initial version

FittingAndMath/CatStructFields.m

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+function S = CatStructFields(S, T, dim)
+fields = fieldnames(S);
+for k = 1:numel(fields)
+  aField     = fields{k}; % EDIT: changed to {}
+  S.(aField) = cat(dim, S.(aField), T.(aField));
+end

FittingAndMath/Vector1stOrderDE.m

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+function xt = Vector1stOrderDE(A,x0,t)
+%Vector1stOrderDE: - solves the vector equation dx/dt=Ax
+
+%inputs: A - matrix of the equation, x0 - x for t=0, t - time axis to
+%evaluate values at. derivation is given at:
+%https://www.unf.edu/~mzhan/chapter4.pdf
+
+%Yair Judkovsky, 3.10.2020
+
+if nargin==0
+A=[.1,.01;-.002,-.002].*i;
+x0=[.3,0.0001];
+t=linspace(0,100,100000);
+end
+nt=length(t);
+if any(~isfinite(A(:))), xt = 123.123; return, end
+[ev,lam]=eig(A);
+nev=length(diag(lam));
+phi0i=inv(ev);
+% add singleton dimension as the first (time) index and replicate
+% eigenvectors along that dimension.
+evp=repmat(reshape(ev,[1,nev,nev]),[length(t),1,1]);
+
+lamt=reshape(exp(diag(lam)*t).',length(t),1,nev);
+lamt=repmat(lamt,1,nev,1);
+phit=lamt.*evp;
+
+xt=reshape(reshape(phit,nev*nt,nev)*(phi0i*x0),nt,nev);
+
+if nargin==0
+figure;
+plot(xt);
+hold on
+plot(real(x0),imag(x0),'o');
+axis equal
+end
+

FittingAndMath/fit_linear.m

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+function [a,b,da,db]=fit_linear(x,y,varargin)
+%fit_linear: 1st order linear regression.
+
+%This function fits a dataset of x and y values to the linear equation
+%y=ax+b. it is optional for the user to insert also y error values for the
+%estimation of a and b errors.
+%
+
+%Yair Judkovsky, 21.8.2013
+
+if nargin==2     %case of no error input - assuming that all errors are equal
+ dy = ones(size(y));
+else
+ dy = varargin{1};
+end
+
+dy2=dy.^2;
+x2=x.^2;
+xy=x.*y;
+
+S=sum(1./dy2);
+Sx=sum(x./dy2);
+Sy=sum(y./dy2);
+Sxx=sum(x2./dy2);
+Sxy=sum(xy./dy2);
+D=S*Sxx-Sx^2;
+
+a=(S*Sxy-Sx*Sy)/D;
+b=(Sxx*Sy-Sxy*Sx)/D;
+
+if nargin==2    %no error given - need to estimate it
+    Ytheo=a*x+b;
+    dy2=mean((Ytheo-y).^2)*ones(size(y));    
+    S=sum(1./dy2);
+    Sx=sum(x./dy2);
+    Sxx=sum(x2./dy2);
+    D=S*Sxx-Sx^2;
+    da=sqrt(S/D);
+    db=sqrt(Sxx/D);
+else
+    da=sqrt(S/D);
+    db=sqrt(Sxx/D);
+end
+
+return

FittingAndMath/horizontal.m

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+function horzvec=horizontal(vec)
+%reshape input vector into row vector
+    
+if min(size(vec))>1
+    horzvec=[];
+    return
+end
+
+horzvec=reshape(vec,1,length(vec));

FittingAndMath/range.m

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+function res = range(X)
+res=max(X(:))-min(X(:));
+return

FittingAndMath/vertical.m

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+function vertvec=vertical(vec)
+%reshape input vector into row vector
+    
+if min(size(vec))>1
+    vertvec=[];
+    return
+end
+
+vertvec=reshape(vec,length(vec),1);