Hi everybody!
I’m trying to solve a fitting curve problem concerning a double-exponential fit.
I have this data set (Data.txt) that behaves like a bi-exponential function following a resting condition. Therefore, since x<0 the signal is almost steady whereas, for x>0 the signal presents a first exponential phase (lasting about 20 sec) followed by a second exponential phase.
The problem is that the resulting fitting does not model the signal behavior in the correct way. Specifically, the first exp phase is too short and/or too low even though correct StartingPoint and Upper and Lower limits are set.
Lastly, I’ve written two algorithms with and without "Exclude" options. The second one presents a strange pattern at the onset of the second exp function.
I’ll appreciate any suggestions.

This is the code.

[x, y] = readvars(‘prova.txt’);

tRest = abs(min(x)); % Resting phase duration (sec)
cdp = 20; % estimated duration (sec) of CardioDynamicPhase (cdp)
cdpEpoch = 5; % epoch duration (sec) to compute mean value of amplitude of cdp
plot(x,y);

% Fitting StartingPoint
yRest = mean( y(1:tRest-1) ); % y value at resting condition before exp onset

A1start = mean( y(1:tRest+cdp-cdpEpoch):y(tRest+cdp) )-yRest; % mean y value of the last 5sec of the cardiodynamic phase
TD1start = 0; % starting value (sec) of the first exponential phase onset
tau1Start = 8; % starting value (sec) of the first exponential phase time constant

A2start = max(y)-A1start-yRest; % starting value of the second exponential phase amplitude
TD2start = 30; % starting value (sec) of the second exponential phase onset
tau2Start = 30; % starting value (sec) of the second exponential phase time constant

% Fitting from exponential onset
g = fittype( @(A1, TD1, tau1, A2, TD2, tau2, yRest, x) yRest+A1.*(1-exp(-(x-TD1)/tau1))+A2.*(1-exp(-(x-TD2)/tau2)), ‘problem’, ‘yRest’);
f1 = fit( x(tRest:size(x,1)), y(tRest:size(x,1)), g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ A1start-100, 0, 5, A2start-200, 10, 10], ‘upper’, [ A1start+200, 20, 40, max(y), 60, 40], ‘MaxIter’, 10000);
pg =coeffvalues(f1);
A1 = pg(1);
TD1 = pg(2);
tau1 = pg(3);
A2 = pg(4);
TD2 = pg(5);
tau2 = pg(6);

yFit( 1:(tRest+floor(TD1)) ) = yRest;
yFit( tRest+floor(TD1)+1 : tRest+floor(TD2) ) = yRest + A1.*(1-exp(-( x(tRest+floor(TD1)+1 : tRest+floor(TD2))-TD1 )/tau1));
yFit( tRest+floor(TD2)+1 : size(y,1)) = yFit(tRest+floor(TD2))+ A2.*(1-exp(-( x(tRest+floor(TD2)+1 : size(y,1))-TD2 )/tau2));

% fitting using Exclude option
f2 = fit( x, y, g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ 390, 0, 5, A2start-200, 10, 10], ‘upper’, [ 400, 20, 40, max(y), 60, 40], ‘Exclude’, x<0); %Same fitting algortihm that exclude negative x values
pg2=coeffvalues(f2);

A1e = pg2(1);
TD1e = pg2(2);
tau1e = pg2(3);
A2e = pg2(4);
TD2e = pg2(5);
tau2e = pg2(6);

yFite( 1:(tRest+floor(TD1e)) ) = yRest;
yFite( tRest+floor(TD1e)+1 : tRest+floor(TD2e) ) = yRest + A1e.*(1-exp(-( x(tRest+floor(TD1e)+1 : tRest+floor(TD2e))-TD1e )/tau1e));
yFite( tRest+floor(TD2e)+1 : size(y,1)) = yFit(tRest+floor(TD2e))+ A2e.*(1-exp(-( x(tRest+floor(TD2e)+1 : size(y,1))-TD2e )/tau2e));

% Plot the fitting curves
hold on
plot (x, yFit, ‘r’);
plot (x, yFite, ‘k’);Hi everybody!
I’m trying to solve a fitting curve problem concerning a double-exponential fit.
I have this data set (Data.txt) that behaves like a bi-exponential function following a resting condition. Therefore, since x<0 the signal is almost steady whereas, for x>0 the signal presents a first exponential phase (lasting about 20 sec) followed by a second exponential phase.
The problem is that the resulting fitting does not model the signal behavior in the correct way. Specifically, the first exp phase is too short and/or too low even though correct StartingPoint and Upper and Lower limits are set.
Lastly, I’ve written two algorithms with and without "Exclude" options. The second one presents a strange pattern at the onset of the second exp function.
I’ll appreciate any suggestions.

This is the code.

[x, y] = readvars(‘prova.txt’);

tRest = abs(min(x)); % Resting phase duration (sec)
cdp = 20; % estimated duration (sec) of CardioDynamicPhase (cdp)
cdpEpoch = 5; % epoch duration (sec) to compute mean value of amplitude of cdp
plot(x,y);

% Fitting StartingPoint
yRest = mean( y(1:tRest-1) ); % y value at resting condition before exp onset

A1start = mean( y(1:tRest+cdp-cdpEpoch):y(tRest+cdp) )-yRest; % mean y value of the last 5sec of the cardiodynamic phase
TD1start = 0; % starting value (sec) of the first exponential phase onset
tau1Start = 8; % starting value (sec) of the first exponential phase time constant

A2start = max(y)-A1start-yRest; % starting value of the second exponential phase amplitude
TD2start = 30; % starting value (sec) of the second exponential phase onset
tau2Start = 30; % starting value (sec) of the second exponential phase time constant

% Fitting from exponential onset
g = fittype( @(A1, TD1, tau1, A2, TD2, tau2, yRest, x) yRest+A1.*(1-exp(-(x-TD1)/tau1))+A2.*(1-exp(-(x-TD2)/tau2)), ‘problem’, ‘yRest’);
f1 = fit( x(tRest:size(x,1)), y(tRest:size(x,1)), g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ A1start-100, 0, 5, A2start-200, 10, 10], ‘upper’, [ A1start+200, 20, 40, max(y), 60, 40], ‘MaxIter’, 10000);
pg =coeffvalues(f1);
A1 = pg(1);
TD1 = pg(2);
tau1 = pg(3);
A2 = pg(4);
TD2 = pg(5);
tau2 = pg(6);

yFit( 1:(tRest+floor(TD1)) ) = yRest;
yFit( tRest+floor(TD1)+1 : tRest+floor(TD2) ) = yRest + A1.*(1-exp(-( x(tRest+floor(TD1)+1 : tRest+floor(TD2))-TD1 )/tau1));
yFit( tRest+floor(TD2)+1 : size(y,1)) = yFit(tRest+floor(TD2))+ A2.*(1-exp(-( x(tRest+floor(TD2)+1 : size(y,1))-TD2 )/tau2));

% fitting using Exclude option
f2 = fit( x, y, g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ 390, 0, 5, A2start-200, 10, 10], ‘upper’, [ 400, 20, 40, max(y), 60, 40], ‘Exclude’, x<0); %Same fitting algortihm that exclude negative x values
pg2=coeffvalues(f2);

A1e = pg2(1);
TD1e = pg2(2);
tau1e = pg2(3);
A2e = pg2(4);
TD2e = pg2(5);
tau2e = pg2(6);

yFite( 1:(tRest+floor(TD1e)) ) = yRest;
yFite( tRest+floor(TD1e)+1 : tRest+floor(TD2e) ) = yRest + A1e.*(1-exp(-( x(tRest+floor(TD1e)+1 : tRest+floor(TD2e))-TD1e )/tau1e));
yFite( tRest+floor(TD2e)+1 : size(y,1)) = yFit(tRest+floor(TD2e))+ A2e.*(1-exp(-( x(tRest+floor(TD2e)+1 : size(y,1))-TD2e )/tau2e));

% Plot the fitting curves
hold on
plot (x, yFit, ‘r’);
plot (x, yFite, ‘k’); Hi everybody!
I’m trying to solve a fitting curve problem concerning a double-exponential fit.
I have this data set (Data.txt) that behaves like a bi-exponential function following a resting condition. Therefore, since x<0 the signal is almost steady whereas, for x>0 the signal presents a first exponential phase (lasting about 20 sec) followed by a second exponential phase.
The problem is that the resulting fitting does not model the signal behavior in the correct way. Specifically, the first exp phase is too short and/or too low even though correct StartingPoint and Upper and Lower limits are set.
Lastly, I’ve written two algorithms with and without "Exclude" options. The second one presents a strange pattern at the onset of the second exp function.
I’ll appreciate any suggestions.

This is the code.

[x, y] = readvars(‘prova.txt’);

tRest = abs(min(x)); % Resting phase duration (sec)
cdp = 20; % estimated duration (sec) of CardioDynamicPhase (cdp)
cdpEpoch = 5; % epoch duration (sec) to compute mean value of amplitude of cdp
plot(x,y);

% Fitting StartingPoint
yRest = mean( y(1:tRest-1) ); % y value at resting condition before exp onset

A1start = mean( y(1:tRest+cdp-cdpEpoch):y(tRest+cdp) )-yRest; % mean y value of the last 5sec of the cardiodynamic phase
TD1start = 0; % starting value (sec) of the first exponential phase onset
tau1Start = 8; % starting value (sec) of the first exponential phase time constant

A2start = max(y)-A1start-yRest; % starting value of the second exponential phase amplitude
TD2start = 30; % starting value (sec) of the second exponential phase onset
tau2Start = 30; % starting value (sec) of the second exponential phase time constant

% Fitting from exponential onset
g = fittype( @(A1, TD1, tau1, A2, TD2, tau2, yRest, x) yRest+A1.*(1-exp(-(x-TD1)/tau1))+A2.*(1-exp(-(x-TD2)/tau2)), ‘problem’, ‘yRest’);
f1 = fit( x(tRest:size(x,1)), y(tRest:size(x,1)), g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ A1start-100, 0, 5, A2start-200, 10, 10], ‘upper’, [ A1start+200, 20, 40, max(y), 60, 40], ‘MaxIter’, 10000);
pg =coeffvalues(f1);
A1 = pg(1);
TD1 = pg(2);
tau1 = pg(3);
A2 = pg(4);
TD2 = pg(5);
tau2 = pg(6);

yFit( 1:(tRest+floor(TD1)) ) = yRest;
yFit( tRest+floor(TD1)+1 : tRest+floor(TD2) ) = yRest + A1.*(1-exp(-( x(tRest+floor(TD1)+1 : tRest+floor(TD2))-TD1 )/tau1));
yFit( tRest+floor(TD2)+1 : size(y,1)) = yFit(tRest+floor(TD2))+ A2.*(1-exp(-( x(tRest+floor(TD2)+1 : size(y,1))-TD2 )/tau2));

% fitting using Exclude option
f2 = fit( x, y, g, ‘problem’, yRest, ‘StartPoint’, [A1start, TD1start, tau1Start, A2start, TD2start, tau2Start], ‘lower’ , [ 390, 0, 5, A2start-200, 10, 10], ‘upper’, [ 400, 20, 40, max(y), 60, 40], ‘Exclude’, x<0); %Same fitting algortihm that exclude negative x values
pg2=coeffvalues(f2);

A1e = pg2(1);
TD1e = pg2(2);
tau1e = pg2(3);
A2e = pg2(4);
TD2e = pg2(5);
tau2e = pg2(6);

yFite( 1:(tRest+floor(TD1e)) ) = yRest;
yFite( tRest+floor(TD1e)+1 : tRest+floor(TD2e) ) = yRest + A1e.*(1-exp(-( x(tRest+floor(TD1e)+1 : tRest+floor(TD2e))-TD1e )/tau1e));
yFite( tRest+floor(TD2e)+1 : size(y,1)) = yFit(tRest+floor(TD2e))+ A2e.*(1-exp(-( x(tRest+floor(TD2e)+1 : size(y,1))-TD2e )/tau2e));

% Plot the fitting curves
hold on
plot (x, yFit, ‘r’);
plot (x, yFite, ‘k’); signal fitting MATLAB Answers — New Questions

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