fitting data with numpy

Question

Let me start by telling that what I get may not be what I expect and perhaps you can help me here  I have the following data    gt  gt  gt  x array   3 08   3 1    3 12   3 14   3 16   3 18   3 2    3 22   3 24      3 26   3 28   3 3    3 32   3 34   3 36   3 38   3 4    3 42      3 44   3 46   3 48   3 5    3 52   3 54   3 56   3 58   3 6       3 62   3 64   3 66   3 68     gt  gt  gt  y array   0 000857   0 001182   0 001619   0 002113   0 002702   0 003351      0 004062   0 004754   0 00546    0 006183   0 006816   0 007362      0 007844   0 008207   0 008474   0 008541   0 008539   0 008445      0 008251   0 007974   0 007608   0 007193   0 006752   0 006269      0 005799   0 005302   0 004822   0 004339   0 00391    0 003481      0 003095     Now  I want to fit these data with  say  a 4 degree polynomial  So I do    gt  gt  gt  coefs   np polynomial polynomial polyfit x  y  4   gt  gt  gt  ffit   np poly1d coefs    Now I create a new grid for x values to evaluate the fitting function ffit    gt  gt  gt  x new   np linspace x 0   x -1   num len x  10    When I do all the plotting  data set and fitting curve  with the command    gt  gt  gt  fig1   plt figure                                                                                               gt  gt  gt  ax1   fig1 add subplot 111                                                                                      gt  gt  gt  ax1 scatter x  y  facecolors  None                                                                         gt  gt  gt  ax1 plot x new  ffit x new                                                                         gt  gt  gt  plt show     I get the following    fitting data png  What I expect is the fitting function to fit correctly  at least near the maximum value of the data   What am I doing wrong   Thanks in advance

User · Answer

Note that you can use the Polynomial class directly to do the fitting and return a Polynomial instance.

from numpy.polynomial import Polynomial

p = Polynomial.fit(x, y, 4)
plt.plot(*p.linspace())

p uses scaled and shifted x values for numerical stability. If you need the usual form of the coefficients, you will need to follow with

pnormal = p.convert(domain=(-1, 1))

User · Answer

Unfortunately  np polynomial polynomial polyfit returns the coefficients in the opposite order of that for np polyfit and np polyval  or  as you used np poly1d    To illustrate   In  40   np polynomial polynomial polyfit x  y  4  Out 40    array    84 29340848  -100 53595376    44 83281408    -8 85931101            0 65459882    In  41   np polyfit x  y  4  Out 41    array     0 65459882    -8 859311      44 83281407  -100 53595375           84 29340846     In general  np polynomial polynomial polyfit returns coefficients  A  B  C  to A   Bx   Cx 2        while np polyfit  returns        Ax 2   Bx   C    So if you want to use this combination of functions  you must reverse the order of coefficients  as in   ffit   np polyval coefs   -1   x new    However  the documentation states clearly to avoid np polyfit  np polyval  and np poly1d  and instead to use only the new er  package   You re safest to use only the polynomial package   import numpy polynomial polynomial as poly  coefs   poly polyfit x  y  4  ffit   poly polyval x new  coefs  plt plot x new  ffit    Or  to create the polynomial function   ffit   poly Polynomial coefs       instead of np poly1d plt plot x new  ffit x new

[python] fitting data with numpy

Examples related to python

Examples related to numpy

Examples related to regression

Examples related to curve-fitting

Examples related to data-fitting