Conversion

Convert the following Matlab code into Mathematica code: function C2=TransformC(C1,dia2,tx,ty,thetaR) dia1=C1(1); % Original pupil diameter C1=C1(2:end); etaS=dia2/dia1; % Scaling factor etaT=2*sqrt(tx^2+ty^2)/dia1; % Translation coordinates thetaT=atan2(ty, tx); thetaR=thetaR*pi/180; % Rotation in radians jnm=length(C1)-1; nmax=ceil((-3+sqrt(9+8*jnm))/2); jmax=nmax*(nmax+3)/2; S=zeros(jmax+1,1); S(1:length(C1))=C1; C1=S; clear S P=zeros(jmax+1); % Matrix P transforms from standard to Campbell order N=zeros(jmax+1); % Matrix N contains the normalization coefficients R=zeros(jmax+1); % Matrix R is the coefficients of the radial polynomials CC1=zeros(jmax+1,1); % CC1 is a complex representation of C1 counter=1; for m=-nmax:nmax % Meridional indexes for n=abs(m):2:nmax % Radial indexes jnm=(m+n*(n+2))/2; P(counter,jnm+1)=1; N(counter,counter)=sqrt(n+1); for s=0:(n-abs(m))/2 R(counter-s,counter)=(-1)^s*factorial(n-s)/ ... (factorial(s)*factorial((n+m)/2-s)*factorial((n-m)/2-s)); end if m<0, CC1(jnm+1)=(C1((-m+n*(n+2))/2+1)+i*C1(jnm+1)) /sqrt(2); elseif m==0, CC1(jnm+1)=C1(jnm+1); else, CC1(jnm+1)=(C1(jnm+1)-i*C1((-m+n*(n+2))/2+1)) /sqrt(2) ;end counter=counter+1; end, end ETA=[]; % Coordinate-transfer matrix for m=-nmax:nmax for n=abs(m):2:nmax ETA=[ETA P*(transform(n,m,jmax,etaS,etaT,thetaT,thetaR))]; end, end C=inv(P)*inv(N)*inv(R)*ETA*R*N*P; CC2=C*CC1; C2=zeros(jmax+1,1); % C2 is formed from the complex Zernike coefficients, CC2 for m=-nmax:nmax for n=abs(m):2:nmax jnm=(m+n*(n+2))/2; if m<0, C2(jnm+1)=imag(CC2(jnm+1)-CC2((-m+n*(n+2))/2+1)) /sqrt(2); elseif m==0, C2(jnm+1)=real(CC2(jnm+1)); else, C2(jnm+1)=real(CC2(jnm+1)+CC2((-m+n*(n+2))/2+1)) /sqrt(2); end, end, end C2=[dia2;C2]; % function Eta=transform(n,m,jmax,etaS,etaT,thetaT,thetaR) % Returns coefficients for transforming a ro^n*exp(i*m*theta)-term into ’-terms Eta=zeros(jmax+1,1); for p=0:((n+m)/2) for q=0:((n-m)/2) nnew=n-p-q; mnew=m-p+q; jnm=(mnew+nnew*(nnew+2))/2; Eta(floor(jnm+1))=Eta(floor(jnm+1))+nchoosek((n+m)/2,p)* ... nchoosek((n-m)/2,q)*etaS^(n-p-q)*etaT^(p+q)*exp(i*((p-q)* ... (thetaT-thetaR)+m*thetaR)); end, end % Use the following variables to test the conversion % C1 = [5 00.00 00.00 00.00 00.04 -0.28 00.06 -0.02 00.03 -0.01 -0.02 ... % -0.01 -0.01 00.04 -0.02 00.00 00.00 00.02 -0.03 00.00 00.02 ... % 00.00 00.01 00.01 00.02 00.02 00.00 -0.01]; % dia2 = 5; % tx = 5; % ty = 5; % thetaR = 5;