Newton Raphson gives answers divided by 0

Question

Jean-Paul 2024-3-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2092801-newton-raphson-gives-answers-divided-by-0

编辑： Matt J 2024-3-11

I'm trying to estimate 4 angles and 2 distances using the newton raphson method with phi4 and theta as the input. I have 6 functions that equal to 0 and when i try substituting to calculate dx (the array of all my values) i get a division by 0. I transposed some arrays to columns, but id be surprised if thats the issue. The functions themselves check out and im mostly using matlab functions to make this work so I don't really know what could be wrong

Angle=3;
phi4=pi/180*Angle;
theta=linspace(0,2*pi, 72);
%First guesses
phi1=ones(1, 72);
phi2=ones(1, 72);
phi3=ones(1, 72);
phi5=ones(1, 72);
d=ones(1,72);
s=ones(1, 72);
syms phi1V phi2V phi3V phi5V dV sV;
xV=[sV, dV, phi1V, phi2V, phi3V, phi5V];
ds=0;
dd=0;
dphi1=0;
dphi2=0;
dphi3=0;
dphi4=0;
dx=[ds, dd, dphi1, dphi2, dphi3, phi5]';
lim=0.01;
i=1;
while(i<73)
%redefine functions for changes in theta
f1=25-sV+dV*cos(phi2V)+3.1*cos(phi3V);
f2=-5+dV*sin(phi2V)+3.1*sin(phi3V);
f3=-25+6.3*cos(theta(i))+27*cos(phi1V)-19.2*cos(phi2V);
f4=11+6.3*sin(theta(i))+27*sin(phi1V)-19.2*sin(phi2V);
f5=-40+6.3*cos(theta(i))+(dV-19.2)*cos(phi2V)+29.1*cos(phi5V)+16*cos(phi4);
f6=-24+6.3*sin(theta(i))+(dV-19.2)*sin(phi2V)+29.1*sin(phi5V)+16*sin(phi4);
f=[f1, f2, f3, f4, f5, f6]';
J=jacobian(f, xV);
M=-inv(J)*f;
x=[s(i), d(i), phi1(i), phi2(i), phi3(i), phi5(i)];
    firstloop=1;
    while(ds > lim | dd > lim | dphi1 > lim | dphi2 > lim | dphi3 > lim | dphi4 > lim | firstloop==1)
        
        dx=subs(M, xV, x);
        x=x+dx;
        firstloop=0;
        
    end
    
    i=i+1;
end
Error using sym/subs
Division by zero.

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Answer 1

Sam Chak 2024-3-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2092801-newton-raphson-gives-answers-divided-by-0#answer_1423441

Hi @Jean-Paul

During the computation of M, certain elements involve divisions by

. In the line 'dx = subs(M, xV, x)', an attempt is made to substitute the variables in 'xV = [sV, dV, phi1V, phi2V, phi3V, phi5V]' with 'x = [1, 1, 1, 1, 1, 1]', which leads to

. Consequently, it triggers the 'Division-by-zero' error message.

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Answer 2

Torsten 2024-3-10

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2092801-newton-raphson-gives-answers-divided-by-0#answer_1423431

编辑：Torsten 2024-3-10

在 MATLAB Online 中打开

Your linear systems in the course of the Newton iterations cannot be solved since the Jacobian is rank-deficient (it has only rank 5 instead of rank 6 as needed). This usually indicates that the equations you try to solve are not independent or even contradictory.

Angle=3;
phi4=pi/180*Angle;
theta=linspace(0,2*pi, 72);
%First guesses
phi1=ones(1, 72);
phi2=ones(1, 72);
phi3=ones(1, 72);
phi5=ones(1, 72);
d=ones(1,72);
s=ones(1, 72);
syms phi1V phi2V phi3V phi5V dV sV;
xV=[sV, dV, phi1V, phi2V, phi3V, phi5V];
ds=0;
dd=0;
dphi1=0;
dphi2=0;
dphi3=0;
dphi4=0;
%dx=[ds, dd, dphi1, dphi2, dphi3, phi5]';
lim=0.01;
i=1;
while(i<73)
%redefine functions for changes in theta
f1=25-sV+dV*cos(phi2V)+3.1*cos(phi3V);
f2=-5+dV*sin(phi2V)+3.1*sin(phi3V);
f3=-25+6.3*cos(theta(i))+27*cos(phi1V)-19.2*cos(phi2V);
f4=11+6.3*sin(theta(i))+27*sin(phi1V)-19.2*sin(phi2V);
f5=-40+6.3*cos(theta(i))+(dV-19.2)*cos(phi2V)+29.1*cos(phi5V)+16*cos(phi4);
f6=-24+6.3*sin(theta(i))+(dV-19.2)*sin(phi2V)+29.1*sin(phi5V)+16*sin(phi4);
f=[f1, f2, f3, f4, f5, f6]';
J=jacobian(f, xV);
%M=-inv(J)*f
x=[s(i), d(i), phi1(i), phi2(i), phi3(i), phi5(i)]
    firstloop=1;
    while(ds > lim | dd > lim | dphi1 > lim | dphi2 > lim | dphi3 > lim | dphi4 > lim | firstloop==1)
        
        dx=-subs(J,xV,x)\subs(f,xV,x);%subs(M, xV, x)
        rank(subs(J,xV,x))
        rank([subs(J,xV,x),subs(f,xV,x)])
        x=x+dx;
        firstloop=0;
        
    end
    
    i=i+1;
end
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6
x = 1×6
     1     1     1     1     1     1
Warning: Solution does not exist because the system is inconsistent.
ans = 5
ans = 6

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Answer 3

Matt J 2024-3-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2092801-newton-raphson-gives-answers-divided-by-0#answer_1423496

编辑：Matt J 2024-3-11

在 MATLAB Online 中打开

Raw Newton-Raphson is a pretty terrible method, but I assume you'll tell us you have no choice...

[f,M]=preanalysis(); %Symbolic pre-analysis
%%%%Numeric stuff -- Newton-Raphson
Angle=3;
phi4=pi/180*Angle;
theta=linspace(0,2*pi, 72);
lim=1e-6;
i=1;
clear solutions
while(i<73)
 
    F=@(x) f(x, theta(i),phi4);
    Update=@(x) M(x, theta(i),phi4);
    x=F(zeros(6,1))/1000; %Initial guess - needs some experimentation
    
    dx=inf;
    firstloop=1;
    while( all(abs(dx)>lim) | firstloop==1)
        
        dx=Update(x);
        if any(~isfinite(dx)),
            warning 'Bad update. Aborting...'
            break; 
        end
        x=x+dx;
        
        x(1:4)=atan2(  sin(x(1:4))  , cos(x(1:4))); %normalize the 2*pi periodicity
        
        firstloop=0;
        
    end
    
    solutions{i}=x;
    i=i+1;
end
solutions=cell2mat(solutions);
solutions(:,1:20)
ans = 6×20
    0.2505    0.2273    0.2054    0.1852    0.1665    0.1495    0.1342    0.1205   -1.3914   -1.3886   -1.3832   -1.3755   -1.3657   -1.3539   -1.3404    0.0657    0.0650   -1.2913   -1.2727   -1.2534
    1.1719    1.1649    1.1619    1.1628    1.1675    1.1756    1.1870    1.2013   -2.5013   -2.5284   -2.5536   -2.5767   -2.5979   -2.6170   -2.6342    1.3896    1.4184   -2.6733   -2.6823   -2.6893
   -1.1402    0.8784    0.7734    2.8885   -0.6993   -2.6619   -0.4288    1.4046    2.4737   -1.4770    1.7734    0.2960   -0.9963   -0.8606    1.4129   -0.8061   -2.7819   -2.7265   -1.8485    0.0196
    0.9171    0.9085    0.8983    0.8866    0.8737    0.8598    0.8450    0.8294    0.7709   -2.6653   -2.6950   -2.7217    0.6895    2.9977    0.6579   -0.1126   -0.9554    3.0019    0.6113    0.6041
   19.2667   18.8273   18.4260   18.0661   17.7507   17.4828   17.2651   17.1002   21.3498  -36.4085  -36.4210  -36.5029   21.1271  -62.8851   20.4115  119.0125   60.3767  -62.0026   18.8311   18.3472
    6.4689   27.3019   31.5546    8.4895    3.5565   10.3017    1.9542   45.0152   31.9151   32.4906   51.2072   24.6759    6.1926  138.3313  -16.2680    8.5029  -95.8681  524.2912   -2.9438   89.7521
function [F,M]=preanalysis()
%%%Symbolic stuff
    
    syms phi1 phi2 phi3 phi5 d s theta phi4  real 
    
    f1=25-s+d*cos(phi2)+3.1*cos(phi3);
    f2=-5+d*sin(phi2)+3.1*sin(phi3);
    f3=-25+6.3*cos(theta)+27*cos(phi1)-19.2*cos(phi2);
    f4=11+6.3*sin(theta)+27*sin(phi1)-19.2*sin(phi2);
    f5=-40+6.3*cos(theta)+(d-19.2)*cos(phi2)+29.1*cos(phi5)+16*cos(phi4);
    f6=-24+6.3*sin(theta)+(d-19.2)*sin(phi2)+29.1*sin(phi5)+16*sin(phi4);
    
    f=[f1, f2, f3, f4, f5, f6]';
    
    x=[phi1 phi2 phi3 phi5 d s]';
    
    J=jacobian(f, x);
    
    M=matlabFunction(-J\f,'Vars',{x,theta,phi4});
    F=matlabFunction(f,'Vars',{x,theta,phi4});
end