Transcript INTRODUCTION TO MATLAB Dr. Hugh Blanton ENTC 4347
INTRODUCTION TO MATLAB
Dr. Hugh Blanton ENTC 4347
TOPICS
1.
2.
3.
4.
5.
6.
Basic MATLAB Matrices Operators Script and function files Flow control Plotting
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optional windows workspace current directory
Basic MATLAB
type commands here command window screen shot of the Matlab window
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Matlab’s help features
type “help” at the command prompt and Matlab returns a list of help topics
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Matlab’s help features
>> help lang Matlab’s
lang
uage constructs
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Matlab’s help features
>> help for how to use Matlab’s “for” statement
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Matlab’s help features
you can also access “on-line” help by clicking the question mark in the toolbar separate window
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MATLAB Variables
all variables are stored in 32bit floating point format no distinction between real and integer >>a = 3; same assignment for “a” >>a = 3.0; Matlab is case sensitive >>A=3; A a >>a=2;
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MATLAB Variables
can use numbers and underscore in variable names >>case34=6.45; OK >>case_34=6.45; names must start with a letter >>34case=23.45; results in a syntax error string (text) variables enclosed in single quotes.
The variable is stored as array of characters >>title=‘This is the title’;
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MATLAB Variables
if a variable is defined, typing the variable name returns its value >>a=45.57; >>a a = 45.57
Matlab returns the value to clear a variable from memory >>a=4 >>clear a
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MATLAB Variables
Matlab will “echo” commands unless a semi-colon is used >>a=23.2; >> >>a=23.2
a = 23.2
>> Matlab echoes the command
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MATLAB Variables
Vectors
column vectors row vectors a 1 2 3 a 1 2 3 >>a=[1;2;3]; >>a a = 1 2 3 use semi-colon to separate rows
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>>a=[1,2,3]; >>a a = 1 2 3 use comma to separate columns
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MATLAB Variables
Matrices
2-dimensional matrices a 1 4 2 5 3 6 >>a=[1,2,3;4,5,6]; >>a a = 1 2 3 4 5 6 again, separate columns with commas and rows with semi-colons
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MATLAB Variables
Indexing Matrix elements A vector is a special type of matrix row vector is a 1 x n matrix, 1 row n columns column vector is a n x 1 matrix, n rows 1 column >>a=[1,2,3]; >>a(2) ans = 2
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could also reference by a(1,2) note, a(2,1) would produce an error because “a” only has one row
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MATLAB Variables
Indexing Matrix elements more examples a 1 4 2 5 3 6 >>a=[1,2,3;4,5,6]; addressing >>a(2,3) ans = 6
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assigning >>a(2,2)=9; >>a a = 1 2 3 4 9 6
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MATLAB Variables
complex-valued numbers
Typically, the variable “i” or “j” is used to represent the complex variable; e.g. i 1 Then, a complex number is represented as z = a + ib Re(z) = a
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Im(z) = b
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MATLAB Variables
complex-valued numbers
Unless i or j has been previously defined, Matlab assigns i and j the complex variable value In Matlab, a complex variable is represented in the following format (assuming all variables are cleared) >>z=23+i*56; >>z=23+j*56; >>z >>z z = z = 23.00 + 56.00i
Matlab always uses the
symbol
23.00 + 56.00i
“i” to represent a complex number
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MATLAB Variables
complex-valued numbers
What happens in this case?
>>i=3; >> z=23+i*56; >>z z = What happens in this case?
>>a=sqrt(-1); >>z=23+a*56; >>z z =
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MATLAB Variables
complex-valued numbers
Note, a real-valued number is a special case of a complex-valued number assigning any element of a matrix as complex-valued makes the entire matrix complex-valued >>a=[1,2]; >>a a = 1 2
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>>a(1)=1+i*5; >>a a = 1.00+5.00i 2.00+0.00i
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MATLAB Variables
Advanced data types n-dimensional arrays structures cell arrays
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MATLAB Variables
Basic operations addition + subtraction multiplication * division right division / left division \ ?
>>a=3;b=4; >>c1=a/b; >>c2=a\b; c1=0.75
c2=1.3333….
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so, be careful!
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MATLAB Variables
Mixed Real and Complex valued Variables if both variables are real-valued, a real-valued result is obtained if one variable is complex-valued, Matlab recasts the real variable as complex and then performs the operation. The result is complex-valued however, the type casting is done internally, the real-valued variable remains real after the operation
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MATLAB Variables
Other (Scalar) Operations Math representation z y x Matlab interpretation >>z=y^x; y e x y ln(x) >>y=exp(x); >>y=log(x); y log(x) >>y=log10(x) y y y sin(x) cos(x) tan(x) y sin 1 (x) y cos 1 (x) y tan 1 (x) >>y=sin(x); >>y=cos(x); >>y=tan(x); >>y=asin(x); >>y=acos(x); >>y=atan(x);
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MATLAB Variables
Examples y x >>y=x^0.5; >>y=x^(1/2); >>y=sqrt(x); All variables in the preceding operations can be real or complex, negative or positive for x < 0, y is complex. Matlab assumes you allow complex valued numbers. If y is
not
to be complex, you must provide error checking.
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MATLAB Variables
Matrices •Only matrices of the same dimension can be added and subtracted •For multiplication, the inner dimensions must be the same
A
1 4 2 5 3 6 No error
B
2 5 3 6 4 7
C
4 6 8 Error 5 7 9 >>D=A+B; >>D=A-B; >>D=A*C; >>D=C*A; Matrix multiplication not commutative >>D=A+C; >>D=A*B; >>D=B*A;
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MATLAB Variables
Left(\) and Right(/) Matrix “division” Math representation
C
C
BA
1 Matlab interpretation >>C=A\B; >>C=B/A; Remember,
A
must be square and full rank (linearly independent rows/columns)
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Matrix Transpose Math representation Matlab interpretation
C
A
T >>C=A’; For complex-valued matrices, complex conjugate transpose
A
1 4 2 5 3 6
a
j2 3 j4 >>B=A’; >>b=a’;
B
1 2 3 4 5 6
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b
1 3 j2 j4
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MATLAB m-files
Two types of m-files script files collection of commands that Matlab executes when the script is “run” function files collection of commands which together represent a function, a procedure or a method Both types are separate files with a “.m” extension
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MATLAB m-files
To create an m-file, open the Matlab text editor Click on the “page” icon The Matlab text editor window will open
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MATLAB m-files
Script Files On the command line In the script file named test.m
>>x=3.0; >>y=x^2; >>y y = 9.0
>>
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On the command line >>test y = 9.0
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>>
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MATLAB m-files
Script Files script files share the workspace memory test.m script >>x=5.0; >>test >>y y = 25.0
>>
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MATLAB m-files
Script Files script files can call other script files inner.m script >>outter y = 36.0
>> outter.m script
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MATLAB m-files
Function Files Matlab identifies function files from script files by using the “function” and “return” keywords the name of the function file must be the same name as the function
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MATLAB m-files
Function Files The function file x2.m
>>r=3; >>d=x2(r); >>d d = 9.0
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>>h=x2(4.2); >>h h = 17.64
>>
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MATLAB m-files
Function Files Multiple Inputs and Outputs outputs in square brackets, [ ]
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inputs in parentheses ( )
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MATLAB m-files
Function Files variables created in the function are not retained in the workspace, except for the output variables the function does not have access to workspace variables, except for the inputs variables passed to the function are “copies” of the workspace variables. Changing their value inside the function has no effect on their value in the workspace.
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MATLAB Flow Control
The “while” and “if” statements while end
expression statements
if end
expression statements
if
expression statements1
else
statements2
end Matlab evaluates
expression
as logical “true” or “false” “false” equivalent to zero “true” equivalent to any non-zero number
statements
, any valid Matlab command
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MATLAB Flow Control
evaluating
expression
any valid equation a=4; b=5; c=5; if a+b if b-c “True” “False” conditional operators == equal to < less than > greater than <= less than or equal to >= greater than or equal to ~= not equal to watch out for round-off and word length error if sin(0) if sin(pi) “False” “True” sin(pi) = 1.22e-16 logical operators & and | or
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while(3<=a)&(a<=5)
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MATLAB Flow Control
The “for” statement for
index
=
start
: [
increment
:]
end statements
end
index
,
start
,
increment
, and
end
do not need to be integer valued
increment
is optional, if
increment
is not specified
increment
defaults to 1
index
can be incremented positive (
increment
> 0) or negative (
increment
< 0) loop stops when
index
>
end
(or
index
<
end
)
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MATLAB Flow Control
example script file to cycle through x values function file to generate the y values
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MATLAB PLOTTING
Basic 2D plotting functions plot(x1,y1[,x2,y2,x3,y3.....]) xlabel(‘x axis name’) ylabel(‘y axis name’) title(‘graph name’) Additional functions grid on grid off axis([xmin,xmax,ymin,ymax])
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MATLAB PLOTTING
example y = sin(t) the “plot” function alone
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MATLAB PLOTTING
example y = sin(t) script file to generate a graph of y = sin(t)
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MATLAB PLOTTING
example y = sin(t) function file to generate a graph of y = sin(t) >>graphsin >>
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MATLAB PLOTTING
Adding a Legend for multiple graphs “legend” remembers the order the graphs were plotted
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