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I am trying to write on paper the piecewise polynomials given by the splinefit function, but I am having some problems figuring out what the coefficients should be. So, the output from the script gives me the following:

  scalar structure containing the fields:

form = pp
breaks =

 Columns 1 through 15:

  -1.00000  -0.93750  -0.87500  -0.81250  -0.75000  -0.68750  -0.62500  -0.56250  -0.50000   0.00000   0.50000   0.56250   0.62500   0.68750   0.75000

 Columns 16 through 19:

   0.81250   0.87500   0.93750   1.00000

coefs =

   2.5644e+03  -3.1686e+02   7.4332e+00  -1.0744e-01
  -2.5013e+02   1.6397e+02  -2.1226e+00  -2.5453e-01
  -2.4859e+03   1.1707e+02   1.5442e+01   1.9225e-01
   2.4278e+03  -3.4904e+02   9.4429e-01   1.0078e+00
   2.0742e+01   1.0618e+02  -1.4235e+01   2.9610e-01
  -9.0213e+02   1.1007e+02  -7.1939e-01  -1.7374e-01
   3.6900e+02  -5.9083e+01   2.4670e+00  -9.0075e-03
  -5.4428e+01   1.0105e+01  -5.9408e-01   4.4780e-03
   9.4209e-02  -1.0004e-01   3.1240e-02  -6.4667e-03
  -5.9852e-02   4.1271e-02   1.8542e-03  -4.0812e-03
  -5.3315e+01  -4.8507e-02  -1.7641e-03  -3.1792e-04
   3.5957e+02  -1.0045e+01  -6.3261e-01  -1.3634e-02
  -8.6341e+02   5.7374e+01   2.3254e+00  -4.6254e-03
  -4.0925e+01  -1.0452e+02  -6.2096e-01   1.5404e-01
   2.4543e+03  -1.1219e+02  -1.4165e+01  -3.0303e-01
  -2.4445e+03   3.4799e+02   5.7280e-01  -1.0274e+00
  -2.7185e+02  -1.1035e+02   1.5426e+01  -2.2903e-01
   2.2566e+03  -1.6132e+02  -1.5531e+00   2.3768e-01

pieces =  18
order =  4
dim =  1

If I plot the function via ppval, I get what I expect. But, if I take the first line of the coeff matrix, as I interpret it, I can write the me the first cubic polynomial as:

$f(x) = 2.5644 \times 10^3 x^3 -3.1686\times10^2 x^2 + 7.4332 x - 1.0744\times10^{-1}, \ -1 < x < -0.9375$

Just as a reference, $f(x=-1)\approx 0$ in the data I have, but clearly from the equation just shown that's not the case.

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    $\begingroup$ I found the answer. The spline is written as. $\sum_{n=0}^3 a_n(x-x_{inf})^n$ not as I previously mentioned $\endgroup$ – Kbzon Mar 20 '19 at 11:55
  • $\begingroup$ Was your question how to interpret the results provided by that specific function of MATLAB/Octave? $\endgroup$ – nicoguaro Mar 20 '19 at 15:25
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    $\begingroup$ @Kbzon: Are you able to answer your own question? It's helpful for closing out open questions. $\endgroup$ – Richard Mar 20 '19 at 17:42
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I found the answer! Octave/MATLAB's function splinefit differs from polyfit in the sense that the polynomial in the former is proposed as:

$\sum_{n=0}^k a_n(x-x_o)^n$

and in the latter

$\sum_{n=0}^k a_n x^n$

Where $x_0$ refers to the range $[x_0,x_f]$ of the absissa.

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