iteration using for loop is not working

Question

shiv gaur 2022-3-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1665004-iteration-using-for-loop-is-not-working

编辑： Walter Roberson 2022-3-6

a(1)=0;
b(1)=1;
c(1)=0;
n=1;
for n=1:5
    
    a(2)=0.5*(a(1)-b(1));
    b(2)=0.5*((a(1))-(b(1))-(a(1)*c(1)));
    c(2)=0.5*((a(1)*b(1)-c(1)));
    
    a(1)=a(2);
    b(1)=b(2);
    c(1)=c(2);
    
    n=n+1;
    
end
disp(a(2))

how to run this program to give from old value to new value using iteration a(2) giving more than five value

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Answer 1

Image Analyst 2022-3-6

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1665004-iteration-using-for-loop-is-not-working#answer_911324

在 MATLAB Online 中打开

Try it like this:

numElements = 5;
a = zeros(1, numElements);
b = ones(1, numElements);
c = zeros(1, numElements);
for n = 2 :  numElements
    a(n) = 0.5*(a(n-1)-b(n-1));
    b(n) = 0.5*((a(n-1))-(b(n-1))-(a(n-1)*c(n-1)));
    c(n) = 0.5*((a(n-1)*b(n-1)-c(n-1)));
end
a
a = 1×5
         0   -0.5000         0         0         0
b
b = 1×5
    1.0000   -0.5000         0         0         0
c
c = 1×5
         0         0    0.1250   -0.0625    0.0312

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Walter Roberson 2022-3-6

在 MATLAB Online 中打开

numElements = 20;

a = sym(zeros(1, numElements));

b = sym(ones(1, numElements));

c = sym(zeros(1, numElements));

for n = 2 : numElements

a(n) = (1/sym(n))*10*(a(n-1)-b(n-1));

b(n) = (1/sym(n))*((28*a(n-1))-(b(n-1))-(a(n-1)*c(n-1)));

c(n) = (1/sym(n))*((a(n-1)*b(n-1)-3.3*c(n-1)));

end

a

a =

b

b =

c

c =

digits(10)

vpa(a)

ans =

vpa(b)

ans =

vpa(c)

ans =

Walter Roberson 2022-3-6

编辑：Walter Roberson 2022-3-6

在 MATLAB Online 中打开

numElements = 10;
syms a [1 numElements]
syms b [1 numElements]
syms c [1 numElements]
for n = 2 :  numElements
    a(n) = (1/sym(n))*10*(a(n-1)-b(n-1));
    b(n) = (1/sym(n))*((28*a(n-1))-(b(n-1))-(a(n-1)*c(n-1)));
    c(n) = (1/sym(n))*((a(n-1)*b(n-1)-3.3*c(n-1)));
end
Ea = expand(a);
Ca  = vpa(findSymType(Ea, 'number'),5);
[~, idx] = sort(abs(Ca), 'desc');
format long g
double(reshape(Ca(idx(1:10)),[],1))
ans = 10×1
	1.0e+00 *

      2.14539347488294e+24
       2.1388215038686e+24
     -1.97683468274523e+24
     -1.66919049501844e+24
      1.57009953308725e+24
     -1.53553980415839e+24
      1.25698231464319e+24
     -1.12800014100977e+24
     -1.03005272271465e+24
      1.02716449593526e+24

So by the time you get to 10, you are working with coefficients as large as 2*10^24

Ca0 = vpa(findSymType(expand(subs(Ea, [sym('a1'), sym('a3')], [0,0])),'number'),5);
[~, idx] = sort(abs(Ca0), 'desc');
double(reshape(Ca0(1:10), [], 1))
ans = 10×1
	1.0e+00 *

     -9.35288582447091e+18
     -6.04096409393064e+18
     -1.99711770767288e+18
     -1.57887744010591e+18
     -1.23085737821287e+18
     -3.24385496525373e+17
     -2.04394672654123e+17
     -5.32546405724897e+16
     -4.96159656693842e+16
     -4.67790559622922e+16

And after you take into account that a and c start out as 0, you are still working with coefficients in the 10^18 range by the time you get to numElements = 10.

It isn't MATLAB messing up: your formulas are not working out for b as large as 1. If b were less than 1, then you might get very different results.

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