[Numpy-discussion] Problem in LinearAlgebra?

[Rob W.W. Hooft]

I am using Polynomial.py from Scientific Python 2.1, together with 
Numeric 17.1.2. This has always served me well, but now we are busy 
upgrading our software, and I am currently porting some code to 
Scientific Python 2.4.1, Numeric 22.0. Suddenly I do no longer manage to 
get proper 2D polynomial fits over 4x4th order. At 5x5 the coefficients 
that come back from LinearAlgebra.linear_least_squares have exploded. In 
the old setup, I easily managed 9x9th order if I needed to, but most of 
the time I'd stop at 6x6th order. Would anyone have any idea how this 
difference can come about? I managed to work around this for the moment 
by using the equivalent code in the fitPolynomial routine that uses 
LinearAlgebra.generalized_inverse (and it doesn't even have problems 
with the same data at 8x8), but this definitely feels not right! I can't 
remember reading anything like this here before.

Together with Konrad Hinsen, I came to the conclusion that the problem 
is not in Scientific Python, so it must be the underlying LinearAlgebra 
code that changed between releases 17 and 22.

I hacked up a simplified example. Not sure whether it is the most simple 
case, but this resembles what I have in my code, and I'm quite sure it 
worked with Numeric 17.x, but currently it is horrible over order (4,4):

--------------------------------------
import Numeric

def func(x,y):
     return x+0.1*x**2+0.01*x**4+0.002*x**6+0.03*x*y+0.001*x**4*y**5

x=[]
y=[]
z=[]
for dx in Numeric.arange(0,1,0.01):
     for dy in Numeric.arange(0,1,0.01):
         x.append(dx)
         y.append(dy)
         z.append(func(dx,dy))

from Scientific.Functions import Polynomial
data=Numeric.transpose([x,y])
z=Numeric.array(z)
for i in range(10):
     print data[i],z[i]
pol=Polynomial.fitPolynomial((4,4),data,z)
print pol.coeff
------------------------------------
for 4,4 this prints:
[[  1.84845529e-05  -7.60502772e-13   2.71314749e-12  -3.66731796e-12
          1.66977148e-12]
  [  9.99422967e-01   3.00000000e-02  -3.26346097e-11   4.42406519e-11
         -2.01549767e-11]
  [  1.03899464e-01  -3.19668064e-11   1.14721790e-10  -1.55489826e-10
          7.08425891e-11]
  [ -9.40275000e-03   4.28456838e-11  -1.53705205e-10   2.08279772e-10
         -9.48840470e-11]
  [  1.80352695e-02  -1.10999843e-04   8.00662570e-04  -2.17266676e-03
          2.47500004e-03]]

for 5,5:

[[ -2.25705839e+03   6.69051337e+02  -6.60470163e+03   6.66572425e+03
         -8.67897022e+02   1.83974866e+03]
  [ -2.58646837e+02  -2.46554689e+03   1.15965805e+03   7.01089888e+03
         -2.11395436e+03   2.10884815e+03]
  [  3.93307499e+03   4.34484805e+02  -4.84080392e+03   5.90375330e+03
          1.16798049e+03  -4.14163933e+03]
  [  1.62814750e+03   2.08717457e+03   1.15870693e+03  -3.37838057e+03
          3.49821689e+03   5.80572585e+03]
  [  4.54127557e+02  -1.56645524e+03   4.58997025e+00   1.69772635e+03
         -1.37751039e+03  -7.59726558e+02]
  [  2.37878239e+03   9.43032094e+02   8.58518644e+02  -8.35846339e+03
         -5.55845668e+02   1.87502761e+03]]

Which is clearly wrong.

I appreciate any help!

Regards,

Rob

-- 
Rob W.W. Hooft  ||  rob at hooft.net  ||  http://www.hooft.net/people/rob/