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  1. PO
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    <p>If I understand your question correctly, I <em>think</em> this is what you're after:</p> <pre><code>from scipy.optimize import minimize import numpy as np def f(coord,x,y,r): return np.sum( ((coord[0] - x)**2) + ((coord[1] - y)**2) - (r**2) ) x = np.array([0, 2, 0]) y = np.array([0, 0, 2]) r = np.array([.88, 1, .75]) # initial (bad) guess at (x,y) values initial_guess = np.array([100,100]) res = minimize(f,initial_guess,args = [x,y,r]) </code></pre> <p>Which yields:</p> <pre><code>&gt;&gt;&gt; print res.x [ 0.66666666 0.66666666] </code></pre> <p>You might also try the least squares method which expects an objective function that returns a vector. It wants to minimize the sum of the squares of this vector. Using least squares, your objective function would look like this:</p> <pre><code>def f2(coord,args): x,y,r = args # notice that we're returning a vector of dimension 3 return ((coord[0]-x)**2) + ((coord[1] - y)**2) - (r**2) </code></pre> <p>And you'd minimize it like so:</p> <pre><code>from scipy.optimize import leastsq res = leastsq(f2,initial_guess,args = [x,y,r]) </code></pre> <p>Which yields:</p> <pre><code>&gt;&gt;&gt; print res[0] &gt;&gt;&gt; [ 0.77961518 0.85811473] </code></pre> <p>This is basically the same as using <code>minimize</code> and re-writing the original objective function as:</p> <pre><code>def f(coord,x,y,r): vec = ((coord[0]-x)**2) + ((coord[1] - y)**2) - (r**2) # return the sum of the squares of the vector return np.sum(vec**2) </code></pre> <p>This yields:</p> <pre><code>&gt;&gt;&gt; print res.x &gt;&gt;&gt; [ 0.77958326 0.8580965 ] </code></pre> <p>Note that <code>args</code> are handled a bit differently with <code>leastsq</code>, and that the data structures returned by the two functions are also different. See the documentation for <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize" rel="noreferrer"><code>scipy.optimize.minimize</code></a> and <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html#scipy.optimize.leastsq" rel="noreferrer"><code>scipy.optimize.leastsq</code></a> for more details.</p> <p>See the <a href="http://docs.scipy.org/doc/scipy/reference/optimize.html" rel="noreferrer"><code>scipy.optimize</code></a> documentation for more optimization options.</p>
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    1. POHow to perform non-linear optimization with scipy/numpy or sympy?
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    1. USJohn Vinyard
    1. USJohn Vinyard
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    1. POHow to perform non-linear optimization with scipy/numpy or sympy?
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    1. COThe result you found doesn't satisfy any of the equations...
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      1. USRoland Smith
    2. COThis is precisely what I was looking for! Thanks for your help and patients trying to understand what I was trying to do.
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      1. USdrbunsen
    3. COGlad to hear it! You might also play with using the l2 norm instead of the sum for your cost function, i.e., use `np.linalg.norm` in place of `np.sum`, and see how that affects your results.
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      1. USJohn Vinyard
 

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