z = peaks(x, y)
= 3*(1-x)^2*exp(-(x^2) - (y+1)^2)
- 10*(x/5 - x^3 - y^5)*exp(-x^2-y^2)
- 1/3*exp(-(x+1)^2 - y^2)
dz/dx =
-6*(1-x)*exp(-x^2-(y+1)^2) - 6*(1-x)^2*x*exp(-x^2-(y+1)^2)
- 10*(1/5-3*x^2)*exp(-x^2-y^2)
+ 20*(1/5*x-x^3-y^5)*x*exp(-x^2-y^2)
- 1/3*(-2*x-2)*exp(-(x+1)^2-y^2);
dz/dy =
3*(1-x)^2*(-2*y-2)*exp(-x^2-(y+1)^2)
+ 50*y^4*exp(-x^2-y^2)
+ 20*(1/5*x-x^3-y^5)*y*exp(-x^2-y^2)
+ 2/3*y*exp(-(x+1)^2-y^2);
d(dz/dx)/dx =
36*x*exp(-x^2-(y+1)^2)
- 18*x^2*exp(-x^2-(y+1)^2)
- 24*x^3*exp(-x^2-(y+1)^2)
+ 12*x^4*exp(-x^2-(y+1)^2)
+ 72*x*exp(-x^2-y^2)
- 148*x^3*exp(-x^2-y^2)
- 20*y^5*exp(-x^2-y^2)
+ 40*x^5*exp(-x^2-y^2)
+ 40*x^2*exp(-x^2-y^2)*y^5
- 2/3*exp(-(x+1)^2-y^2)
- 4/3*exp(-(x+1)^2-y^2)*x^2
- 8/3*exp(-(x+1)^2-y^2)*x
d(dz/dx)/dy =
-6*(1-x)*(-2*y-2)*exp(-x^2-(y+1)^2)
- 6*(1-x)^2*x*(-2*y-2)*exp(-x^2-(y+1)^2)
+ 20*(1/5-3*x^2)*y*exp(-x^2-y^2)
- 100*y^4*x*exp(-x^2-y^2)
- 40*(1/5*x-x^3-y^5)*x*y*exp(-x^2-y^2)
+ 2/3*(-2*x-2)*y*exp(-(x+1)^2-y^2)
d(dz/dy)/dy =
-6*(1-x)^2*exp(-x^2-(y+1)^2)
+ 3*(1-x)^2*(-2*y-2)^2*exp(-x^2-(y+1)^2)
+ 200*y^3*exp(-x^2-y^2)-200*y^5*exp(-x^2-y^2)
+ 20*(1/5*x-x^3-y^5)*exp(-x^2-y^2)
- 40*(1/5*x-x^3-y^5)*y^2*exp(-x^2-y^2)
+ 2/3*exp(-(x+1)^2-y^2)-4/3*y^2*exp(-(x+1)^2-y^2)