"""
Lucija Ersek, Ivana Pavlek
"""
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#funkcija jedne varijable
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f = lambda x: x*cos(x)
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type(f)
<type 'function'> |
plot(f,1,5)
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find_minimum_on_interval(f, 1, 5)
(-3.2883713955908962, 3.425618469566611) |
#problem: moramo paziti koja je koordinata x, a koja y
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plot(f,1,20)
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.png)
find_minimum_on_interval(f, 1, 20) #problem: na prevelikom intervalu javlja "srednji" minimum
(-9.4772942594797804, 9.5293344598683429) |
find_minimum_on_interval(f, 8, 20)
(-15.739676962133709, 15.771284820967489) |
x,y = var('x y')
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g = sin(x*y)
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plot3d(lambda x, y: sin(x*y),(-2,2), (-2,2))
minimize(g,[-2,2])
Optimization terminated successfully.
Current function value: -1.000000
Iterations: 6
Function evaluations: 8
Gradient evaluations: 8
(-1.25331247133, 1.25331247133)
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minimize(g,[-2,2], disp=0)
(-1.25331247133, 1.25331247133) |
minimize(g,[-2,2], disp=0,algorithm="ncg")
(-1.25331413734, 1.25331413734) |
vars=var('x y z')
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h=100*(y-x^2)^2+(1-x)^2+100*(z-y^2)^2+(1-y)^2
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minimize(h,[0,1,2],disp=0)
(0.999999982858, 0.999999988285, 0.999999971261) |
minimize_constrained(g, [(None,None),(None,None)],[-2,2])
(-1.25331419334, 1.25331419334) |
minimize_constrained(g, [(-1,1),(-1,1)],[-2,2])
(-1.0, 1.0) |