[SciPy-dev] Type handling of matrices

Nils Wagner nwagner at mecha.uni-stuttgart.de
Wed Nov 17 03:39:33 CST 2004


Pearu Peterson wrote:

>
>
> On Wed, 17 Nov 2004, Nils Wagner wrote:
>
>> BTW, how can I compute the gap function of A in scipy, where A is a 
>> dense normal matrix
>> and gap(A) is defined as follows
>>
>> gap(A) = \min\limits_{i \ne j} | \lambda_i-\lambda_j | / 2
>>
>> This approach seems to be not very efficient
>>
>> def gap(A):
>> w = linalg.eigvals(A) # Compute the spectrum of A
>> min = 1.e10 # Initialize
>
>
>   ^^^ min is builtin function, don't use it as a variable name
>
>> for i in len(w):
>
>
>            ^^^^^^ you probably mean range(len(w)) here
>
>> for j in len(w):
>>       if i <> j:
>>             min1 = abs(w[i]-w[j])
>>             if min1 < min:
>>                 min=min1
>> return min/2
>
>
> If len(w) is small then you should not worry about efficiency.
> Anyway, by using
>
> def gap(A)
>  w = linalg.eigvals(A)
>  mn = abs(w[0]-w[1])
>  for i in range(len(w))
>   for j in range(i):
>      mn = min(mn,abs(w[i]-w[j]))
>  return mn/2
>
> should give speedup 2x at least.
>
> Pearu
>
And how can I return the associated indices \bar{i}, \bar{j} with 
respect to gap(A) ?

Nils
 

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