If I use multi funcions with syms variable, How can I get track min value among that funcions?

clear; clc; close all;
syms seta
Rx1= cos(seta)
Rx2= sin(seta)

If I set Rx1, Rx2 funcion like that, How can I get the graph with min value among Rx1, Rx2?

If I use discrete value, I can use like this

xmin=min([R1(x(:)');R2(x(:)');])
plot(x,xmin,'.-');

but, In this case I using Symbolic Math Toolbox, I don't know how I can make it works with syms variable...

Answer 1

[Walter Roberson]

You need to use something like

Min = @(tworows) arrayfun( @(colidx) piecewise(tworows(1,colidx) <= tworows(2,colidx), tworows(1,colidx), tworows(2,colidx)), 1:size(tworows,2);

The code could be simplified if you were willing to use R1 and R2 as separate arguments instead of putting them together in one array.

[Gookki Jeong]

clear; clc; close all;

syms seta
gamma = 1;
Rx_ = 1;
Ry_ = Rx_*gamma;

% 등가 정적 적용
gamma = 1;

Rx1= matlabFunction(( cos(seta)-0.3*sin(seta) )*Rx_ );   Rx(1)= "(cos(seta)-0.3 * sin(seta)) * Rx_" ; 
Rx2= matlabFunction(( cos(seta)+0.3*sin(seta) )*Rx_);    Rx(2)= "(cos(seta)+0.3 * sin(seta)) * Rx_";
Rx3= matlabFunction(( 0.3*cos(seta)-sin(seta) )*Rx_);      Rx(3)= "(0.3*cos(seta)-sin(seta)) * Rx_";
Rx4= matlabFunction(( -0.3*cos(seta)-sin(seta) )*Rx_);   Rx(4)= "(-0.3*cos(seta)-sin(seta)) * Rx_";
Ry1= (0.3*cos(seta) + sin(seta) )*Ry_;      Ry(1)= "(0.3*cos(seta) + sin(seta)) * Ry_";
Ry2= (-0.3*cos(seta) + sin(seta) )*Ry_;     Ry(2)= "(-0.3*cos(seta) + sin(seta)) * Ry_";
Ry3= (cos(seta) + 0.3*sin(seta) )*Ry_;      Ry(3)= "(cos(seta) + 0.3*sin(seta)) * Ry_";
Ry4= (cos(seta) - 0.3*sin(seta) )*Ry_;      Ry(4)= "(cos(seta) - 0.3*sin(seta)) * Ry_";


N=4;
for ii=1:N
   temp=['RR',num2str(ii),'=matlabFunction(','Rx',num2str(ii),'+Ry',num2str(ii),');'];
   eval(temp);   
   minx=['a',num2str(ii),'=fminbnd(RR',num2str(ii),',0,2*pi);'];
   maxx=['b',num2str(ii),'=fminbnd(@(seta)-RR',num2str(ii),'(seta),0,2*pi);'];
   eval(minx);
   eval(maxx); 
end
 
for ii=1:N    
    subplot(4,1,ii)
    gx=['g',num2str(ii),'x=fplot(Rx',num2str(ii),',[0 2*pi],''--''); hold on'];
    gy=['g',num2str(ii),'y=fplot(Ry',num2str(ii),',[0 2*pi]); hold on'];
    g1=['g',num2str(ii),'=fplot(RR',num2str(ii),',[0 2*pi]); hold on'];
    min=['min=plot(a',num2str(ii),',RR',num2str(ii), ' (a',num2str(ii),'),''*''); hold on '];
    max=['max=plot(b',num2str(ii),',RR',num2str(ii), ' (b',num2str(ii),'),''*''); hold on '];
    a= ['a11=a',num2str(ii),';'];
    b= ['b11=b',num2str(ii),';'];
    RR= ['RR11=RR',num2str(ii),';'];
    eval(gx);    eval(gy);    eval(g1);    eval(min);    eval(max);   eval(a);   eval(b);   eval(RR);
  
    
    
    a="(" + num2str(round(a11/pi,2))+"pi [" + num2str(round(a11/pi*180,2))+"\circ]";
    a_= " , " + num2str(round(RR11(a11),2))+")";
    a= a + a_;
    b="(" + num2str(round(b11/pi,2))+"pi [" + num2str(round(b11/pi*180,2))+"\circ]";
    b_= " , " + num2str(round(RR11(b11),2))+")";
    b= b + b_;
    xticks([0 0.5*pi pi 1.5*pi 2*pi])
    xticklabels({'0','0.5\pi','\pi','1.5\pi','2\pi'})
    legend('x축','y축',"단순합",a,b,'location','best')
    title(Rx(ii)+" + "+Ry(ii),'interpreter','none');

    
end

I'm sorry I can't understand. here is my code then how I can use that if I trace min value graph within RR1~RR4.

[Walter Roberson]

Your use of eval() for dynamic variable names is... distracting... Sufficiently distracting that I would not bother to try to debug that code. I advise you to scrap it and rewrite it without using dynamic variable names.

http://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

[Gookki Jeong]

clear; clc; close all;

syms seta
gamma = 1;
Rx_ = 1;
Ry_ = Rx_*gamma;

% 등가 정적 적용
gamma = 1;

Rx1= matlabFunction(( cos(seta)-0.3*sin(seta) )*Rx_ );   Rx(1)= "(cos(seta)-0.3 * sin(seta)) * Rx_" ; 
Rx2= matlabFunction(( cos(seta)+0.3*sin(seta) )*Rx_);    Rx(2)= "(cos(seta)+0.3 * sin(seta)) * Rx_";
Rx3= matlabFunction(( 0.3*cos(seta)-sin(seta) )*Rx_);      Rx(3)= "(0.3*cos(seta)-sin(seta)) * Rx_";
Rx4= matlabFunction(( -0.3*cos(seta)-sin(seta) )*Rx_);   Rx(4)= "(-0.3*cos(seta)-sin(seta)) * Rx_";
Ry1= (0.3*cos(seta) + sin(seta) )*Ry_;      Ry(1)= "(0.3*cos(seta) + sin(seta)) * Ry_";
Ry2= (-0.3*cos(seta) + sin(seta) )*Ry_;     Ry(2)= "(-0.3*cos(seta) + sin(seta)) * Ry_";
Ry3= (cos(seta) + 0.3*sin(seta) )*Ry_;      Ry(3)= "(cos(seta) + 0.3*sin(seta)) * Ry_";
Ry4= (cos(seta) - 0.3*sin(seta) )*Ry_;      Ry(4)= "(cos(seta) - 0.3*sin(seta)) * Ry_";


RR1=@(seta)cos(seta).*(1.3e+1./1.0e+1)+sin(seta).*(7.0./1.0e+1);
RR2=@(seta)cos(seta).*(7.0./1.0e+1)+sin(seta).*(1.3e+1./1.0e+1);
RR3=@(seta)cos(seta).*(1.3e+1./1.0e+1)-sin(seta).*(7.0./1.0e+1);
RR4=@(seta)cos(seta).*(1.3e+1./1.0e+1)-sin(seta).*(7.0./1.0e+1);
a1=fminbnd(RR1,0,2*pi);
b1=fminbnd(@(seta)-RR1(seta),0,2*pi);
a2=fminbnd(RR2,0,2*pi);
b2=fminbnd(@(seta)-RR2(seta),0,2*pi);
a3=fminbnd(RR3,0,2*pi);
b3=fminbnd(@(seta)-RR3(seta),0,2*pi);
a4=fminbnd(RR4,0,2*pi);
b4=fminbnd(@(seta)-RR4(seta),0,2*pi);



% % 위에 반복문의  기준이 된 코드::
subplot(4,1,1);
g1x=fplot(Rx1,[0 2*pi]); hold on
g1y=fplot(Ry1,[0 2*pi]);  hold on
g1=fplot(RR1,[0 2*pi]);
min=plot(a1,RR1(a1),'*');
max=plot(b1,RR1(b1),'*');

a="(" + num2str(round(a1/pi,2))+"pi [" + num2str(round(a1/pi*180,2))+"\circ]";
a_= " , " + num2str(round(RR1(a1),2))+")";
a= a + a_;
b="(" + num2str(round(b1/pi,2))+"pi [" + num2str(round(b1/pi*180,2))+"\circ]";
b_= " , " + num2str(round(RR1(b1),2))+")";
b= b + b_;
xticks([0 0.5*pi pi 1.5*pi 2*pi])
xticklabels({'0','0.5\pi','\pi','1.5\pi','2\pi'})
legend('x축','y축',"단순합",a,b,'location','best')

subplot(4,1,2);
g1x=fplot(Rx2,[0 2*pi]); hold on
g1y=fplot(Ry2,[0 2*pi]);  hold on
g1=fplot(RR2,[0 2*pi]);
min=plot(a2,RR2(a2),'*');
max=plot(b2,RR2(b2),'*');

a="(" + num2str(round(a2/pi,2))+"pi [" + num2str(round(a2/pi*180,2))+"\circ]";
a_= " , " + num2str(round(RR2(a2),2))+")";
a= a + a_;
b="(" + num2str(round(b2/pi,2))+"pi [" + num2str(round(b2/pi*180,2))+"\circ]";
b_= " , " + num2str(round(RR2(b2),2))+")";
b= b + b_;
xticks([0 0.5*pi pi 1.5*pi 2*pi])
xticklabels({'0','0.5\pi','\pi','1.5\pi','2\pi'})
legend('x축','y축',"단순합",a,b,'location','best')

ㅠㅠ I'm so sorry to bother you. here is my rewiting code.

[Walter Roberson]

MIN2 = @(v1, v2) piecewise(v1 <= v2, v1, v2);
MIN4 = @(v1, v2, v3, v4) MIN2(MIN2(v1,v2),MIN2(v3,v4));
RR1234 = MIN4(R1,R2,R3,R4);
fplot(RR1234, [0 2*pi])

[Gookki Jeong]

Thanks, I think almost done, but I had error message

Undefined operator '<=' for input arguments of type 'function_handle'.

[Walter Roberson]

close all;

syms seta
gamma = 1;
Rx_ = 1;
Ry_ = Rx_*gamma;

% 등가 정적 적용
gamma = 1;

Rx1= matlabFunction(( cos(seta)-0.3*sin(seta) )*Rx_ );   Rx(1)= "(cos(seta)-0.3 * sin(seta)) * Rx_" ; 
Rx2= matlabFunction(( cos(seta)+0.3*sin(seta) )*Rx_);    Rx(2)= "(cos(seta)+0.3 * sin(seta)) * Rx_";
Rx3= matlabFunction(( 0.3*cos(seta)-sin(seta) )*Rx_);      Rx(3)= "(0.3*cos(seta)-sin(seta)) * Rx_";
Rx4= matlabFunction(( -0.3*cos(seta)-sin(seta) )*Rx_);   Rx(4)= "(-0.3*cos(seta)-sin(seta)) * Rx_";
Ry1= (0.3*cos(seta) + sin(seta) )*Ry_;      Ry(1)= "(0.3*cos(seta) + sin(seta)) * Ry_";
Ry2= (-0.3*cos(seta) + sin(seta) )*Ry_;     Ry(2)= "(-0.3*cos(seta) + sin(seta)) * Ry_";
Ry3= (cos(seta) + 0.3*sin(seta) )*Ry_;      Ry(3)= "(cos(seta) + 0.3*sin(seta)) * Ry_";
Ry4= (cos(seta) - 0.3*sin(seta) )*Ry_;      Ry(4)= "(cos(seta) - 0.3*sin(seta)) * Ry_";


RR1=@(seta)cos(seta).*(1.3e+1./1.0e+1)+sin(seta).*(7.0./1.0e+1);
RR2=@(seta)cos(seta).*(7.0./1.0e+1)+sin(seta).*(1.3e+1./1.0e+1);
RR3=@(seta)cos(seta).*(1.3e+1./1.0e+1)-sin(seta).*(7.0./1.0e+1);
RR4=@(seta)cos(seta).*(1.3e+1./1.0e+1)-sin(seta).*(7.0./1.0e+1);
a1=fminbnd(RR1,0,2*pi);
b1=fminbnd(@(seta)-RR1(seta),0,2*pi);
a2=fminbnd(RR2,0,2*pi);
b2=fminbnd(@(seta)-RR2(seta),0,2*pi);
a3=fminbnd(RR3,0,2*pi);
b3=fminbnd(@(seta)-RR3(seta),0,2*pi);
a4=fminbnd(RR4,0,2*pi);
b4=fminbnd(@(seta)-RR4(seta),0,2*pi);



% % 위에 반복문의  기준이 된 코드::
subplot(4,1,1);
fplot(Rx1,[0 2*pi]); hold on
fplot(Ry1,[0 2*pi]);  hold on
fplot(RR1,[0 2*pi]);
plot(a1,RR1(a1),'*');
plot(b1,RR1(b1),'*');

a="(" + num2str(round(a1/pi,2))+"pi [" + num2str(round(a1/pi*180,2))+"\circ]";
a_= " , " + num2str(round(RR1(a1),2))+")";
a= a + a_;
b="(" + num2str(round(b1/pi,2))+"pi [" + num2str(round(b1/pi*180,2))+"\circ]";
b_= " , " + num2str(round(RR1(b1),2))+")";
b= b + b_;
xticks([0 0.5*pi pi 1.5*pi 2*pi])
xticklabels({'0','0.5\pi','\pi','1.5\pi','2\pi'})
legend('x축','y축',"단순합",a,b,'location','best')

subplot(4,1,2);
fplot(Rx2,[0 2*pi]); hold on
fplot(Ry2,[0 2*pi]);  hold on
fplot(RR2,[0 2*pi]);
plot(a2,RR2(a2),'*');
plot(b2,RR2(b2),'*');

a="(" + num2str(round(a2/pi,2))+"pi [" + num2str(round(a2/pi*180,2))+"\circ]";
a_= " , " + num2str(round(RR2(a2),2))+")";
a= a + a_;
b="(" + num2str(round(b2/pi,2))+"pi [" + num2str(round(b2/pi*180,2))+"\circ]";
b_= " , " + num2str(round(RR2(b2),2))+")";
b= b + b_;
xticks([0 0.5*pi pi 1.5*pi 2*pi])
xticklabels({'0','0.5\pi','\pi','1.5\pi','2\pi'})
legend('x축','y축',"단순합",a,b,'location','best')

MIN2 = @(v1, v2) piecewise(v1 <= v2, v1, v2);
MIN4 = @(v1, v2, v3, v4) MIN2(MIN2(v1,v2),MIN2(v3,v4));
R1 = RR1(seta);
R2 = RR2(seta);
R3 = RR3(seta);
R4 = RR4(seta);
RR1234 = MIN4(R1,R2,R3,R4);
figure
fplot(RR1234, [0 2*pi])

[Gookki Jeong]

WOW wonderful. amazing. thank you very much