vlachopoulos georgios lecturer of computer science and informatics technological institute of...

Research Methodology

Programming in Matlab

Vlachopoulos GeorgiosLecturer of Computer Science and Informatics

Technological Institute of Patras, Department of Optometry, Branch of EgionLecturer of Biostatistics

Technological Institute of Patras, Department of Physiotherapy, Branch of Egion

Matrices in Matlab

Vlachopoulos Georgios

Arrays and Matrices Matlab (Matrix Laboratory)

◦ A powerful tool to handle Matrices


Define an array 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)


E=[1,2,3↲ 4,5,6] F=[1,2,3;4,5,6]G=[1;2;3]H=[1,2,3;

4,5]

Define a Matrix


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)]

Define a Matrix


Special functionszeros(2,4)zeros(2,2)zeros(2)ones(2,4)ones(2,2)ones(2)eye(2,2)eye(2)eye(2,4)

Define a Matrix


Special functionsrand (2,4)rand(2,2)rand(2)magic(3)hilb(3)

Define a Matrix


+ - * / \ .* ./ .\ ^ (base and exp) inv size

Basic Operators to Matrices


Inner Product◦ dot(array1,array2)

Cross Product◦ cross(array1,array2)

Special Operators to Matrices


Every polynomial corresponds to an array with elements the coefficients of the polynomial

Examplef1(x)=x2-5x+6f1=[1,-5,6]

f2(x)=x3-5x+6f2=[1,0,-5,6]

Polynomials as arrays


Add polynomials◦ array1+array2◦ If we have different order polynomials we create equal

sizes arrays adding zeros on missing coefficients Add polynomials

◦ array1-array2◦ If we have different order polynomials we create equal

sizes arrays adding zeros on missing coefficients Multiply polynomials

◦ conv(array1,array2) Divide polynomials

◦ deconv(array1,array2)



Roots of a polynomial roots(array)

Polynomial with roots the elements of the array poly(array)

First order derivative of the Polynomialpolyder(array)

Value of the Polynomial p for x=apolyval(p,a)



Examplesk1=root(f1)k2=root(f2) poly(k1)kder=polyder(f2)polyval(s2,5)



A∪Bunion(array1,array2) A∩B intersect(array1,array2) A∼B setdiff(array1,array2)

Example◦ a=1:6◦ b=0:2:10◦ c=union(a,b)◦ d=intersect(a,b)◦ e1=setdiff(a,b)◦ e2=setdiff(b,a)

Set Operations


Unique Elements unique(array) Elements of A that are members of B

ismember(array1,array2)Example

◦ f1=ismember(a,b)◦ f2=ismember(b,a)◦ g=[1,1,2,2,3,3]◦ h=unique(g)

Set Operations


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)

Calculation Functions


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????



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????



Matrices◦ Cumulative sum per column cumsum(matrix) or cumsum (matrix,1)◦ Cumulative sum per row cumsum (matrix,2)



Matrices◦ Cumulative sum per column cumprod(matrix) or cumprod (matrix,1)◦ Cumulative sum per row cumprod(matrix,2)



Matrix element A(i,j)Example:

A=[1,2,3;4,5,6]A(2,1)↲A(2,1)=4

Reference to Martix elements


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(:)

Reference to Martix elements


Delete elementsExample

◦ 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

Edit Matrices


Replace ElementsExample

◦ 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]

Edit Matrices


Insert ElementsExample

◦ Clear all;◦ A=magic(5)◦ A(6,:)=[1,2,3,4,5,6]◦ A(9,:)=[11,12,13,14,15,16]

Edit Matrices

vlachopoulos georgios lecturer of computer science and informatics technological institute of...

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