% NEWTON-RAPHSON ALGORITHM 2.3               
 %
 % To find a solution to f(x) = 0 given an
 % initial approximation p0:
 %
 % INPUT:   initial approximation p0; tolerance TOL;
 %          maximum number of iterations NO.
 %
 % OUTPUT:  approximate solution p or a message of failure
 syms('OK', 'P0', 'TOL', 'NO', 'FLAG', 'NAME', 'OUP', 'F0');
 syms('I', 'FP0', 'D','x','s');
 TRUE = 1;
 FALSE = 0;
 fprintf(1,'This is Newtons Method\n');
 fprintf(1,'Input the function F(x) in terms of x\n');
 fprintf(1,'For example: cos(x)\n');
 s = input(' ','s');
 F = inline(s,'x');
 fprintf(1,'Input the derivative of F(x) in terms of x\n');
 s = input(' ');
 FP = inline(s,'x');
 OK = FALSE;
 fprintf(1,'Input initial approximation\n');
 P0 = input(' '); 
 while OK == FALSE 
 fprintf(1,'Input tolerance\n');
 TOL = input(' ');
 if TOL <= 0 
 fprintf(1,'Tolerance must be positive\n');
 else 
 OK = TRUE;
 end
 end
 OK = FALSE;
 while OK == FALSE 
 fprintf(1,'Input maximum number of iterations - no decimal point\n');
 NO = input(' ');
 if NO <= 0 
 fprintf(1,'Must be positive integer\n');
 else 
 OK = TRUE;
 end
 end
 if OK == TRUE 
 fprintf(1,'Select output destination\n');
 fprintf(1,'1. Screen\n');
 fprintf(1,'2. Text file\n');
 fprintf(1,'Enter 1 or 2\n');
 FLAG = input(' ');
 if FLAG == 2 
 fprintf(1,'Input the file name in the form - drive:\\name.ext\n');
 fprintf(1,'For example:   A:\\OUTPUT.DTA\n');
 NAME = input(' ','s');
 OUP = fopen(NAME,'wt');
 else
 OUP = 1;
 end
 fprintf(1,'Select amount of output\n');
 fprintf(1,'1. Answer only\n');
 fprintf(1,'2. All intermediate approximations\n');
 fprintf(1,'Enter 1 or 2\n');
 FLAG = input(' ');
 fprintf(OUP, 'Newtons Method\n');
 if FLAG == 2 
 fprintf(OUP, '  I   P                 F(P)\n');
 end
 F0 = F(P0);
% STEP 1
 I = 1;
 OK = TRUE;        
% STEP 2
 while I <= NO & OK == TRUE   
% STEP 3
% compute P(I)
 FP0 = FP(P0);
 D = F0/FP0;
% STEP 6
 P0 = P0 - D;  
 F0 = F(P0);
 if FLAG == 2 
 fprintf(OUP,'%3d   %14.8e   %14.7e\n',I,P0,F0);
 end
% STEP 4
 if abs(D) < TOL 
% procedure completed successfully
 fprintf(OUP,'\nApproximate solution = %.10e\n',P0);
 fprintf(OUP,'with F(P) = %.10e\n',F0);
 fprintf(OUP,'Number of iterations = %d\n',I);
 fprintf(OUP,'Tolerance = %.10e\n',TOL);
 OK = FALSE;
% STEP 5
 else
 I = I+1;
 end
 end
 if OK == TRUE 
% STEP 7
% procedure completed unsuccessfully
 fprintf(OUP,'\nIteration number %d',NO);
 fprintf(OUP,' gave approximation %.10e\n',P0);
 fprintf(OUP,'with F(P) = %.10e not within tolerance  %.10e\n',F0,TOL);
 end
 if OUP ~= 1
 fclose(OUP);
 fprintf(1,'Output file %s created successfully \n',NAME);
 end
 end