creating loop that stops at correct formula for the given input.
I am writting a program the finds the polynomial using the least-square method and Gausian elimination and from there displays the correct polynomial equation. The code for the least-square and the Gaussian elimination works fine, where I am having trouble is at the end getting the display of the polynomial equation depending on what value of "n" you show correcty and nothing lower then or higher then the corresponding the chosen value of "n". What loop would for best to do this? My fist thought is and if else loop but how would I set this up to run correctly?
clear, close, clc
%input
x=[0 1 2 3 4 5];
y=[2.1 7.7 13.6 27.2 40.9 61.1];
n=8; %order of the polynomial you want to find
%%%LEAST SQUARE METHOD-FINDS POLYNOMIAL FOR GIVEN DATA SET%%%%%
%INPUT SECTION
x=x; %x-cordinates from data-input; independent vairiables
y=y; %y-cordinates from data-output; dependent vairiables
%CALCULATIONS SECTION
k=length(x); %NUMBER OF AVAILABLE DATA POINTS
m=n+1; %SIZE OF THE COEFFICENT MATRIX
A=zeros(m,m); %COEFFICENT MATRIX
for j=1:m
for i=1:m
A(j,i)=sum(x.^(i+j-2));
end
end
B=zeros(m,1); %FORCING FUNCTION VECTOR
for i=1:m;
B(i)=sum(y.*x.^(i-1));
end
a1=AB %COEFFICIENTS FOR THE POLYNOMINAL–> y=a0+a1*x+a2*x^2….an*x^n CAN BE REPLACED BY GAUSSIAN ELIMINATION
%%%%%=========GAUSSIAN ELIMINATION TO FIND "a"========%%%%%%
%%%INPUT SECTION
%CALCULATION SECTION
AB=[A B]; %Augumentent matrix
R=size(AB,1); %# OF ROWS IN AB
C=size(AB,2); %# OF COLUMNS IN AB
%%%%FOWARD ELIMINATION SECTION
for J=1:R-1
[M,I]=max(abs(AB(J:R,J))); %M=MAXIMUM VALUE, I=LOCATION OF THE MAXIMUM VALUE IN THE 1ST ROW
temp=AB(J,:);
AB(J,:)=AB(I+(J-1),:);
AB(I+(J-1),:)=temp;
for i=(J+1):R;
if AB(i,J)~=0;
AB(i,:)=AB(i,:)-(AB(i,J)/AB(J,J))*AB(J,:);
end
end
end
%%%%BACKWARDS SUBSTITUTION
a(R)=AB(R,C)/AB(R,R);
for i=R-1:-1:1
a(i)=(AB(i,C)-AB(i,i+1:R)*a(i+1:R)’)/AB(i,i);
end
disp(a)
%========END OF GAUSSIAN ELIMINATION=======%%%%%%%%
%STANDARD DEVIATION
Y_bar=mean(y); %ADVERAGE OF y
St=sum((y-Y_bar).^2);
SD=sqrt(St/(k-1)); %STANDARD DEVIATION
%STANDARD ERROR
for i=1:m;
T(:,i)=a(i)*x.^(i-1); %T=INDIVIDUAL POLYNOMIAL TERMS
end
for i=1:k
y_hat(i)=sum(T(i,:));
end
Sr=sum((y-y_hat).^2);
Se=sqrt(Sr/(k-(n+1))); %STANDARD ERROR-Se
%COEFFICIENT OF DETERMINATION
Cd=(St-Sr)/St %COEFFICIENT OF DETERMINATION (r^2)
fprintf(‘For n=%d. Coefficient of Determination=%0.5fn’,n,Cd)
%EQUATION FOR THE POLYNOMIAL
syms x y
for n=1
a0=a(:,1);a1=a(:,2);a2=a(:,3);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2
end
for n=2
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3
end
for n=3
a0=a(:,1);a1=a(:,2);a2=a(:,2);a3=a(:,4);a4=a(:,5);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4
end
for n=4
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5
end
for n=5
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7)
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6
end
for n=6
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7
end
for n=7
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8
end
for n=8
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9
end
for n=9
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);a10=a(:,11);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9+a10*x.^10
endI am writting a program the finds the polynomial using the least-square method and Gausian elimination and from there displays the correct polynomial equation. The code for the least-square and the Gaussian elimination works fine, where I am having trouble is at the end getting the display of the polynomial equation depending on what value of "n" you show correcty and nothing lower then or higher then the corresponding the chosen value of "n". What loop would for best to do this? My fist thought is and if else loop but how would I set this up to run correctly?
clear, close, clc
%input
x=[0 1 2 3 4 5];
y=[2.1 7.7 13.6 27.2 40.9 61.1];
n=8; %order of the polynomial you want to find
%%%LEAST SQUARE METHOD-FINDS POLYNOMIAL FOR GIVEN DATA SET%%%%%
%INPUT SECTION
x=x; %x-cordinates from data-input; independent vairiables
y=y; %y-cordinates from data-output; dependent vairiables
%CALCULATIONS SECTION
k=length(x); %NUMBER OF AVAILABLE DATA POINTS
m=n+1; %SIZE OF THE COEFFICENT MATRIX
A=zeros(m,m); %COEFFICENT MATRIX
for j=1:m
for i=1:m
A(j,i)=sum(x.^(i+j-2));
end
end
B=zeros(m,1); %FORCING FUNCTION VECTOR
for i=1:m;
B(i)=sum(y.*x.^(i-1));
end
a1=AB %COEFFICIENTS FOR THE POLYNOMINAL–> y=a0+a1*x+a2*x^2….an*x^n CAN BE REPLACED BY GAUSSIAN ELIMINATION
%%%%%=========GAUSSIAN ELIMINATION TO FIND "a"========%%%%%%
%%%INPUT SECTION
%CALCULATION SECTION
AB=[A B]; %Augumentent matrix
R=size(AB,1); %# OF ROWS IN AB
C=size(AB,2); %# OF COLUMNS IN AB
%%%%FOWARD ELIMINATION SECTION
for J=1:R-1
[M,I]=max(abs(AB(J:R,J))); %M=MAXIMUM VALUE, I=LOCATION OF THE MAXIMUM VALUE IN THE 1ST ROW
temp=AB(J,:);
AB(J,:)=AB(I+(J-1),:);
AB(I+(J-1),:)=temp;
for i=(J+1):R;
if AB(i,J)~=0;
AB(i,:)=AB(i,:)-(AB(i,J)/AB(J,J))*AB(J,:);
end
end
end
%%%%BACKWARDS SUBSTITUTION
a(R)=AB(R,C)/AB(R,R);
for i=R-1:-1:1
a(i)=(AB(i,C)-AB(i,i+1:R)*a(i+1:R)’)/AB(i,i);
end
disp(a)
%========END OF GAUSSIAN ELIMINATION=======%%%%%%%%
%STANDARD DEVIATION
Y_bar=mean(y); %ADVERAGE OF y
St=sum((y-Y_bar).^2);
SD=sqrt(St/(k-1)); %STANDARD DEVIATION
%STANDARD ERROR
for i=1:m;
T(:,i)=a(i)*x.^(i-1); %T=INDIVIDUAL POLYNOMIAL TERMS
end
for i=1:k
y_hat(i)=sum(T(i,:));
end
Sr=sum((y-y_hat).^2);
Se=sqrt(Sr/(k-(n+1))); %STANDARD ERROR-Se
%COEFFICIENT OF DETERMINATION
Cd=(St-Sr)/St %COEFFICIENT OF DETERMINATION (r^2)
fprintf(‘For n=%d. Coefficient of Determination=%0.5fn’,n,Cd)
%EQUATION FOR THE POLYNOMIAL
syms x y
for n=1
a0=a(:,1);a1=a(:,2);a2=a(:,3);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2
end
for n=2
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3
end
for n=3
a0=a(:,1);a1=a(:,2);a2=a(:,2);a3=a(:,4);a4=a(:,5);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4
end
for n=4
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5
end
for n=5
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7)
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6
end
for n=6
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7
end
for n=7
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8
end
for n=8
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9
end
for n=9
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);a10=a(:,11);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9+a10*x.^10
end I am writting a program the finds the polynomial using the least-square method and Gausian elimination and from there displays the correct polynomial equation. The code for the least-square and the Gaussian elimination works fine, where I am having trouble is at the end getting the display of the polynomial equation depending on what value of "n" you show correcty and nothing lower then or higher then the corresponding the chosen value of "n". What loop would for best to do this? My fist thought is and if else loop but how would I set this up to run correctly?
clear, close, clc
%input
x=[0 1 2 3 4 5];
y=[2.1 7.7 13.6 27.2 40.9 61.1];
n=8; %order of the polynomial you want to find
%%%LEAST SQUARE METHOD-FINDS POLYNOMIAL FOR GIVEN DATA SET%%%%%
%INPUT SECTION
x=x; %x-cordinates from data-input; independent vairiables
y=y; %y-cordinates from data-output; dependent vairiables
%CALCULATIONS SECTION
k=length(x); %NUMBER OF AVAILABLE DATA POINTS
m=n+1; %SIZE OF THE COEFFICENT MATRIX
A=zeros(m,m); %COEFFICENT MATRIX
for j=1:m
for i=1:m
A(j,i)=sum(x.^(i+j-2));
end
end
B=zeros(m,1); %FORCING FUNCTION VECTOR
for i=1:m;
B(i)=sum(y.*x.^(i-1));
end
a1=AB %COEFFICIENTS FOR THE POLYNOMINAL–> y=a0+a1*x+a2*x^2….an*x^n CAN BE REPLACED BY GAUSSIAN ELIMINATION
%%%%%=========GAUSSIAN ELIMINATION TO FIND "a"========%%%%%%
%%%INPUT SECTION
%CALCULATION SECTION
AB=[A B]; %Augumentent matrix
R=size(AB,1); %# OF ROWS IN AB
C=size(AB,2); %# OF COLUMNS IN AB
%%%%FOWARD ELIMINATION SECTION
for J=1:R-1
[M,I]=max(abs(AB(J:R,J))); %M=MAXIMUM VALUE, I=LOCATION OF THE MAXIMUM VALUE IN THE 1ST ROW
temp=AB(J,:);
AB(J,:)=AB(I+(J-1),:);
AB(I+(J-1),:)=temp;
for i=(J+1):R;
if AB(i,J)~=0;
AB(i,:)=AB(i,:)-(AB(i,J)/AB(J,J))*AB(J,:);
end
end
end
%%%%BACKWARDS SUBSTITUTION
a(R)=AB(R,C)/AB(R,R);
for i=R-1:-1:1
a(i)=(AB(i,C)-AB(i,i+1:R)*a(i+1:R)’)/AB(i,i);
end
disp(a)
%========END OF GAUSSIAN ELIMINATION=======%%%%%%%%
%STANDARD DEVIATION
Y_bar=mean(y); %ADVERAGE OF y
St=sum((y-Y_bar).^2);
SD=sqrt(St/(k-1)); %STANDARD DEVIATION
%STANDARD ERROR
for i=1:m;
T(:,i)=a(i)*x.^(i-1); %T=INDIVIDUAL POLYNOMIAL TERMS
end
for i=1:k
y_hat(i)=sum(T(i,:));
end
Sr=sum((y-y_hat).^2);
Se=sqrt(Sr/(k-(n+1))); %STANDARD ERROR-Se
%COEFFICIENT OF DETERMINATION
Cd=(St-Sr)/St %COEFFICIENT OF DETERMINATION (r^2)
fprintf(‘For n=%d. Coefficient of Determination=%0.5fn’,n,Cd)
%EQUATION FOR THE POLYNOMIAL
syms x y
for n=1
a0=a(:,1);a1=a(:,2);a2=a(:,3);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2
end
for n=2
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3
end
for n=3
a0=a(:,1);a1=a(:,2);a2=a(:,2);a3=a(:,4);a4=a(:,5);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4
end
for n=4
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5
end
for n=5
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7)
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6
end
for n=6
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7
end
for n=7
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8
end
for n=8
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9
end
for n=9
a0=a(:,1);a1=a(:,2);a2=a(:,3);a3=a(:,4);a4=a(:,5);a5=a(:,6);a6=a(:,7);a7=a(:,8);a8=a(:,9);a9=a(:,10);a10=a(:,11);
sympref("FloatingPointOutput",true);
y=a0+a1*x+a2*x.^2+a3*x.^3+a4*x.^4+a5*x.^5+a6*x.^6+a7*x.^7+a8*x.^8+a9*x.^9+a10*x.^10
end loop to display equation for changing input, loop MATLAB Answers — New Questions
