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>> syms a b c d
>> [x] = solve(a-(29.6-b*sin(c-d)),b-((34.7-a)/sin(2*c-d)),a+b*sin(3*c-d)-46.1,a+b*sin(4*c-d)-59.0,'a','b','c','d')
Parte de un x=[0.4248; -0.0104; -0.5884; -0.9603; 1.5596]
A=[-1,-1,-1,-1,-1;-2,-1,-2,-1,-2;-1,-1,-1,1,1;-3,-2,-1,0,1;-2,-4,1,2,0;1,1,1,0,0;0,1,1,1,0;0,0,1,1,1]
%% Restriciones ativas 2 3 4 5 6
Aq=A([2,6,8],:)
I=eye(5)
Aux=Aq*Aq';
Au=inv(Aux)
Pk=I-Aq'*Au*Aq
f = x(1)^2+2*x(2)^2+3*x(3)^2+x(4)^2+3*x(5)^2-0.1*x(1)*sin(x(1)/5)-0.5*x(2)*cos(x(2)/4)+x(1)*x(3)-x(2)*x(4)+x(3)*x(5)-(2*x(1)/(x(3)^2+1))+(2*x(3)/(x(5)^2+1))-(30*x(5)/(x(1)^2+4))+x(2)+x(4)
% gradiente
gradiente=[ 2*x(1) + x(3) - sin(x(1)/5)/10 - (x(1)*cos(x(1)/5))/50 - 2/(x(3)^2 + 1) + (60*x(5)*x(1))/(x(1)^2 + 1)^2
4*x(2) - x(4)- cos(x(2)/4)/2 + (x(2)*sin(x(2)/4))/8 + 1
x(5)+ x(1) + 6*x(3) + 2/(x(5)^2 + 1) + (4*x(1)*x(3))/(x(3)^2 + 1)^2
2*x(4)- x(2) + 1
6*x(5) + x(3) - 30/(x(1)^2 + 1) - (4*x(5)*x(3))/(x(5)^2 + 1)^2]
Direcion=-Pk*gradiente
digits(5)
x=sym(x,'d')
Direcion=sym(Direcion,'d')
funcaoalfa=((x(1)+alfa*Direcion(1))^2+2*(x(2)+alfa*Direcion(2))^2+3*(x(3)+alfa*Direcion(3))^2+(x(4)+alfa*Direcion(4))^2+3*(x(5)+alfa*Direcion(5))^2-0.1*(x(1)+alfa*Direcion(1))*sin((x(1)+alfa*Direcion(1))/5)-0.5*(x(2)+alfa*Direcion(2))*cos((x(2)+alfa*Direcion(2))/4)+(x(1)+alfa*Direcion(1))*(x(3)+alfa*Direcion(3))-(x(2)+alfa*Direcion(2))*(x(4)+alfa*Direcion(4))+(x(3)+alfa*Direcion(3))*(x(5)+alfa*Direcion(5))-(2*(x(1)+alfa*Direcion(1))/((x(3)+alfa*Direcion(3)).^2+1))+2*(x(3)+alfa*Direcion(3))-(30*(x(5)+alfa*Direcion(5))/((x(1)+alfa*Direcion(1)).^2+4))+(x(2)+alfa*Direcion(2))+(x(4)+alfa*Direcion(4))==0)
[alfa]=solve(funcaoalfa)
>> sistemas
x = 0.4248-0.0104
-0.5884
-0.9603
1.5596A =-1 -1 -1 -1 -1
-2 -1 -2 -1 -2
-1 -1 -1 1 1
-3 -2 -1 0 1
-2 -4 1 2 0
1 1 1 0 0
0 1 1 1 0
0 0 1 1 1
Aq =-2 -1 -2 -1 -2
1 1 1 0 0
0 0 1 1 1
I =1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
Au =0.6667 0.8333 0.8333
0.8333 1.4167 0.9167
0.8333 0.9167 1.4167
Pk =0.2500 -0.2500 0.0000 0.2500 -0.2500
-0.2500 0.5833 -0.3333 0.0833 0.2500
0.0000 -0.3333 0.3333 -0.3333 0
0.2500 0.0833 -0.3333 0.5833 -0.2500
-0.2500 0.2500 0 -0.2500 0.2500
f =-4.8742
gradiente = 27.2852 1.4187-1.5150
-0.9102
-16.3332
Direcion =-10.3224
9.6479 0.6745-10.9969
10.3224x = 0.4248-0.0104
-0.5884
-0.9603
1.5596Direcion =-10.322
9.6479 0.6745-10.997
10.322funcaoalfa =3*(10.322*alfa + 1.5596)^2 - 0.0001*alfa - (309.66*alfa + 46.788)/((10.322*alfa - 0.4248)^2 + 4) + (10.997*alfa + 0.9603)^2 + (0.6745*alfa - 0.5884)*(10.322*alfa + 1.5596) + (10.322*alfa - 0.4248)^2 + (9.6479*alfa - 0.0104)*(10.997*alfa + 0.9603) + 2*(9.6479*alfa - 0.0104)^2 + 3*(0.6745*alfa - 0.5884)^2 - (10.322*alfa - 0.4248)*(0.6745*alfa - 0.5884) + (20.644*alfa - 0.8496)/((0.6745*alfa - 0.5884)^2 + 1) - sin(2.0644*alfa - 0.08496)*(1.0322*alfa - 0.04248) - cos(2.412*alfa - 0.0026)*(4.8239*alfa - 0.0052) - 2.1475 == 0
alfa =0.060195input en matlab
>> ec1='0=(x1*(sxx-s1))+(x2*sxy)+(x3*sxz)';
ec2='0=(x1*sxy)+(x2*(syy-s1))+(x3*syz)';
ec3='0=(x1*sxz)+(x2*syz)+(x3*(szz-s1))';
ec4='1=(x1^2)+(x2^2)+(x3^2)';
[x1,x2,x3]=solve(ec1,ec2,ec3,ec4, 'x1,x2,x3')
syms coef_flujo_c cr_2c c_1c cteta_2c c_2c T_2c T_1c;
ec1_compr='coef_flujo_c=cr_2c/u_2c';
ec2_compr='c_1c=cr_2c'; %entrada axial
ec3_compr='cteta_2c=u_2c*sigma_2c';
ec4_compr='c_2c=sqrt(cteta_2c^2+cr_2c^2)';
ec5_compr='T_2c=T_02c-(c_2c^2/(2*Cp_air))';
ec6_compr='T_1c=T_2c-(Reaccion_c*W_C/Cp_air)';
ec7_compr='c_1c=sqrt((T_01c-T_1c)*2*Cp_air)';
% A=zeros(1,7);
[coef_flujo_c cr_2c c_1c cteta_2c c_2c T_2c T_1c]=solve(ec1_compr,ec2_compr,ec3_compr,ec4_compr,ec5_compr,ec6_compr,ec7_compr,'coef_flujo_c','cr_2c','c_1c','cteta_2c','c_2c','T_2c','T_1c');
% coef_flujo_c=A(1,1);
% cr_2c=A(1,2);
% c_1c=A(1,3);
% cteta_2c=A(1,4);
% c_2c=A(1,5);
% T_2c=A(1,6);
% T_1c=A(1,7);