I am trying to solve a system of non-linear equations using fsolve. For that purpose I have defined a function "root2d" of the vector x (which shall represent 15 variables).
The first error I get is " Index exceeds matrix dimensions" with the addition that the error occurs when defining the 15th variable (i.e. vector element) – "Error in root2d (line 19) yd = x(15);". The error is not related to the specific variable but to the 15th position – for whatever reason.
Has anyone had this issue before? Do you have any clue what the reason for this could be?
For your reference there is my code below, the function (system of non-linear equations) as well as the fsolve referring to the function.
function F = root2d(x)%defining the vector x of 19 endogenous input variables
c = x(1);lambda = x(2);r = x(3);gammma1 = x(4);f = x(5);wstar = x(6);Pistarw = x(7);ld = x(8);g1 = x(9);mc = x(10);g2 = x(11);Pistar = x(12);k = x(13);x = x(14);yd = x(15);vp = x(16);l = x(17);vw = x(18);Rbar = x(19);%defining the parameters
delta = 0.025;epsilon = 10;eta = 10;Phi = 0;gammma2 = 0.001;betta = 0.998;h = 0.97;varpsi = 8.92;gammma = 1.17;kappa = 9.51;alppha = 0.21;thetap = 0.82;chi = 0.63;thetaw = 0.68;chiw = 0.62;gammmaR = 0.77;gammmay = 0.19;gammmaPI= 1.29;PIbar = 1.01;rhod = 0.12;rhophi = 0.93;sigma_A = -3.97;sigma_d = -1.51;sigma_phi= -2.36;sigma_mu= -5.43;sigma_m = -5.85;Lambdamu= 3.4e-3;LambdaA = 2.8e-3;LambdaYd= (LambdaA+alppha*Lambdamu)/(1-alppha);Lambdaz = LambdaYd;Lambdac = LambdaYd;Lambdaw = LambdaYd;%specifying the function
F1 = (1-h*betta*Lambdaz)/((1-h/Lambdaz)*c)-lambda; F2 = Rbar-(PIbar*Lambdaz/betta); F3 = r-gammma1; F4 = r-(1-(betta/(exp(Lambdaz)*exp(Lambdamu))))*(1-delta)/(betta/(exp(Lambdaz)*exp(Lambdamu))); F5 = (1-betta*thetaw*exp(Lambdaz)^(eta-1)*PIbar^(-(1-chiw)*(1-eta)))*f-((eta-1)/eta)*wstar*lambda*PIstarw^(-eta)*ld; F6 = (1-betta*thetaw*exp(Lambdaz)^(eta*(1+gammma))*PIbar^(eta*(1-chiw)*(1+gammma)))*f-varpsi*PIstarw^(-eta*(1+gammma))*ld^(1+gammma); F7 = (1-betta*thetap*PIbar^((1-chi)*epsilon))*g1-lambda*mc*LambdaYd; F8 = (1-betta*thetap*PIbar^(-(1-chi)*(1-epsilon)))*g2-lambda*PIstar*LambdaYd; F9 = epsilon*g1-(epsilon-1)*g2; F10= k/ld-(alppha/(1-alppha))*(w/r)*exp(Lambdaz)*exp(Lambdamu); F11= mc-(1/(1-alppha))^(1-alppha)*(1/alppha)^alppha*w^(1-alppha)*r^alppha; F12= (1-thetaw*PIbar^(-(1-chiw)*(1-eta))*exp(Lambdaz)^(-(1-eta)))/(1-thetaw)-PIstarw^(1-eta); F13= (1-thetap*PIbar^(-(1-chi)*(1-epsilon)))/(1-thetap)-PIstar^(1-epsilon); F14= c+x-yd; F15= vp*yd-(exp(LambdaA)/exp(Lambdaz))*k^alppha*ld^(1-alppha)-Phi; F16= l-vw*ld; F17= (1-thetap*PIbar^((1-chi)*epsilon))*vp/(1-thetap)-PIstar^(-epsilon); F18= (1-thetaw*exp(Lambdaz)^eta*PIbar^((1-chiw)*eta))/(1-thetaw)-PIstarw^(-eta); F19= k-(exp(Lambdaz)*exp(Lambdamu)*x)/(x*exp(Lambdamu)-(1-delta));F = [F1; F2; F3; F4; F5; F6; F7; F8; F9; F10; F11; F12; F13; F14; F15; F16; F17; F18; F19];--------------------------------------------------------------------------------------------------------------------------------------------------------------SEPERATE CODE---------------------------------------------------------------------------------------------------------------------------------------------------------------%initial guess
c0 = 0.40819;lambda0 = 2.58777;r0 = 0.0348988;gammma10 = 1f0 = 2.55673;wstar0 = 1.13352;PIstarw0 = 1.02002;ld0 = 0.317845;g10 = 7.64784;mc0 = 0.89825;g20 = 8.4976;PIstar0 = 1.01869;k0 = 2.71161;x0 = 0.0884579;yd0 = 0.496648;vp0 = 1.00222;l0 = 0.318814;vw0 = 1.00305;Rbar0 = 0;x0 = [c0; lambda0; r0; gammma10; f0; wstar0; PIstarw0; ld0; g10; mc0; g20; PIstar0; k0; x0; yd0; vp0; l0; vw0; Rbar0]fun = @root2d;F = fsolve(fun,x0);
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