getPolyDec(PolyCoef,EncVec,Cmatrix,Moments,Nsvd,noise)

function  PolyDecWeights = getPolyDec(PolyCoef,EncVec,Cmatrix,Moments,Nsvd,noise)
%% Compute the linear decoding vectors for a polynomial using the results of genDecVecParms.m

%% The Poly coefficients define the f(x) = sum_{n=0}^5(PolyCoef(n)x^n) 

%% Nsvd sets the number of singular values used.
%% noise is optional, default is zero.

%% Maximum number of terms is limited to 6 by genDecVecParms.m

%% Feb. 25, 2001 Consolidation

%% Jan. 17, 2001
%% Copyright (C) by Charles. H. Anderson (All Rights Reserved)
%% Dept. Anatomy and Neurobiology
%% Washington Univ. School of Medicine
%% St. Louis, MO
%% [e-mail]
% 
%%
if(nargin==5)
    noise = 0;
end

[N, D] = size(EncVec); % Only use for EncVec, also compatible with getBilinearDec.m
if(D~=1)
    error('Only 1 dimensional polynomials');
end
[Num, Np] = size(PolyCoef);
if(Np>6)
    error('Maximum number of polynomial coefficients is 6');
end

if(Nsvd>N)
    msg = sprintf('Changing Nsvd %d to Neuron Number %d',Nsvd,N);
    warning(msg);
    Nsvd = N;
end

[U,S,UT] = svds(Cmatrix,Nsvd);
S = diag(S);
Sinv = 1./(S+noise^2*ones(Nsvd,1));
Sinv = diag(Sinv);

for(l=1:Num)
    V = Moments(:,1:Np)*PolyCoef(l,:)';
    PolyDecWeights(:,l) = U*Sinv*(U'*V);
end