Transcript Matrices in Matlab Vlachopoulos Georgios Lecturer of Computer Science and Informatics Technological Institute of Patras, Department of Optometry, Branch of Egion Lecturer of Biostatistics Technological.

Matrices in Matlab
Vlachopoulos Georgios
Lecturer of Computer Science and Informatics
Technological Institute of Patras, Department of Optometry, Branch of Egion
Lecturer of Biostatistics
Technological Institute of Patras, Department of Physiotherapy, Branch of Egion
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Matlab  (Matrix Laboratory)
◦ A powerful tool to handle Matrices
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A=[2,4,7]
B=[1:1:10]
C=[10:3:40]
D=[30:-3:0]
D1=[1:pi:100]
Length(D1)
D2=linspace(2,10,20)
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E=[1,2,3↲
 4,5,6]
 F=[1,2,3;4,5,6]
G=[1;2;3]
H=[1,2,3;
4,5]
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X=2;
H=[x,sin(pi/4), 3,2*x;
sqrt(5), x^2,log(x),4]
H1=[x,sin(pi/4), 3,2*x;
sqrt(5), x^2,log(x),4;
linspace(1,2,4)]
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Special functions
zeros(2,4)
zeros(2,2)
zeros(2)
ones(2,4)
ones(2,2)
ones(2)
eye(2,2)
eye(2)
eye(2,4)
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Special functions
rand (2,4)
rand(2,2)
rand(2)
magic(3)
hilb(3)
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+
*
/
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.*
./
.\
^ (base and exp)
inv
size
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Inner Product
◦ dot(array1,array2)
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Cross Product
◦ cross(array1,array2)
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Every polynomial corresponds to an array
with elements the coefficients of the
polynomial
Example
f1(x)=x2-5x+6f1=[1,-5,6]
f2(x)=x3-5x+6f2=[1,0,-5,6]
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Add polynomials
◦ array1+array2
◦ If we have different order polynomials we create equal
sizes arrays adding zeros on missing coefficients
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Add polynomials
◦ array1-array2
◦ If we have different order polynomials we create equal
sizes arrays adding zeros on missing coefficients
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Multiply polynomials
◦ conv(array1,array2)
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Divide polynomials
◦ deconv(array1,array2)
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Roots of a polynomial
roots(array)
Polynomial with roots the elements of the
array
poly(array)
First order derivative of the Polynomial
polyder(array)
Value of the Polynomial p for x=a
polyval(p,a)
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Examples
k1=root(f1)
k2=root(f2)
poly(k1)
kder=polyder(f2)
polyval(s2,5)
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A∪Bunion(array1,array2)
A∩B intersect(array1,array2)
A∼B setdiff(array1,array2)
Example
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a=1:6
b=0:2:10
c=union(a,b)
d=intersect(a,b)
e1=setdiff(a,b)
e2=setdiff(b,a)
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Unique Elements  unique(array)
 Elements of A that are members of B 
ismember(array1,array2)
Example
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f1=ismember(a,b)
f2=ismember(b,a)
g=[1,1,2,2,3,3]
h=unique(g)
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Arrays
◦ Sum of array elements  sum(array)
◦ Product of array elements  prod(array)
◦ Cumulative sum of an array elements
cumsum(array)
◦ Cumulative prod of an array elements
cumprod(array)
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Matrices
◦ Sum of elements of each matrix column
 sum(matrix)
or
 sum(matrix,1)
◦ Sum of elements of each matrix row
 sum(matrix,2)
Overall sum????
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Matrices
◦ Product of elements of each matrix column
 prod(matrix)
or
 prod(matrix,1)
◦ Product of elements of each matrix row
 prod(matrix,2)
Overall product????
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Matrices
◦ Cumulative sum per column
 cumsum(matrix)
or
 cumsum (matrix,1)
◦ Cumulative sum per row
 cumsum (matrix,2)
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Matrices
◦ Cumulative sum per column
 cumprod(matrix)
or
 cumprod (matrix,1)
◦ Cumulative sum per row
 cumprod(matrix,2)
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Matrix element A(i,j)
Example:
A=[1,2,3;4,5,6]
A(2,1)↲
A(2,1)=4
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Example:
A=[1,2,3;4,5,6;3,2,1]
B=A(1:2,2,3)
y=A(:,1)
Z=A(1,:)
W=A([2,3],[1,3])
A(:)
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Delete elements
Example
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Clear all;
A=magic(5)
A(2,: )=[] % delete second row
A(:[1,4])=[] % delete columns 1 and 4
A=magic(5)
A(1:3,:)=[] % delete rows 1 to 3
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Replace Elements
Example
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Clear all;
A=magic(5)
A(2,3 )=5 % Replace Element (2,3)
A(3,:)=[12,13,14,15,16] % replace 3rd row
A([2,5]=[22,23,24,25,26; 32,33,34,35,36]
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Insert Elements
Example
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Clear all;
A=magic(5)
A(6,:)=[1,2,3,4,5,6]
A(9,:)=[11,12,13,14,15,16]
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