how to get the x and y according to numpy.min()'s minimum value

Question

I have a problem with numpy,I use the numpy.min() to get expression's minimum value，but when I get the minimum value,how can i get the x and y value on the contrary.The x,y was in the expression.，

    x=np.linspace(-300,300,10000)
    y=np.linspace(-300,300,10000)
    D=np.min((np.sqrt((x)**2+(y)**2)-2))**2+(np.sqrt((x-3)**2+(y-2)**2)-2)**2)

I write the f() as u teach me like this:

def f(self,xy,k):
    expression=0
    x, y= xy
    cols=self.maintablewidget.columnCount()-1
    #for k in range(3,cols):
    for i in range(1,k):
        d=string.atof(self.maintablewidget.item(i-1,k-1).text())
        xi=string.atof(self.xytablewidget.item(i-1,0).text())
        yi=string.atof(self.xytablewidget.item(i-1,1).text())
        expression=np.sum((np.sqrt((x-xi)**2+(y-yi)**2)-d)**2)
    return expression

 #I do not know how to call the f() here, because the parameter k I do not know pass it
 for k in range(3,12):
        res=optimize.minimize(self.f,(0,0),k)#here is an error
        print(res['x'][0])
        print(res['x'],res['fun'])

I do not know how to pass the K to f(self,xy,k),when i call it !

might be related: http://stackoverflow.com/questions/13370570/elegant-grid-search-in-python-numpy — cel, Dec 23 '14 at 11:09
Are you trying to minimize the function over 2 dimensions? As it stands, the expression for `D` takes the `min` of a 1-dimensional array (assuming you fix that unbalanced parenthesis). And do you have `scipy`? — unutbu, Dec 23 '14 at 11:52
I just write the expression to express.i have install the scipy — Hmily, Dec 23 '14 at 12:06

unutbu · Answer 1 · 2014-12-23T14:55:48.163

Using scipy, you could try to find the minimum of the function using optimize.minimize:

import numpy as np
from scipy import optimize
def f(xy):
    x, y = xy
    return (np.sqrt((x)**2+(y)**2)-2)**2+(np.sqrt((x-3)**2+(y-2)**2)-2)**2

res = optimize.minimize(f, (0,0))

This shows x and y value coorsponding to the minimum of f:

print(res['x'])
# [ 1.01961249  1.72058165]

This is the minimum value of f found:

print(res['fun'])
# 1.27566100252e-11

optimize.minimize uses the BFGS algorithm by default when there are no bounds or constraints.

As cel points out, you could also use optimize.brute to do a brute force search for the minimum:

In [68]: optimize.brute(f, (slice(-300, 300, 10000), slice(-300, 300, 10000)))
Out[68]: array([ 1.98035504,  0.27946845])

Brute can be use to find interesting starting points which can then by "polished" by other algorithms. For example, you can use optimize.minimize to polish the point found by brute:

def minimize_wrapper(func, xmin, args, full_output, disp):
    res = optimize.minimize(func, xmin, args)
    return res['x'], res['fun']

z, fval, grid, Jout = optimize.brute(
    f, (slice(-300, 300, 1000), slice(-300, 300, 1000)), 
    finish=minimize_wrapper, full_output=True)

This is the (x,y) location found:

print(z)  
# array([ 1.98038404,  0.27942339])

and this is the corresponding value of f:

print(fval)
# 1.8566073609451249e-13

You may want to add a solution using `scipy.optimize.brute` http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brute.html#scipy.optimize.brute to your answer. Your solution finds the optimum, but does not use a grid search as suggested in the question. — cel, Dec 23 '14 at 14:04

how to get the x and y according to numpy.min()'s minimum value

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