# [Numpy-discussion] quadratic function

Robert Kern robert.kern@gmail....
Thu Oct 28 14:05:06 CDT 2010

```On Thu, Oct 28, 2010 at 12:47, Brennan Williams
<brennan.williams@visualreservoir.com> wrote:
>  On 29/10/2010 6:35 a.m., Robert Kern wrote:
>> On Thu, Oct 28, 2010 at 12:33, Brennan Williams
>> <brennan.williams@visualreservoir.com>  wrote:
>>>   On 29/10/2010 2:34 a.m., Robert Kern wrote:
>>>> On Thu, Oct 28, 2010 at 06:38, Brennan Williams
>>>> <brennan.williams@visualreservoir.com>    wrote:
>>>>>    I have used both linear least squares and radial basis functions as a
>>>>> proxy equation, calculated from the results of computer simulations
>>>>> which are calculating some objective function value based on a number of
>>>>> varied input parameters.
>>>>>
>>>>> As an alternative option I want to add a quadratic function so if there
>>>>> are parameters/variables x,y,z then rather than just having a linear
>>>>> function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to
>>>>> have the option not to include all the different second order terms.
>>>> A = np.column_stack([
>>>>       np.ones_like(x),
>>>>       x, y, z,
>>>>       x*x, y*y, z*z,
>>>>       x*y, y*z, x*z,
>>>> ])
>>>> x, res, rank, s = np.linalg.lstsq(A, f)
>>>>
>>> OK, so in other words, you can use linalg.lstsq for whatever higher
>>> order terms you want to include or exclude. Very nice. Thanks.
>> Right. Just as long as the problem is linear in the coefficients, the
>> design matrix can be derived however you like.
>>
> So I could optionally put log terms in if I thought it was linear in
> log(x) for example?

Yup!

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
```