Cantera  2.0
polyfit.h
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1 /**
2  * @file polyfit.h C interface for Fortran DPOLFT subroutine
3  */
4 /*
5  * Copyright 2001-2003 California Institute of Technology
6  * See file License.txt for licensing information
7  */
8
9 #ifndef CT_POLYFIT_H
10 #define CT_POLYFIT_H
11
12 #include <vector>
13
14 #include "cantera/base/ct_defs.h"
15
16 namespace Cantera
17 {
18
19 //! Fits a polynomial function to a set of data points
20 /*!
21  * Given a collection of points X(I) and a set of values Y(I) which
22  * correspond to some function or measurement at each of the X(I),
23  * subroutine DPOLFT computes the weighted least-squares polynomial
24  * fits of all degrees up to some degree either specified by the user
25  * or determined by the routine. The fits thus obtained are in
26  * orthogonal polynomial form. Subroutine DP1VLU may then be
27  * called to evaluate the fitted polynomials and any of their
28  * derivatives at any point. The subroutine DPCOEF may be used to
29  * express the polynomial fits as powers of (X-C) for any specified
30  * point C.
31  *
32  * @param n The number of data points.
33  *
34  * @param x A set of grid points on which the data is specified.
35  * The array of values of the independent variable. These
36  * values may appear in any order and need not all be
37  * distinct. There are n of them.
38  *
39  * @param y array of corresponding function values. There are n of them
40  *
41  * @param w array of positive values to be used as weights. If
42  * W is negative, DPOLFT will set all the weights
43  * to 1.0, which means unweighted least squares error
44  * will be minimized. To minimize relative error, the
45  * user should set the weights to: W(I) = 1.0/Y(I)**2,
46  * I = 1,...,N .
47  *
48  * @param maxdeg maximum degree to be allowed for polynomial fit.
49  * MAXDEG may be any non-negative integer less than N.
50  * Note -- MAXDEG cannot be equal to N-1 when a
51  * statistical test is to be used for degree selection,
52  * i.e., when input value of EPS is negative.
53  *
54  * @param ndeg output degree of the fit computed.
55  *
56  * @param eps Specifies the criterion to be used in determining
57  * the degree of fit to be computed.
58  * (1) If EPS is input negative, DPOLFT chooses the
59  * degree based on a statistical F test of
60  * significance. One of three possible
61  * significance levels will be used: .01, .05 or
62  * .10. If EPS=-1.0 , the routine will
63  * automatically select one of these levels based
64  * on the number of data points and the maximum
65  * degree to be considered. If EPS is input as
66  * -.01, -.05, or -.10, a significance level of
67  * .01, .05, or .10, respectively, will be used.
68  * (2) If EPS is set to 0., DPOLFT computes the
69  * polynomials of degrees 0 through MAXDEG .
70  * (3) If EPS is input positive, EPS is the RMS
71  * error tolerance which must be satisfied by the
72  * fitted polynomial. DPOLFT will increase the
73  * degree of fit until this criterion is met or
74  * until the maximum degree is reached.
75  *
76  * @param r Output vector containing the first ndeg+1 Taylor coefficients
77  *
78  * P(X) = r + r*(X-C) + ... + r[ndeg] * (X-C)**ndeg
79  * ( here C = 0.0)
80  *
81  * @return Returned value is the value of the rms of the interpolated
82  * function at x.
83  */
84 doublereal polyfit(int n, doublereal* x, doublereal* y, doublereal* w,
85  int maxdeg, int& ndeg, doublereal eps, doublereal* r);
86
87 }
88 #endif
89
90