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# Random Min/Max Scripts
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#
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# Johann Thiel
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# ver 11.25.17
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# Functions to implement Newton's
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# method.
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#
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# Finding a min via random trials
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##########################################
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# g = function
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# x0 = lower x-value bound
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# x1 = upper x-value bound
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# y0 = lower y-value bound
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# y1 = upper y-value bound
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# n  = number of iterations
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##########################################
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def randomMin(g,x0,x1,y0,y1,n):
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    x = var('x')
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    y = var('y')
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    f(x,y) = g(x,y)
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    xmin = x0
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    ymin = y0
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    fmin = f(x0,y0)
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    for i in range(n):
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        x00 = x0+(x1-x0)*random()
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        y00 = y0+(y1-y0)*random()
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        if f(x00,y00) < fmin:
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            xmin = x00
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            ymin = y00
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            fmin = f(xmin,ymin)
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    return (xmin, ymin, fmin)
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##########################################
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##########################################
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# Finding a max via random trials
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##########################################
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# g = function
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# x0 = lower x-value bound
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# x1 = upper x-value bound
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# y0 = lower y-value bound
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# y1 = upper y-value bound
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# n  = number of iterations
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##########################################
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def randomMax(g,x0,x1,y0,y1,n):
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    x = var('x')
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    y = var('y')
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    f(x,y) = g(x,y)
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    xmin = x0
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    ymin = y0
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    fmin = f(x0,y0)
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    for i in range(n):
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        x00 = x0+(x1-x0)*random()
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        y00 = y0+(y1-y0)*random()
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        if f(x00,y00) > fmin:
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            xmin = x00
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            ymin = y00
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            fmin = f(xmin,ymin)
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    return (xmin, ymin, fmin)
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##########################################
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