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3 >> -- Graphics

4 >>

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Introduction

• Engineers use graphic techniques to make the information easier to understand.

• With graphs, it is easy to identify trends, pick out highs and lows, and isolate data points that may be measurement or calculation errors.

• Graphs can also be used as a quick check to determine if a computer solution is yielding expected results.

• A set of ordered pairs is used to identify points on a 2D graph.

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2D Line Plot

• plot(x , y ) creates a 2D line plot for all (x , y ) pairs in order.

• You may use more parameters for the plot as follows:

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Example

1 clear; clc; close all;

2

3 x = linspace(0, 2 * pi, 20);

4 y = sin(x);

5

6 figure; plot(x, y, "r-o");

7 grid on;

• Call figure to create a figure.

• Use close to close all figures or specific one.

• Use grid to add the gray grid as the background.

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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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Example: Multiple Curves

2

3 x = linspace(0, 2 * pi, 50);

4 figure; hold on; grid on;

5 plot(x, sin(x), '*');

6 plot(x, cos(x), 'o');

7 plot(x, sin(x) + cos(x), '+');

• Use hold to put multiple curves in the same figure.

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0 1 2 3 4 5 6 7 -1.5

-1 -0.5 0 0.5 1 1.5

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Selected Annotations

• Use title to add a title to the plot.

• Use xlabel to add a label to the x axis of the plot.

• Use ylabel to add a label to the y axis of the plot.

• Use legend to add legends for lines.

• More annotations can be created by annotation.

¹

• Note that you can always generate the codes associated with the plot you modified.

1See https:

//www.mathworks.com/help/matlab/examples/annotating-plots.html.

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Example

2

3 x = linspace(0, 2 * pi, 30);

4 y = sin(x); z = cos(x);

5

7 plot(x, y, "o--");

8 plot(x, z, "x:");

9 legend("Input", "Output", "location", "best");

10

11 xlabel("Time (s)"); ylabel("Amplitude (unit)");

12 title("Title");

13 annotation("textarrow", [.3, .6], [.7, .4] , ...

14 "String", "ABC");

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0 1 2 3 4 5 6 7 Time (s)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Amplitude (unit)

Title

Input Output ABC

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Graphics Objects

• You can use plot tool (in the figures) to change the properties.

• Graphics objects are the components for data visualization.

• Each object can be assigned to a unique identifier, called a graphics handle.

• Via graphics handles, you can manipulate their properties

²

by the following instructions:

• set: set properties.

• get: query properties.

2See http:

//www.mathworks.com/help/matlab/graphics-object-properties.html.

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Example

2

3 x = linspace(-1, 1, 100);

4 h = plot(x, sin(1 ./ x));

5 grid on;

6 set(h, "Marker", "o");

7 set(h, "MarkerSize", 5);

8 set(h, "LineWidth", 1.5);

9 set(h, "LineStyle", ":");

10 set(h, "MarkerEdgeColor", "r");

11 set(h, "MarkerFaceColor", "g");

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Graphics Object Identification

³

• gcf: get current figure

• gca: get current axis

• gco: get current object

3See http://www.mathworks.com/help/matlab/creating_plots/

accessing-object-handles.html.

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Output Figures

• You can save one figure as a specific image format.

• For example, bmp, jpeg, and eps.

• Use the hot key ctrl + s .

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• You can also use print to save the figures.

⁴

2

3 x = linspace(0, 2 * pi, 20);

4 y = sin(x);

5

6 figure; plot(x, y, "r-o"); grid on;

7 print(gcf, "-djpeg", "sin.jpg", "-r300");

• Use saveas to save figure in a specific file format.

⁵

• Use savefig to save figure and contents to fig-file.

⁶

4See http://www.mathworks.com/help/matlab/ref/print.html.

5See https://www.mathworks.com/help/matlab/ref/saveas.html.

6See https://www.mathworks.com/help/matlab/ref/savefig.html.

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Exercise: TWSE:IND

2

3 [~, ~, raw] = xlsread("y9999.xlsx");

4 prices = [raw{4 : end, 2}];

5 dates = datetime(raw(4 : end, 1), ...

6 "format", "yyyy/MM/dd");

7

8 fig1 = figure;

9 plot(dates, prices); grid on;

10 ylabel("TWSE:IND");

11 annotation(fig1, "arrow", [0.4 0.88], [0.28 0.65]);

• Use datetime to convert a date string to a datetime object.

• Note that you need to specify a date format, say

"yyyy/MM/dd"

.

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2008 2010 2012 2014 2016 2018 2020 4000

5000 6000 7000 8000 9000 10000 11000 12000 13000

TWSE:IND

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Bar Plot

⁷

• Use bar to draws a bar chart, for example,

2

3 x = randi(100, 8, 3);

4 bar(x); grid on;

• Try barh.

7See http://www.mathworks.com/help/matlab/ref/bar.html and http://www.mathworks.com/help/matlab/creating_plots/

overlay-bar-graphs.html.

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1 2 3 4 5 6 7 8 0

10 20 30 40 50 60 70 80 90 100

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Exercise: Traded Volumes of TWSE:IND

2

4 volumes = [raw{4 : end, 3}];

7

8 figure;

9 bar(dates, volumes); grid on;

10 ylabel("Traded volume");

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1975 1980 1985 1990 1995 2000 2005 2010 2015 0

0.5 1 1.5 2 2.5 3 3.5

Traded volume

10⁸

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Dual y-Axes Plot

• Use yyaxis to specify the left/right y axis, for example,

2

3 x = linspace(0, 30, 300);

4 y1 = 10 * exp(-0.05 * x) .* sin(x);

5 y2 = 0.8 * exp(-0.5 * x) .* sin(10 * x);

6

7 figure;

8 yyaxis left;

9 plot(x, y1); grid on;

10 yyaxis right;

11 plot(x, y2);

• Use plotyy in old version.

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0 5 10 15 20 25 30 -8

-6 -4 -2 0 2 4 6 8 10

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

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Exercise: Index feat. Volume in One Figure

2

8

9 yyaxis left; plot(dates, prices);

10 ylabel("TWSE:IND"); grid on;

11 yyaxis right; bar(dates, volumes);

12 ylabel("Traded volume"); grid on;

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1975 1980 1985 1990 1995 2000 2005 2010 2015 0

2000 4000 6000 8000 10000 12000 14000

TWSE:IND

0 0.5 1 1.5 2 2.5 3 3.5

Traded volume

10⁸

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Histogram Plot

⁹

• Histograms group the numeric data into bins.

• Use histogram to create histogram plots.

⁸

2

3 data = randn(1, 1e3) .ˆ 2;

4 figure;

5 histogram(data, ...

6 "BinMethod", "integers", ...

7 "Normalization", "probability");

8 grid on;

8If your version is before 2014, use hist.

9More details could be found in https://www.mathworks.com/help/

matlab/ref/matlab.graphics.chart.primitive.histogram.html.

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0 2 4 6 8 10 0

0.1 0.2 0.3 0.4 0.5 0.6

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Exercise: Distribution of Return Rates of TWSE:IND

2

7 return rates = diff(prices) ./ prices(1 : end - 1);

8

9 figure;

10 histogram(return rates * 100, ...

11 "binmethod", "integer", ...

12 "normalization", "probability");

13 xlabel("Return rate (%)");

14 ylabel("Probability"); grid on;

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-8 -6 -4 -2 0 2 4 6 8 Return rate (%)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Probability

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Grid Plot: subplot

¹⁰

1975 1980 1985 1990 1995 2000 2005 2010 2015 0

5000 10000 15000

TWSE:IND

1975 1980 1985 1990 1995 2000 2005 2010 2015 0

1 2 3 4

Traded volume

10⁸

10See https://www.mathworks.com/help/matlab/ref/subplot.html.

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2

8

9 figure;

10 subplot(2, 1, 1); plot(dates, prices); grid on;

11 ylabel("TWSE:IND");

12 subplot(2, 1, 2); bar(dates, volumes, "r"); grid on;

13 ylabel("Traded volume");

• Use subplot(m, n, p) to divide the current figure into an m-by-n grid and use p to specify the certain subplot.

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Digression: Table

¹¹

• Use table to create a table for column-oriented or tabular data that is often stored as columns in a spreadsheet.

• Use detectImportOptions to create import options based on the contents of a file (if readtable cannot read files correctly).

• Use stackedplot to draw a stacked plot of several variables with common x-axis.

11See https://www.mathworks.com/help/matlab/tables.html.

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2

3 filename = "2330.csv";

4 s2330 = readtable(filename);

5 % Delete the first two rows.

6 s2330(1 : 2, :) = [];

7 % Assign the header name for each column.

8 s2330.Properties.VariableNames = ["Date", "Open", ...

"High", "Low", "Close", "Volume"];

9 % Convert date strings to datetime objects.

10 s2330.Date = datetime(s2330.Date, ...

11 "format", "yyyy-MM-dd");

12 % Use stackedplot to draw an interactive plot!

13 stackedplot(s2330, {"Close", "Volume"}, ...

14 "xvar", "Date"); grid on;

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200 250 300

Close

Jul 2017 Jan 2018 Jul 2018 Jan 2019 Jul 2019 Date

2 4 6 8 10 12 14

Volume 10⁴

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Selected Table Functions

• File I/O: readtable, writetable.

• Summary information: head, tail, summary, stackedplot.

• Sort, rearrange, and customize: sortrows, unique, addvars, removevars, rows2vars, stack, unstack, inner2outer.

• Join and set operations: join, innerjoin, outerjoin, union, intersect, ismember, setdiff, setxor.

• Apply functions to table contents: varfun, rowfun, findgroups, splitapply, groupsummary

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Exercise: Merging Two Tables

2

3 gspc = readtable("ˆGSPC.csv");

4 twii = readtable("ˆTWII.csv");

5 % Merge two time series by union of dates.

6 merged table = outerjoin(twii, gspc, ...

7 "Keys", "Date", ...

8 "MergeKeys", 1);

9 stackedplot(merged table, ...

10 {"Close twii", "Close gspc"}, ...

11 "xvariable", "Date"); grid on;

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8000 9000 10000 11000

Close_twii

Jan 2015 Jan 2016 Jan 2017 Jan 2018 Jan 2019

Date 2000

2200 2400 2600 2800

Close_gspc

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Candle Chart with Timetable

¹²

1 % Ingore the part identical to the previous ...

example of 2330.

2

3 s2330 = table2timetable(s2330, "RowTimes", "Date");

4 candle(s2330(end - 30 : end, :)); % last 30 days

5 ylabel("Daily price (TWD)");

• Use timetable to convert the table (with variable names:

"Open"

,

"High"

,

"Low"

,

"Close"

) to a timetable by specifying the RowTimes.

• Try priceandvol.

12See https://www.mathworks.com/help/finance/candle.html and https://www.mathworks.com/help/matlab/timetables.html with https://www.mathworks.com/help/finance/examples/

using-timetables-in-finance.html.

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Nov 01 Nov 08 Nov 15 Nov 22 Nov 29 Dec 06 Dec 13 Dec 20 Dec 27 2019 300

305 310 315 320 325 330 335 340 345

Daily price (TWD)

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Smart Plot: fplot

• Use fplot to make a line plot over a specific range with adaptive steps.

• You may assign a function in a string form to fplot.

¹³

2

3 fplot("sin(1 / x)", [-0.05, 0.05]); grid on;

13Warning: fplot will not accept character vector or string inputs in a future release.

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-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

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errorbar

¹⁴

2

3 x = 0 : 10 : 100;

4 y = [20 30 45 40 60 65 80 75 95 90];

5 yneg = [1 3 5 3 5 3 6 4 3 3];

6 ypos = [2 5 3 5 2 5 2 2 5 5];

7 xneg = [1 3 5 3 5 3 6 4 3 3];

8 xpos = [2 5 3 5 2 5 2 2 5 5];

9 errorbar(x, y, yneg, ypos, xneg, xpos, "o");

10 grid on;

14See https://www.mathworks.com/help/matlab/ref/errorbar.html.

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0 10 20 30 40 50 60 70 80 90 100 10

20 30 40 50 60 70 80 90 100

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Pie Chart

26%

19%

21%

13%

21%

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2

3 X = rand(1, 5);

4 labels = {"A", "B", "C", "D", "E"};

5 explode = [0, 1, 0, 1, 0];

6 pie(X, explode, labels);

• Use pie to create a pie chart.

¹⁵

• Note that the explode vector is used to offset slices for the nonzero elements.

15See https://www.mathworks.com/help/matlab/ref/pie.html.

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Word Cloud

market_values

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2

3 [~, ~, raw] = xlsread("twse mktValue.xlsx");

4

5 stock ticks = string(raw(4 : end, 1));

6 idx = strcmp(raw(:, 3), "-"); % Find all "-"s.

7 raw(idx, 3) = {0}; % Replace them by 0.

8 market values = [raw{4 : end, 3}]';

9

10 tbl = table(stock ticks, market values);

11 figure;

12 wordcloud(tbl, "stock ticks", "market values");

• Use strcmp to compare strings and return a boolean vector.

• Use wordcloud to create a word cloud chart from text data.

¹⁶

16See https://www.mathworks.com/help/matlab/ref/wordcloud.html.

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Contours

¹⁷

• Use meshgrid to partition the specified range of x and y .

• Note that the return values are in form of matrices. (Why?)

2

3 x = linspace(-2 * pi, 2 * pi);

4 y = linspace(0, 4 * pi);

5 [X, Y] = meshgrid(x, y);

6 Z = sin(X) + cos(Y); % Using vectorization.

7 figure; contour(X, Y, Z, "showtext", "on");

17See https://www.mathworks.com/help/matlab/ref/contour.html.

You may try contourf.

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-1.5 -1.5

-1

-1 -1

-0.5 -0.5 -0.5

-0.5

-0.5 -0.5

-0.5

0 0

0

0 0

0

0 0

0.5 0.5

0.5

0.5 0.5

1 1

1

1.5 1.5

-6 -4 -2 0 2 4 6

0 2 4 6 8 10 12

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Quiver (Velocity) Plot

• Use quiver(x , y , u, v ) to plot a vector (u, v ) at the coordinate (x , y ).

• Use peaks with a positive number as sample size to generate a set of 3d points.

¹⁸

2

3 [x, y, z] = peaks(20);

4 [u, v] = gradient(z);

6 contour(x, y, z, 10);

7 quiver(x, y, u, v);

18See https://www.mathworks.com/help/matlab/ref/peaks.html.

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

-2 -1 0 1 2 3

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Mesh Plot

• Use mesh to draw a wireframe mesh.

2

3 x = linspace(-3, 3, 50);

4 y = x + pi / 2;

5 [X, Y] = meshgrid(x, y);

6 Z = cos(X) .* sin(Y);

7 figure; mesh(X, Y, Z); grid on;

8 xlabel("x"); ylabel("y"); zlabel("z");

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-1 6 -0.5

4 4

z 0

2 0.5

y 2

x 1

0 0

-2 -2 -4

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Surface Plot

• Use surf to draw a colored surface.

• Try meshz, meshc, surfc, and waterfall.

2

3 x = linspace(-2, 2, 25);

4 y = linspace(-2, 2, 25);

5 [X, Y] = meshgrid(x, y); % form all x-y pairs

6 Z = X .* exp(-X .ˆ 2 - Y .ˆ 2);

7 surf(X, Y, Z);

8 xlabel("x"); ylabel("y"); zlabel("z");

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-0.5 2

1 2

z 0

1

y 0

x 0.5

-1 0

-1 -2 -2

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Exercise

• Write a program to draw a surface plot for sinc(R) =

^sin(R)_R

.

• Note that there exists a singularity at R = 0, which should be removed by replacing a zero with eps = 2.2204 × 10

⁻¹⁶

.

2

3 [X, Y] = meshgrid(linspace(-10, 10, 51));

4 R = sqrt(X .ˆ 2 + Y .ˆ 2);

5 R(R == 0) = eps; % Avoid the singularity.

6 Z = sin(R) ./ R;

7 surf(X, Y, Z);

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-0.5 10 0

5 10

0.5

0 5 1

-5 0

-5 -10 -10

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3D Line Plot

• Use plot3 to draw a 3d curve.

2

3 t = linspace(0, 10 * pi, 100);

4 x = t .* sin(t); y = t .* cos(t);

5

6 figure;

7 plot3(x, y, t); hold on;

8 plot3(x, y, -t, "r");

9 axis equal; grid on;

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-30 -20 -10

20 0

20 10

20

0 0

30

-20 -20

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Misc

²¹

• Use the button Rotate 3D to change the view angle.

• Use view to set the view angle.

¹⁹

• Try colorbar and colormap.

²⁰

2

3 peaks;

4 view([117, 58]); % View angle in degree.

5 colorbar; % Appends a colorbar to the current axes.

6 colormap summer; % Change the colormap.

19az: azimuth (horizontal) rotation; el: vertical elevation.

20See https://www.mathworks.com/help/matlab/ref/colormap.html.

21See

https://www.mathworks.com/products/matlab/plot-gallery.html.

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-3 -2 -1

x -3 0

-2 -5

-1 1

y

0 1 2

2 3 3

Peaks

0 5

-6 -4 -2 0 2 4 6 8

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