Skip to content
Permalink
3f676141d4
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?

ME3255S2017/lecture_04/lecture_4.md

Go to file
 
 
Cannot retrieve contributors at this time
309 lines (214 sloc) 8.61 KB
Raw Blame
```matlab
## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
```
Error: The input character is not valid in MATLAB statements or expressions.

```matlab
%myscript
```
```matlab
%plot --format svg
```
When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both
Creating a default graph script: `setdefaults.m`
```matlab
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
```
```matlab
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
```
```matlab
t_linear=linspace(0,10,100);
plot(t_linear,t_linear.^2)
xlabel('time (s)')
ylabel('displacement (m)')
```
![png](output_5_0.png)
#EOL
## Graphics can be produced with a number of functions
2-D plots, 3-D plots, contour plots, 3D contour plots ...
```matlab
x=linspace(-1,1,21); y=linspace(-1,1,21);
[X,Y]=meshgrid(x,y);
Z=(X.*Y.^3-X.^3.*Y)
```
Z =
Columns 1 through 7
0 0.1710 0.2880 0.3570 0.3840 0.3750 0.3360
-0.1710 0 0.1224 0.2016 0.2430 0.2520 0.2340
-0.2880 -0.1224 0 0.0840 0.1344 0.1560 0.1536
-0.3570 -0.2016 -0.0840 0 0.0546 0.0840 0.0924
-0.3840 -0.2430 -0.1344 -0.0546 0 0.0330 0.0480
-0.3750 -0.2520 -0.1560 -0.0840 -0.0330 0 0.0180
-0.3360 -0.2340 -0.1536 -0.0924 -0.0480 -0.0180 0
-0.2730 -0.1944 -0.1320 -0.0840 -0.0486 -0.0240 -0.0084
-0.1920 -0.1386 -0.0960 -0.0630 -0.0384 -0.0210 -0.0096
-0.0990 -0.0720 -0.0504 -0.0336 -0.0210 -0.0120 -0.0060
0 0 0 0 0 0 0
0.0990 0.0720 0.0504 0.0336 0.0210 0.0120 0.0060
0.1920 0.1386 0.0960 0.0630 0.0384 0.0210 0.0096
0.2730 0.1944 0.1320 0.0840 0.0486 0.0240 0.0084
0.3360 0.2340 0.1536 0.0924 0.0480 0.0180 0.0000
0.3750 0.2520 0.1560 0.0840 0.0330 0 -0.0180
0.3840 0.2430 0.1344 0.0546 -0.0000 -0.0330 -0.0480
0.3570 0.2016 0.0840 0 -0.0546 -0.0840 -0.0924
0.2880 0.1224 0 -0.0840 -0.1344 -0.1560 -0.1536
0.1710 0.0000 -0.1224 -0.2016 -0.2430 -0.2520 -0.2340
0 -0.1710 -0.2880 -0.3570 -0.3840 -0.3750 -0.3360
Columns 8 through 14
0.2730 0.1920 0.0990 0 -0.0990 -0.1920 -0.2730
0.1944 0.1386 0.0720 0 -0.0720 -0.1386 -0.1944
0.1320 0.0960 0.0504 0 -0.0504 -0.0960 -0.1320
0.0840 0.0630 0.0336 0 -0.0336 -0.0630 -0.0840
0.0486 0.0384 0.0210 0 -0.0210 -0.0384 -0.0486
0.0240 0.0210 0.0120 0 -0.0120 -0.0210 -0.0240
0.0084 0.0096 0.0060 0 -0.0060 -0.0096 -0.0084
0 0.0030 0.0024 0 -0.0024 -0.0030 0
-0.0030 0 0.0006 0 -0.0006 0 0.0030
-0.0024 -0.0006 0 0 0.0000 0.0006 0.0024
0 0 0 0 0 0 0
0.0024 0.0006 -0.0000 0 0 -0.0006 -0.0024
0.0030 0 -0.0006 0 0.0006 0 -0.0030
0 -0.0030 -0.0024 0 0.0024 0.0030 0
-0.0084 -0.0096 -0.0060 0 0.0060 0.0096 0.0084
-0.0240 -0.0210 -0.0120 0 0.0120 0.0210 0.0240
-0.0486 -0.0384 -0.0210 0 0.0210 0.0384 0.0486
-0.0840 -0.0630 -0.0336 0 0.0336 0.0630 0.0840
-0.1320 -0.0960 -0.0504 0 0.0504 0.0960 0.1320
-0.1944 -0.1386 -0.0720 0 0.0720 0.1386 0.1944
-0.2730 -0.1920 -0.0990 0 0.0990 0.1920 0.2730
Columns 15 through 21
-0.3360 -0.3750 -0.3840 -0.3570 -0.2880 -0.1710 0
-0.2340 -0.2520 -0.2430 -0.2016 -0.1224 -0.0000 0.1710
-0.1536 -0.1560 -0.1344 -0.0840 0 0.1224 0.2880
-0.0924 -0.0840 -0.0546 0 0.0840 0.2016 0.3570
-0.0480 -0.0330 0.0000 0.0546 0.1344 0.2430 0.3840
-0.0180 0 0.0330 0.0840 0.1560 0.2520 0.3750
-0.0000 0.0180 0.0480 0.0924 0.1536 0.2340 0.3360
0.0084 0.0240 0.0486 0.0840 0.1320 0.1944 0.2730
0.0096 0.0210 0.0384 0.0630 0.0960 0.1386 0.1920
0.0060 0.0120 0.0210 0.0336 0.0504 0.0720 0.0990
0 0 0 0 0 0 0
-0.0060 -0.0120 -0.0210 -0.0336 -0.0504 -0.0720 -0.0990
-0.0096 -0.0210 -0.0384 -0.0630 -0.0960 -0.1386 -0.1920
-0.0084 -0.0240 -0.0486 -0.0840 -0.1320 -0.1944 -0.2730
0 -0.0180 -0.0480 -0.0924 -0.1536 -0.2340 -0.3360
0.0180 0 -0.0330 -0.0840 -0.1560 -0.2520 -0.3750
0.0480 0.0330 0 -0.0546 -0.1344 -0.2430 -0.3840
0.0924 0.0840 0.0546 0 -0.0840 -0.2016 -0.3570
0.1536 0.1560 0.1344 0.0840 0 -0.1224 -0.2880
0.2340 0.2520 0.2430 0.2016 0.1224 0 -0.1710
0.3360 0.3750 0.3840 0.3570 0.2880 0.1710 0
```matlab
contour(X,Y,Z)
```
![png](output_10_0.png)
```matlab
mesh(X,Y,Z)
```
![png](output_11_0.png)
```matlab
pcolor(X,Y,Z)
```
![png](output_12_0.png)
## Functions
So far, everything has been executed as a script, or calling a built-in function. Now we begin building our own functions.
Functions are saved in memory (or better yet) in a folder in your path or current directory
Example of storing function in memory
$f(x,y) = (xy^{3}-x^{3}y)$
```matlab
f= @(x,y) (x.*y.^3-x.^3.*y)
```
f =
@(x,y)(x.*y.^3-x.^3.*y)
```matlab
f(0.1,-0.5)
```
ans =
-0.0120
Here we will save a function called `my_function` as `my_function.m`
```matlab
function [vx,vy] = my_function(x,y,t)
% Help documentation of "my_function"
% This function computes the velocity in the x- and y-directions given
% three vectors of position in x- and y-directions as a function of time
% x = x-position
% y = y-position
% t = time
% output
% vx = velocity in x-direction
% vy = velocity in y-direction
vx=zeros(length(t),1);
vy=zeros(length(t),1);
vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
vx(end) = vx(end-1);
vy(end) = vy(end-1);
end
```
```matlab
help my_function
```
Help documentation of "my_function"
This function computes the velocity in the x- and y-directions given
three vectors of position in x- and y-directions as a function of time
x = x-position
y = y-position
t = time
output
vx = velocity in x-direction
vy = velocity in y-direction
```matlab
t=linspace(0,10,100)';
x=t.^3; % vx = 3*t^2
y=t.^2/2; % vy = t
[vx,vy]=my_function(x,y,t);
```
```matlab
yyaxis left
plot(t(1:10:end),vx(1:10:end),'o',t,3*t.^2)
ylabel('v_{x}')
yyaxis right
plot(t(1:10:end),vy(1:10:end),'s',t, t)
ylabel('v_{y}')
xlabel('time')
```
![png](output_20_0.png)
Now, create a new function that calls 'my_function' called, `my_caller.m`
```matlab
help my_caller
```
Help documentation of "my_caller"
This function computes the acceleration in the x- and y-directions given
three vectors of position in x- and y-directions as a function of time
x = x-position
y = y-position
t = time
output
ax = velocity in x-direction
ay = velocity in y-direction
```matlab
[ax,ay]=my_caller(x,y,t);
```
```matlab
yyaxis left
plot(t(1:10:end),ax(1:10:end),'o',t,6*t)
ylabel('a_{x}')
yyaxis right
plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t)
ylabel('a_{x}')
xlabel('time')
axis([0,10,0,3])
```
![png](output_24_0.png)
```matlab
diff_match_dims(x,t)
```
Undefined function 'diff_match_dims' for input arguments of type 'double'.

```matlab
```