how to perform data fit like excel? and plot

Question

Anand Ra 2021 年 6 月 16 日

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https://jp.mathworks.com/matlabcentral/answers/857320-how-to-perform-data-fit-like-excel-and-plot

コメント済み: Anand Ra 2021 年 6 月 26 日

採用された回答: Walter Roberson

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I have observed array of data ( y_obs) and predicted data (y_pred)
Predicted data is obtained from an equation
How do I fit the observed data to the predicted data by minimizing the coefficient "d" in the equation? ( This is possible in excel, but I could not find a suitable method in matlab

Below is my code for steps 1 and 2:

% observed data
y_obs = [0.3 0.2 0.28 0.318 0.421 0.492 0.572 0.55 0.63 0.61 0.73 0.8 0.81 0.84 0.93 0.91]'; % If y_obs should equal to predicted, I can have more data. J us fo rthe code, I am providing limited observed data
t1 = [300:300:21600]';
a=0.0011;
gama = 0.01005;
d=0.000000000302;
n=1;
t=300;
L2 = zeros(14,1);
     L3 = zeros(14,1);
     L4 = zeros(14,1);
     At = zeros(14,1);
 t = 300; 
  n =1;
L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));
format shortE
  for t= 300:300:21600
    for n=1:1:14
L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));
  
L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);
  
L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);
 
L5(n) = ((L2(n).*L3(n))/L4(n));
    end
  S(t/300) = sum(L5);
  
y_pred(t/300) = 1 -L1*S(t/300); % predicted data
 
  end
 

2 件のコメント
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Walter Roberson 2021 年 6 月 16 日

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L2 = zeros(14);

that should probably be

L2 = zeros(14,1);

like the other variables.

Anand Ra 2021 年 6 月 16 日

Thanks for the response, I can update it.

Can you please guide me on how to perform the data fitting in the fashion I described in bullet point 3?

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Answer 1

Walter Roberson 2021 年 6 月 16 日

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この回答への直接リンク

https://jp.mathworks.com/matlabcentral/answers/857320-how-to-perform-data-fit-like-excel-and-plot#answer_725815

編集済み: Walter Roberson 2021 年 6 月 16 日

MATLAB Online で開く

format shortE

% observed data

y_obs = [0.3 0.2 0.28 0.318 0.421 0.492 0.572 0.55 0.63 0.61 0.73 0.8 0.81 0.84 0.93 0.91]'; % If y_obs should equal to predicted, I can have more data. J us fo rthe code, I am providing limited observed data

t1 = [300:300:21600]';

T1 = t1(1:length(y_obs)).';

a=0.0011;

gama = 0.01005;

d0 = 0.000000000302;

syms d

n=1;

t=300;

L2 = sym(zeros(14,1));

L3 = sym(zeros(14,1));

L4 = sym(zeros(14,1));

At = sym(zeros(14,1));

t = 300;

n =1;

L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));

y_pred = sym(zeros(length(T1),1));

for t = T1

for n=1:1:14

L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));

L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);

L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);

L5(n) = ((L2(n).*L3(n))/L4(n));

end

S(t/300) = sum(L5);

y_pred(t/300) = 1 -L1*S(t/300); % predicted data

end

sse = expand(sum((y_pred - y_obs(:)).^2));

f = matlabFunction(sse)

ans =

opt1 = fmincon(f, d0)

opt2 = fminsearch(f, d0)

35 件のコメント
33 件の古いコメントを表示33 件の古いコメントを非表示

Walter Roberson 2021 年 6 月 17 日

MATLAB Online で開く

format long g

% observed data

y_obs = [0.3 0.2 0.28 0.318 0.421 0.492 0.572 0.55 0.63 0.61 0.73 0.8 0.81 0.84 0.93 0.91]'; % If y_obs should equal to predicted, I can have more data. J us fo rthe code, I am providing limited observed data

t1 = [300:300:21600]';

T1 = t1(1:length(y_obs)).';

a=0.0011;

gama = 0.01005;

d0 = 0.000000000302;

syms d

n=1;

t=300;

L2 = sym(zeros(14,1));

L3 = sym(zeros(14,1));

L4 = sym(zeros(14,1));

At = sym(zeros(14,1));

t = 300;

n =1;

L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));

y_pred = sym(zeros(length(T1),1));

for t = T1

for n=1:1:14

L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));

L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);

L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);

L5(n) = ((L2(n).*L3(n))/L4(n));

end

S(t/300) = sum(L5);

y_pred(t/300) = 1 -L1*S(t/300); % predicted data

end

sse = expand(sum((y_pred - y_obs(:)).^2));

f = matlabFunction(sse)

f = function_handle with value: 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
[opt_mc, err_mc] = fmincon(f, d0)

Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.

opt_mc =

1.82376530468465e-11

err_mc =

2.75102571512948

[opt_ms, err_ms] = fminsearch(f, d0)

opt_ms =

-3.31787109375621e-13

err_ms =

1.68163295678904

y_pred_n = double(subs(y_pred, d, opt_mc));

plot(T1, y_obs, 'k*', T1, y_pred_n, 'b')

legend({'observed', 'modeled'})

title('fmincon predictions')

y_pred_n = double(subs(y_pred, d, opt_ms));

plot(T1, y_obs, 'k*', T1, y_pred_n, 'b')

legend({'observed', 'modeled'})

title('fminsearch predictions')

These are not straight lines, and the predicted minimum is not the same as d0.

The visual fit is not good in either case.

Walter Roberson 2021 年 6 月 18 日

MATLAB Online で開く

format long g

% observed data

y_obs = [0.3 0.2 0.28 0.318 0.421 0.492 0.572 0.55 0.63 0.61 0.73 0.8 0.81 0.84 0.93 0.91]'; % If y_obs should equal to predicted, I can have more data. J us fo rthe code, I am providing limited observed data

t1 = [300:300:21600]';

T1 = t1(1:length(y_obs)).';

a=0.0011;

gama = 0.01005;

d0 = 0.000000000302;

syms d

n=1;

t=300;

L2 = sym(zeros(14,1));

L3 = sym(zeros(14,1));

L4 = sym(zeros(14,1));

At = sym(zeros(14,1));

t = 300;

n =1;

L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));

y_pred = sym(zeros(length(T1),1));

for t = T1

for n=1:1:14

L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));

L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);

L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);

L5(n) = ((L2(n).*L3(n))/L4(n));

end

S(t/300) = sum(L5);

y_pred(t/300) = 1 -L1*S(t/300); % predicted data

end

flsq = matlabFunction(y_pred(:))

flsq = function_handle with value:

@(d)[exp(d.*pi.^2.*(-7.5e+9)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-5.212809917355372e+10)).*9.638060662976441e-4-exp(d.*pi.^2.*(-4.518595041322314e+10)).*1.111879404329578e-3-exp(d.*pi.^2.*(-3.87396694214876e+10)).*1.296897543527722e-3-exp(d.*pi.^2.*(-3.278925619834711e+10)).*1.532249550596395e-3-exp(d.*pi.^2.*(-2.733471074380165e+10)).*1.838006919804312e-3-exp(d.*pi.^2.*(-2.237603305785124e+10)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.791322314049587e+10)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.394628099173554e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-1.047520661157025e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-5.020661157024793e+9)).*1.000693550667001e-2-exp(d.*pi.^2.*(-3.037190082644628e+9)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.549586776859504e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-5.578512396694215e+8)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-1.5e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-1.042561983471074e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-9.037190082644628e+10)).*1.111879404329578e-3-exp(d.*pi.^2.*(-7.74793388429752e+10)).*1.296897543527722e-3-exp(d.*pi.^2.*(-6.557851239669421e+10)).*1.532249550596395e-3-exp(d.*pi.^2.*(-5.46694214876033e+10)).*1.838006919804312e-3-exp(d.*pi.^2.*(-4.475206611570248e+10)).*2.245318304241606e-3-exp(d.*pi.^2.*(-3.582644628099173e+10)).*2.804709963564875e-3-exp(d.*pi.^2.*(-2.789256198347107e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-2.095041322314049e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-1.004132231404959e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-6.074380165289256e+9)).*1.654201792665767e-2-exp(d.*pi.^2.*(-3.099173553719008e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-1.115702479338843e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-2.25e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-1.563842975206611e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-1.355578512396694e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-1.162190082644628e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-9.836776859504132e+10)).*1.532249550596395e-3-exp(d.*pi.^2.*(-8.200413223140495e+10)).*1.838006919804312e-3-exp(d.*pi.^2.*(-6.712809917355372e+10)).*2.245318304241606e-3-exp(d.*pi.^2.*(-5.37396694214876e+10)).*2.804709963564875e-3-exp(d.*pi.^2.*(-4.183884297520661e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-3.142561983471074e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-1.506198347107438e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-9.111570247933884e+9)).*1.654201792665767e-2-exp(d.*pi.^2.*(-4.648760330578512e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-1.673553719008264e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-3.0e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-2.085123966942149e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-1.807438016528926e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-1.549586776859504e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-1.311570247933884e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-1.093388429752066e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-8.950413223140495e+10)).*2.245318304241606e-3-exp(d.*pi.^2.*(-7.165289256198347e+10)).*2.804709963564875e-3-exp(d.*pi.^2.*(-5.578512396694215e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-4.190082644628099e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-2.008264462809917e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-1.214876033057851e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-6.198347107438016e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-2.231404958677686e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-3.75e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-2.606404958677686e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-2.259297520661157e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-1.93698347107438e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-1.639462809917355e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-1.366735537190083e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-1.118801652892562e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-8.956611570247933e+10)).*2.804709963564875e-3-exp(d.*pi.^2.*(-6.973140495867768e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-5.237603305785124e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-2.510330578512397e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-1.518595041322314e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-7.74793388429752e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-2.789256198347107e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-4.5e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-3.127685950413223e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-2.711157024793388e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-2.324380165289256e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-1.967355371900826e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-1.640082644628099e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-1.342561983471074e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.074793388429752e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-8.367768595041322e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-6.285123966942148e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-3.012396694214876e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-1.822314049586777e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-9.297520661157024e+9)).*3.242251160829167e-2-exp(d.*pi.^2.*(-3.347107438016529e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-5.25e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-3.64896694214876e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-3.16301652892562e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-2.711776859504132e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-2.295247933884297e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-1.913429752066116e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-1.566322314049587e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.253925619834711e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-9.762396694214876e+10)).*3.602487767549398e-3-exp(d.*pi.^2.*(-7.332644628099173e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-3.514462809917355e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-2.12603305785124e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.084710743801653e+10)).*3.242251160829167e-2-exp(d.*pi.^2.*(-3.90495867768595e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-6.0e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-4.170247933884297e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-3.614876033057851e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-3.099173553719008e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-2.623140495867768e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-2.186776859504132e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-1.790082644628099e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.433057851239669e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.115702479338843e+11)).*3.602487767549398e-3-exp(d.*pi.^2.*(-8.380165289256198e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-4.016528925619835e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-2.429752066115702e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.239669421487603e+10)).*3.242251160829167e-2-exp(d.*pi.^2.*(-4.462809917355372e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-6.75e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-4.691528925619834e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-4.066735537190082e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-3.486570247933884e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-2.95103305785124e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-2.460123966942149e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-2.013842975206611e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.612190082644628e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.255165289256198e+11)).*3.602487767549398e-3-exp(d.*pi.^2.*(-9.427685950413223e+10)).*4.796221218789088e-3-exp(d.*pi.^2.*(-4.518595041322314e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-2.733471074380165e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.394628099173554e+10)).*3.242251160829167e-2-exp(d.*pi.^2.*(-5.020661157024793e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-7.5e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-5.212809917355372e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-4.518595041322314e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-3.87396694214876e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-3.278925619834711e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-2.733471074380165e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-2.237603305785124e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.791322314049587e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.394628099173554e+11)).*3.602487767549398e-3-exp(d.*pi.^2.*(-1.047520661157025e+11)).*4.796221218789088e-3-exp(d.*pi.^2.*(-5.020661157024793e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-3.037190082644628e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.549586776859504e+10)).*3.242251160829167e-2-exp(d.*pi.^2.*(-5.578512396694215e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-5.734090909090909e+11)).*(-9.638060662976441e-4)-exp(d.*pi.^2.*(-4.970454545454545e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-4.261363636363636e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-3.606818181818182e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-3.006818181818182e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-2.461363636363636e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-1.970454545454545e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.534090909090909e+11)).*3.602487767549398e-3-exp(d.*pi.^2.*(-1.152272727272727e+11)).*4.796221218789088e-3-exp(d.*pi.^2.*(-8.25e+10)).*6.698838604180037e-3-exp(d.*pi.^2.*(-5.522727272727272e+10)).*1.000693550667001e-2-exp(d.*pi.^2.*(-3.340909090909091e+10)).*1.654201792665767e-2-exp(d.*pi.^2.*(-1.704545454545454e+10)).*3.242251160829167e-2-exp(d.*pi.^2.*(-6.136363636363636e+9)).*9.006185612967756e-2+1.0;exp(d.*pi.^2.*(-9.0e+10)).*(-6.698838604180037e-3)-exp(d.*pi.^2.*(-6.255371900826446e+11)).*9.638060662976441e-4-exp(d.*pi.^2.*(-5.422314049586777e+11)).*1.111879404329578e-3-exp(d.*pi.^2.*(-4.648760330578512e+11)).*1.296897543527722e-3-exp(d.*pi.^2.*(-3.934710743801653e+11)).*1.532249550596395e-3-exp(d.*pi.^2.*(-3.280165289256198e+11)).*1.838006919804312e-3-exp(d.*pi.^2.*(-2.685123966942149e+11)).*2.245318304241606e-3-exp(d.*pi.^2.*(-2.149586776859504e+11)).*2.804709963564875e-3-exp(d.*pi.^2.*(-1.673553719008264e+11)).*3.602487767549398e-3-exp(d.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[opt_lsq, err_lsq] = lsqnonlin(flsq, d0)

Local minimum possible. lsqnonlin stopped because the size of the current step is less than the value of the step size tolerance.

opt_lsq =

3.02e-10

err_lsq =

15.9575171934164

y_pred_n = double(subs(y_pred, d, opt_lsq));

plot(T1, y_obs, 'k*', T1, y_pred_n, 'b')

legend({'observed', 'modeled'})

title('lsqnonlin predictions')

Walter Roberson 2021 年 6 月 19 日

MATLAB Online で開く

Your model cannot even get close if you confine to two observations :(

If you confine to one observation, then the fminsearch() version can get quite close for that one point, but the fmincon() version doesn't get close.

Taylor series doesn't help it seems.

format long g

% observed data

y_obs = [0.3 0.2 0.28 0.318 0.421 0.492 0.572 0.55 0.63 0.61 0.73 0.8 0.81 0.84 0.93 0.91]'; % If y_obs should equal to predicted, I can have more data. J us fo rthe code, I am providing limited observed data

t1 = [300:300:21600]';

T1 = t1(1:length(y_obs)).';

y_obsX = y_obs([1 3]);

T1X = T1([1 3]);

a=0.0011;

gama = 0.01005;

d0 = 0.000000000302;

syms d

n=1;

t=300;

L2 = sym(zeros(14,1));

L3 = sym(zeros(14,1));

L4 = sym(zeros(14,1));

At = sym(zeros(14,1));

t = 300;

n =1;

L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));

y_pred = sym(zeros(length(T1X),1));

for tidx = 1 : length(T1X)

t = T1X(tidx);

for n=1:1:14

L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));

L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);

L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);

L5(n) = ((L2(n).*L3(n))/L4(n));

end

S(tidx) = sum(L5);

y_pred(tidx) = 1 - L1*S(tidx); % predicted data

end

sse = expand(sum((y_pred - y_obsX(:)).^2));

f = matlabFunction(sse)

f = function_handle with value:

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[opt_mc, err_mc] = fmincon(f, d0)

Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.

opt_mc =

1.82376530468464e-11

err_mc =

0.737074171900867

[opt_ms, err_ms] = fminsearch(f, d0)

opt_ms =

-3.48007812500063e-12

err_ms =

0.237225768747742

y_pred_n = double(subs(y_pred, d, opt_mc));

plot(T1, y_obs, 'k*', T1X, y_pred_n, 'r-v')

legend({'observed', 'modeled'})

title('fmincon predictions')

y_pred_n = double(subs(y_pred, d, opt_ms));

plot(T1, y_obs, 'k*', T1X, y_pred_n, 'r-v')

legend({'observed', 'modeled'})

title('fminsearch predictions')

best_d = vpasolve(diff(sse, d))

best_d =

1.0

f(double(best_d))

ans =

1.0084

FT = taylor(sse, d, 0, 'order', 10)

FT =

trial_sol = vpasolve(FT)

trial_sol =

f(double(trial_sol))

ans =

320.450229336017 + 0i 0.343266356293643 + 0i 0.654561380806186 + 0i 0.562484132868365 + 0.0790092483031968i 0.562484132868365 - 0.0790092483031968i 0.630971889213914 + 0.068321190380106i 0.630971889213914 - 0.068321190380106i 0.648768811395252 + 0.0351822086775853i 0.648768811395252 - 0.0351822086775853i

Anand Ra 2021 年 6 月 19 日

編集済み: Anand Ra 2021 年 6 月 19 日

MATLAB Online で開く

Oh ok.

Btw, wanted to share the full set of data for y_obs to you. The previous "y_obs" data that I gave could probably be the issue. I am sorry about that. Below is the complete set of observed data

format long g
% observed data
y_obs = [         0
   1.6216e-01
   2.9813e-01
   4.0805e-01
   4.9338e-01
   5.5928e-01
   6.0894e-01
   6.5506e-01
   6.8876e-01
   7.1773e-01
   7.4284e-01
   7.6433e-01
   7.8448e-01
   7.9912e-01
   8.1484e-01
   8.2950e-01
   8.3760e-01
   8.4707e-01
   8.5767e-01
   8.6299e-01
   8.6862e-01
   8.7433e-01
   8.7879e-01
   8.8736e-01
   8.9152e-01
   8.9903e-01
   9.0343e-01
   9.0984e-01
   9.1344e-01
   9.1615e-01
   9.2046e-01
   9.2313e-01
   9.2640e-01
   9.2992e-01
   9.3134e-01
   9.3242e-01
   9.3616e-01
   9.3986e-01
   9.4201e-01
   9.4145e-01
   9.4434e-01
   9.4252e-01
   9.4131e-01
   9.4249e-01
   9.4283e-01
   9.4395e-01
   9.4355e-01
   9.4690e-01
   9.4919e-01
   9.5255e-01
   9.5626e-01
   9.6282e-01
   9.6283e-01
   9.6672e-01
   9.6439e-01
   9.6887e-01
   9.7099e-01
   9.7529e-01
   9.8034e-01
   9.8302e-01
   9.8494e-01
   9.8828e-01
   9.8769e-01
   9.9130e-01
   9.9108e-01
   9.9422e-01
   9.9561e-01
   9.9737e-01
   1.0002e+00
   1.0034e+00
   1.0044e+00]
t1 = [300:300:21600]';
T1 = t1(1:length(y_obs)).';
a=0.0011;
gama = 0.01005;
d0 = 0.000000000302;
syms d
n=1;
t=300;
    L2 = sym(zeros(14,1));
     L3 = sym(zeros(14,1));
     L4 = sym(zeros(14,1));
     At = sym(zeros(14,1));
 t = 300; 
  n =1;
L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));
y_pred = sym(zeros(length(T1),1));
  for t = T1
    for n=1:1:14
L2(n) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));
  
L3(n) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);
  
L4(n)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);
 
L5(n) = ((L2(n).*L3(n))/L4(n));
    end
  S(t/300) = sum(L5);
  
y_pred(t/300) = 1 -L1*S(t/300); % predicted data
 
  end
  
  sse = expand(sum((y_pred - y_obs(:)).^2));
  
 f = matlabFunction(sse)
 [opt_mc, err_mc] = fmincon(f, d0)
 
 [opt_ms, err_ms] = fminsearch(f, d0)
  
y_pred_n = double(subs(y_pred, d, opt_mc));
plot(T1, y_obs, 'k*', T1, y_pred_n, 'b')
legend({'observed', 'modeled'})
title('fmincon predictions')
y_pred_n = double(subs(y_pred, d, opt_ms));
plot(T1, y_obs, 'k*', T1, y_pred_n, 'b')
legend({'observed', 'modeled'})
title('fminsearch predictions')

Anand Ra 2021 年 6 月 20 日

編集済み: Anand Ra 2021 年 6 月 21 日

MATLAB Online で開く

I went and coded the model assignment again and verified the two sets of data. The problem was that when the assignments were changed to syms, I am unable to verify the array coming out of the equation..

Below is the code:

y_obs = [         
    0
   1.6216e-01
   2.9813e-01
   4.0805e-01
   4.9338e-01
   5.5928e-01
   6.0894e-01
   6.5506e-01
   6.8876e-01
   7.1773e-01
   7.4284e-01
   7.6433e-01
   7.8448e-01
   7.9912e-01
   8.1484e-01
   8.2950e-01
   8.3760e-01
   8.4707e-01
   8.5767e-01
   8.6299e-01
   8.6862e-01
   8.7433e-01
   8.7879e-01
   8.8736e-01
   8.9152e-01
   8.9903e-01
   9.0343e-01
   9.0984e-01
   9.1344e-01
   9.1615e-01
   9.2046e-01
   9.2313e-01
   9.2640e-01
   9.2992e-01
   9.3134e-01
   9.3242e-01
   9.3616e-01
   9.3986e-01
   9.4201e-01
   9.4145e-01
   9.4434e-01
   9.4252e-01
   9.4131e-01
   9.4249e-01
   9.4283e-01
   9.4395e-01
   9.4355e-01
   9.4690e-01
   9.4919e-01
   9.5255e-01
   9.5626e-01
   9.6282e-01
   9.6283e-01
   9.6672e-01
   9.6439e-01
   9.6887e-01
   9.7099e-01
   9.7529e-01
   9.8034e-01
   9.8302e-01
   9.8494e-01
   9.8828e-01
   9.8769e-01
   9.9130e-01
   9.9108e-01
   9.9422e-01
   9.9561e-01
   9.9737e-01
   1.0002e+00
   1.0034e+00
   1.0044e+00
   1.00329
   1.0];
t1 = [0:300:21600]';
a=0.0011;
gama = 0.01005;
d=0.000000000302;
n=1;
L2 = zeros(14,1);
     L3 = zeros(14,1);
     L4 = zeros(14,1);
       L5 = zeros(14,1);
       S= zeros(73,1);
       y_pred = zeros(73,1);
     At = zeros(73,1);
% t = 0; 
  
L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));
format longE
j=1;
k =1;
 for t= 0:300:21600
    for n=0:1:14
L2(n+1) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));
  
L3(n+1) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);
  
L4(n+1)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);
 
L5(n+1) = ((L2(n+1)*L3(n+1))/L4(n+1));
        
    end
 S((t/300) +1) = sum(L5);
y_pred((t/300)+1)= 1 -(L1*S((t/300) +1)); % predicted data
 
 end
plot(t1, y_obs, 'k*', t1, y_pred, 'b')
legend({'observed', 'model data from equation'})
title('Plot before data fitting')
 

Anand Ra 2021 年 6 月 21 日

MATLAB Online で開く

Thanks, and its executing. However, its not minimizing the d or performing the fitting process. It throws back the same initial assignment. The reason is as you mentioned earlier? the data is very sensitive? I am wondering why its not working because, I looking to replicate the fitting in the literature.

t1 = [0:300:21600]';
y_obs = [         
    0
   1.6216e-01
   2.9813e-01
   4.0805e-01
   4.9338e-01
   5.5928e-01
   6.0894e-01
   6.5506e-01
   6.8876e-01
   7.1773e-01
   7.4284e-01
   7.6433e-01
   7.8448e-01
   7.9912e-01
   8.1484e-01
   8.2950e-01
   8.3760e-01
   8.4707e-01
   8.5767e-01
   8.6299e-01
   8.6862e-01
   8.7433e-01
   8.7879e-01
   8.8736e-01
   8.9152e-01
   8.9903e-01
   9.0343e-01
   9.0984e-01
   9.1344e-01
   9.1615e-01
   9.2046e-01
   9.2313e-01
   9.2640e-01
   9.2992e-01
   9.3134e-01
   9.3242e-01
   9.3616e-01
   9.3986e-01
   9.4201e-01
   9.4145e-01
   9.4434e-01
   9.4252e-01
   9.4131e-01
   9.4249e-01
   9.4283e-01
   9.4395e-01
   9.4355e-01
   9.4690e-01
   9.4919e-01
   9.5255e-01
   9.5626e-01
   9.6282e-01
   9.6283e-01
   9.6672e-01
   9.6439e-01
   9.6887e-01
   9.7099e-01
   9.7529e-01
   9.8034e-01
   9.8302e-01
   9.8494e-01
   9.8828e-01
   9.8769e-01
   9.9130e-01
   9.9108e-01
   9.9422e-01
   9.9561e-01
   9.9737e-01
   1.0002e+00
   1.0034e+00
   1.0044e+00
   1.00329
   1.0];
d0 = 0.000000000302;
fun = @(d) ypred(d, t1) - y_obs;
best_d = lsqnonlin(fun, d0)
predicted_y = ypred(best_d, t1);
plot(t1, y_obs, '*', t1, predicted_y, '-');
legend({'observed', 'predicted'})
title('lsqnonlin data fitting')
function y_pred = ypred(d, t1)
  t1 = [0:300:21600]';
a=0.0011;
gama = 0.01005;
d=0.000000000302;
L2 = zeros(14,1);
     L3 = zeros(100,1);
     L4 = zeros(100,1);
       L5 = zeros(100,1);
       S= zeros(73,1);
       y_pred = zeros(73,1);
     
% t = 0; 
  
L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));
format longE
k =1;
 for t= 0:300:21600
    for n=0:1:100
L2(n+1) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));
  
L3(n+1) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);
  
L4(n+1)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);
 
L5(n+1) = ((L2(n+1)*L3(n+1))/L4(n+1));
        
    end
 S((t/300) +1) = sum(L5);
y_pred((t/300)+1)= 1 -(L1*S((t/300) +1)); % predicted data
 
 end
end

Walter Roberson 2021 年 6 月 21 日

編集済み: Walter Roberson 2021 年 6 月 21 日

MATLAB Online で開く

You overwrote d and t1 in the function and you hardcoded t1 in the function.

t1 = [0:300:21600]';

y_obs = [

0

1.6216e-01

2.9813e-01

4.0805e-01

4.9338e-01

5.5928e-01

6.0894e-01

6.5506e-01

6.8876e-01

7.1773e-01

7.4284e-01

7.6433e-01

7.8448e-01

7.9912e-01

8.1484e-01

8.2950e-01

8.3760e-01

8.4707e-01

8.5767e-01

8.6299e-01

8.6862e-01

8.7433e-01

8.7879e-01

8.8736e-01

8.9152e-01

8.9903e-01

9.0343e-01

9.0984e-01

9.1344e-01

9.1615e-01

9.2046e-01

9.2313e-01

9.2640e-01

9.2992e-01

9.3134e-01

9.3242e-01

9.3616e-01

9.3986e-01

9.4201e-01

9.4145e-01

9.4434e-01

9.4252e-01

9.4131e-01

9.4249e-01

9.4283e-01

9.4395e-01

9.4355e-01

9.4690e-01

9.4919e-01

9.5255e-01

9.5626e-01

9.6282e-01

9.6283e-01

9.6672e-01

9.6439e-01

9.6887e-01

9.7099e-01

9.7529e-01

9.8034e-01

9.8302e-01

9.8494e-01

9.8828e-01

9.8769e-01

9.9130e-01

9.9108e-01

9.9422e-01

9.9561e-01

9.9737e-01

1.0002e+00

1.0034e+00

1.0044e+00

1.00329

1.0];

d0 = 1e-10;

fun = @(d) ypred(d, t1) - y_obs;

best_d = lsqnonlin(fun, d0)

Local minimum possible. lsqnonlin stopped because the size of the current step is less than the value of the step size tolerance.

best_d =

1.000000000000000e-10

predicted_y = ypred(best_d, t1);

plot(t1, y_obs, '*', t1, predicted_y, '-');

legend({'observed', 'predicted'})

title('lsqnonlin data fitting')

function y_pred = ypred(d, t1)

a=0.0011;

gama = 0.01005;

L2 = zeros(14,1);

L3 = zeros(100,1);

L4 = zeros(100,1);

L5 = zeros(100,1);

S= zeros(73,1);

y_pred = zeros(73,1);

% t = 0;

L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));

format longE

k =1;

for t = t1(:).'

for n=0:1:100

L2(n+1) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));

L3(n+1) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);

L4(n+1)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);

L5(n+1) = ((L2(n+1)*L3(n+1))/L4(n+1));

end

S((t/300) +1) = sum(L5);

y_pred((t/300)+1)= 1 -(L1*S((t/300) +1)); % predicted data

end

Anand Ra 2021 年 6 月 25 日

MATLAB Online で開く

Hello,

All of a sudden, the curvesa are fitting. I have no idea what I did.

t1 = [0:300:21600]';
y_obs = [         
    0
   1.6216e-01
   2.9813e-01
   4.0805e-01
   4.9338e-01
   5.5928e-01
   6.0894e-01
   6.5506e-01
   6.8876e-01
   7.1773e-01
   7.4284e-01
   7.6433e-01
   7.8448e-01
   7.9912e-01
   8.1484e-01
   8.2950e-01
   8.3760e-01
   8.4707e-01
   8.5767e-01
   8.6299e-01
   8.6862e-01
   8.7433e-01
   8.7879e-01
   8.8736e-01
   8.9152e-01
   8.9903e-01
   9.0343e-01
   9.0984e-01
   9.1344e-01
   9.1615e-01
   9.2046e-01
   9.2313e-01
   9.2640e-01
   9.2992e-01
   9.3134e-01
   9.3242e-01
   9.3616e-01
   9.3986e-01
   9.4201e-01
   9.4145e-01
   9.4434e-01
   9.4252e-01
   9.4131e-01
   9.4249e-01
   9.4283e-01
   9.4395e-01
   9.4355e-01
   9.4690e-01
   9.4919e-01
   9.5255e-01
   9.5626e-01
   9.6282e-01
   9.6283e-01
   9.6672e-01
   9.6439e-01
   9.6887e-01
   9.7099e-01
   9.7529e-01
   9.8034e-01
   9.8302e-01
   9.8494e-01
   9.8828e-01
   9.8769e-01
   9.9130e-01
   9.9108e-01
   9.9422e-01
   9.9561e-01
   9.9737e-01
   1.0002e+00
   1.0034e+00
   1.0044e+00
   1.00329
   1.0];
d0 = 3.0e-10;
fun = @(d) ypred(d, t1) - y_obs;
best_d = lsqnonlin(fun, d0)
predicted_y = ypred(best_d, t1);
plot(t1, y_pred, '*', t1, predicted_y, '-');
legend({'observed', 'predicted'})
%title('lsqnonlin data fitting')
function y_pred = ypred(d, t1)
  
a=0.0011;
gama = 0.01005;
L2 = zeros(14,1);
     L3 = zeros(100,1);
     L4 = zeros(100,1);
       L5 = zeros(100,1);
       S= zeros(73,1);
       y_pred = zeros(73,1);
     
 
L1 = ((8*gama)/((pi*(1-exp(-2*gama*a)))));
format longE
 for t= t1(:).'
    for n=0:1:100
L2(n+1) = exp((((2*n + 1)^2)*-d*pi*pi*t)/(4*a*a));
  
L3(n+1) = (((-1)^n)*2*gama)+(((2*n+1)*pi)*exp(-2*gama*a))/(2*a);
  
L4(n+1)= ((2*n)+1)*((4*gama*gama)+((((2*n)+1)*pi)/(2*a))^2);
 
L5(n+1) = ((L2(n+1)*L3(n+1))/L4(n+1));
        
    end
 S((t/300) +1) = sum(L5);
y_pred((t/300)+1)= 1 -(L1*S((t/300) +1)); % predicted data
 
 end
end

Anand Ra 2021 年 6 月 25 日

However, I had to keep attempting the inital value to get the right number that would produce a fit. The optimized coefficient is same as my initial assumption.

When I tried with different datab set for y_obs, I am unable to find that perfect inital guess that would produce me a good fit.

Not sure what is going wrong.

Anand Ra 2021 年 6 月 26 日

Did I make any mistake like earlier with the code? Is there a way to get a good fit with an arbitrary initial guess?

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