MATLAB

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MATLAB
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Running MATLAB

• Basic operations in MATLAB

Lowest
Highest
53/39
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Display formats

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Variables

• Up to 31 characters
• Case sensitive
• Start with a letter
• Information about variables
• WHO
• WHOS

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MATLAB Environment

• Command Window
• Command History
• Workspace
• Current Directory

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Mathematical functions
pi is a predefined variable ( 3.14....)
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• Vectors and vector computation
• first_nb step last_nb
• (y 2 0.5 4) ? y2 2.5 3 3.5 4
• y 1 3 ? y 1 2 3 Default step is 1
• linspace(first_nb , last_nb , n_points)
• (y linspace(2 , 4 , 5)) ? y 2 2.5 3 3.5
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• z x y
• x1 2 3, y4 5 ? z 1 2 3 4 5
• Accesing elements x(3), x(24), x(125), x(3 1
  4)
• Column vector
• x 1234 , x 1 2 3 4
• Array operations (mult.(), div.(/), add.(),..
  )

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Matrices and matrix computation

• x 1 2 34 5 67 8 9, x 127 3-10
  -12
• Special matrices
• zeros(3,2)
• ones(3,2)
• eye(3) (identity matrix)
• size(a), length(b)
• Matrix operations
• det(x), inv(x)
• System of linear equations

0 0 0 0 0 0
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Input-Output Commands

• Input
• variable input(text)

r input( Enter a number )

• Output
• disp(x), disp(the value is ),
• disp ( The value is num2str ( x ) )

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2D Graphics

• plot(x , y), plot(x , y , r)

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x -pi .1 pi y sin(x) plot(x,y)
x -pi .1 pi y sin(x) plot(x,y,m)
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2D Graphics

• fplot(function, xmin xmax )
• fplot('sin(x.x)', 0 4)

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2D Graphics

• xlabel('x values'), title('exp(-x) and xx
  curves')
• title(text) writes the text as a title at the
  top of the current plot
• xlabel(text) adds text to the current plot
  beneath the x-axis
• ylabel(text) adds text to the current plot
  beside the y-axis
• grid on adds grid lines on the current axes
• grid off takes them off
• text(x,y,text) adds text to the location
  identified by the point (x, y)
• gtext(text) text is positioned at a location
  by pressing the mouse
• Try to run this code
• plot(5 5 4 3 2,8 2 1 1 2,r', 4 6,8
  8,y') xlim(0 10) ylim(0 10)

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3D Graphics

• gtgt t0pi/306pi xt.cos(t) yt.sin(t)
  zt plot3(x,y,z)

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Script files

• File ? New ?M-file
• sample.m
• roots of the quadratic equation ax2bxc0
• a input('Enter the coefficient a ')
• b input('Enter the coefficient b ')
• c input('Enter the coefficient c ')
• discbb-4ac
• x1 (-b sqrt(disc)) / (2 a)
• x2 (-b - sqrt(disc)) / (2 a)
• Displays the roots
• disp('Roots are ', num2str(x1),' and
  ',num2str(x2))

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Operators in Matlab

• Relational Operators
• lt Less than
• lt Less than or equal
• gt Greater than
• gt Greater than or equal
• Equal
• Not Equal
• Logical Operators
• not
• and
• or

Priority Increases
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if else end
if expression-1 commands-1 elseif
expression-2 commands-2 . . . elseif
expression-(n-1) commands-(n-1) else commands-
n end
A1 2 -3 6 if det(A)gt0
Ainvinv(A) disp(Ainv) end
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switch
switch (selector) case label-1 commands-1
case label-2 commands-2 . .
. case label-n commands-n
otherwise commands-m end
switch (det(a)) case 1
ba' disp(b) case 2
baa disp(b) end
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for loops
for xarray commands end
for num6 37 23 -1 disp(num2str(k), ' th
element is ', num2str(num)) kk1 end
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while loops
while expression commands end
while xgt0 yyx xx-1 disp(y)
end
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User defined functions

• function output-parametersfunction-name(input-
  parameters)
• function x1,x2 quadratic(a,b,c)
• Finds the roots of the quadratic equation
• ax2bxc0
• discbb-4ac
• x1(-bsqrt(disc))/(2a)
• x2(-b-sqrt(disc))/(2a)
• gtgt a,b quadratic (1, -2 ,7)

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Example (islem.m)

function top,cik,bol,carp islem(a,b) top
ab cik a-b bol a/b carp ab end
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Example (vectorislem.m)
function top,cik,dot vectorislem(a,b) top
ab cik a-b dot ab' end

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Example 1

• The series ex is given by
• Write a MATLAB script to find the sum of the
  series while the value of the current term is
  greater than to the variable tol. Your program
  should input x and tol and should output the sum
  with proper messages. The result should be
  checked by using the MATLAB function exp().

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Possible Matlab Code

• x input('Enter a value for x of exp(x)')
• tol input('Enter the tolerance')
• k1
• sum1
• term1
• fact1
• sqx
• format long
• while termgttol
• termsq/fact a single term is calculated
  xn / n!
• sumsumterm calculated term is added to
  general sum
• sqsqx next xn1 is calculated
• factfact(k1) next (x1)! is calculated
• kk1
• end
• disp(sum)
• disp(term)

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Example 2

• Write a MATLAB function to generate and return
  the matrix in the form
• Your function should accept the parameters d, t,
  s and the size of the square matrix.

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Possible Matlab Code
function matrix matrix_ex(d,t,s,N) sM
zeros(N-1,1) , eye(N-1) zeros(1,N) s
superior 1's tM zeros(1,N) eye(N-1) ,
zeros(N-1,1) t lower 1's dM eye(N)
d identity matrix sM tM dM
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Thank you!