SOLVING LARGE SYSTEM OF EQUATIONS

Question

idriskameni 2019-4-5

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/454650-solving-large-system-of-equations

评论： Stephan 2019-4-5

Hi, this is my code (the only think that matters is the last line)

a = sym('a',[1 15]);
sym r
p1 = poly2sym(a,r);
diff = sym('diff');
eq = sym('eq');
fprintf('\n polynomial: %s\n', p1);
p2 =poly2sym(a,r);
p2=subs(p2,r,r-1);
%fprintf('\n p2: %s\n', p2);
diff= p1-p2;
%fprintf('\n diff: %s\n', simplify(diff));
diff = coeffs(diff,r);
branch2=prod(r-3:r+5)*(((1/1920)*(r+4)*(r+3)*(r^2+r-10))+((1/5120)*r*(r+1)*(r^2+r-10))+((1/9216)*(r+4)*(r+3)*(r+3)*(r-2)*(r-4)));
%fprintf('\n branch: %s\n', simplify(branch2));
%display(diff);
branch2=coeffs(branch2,r);
for u=1:14
    %fprintf('DIFF: %d = %s\n', u, diff(u));
    %fprintf('BRANCH: %d = %s\n', u, branch2(u));
    eq(u)= diff(u)==branch2(u);
    fprintf('EQ %d : %s\n', u, eq(u));
    %eqcoef(u)=coeffs(diff(u),[a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14]);
    % fprintf('EQCOEF %d : %s\n', u, eqcoef(u));
end
[A,B] = equationsToMatrix([eq(1), eq(2), eq(3),eq(4), eq(5), eq(6),eq(7), eq(8), eq(9),eq(10), eq(11), eq(12),eq(13),eq(14)], [a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14]);

I would like to solve the system. But this gives me an error that a1 is not defined. But it is. Any help?

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Answer 1

Stephan 2019-4-5

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/454650-solving-large-system-of-equations#answer_369250

在 MATLAB Online 中打开

Hi,

try:

a = sym('a',[1 15]);
syms r
p1 = poly2sym(a,r);
diff = sym('diff');
eq = sym('eq');
fprintf('\n polynomial: %s\n', p1);
p2 =poly2sym(a,r);
p2=subs(p2,r,r-1);
%fprintf('\n p2: %s\n', p2);
diff= p1-p2;
%fprintf('\n diff: %s\n', simplify(diff));
diff = coeffs(diff,r);
branch2=prod(r-3:r+5)*(((1/1920)*(r+4)*(r+3)*(r^2+r-10))+((1/5120)*r*(r+1)*(r^2+r-10))+((1/9216)*(r+4)*(r+3)*(r+3)*(r-2)*(r-4)));
%fprintf('\n branch: %s\n', simplify(branch2));
%display(diff);
branch2=coeffs(branch2,r);
for u=1:14
    %fprintf('DIFF: %d = %s\n', u, diff(u));
    %fprintf('BRANCH: %d = %s\n', u, branch2(u));
    eq(u)= diff(u)==branch2(u);
    fprintf('EQ %d : %s\n', u, eq(u));
    %eqcoef(u)=coeffs(diff(u),[a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14]);
    % fprintf('EQCOEF %d : %s\n', u, eqcoef(u));
end
[A,B] = equationsToMatrix([eq(1), eq(2), eq(3),eq(4), eq(5), eq(6),eq(7), eq(8), eq(9),eq(10), eq(11), eq(12),eq(13),eq(14)],a);

this results in:

 polynomial: a15 + a14*r + a1*r^14 + a2*r^13 + a3*r^12 + a4*r^11 + a5*r^10 + a6*r^9 + a7*r^8 + a8*r^7 + a9*r^6 + a10*r^5 + a11*r^4 + a12*r^3 + a13*r^2
EQ 1 : a2 - a1 - a3 + a4 - a5 + a6 - a7 + a8 - a9 + a10 - a11 + a12 - a13 + a14 == 45/2
EQ 2 : 14*a1 - 13*a2 + 12*a3 - 11*a4 + 10*a5 - 9*a6 + 8*a7 - 7*a8 + 6*a9 - 5*a10 + 4*a11 - 3*a12 + 2*a13 == 945/32
EQ 3 : 78*a2 - 91*a1 - 66*a3 + 55*a4 - 45*a5 + 36*a6 - 28*a7 + 21*a8 - 15*a9 + 10*a10 - 6*a11 + 3*a12 == -10541/640
EQ 4 : 364*a1 - 286*a2 + 220*a3 - 165*a4 + 120*a5 - 84*a6 + 56*a7 - 35*a8 + 20*a9 - 10*a10 + 4*a11 == -50033/1280
EQ 5 : 715*a2 - 1001*a1 - 495*a3 + 330*a4 - 210*a5 + 126*a6 - 70*a7 + 35*a8 - 15*a9 + 5*a10 == -275051/23040
EQ 6 : 2002*a1 - 1287*a2 + 792*a3 - 462*a4 + 252*a5 - 126*a6 + 56*a7 - 21*a8 + 6*a9 == 86971/9216
EQ 7 : 1716*a2 - 3003*a1 - 924*a3 + 462*a4 - 210*a5 + 84*a6 - 28*a7 + 7*a8 == 38813/5760
EQ 8 : 3432*a1 - 1716*a2 + 792*a3 - 330*a4 + 120*a5 - 36*a6 + 8*a7 == 7883/23040
EQ 9 : 1287*a2 - 3003*a1 - 495*a3 + 165*a4 - 45*a5 + 9*a6 == -3233/3840
EQ 10 : 2002*a1 - 715*a2 + 220*a3 - 55*a4 + 10*a5 == -181/768
EQ 11 : 286*a2 - 1001*a1 - 66*a3 + 11*a4 == 7/720
EQ 12 : 364*a1 - 78*a2 + 12*a3 == 311/23040
EQ 13 : 13*a2 - 91*a1 == 49/23040
EQ 14 : 14*a1 == 1/9216
>> A
 
A =
 
[    -1,     1,   -1,    1,   -1,    1,  -1,   1,  -1,   1, -1,  1, -1, 1, 0]
[    14,   -13,   12,  -11,   10,   -9,   8,  -7,   6,  -5,  4, -3,  2, 0, 0]
[   -91,    78,  -66,   55,  -45,   36, -28,  21, -15,  10, -6,  3,  0, 0, 0]
[   364,  -286,  220, -165,  120,  -84,  56, -35,  20, -10,  4,  0,  0, 0, 0]
[ -1001,   715, -495,  330, -210,  126, -70,  35, -15,   5,  0,  0,  0, 0, 0]
[  2002, -1287,  792, -462,  252, -126,  56, -21,   6,   0,  0,  0,  0, 0, 0]
[ -3003,  1716, -924,  462, -210,   84, -28,   7,   0,   0,  0,  0,  0, 0, 0]
[  3432, -1716,  792, -330,  120,  -36,   8,   0,   0,   0,  0,  0,  0, 0, 0]
[ -3003,  1287, -495,  165,  -45,    9,   0,   0,   0,   0,  0,  0,  0, 0, 0]
[  2002,  -715,  220,  -55,   10,    0,   0,   0,   0,   0,  0,  0,  0, 0, 0]
[ -1001,   286,  -66,   11,    0,    0,   0,   0,   0,   0,  0,  0,  0, 0, 0]
[   364,   -78,   12,    0,    0,    0,   0,   0,   0,   0,  0,  0,  0, 0, 0]
[   -91,    13,    0,    0,    0,    0,   0,   0,   0,   0,  0,  0,  0, 0, 0]
[    14,     0,    0,    0,    0,    0,   0,   0,   0,   0,  0,  0,  0, 0, 0]
 
>> B
 
B =
 
          45/2
        945/32
    -10541/640
   -50033/1280
 -275051/23040
    86971/9216
    38813/5760
    7883/23040
    -3233/3840
      -181/768
         7/720
     311/23040
      49/23040
        1/9216

Best regards

Stephan

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idriskameni 2019-4-5

But this is not correct. Since the coefficients of a_1 are the ones in the diagonal. But they should be the ones in the first column. How can I fix that?

Thank you anyways!