How to fit power-law to each column of data arranged in a table?

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Sara Woods
Sara Woods 2024-8-17
评论： Star Strider 2024-8-17
Hello all! Here my question:
I have a table displaying 1000 columns (spikes_mtx). Each column has 400 rows of data displaying exponential decay over 100s time (std_time).
I'd like to fit a three-coefficient power-fit model (y = a*x^b+c) to each column so as to obtain:
A table with x1000 a coefficient (coming from the 1000 exponential decays)
A table with x1000 b coefficient (coming from the 1000 exponential decays)
A table with x1000 c coefficient (coming from the 1000 exponential decays)
A table with x1000 fit goodness parameters (coming from the 1000 exponential decays)
All tables stored in one single structure (results.STD). My code doesn't function, any recommendation? Thanks in advance!
ft = fittype( 'power2' ); % Power Fit: y = a*x^b+c
opts = fitoptions(ft); % Power fit options
opts.StartPoint = [1 -1 0];
opts.Lower = [0 -Inf -Inf];
opts.Upper = [Inf 0 Inf];
for i=1:length (spikes_mtx)
[xData, yData] = prepareCurveData(std_time,spikes_mtx(:,i)); % x = std_time y = spikes_mtx
[fitresult, gof] = fit( xData, yData, ft, opts ); % Goodnes of the Fit R^2
results.STD.Coeff.a(1,i)=S.std.fitmodel.a;
results.STD.Coeff.b(1,i)=S.std.fitmodel.b;
results.STD.Coeff.c(1,i)=S.std.fitmodel.c;
results.STD.gof.sse(1,i)=S.std.gof.sse;
results.STD.gof.rsquare(1,i)=S.std.gof.rsquare;
results.STD.gof.dfe(1,i)=S.std.gof.dfe;
results.STD.gof.adjrsquare(1,i)=S.std.gof.adjrsquare;
results.STD.gof.rmse(1,i)=S.std.gof.rmse;
end

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Star Strider
Star Strider 2024-8-17
编辑：Star Strider 2024-8-17
Ran in:
It might be best to put all the parameters in a single table, and for that matter, put everything in a single table.
Since you want them in different tables, try this —
load('spikes_mtx.mat')
load('std_time')
% new_time = linspace(min(std_time), max(std_time), 1000*400);
% new_spikes = interp1(std_time, std_spk_avg, new_time);
%
% spikes_mtx = reshape(new_spikes, 1000, []).'
ft = fittype( 'power2' ); % Power Fit: y = a*x^b+c
opts = fitoptions(ft); % Power fit options
opts.StartPoint = [1 -1 0];
opts.Lower = [0 -Inf -Inf];
opts.Upper = [Inf 0 Inf];
for i=1:size(spikes_mtx,2)
[xData, yData] = prepareCurveData(std_time,spikes_mtx(:,i)); % x = std_time y = spikes_mtx
[fitresult, gof] = fit( xData, yData, ft, opts ); % Goodnes of the Fit R^2
results_a(i,:)=fitresult.a;
results_b(i,:)=fitresult.b;
results_c(i,:)=fitresult.c;
results_sse(i,:)=gof.sse;
results_rsquare(i,:)=gof.rsquare;
results_dfe(i,:)=gof.dfe;
results_adjrsquare(i,:)=gof.adjrsquare;
results_rmse(i,:)=gof.rmse;
end
Results_a = table(results_a)
Results_a = 1000x1 table
results_a _________ 0.41545 0.41543 0.41541 0.41538 0.41535 0.41531 0.41528 0.41524 0.41521 0.41519 0.41516 0.41514 0.41511 0.41509 0.41506 0.41504
Results_b = table(results_b)
Results_b = 1000x1 table
results_b _________ -0.36158 -0.36163 -0.36167 -0.3617 -0.3617 -0.3617 -0.3617 -0.3617 -0.36171 -0.36171 -0.36172 -0.36173 -0.36174 -0.36174 -0.36175 -0.36176
Results_c = table(results_c)
Results_c = 1000x1 table
results_c _________ 0.23473 0.23475 0.23478 0.23479 0.2348 0.23481 0.23482 0.23483 0.23483 0.23484 0.23485 0.23486 0.23487 0.23488 0.23489 0.2349
Results_GOF = table(results_sse, results_rsquare, results_dfe, results_adjrsquare, results_rmse)
Results_GOF = 1000x5 table
results_sse results_rsquare results_dfe results_adjrsquare results_rmse ___________ _______________ ___________ __________________ ____________ 0.52615 0.7517 397 0.75045 0.036405 0.52621 0.75167 397 0.75042 0.036407 0.52628 0.75164 397 0.75039 0.036409 0.52632 0.75161 397 0.75036 0.036411 0.52633 0.75158 397 0.75033 0.036411 0.52634 0.75155 397 0.7503 0.036411 0.52635 0.75151 397 0.75026 0.036412 0.52636 0.75148 397 0.75023 0.036412 0.52636 0.75145 397 0.7502 0.036412 0.52637 0.75143 397 0.75018 0.036412 0.52638 0.7514 397 0.75015 0.036413 0.52638 0.75138 397 0.75013 0.036413 0.52639 0.75136 397 0.75011 0.036413 0.52641 0.75134 397 0.75008 0.036414 0.52642 0.75131 397 0.75006 0.036414 0.52644 0.75128 397 0.75003 0.036415
Single table —
Results = table(results_a, results_b, results_c, results_sse, results_rsquare, results_dfe, results_adjrsquare, results_rmse)
Results = 1000x8 table
results_a results_b results_c results_sse results_rsquare results_dfe results_adjrsquare results_rmse _________ _________ _________ ___________ _______________ ___________ __________________ ____________ 0.41545 -0.36158 0.23473 0.52615 0.7517 397 0.75045 0.036405 0.41543 -0.36163 0.23475 0.52621 0.75167 397 0.75042 0.036407 0.41541 -0.36167 0.23478 0.52628 0.75164 397 0.75039 0.036409 0.41538 -0.3617 0.23479 0.52632 0.75161 397 0.75036 0.036411 0.41535 -0.3617 0.2348 0.52633 0.75158 397 0.75033 0.036411 0.41531 -0.3617 0.23481 0.52634 0.75155 397 0.7503 0.036411 0.41528 -0.3617 0.23482 0.52635 0.75151 397 0.75026 0.036412 0.41524 -0.3617 0.23483 0.52636 0.75148 397 0.75023 0.036412 0.41521 -0.36171 0.23483 0.52636 0.75145 397 0.7502 0.036412 0.41519 -0.36171 0.23484 0.52637 0.75143 397 0.75018 0.036412 0.41516 -0.36172 0.23485 0.52638 0.7514 397 0.75015 0.036413 0.41514 -0.36173 0.23486 0.52638 0.75138 397 0.75013 0.036413 0.41511 -0.36174 0.23487 0.52639 0.75136 397 0.75011 0.036413 0.41509 -0.36174 0.23488 0.52641 0.75134 397 0.75008 0.036414 0.41506 -0.36175 0.23489 0.52642 0.75131 397 0.75006 0.036414 0.41504 -0.36176 0.2349 0.52644 0.75128 397 0.75003 0.036415
EDIT — (17 Aug 2024 at 14:33)
Added code to create a single table.
.
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更多回答（1 个）

John D'Errico
John D'Errico 2024-8-17
编辑：John D'Errico 2024-8-17
Ran in:
Why should it work? I see these lines:
[fitresult, gof] = fit( xData, yData, ft, opts ); % Goodnes of the Fit R^2
results(i).STD.Coeff.a(1,i)=S.std.fitmodel.a;
What is S.std.fitmodel? Where do you think that comes from? You create something called fitresult and gof. So use it. Use the variable gof as returned. Should MATLAB be able to know what you want? It tries to execute the code you give it.
load std_time.mat
load spikes_mtx.mat
ft = fittype( 'power2' ) % Power Fit: y = a*x^b+c
ft =
General model Power2: ft(a,b,c,x) = a*x^b+c
opts = fitoptions(ft); % Power fit options
opts.StartPoint = [1 -1 0];
opts.Lower = [0 -Inf -Inf];
opts.Upper = [Inf 0 Inf];
The results struct is a highly confusing thing you are creating. I have no clue what you really wanted to do, so I'll make a guess.
N = length(spikes_mtx);
results.Coeff.a = zeros(1,N);
results.Coeff.b = zeros(1,N);
results.Coeff.c = zeros(1,N);
results.gof.sse = zeros(1,N);
results.gof.rsquare = zeros(1,N);
results.gof.dfe = zeros(1,N);
results.gof.adjrsquare = zeros(1,N);
results.gof.rmse = zeros(1,N);
for i=1:10 % Should be N, but I've just used 10 here.
[xData, yData] = prepareCurveData(std_time,spikes_mtx(:,i)); % x = std_time y = spikes_mtx
[fitresult, gof] = fit( xData, yData, ft, opts ); % Goodnes of the Fit R^2
results.Coeff.a(i)=fitresult.a;
results.Coeff.b(i)=fitresult.b;
results.Coeff.c(i)=fitresult.c;
results.gof.sse(i) = gof.sse;
results.gof.rsquare(i) = gof.rsquare;
results.gof.dfe(i) = gof.dfe;
results.gof.adjrsquare(i) = gof.adjrsquare;
results.gof.rmse(i) = gof.rmse;
end
results.Coeff
ans = struct with fields:
a: [0.4155 0.4154 0.4154 0.4154 0.4153 0.4153 0.4153 0.4152 0.4152 0.4152 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) b: [-0.3616 -0.3616 -0.3617 -0.3617 -0.3617 -0.3617 -0.3617 -0.3617 -0.3617 -0.3617 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) c: [0.2347 0.2348 0.2348 0.2348 0.2348 0.2348 0.2348 0.2348 0.2348 0.2348 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double)
results.gof
ans = struct with fields:
sse: [0.5261 0.5262 0.5263 0.5263 0.5263 0.5263 0.5263 0.5264 0.5264 0.5264 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) rsquare: [0.7517 0.7517 0.7516 0.7516 0.7516 0.7515 0.7515 0.7515 0.7515 0.7514 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) dfe: [397 397 397 397 397 397 397 397 397 397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) adjrsquare: [0.7504 0.7504 0.7504 0.7504 0.7503 0.7503 0.7503 0.7502 0.7502 0.7502 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double) rmse: [0.0364 0.0364 0.0364 0.0364 0.0364 0.0364 0.0364 0.0364 0.0364 0.0364 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... ] (1x1000 double)

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