The usage of SOLVE or FSOLVE for equation in string format

I develop program using MATLAB. But there is some errors in my code. My problems are: (1) there is any error message "??? Operands to the and && operators must be convertible to logical scalar values. at line 83". (2) Since equation "eq1" and "eq2" is string, to solve the equations, I use function "SOLVE", but it takes long time. On mathworks forums, Mr. Zhang lu suggest me to use FSOLVE, after changing with the FSOLVE function, the result is always 1. Probably because "eq1" and "eq2" in string format. Is there any other way to write eq1 and eq2 in my case.

Could you please help me.

Here it is my full code:

clc;
clear all;
x=[15.5, 39.8, 21.3, 18.2, 48.5, 0.2, 40.6, 2.1, 0.7, 2.5, 2.9, 6.1, 0.8, 6.5, 9.4, 33.6, 29, 2.5, 5.9, 1.5, 0.5, 45, 0.3, 1.4, 23.2, 0.3, 0.2, 0.3, 3, 0.03, 0.4, 8.3, 0.2, 12, 2.8, 3.6, 21.8, 1.5, 35.5, 29.5, 53, 24, 0.06, 39, 20, 0.8, 2.2, 3.9, 0.6, 20.3, 34, 37.4, 3.7, 20.2, 2.6, 0.6, 2, 2.7, 3.4, 3, 0.2, 0.3, 25.3, 5, 1.6, 4, 6.1, 8.7, 37.1, 0.1, 0.2, 0.2, 0.03, 0.6, 0.2, 0.4, 0.06, 0.8, 0.4, 0.1, 0.1, 0.1, 0.2, 0.1, 12.3, 3, 0.1, 0.2, 0.1, 0.5, 1.3, 0.6, 1.5, 0.4, 1, 0.1, 4, 1, 1.6, 1.1];
y=[0.5, 3, 4, 2, 1];
epsilon=0.001;
savefile='Hasil.mat';
ts1=[];
ts2=[];
ts3=[];
ts4=[];
Hasil={ts1,ts2,ts3,ts4};
save(savefile,'Hasil');
n=length(x);
jumt1=0;
jumt2=0;
jumt3=0;
jumt4=0;
jumt5=0;
iterasi=0;
selisih=epsilon;

while(selisih >= epsilon) || (y(4)>0) || (y(5)>0) (y(1)>0) && (y(1)<1)
    tStart=tic;
    plama=y(1);
    teta1lama=y(2);
    teta2lama=y(3);
    beta1lama=y(4);
    beta2lama=y(5);
    Ep =(y(1).*wblpdf(x,y(2),y(4)))./((y(1).*wblpdf(x, y(2), y(4))) +(1-y(1)).*wblpdf(x, y(3),y(5)));
    p= mean(Ep)

      for i=1:n
          jumt1=jumt1+x(i).^(y(4).*Ep(i));
          jumt2=jumt2+((x(i).^y(5))./(x(i).^(y(5).*Ep(i))));
          jumt3=jumt3+(Ep(i).*log(x(i)));
          jumt4=jumt4+log(x(i));
          jumt5=jumt5+(Ep(i).*log(x(i)));
          t1(i)=x(i).^Ep(i);
          t2(i)= Ep(i).*log(x(i));
          t3(i)=x(i).^(1-Ep(i));
          t4(i)=(1-Ep(i)).*log(x(i));
          ts1 = strcat('(',num2str(t1(1,i)),'^b1)*(',num2str(t2(1,i)),')+');
          ts2 = strcat('(',num2str(t1(1,i)),'^b1)+');
          ts3 = strcat('((',num2str(t3(1,i)),'^b2)*(',num2str(t4(1,i)),'))+');
          ts4 = strcat('(',num2str(t3(1,i)),'^b2)+');

          st=sum(t2);
          savefile='Hasil.mat'; %nama file data yang akan dibuat
          [v,w]=size(Hasil);
          if isempty(Hasil{1,1}) && isempty(Hasil{1,2}) && isempty(Hasil{1,3}) && isempty(Hasil{1,4})
               Hasil(1,:)={ts1,ts2,ts3,ts4}; %menambahkan record baru
          else
               Hasil(v+1,:)={ts1,ts2,ts3,ts4}; %menambahkan record baru
          end
          save(savefile,'Hasil');       
      end;
     load('Hasil.mat');
     gab1=cell2mat(Hasil(:,1).');
     gab2=cell2mat(Hasil(:,2).');
     gab3=cell2mat(Hasil(:,3).');
     gab4=cell2mat(Hasil(:,4).');
     eq1=strcat('(',num2str(sum(Ep)),'/b1)-(',num2str(sum(Ep)*log(y(2))),')+(',num2str(st),')-((',gab1,'0)/(',num2str(y(2)),'^(b1*',num2str(sum(Ep)),')))+(((',gab2,'0)*',num2str(sum(Ep)*log(y(2))),')/(',num2str(y(2)),'^(b1*',num2str(sum(Ep)),')))=0');
     eq1=sprintf(eq1)
     eq2=strcat('(',num2str(n-sum(Ep)),'/b2)-(',num2str((n-sum(Ep))*log(y(3))),')+(',num2str(jumt4),')-(',num2str(jumt5),')-(((',num2str(y(3)),')^((-b2)*(',num2str(n-sum(Ep)),')))*(',gab3,'0))+(((',gab4,'0)*',num2str((n-sum(Ep))*log(y(3))),')*((',num2str(y(3)),')^((-b2)*(',num2str(n-sum(Ep)),'))))=0');
     eq2=sprintf(eq2);
     teta1 = exp(log(jumt1)./(y(4).*sum(Ep)))
     teta2 = exp(log(jumt2)./(y(5).*(-sum(Ep)+n)))
     syms b1 b2;
     beta1=fsolve(@(b1)(eq1),1);
     beta2=fsolve(@(b2)(eq2),1);
     beta1=double(beta1)
     beta2=double(beta2)
     selisih(iterasi+1) = sum(abs(plama - p)) + sum(abs(teta1lama - teta1)) + sum(abs(teta2lama - teta2))+ sum(abs(beta1lama - beta1)) + sum(abs(beta2lama - beta2))
     tElapsed = toc(tStart)
     iterasi=iterasi+1
      if (y(4)<0) || (y(5)<0) || (y(1)<0) || (y(1)>1)

         y=[plama, teta1lama, teta2lama, beta1lama, beta2lama];
         break
     else
         y=[p, teta1, teta2, beta1, beta2];
     end
  end
  Jumlah_Iterasi = iterasi
  waktu=tElapsed
  p=y(1)
  teta1=y(2)
  teta2=y(3)
  beta1=y(4)
  beta2=y(5)
  Nilai_epsilon=selisih

Answer 1

[Zhang lu]

u can define variable x but not b1 and b2 before the loop , the code as follow

clc; clear all; x=[15.5, 39.8, 21.3, 18.2, 48.5, 0.2, 40.6, 2.1, 0.7, 2.5, 2.9, 6.1, 0.8, 6.5, 9.4, 33.6, 29, 2.5, 5.9, 1.5, 0.5, 45, 0.3, 1.4, 23.2, 0.3, 0.2, 0.3, 3, 0.03, 0.4, 8.3, 0.2, 12, 2.8, 3.6, 21.8, 1.5, 35.5, 29.5, 53, 24, 0.06, 39, 20, 0.8, 2.2, 3.9, 0.6, 20.3, 34, 37.4, 3.7, 20.2, 2.6, 0.6, 2, 2.7, 3.4, 3, 0.2, 0.3, 25.3, 5, 1.6, 4, 6.1, 8.7, 37.1, 0.1, 0.2, 0.2, 0.03, 0.6, 0.2, 0.4, 0.06, 0.8, 0.4, 0.1, 0.1, 0.1, 0.2, 0.1, 12.3, 3, 0.1, 0.2, 0.1, 0.5, 1.3, 0.6, 1.5, 0.4, 1, 0.1, 4, 1, 1.6, 1.1]; x1=x; y=[0.5, 3, 4, 2, 1]; epsilon=0.001; savefile='Hasil.mat'; ts1=[]; ts2=[]; ts3=[]; ts4=[]; Hasil={ts1,ts2,ts3,ts4}; save(savefile,'Hasil'); n=length(x1); jumt1=0; jumt2=0; jumt3=0; jumt4=0; jumt5=0; iterasi=0; selisih=epsilon; syms x (selisih >= epsilon) | (y(4)>0) | (y(5)>0)&(y(1)>0) & (y(1)<1) tStart=tic; plama=y(1); teta1lama=y(2); teta2lama=y(3); beta1lama=y(4); beta2lama=y(5); Ep =(y(1).*wblpdf(x1,y(2),y(4)))./((y(1).*wblpdf(x1, y(2), y(4))) +(1-y(1)).*wblpdf(x1, y(3),y(5))); p= mean(Ep) for i=1:1 jumt1=jumt1+x1(i)^(y(4).*Ep(i)); jumt2=jumt2+((x1(i)^y(5))./(x1(i).^(y(5).*Ep(i)))); jumt3=jumt3+(Ep(i).*log(x1(i))); jumt4=jumt4+log(x1(i)); jumt5=jumt5+(Ep(i).*log(x1(i))); t1(i)=x1(i).^Ep(i); t2(i)= Ep(i).*log(x1(i)); t3(i)=x1(i).^(1-Ep(i)); t4(i)=(1-Ep(i)).*log(x1(i)); ts1 = strcat('(',num2str(t1(1,i)),'^x)*(',num2str(t2(1,i)),')+'); ts2 = strcat('(',num2str(t1(1,i)),'^x)+'); ts3 = strcat('((',num2str(t3(1,i)),'^x)*(',num2str(t4(1,i)),'))+'); ts4 = strcat('(',num2str(t3(1,i)),'^x)+'); st=sum(t2); savefile='Hasil.mat'; %nama file data yang akan dibuat [v,w]=size(Hasil); if isempty(Hasil{1,1}) & isempty(Hasil{1,2}) & isempty(Hasil{1,3}) & isempty(Hasil{1,4}) Hasil(1,:)={ts1,ts2,ts3,ts4}; %menambahkan record baru else Hasil(v+1,:)={ts1,ts2,ts3,ts4}; %menambahkan record baru end save(savefile,'Hasil'); end; load('Hasil.mat'); gab1=cell2mat(Hasil(:,1).'); gab2=cell2mat(Hasil(:,2).'); gab3=cell2mat(Hasil(:,3).'); gab4=cell2mat(Hasil(:,4).'); eq1=strcat('(',num2str(sum(Ep)),'/x)-(',num2str(sum(Ep)*log(y(2))),')+(',num2str(st),')-((',gab1,'0)/(',num2str(y(2)),'^(x*',num2str(sum(Ep)),')))+(((',gab2,'0)*',num2str(sum(Ep)*log(y(2))),')/(',num2str(y(2)),'^(x*',num2str(sum(Ep)),')))'); eq1=sprintf(eq1) eq2=strcat('(',num2str(n-sum(Ep)),'/x)-(',num2str((n-sum(Ep))*log(y(3))),')+(',num2str(jumt4),')-(',num2str(jumt5),')-(((',num2str(y(3)),')^((-x)*(',num2str(n-sum(Ep)),')))*(',gab3,'0))+(((',gab4,'0)*',num2str((n-sum(Ep))*log(y(3))),')*((',num2str(y(3)),')^((-x)*(',num2str(n-sum(Ep)),'))))'); eq2=sprintf(eq2); teta1 = exp(log(jumt1)./(y(4).*sum(Ep))) teta2 = exp(log(jumt2)./(y(5).*(-sum(Ep)+n))) beta1=fsolve(eq1,1); beta2=fsolve(eq2,1); beta1=double(beta1) beta2=double(beta2)

Answer 2

[Walter Roberson]

You have the Symbolic Toolbox or else you would not be able to use solve(). So instead of constructing a string to be solved, construct a symbolic expression.