# [SciPy-User] multidimensional polynomial fit

josef.pktd@gmai... josef.pktd@gmai...
Sat Jun 12 14:44:30 CDT 2010

```On Sat, Jun 12, 2010 at 3:43 PM,  <josef.pktd@gmail.com> wrote:
> On Sat, Jun 12, 2010 at 2:36 PM, Oscar Gerardo Lazo Arjona
> <algebraicamente@gmail.com> wrote:
>> Hello!
>>
>> Is there some way to get a polynomial fit to a set of n-tuples? I've got
>> a set of 4-tuples: (x1,x2,x3,T), and i would like to get a polynomial
>> T(x1,x2,x3).
>>
>> I've seen numpy.polyfit, but that doesn't work for multidimensional sets.
>>
>> If there is no method available, I would be willing to write the
>> necessary code, just tell me how to get it included.
>
> Assuming I understand correctly,  fitting the last variable to a
> polynomial of the first three
>
> depends on how many cross terms you want.
>
> here is an example which restricts the powers in the cross-terms
>
>
>>>> x = np.arange(5)[:,None]+ [0,10,100]
>>>> x = x[:,::-1] #reverse for ndindex
>>>> x
> array([[100,  10,   0],
>       [101,  11,   1],
>       [102,  12,   2],
>       [103,  13,   3],
>       [104,  14,   4]])
>>>> simplex = [ind for ind in np.ndindex(*[3]*x.shape[1]) if sum(ind)<=2]
>>>> simplex
> [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 1), (0, 2, 0), (1,
> 0, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0)]
>>>> np.array([np.prod(x**ind,1) for  ind in simplex]).T
> array([[    1,     0,     0,    10,     0,   100,   100,     0,  1000,
>        10000],
>       [    1,     1,     1,    11,    11,   121,   101,   101,  1111,
>        10201],
>       [    1,     2,     4,    12,    24,   144,   102,   204,  1224,
>        10404],
>       [    1,     3,     9,    13,    39,   169,   103,   309,  1339,
>        10609],
>       [    1,     4,    16,    14,    56,   196,   104,   416,  1456,
>        10816]])
>
>
>
>
>>>> nobs = 100
>>>> x0 = np.random.randn(nobs,3)
>>>> x = np.array([np.prod(x0**ind,1) for  ind in simplex]).T
>>>> y = x.sum(1) + 0.1*np.random.randn(nobs)
>>>> y.shape
> (100,)
>>>> from scikits.statsmodels import OLS
>>>> res = OLS(y, x).fit()
>>>> res.params
> array([ 1.02381284,  1.00619277,  0.99437357,  0.96839791,  1.00923175,
>        1.00342817,  0.99046168,  1.00125689,  0.99069758,  0.98808115])
>>>> yest = res.model.predict(x)
>>>> import matplotlib.pyplot as plt
>>>> plt.plot(y, yest)

correction for scatter plot:
plt.plot(y, yest, 'o')

>
>
> use of OLS can be replaced by np.linalg.lstsq
>
> Josef
>
>
>>
>> thanks!
>>
>> Oscar
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>>
>
```