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cantera/ext/f2c_math/polfit.c
Nicholas Malaya 0c26ea8c72 [cantera]: moving some folders around
2012-02-03 23:41:00 +00:00

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/* polfit.f -- translated by f2c (version 20030320).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* DECK POLFIT */
/* Subroutine */ int polfit_(integer *n, real *x, real *y, real *w, integer *
maxdeg, integer *ndeg, real *eps, real *r__, integer *ierr, real *a)
{
/* System generated locals */
integer i__1;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, m, k1, k2, k3, k4, k5;
real w1, w11, xm, yp;
integer jp1;
real sig;
integer k1pj, k2pj, k4pi, k3pi, k5pi, mop1, nder;
real sigj;
integer jpas;
real temp, etst;
doublereal temd1, temd2;
integer nfail;
real sigjm1, sigpas;
extern /* Subroutine */ int pvalue_(integer *, integer *, real *, real *,
real *, real *);
/* ***BEGIN PROLOGUE POLFIT */
/* ***PURPOSE Fit discrete data in a least squares sense by polynomials */
/* in one variable. */
/* ***LIBRARY SLATEC */
/* ***CATEGORY K1A1A2 */
/* ***TYPE SINGLE PRECISION (POLFIT-S, DPOLFT-D) */
/* ***KEYWORDS CURVE FITTING, DATA FITTING, LEAST SQUARES, POLYNOMIAL FIT */
/* ***AUTHOR Shampine, L. F., (SNLA) */
/* Davenport, S. M., (SNLA) */
/* Huddleston, R. E., (SNLL) */
/* ***DESCRIPTION */
/* Abstract */
/* Given a collection of points X(I) and a set of values Y(I) which */
/* correspond to some function or measurement at each of the X(I), */
/* subroutine POLFIT computes the weighted least-squares polynomial */
/* fits of all degrees up to some degree either specified by the user */
/* or determined by the routine. The fits thus obtained are in */
/* orthogonal polynomial form. Subroutine PVALUE may then be */
/* called to evaluate the fitted polynomials and any of their */
/* derivatives at any point. The subroutine PCOEF may be used to */
/* express the polynomial fits as powers of (X-C) for any specified */
/* point C. */
/* The parameters for POLFIT are */
/* Input -- */
/* N - the number of data points. The arrays X, Y and W */
/* must be dimensioned at least N (N .GE. 1). */
/* X - array of values of the independent variable. These */
/* values may appear in any order and need not all be */
/* distinct. */
/* Y - array of corresponding function values. */
/* W - array of positive values to be used as weights. If */
/* W(1) is negative, POLFIT will set all the weights */
/* to 1.0, which means unweighted least squares error */
/* will be minimized. To minimize relative error, the */
/* user should set the weights to: W(I) = 1.0/Y(I)**2, */
/* I = 1,...,N . */
/* MAXDEG - maximum degree to be allowed for polynomial fit. */
/* MAXDEG may be any non-negative integer less than N. */
/* Note -- MAXDEG cannot be equal to N-1 when a */
/* statistical test is to be used for degree selection, */
/* i.e., when input value of EPS is negative. */
/* EPS - specifies the criterion to be used in determining */
/* the degree of fit to be computed. */
/* (1) If EPS is input negative, POLFIT chooses the */
/* degree based on a statistical F test of */
/* significance. One of three possible */
/* significance levels will be used: .01, .05 or */
/* .10. If EPS=-1.0 , the routine will */
/* automatically select one of these levels based */
/* on the number of data points and the maximum */
/* degree to be considered. If EPS is input as */
/* -.01, -.05, or -.10, a significance level of */
/* .01, .05, or .10, respectively, will be used. */
/* (2) If EPS is set to 0., POLFIT computes the */
/* polynomials of degrees 0 through MAXDEG . */
/* (3) If EPS is input positive, EPS is the RMS */
/* error tolerance which must be satisfied by the */
/* fitted polynomial. POLFIT will increase the */
/* degree of fit until this criterion is met or */
/* until the maximum degree is reached. */
/* Output -- */
/* NDEG - degree of the highest degree fit computed. */
/* EPS - RMS error of the polynomial of degree NDEG . */
/* R - vector of dimension at least NDEG containing values */
/* of the fit of degree NDEG at each of the X(I) . */
/* Except when the statistical test is used, these */
/* values are more accurate than results from subroutine */
/* PVALUE normally are. */
/* IERR - error flag with the following possible values. */
/* 1 -- indicates normal execution, i.e., either */
/* (1) the input value of EPS was negative, and the */
/* computed polynomial fit of degree NDEG */
/* satisfies the specified F test, or */
/* (2) the input value of EPS was 0., and the fits of */
/* all degrees up to MAXDEG are complete, or */
/* (3) the input value of EPS was positive, and the */
/* polynomial of degree NDEG satisfies the RMS */
/* error requirement. */
/* 2 -- invalid input parameter. At least one of the input */
/* parameters has an illegal value and must be corrected */
/* before POLFIT can proceed. Valid input results */
/* when the following restrictions are observed */
/* N .GE. 1 */
/* 0 .LE. MAXDEG .LE. N-1 for EPS .GE. 0. */
/* 0 .LE. MAXDEG .LE. N-2 for EPS .LT. 0. */
/* W(1)=-1.0 or W(I) .GT. 0., I=1,...,N . */
/* 3 -- cannot satisfy the RMS error requirement with a */
/* polynomial of degree no greater than MAXDEG . Best */
/* fit found is of degree MAXDEG . */
/* 4 -- cannot satisfy the test for significance using */
/* current value of MAXDEG . Statistically, the */
/* best fit found is of order NORD . (In this case, */
/* NDEG will have one of the values: MAXDEG-2, */
/* MAXDEG-1, or MAXDEG). Using a higher value of */
/* MAXDEG may result in passing the test. */
/* A - work and output array having at least 3N+3MAXDEG+3 */
/* locations */
/* Note - POLFIT calculates all fits of degrees up to and including */
/* NDEG . Any or all of these fits can be evaluated or */
/* expressed as powers of (X-C) using PVALUE and PCOEF */
/* after just one call to POLFIT . */
/* ***REFERENCES L. F. Shampine, S. M. Davenport and R. E. Huddleston, */
/* Curve fitting by polynomials in one variable, Report */
/* SLA-74-0270, Sandia Laboratories, June 1974. */
/* ***ROUTINES CALLED PVALUE, XERMSG */
/* ***REVISION HISTORY (YYMMDD) */
/* 740601 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890531 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* 920527 Corrected erroneous statements in DESCRIPTION. (WRB) */
/* ***END PROLOGUE POLFIT */
/* DIMENSION CO(4,3) */
/* SAVE CO */
/* DATA CO(1,1), CO(2,1), CO(3,1), CO(4,1), CO(1,2), CO(2,2), */
/* 1 CO(3,2), CO(4,2), CO(1,3), CO(2,3), CO(3,3), */
/* 2 CO(4,3)/-13.086850,-2.4648165,-3.3846535,-1.2973162, */
/* 3 -3.3381146,-1.7812271,-3.2578406,-1.6589279, */
/* 4 -1.6282703,-1.3152745,-3.2640179,-1.9829776/ */
/* ***FIRST EXECUTABLE STATEMENT POLFIT */
/* Parameter adjustments */
--a;
--r__;
--w;
--y;
--x;
/* Uninitialized local variables -> note, I don't see how this
* function can be working */
k1=0;
k2 = 0;
k3 = 0;
k4 = 0;
k5 = 0;
etst = 1.0E-13f;
xm = 1.0;
/* Function Body */
m = abs(*n);
if (m == 0) {
goto L30;
}
if (*maxdeg < 0) {
goto L30;
}
a[1] = (real) (*maxdeg);
mop1 = *maxdeg + 1;
if (m < mop1) {
goto L30;
}
if (*eps < 0.f && m == mop1) {
goto L30;
}
j = 0;
/* SEE IF POLYNOMIAL OF DEGREE 0 SATISFIES THE DEGREE SELECTION CRITERION */
if (*eps < 0.f) {
goto L24;
} else if (*eps == 0) {
goto L26;
} else {
goto L27;
}
/* INCREMENT DEGREE */
L16:
++j;
jp1 = j + 1;
k1pj = k1 + j;
k2pj = k2 + j;
sigjm1 = sigj;
/* COMPUTE NEW B COEFFICIENT EXCEPT WHEN J = 1 */
if (j > 1) {
a[k1pj] = w11 / w1;
}
/* COMPUTE NEW A COEFFICIENT */
temd1 = 0.;
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
k4pi = k4 + i__;
temd2 = a[k4pi];
temd1 += (doublereal) x[i__] * (doublereal) w[i__] * temd2 * temd2;
/* L18: */
}
a[jp1] = (real) (temd1 / w11);
/* EVALUATE ORTHOGONAL POLYNOMIAL AT DATA POINTS */
w1 = w11;
w11 = 0.f;
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
k3pi = k3 + i__;
k4pi = k4 + i__;
temp = a[k3pi];
a[k3pi] = a[k4pi];
a[k4pi] = (x[i__] - a[jp1]) * a[k3pi] - a[k1pj] * temp;
/* L19: */
/* Computing 2nd power */
r__1 = a[k4pi];
w11 += w[i__] * (r__1 * r__1);
}
/* GET NEW ORTHOGONAL POLYNOMIAL COEFFICIENT USING PARTIAL DOUBLE */
/* PRECISION */
temd1 = 0.;
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
k4pi = k4 + i__;
k5pi = k5 + i__;
temd2 = (doublereal) w[i__] * (doublereal) (y[i__] - r__[i__] - a[
k5pi]) * (doublereal) a[k4pi];
/* L20: */
temd1 += temd2;
}
temd1 /= (doublereal) w11;
a[k2pj + 1] = (real) temd1;
/* UPDATE POLYNOMIAL EVALUATIONS AT EACH OF THE DATA POINTS, AND */
/* ACCUMULATE SUM OF SQUARES OF ERRORS. THE POLYNOMIAL EVALUATIONS ARE */
/* COMPUTED AND STORED IN EXTENDED PRECISION. FOR THE I-TH DATA POINT, */
/* THE MOST SIGNIFICANT BITS ARE STORED IN R(I) , AND THE LEAST */
/* SIGNIFICANT BITS ARE IN A(K5PI) . */
sigj = 0.f;
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
k4pi = k4 + i__;
k5pi = k5 + i__;
temd2 = (doublereal) r__[i__] + (doublereal) a[k5pi] + temd1 * (
doublereal) a[k4pi];
r__[i__] = (real) temd2;
a[k5pi] = (real) (temd2 - r__[i__]);
/* L21: */
/* Computing 2nd power */
r__1 = y[i__] - r__[i__] - a[k5pi];
sigj += w[i__] * (r__1 * r__1);
}
/* SEE IF DEGREE SELECTION CRITERION HAS BEEN SATISFIED OR IF DEGREE */
/* MAXDEG HAS BEEN REACHED */
if (*eps < 0.f) {
goto L23;
} else if (*eps == 0) {
goto L26;
} else {
goto L27;
}
/* COMPUTE F STATISTICS (INPUT EPS .LT. 0.) */
L23:
if (sigj == 0.f) {
goto L29;
}
/* DEGF = M - J - 1 */
/* DEN = (CO(4,KSIG)*DEGF + 1.0)*DEGF */
/* FCRIT = (((CO(3,KSIG)*DEGF) + CO(2,KSIG))*DEGF + CO(1,KSIG))/DEN */
/* FCRIT = FCRIT*FCRIT */
/* F = (SIGJM1 - SIGJ)*DEGF/SIGJ */
/* IF (F .LT. FCRIT) GO TO 25 */
/* POLYNOMIAL OF DEGREE J SATISFIES F TEST */
L24:
sigpas = sigj;
jpas = j;
nfail = 0;
if (*maxdeg == j) {
goto L32;
}
goto L16;
/* POLYNOMIAL OF DEGREE J FAILS F TEST. IF THERE HAVE BEEN THREE */
/* SUCCESSIVE FAILURES, A STATISTICALLY BEST DEGREE HAS BEEN FOUND. */
/* L25: */
++nfail;
if (nfail >= 3) {
goto L29;
}
if (*maxdeg == j) {
goto L32;
}
goto L16;
/* RAISE THE DEGREE IF DEGREE MAXDEG HAS NOT YET BEEN REACHED (INPUT */
/* EPS = 0.) */
L26:
if (*maxdeg == j) {
goto L28;
}
goto L16;
/* SEE IF RMS ERROR CRITERION IS SATISFIED (INPUT EPS .GT. 0.) */
L27:
if (sigj <= etst) {
goto L28;
}
if (*maxdeg == j) {
goto L31;
}
goto L16;
/* RETURNS */
L28:
*ierr = 1;
*ndeg = j;
sig = sigj;
goto L33;
L29:
*ierr = 1;
*ndeg = jpas;
sig = sigpas;
goto L33;
L30:
*ierr = 2;
/* CALL XERMSG ('SLATEC', 'POLFIT', 'INVALID INPUT PARAMETER.', 2, */
/* + 1) */
goto L37;
L31:
*ierr = 3;
*ndeg = *maxdeg;
sig = sigj;
goto L33;
L32:
*ierr = 4;
*ndeg = jpas;
sig = sigpas;
L33:
a[k3] = (real) (*ndeg);
/* WHEN STATISTICAL TEST HAS BEEN USED, EVALUATE THE BEST POLYNOMIAL AT */
/* ALL THE DATA POINTS IF R DOES NOT ALREADY CONTAIN THESE VALUES */
if (*eps >= 0.f || *ndeg == *maxdeg) {
goto L36;
}
nder = 0;
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
pvalue_(ndeg, &nder, &x[i__], &r__[i__], &yp, &a[1]);
/* L35: */
}
L36:
*eps = (real) sqrt(sig / xm);
L37:
return 0;
} /* polfit_ */
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