Lecture 3 - Simple Data Analysis and Graphics

8/16/2019 Lecture 3 - Simple Data Analysis and Graphics

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Eran Eden, Weizmann 2008 © 1

Introduction to Matlab

& Data Analysis

Lecture 3:Simple Data Analysis and Graphics

Some of the slides are based on Introduction to Matlab by Dori Peleg


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Today on the menu …

Previous lecture reminder

2D and 3D arrays continuation

Matlab Graphics - How to Visualize your data

2D graphics 3D graphics

Animation


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Previous lecture reminder…

1D arrays


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Indexing 1D Arrays Question: How do we retrieve/manipulate the content

of a specific element inside an array?

Answer: We use a mailbox like system called indexing

x(i) is the i’th element of x

1 2 3 4 5


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Indexing 1D Arrays

x = 10 : -1 : 1;

y = x(3);disp(y);8

10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

8

x y


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Indexing 1D Arrays

We can retrieve more than one element at a time:

x = 10 : -1 : 1;

y = x([3,9,4]);disp(y)

10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

8

x

y 2 7


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Using indexing to edit 2D arrays

We can erase parts of an array

x = 10 : -1 : 1;

x(2 : 4) = [];disp(x);

10 9 8 7 6 5 4 3 2 1

10 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7


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Sub-array searching

Find the indexes of values in x that are larger than 3

>> x = [2 8 7 0 6 2 3];

>> find (x > 3)2 3 5

Find the actual values in x that are larger than 3

>> x = [2 8 7 0 6 2 3];

>> x(find (x > 3))

8 7 6

Very important tounderstand this example!

We can also get the same resultby breaking this into 2 steps:

>> inds = find(x > 3);

>> x(inds)

8 7 6


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Previous lecture reminder…

Matrix

(2D Arrays)


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Indexing 2D arrays

x(h,w) is the h row and the w column

what is the value of x(3,4)?

10 21 10 4

73 21 18 10

10 4 8 21

3 21 10 45

8 21 2 21

3

4

what is the value of x(1 : 3, 4)?

10 21 10 4

73 21 18 10

10 4 8 21

3 21 10 458 21 2 21

3

4

21


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Indexing 2D arrays

>> a = [1 2 3; 4 5 6; 7 8 9];

>> disp(a)

1 2 3

4 5 6

7 8 9

>> a(1)

ans =

1

>> a(2)ans =

4

>> a(3)

ans =

7

It’s possible to index a 2D array using a single coordinate

>> a(5 : 8)

ans =

5 8 3 6


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y =

0 0 0

0 0 0

0 0 0

The matrices on the left and right of the assignment (=) shouldmatch in size...

y = zeros(3,3);

x = ones(2,2);

Size 3 x 3 Size 2 x 2

x =

1 1

1 1

=


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y =

0 0 0

0 0 0

0 0 0


y = zeros(3,3);

x = ones(2,2);y(1 : 2, 1 : 2) = x


x =

1 1

1 1

=


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y =

0 0 0

0 0 0

0 0 0


y = zeros(3,3);

x = ones(2,2);y(1 : 2, 1 : 2) = x

1 1

1 1

x =

1 1

1 1


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y = zeros(3,3);

x = 4;y(1:2,1:2) = x

. . . unless the right matrix has a size of 1 x 1

y =

0 0 0

0 0 0

0 0 0


x =

4

=

4 4 4 4 4


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y = zeros(5,5);

x = ones(2,2);

y = x

y =

1 1

1 1

... ORunless you are overwriting a matrix



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y = zeros(3,3);

x = ones(3,3);y(1, 2 : 3) = x(1 : 2, 2 : 3)

??? Subscripted assignment dimension mismatch.

What happens when sizes of matrices don’t match?

y =

0 0 0

0 0 0

0 0 0

x =

1 1 1

1 1 1

1 1 1


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>> y = [1 2 3; 4 5 6; 7 8 9];

>> disp(y)

1 2 3

4 5 67 8 9

>> y(2, :) = [];

>> disp(y);

1 2 3

7 8 9

>> y(: , [1 3]) = [];

>> disp(y);

disp(y);

2

8

Erasing part of a matrix


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Simple operations on 2D arrays

Finding the size of a matrix

x =[ 2 4 6

3 6 9];

size(x)

2 3

Finding the length of a matrix

length(x)

3

Number of rows Number of columns


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Simple operations on 2D arrays

Finding the maximal numbers in each matrix column

>> x = [1 8 3; 7 2 6; 4 5 9]

>> max(x)

ans =

7 8 9

How do we get the maximal element in the entire matrix?

>> max(max(x))

ans =

9


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Finding things within arraysusing 1 coordinate indexing

>> x = [1 2 3;

7 8 9

4 5 6];

Find the indices of the values in x that are larger than 5.

>> inds = find (x > 5)

inds =

2 5 8 9

Find the actual values of all elements in x that are larger than 5.>> x(find(x > 5))

ans =

7 8 9 6

Alternatively we could break this intotwo steps:

>> inds = find(x > 5);

>> x(inds)


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2D and 3D arrays continuation…


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Arithmetic operations on 2D arrays The plus (+) and minus (-) operations are naturaly extended

to 2D arrays

Example 1:

x =[ 2 4 6

3 6 9];

y = x – 1

y =

1 3 5

2 5 8

Example 2:

x = x + x

x =

4 8 12

6 12 18


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y =

1 3 42 4 7 24

Arithmetic operations on 2D arrays

Question: write a commmand that subtracts 1 from all the valuesin y that are larger than 4 and stores it back into y

y = [1 3 5

2 5 8];

Answer: y(find(y > 4)) = y(find(y > 4)) - 1

y(find(y > 4)) = y([4 5 6]) - 1

y(find(y > 4)) = [5 5 8] - 1

y(find(y > 4)) = [4 4 7]

y([4 5 6]) = [4 4 7]


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(1) Scalar multiplication

price = [10 20 30; 2 3 4];

new_price = price * 2

new_price =

20 40 60

4 6 8

25



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(2) Matrix multiplicaiton

price = [2 3 4; 2 4 5];

quantity = [4 1; 0 2; 2 1];

price * quantity

ans =

16 12

18 15

4 1

0 2

2 1

2 3 4

2 4 5

* = 16 12

18 15


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(3) Element-by-element multiplicaiton

price = [2 3 4; 2 4 5];

quantity = [4 0 2; 1 2 1];

price .* quantity

ans =

8 0 8

2 8 5

2 3 4

2 4 5.* =

4 0 2

1 2 1

8 0 8

2 8 5


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“Flattening” 2D arrays We can turn a matrix into a vector

(ordered according to columns)

x = [1 2 3

4 5 6

7 8 9];

y= [x(:, 1); x(:, 2); x(:, 3)]

y =

1

4

7

2

5

8

3

6

9

Alternatively the following command willdo the trick…

y = x(:)

y =

1

4

7

2

5

8

3

6

9


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Final example In the matrix vac_days each column represents the number of vacations days an employee

took in the last 3 months.

In the matrix salaries each column represents that employee’s salary in the last 3 months.

Correct the salaries so that employees that took less then 3 days of vacation in a certainmonth get a 10% bonus to their salary.

>> vac_days = [1 5 10 0; 0 0 1 10 ; 0 0 5 7 ]

vac_days =

1 5 10 0

0 0 1 10

0 0 5 7

>> salaries = [6000 6000 7000 20000; 6000 6000 7000 20000; 7000 7000 7000 20000;]

salaries =

6000 6000 7000 20000

6000 6000 7000 200007000 7000 7000 20000


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Final small example

Answer:

>> inds = find(vac_days < 3);

>> salaries(inds) = salaries(inds) * 110/100;

>> disp(salaries)

6600 6000 7000 22000

6600 6600 7700 20000

7700 7700 7000 20000

Or

>> salaries(find(vac_days


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3D arrays…

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10 21 10 21

73 21 18 21

10 4 8 213 21 10 45

8 21 2 21

10 21 10 21

73 21 18 21

10 4 8 21

3 21 10 45

8 21 2 21

10 21 10 21

73 21 18 21

10 4 8 21

3 21 10 45

8 21 2 21

Color images are 3D arrays

(We will learn this at the endof the course)

Why the heck do we need 3D arrays ?#@!?

R

G

B


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3D arrays

All the (initialization / indexing / operations) that welearnt on 2D arrays can be applied to 3D arrays.

In fact, they can be applied to any N dimensionalarray.


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3D arrays - example>> x = zeros(3,3,3)

x(:,:,1) =

0 0 0

0 0 0

0 0 0

x(:,:,2) =

0 0 0

0 0 0

0 0 0

x(:,:,3) =

0 0 0

0 0 0

0 0 0


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3D arrays (example continued)>> x(:, :, 3) = ones(3,3)

x(:,:,1) =

0 0 0

0 0 0

0 0 0

x(:,:,2) =

0 0 0

0 0 0

0 0 0

x(:,:,3) =

1 1 1

1 1 1

1 1 1


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3D arrays (example continued)>> x(2, 2, :) = 3

x(:,:,1) =

0 0 0

0 3 0

0 0 0

x(:,:,2) =

0 0 0

0 3 0

0 0 0

x(:,:,3) =

1 1 1

1 3 1

1 1 1


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Tip of the day… improving your code readbility

Use spaces and tabs to make your code more clear

This code is ugly...

This code is pretty and readable!

age=10; weight=50;height= 1 :0.1:4;hair=2:0.1:5;

age = 10; weight = 50;height = 1 : 0.1 : 4;

hair = 2 : 0.1 : 5;


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The Matlab graphics


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Excel vs. Matlab Graphics

Why should we learn graphics and visualization inMatlab? Why not use Excel?

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Matlabvisualization

Excelvisualization


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Plot of dots plot is the most basic function for creating 2D graphics

plot(x1, y1, c1, x2, y2, c2, …)

x coordinate

of first dot

y coordinate of

first dot

Color & marker

of first dot

Symbol Color Symbol Marker Symbol Line styleb blue . point - solidg green o circle : dotted

r red x x-mark -. dashdotc cyan + plus -- dashedm magenta * star (none) no liney yellow s squarek black d diamond

v triangle (down)^ triangle (up)< triangle (left)> triangle (right)

p pentagramh hexagram


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Plot of dots Example:

%Group #1

w_pre1 = [ 148 153 170 159 162]; %weight in previous month

w_cur1 = [ 90 85 92 91 88 ]; %weight in current month

%Group #2

w_pre2 = [157 172 179 167 179]; %weight in previous month

w_cur2 = [81 69 87 70 77 ]; %weight in current month

%Plotting the previous vs. current week weights of each contestantplot(w_pre1(1), w_cur1 (1),'bo', w_pre1(2), w_cur1 (2), 'bo', ...

w_pre1(3), w_cur1 (3), 'bo', w_pre1(4), w_cur1 (4), 'bo', ...

w_pre1(5), w_cur1 (5), 'bo', ...

w_pre2(1), w_cur2 (1),'r*', w_pre2(2), w_cur2 (2), 'r*', ...

w_pre2(3), w_cur2 (3), 'r*', w_pre2(4), w_cur2 (4), 'r*', ...

w_pre2(5), w_cur2 (5), 'r*');


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Plot

145 150 155 160 165 170 175 18065

70

75

80

85

90

95

Notice that Matlab

automatically choosesthe axes borders thatfit the plot…


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Plot Example:

%Group #1

w_pre1 = [ 148 153 170 159 162]; %weight in previous month

w_cur1 = [ 90 85 92 91 88 ]; %weight in current month

%Group #2

w_pre2 = [157 172 179 167 179]; %weight in previous month

w_cur2 = [81 69 87 70 77 ]; %weight in current month

plot(w_pre1(1), w_cur1 (1),'bo', w_pre1(2), w_cur1 (2), 'bo', ...w_pre1(3), w_cur1 (3), 'bo', w_pre1(4), w_cur1 (4), 'bo', ...

w_pre1(5), w_cur1 (5), 'bo', ...

w_pre2(1), w_cur2 (1),'r*', w_pre2(2), w_cur2 (2), 'r*', ...

w_pre2(3), w_cur2 (3), 'r*', w_pre2(4), w_cur2 (4), 'r*', ...

w_pre2(5), w_cur2 (5), 'r*');

This is very labor intensive… The same result can be achieved with much less work using vector notation.


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Plot of dots using vectors

plot(x, y, c)

Example (continued)…

plot(w_pre1, w_cur1, 'bo');

hold on

plot(w_pre2, w_cur2, 'r+');

hold off

A vector containing

coordinates x1 … xn Color & markerof the line

A vector containing

coordinates y1 … yn

From now on all other plots will besuperimposed on the original figure

Cancel hold on. The following plot

will override current figureIf we omit the color and markerindication Matlab will try toconnect the dots


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Plot of dots using vectors

145 150 155 160 165 170 175 18065

70

75

80

85

90

95

We get the exact same

plot


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Plot (opening and closing)

Some Remarks:

Notice that every time we plot a figure it overrides theprevious figure (unless we use hold on)

If we want to open a new figure without erasing theprevious one we use a command called figure

If we want to close all the figures we use the commandclose all


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Plot (adding labels)

145 150 155 160 165 170 175 18065

70

75

80

85

90

95

Previous month weight(kg)

C u

r r e n t m o n t h w e i g h t ( k g )

Weight contest , group 1 vs. group 2


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Plot (adding labels)

60 80 100 120 140 160 18060

80

100

120

140

160

180

Previous month weight(kg)

C u r r e n t m o n t h w e i g h t ( k g )

Weight contest, group 1 vs. group 2


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Plotting lines Example #1

x = 0 : 2 * pi;

y = sin(x);

plot(x, y);

0 1 2 3 4 5 6-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

By default Matlab willconnect the dots…

If we use: plot(x, y,'ro')

Matlab will display a dot plot

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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x = 0 : 0.01 :2 * pi;

y = sin(x);

plot(x, y, 'r:')

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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x = 0 : 0.1 : 4*pi

y_sin1 = sin(x);

y_sin2 = sin(x + 0.2);y_sin3 = sin(2 * x);

plot(x, y_sin1);

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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Plotting lines Drawing several plots in one figure:

x = 0 : 0.1 : 4*pi

y_sin1 = sin(x);


plot(x, y_sin1);

hold on

By default every new plot replacesthe previous plot

When hold on is used thesubsequent plots are made in thesame figure using the same axes

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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Plotting lines Drawing several plots in one figure:

x = 0 : 0.1 : 4*pi

y_sin1 = sin(x);


plot(x, y_sin1);

hold on

plot(x, y_sin2, 'r');

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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Plotting lines

x = 0 : 0.1 : 4*pi

y_sin1 = sin(x);


plot(x, y_sin1);

hold on


plot(x, y_sin3, 'm--');

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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Plotting lines

x = 0 : 0.1 : 4*pi

y_sin1 = sin(x);


plot(x, y_sin1);

hold on


plot(x, y_sin3, 'm--');legend('sin(x)', 'sin(x + 0.2)', 'sin(2x)');

hold off

A figure legend can be added using the legend command

hold off restores default setting where each subsequent plot erases the previous one

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

sin(x)

sin(x + 0.2)

sin(2x)


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You can make additional modificationsto your plot using the plot browser


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You can make additional modificationsto your plot using the plot browser


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Plotting multiple rows

The variable gene_vals contains the expression values of 170genes in 24 different samples.

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gene_vals =

S1 S2 S3 S4 S5 S6 . . .

0.3767 0.4701 0.0175 0.0712- 0.0300 - 0.0220 . . .

0.5128 0.5367 0.0056 0.0179 0.0443 0.0291 . . .

0.4303 0.4447 0.0326 0.0498 0.1646 0.0490 . . . 0.4745 0.5575 0.1232 0.1444 0.0259 0.0187 . . .

0.2148 0.2380 0.1591 0.1438 0.1826 0.1717 . . .

0.4852 0.4029 0.0542 0.1435 0.1424 0.0546 . . .

0.4258 0.3948 0.0230 0.1261 0.0398 0.0199 . . .

. . .

Gene1

Gene2

Gene3

Gene4Gene5

Gene6


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Plot the expression of the first gene>> gene_val = gene_vals(1, :)

>> plot(gene_val, '-*')

60 0 5 10 15 20 25-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

If the x coordinatesare NOT specified,

Matlab uses defaultcoordinates


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Plot the expression of all the genes>> plot(gene_vals')

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Plot can be used on a matrix.

It automatically generates a line foreach column (connecting all thepoints in the column).

Each line is assigned a different color.


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Plotting other types of graphs

Matlab has many other types of plotting capabilities

x = -2 : 0.2 : 2;

y = x .* x;

bar(x, y, 'r');

title('Bar plot')

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4Bar plot


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Plotting a histogram

norm_rand_values = randn(1, 1000);

hist(norm_rand_values, 20);

title('Histogram plot');

-3 -2 -1 0 1 2 30

20

40

60

80

100

120Histogram plot

Randomly generatednumbers from a normaldistribution with mean zeroand standard deviation one

randn(3) mean 0 std 1

ans =

-0.4326 0.2877 1.1892-1.6656 -1.148975 -0.03760.1253 1.1909 0.3273


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Plotting a pie chart

pie3([3000 2000 1000 5000],[0 0 0 1], ...

{'Bibi', 'Tsipi','Liberman','Donald Duck'});

title('Fraction of votes');

Votes vector

Donald Duck

Liberman

Fraction of votes

Barak

Bibi

Label vector-What are thosecurly braces?

“Explode” vector-which piece toseparate

Curly braces in this case define thedifferent titles as a cell array .

If we use:

title({'Fraction of', 'votes'});

We will get a two-line title.

Tsipi


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Making scatter plots

x1 = randn(1, 100);

y1 = randn(1, 100);

scatter(x1, y1, 25, [1 0 0], 'filled');

size ofeach point

Color ofeach point

Fill theinterior ofeach point

-3 -2 -1 0 1 2 3-4

-3

-2

-1

0

1

2

3


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-3 -2 -1 0 1 2 3-4

-3

-2

-1

0

1

2

3

66


-3 -2 -1 0 1 2 3-4

-3

-2

-1

0

1

2

3


x1 = randn(1, 100);

y1 = randn(1, 100);


hold onx2 = rand(1, 100) + 2;

y2 = randn(1, 100);

scatter(x2, y2, 25, [0 1 0] , 'filled');


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-3 -2 -1 0 1 2 3-4

-3

-2

-1

0

1

2

3

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-3 -2 -1 0 1 2 3 4-6

-4

-2

0

2

4

6Scatter plot


x1 = randn(1, 100);

y1 = randn(1, 100);


hold onx2 = rand(1, 100) + 2;

y2 = randn(1, 100);

scatter(x2, y2, 25, [0 1 0] , 'filled');

x3 = rand(1, 100) + 3;

y3 = randn(1, 100) * 2;

scatter(x3, y3, 25, [0 0 1], 'filled');title('Scatter plot');

hold off


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There are many other types of plots and graphs…

Some will be taught in the tutorial Some will be taught in next lectures

All can be found in the Matlab guide and Google


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Putting multiple plots in the same figure

subplot(# rows, # columns, current plot position)


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figure;

subplot(2, 2, 1)x = -2 : 0.2 : 2;y = x .*x;

bar(x,y, 'r');

title('Bar plot')

subplot(2, 2, 2);norm_rand_values = randn(1, 1000);hist(norm_rand_values, 20);title('Histogram plot');

subplot(2, 2, 3);pie3([3 2 1 5],[0 0 0 1],{'Bibi','Barak','Liberman','Donald Duck'})title('Pie plot');

subplot(2, 2, 4);x1 = randn(1, 100)x2 = rand(1, 100) + 2

x3 = rand(1, 100) + 3

y1 = randn(1, 100);y2 = randn(1, 100);

y3 = randn(1, 100) * 2;

z = [repmat([1 0 0], 100, 1); ...repmat([0 1 0], 100, 1); repmat([0 0 1], 100, 1)];

scatter([x1 x2 x3], [y1 y2 y3], 10, z);

title('Scatter plot');

repmat =replicatematrix

z is a [300x3] matrixfor indicating color.


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3D graphics – making surfaces

A 3D surface is defined as:

z = f(x, y)

We will create 3D surfaces using 2 functions: mesh(x, y, z);

surf(x, y, z);

x1

z1

y1


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Exploring the behavior of a function using mesh: how does the following function

behave in the range -3 < x, y < 3?

2 22 ( )5 (sin( /15 )) 10 x y

x y e


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xx =

-3 -2 -1 0 1 2 3

yy =

-3 -2 -1 0 1 2 3

x =

-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

y =

-3 -3 -3 -3 -3 -3 -3

-2 -2 -2 -2 -2 -2 -2

-1 -1 -1 -1 -1 -1 -1

0 0 0 0 0 0 0

1 1 1 1 1 1 1

2 2 2 2 2 2 2

3 3 3 3 3 3 3z =

5.5225 5.5226 2.7279 1.0012 2.7279 5.5226 5.5225

5.5226 3.7647 1.8946 1.1832 1.8946 3.7647 5.5226

2.7279 1.8946 2.5695 4.6788 2.5695 1.8946 2.7279

1.0012 1.1832 4.6788 11.0000 4.6788 1.1832 1.0012

2.7279 1.8946 2.5695 4.6788 2.5695 1.8946 2.7279

5.5226 3.7647 1.8946 1.1832 1.8946 3.7647 5.5226

5.5225 5.5226 2.7279 1.0012 2.7279 5.5226 5.5225

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3D graphics – making surfacesxx = -3 : 1 : 3

yy = -3 : 1 : 3

[x, y] = meshgrid(xx, yy)

z = 5 * sin(pi / 15 * x .* y).^2 + . . .

10 * exp( -(x.^2 + y.^2)) + 1

figure;

mesh(x, y, z);

xlabel('x'); ylabel('y'); zlabel('z');

-4-2 0

24

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z

#rows


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Lets use a finer grid…

xx = -3 : 0.2 : 3;

yy = -3 : 0.2 : 3;

[x, y] = meshgrid(xx, yy);

z = 5 * sin(pi / 15 * x .* y).^2 + 10 * exp( -(x.^2 + y.^2)) + 1;

figure;

mesh(x, y, z);


view(30, 50);

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3 -3

-2

-1

0

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y

x

z

view([az, el]) sets the angle of the view from

which an observer sees the current 3-D plot.az is the azimuth or horizontal rotation (degrees).el is the vertical elevation (degrees).


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We can look at the actual surface

figure;

surf(x, y, z);


view(30, 50);

-3-2

-10

12

3 -3

-2

-1

0

1

2

3

0

5

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y

x

z


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Omitting the edges of the surface

figure;

surf(X, Y, Z, 'EdgeColor', 'none');

xlabel('x'); ylabel('y'); zlabel('z');view(30, 50);

-3-2

-10

12

3 -3

-2

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0

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Headlight means at theangle of the camera.Phong is good for curvedsurfaces.

78


Playing with light…

figure;

surf(x, y, z, 'EdgeColor', 'none');


view(30, 50);camlight headlight

lighting phong


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Lets make the grid even finer

xx = -3 : 0.01 : 3;

yy = -3 : 0.01 : 3;[x, y] = meshgrid(xx, yy);

z = 5 * sin(pi / 15 * x .* y).^2 + 10 * exp( -(x.^2 + y.^2)) + 1;

surf(x, y, z, 'EdgeColor', 'none');


view(30, 50);

camlight headlight

lighting phong


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Playing with the colors…

Colors can be represented as a combination of R ed Green Blue.

R G B Color

1 0 0 Red

0 1 0 Green

0 0 1 Blue

0 0 0 Black1 1 1 White

1 1 0 Yellow

1 0.6 0.4 Copper

… … …


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3D graphics – making surfacescolormap([1 0 0]) colormap([0 1 0])

colormap([0 0 1]) colormap([1 1 0])


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show several surfaces on the same plotsurf(x, y, z, 'EdgeColor', 'none', 'FaceColor', 'red');


hold on;

z2 = x.^2 + y.^2 + 2;

surf(x, y, z2, 'EdgeColor', 'none','FaceColor', 'yellow', 'FaceAlpha', 0.7);

view(30, 40);

camlight headlight

lighting phong

1-opaque

0-transparent

U i 3D hi i li


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Kaplan, Bren et al. Mol Cell. 2008

Mapping gene expression output function in response to a 2 inputsugar signal…

S u g

a r # 1

c o n

c e n t r a t i o n

Sugar #2concentration

Using 3D graphics to visualizeyour experimental data

U i 3D hi t i li


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%Kaplan, Bren et al. Mol Cell. 2008

ara_bad = [

0.003 0.026 0.104 0.26 0.38 0.464 0.565 0.73 0.858 0.883 0.925 1

0.003 0.007 0.026 0.104 0.26 0.38 0.464 0.507 0.571 0.609 0.609 0.783

0.002 0.002 0.007 0.023 0.063 0.168 0.329 0.418 0.446 0.482 0.496 0.503

0.002 0.002 0.002 0.002 0.003 0.021 0.075 0.147 0.231 0.269 0.275 0.294

0.002 0.002 0.002 0.002 0.002 0.002 0.009 0.054 0.136 0.164 0.198 0.203

0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.004 0.037 0.079 0.124 0.137 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.03 0.077 0.099

0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.004 0.03 0.077 ];

subplot(3, 1, 1);

surf(flipud(ara_bad));

xlabel('cAMP');ylabel('Arabinose');

camlight headlight

lighting phong

surf uses default xand y grid the size

of the matrix z.

Flip updown

U i 3D hi t i li


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mal_t = [

0.928 0.982 0.979 0.945 0.912 0.903 0.89 0.888 0.934 0.95 0.962 0.961

1 0.932 0.876 0.825 0.805 0.78 0.785 0.788 0.797 0.821 0.821 0.896

0.789 0.813 0.783 0.775 0.753 0.743 0.734 0.727 0.721 0.733 0.726 0.787

0.591 0.583 0.548 0.541 0.521 0.501 0.485 0.498 0.489 0.501 0.539 0.554

0.483 0.44 0.419 0.408 0.387 0.388 0.399 0.405 0.40.434 0.444 0.507

0.325 0.296 0.278 0.266 0.245 0.235 0.234 0.243 0.255 0.274 0.30.276

0.127 0.168 0.164 0.171 0.166 0.152 0.164 0.174 0.193 0.216 0.249 0.267

0.198 0.179 0.164 0.146 0.128 0.119 0.11 0.106 0.109 0.13 0.146 0.185];

subplot(3, 1, 2);

surf(flipud(mal_t));

xlabel('cAMP');

ylabel('Maltose');camlight headlight

lighting phong


U i 3D hi t i li


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gal_p = [

0.125 0.123 0.123 0.123 0.132 0.14 0.156 0.156 0.194 0.294 0.294 0.294

0.14 0.14 0.212 0.155 0.17 0.156 0.194 0.339 0.43 0.43 0.542 0.786

0.241 0.212 0.218 0.212 0.226 0.229 0.339 0.464 0.542 0.665 0.786 1

0.256 0.256 0.245 0.226 0.245 0.361 0.464 0.527 0.665 0.741 0.923 1

0.241 0.241 0.315 0.226 0.336 0.336 0.392 0.503 0.634 0.739 0.752 0.752

0.256 0.296 0.315 0.308 0.308 0.308 0.369 0.369 0.392 0.599 0.739 0.739

0.197 0.197 0.25 0.188 0.188 0.188 0.297 0.233 0.239 0.239 0.376 0.605 0.197 0.197 0.214 0.152 0.119 0.119 0.181 0.233 0.233 0.233 0.322 0.376

];

subplot(3, 1, 3);

surf(flipud(gal_p));

xlabel('cAMP');ylabel('Galactose');

camlight headlight

lighting phong



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Animation

An animation is a sequence of images


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Making simple animations

Example #1

x = 0 : 0.1 : 8 * pi

phi = 0.0; plot(x, sin(x + phi));

mov(1) = getframe;

phi = 0.2; plot(x, sin(x + phi));mov(2) = getframe;


mov(3) = getframe;

…


mov(17) = getframe;

movie(mov, 30, 10);

Number of timesthe movie is played

Frames per secondFrames


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Making simple animations Example #1

x = 0 : 0.1 : 8*pi


mov(1) = getframe;



mov(3) = getframe;

…


mov(17) = getframe;

movie(mov, 30, 10);

movie2avi(mov, 'C:\sin_animation.avi');

Name of movie


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Making simple animations

http://localhost/Eran/Eran%20teachings/Matlab%20and%20Data%20Analysis/scripts/Lecture3/files_for_animation/sin_animation.avi


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Making simple animations Example #1

x = 0 : 0.1 : 8*pi


mov(1) = getframe;



mov(3) = getframe;

…


mov(17) = getframe;

movie(mov, 30, 10);

movie2avi(mov, 'C:\sin_animation.avi');

Remark: writing multiple copiesof similar lines is tedious andtime consuming!

In the next lecture we will see

how to circumvent this…


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Animation Example #2:

% Animating climatology data

title('Sea Surface Temprature (SST)')

% Loading data

load sstjan.dat

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

x coordinate

y c o o r d i n a t e

Sea surfacetemperature atcoordinate (x,y)


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Animation Example #2:


title('Sea Surface Temprature (SST)')

% Loading data

load sstjan.dat

contourf(sstjan);

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

15 18 20 21 23 20 21 23 20 21 23 21 19

16 14 21 22 32 21 31 32 21 31 32 23 20

15 15 22 30 32 22 30 32 22 30 32 28 24

12 13 24 29 30 24 29 30 24 29 30 29 …

x coordinate

y c o o r d i n a t e

Sea surfacetemperature atcoordinate (x,y)

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Animation Making a simple animation - example #2


title('Sea Surface Temperature (SST)')

%cd 'C:\Eran\Eran teachings\Matlab and Data Analysis\scripts\Lecture3\files_for_animation' % Loading data

load sstjan.dat;

load sstfeb.dat;

load sstmar.dat;

load sstapr.dat;

load sstmay.dat;

load sstjun.dat;load sstjul.dat;

load sstaug.dat;

load sstsep.dat;

load sstoct.dat;

load sstnov.dat;

load sstdec.dat;

contourf(sstjan); frame(1) = getframe;

contourf(sstfeb); frame(2) = getframe;

contourf(sstmar); frame(3) = getframe;

contourf(sstapr); frame(4) = getframe;contourf(sstmay); frame(5) = getframe;

contourf(sstjun); frame(6) = getframe;

contourf(sstjul); frame(7) = getframe;

contourf(sstaug); frame(8) = getframe;

contourf(sstsep); frame(9) = getframe;

contourf(sstoct); frame(10) = getframe;

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Documents

Lecture 3 - Simple Data Analysis and Graphics