function [fFac,uFac]=TPXOnodalfactors(dnum,Names)

%f and u factors for the harmonics listed in cell array Names.
%(e.g. Names={'MM' 'M2' S2'};
%Only those which are in the TPXO model are evaluated.  
%They are evaluated at time dnum (a Matlab datenumber).
%See Table xxvi in A.T. Doodson (1928) 'On the Analysis of Tidal Observations'
%Philosophical Transactions of the Royal Society of London. Series A, Vol. 227
%J. Luick, Thanksgiving Day, 2011, Adelaide

N_TPXO=13;

%if f and u are not reassigned below, they are probably solar 
%terms, i.e. have f=1 and u=0.
f=ones(N_TPXO,1); 
u=zeros(N_TPXO,1); 
fFac=ones(length(Names),1);
uFac=zeros(length(Names),1);

t=(dnum+0.5-datenum(1900,1,1))/36525;
VN=mod(360*(0.719954-5.372617*t+0.000006*t*t),360);
VN(VN<0)=VN(VN<0)+360;
VN=VN*pi/180;

%coefficients
cN=cos(VN);
c2N=cos(2*VN);
c3N=cos(3*VN);
sN=sin(VN);
s2N=sin(2*VN);
s3N=sin(3*VN);

%   same list, in same order, as ALL_Constituents, ten per row, 112 in total
TPXOnames={'MM' 'MF' 'Q1' 'O1' 'P1' 'K1' 'N2' 'M2' 'S2' 'K2' 'MN4' 'M4' 'MS4'}; 

%Set up variable names (e.g. hM2) and assign them each a value
%(which is simply its position in the cell array).
for n=1:length(TPXOnames)
   var=['h' TPXOnames{n}];
   eval([var ' =  n;'])
end

%Assign values for f and u of nonsolar constituents
%Doodson Table XXVI (with u*pi/180)
f(hMM)=1.0-0.1300*cN+0.0013*c2N;
u(hMM)=0;
f(hMF)=1.0429+0.4135*cN-0.004*c2N;
u(hMF)=-0.4143*sN+0.0468*s2N-0.0066*s3N;
f(hO1)=1.0089+.1871*cN-0.0147*c2N+0.0014*c3N;
u(hO1)=0.1885*sN-0.0234*s2N+0.0033*s3N;
f(hK1)=1.0060+0.1150*cN-0.0088*c2N+0.0006*c3N;
u(hK1)=-0.1546*sN+0.0119*s2N-0.0012*s3N;
f(hM2)=1.0004-0.0373*cN+0.0002*c2N;
u(hM2)=-0.0374*sN;
f(hK2)=1.0241+0.2863*cN+0.0083*c2N-0.0015*c3N;
u(hK2)=-0.3096*sN+0.0119*s2N-0.0007*s3N;
f(hQ1)=f(hO1);
u(hQ1)=u(hO1);
f(hN2)=f(hM2);
u(hN2)=u(hM2);
f(hMN4)=f(hM2)^2;
u(hMN4)=2*u(hM2);
f(hM4)=f(hM2)^2;
u(hM4)=2*u(hM2);
f(hMS4)=f(hM2);
u(hMS4)=u(hM2);

%Assign fFac and uFac
for n=1:length(Names)
   var=['h' Names{n}];
   eval(['fFac(n)= f(' var ');'])
   eval(['uFac(n)=u(' var ');'])
end

uFac=uFac*180/pi;
uFac=mod(uFac,360);