS�

www.itn.liu.se/~tatpo46/

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Course Overview

• Introduction to programming
• Variables and data types
• Algorithms and scripts
• Input/output statements
• Conditional statements
• Loops, nested loops
• Vectors
• Matrices and graphs
• Plotting: graphical functions
• Good programming practices
• Data management

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Course Overview

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• Introduction to programming
• Variables and data types
• Algorithms and scripts
• Input/output statements
• Conditional statements
• Loops, nested loops
• Vectors
• Matrices and graphs
• Plotting: graphical functions
• Good programming practices
• Data management

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Flashback: Lecture 3

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4

2D Arrays: Matrices

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>> A = zeros (5,5)

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A =

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

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>> B = ones (3,4)

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B =

1 1 1 1

1 1 1 1

1 1 1 1

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>> C = rand (2,3)

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C =

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0.5504 0.0791 0.8982

0.5963 0.5766 0.4633

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range

Matrix Indexing

6

• Matrices can be indexed in two ways
• using subscripts (row and column)
• using linear indices (as if matrix is a vector)
• Matrix indexing: subscripts or linear indexing

b(1)

b(2)

b(3)

b(4)

b(1,1)

b(1,2)

b(1,1)

b(2,1)

b(1,2)

b(2,2)

Adding Elements to Matrix

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It is not possible to add just 1 element to the matrix!

But we can add entire rows or columns:

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EXAMPLE:

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A = 3 3 4 A(:,4)= [1, 1, 1, 1]’ 3 13 4 1

5 3 2 5 3 2 1

2 3 2 2 3 2 1

1 3 1 1 3 1 1

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A = 3 3 4 A(:,5)= [1,1,1,1]’ 3 13 4 0 1

5 3 2 5 3 2 0 1

2 3 2 2 3 2 0 1

1 3 1 1 3 1 0 1

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Size, Length and Numel

• Size function returns the vector [#rows, #columns]:

A =

10 2 9

7 4 6

• Length function returns either # rows, or #columns, whichever is largest:

>> length(A) =

ans =

3

• Numel function returns the total number of elements in the array

>> numel(A) =

ans =

6

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>> size(A)

ans =

2 3

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Operators

Matrix Operations

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Element-wise functions

Element-wise operations

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Graphs

• A graph is a pair (V, E), where
• V is a set of nodes, called vertices
• E is a collection of pairs of vertices, called edges
• Vertices and edges are positions and store elements
• Example:
• A vertex represents an airport and stores the three-letter airport code
• An edge represents a flight route between two airports and stores the mileage of the route

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ORD

PVD

MIA

DFW

SFO

LAX

LGA

HNL

849

802

1387

1743

1843

1099

1120

1233

337

2555

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Implementing a Graph

• To program a graph data structure, what information would we need to store?
• For each vertex?
• For each edge?

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i

j

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Next: Plotting

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Questions?

Image Processing using Matlab

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Plotting

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• Plot values against their index

» plot(y);

• Usually we want to plot y versus x

» plot(x,y);

�Example: plotting a point

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x = 11;

y = 18;

plot(x,y,'r*')

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Plotting

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x = 11;

y = 18;

plot(x,y,'r*')

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xlabel('Time')

ylabel('Temperature')

title('Time and Temp')

Plotting

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x = 11;

y = 18;

plot(x,y,'r*')

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xlabel('Time')

ylabel('Temperature')

title('Time and Temp')

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axis([x-2 x+2 y-5 y+5])

Plotting a line

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• Plotting a straight line

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» x = 1:10

» y = 2*x

» plot (x,y)

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Plot Options

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• Can change the line color, marker style, and line style by adding a string argument

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• Can plot without connecting the dots by omitting line style argument

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• Look at help plot for a full list of colors, markers, and line styles

More plotting options

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Colors Plot symbols Line types

More Plot Controls

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Axis control:

axis - Control axis scaling and appearance

zoom - Zoom in and out on a 2-D plot

grid - Grid lines

box - Axis box

rbbox - Rubberband box

hold - Hold current graph (hold on, hold off options)

axes - Create axes in arbitrary positions

subplot - Create axes in tiled positions

Graph annotation:

title - Graph title

xlabel - X-axis label

ylabel - Y-axis label

texlabel - Produces the TeX format from a character string

text - Text annotation

gtext - Place text with mouse

Playing with the Plot

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to select lines and delete or change properties

to zoom in/out

to slide the plot around

to see all plot tools at once

Copy/Paste Figures

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• Figures can be pasted into other apps (word, ppt, etc)
• Edit→ copy options→ figure copy template
• Change font sizes, line properties; presets for word and ppt
• Edit→ copy figure to copy figure
• Paste into document of interest

Saving Figures

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• Figures can be saved in many formats. The common ones are:

.fig preserves all information

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.bmp uncompressed image

.eps high-quality scaleable format

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.pdf compressed image

3D Line Plots

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• We can plot in 3 dimensions just as easily as in 2D

» t=0:0.001:4*pi;

» x = sin(t);

» y = cos(t);

» plot3(x,y,t,'k','LineWidth',2);

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• Use tools on figure to rotate it

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• Can set limits on all 3 axes

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» xlim, ylim, zlim

Surface Plots

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• It is more common to visualize surfaces in 3D

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• Example:

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• surf puts vertices at specified points in space x,y,z, and connects all the vertices to make a surface

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• The vertices can be denoted by matrices X,Y,Z

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• How can we make these matrices
• built-in function: meshgrid

Visualizing matrices

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• Any matrix can be visualized as an image

» mat = reshape (1:10000,100,100);

» imagesc (mat);

» colorbar

• imagesc automatically scales the values to span the entire colormap

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• Can set limits for the color axis (analogous to xlim, ylim)

» caxis ([3000 7000])

surf

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• Make the x and y vectors

» x = -pi:0.1:pi;

» y = -pi:0.1:pi;

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• Use meshgrid to make matrices

» [X,Y] = meshgrid (x,y);

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To get function values, evaluate the matrices

» Z = sin(X) .*cos(Y);

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• Plot the surface

» surf (X,Y,Z)

» surf(X,Y,Z);

)

rane

*Try typing surf(memb

surf Options

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faceted

flat

See help surf for more options

There are three types of surface shading

» shading facetad

» shading flat

» shading

• You can also change the colormap

» colormap (grey)

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interp

flat

contour

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• You can make surfaces two-dimensional by using contour

» contour (X,Y,Z, ‘LineWidth’, 2)

• takes same arguments as surf
• color indicates height
• can modify linestyle properties
• can set colormap

» hold on

» mesh (X,Y,Z)

Specialized Plotting Functions

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• MATLAB has a lot of specialized plotting functions
• polar-to make polar plots

» polar (0:0.01:2*pi, cos ((0:0.01:2*pi)*2));

• bar-to make bar graphs

» bar (1:10, rand(1,10));

• quiver-to add velocity vectors to a plot

» [X,Y] = meshgrid (1:10,1:10);

» quiver(X,Y, rand(10),rand(10));

• stairs-plot piecewise constant functions

» stairs(1:10, rand(1,10));

• fill-draws and fills a polygon with specified vertices

» fill ([0 1 0.5], [0 0 1], ‘r’);

• see help on these functions for syntax
• doc specgraph – for a complete list

Visualizing Graphs

graph objects represent undirected graphs, which have direction-less edges connecting the nodes

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>>clear ;

A = [

0 1 0 1;

1 0 1 0;

0 1 0 1;

1 0 1 0

];

figure;

G = graph (A);

plot (G);

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Graph created using adjacency matrix

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Visualizing Graphs

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digraph objects represent directed graphs, which have directional edges connecting the nodes

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clear ;

A = [

0 1 0 1;

1 0 1 0;

0 1 0 1;

1 0 1 0

];

figure;

G = digraph (A);

plot (G);

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Visualizing Graphs

Defining edge list - another way of creating graphs

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E_list = [

1, 2;

1, 3;

2, 3

]; % edge list

E_weights = [1 1 2];

G = graph(E_list(:,1), E_list(:,2), E_weights);

plot (G);

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Visualizing Graphs

Defining edge list - another way of creating graphs

E_list = [

1, 2;

1, 3;

2, 3

]; % edge list

E_weights = [1 1 2];

G = graph(E_list(:,1), E_list(:,2), E_weights);

% to add labels to the nodes:

G.Nodes.Name = { 'Olle ' 'Sara ' 'Karl ' }';

% to mark weights on the graph:

plot (G );

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Visualizing Graphs

Defining edge list - another way of creating graphs

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E_list = [

1, 2;

1, 3;

2, 3

]; % edge list

E_weights = [1 1 2];

G = graph(E_list(:,1), E_list(:,2), E_weights);

% to add labels to the nodes:

G.Nodes.Name = { 'Olle ' 'Sara ' 'Karl ' }';

% OR: to mark weights on the graph:

plot (G , 'EdgeLabel', G.Edges.Weight);

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Questionnaire

mid-course evaluation form

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https://tinyurl.com/midcourse2026

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Next: Data Management

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Questions?

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File Operations

• Read from the file: extract data from files

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• Write to the file: write data to the file starting from the very beginning

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• Append to the file: write data to the file, adding information to what is already there

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• Display content of the file:show file content

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Read from the file

• Read from the file: extract data from the file

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load filename

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• assigns file content to the array filename
• use files with extensions .dat, .txt, .mat, etc.
• only with the data of the same format!
• only data in matrix format (same number of elements in each row)

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File Operations

• Write to the file: write data to the file starting from the very beginning

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save filename matrixname -ascii

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• creates file filename
• uses file extensions .txt, .dat, ect.
• .mat used to store variables from your workspace
• writes the data from array matrixname
• if file not empty -- overwrites the data!!
• ‘-ascii’ provides correct data format

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File Operations

• Append to the file: write data to the file, adding information to what is already there

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save filename matrixname -ascii -append

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• adds the data from array matrixname to the end of file filename

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File Operations

• Display content of the file: show file content

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type filename

Example:

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» type testfile.dat

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2 4 6 1 0 0 4

2 3 4 1 2 3 4

1 1 2 3 4 5 1

1 2 5 6 2 3 5

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File Operations

Example: delete the first column from the matrix in file testfile.dat

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» type testfile.dat

2 4 6 1 0 0 4

2 3 4 1 2 3 4

1 1 2 3 4 5 1

1 2 5 6 2 3 5

» load testfile.dat

» testfile(:,1) = []; % to delete first column in the matrix

» save testfile.dat testfile -ascii

» type testfile.dat

4.0000000e+00 6.0000000e+00 1.0000000e+00 0.0000000e+00 0.0000000e+00 4.0000000e+00

3.0000000e+00 4.0000000e+00 1.0000000e+00 2.0000000e+00 3.0000000e+00 4.0000000e+00

1.0000000e+00 2.0000000e+00 3.0000000e+00 4.0000000e+00 5.0000000e+00 1.0000000e+00

2.0000000e+00 5.0000000e+00 6.0000000e+00 2.0000000e+00 3.0000000e+00 5.0000000e+00

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File Operations

Example: delete the first column from the matrix in file testfile.dat

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» type testfile.dat

4.0000000e+00 6.0000000e+00 1.0000000e+00 0.0000000e+00 0.0000000e+00 4.0000000e+00

3.0000000e+00 4.0000000e+00 1.0000000e+00 2.0000000e+00 3.0000000e+00 4.0000000e+00

1.0000000e+00 2.0000000e+00 3.0000000e+00 4.0000000e+00 5.0000000e+00 1.0000000e+00

2.0000000e+00 5.0000000e+00 6.0000000e+00 2.0000000e+00 3.0000000e+00 5.0000000e+00

» testfile = int8(testfile)

testfile =

4×6 int8 matrix

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4 6 1 0 0 4

3 4 1 2 3 4

1 2 3 4 5 1

2 5 6 2 3 5

>> save testfile.dat testfile -ascii

Warning: Attempt to write an unsupported data type to an ASCII file.

Variable 'testfile' not written to file.

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Advanced File Operations

• Low-level I/O functions to work with different file formats

fopen, fclose, fscanf, textscan, fgetln, xlsread

fread, fwrite, fseek, and frewind, and more...

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Some examples:

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https://www.mathworks.com/help/matlab/learn_matlab/data-analysis.html

https://www.mathworks.com/help/matlab/examples.html?category=data-import-and-analysis

https://www.mathworks.com/help/matlab/import_export/add_spreadsheet_data_arrays_variables.html

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Advanced File Operations

• Read table of mixed data types

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T = readtable(filename)

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• creates a table T by reading column oriented data from a file
• determines the file format from the file extension:

.txt, .dat, or .csv for delimited text files

.xls, .xlsb, .xlsm, .xlsx, .xltm, .xltx, or .ods for spreadsheet files

• creates one variable in T for each column in the file and reads variable names from the first row of the file
• by default, creates variables that have data types that are appropriate for the data values detected in each column of the input file

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Advanced File Operations

• Read table of mixed data types

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T = readtable(filename)

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• To access variables representing columns of the table:

T.columnname

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• Write of different data types to a file

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writetable(T, filename)

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Cell Arrays

• Elements in cell arrays are containters that can store different types of values

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• stores pointers do different data
• unique data structure for Matlab
• use {} to create such arrays

Example:

» cellrowvec = {23, 'a', 1:2:9, 'hello'}

cellrowvec =

[23] 'a' [1x5 double] 'hello'

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Cell Arrays: Indexing

• Indexing is different from the data arrays

Example:

» cellrowvec = {23, 'a', 1:2:9, 'hello'}

cellrowvec =

[23] 'a' [1x5 double] 'hello'

» cellrowvec(3)

ans =

1×1 cell array

{1×5 double}

» cellrowvec{3}

ans =

1 3 5 7 9

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Use curly braces {}

to access values stored in cell array!

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Table Arrays

• Elements in cell arrays are columns, each assigned a header name

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• same datatype per column (can be strings, numbers or other )
• use table function to create such arrays
• access columns using .

Example:

» T = table(var1, … , varN)

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» T = table(Age,Height,Weight,'RowNames', LastName)

» disp (T.Age)

» meanHeight = mean (T.Height)

• use readtable/writetable functions to read from/to the file

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Advanced File Operations

Example: extract data subset from a data file

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% clear Workspace

clear; clear all

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% load flight delay data into the array variable delay_data

delay_data = readtable('alldelays.csv');

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Advanced File Operations

EUROCONTROL Performance Review Unit (PRU): ATFM arrival flight delays

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Advanced File Operations

EUROCONTROL Performance Review Unit (PRU): ATFM arrival flight delays

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Data covers:

Years 2016-2024 (not much data for the pandemics years 2020-2021)

All European airports

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Advanced File Operations

Example: extract data subset from a data file

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% clear Workspace

clear; clear all

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% load flight delay data into the array variable delay_data

delay_data = readtable('all delay.csv');

% extract delay data for the particular airport of Munich

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munich_data = delay_data(strcmp(delay_data.APT_ICAO, 'EDDM'), :);

% save the delay data for Munich airport in a separate data file

writetable(flight_data, 'munich.csv');

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Advanced File Operations

EUROCONTROL Performance Review Unit (PRU): ATFM arrival flight delays

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Query examples:

• What is the total number of flights delayed at Munich airport in July 2019?
• What is the total amount of delays in minutes recorded at Munich airport in 2023?
• For how many days in May 2023 the airport has experienced delays?
• What were the main causes of Munich airport delays in 2023?
• What is the share of the airport delays attributed to weather at Munich airport in 2023?
• Compare the delay records (in total number of delayed flights and minutes of delays) at two airports of your choice, etc.

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Advanced File Operations

Example: analyse the delays in Munich airport

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% Clean the data to leave only the rows containing information about the delays

num_lines = size(flight_data,1)

count = 0;

for i=1:(num_lines-1)

if (munich_data.DLY_APT_ARR_1{i}>0)

count = count +1;

delay_data_munich(count,:) = flight_data(i,:);

end

end

writetable(delay_data1,'munich_delays.csv')

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THANK YOU!

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Questions?