unable to convert sym value to double

WHEN I RUN THE FOLLOWING CODE I GET THE ERROR THAT MATLAB IS NOT ABLE TO CONVERT SYMBOLIC TO DOUBLE, IT RUNS THE FIRST ITERATION AND THEN STOP DISPLAYING THIS ERROR

f(x,y)=x*sin(y)+y*sin(x)-0.5;
g(x,y)=x*cos(y)-y*cos(x)+0.5;
x0=input('Value for  x:');
y0=input('Value for  y:');
N = input('Enter number of iterations = ');
tol=0.0001;
f1(x)=diff(f(x,y),x);
f2(y)=diff(f(x,y),y);
g1(x)=diff(g(x,y),x);
g2(y)=diff(g(x,y),y);
for i= 1:N
    x1=x0-(((f(x0,y0)*g2(y0))-(g(x0,y0)*f2(y0)))/((f1(x0)*g2(y0))-(f2(y0)*g1(x0))));
    y1=y0-(((g(x0,y0)*f1(x0))-(f(x0,y0)*g1(x0)))/((f1(x0)*g2(y0))-(f2(y0)*g1(x0))));
    
    fprintf ('%3i %11.4f %11.4f %11.4f %11.4f %11.4f \n',i,x0,y0,f(x0,y0),g(x0,y0), tol)
    if  abs(f(x0,y0)) < tol || abs(g(x0,y0)) < tol
        fprintf('Iteration Count = %g\n', N)  
        fprintf('The X Root = %0.5f\n', x1)
        fprintf('The Y Root = %0.5f\n', y1)
        break
    else
        x0 = x1; 
        y0 = y1;
    end
    if i==N
        fprintf('Root not obtained in %1i iterations',N)
    end
end

[Star Strider]

The ‘x1’ and ‘y1’ values are function of symbolic variables x and y. They need to be evaluated in order to convert them to double variables.

syms x y 
sympref('AbbreviateOutput',false);
f(x,y)=x*sin(y)+y*sin(x)-0.5;
g(x,y)=x*cos(y)-y*cos(x)+0.5;
% x0=input('Value for  x:');
% y0=input('Value for  y:');
% N = input('Enter number of iterations = ');
x0 = 3;
y0 = 5;
N = 2;
tol=0.0001;
f1(x)=diff(f(x,y),x);
f2(y)=diff(f(x,y),y);
g1(x)=diff(g(x,y),x);
g2(y)=diff(g(x,y),y);
for i= 1:N
    x1=x0-(((f(x0,y0)*g2(y0))-(g(x0,y0)*f2(y0)))/((f1(x0)*g2(y0))-(f2(y0)*g1(x0))));
    y1=y0-(((g(x0,y0)*f1(x0))-(f(x0,y0)*g1(x0)))/((f1(x0)*g2(y0))-(f2(y0)*g1(x0))));
   vpax1 = vpa(x1)
   vpay1 = vpa(y1)
     fprintf ('%3i %11.4f %11.4f %11.4f %11.4f %11.4f \n',i,x0,y0,f(x0,y0),g(x0,y0), tol)
if  abs(f(x0,y0)) < tol || abs(g(x0,y0)) < tol
        fprintf('Iteration Count = %g\n', N)  
        fprintf('The X Root = %0.5f\n', x1)
        fprintf('The Y Root = %0.5f\n', y1)
        break
else
    x0 = x1; 
    y0 = y1;
end
    if i==N
        fprintf('Root not obtained in %1i iterations',N)
    end
end

vpax1 = 

vpay1 = 

  1      3.0000      5.0000     -2.6712      6.3009      0.0001 

vpax1 = 

vpay1 = 

  2 

Error using fprintf
Conversion to double from sym is not possible.

.

[Walter Roberson]

The problem was in assuming that the partial derivatives with respect to one variable would be independent of the other variable.

syms x y 
sympref('AbbreviateOutput',false);
f(x,y)=x*sin(y)+y*sin(x)-0.5;
g(x,y)=x*cos(y)-y*cos(x)+0.5;
% x0=input('Value for  x:');
% y0=input('Value for  y:');
% N = input('Enter number of iterations = ');
x0 = 3;
y0 = 5;
N = 50;
tol=0.0001;
f1(x,y)=diff(f(x,y),x);
f2(x,y)=diff(f(x,y),y);
g1(x,y)=diff(g(x,y),x);
g2(x,y)=diff(g(x,y),y);
for i= 1:N
    x1=x0-(((f(x0,y0)*g2(x0,y0))-(g(x0,y0)*f2(x0,y0)))/((f1(x0,y0)*g2(x0,y0))-(f2(x0,y0)*g1(x0,y0))));
    y1=y0-(((g(x0,y0)*f1(x0,y0))-(f(x0,y0)*g1(x0,y0)))/((f1(x0,y0)*g2(x0,y0))-(f2(x0,y0)*g1(x0,y0))));
    %vpax1 = vpa(x1)
    %vpay1 = vpa(y1)
     fprintf ('%3i %11.4f %11.4f %11.4f %11.4f %11.4f \n',i,x0,y0,f(x0,y0),g(x0,y0), tol)
if  abs(f(x0,y0)) < tol || abs(g(x0,y0)) < tol
        fprintf('Iteration Count = %g\n', i)  
        fprintf('The X Root = %0.5f\n', x1)
        fprintf('The Y Root = %0.5f\n', y1)
        break
else
    x0 = double(x1); 
    y0 = double(y1);
end
    if i==N
        fprintf('Root not obtained in %1i iterations',N)
    end
end

  1      3.0000      5.0000     -2.6712      6.3009      0.0001 
  2      2.3042      3.5485      1.2242      0.7593      0.0001 
  3      3.7763      1.4693      2.3857      2.0659      0.0001 
  4     20.5512     -2.2059    -19.2308    -11.9802      0.0001 
  5      9.1136     -3.3946      0.7417    -11.5549      0.0001 
  6      4.5388     -5.1777      8.6561      1.6420      0.0001 
  7      1.7730     -8.7064    -10.1959     -2.5835      0.0001 
  8     -6.4568    -62.6676      9.2683     55.8558      0.0001 
  9    -11.4787    -13.9977     -1.5287      5.4063      0.0001 
 10    -11.7530    -13.2566     -2.6494      0.5449      0.0001 
 11    -16.3129     -8.2441      9.8985     -0.0771      0.0001 
 12    -19.1719     -7.2335     17.3906     -3.7856      0.0001 
 13    -17.1013     -7.1028      5.0074    -12.4262      0.0001 
 14    -19.7343     -6.7631     13.8453    -12.7202      0.0001 
 15    -17.4105     -6.6091     -1.4779    -15.1260      0.0001 
 16    -20.2326     -6.4881      9.9908    -18.0983      0.0001 
 17    -17.5951     -6.1870     -8.0697    -15.0891      0.0001 
 18    -20.7242     -6.3288      6.4830    -22.0960      0.0001 
 19    -17.5322     -5.7571    -14.8776    -13.2176      0.0001 
 20    -21.7371     -6.5264      6.3753    -26.9143      0.0001 
 21     -1.5441     -0.4805      0.6941     -0.8565      0.0001 
 22     -0.8359     -0.3295      0.0150     -0.0699      0.0001 
 23     -0.7840     -0.3382     -0.0011     -0.0001      0.0001 

Iteration Count = 23

The X Root = -0.78439

The Y Root = -0.33879