[SciPy-User] 2d inverse parabolic interpolation

[Neal Becker]

Charles R Harris wrote:

> On Tue, Aug 10, 2010 at 12:49 PM, Neal Becker <ndbecker2 at gmail.com> wrote:
> 
>> In 1-d, inverse parabolic interpolation is a useful operation.  It is
>> described in e.g., NRC sec 10.2 (Numerical Recipes in C).
>>
>> Is there an equivalent for 2d?  Is there any scipy code?
>>
>>
> What do you want to do? What do you mean by equivalent? I suspect the
> answer is no since a map from 2d to 1d doesn't have an inverse and the
> inverse image is likely to be a manifold.
> 
> Chuck

In 1d, the operation is: giving 3 grid points of which the center point is 
the minimum of the 3, find the location of the minimum (a position not 
necessarily on the grid) (of a parabola passing through these 3 points).

I was wondering if there is a similar operation for 2d, which would take 
perhaps the 8 grid points surrounding 1 point and find position of a 
minimum.

The application is a time-frequency search.  A set of points is given in 2d, 
quantized in time and frequency.  Find the position (time and frequency) of 
the true minimum (approximately, and inexpensively).