solution using newton raphson method?

this is my code i am unable to substitue x1,x2,x3,x4 values in the matrix.Please help in solve this.

syms  x1 x2 x3 x4
g1=cos(x1)+cos(x2)+cos(x3)+cos(x4)-0.9424;
g2=cos(5*x1)+cos(5*x2)+cos(5*x3)+cos(5*x4);
g3=cos(7*x1)+cos(7*x2)+cos(7*x3)+cos(7*x4);
g4=cos(11*x1)+cos(11*x2)+cos(11*x3)+cos(11*x4);
g=[g1;g2;g3;g4];
x=[x1;x2;x3;x4];
j=jacobian(g,x)
j_inv=inv(j)
p=j_inv*-g
x1=input('enter initial values of x1')
x2=input('enter initial values of x2')
x3=input('enter initial values of x3')
x4=input('enter initial values of x4')
disp(x)
disp(p)
subs(p)

Answer 1

[Ameer Hamza]

MATLAB does not automatically know which values to substitute. You need to specify this in the call to subs() explicitly. Try the following code

syms  x1 x2 x3 x4
g1=cos(x1)+cos(x2)+cos(x3)+cos(x4)-0.9424;
g2=cos(5*x1)+cos(5*x2)+cos(5*x3)+cos(5*x4);
g3=cos(7*x1)+cos(7*x2)+cos(7*x3)+cos(7*x4);
g4=cos(11*x1)+cos(11*x2)+cos(11*x3)+cos(11*x4);
g=[g1;g2;g3;g4];
x=[x1;x2;x3;x4];
j=jacobian(g,x);
j_inv=inv(j);
p=j_inv*-g;
X1=input('enter initial values of x1');
X2=input('enter initial values of x2');
X3=input('enter initial values of x3');
X4=input('enter initial values of x4');

disp(x)
disp(p)
subs(p, [x1 x2 x3 x4], [X1 X2 X3 X4])

[omkari sai krishna]

Thank you sir for your suggestion.

it is showing

Error using symengine

Division by zero.

Error in sym/subs>mupadsubs (line 160)

G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 145)

G = mupadsubs(F,X,Y);

Error in sai (line 19)

subs(p, [x1 x2 x3 x4], [90 60 60 60])

[Ameer Hamza]

omkari, the matrix p is quite complex and has several terms in the denominators of each element too. For some of the values of [x1 x2 x3 x4], the denominator becomes zero, and it gives the error about division by zero. For example, you can try this

subs(p, [x1 x2 x3 x4], [1 4 3 2])

and it will not give an error. You will need to see your model and find out which values are not allowed.

[omkari sai krishna]

yes sir, thank you it is not showing error i had changed the initial values.

But i am not able to convert my p matrix in to a value althought i am using 'double' syntax.

It is showing unable to converter your expression in to double array.

please help me why it is showing that error.

[Ameer Hamza]

You should call double like this

syms  x1 x2 x3 x4
g1=cos(x1)+cos(x2)+cos(x3)+cos(x4)-0.9424;
g2=cos(5*x1)+cos(5*x2)+cos(5*x3)+cos(5*x4);
g3=cos(7*x1)+cos(7*x2)+cos(7*x3)+cos(7*x4);
g4=cos(11*x1)+cos(11*x2)+cos(11*x3)+cos(11*x4);
g=[g1;g2;g3;g4];
x=[x1;x2;x3;x4];
j=jacobian(g,x);
j_inv=inv(j);
p=j_inv*-g;

double(subs(p, [x1 x2 x3 x4], [1 4 3 2]))

[omkari sai krishna]

Yes sir thank you i am able to get solution with your help.

[Ameer Hamza]

I am glad to be of help.

[omkari sai krishna]

Sir one more doubt in this code the values in k matrix is not changing eventhough X matrix values are changing in each itteration.

This is my code

while (1)
    k=double(subs(p, [x1 x2 x3 x4], [X1 X2 X3 X4]))
    if k(1,1)&&k(2,1)&&k(3,1)&&k(4,1)<10e-2
        disp(X)
        break
    else
        y1=X(1,1)+k(1,1);
        y2=X(2,1)+k(2,1);
        y3=X(3,1)+k(3,1);
        y4=X(4,1)+k(4,1);
        X(1,1)=y1;
        X(2,1)=y2;
        X(3,1)=y3;
        X(4,1)=y4;
        disp(X)
    end
end

For this code k is not substituting the updated values of X matrix.

[Ameer Hamza]

You need to use same variable names for substitution

while (1)
    k=double(subs(p, [x1 x2 x3 x4], [X1 X2 X3 X4]));
    if k(1,1)&&k(2,1)&&k(3,1)&&k(4,1)<10e-2
        disp(X)
        break
    else
        y1=X(1,1)+k(1,1);
        y2=X(2,1)+k(2,1);
        y3=X(3,1)+k(3,1);
        y4=X(4,1)+k(4,1);
        X1=y1;
        X2=y2;
        X3=y3;
        X4=y4;
        disp(X)
    end
end

[Ameer Hamza]

if you want to save the values of each iteration, the do something like this

count = 1;
while (1)
    k=double(subs(p, [x1 x2 x3 x4], [X1(count) X2(count) X3(count) X4(count)]));
    count = count + 1;
    if k(1,1)&&k(2,1)&&k(3,1)&&k(4,1)<10e-2
        disp(X)
        break
    else
        y1=X(1,1)+k(1,1);
        y2=X(2,1)+k(2,1);
        y3=X(3,1)+k(3,1);
        y4=X(4,1)+k(4,1);
        X1(count)=y1;
        X2(count)=y2;
        X3(count)=y3;
        X4(count)=y4;
        disp(X)
    end
end

[omkari sai krishna]

Sir i am working with your suggestion but i am not getting correct solution using this code i am not understanding what will be reason. Please help me to know the concept.

clc;clear all
syms  x1 x2 x3 x4 X1 X2 X3 X4
g1=cosd(x1)+cosd(x2)+cosd(x3)+cosd(x4)-0.9424;
g2=cosd(5*x1)+cosd(5*x2)+cosd(5*x3)+cosd(5*x4);
g3=cosd(7*x1)+cosd(7*x2)+cosd(7*x3)+cosd(7*x4);
g4=cosd(11*x1)+cosd(11*x2)+cosd(11*x3)+cosd(11*x4);
g=[g1;g2;g3;g4];
x=[x1;x2;x3;x4];
j=jacobian(g,x);
j_inv=inv(j);
p=j_inv*-g;
X1=input('enter initial values of x1');
X2=input('enter initial values of x2');
X3=input('enter initial values of x3');
X4=input('enter initial values of x4');
X=[X1;X2;X3;X4];
while (1)
    k=double(subs(p, [x1 x2 x3 x4],[X1 X2 X3 X4]));
    if k(1,1)&&k(2,1)&&k(3,1)&&k(4,1)<0.000001
        disp(X1)
        disp(X2)
        disp(X3)
        disp(X4)
        disp(k)
        break
    else
        y1=X1+k(1,1);
        y2=X2+k(2,1);
        y3=X3+k(3,1);
        y4=X4+k(4,1);
        X1=y1;
        X2=y2;
        X3=y3;
        X4=y4;
        
    end
end

results are showing wrong values please find a solution

[Ameer Hamza]

What are you trying to do in this condition?

k(1,1)&&k(2,1)&&k(3,1)&&k(4,1)<0.000001

[omkari sai krishna]

sir i am comparing each value in column matrix k with 0.001

[Ameer Hamza]

The correct condition is

if (k(1,1)<0.000001)&&(k(2,1)<0.000001)&&(k(3,1)<0.000001)&&(k(4,1)<0.000001)

or in a compact form

if all([k(1,1) k(2,1) k(3,1) k(4,1)]<0.000001)

However, note that this condition become true with all variable become negative, e.g., -1000 < 0.000001 is also true.

[omkari sai krishna]

yes sir and it is not showing exact results loop is executing continously it is not showing any results.

sir is my equation is wrong? ?

[Ameer Hamza]

I don't know the details of this method, so I cannot say if it is correct. But if you want to display values for all the iterations, then add these lines

disp(X1)
disp(X2)
disp(X3)
disp(X4)
disp(k)

inside the else block too. Right now, they are only displayed when the condition of 'if' block become true.

[omkari sai krishna]

i am solving a set of non linear equations using newton raphson method using code.

i am not getting exact solution.

yes sir i had used in my code.

thank you sir its a great help for me .thank you so much.

[omkari sai krishna]

sir i want one more help can u help me to get the code for the THD equation which i am placed below.

i had tried myself but it is always showing 1 as a answer. please help me to solve this.

[Ameer Hamza]

Can you start a new question and post the details of your question? You can then post the link of your question in the next comment.

[omkari sai krishna]

https://in.mathworks.com/matlabcentral/answers/522689-fourier-series-code-in-matlab?s_tid=prof_contriblnk