function [spot,spot_size,spot_vol_bkg,spot_vol_no_bkg] = gen2dgauss(n,varx,vary, max_gray,min_gray,resolution,file_name);

%n is the square in which the gaussian is to be placed
%varx is the variance along the x axis
%vary is the variance along the y axis
%max_gray is the maximum gray level desired at the spot center
%min_gray is the minimum gray level desired as the background
%resolution is the dpi resolution required for the tiff file to which we
%write.
%file_name is the strng that gives the file name to write

%2-D gaussian is given by
% 1/((2*pi)^(N/2)*|A|^(1/2)) exp-(1/2( (x-mx)'*A^(-1)*(y-my)))

%initialize the spot
spot = zeros(n,n);

%find the mean along the x and y axes

x_mean = ceil(n/2);
y_mean = ceil(n/2);


%whether or not to insert side spots
insert_side_spots = 1;


%defining the covariance matrix
var = [varx 0
   0 vary];

%computing the determinant of the covariance matrix
det_var = varx*vary;

%computing the inverse of the covariance matrix
inv_var = [(1/vary) 0
   0 (1/varx)];

%determining the peak of the gaussian
max_val = (1/(2*pi*sqrt(det_var)));

for x = 1:n
   for y = 1:n
      
     %the 2-d vector corresponding to the 2 dimensions
     Z = [(x-x_mean) 
          (y-y_mean)];
      
       spot(x,y) = (1/(2*pi*sqrt(det_var)))*exp(-(1/2)*(Z.')*inv_var*Z);
              
    end
 end
 
 %normalizing and scaling the gaussian
 spot = round(((max_gray-min_gray)*spot./max_val)+min_gray); 
 
 
 spot_size = sum(sum(spot>min_gray));
 
 spot_vol_bkg = sum(sum(spot(spot > min_gray)));
 
 spot_vol_no_bkg = sum(sum(spot(spot > min_gray))) - min_gray*spot_size;
 
 

 if(insert_side_spots)

%mean of the side spots at the four corners
side1_x_mean = ceil(n/8);
side1_y_mean = ceil(n/8);

side2_x_mean = ceil(7*n/8);
side2_y_mean = ceil(n/8);

side3_x_mean = ceil(n/8);
side3_y_mean = ceil(7*n/8);

side4_x_mean = ceil(7*n/8);
side4_y_mean = ceil(7*n/8);

side5_x_mean = ceil(n/2);
side5_y_mean = ceil(n/8);

side6_x_mean = ceil(7*n/8);
side6_y_mean = ceil(n/2);

side7_x_mean = ceil(n/2);
side7_y_mean = ceil(7*n/8);

side8_x_mean = ceil(n/8);
side8_y_mean = ceil(n/2);

side9_x_mean = ceil(n/4);
side9_y_mean = ceil(n/4);

side10_x_mean = ceil(3*n/4);
side10_y_mean = ceil(n/4);

side11_x_mean = ceil(3*n/4);
side11_y_mean = ceil(3*n/4);

side12_x_mean = ceil(n/4);
side12_y_mean = ceil(3*n/4);


varx_side = 40;
vary_side = 40;

var_side = [varx_side 0 
            0  vary_side];
        
%computing the determinant of the covariance matrix
det_var_side = varx_side*vary_side;

%computing the inverse of the covariance matrix
inv_var_side = [(1/vary_side) 0
   0 (1/varx_side)];

%determining the peak of the gaussian
max_val = (1/(2*pi*sqrt(det_var_side)));

for x = 1:n
   for y = 1:n
      
     %the 2-d vector corresponding to the 2 dimensions
     Z = [(x-side1_x_mean) 
          (y-side1_y_mean)];
      
       side1_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side2_x_mean) 
          (y-side2_y_mean)];
      
       side2_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side3_x_mean) 
          (y-side3_y_mean)];
      
       side3_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side4_x_mean) 
          (y-side4_y_mean)];
      
       side4_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side5_x_mean) 
          (y-side5_y_mean)];
      
       side5_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side6_x_mean) 
          (y-side6_y_mean)];
      
       side6_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side7_x_mean) 
          (y-side7_y_mean)];
      
       side7_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side8_x_mean) 
          (y-side8_y_mean)];
      
       side8_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
              
     Z = [(x-side9_x_mean) 
          (y-side9_y_mean)];
      
       side9_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
        
     Z = [(x-side10_x_mean) 
          (y-side10_y_mean)];
      
       side10_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side11_x_mean) 
          (y-side11_y_mean)];
      
       side11_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);
       
     Z = [(x-side12_x_mean) 
          (y-side12_y_mean)];
      
       side12_spot(x,y) = (1/(2*pi*sqrt(det_var_side)))*exp(-(1/2)*(Z.')*inv_var_side*Z);

       
   end
 end
         
 %normalizing and scaling the gaussian
 side1_spot = round(255*(side1_spot./max_val));        
   
 %normalizing and scaling the gaussian
 side2_spot = round(255*(side2_spot./max_val));      
 
 %normalizing and scaling the gaussian
 side3_spot = round(255*(side3_spot./max_val));      
 
 %normalizing and scaling the gaussian
 side4_spot = round(255*(side4_spot./max_val));
 
 %normalizing and scaling the gaussian
 side5_spot = round(255*(side5_spot./max_val));
 
 %normalizing and scaling the gaussian
 side6_spot = round(255*(side6_spot./max_val));
 
 %normalizing and scaling the gaussian
 side7_spot = round(255*(side7_spot./max_val));
 
 %normalizing and scaling the gaussian
 side8_spot = round(255*(side8_spot./max_val));
 
 %normalizing and scaling the gaussian
 side9_spot = round(255*(side9_spot./max_val));
 
 %normalizing and scaling the gaussian
 side10_spot = round(255*(side10_spot./max_val));
 
 %normalizing and scaling the gaussian
 side11_spot = round(255*(side11_spot./max_val));
 
 %normalizing and scaling the gaussian
 side12_spot = round(255*(side12_spot./max_val));
 
 
 side_spot = side1_spot + side2_spot + side3_spot + side4_spot + side5_spot + side6_spot + side7_spot + side8_spot + side9_spot + side10_spot + side11_spot + side12_spot;
 
 spot = spot + side_spot;
 
 spot(spot>255) = 255;
        
end


 %inverting : because the spot is such that it is white at the center and black towards
 %the tails and what we want is black at the center and white towards the tails
 spot = 255 - spot;
 

 spot = uint8(spot);
  
 image(spot);
 colormap('gray');
 axis equal;
 xlim([1 n]);
 ylim([1 n]);
 
 axis off;
 
 file_name = strcat(file_name,'.tif');
 
 imwrite(spot,file_name,'tif','Compression','none','Resolution',resolution);