Matlab - Fracción/Decimal

clear all;

clc;

f='x^2+7*y^2-4*x*y+3*x+2*y+1'

gradf=[diff(f,'x') diff(f,'y')]

x0=[20 30]'

d0=[77 -342]'

gradf2=[diff(gradf(1),'x') diff(gradf(1),'y'); diff(gradf(2),'x') diff(gradf(2),'y')]

Q=gradf2;

alfa0=-(subs(gradf,'[x y]', x0')*d0)/(d0'*Q*d0)

f =

x^2+7*y^2-4*x*y+3*x+2*y+1

gradf =

[ 2*x - 4*y + 3, 14*y - 4*x + 2]

x0 =

    20

    30

d0 =

    77

  -342

gradf2 =

[  2, -4]

[ -4, 14]

alfa0 =

122893/1860026

lear all;

clc;

syms x y

f=x^2+7*y^2-4*x*y+3*x+2*y+1;

gradf=[diff(f,'x') diff(f,'y')];

x0=[20 30]';

d0=[77 -342]';

gradf2=[diff(gradf(1),'x') diff(gradf(1),'y'); diff(gradf(2),'x') diff(gradf(2),'y')];

Q=gradf2;

alfa0=-(subs(gradf,'[x y]', x0')*d0)/(d0'*Q*d0);

alfa0=double(alfa0)

%OTRA FORMA:

clear all;

syms x y

f=x^2+7*y^2-4*x*y+3*x+2*y+1;

gradiente=gradient(f,[x y]);

jacobiano=jacobian(gradiente,[x y]);

x0=[20 30];

d0=[77 -342]';

fgradiente=inline(gradiente,'x','y');

alfa=-(fgradiente(x0(1),x0(2)))'*d0/(d0'*jacobiano*d0);

alfa=double(alfa)

>> gradiente_jacobiano

alfa0 =

    0.0661

alfa =

    0.0661