Engr/Math/Physics 25
Chp5 MATLAB
Plots & Models 2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Learning Goals
 List the Elements of a COMPLETE
Plots
• e.g.; axis labels, legend, units, etc.
 Construct Complete Cartesian (XY)
plots using MATLAB
• Modify or Specify MATLAB Plot Elements:
Line Types, Data Markers,Tic Marks
 Distinguish between INTERPolation
and EXTRAPolation
Engineering/Math/Physics 25: Computational Methods
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Learning Goals cont
 Construct using MATLAB SemiLog
and LogLog Cartesian Plots
 Use MATLAB’s InterActive Plotting
Utility to Fine-Tune Plot Appearance
 Create “Linear-Transform” Math Models
for measured Physical Data
• Linear Function → No Xform
• Power Function → Log-Log Xform
• Exponential Function → SemiLog Xform
Engineering/Math/Physics 25: Computational Methods
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Learning Goals cont
 Use Regression Analysis as quantified
by the “Least Squares” Method
• Calculate
– Sum-of-Squared Errors (SSE or J)
 The Squared Errors are Called “Residuals”
– “Best Fit” Coefficients
– Sum-of-Squares About the Mean (SSM or S)
– Coefficient of Determination (r2)
• Scale Data if Needed
– Creates more meaningful spacing
Engineering/Math/Physics 25: Computational Methods
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Learning Goals cont
 Build Math Models for
Physical Data using
“nth” Degree Polynomials
 Use MATLAB’s “Basic Fitting” Utility to
find Math models for Plotted Data
 Use MATLAB to Produce 3-Dimensional
Plots, including
• Surface Plots
• Contour Plots
Engineering/Math/Physics 25: Computational Methods
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Why Plot?
 Engineering, Math, and Science are
QUANTITATIVE Endeavors, we want
NUMBERS as Well as Words
 Many times we Need to
• Understand The (functional)
relationship between two
or More Variables
• Compare the Values of
MANY Data Values
Engineering/Math/Physics 25: Computational Methods
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Sys3 2X200 MultiBlok, 997671 250-13.8 PreWeld Pi Tube-1
200
Individual Hole  P (10X Torr)
175
Tic Mark Label
150
125
Connecting Line
Axis UNITS
Data Symbol
100
Tic Mark
75
50
25
PARAMETERS
• For Single Tube Manifold
• Flow = ??/0.24 slpm/hole
• Exh to Atm Pressure (~750Torr)
• Test Engr = DNStoddard, BMayer
• Test Date = 09Mar00/10Mar
DNS Tube-1
BMayer Tube1
DNS Normalized
BMayer Normalized
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Hole Number (1 = closest to Manifold Block)
file = HbH997671PreW09Mar00.xls
Engineering/Math/Physics 25: Computational Methods
7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
SubPlots
 The subplot command creates several
smaller “subplots” in the same figure.
 The syntax is subplot(m,n,p)
 This command divides the Figure window into
an array of rectangular panes with m rows
and n columns.
 The variable p tells MATLAB to place the
output of the plot command following the
subplot command into the pth pane.
Engineering/Math/Physics 25: Computational Methods
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
SubPlot Example
 Consider
an End-Loaded Cantilever Beam
y
F
b
x
h
L
 In ENGR36 & ENGR45 we will learn how the
Applied Force-Load, F, affects the Beam
Engineering/Math/Physics 25: Computational Methods
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
y
F
b
SubPlot Example
h
L
 By the ENGR36 &
ENGR45 Methods
Analyze how the
load affects the
Beam in Terms of
• SHEARING Force, V
• BENDING-Moment,
M
• Vertical
DEFLECTION, y
Engineering/Math/Physics 25: Computational Methods
10
 The V, M, and y
functions vs the
Normalized
Distance Dimension
x/L
V x  F
 1
Vmax
F
M ( x) F  x  L  x  L x


 1
M max
FL
L
L
3
2
2
y x  1  x 
 x   1  x   x  
    3         3
ymax 2  L 
 L   2  L   L  
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
x
y
F
SubPlot Example
b
h
L
 We Want to Plot V,
M, and y ON TOP of
each other vs the
common
independent
Variable, x/L
 This is a perfect
Task for subplot
 First Construct the
functions
Engineering/Math/Physics 25: Computational Methods
11
>> XoverL = [0:0.01:1];
V = ones(1,
length(XoverL))
>> M = XoverL - 1;
>> y =
0.5*((XoverL).^2)
.*(XoverL -3);
• Note the use of the
ones Command to
construct the
Constant Shear (V)
vector
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
x
y
F
b
SubPlot Example
h
L
 Next Make 3 subplots in an array with
THREE Rows and ONE Column
>> subplot(3,1,1)
>> plot(XoverL,V), xlabel('x/L'),
ylabel('V/Vmax'),...
title('Cantilever Beam - Shear'), grid
>> subplot(3,1,2)
>> plot(XoverL,M), xlabel('x/L'),
ylabel('M/Mmax'),...
title('Cantilever Beam - Bending'), grid
>> subplot(3,1,3)
>> plot(XoverL,y), xlabel('x/L'),
ylabel('y/ymax'),...
title('Cantilever Beam - Deflection'), grid
Engineering/Math/Physics 25: Computational Methods
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
x
SubPlot Result
Cantilever Beam - Shear
V/Vmax
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/L
Cantilever Beam - Bending
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.8
0.9
1
M/Mmax
0
-0.5
-1
0.5
0.6
0.7
x/L
Cantilever Beam - Deflection
y/ymax
0
-0.5
-1
Engineering/Math/Physics 25: Computational Methods
13
0.5
x/L
0.6
0.7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Data-Markers & Line-Types
 The Data Marker and Line Type specifications
in a Plot consist of optional Fields in the Basic
plot statement
 To plot y versus x with a solid line, and then
v versus u with a dashed line, type
plot(x,y,u,v,’--’)
• The symbols ’--’ represent a dashed line
 To plot y versus x with asterisks (*) connected
with a dotted line, we must plot the data twice
by typing plot(x,y,’*’,x,y,’:’).
Engineering/Math/Physics 25: Computational Methods
14
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
DataMark & LineType Example
 To plot y versus x
with green asterisks
(*) connected with a
red dashed line,
again plot the data
twice by typing
plot(x,y,’g*’,x
,y,’r--’)
 Consider a
PolyStryene
Cantilever Beam (c.f.
sld-8) Heavily Loaded
for a “long” time
 Example:
Mechanical Creep
Engineering/Math/Physics 25: Computational Methods
15
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
DataMark & LineType Example
 We Would Like to
plot the Vertical
Deflection, Y, versus
time, t, for a Constant
Load using
• Blue Colored Data
Makers in the from
of a + mark
• Magenta Colored
Dash-Dot (- .) Line to
connect the Data
Points
Engineering/Math/Physics 25: Computational Methods
16
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
DataMark & LineType Example
 The Command Session for the Creep Plot
• The Data Set as Row Vectors
>> delY_mm = [0, 2, 4, 4.5, 5.5, 6, 6.5, 8, 9, 11];
>> t_min = [0, 2, 4, 6, 9, 12, 15, 18, 21, 24];
• The Plot Statement
>> plot(t_min,delY_mm, ’b+’, t_min,delY_mm,
'm-.’),...
xlabel('Load Application Time, t (min)'),...
ylabel('Vertical Deflection, y (mm)'),...
title('Polystrene Cantilever Beam Creep'), grid
• Notice the Data
is plotted Twice
Engineering/Math/Physics 25: Computational Methods
17
• Notice also the BluePlus, and Magenta
Dash-Dot Specs
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
DataMaker & LineType Result
Polystrene Cantilever Beam Creep
12
Vertical Deflection, y (mm)
10
8
6
4
2
0
0
5
10
15
Load Application Time, t (min)
Engineering/Math/Physics 25: Computational Methods
18
20
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
25
More: Markers, Lines, Colors
 MATLAB Provides a Wide Range of Options
for Plot-Lines & Plot-Markers
Data markers†
Dot (.)
Asterisk (*)
Cross ()
Circle ( )
Plus sign (+)
Square ( )
Diamond ( )
Five-pointed star ()
Line types
.
*

+
s
d
p
Solid line
Dashed line
Dash-dotted line
Dotted line
Colors
––
––
–.
….
Black
Blue
Cyan
Green
Magenta
Red
White
Yellow
k
b
c
g
m
r
w
y
†Other
data markers are available. Search for “markers” or “LineSpec” in
MATLAB help.
 Don’t forget the 'LineWidth', n Command
to make thicker lines
Engineering/Math/Physics 25: Computational Methods
19
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Labeling Curves
 The legend command automatically obtains
from the plot the line type used for each data
set and displays a sample of this line type in
the legend box next to the selected text-string
 For Example again
Consider RLC
Circuit “Ringing”
V t   9V e 0.3t cos13t
Engineering/Math/Physics 25: Computational Methods
20
 We Now wish to plot
e−0.3t to Show the
ENVELOPE of
Exponential Decay
d t   9V e
0.3t
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Labeling Curves Example
 Use Defaults for the main Function, V(t)
 Use Red, Dashed (--) Lines for the d(t) Decay
 The Calc and Plot statements
>> t = [0:0.02:9];
>> V_t = (exp(-0.3*t)).*(9*cos(13*t));
>> d1 = 9*exp(-0.3*t);
>> d2 = -9*exp(-0.3*t);
>> plot(t,V_t, t, d1, 'r--', t, d2, 'r--'),
xlabel('t'),...
ylabel('V'), title('RLC Repsonse'),grid,...
legend('Sinusoidal Oscillations',
’Exponential Decay')
Engineering/Math/Physics 25: Computational Methods
21
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
legend Use Result
RLC Repsonse
10
Sinusoidal Oscillations
Exponential Decay
8
6
4
2
V
0
-2
-4
-6
-8
-10
0
1
2
3
4
5
t
Engineering/Math/Physics 25: Computational Methods
22
6
7
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
9
Labeling Curves with gtext
 The gtext Command allows
the USER to Place the curve
Labels at Any Location on
the Plot with the Mouse.
 Let’s use gtext(‘string’)
to Label the Decaying
Sinusoid Plot with Labels
Located in Close Proximity
with the two Curves
Engineering/Math/Physics 25: Computational Methods
23
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
gtext Use Result
RLC Repsonse
10
8
6
Exponential Decay
4
Sinusoid
V
2
0
-2
-4
Exponential Decay
-6
-8
-10
0
1
2
3
4
5
6
7
8
t
Engineering/Math/Physics 25: Computational Methods
24
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
9
The hold command TYU T5.2-5
 The hold
Command “Freezes”
plots for subsequent
modification.
 Illustrate by T5.2-5
Example
 Say we Want to Plot
over 0x1
 Over this Range
These functions are
too difficult to
Distinguish for gtext
Labeling
 Solution →
• Plot & Label y1 First
• Plot & Label y2 2nd
y1  sin x
y2  x  x 3
3
Engineering/Math/Physics 25: Computational Methods
25
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Making BETTER Plots

The following actions, while not
required, can nevertheless improve
the appearance & clarity of your plots:
1. Start scales from Zero when possible
– This prevents a false impression of the
magnitudes of variations shown on the plot

Invalid if we want to emphasize DIFFERENCES
2. Use sensible tick-mark spacing
– If the quantities are months, choose a spacing
of 12 because 1/10 of a year is not a
convenient division.
Engineering/Math/Physics 25: Computational Methods
26
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Making BETTER Plots cont
– Tic marks should be Neither “Too” Course/Fine
3. Minimize the number of Zeros and
Scientific-Notation in the data being plotted
– For example, use a scale in µW (microWatts) to
show Power Data Ranging Over 0.000011 –
0.000137 Watts (11 – 137 µW)
4. Determine the min & max data values for
each axis before plotting the data. Then set
the axis limits to cover the entire data range
(or Span) plus an additional amount to
allow for clearly understood tick-marking
Engineering/Math/Physics 25: Computational Methods
27
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Making BETTER Plots cont
– e.g; if the data on the x-axis ranges from 1.2
to 9.6, a good choice for axis limits is 0 to 10
 This choice permits a tick spacing of 1 or 2.
5. Use a different line type for each curve
when several are plotted on a single plot
and they cross each other;
– For example, use a solid line, a dashed line,
and combinations of lines and symbols.
 Beware of using colors to distinguish plots if
you are going to make black-and-white printouts
and/or photocopies.
Engineering/Math/Physics 25: Computational Methods
28
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Making BETTER Plots cont
6. Do not put too many curves on one plot,
particularly if they will
– Be close to each other
– Cross one another at several points.
7. Use the same scale limits and tick
spacing on each plot if you, or the plot
Users, need to compare information on
more than one plot.
– This is VERY Important
 The Instructor Made this Mistake on the 1st Draft of
His 1st Publication – Luckily a colleague spotted
the error during her careful review of the draft
Engineering/Math/Physics 25: Computational Methods
29
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Proper Comparison Scaling
Same Scales
Same Scales
Same Scales
Engineering/Math/Physics 25: Computational Methods
30
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Select Plot: WorkSpace Browser
>> a = linspace(0,10,500);
>> y = 4*cos(a)-22*sin(1.5*a+4);
Engineering/Math/Physics 25: Computational Methods
31
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Select Plot: WorkSpace Browser
 Results can be a Plot of your choice
>> B =[7, 19, 23, 3 ,17, 11]
B =
7
Engineering/Math/Physics 25: Computational Methods
32
19
23
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
17
11
Other Useful Plots
Command
bar(x,y)
plotyy(x1,y1,x2,y2)
Plot Description
Bar chart of y versus x.
Produces a plot with two y-axes,
y1 on the left and y2 on the right
Polar plot from the polar
coordinates theta and r, using
polar(theta,r,’type’) the line type, data marker, and
colors specified in the string
type.
stairs(x,y)
Stairs plot of y versus x
stem(x,y)
Engineering/Math/Physics 25: Computational Methods
33
Stem plot of y versus x.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Column & Bar Chart
 MATLAB Col Chart
 MATLAB Bar Chart
25
>> Y = round(rand(5,3)*10);
>> bar(Y,'stack')
5
20
4
15
y
3
10
2
5
1
3
sin(x)
x-x /3
3
x
4
5
6
0
1
18
t0 = Dep-On Time
Tcln
Thc
16
System Description
14
12
10
8
6
3
4
5
6
7
Key Model Parameters (Cons/Opt)
47.96
• Adm = 4663/5362 Å-mm/s
• Heat/Cool/Handling OH = 100/60 s/Dep-Cycle
63.76 • NF3 flow per aF-Gen = 1.2/1.2 slpm
42.36
62.48
file = ThruPut_Calc.xls
2
• Clean Efficiency = 2222/2222 scc-R/litre-NF3
• Clean Pre & Post Pumping & Venting = 4.8/3 min
• 1 Astron per MultiBlok
• Wfrs Between Cln = 5/15 (< 2.5/7.5 µm)
• Lch assumes moveable (up/dwn) ceiling over the
wafer load position
47.56
Conservative
72.68
Optimistic
63.54
93.72
6Ch-LT
2@3X
4
71.34
109.02
0
USG: mill sys3
USG: 2@3X/1
USG:2@3X/2
BPSG: mill sys3
BPSG: 2@3X/1
BPSG:2@3X/2
Engineering/Math/Physics 25: Computational Methods
34
2
APNext™ Advanced Architecture for 300mm/5kÅ-BPSG • Jun00
4Ch MillSys3
(200mm)
2
Wafer Processing Time Budget for 8k-USG and 5k-BPSG • Apr00
20
4Ch 1@3X
1
6Ch-T 1@3X 4Ch-L 2@3X
0
Processing Time (min/wafer)
0
0
20
40
60
80
100
120
Bruce Mayer, PE
System ThruPut for 300mm Wafers (wph)
file = ThruPut_Calc.xls
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
8
9
10
Greek Letters on Plots (ΠΣλξ)
 Use the “\” then a “Character Sequence”
in a Labeling Field
Engineering/Math/Physics 25: Computational Methods
35
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Greek Letters on Plots (ωφΘΔ)
 Use the “\” then a “Character Sequence”
in a Labeling Field
Character Sequence Symbol Character Sequence Symbol Character Sequence Symbol
\rho
\forall
\partial
\sigma
\exists
\bullet
•
\varsigma
\ni
\div
÷
\tau
\cong
\neq
\equiv
\approx
\aleph
\Im
\Re
\wp
\otimes
\oplus
\oslash
\cap
\cup
\supseteq
\supset
\subseteq
\subset
\int
\in
\o
\rfloor
\lceil
\nabla
\lfloor
\cdot
·
\ldots
...
\perp
\neg
¬
\prime
'
\wedge
\times
x
\0
\rceil
\surd
\mid
|
\vee
\varpi
\copyright
©
\langle
\rangle
Engineering/Math/Physics 25: Computational Methods
36
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
In the Greek….
ENGR25 • Engr Honor Soc  --
6
4
 =  ( )
2
0
-2
-
-4
-6
-6
-4
-2
Engineering/Math/Physics 25: Computational Methods
37
0

2
4
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Engineering/Math/Physics 25: Computational Methods
38
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Greek Code
% Bruce Mayer, PE
% ENGR-25 • 02Jul13
% XY_fcn_Graph_6x6_BlueGreen_BkGnd_Template_1306.m
%
% The FUNCTION
x = linspace(-6,6,500); y = -x.^2/3 +5.5;
%
% The ZERO Lines
zxh = [-6 6]; zyh = [0 0]; zxv = [0 0]; zyv = [-6 6];
%
% the 6x6 Plot
axes; set(gca,'FontSize',12);
whitebg([0.8 1 1]); % Chg Plot BackGround to Blue-Green
plot(x,y, zxv,zyv, 'k', zxh,zyh, 'k', 'LineWidth',
3),axis([-6 6 -6 6]),...
grid, xlabel('\fontsize{18}\Theta'),
ylabel('\fontsize{18}\Psi = \phi(\Theta)'),...
title(['\fontsize{16}ENGR25 • Engr Honor Soc
\rightarrow \tau-\beta-\pi',]),...
annotation('textbox',[.70 .25 .0 .1], 'FitBoxToText',
'on', 'EdgeColor', 'none', 'String', '\infty','FontSize',48)
Plot Additions  hold non/off
 Use the hold command to add lines,
markers, and others with DIFFERENT
formatting to an Existing Plot
 Some Help Searches that assist with
formatting
• Text Properties
• LineSpec
Engineering/Math/Physics 25: Computational Methods
39
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Example  hold non/off
ENGR25 • Bruce Mayer, PE • HOLD
y  ()
10
9
8
7
6
XY f cnGraphBlueGreenBkGndSolidMarkerTemplate1306.m
5
4
3
2
1
0
-1
-2
-3
-4
-3
-2
-1
Engineering/Math/Physics 25: Computational Methods
40
0

1
2
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
hold non/off Code
% Bruce Mayer, PE
% ENGR-25 • 01Jul13
% XY_fcn_Graph_BlueGreenBkGnd_Solid_Marker_Template1306.m
%
% The Limits
xmin = -3; xmax1 = 1; xmin2 = xmax1; xmax = 3; ymin = -4; ymax = 10;
% The FUNCTION
x1 = linspace(xmin,xmax1,500); y1 = 1-x1.^2;
x2 = linspace(xmin2,xmax,500); y2 = 3*x2+1;
%
% The ZERO Lines
zxh = [xmin xmax]; zyh = [0 0]; zxv = [0 0]; zyv = [ymin ymax];
%
% the BASE Plot
axes; set(gca,'FontSize',12);
whitebg([0.8 1 1]); % Chg Plot BackGround to Blue-Green
plot(x1,y1,'b', x2,y2,'b', x1(end),y1(end), 'ob', 'MarkerSize', 16,
'MarkerFaceColor', [0.8 1 1],...
'LineWidth', 5),axis([xmin xmax ymin ymax]),...
grid, xlabel('\fontsize{16}\chi'), ylabel('\fontsize{16}y \equiv
\phi(\chi)'),...
title(['\fontsize{16}ENGR25 • Bruce Mayer, PE • HOLD',]),...
annotation('textbox',[.15 .8 .0 .1], 'FitBoxToText', 'on', 'EdgeColor',
'none', 'String',
'XYfcnGraphBlueGreenBkGndSolidMarkerTemplate1306.m','FontSize',7)
%
% Turn-ON hold to ADD to BASE Plot Lines & Markers of different formats
hold on
plot(x2(1),y2(1), 'ob', 'MarkerSize', 11, 'MarkerFaceColor', 'g')
plot(zxv,zyv, 'k', zxh,zyh, 'k', 'LineWidth', 3)
plot([xmin xmax], [4 4], '-.m', [1 1], [ymin ymax], '-.m', 'LineWidth', 2)
set(gca,'XTick',[xmin:1:xmax]); set(gca,'YTick',[ymin:1:ymax])
hold off
Dual Y-Axis Plot

8%
40
y = -0.0048x2 + 0.9162x
R2 = 0.9989
6%
30
p
4%
20
y = 9E-07x2 - 0.0004x + 0.0582
R2 = 0.9885
2%
10
Relative molar source vapor concentrations held constant:
CS = 78.5% • CB = 12.1% • CP = 9.4%
0%
0
20
30
40
50
60
70
80
90
Source Chemical Flow Rate, Qv,tot (sccm)
Engineering/Math/Physics 25: Computational Methods
42
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
-2
-1
b
(nmol•cm •s )
50
y = -5E-06x2 + 0.0009x + 0.0556
R2 = 0.983
BPSG Depostion Rate,
BPSG Film Doping, b & p (mol% oxide)
10%
poltyy in MATLAB
Engineering/Math/Physics 25: Computational Methods
43
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
stairs Plot – sin(x)
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
>> x=0:0.25:10;
>> stairs(x,sin(x));
-0.8
-1
0
1
2
3
4
Engineering/Math/Physics 25: Computational Methods
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5
6
7
8
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
10
stem Plot -
x
y  e sin x
2
0.35
>> x = 0:0.1:4;
>> y = sin(x.^2).*exp(-x);
>> stem(x,y)
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
0
0.5
1
1.5
Engineering/Math/Physics 25: Computational Methods
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2
2.5
3
3.5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
4
TYU T5.3-3 Polar Plot
 Archimedes Spiral
r  2
 The BMayer Plot
: 0    4
Spiral of Archimedes
90
120
 The interactive
Session
>> theta =
linspace(0, 4*pi, 500);
>> a = 2;
>> r = a*theta;
>> subplot(1,1,1)
>> polar(theta, r),
title('Spiral of
Archimedes')
60
20
150
30
10
180
0
210
330
240
Engineering/Math/Physics 25: Computational Methods
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30
300
270
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
All Done for Today
SeaShell
Built on
Archimedes
Spiral
Engineering/Math/Physics 25: Computational Methods
47
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
Engr/Math/Physics 25
Appendix
f x   2 x  7 x + 9 x  6
3
2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
48
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
gtext Demo
 The Command Session
>> t = [0:0.02:9];
>> V_t = (exp(-0.3*t)).*(9*cos(13*t));
>> d1 = 9*exp(-0.3*t);
>> d2 = -9*exp(-0.3*t);
>> plot(t,V_t, t, d1, 'r--', t, d2, 'r--'),
xlabel('t'),...
ylabel('V'), title('RLC Repsonse'),grid,...
gtext('Sinusoid'), gtext('Exponential Decay'),...
gtext('Exponential Decay')
• TWO “Exponential Decay” Labels; one each for the
TOP and BOTTOM Curves
– Demo_Chp5_gtext_6010.m
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
hold Demo
0.9
>> x = [0:0.01:1];
>> y1 = sin(x); y2 = x-x.^3/3;
>> plot(x,y1),
gtext('sin(x)'), hold,
plot(x,y2), xlabel('x'),...
ylabel('y'), gtext('x-x^3/3')
Current plot held
0.8
0.7
0.6
x-x 3/3
y
0.5
sin(x)
0.4
Formatting Info
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
Engineering/Math/Physics 25: Computational Methods
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0.5
x
0.6
0.7
0.8
0.9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-2.ppt
1