to Introduction Scientific Computing and Problem Solving
Lecture #6 Plotting
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.0
Announcements
Assignments
Review lecture slides Study examples and corresponding M-files Work on your own examples! Get help when needed! TA hours Ask questions if some concepts are not well understood!
Please always check the course web page
Announcements, updated documents, lecture materials
No labs but regular TA hours over Long Weekend! :)
lab3 = []; TA_hours_during_long_weekend = true;
HW#2 due on Thu 2:30pm Now 11:59pm!
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.1
Where we are
First two weeks
MATLAB programming environment arrays and operations logical type, flow control and selection
This lecture
HW2 clarifications Conditionals revisited through examples Plotting capabilities with MATLAB Examples - applications
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.2
Data types
So far: double, char, logical They determine the type of data stored at variables
Some more to come
Built-in conversion functions Often: source of errors
How much memory space is used How data is represented What types of operations can be applied to data E.g., num2str, str2num, int2str, char, double E.g., assignments of inconsistent data types
2009 - 6.3
CSCI0040 - Introduction to Scientific Computing and Problem Solving
Motion of a Projectile
Laws of motion describing the trajectory of an object with initial velocity of v0 m/s at an angle of ! Appears in two of the problems of HW#2
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.4
Motion of a Projectile (cont.)
Initial velocity v0 has horizontal and vertical components
v0 x = v0 cos ! and v0 y = v0 sin !
Vertical motion is governed by
1 v y = v0 y ! gt and y = v0 y t ! gt 2 2
Highest point is reached when
t hmax =
v0 y g
and hmax =
v
2 0y
2g
2009 - 6.5
CSCI0040 - Introduction to Scientific Computing and Problem Solving
Motion of a Projectile (cont.)
Total flying time: solve for y = 0 2v0 y 1 2 y = v0 y t ! gt = 0 or ttot = = 2t hmax 2 g Horizontal velocity is constant and position is
x = v0 x t
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.6
Linear indices
m " n array
Elements are stored in column major order One-dimension alternative indexing A=[0 2 3;4 5 0]; A(5) is equal to A(1,3)=3
Some functions use linear indices
Referencing to elements of arrays according to their column major order E.g., find(A) returns column vector [2 3 4 5]
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.7
Example 5-1 Analysis of Temperature Data
The U.S. National Oceanic and Atmospheric Administration (NOAA) reports the daily maximum temperatures for Washington, D.C. in April 2002 were:
58 73 73 53 50 48 56 73 73 66 69 63 74 82 84 91 93 89 91 80 59 69 56 64 63 66 64 74 63 69
Find
Number of days the temperature was above 75 Number of days the temperature was between 65 and 80 Days of the month the temperature was between 50 and 60
m-files: Ex5_1
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.8
If-end
...| ...| MATLAB commands ...| if conditional expression ...| ...| MATLAB commands ...| end ...| ...| MATLAB commands ...|
False
if True
Commands
m-files: Ex5_2
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.9
If-else-end
...| ...| MATLAB commands ...| if conditional expression ...| ...| Group 1 commands ...| else ...| ...| Group 2 commands ...| end ...| ...| MATLAB commands ...|
2009 - 6.10
False
if True
Commands Group 2
Commands Group 1
CSCI0040 - Introduction to Scientific Computing and Problem Solving
Example 5-3 Water Level in a Tower
A water tower has a cylindrical base and upper section that is an inverted frustum cone Write a script that calculates the volume of water in the tank given the water level height h provided by the user Water height h has two components, hcyl and hcone
2 Vcyl = ! rcyl hcyl
Vcone = where
! hcone 2 (r1 + r1r2 + r22 ) 3
10.5 hcone 14
r1 = rcyl and r2 = rh = r1 +
m-files: Ex5_3
2009 - 6.11
CSCI0040 - Introduction to Scientific Computing and Problem Solving
If-elseif-else-end
False
if
True
False
elseif
True
Commands Group 3
Commands Group 2
Commands Group 1
...| ...| MATLAB commands ...| if conditional expression ...| ...| Group 1 commands ...| elseif conditional expression ...| ...| Group 2 commands ...| else ...| ...| Group 3 commands ...| end ...| ...| MATLAB commands ...|
In general: elseif can appear 0 or more times and else at most once) Nesting is possible: conditional statements are commands themselves!
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.12
switch
Expression is scalar or string Many cases can be included Statements associated with first matching case are executed If no matches, otherwise group is executed At most one group (block) is executed Each case may include more than one value to test matching: {valueA, valueB}
switch switch expression case value1 ...| ...| Group 1 commands ...| case value2 ...| ...| Group 2 commands ...| case value3 ...| ...| Group 3 commands ...| otherwise ...| ...| Group 4 commands ...| m-files: lect5_12 end
2009 - 6.13
CSCI0040 - Introduction to Scientific Computing and Problem Solving
Visualizing Data
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.14
plot Command
plot(x,y) where x and y are vectors with same number of elements plot(x,y,'line specifiers', 'PropertyName', PropertyValue) Line Specifiers
Style: solid, dashed, dotted, dash-dot Color: red, green, blue, cyan, Marker: etc. plus, circle, asterisk, point, square, etc. doc plot
m-files: lect6_1
2009 - 6.15
CSCI0040 - Introduction to Scientific Computing and Problem Solving
plot Command (cont.)
plot(x,y,'line specifiers', 'PropertyName', PropertyValue) Property Name and Value
LineWidth MarkerSize MarkerEdgeColor MarkerFaceColor doc plot
m-files: lect6_2
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.16
Plotting Functions
plot command
Create vector of values using function Plot it
y = 3.5"0.5 x cos(6 x) for " 2 ! x ! 4
Copy Figure in Edit menu
m-files: lect6_3
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.17
Plotting Functions
fplot command
fplot('function','limits','line specifiers')
Function typed as a string using any letter as the independent variable
'8*x^2+5*cos(x)' '8*t^2+5*cos(t)'
Can't include any previously defined variables. Limits is a vector
[xmin, xmax] or [xmin, xmax, ymin, ymax] Example
y = x 2 + 4 sin( 2 x) " 1 for " 3 ! x ! 3
CSCI0040 - Introduction to Scientific Computing and Problem Solving
m-files: lect6_3
2009 - 6.18
Multiple Graphs
Using plot command
If x, y, u, v, t, h are pairs of vectors of equal length plot(x,y,u,v,t,h) A function and its first and second derivatives. A derivate describes how a function changes as its dependent variable changes (e.g., position, velocity, acceleration) y = 3 x 3 " 26 x + 10
Example
y! = 9 x 2 " 26 y!! = 18 x
CSCI0040 - Introduction to Scientific Computing and Problem Solving
m-files: lect6_4
2009 - 6.19
Multiple Plots (cont.)
hold command
Plot first graph Type hold on Plot additional graphs Type hold off
line command
Like plot command but adds graphs to existing plot line(x,y,'PropertyName',PropertyValue) Use plot first then line commands
m-files: lect6_5, lect6_6
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.20
Formatting Plots
Labels xlabel('horizontal axis text') ylabel('vertical axis text') Title title('title text') General text text(x, y,'text to go at (x,y)')
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.21
Formatting Plots (cont.)
Legends legend('label1', 'label2',,pos)
where pos specifies location (see Help)
Text formatting
Style: bold, italic, fonts Subscripts and superscripts Greek characters Color
CSCI0040 - Introduction to Scientific Computing and Problem Solving
2009 - 6.22
Formatting Plots (cont.)
Axis formatting axis([xmin, xmax, ymin, ymax]) axis equal axis square axis tight Grid grid on grid off Plot Editor
CSCI0040 - Introduction to Scientific Computing and Problem Solving
m-files: lect6_7
2009 - 6.23
Logarithmic Plots
Present data over a wide range of values semilogy(x, y) log (base 10) for y semilogx(x, y) log (base 10) for x loglog(x, y) log (base 10) for both Line specifiers and Property Names can be applied
y=2
( "0.2 x +10 )
for 0.1 ! x ! 60
m-files: lect6_8
2009 - 6.24
CSCI0040 - Introduction to Scientific Computing and Problem Solving
Error Bars in Plots
Shows scatter or uncertainty in data Vertical line attached to data point Can extend equally above and below the point or be asymmetric errorbar(x, y, e) e is vector of error values errorbar(x, y, u, l) u, l are vectors of upper and lower error bounds
m-files: lect6_9
CSCI0040 - Introduction to Scientific Computing and Problem Solving 2009 - 6.25
Special Plots
...