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Introduction to MATLAB
- Very sophisticated āgraphing calculatorā
- High-level programming language for sci- entific computing
- Similar to PYTHON, with more built-in BUT not open-source
- vs. c or FORTRAN, many built-in com- mands, less-complex syntax
- vs. c or FORTRAN, Interpreted language (code translated during run), with some pre- compiled functions
- IF used carefully, good balance of speed and ease of use
Our introduction follows, in part, section 1 of the excellent āAn introduction to Matlab for dynamic modelingā by Guckenheimer and Ell- ner: www.cam.cornell.edu/ ā¼ dmb/DMBsupplements.html, as well as mate- rial from Prof. Mark Goldman, UC Davis
Launch matlab! Command window (graphing calculator) mode
1+ ans = 4
Assigning values to variables
a=1+ a = 4 Displaying values a a = 4 Suppressing display of output in MATLAB a=1+3;
BASIC OPERATIONS:
Arithmetic
/ (divide)
- (multiply) Ė (exponent) abs(x) (absolute value) cos(x), sin(x), tan(x) exp(x) exponential function eĖx log(x) log to base e sqrt(x) square root
The latter are built-in functions
a = sqrt(5) a = 1. a=2 ; b=4 ; c=aĖb c = 16
There are also some built-in variables
pi ans = 3. cos(pi) ans = -
Variable names:
a1= my_favorite_variable_number_2=
VALID: Letter followed by letters, numbers, un- derscore character. NOTE! capitalization matters. A 6 = a !!
NOT VALID:
my_favorite_variable#2= ??? my_favorite_variable#2= 2a= Error: Unexpected MATLAB expression.
And using periods gives a different, more advanced type of variable (data structure) that we wonāt discuss now
my.favorite.variable.name= my = favorite: [1x1 struct]
ORDER OF OPERATIONS:
PEMDAS
parenthesis exponentiation multiplication division addition subtraction Say we want: a = 2 , b = 4 , c = (^) a+ab
a=1 ; b=4 ; c=a/a+b c = 5
a=1 ; b=4 ; c=a/(a+b) c = 0. !! When in doubt, put lots of parentheses !!
CHECK: What do you get for the below, and why?
a=1 ; b=4 ; c =0 ; d=a/0+b d=a/(0+b) d=-aĖ d=(-a)Ė
Representation of numbers in scientific computing: finite precision Standard: IEEE floating point arithmetic. Important feature ā finite precision: approx 16 significant digits
Display more digits:
a=0. a =
format long a a = 0.
Roundoff error:
a=4/3 ; b=a-1 ; c = (3*b)-
c =
-2.220446049250313e-
OVERFLOW AND UNDERFLOW:
Maximum number: ā 10308 Minimum number: ā 10 ā^308 Overflow:
a=10Ė a = Inf
Underflow
a=10Ė- a = 0
Another special number: not defined
ans = NaN
VECTORS
A vector value is just a list of scalar values. Arranged horizontally into a row vector:
~x = (6 12 5). (1) Or vertically into a column vector:
~x =
In MATLAB, row vector:
x=[6 12 5] x = 6 12 5
OR
x=[6 ,12 ,5] x = 6 12 5
In MATLAB, column vector:
x=[6 ; 12 ; 5]
x =
6 12 5
The transpose operation switches between row and column vectors. This is given by dot prime in MATLAB. That is, in MATLAB:
y=x.ā
Exercise 0.1 : Have MATLAB compute the values of
- Make a list numbers spaced by 0.2, between a minimum value of 1 and a maximum value of 20. Assign that list to the variable name myvector.
- use help to look up the linspace command, and repeat the previous command using linspace
- pick out the 4th value of myvector and assign it to the variable name fourthelement
TWO BASIC OPERATIONS ON VECTORS:
Multiplication by scalar
c~x =
x 1 x 2 x 3
cx 1 cx 2 cx 3
ļ£ø; that is, xj ā c xj
Matlab *
x=[1;2;3] ; 3*x
ans = 3 6 9
Addition of two vectors
~x + ~y =
x 1 + y 1 x 2 + y 2 x 3 + y 3
Subtraction similar
Works the same for row and column vectors
Matlab + and -
x=[1;2] ; y=[0;-2]; z=x+y z = 1 0 z+ [2 2] ??? Error using ==> plus
Matrix dimensions must agree: add row + row or col + col
CAUTION! Multiplication of vectors does NOT work the same way ... more later (matrix- vec- tor multiplication)
FUNDAMENTAL CONCEPT: Matrix-vector multiplication
( A 1 , 1 A 1 , 2 A 2 , 1 A 2 , 2
x 1 x 2
= x 1
A 1 , 1
A 2 , 1
A 1 , 2
A 2 , 2
e.g. (^) ( 1 1 1 2
In general, ļ£« ļ£
a 1 Ā· Ā· Ā· an | Ā· Ā· Ā· |
x 1 ... xn
j
xj
aj |
Exercise 0.3 : Compute the below by hand ...
MATLAB * operator
A=[1 1 ; 1 2] ; A*[1 ; 2]
ans =
3 5
In y = Ax, A must have same number of columns as x has rows. Nonsense:
( 1 1 1 2
>> A=[1 1 ; 1 2] ; A*[1 ; 2 ; 4]
??? Error using ==> mtimes Inner matrix dimensions must agree.
Exercise 0.4 :
- Check your answers to the hand calcula- tions from the previous exercise, using MAT- LAB.
PLOTTING
- Plotting is MATLAB is great, and best learne just by doing ...
- Write a program plot_a_sin_wave.m tha plots sin(x) from x = āĻ to x = Ļ. HINT: type doc plot!
The for loop
Use for repeated operations. Basic structure: MATLAB CODE
for n= 1: disp(n) end
- Use edit to code this into a program myloop.m, save it and run it!
COMPONENTS OF THE FOR LOOP:
n loop variable 1:3 loop vector disp(n) or print(n) command
Code starts with n equal to first element in loop vector runs command advances n to next element repeats quits when have covered all elements of loop vector
In more detail:
- in any for loop, we define a list of numbers, here 1 through 9. think of this as the āloop vector.ā The loop vector can be any list of numbers ā it does not have to be āintegers counting up.ā
- the loop variable, n, starts at the first num- ber in the list. it is set equal to that value
- the commands (here, just printing the value of n to the screen) are run
- then when end is reached, n is reset to the NEXT number in the list, the commands are run, and the process is repeated
- it terminates when all entries of the loop vector have been used.
Run and describe what happens for these examples:
for p=[4 6 67 -1] disp(p) end
for k=1:2: disp(k) end
a= for k=1: a=a+k end
