Function value and YDATA sizes are not equal using lsqcurvefit

Thank you very much for the help so far,

I am attempting to estimate parameters for a set of differential equations as shown in the code below, however in equation 4, when the function is switched from

dcdt(4)= theta(3).*c(4)-0.01.*c(4)

to

dcdt(4)= theta(3).*c(4).*(c(1)+c(2))-0.01.*c(4)

the following error message is returned: Error using lsqcurvefit (line 286). Function value and YDATA sizes are not equal.

I have included the dcdt(4)= theta(3).*c(4).*(c(1)+c(2))-0.01.*c(4) adaptation of my code below for reference.

function ParameterEstimates

function C=kinetics(theta,t)
c0=[0;0;20000;18632080.08];
[T,Cv]=ode15s(@DifEq,t,c0);

    function dC=DifEq(t,c)
    dcdt=zeros(4,1);
    dcdt(1)= 20.*c(3)-0.33.*c(1);
    dcdt(2)= 20.*c(3)-theta(1).*c(2)-theta(2).*c(4).*c(2);
    dcdt(3)= 0.02.*c(1)+0.02.*c(2)-40.*c(3);
    dcdt(4)= theta(3).*c(4).*(c(1)+c(2))-0.01.*c(4);
    dC=dcdt;
    end
C=Cv;
end



t = [
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
1,
1.1,
1.2,
1.3,
1.4,
1.5,
1.6,
1.7,
1.8,
1.9,
2,
2.1,
2.2,
2.3,
2.4,
2.5,
2.6,
2.7,
2.8,
2.9,
3,
3.1,
3.2,
3.3,
3.4,
3.5,
3.6,
3.7,
3.8,
3.9,
4,
4.1,
4.2,
4.3,
4.4,
4.5,
4.6,
4.7,
4.8,
4.9,
5,
5.1,
5.2,
5.3,
5.4,
5.5,
5.6,
5.7,
5.8,
5.9,
6];

Liver = [1348.29506832772;2005.14924465480;3254.48028488375;5124.72602075486;7829.13399421537;12328.2869399683;18834.1405923453;31035.1405834789;37215.9680323785;43957.3958719222;51919.9890262101;63209.6174575039;75798.1777562693;89528.5191319988;107358.640668647;130703.005426235;154378.995580650;185124.463958724;235847.504315023;319220.389375715;406684.943474129;526015.488352822;680360.307874421;907037.705438451;1173183.04804904;1517421.43993357;1962667.15198536;2500426.68428754;2738116.52311521;2953362.53283321;3137679.85208163;3333500.28045675;3595549.98787599;3878199.67831042;4120235.43661992;4377376.48920232;4721486.32323604;5092646.95512564;5410475.54007316;5748139.58785559;6200006.43137868;6687394.98234579;7104750.69204894;7548153.26643603;8141520.95463497;8781533.85537407;9329583.30669371;9911836.16785702;10530427.0286059;11358234.1390003;12251115.9996602;13015699.7017134;13828000.5135698;14915033.1171122;16087518.4135442;17091529.3055869;18158199.8644633;19512934.2423026]
Spleen = [5296.69267490515;10227.3087507503;19289.1179170183;37685.2809190182;73625.9897448358;138861.593923331;261898.581983822;493951.316193815;632183.081414251;762935.125052513;953763.591782546;1151026.92014362;1389089.47590313;1676389.61586326;2023110.96075868;2499597.23736815;3016579.51143867;3640487.28042792;3555935.91071807;3275173.79878704;3052232.23024447;2844466.32094523;2682173.17053339;2499597.23736815;2302239.29364786;2170883.31625475;2023110.96075868;1885397.49183905;1599424.62057788;1325314.76389575;1124293.98711175;953763.591782546;771952.194224899;654864.213353809;555535.875329819;460327.975433029;381436.833112652;323581.348079842;268125.882529280;227457.148844088;188475.476517165;158020.308745250;132486.296784471;112391.071847443;95343.8456474215;77168.9037907287;65464.0971997401;55534.6494722643;46017.1049869811;38130.6802376093;32347.1040114341;26803.4479174991;22737.9609345979;18841.1225760795;15612.1255088756;13244.1132580966;11235.2758049230;9201.02479406369]
Blood = [0;0;0;0;0;0;0;0;0;0;52.2014133300000;101.212603400000;100.332610600000;158.349065400000;168.029595700000;211.000025000000;236.931893500000;262.698760300000;305.810229500000;315.198283900000;373.497283200000;372.632137200000;421.480608400000;451.089518400000;473.650283900000;519.348867100000;522.308799600000;583.994896000000;583.601187900000;730.737827100000;1243.55573200000;1759.05491500000;2273.82061800000;2788.50042700000;3302.89718600000;3816.87852900000;4330.43718800000;4855.66067000000;5361.42520000000;5872.68671900000;6390.09304900000;6906.84082300000;7417.25482000000;7946.45088800000;8445.36977700000;8986.19744300000;9478.10745500000;10020.6616800000;10516.9369500000;11049.6286300000;11557.1411400000;12076.6875300000;12593.0145500000;13108.4890300000;13622.8341400000;14136.5140900000;14649.9922200000;15163.7253500000]
Tcell = [18632080.0800000;18632080.0800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18368660;18280853.2800000;18280853.2800000;18280853.2800000;18280853.2800000;18280853.2800000;18105239.8800000;18105239.8800000;18105239.8800000;18193046.5800000;19246726.9900000;20124794;21178474.4100000;22319961.5100000;23110221.8200000;24251708.9300000;25393196.0400000;26183456.3500000;27324943.4500000;28115203.7600000;29256690.8700000;30310371.2800000;31188438.2900000;32242118.6900000;33120185.7000000;34173866.1100000;35315353.2200000;36105613.5300000;37247100.6400000;38388587.7400000;39178848.0500000;40320335.1600000;41110595.4700000;42252082.5800000;43305762.9800000;44183829.9900000;45237510.4000000;46115577.4100000;47169257.8200000;48398551.6300000;49188811.9300000;50330299.0400000;51383979.4500000;52262046.4600000;53315726.8700000;54193793.8700000;55247474.2800000;56388961.3900000;57179221.7000000;58320708.8100000]

c = [Liver, Spleen, Blood, Tcell];

theta0=[1;1;1];

[theta,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat]=lsqcurvefit(@kinetics,theta0,t,c);

fprintf(1,'\tRate Constants:\n')
for k1 = 1:length(theta)
    fprintf(1, '\t\tTheta(%d) = %8.5f\n', k1, theta(k1))
end

tv = linspace(min(t), max(t));
Cfit = kinetics(theta, tv);

figure(1)
plot(t, c, '+')
hold on
hlp = plot(tv, Cfit);
hold off
grid
xlabel('Time')
ylabel('Concentration')
legend(hlp, 'Liver(t)', 'Spleen(t)', 'Blood(t)', 'Tcell(t)', 'Location','N')

end

Answer 1

[Torsten]

The integrator was not able to integrate your system of differential equations. So there was no or only an incomplete solution returned to lsqcurvefit and thus, the number of simulated y-data was less than the size of the matrix c.

t = [
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
1,
1.1,
1.2,
1.3,
1.4,
1.5,
1.6,
1.7,
1.8,
1.9,
2,
2.1,
2.2,
2.3,
2.4,
2.5,
2.6,
2.7,
2.8,
2.9,
3,
3.1,
3.2,
3.3,
3.4,
3.5,
3.6,
3.7,
3.8,
3.9,
4,
4.1,
4.2,
4.3,
4.4,
4.5,
4.6,
4.7,
4.8,
4.9,
5,
5.1,
5.2,
5.3,
5.4,
5.5,
5.6,
5.7,
5.8,
5.9,
6];

Liver = [1348.29506832772;2005.14924465480;3254.48028488375;5124.72602075486;7829.13399421537;12328.2869399683;18834.1405923453;31035.1405834789;37215.9680323785;43957.3958719222;51919.9890262101;63209.6174575039;75798.1777562693;89528.5191319988;107358.640668647;130703.005426235;154378.995580650;185124.463958724;235847.504315023;319220.389375715;406684.943474129;526015.488352822;680360.307874421;907037.705438451;1173183.04804904;1517421.43993357;1962667.15198536;2500426.68428754;2738116.52311521;2953362.53283321;3137679.85208163;3333500.28045675;3595549.98787599;3878199.67831042;4120235.43661992;4377376.48920232;4721486.32323604;5092646.95512564;5410475.54007316;5748139.58785559;6200006.43137868;6687394.98234579;7104750.69204894;7548153.26643603;8141520.95463497;8781533.85537407;9329583.30669371;9911836.16785702;10530427.0286059;11358234.1390003;12251115.9996602;13015699.7017134;13828000.5135698;14915033.1171122;16087518.4135442;17091529.3055869;18158199.8644633;19512934.2423026]
Spleen = [5296.69267490515;10227.3087507503;19289.1179170183;37685.2809190182;73625.9897448358;138861.593923331;261898.581983822;493951.316193815;632183.081414251;762935.125052513;953763.591782546;1151026.92014362;1389089.47590313;1676389.61586326;2023110.96075868;2499597.23736815;3016579.51143867;3640487.28042792;3555935.91071807;3275173.79878704;3052232.23024447;2844466.32094523;2682173.17053339;2499597.23736815;2302239.29364786;2170883.31625475;2023110.96075868;1885397.49183905;1599424.62057788;1325314.76389575;1124293.98711175;953763.591782546;771952.194224899;654864.213353809;555535.875329819;460327.975433029;381436.833112652;323581.348079842;268125.882529280;227457.148844088;188475.476517165;158020.308745250;132486.296784471;112391.071847443;95343.8456474215;77168.9037907287;65464.0971997401;55534.6494722643;46017.1049869811;38130.6802376093;32347.1040114341;26803.4479174991;22737.9609345979;18841.1225760795;15612.1255088756;13244.1132580966;11235.2758049230;9201.02479406369]
Blood = [0;0;0;0;0;0;0;0;0;0;52.2014133300000;101.212603400000;100.332610600000;158.349065400000;168.029595700000;211.000025000000;236.931893500000;262.698760300000;305.810229500000;315.198283900000;373.497283200000;372.632137200000;421.480608400000;451.089518400000;473.650283900000;519.348867100000;522.308799600000;583.994896000000;583.601187900000;730.737827100000;1243.55573200000;1759.05491500000;2273.82061800000;2788.50042700000;3302.89718600000;3816.87852900000;4330.43718800000;4855.66067000000;5361.42520000000;5872.68671900000;6390.09304900000;6906.84082300000;7417.25482000000;7946.45088800000;8445.36977700000;8986.19744300000;9478.10745500000;10020.6616800000;10516.9369500000;11049.6286300000;11557.1411400000;12076.6875300000;12593.0145500000;13108.4890300000;13622.8341400000;14136.5140900000;14649.9922200000;15163.7253500000]
Tcell = [18632080.0800000;18632080.0800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18456466.6800000;18368660;18280853.2800000;18280853.2800000;18280853.2800000;18280853.2800000;18280853.2800000;18105239.8800000;18105239.8800000;18105239.8800000;18193046.5800000;19246726.9900000;20124794;21178474.4100000;22319961.5100000;23110221.8200000;24251708.9300000;25393196.0400000;26183456.3500000;27324943.4500000;28115203.7600000;29256690.8700000;30310371.2800000;31188438.2900000;32242118.6900000;33120185.7000000;34173866.1100000;35315353.2200000;36105613.5300000;37247100.6400000;38388587.7400000;39178848.0500000;40320335.1600000;41110595.4700000;42252082.5800000;43305762.9800000;44183829.9900000;45237510.4000000;46115577.4100000;47169257.8200000;48398551.6300000;49188811.9300000;50330299.0400000;51383979.4500000;52262046.4600000;53315726.8700000;54193793.8700000;55247474.2800000;56388961.3900000;57179221.7000000;58320708.8100000]

c = [Liver, Spleen, Blood, Tcell];

theta0=[1;1;1];

[theta,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat]=lsqcurvefit(@kinetics,theta0,t,c);

fprintf(1,'\tRate Constants:\n')
for k1 = 1:length(theta)
    fprintf(1, '\t\tTheta(%d) = %8.5f\n', k1, theta(k1))
end

tv = linspace(min(t), max(t));
Cfit = kinetics(theta, tv);

figure(1)
plot(t, c, '+')
hold on
hlp = plot(tv, Cfit);
hold off
grid
xlabel('Time')
ylabel('Concentration')
legend(hlp, 'Liver(t)', 'Spleen(t)', 'Blood(t)', 'Tcell(t)', 'Location','N')


function C=kinetics(theta,t)
c0=[0;0;20000;18632080.08];
[T,Cv]=ode15s(@DifEq,t,c0);

    function dC=DifEq(t,c)
    dcdt=zeros(4,1);
    dcdt(1)= 20.*c(3)-0.33.*c(1);
    dcdt(2)= 20.*c(3)-theta(1).*c(2)-theta(2).*c(4).*c(2);
    dcdt(3)= 0.02.*c(1)+0.02.*c(2)-40.*c(3);
    dcdt(4)= theta(3).*c(4).*(c(1)+c(2))-0.01.*c(4);
    dC=dcdt;
    end
C=Cv;
end