1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
|
# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include <math/gsurfit.h>
include "dgsurfitdef.h"
# GSFIT1 -- Procedure to solve the normal equations for a surface.
#
# This version modifies the fitting matrix to remove the first
# term from the fitting. For the polynomial functions this means
# constraining the constant term to be zero. Note that the first
# coefficent is still returned but with a value of zero.
procedure dgsfit1 (sf, x, y, z, w, npts, wtflag, ier)
pointer sf # surface descriptor
double x[npts] # array of x values
double y[npts] # array of y values
double z[npts] # data array
double w[npts] # array of weights
int npts # number of data points
int wtflag # type of weighting
int ier # ier = OK, everything OK
# ier = SINGULAR, matrix is singular, 1 or more
# coefficients are 0.
# ier = NO_DEG_FREEDOM, too few points to solve matrix
begin
call dgszero (sf)
call dgsacpts (sf, x, y, z, w, npts, wtflag)
call dgssolve1 (sf, ier)
end
# GSSOLVE1 -- Solve the matrix normal equations of the form ca = b for
# a, where c is a symmetric, positive semi-definite, banded matrix with
# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
# GS_NYCOEFF(sf)-vectors. Initially c is stored in the matrix MATRIX and b
# is stored in VECTOR. The Cholesky factorization of MATRIX is calculated
# and stored in CHOFAC. Finally the coefficients are calculated by forward
# and back substitution and stored in COEFF.
#
# This version modifies the fitting matrix to remove the first
# term from the fitting. For the polynomial functions this means
# constraining the constant term to be zero. Note that the first
# coefficent is still returned but with a value of zero.
procedure dgssolve1 (sf, ier)
pointer sf # curve descriptor
int ier # ier = OK, everything OK
# ier = SINGULAR, matrix is singular, 1 or more
# coefficients are 0.
# ier = NO_DEG_FREEDOM, too few points to solve matrix
int i, ncoeff, offset
pointer sp, vector, matrix
begin
# test for number of degrees of freedom
offset = 1
ncoeff = GS_NCOEFF(sf) - offset
ier = OK
i = GS_NPTS(sf) - ncoeff
if (i < 0) {
ier = NO_DEG_FREEDOM
return
}
# allocate working space for the reduced vector and matrix
call smark (sp)
call salloc (vector, ncoeff, TY_DOUBLE)
call salloc (matrix, ncoeff*ncoeff, TY_DOUBLE)
# eliminate the first term from the vector and matrix
call amovd (VECTOR(GS_VECTOR(sf)+offset), Memd[vector], ncoeff)
do i = 0, ncoeff-1
call amovd (MATRIX(GS_MATRIX(sf)+(i+offset)*GS_NCOEFF(sf)),
Memd[matrix+i*ncoeff], ncoeff)
# solve for the coefficients.
switch (GS_TYPE(sf)) {
case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
# calculate the Cholesky factorization of the data matrix
call dgschofac (Memd[matrix], ncoeff, ncoeff,
CHOFAC(GS_CHOFAC(sf)), ier)
# solve for the coefficients by forward and back substitution
COEFF(GS_COEFF(sf)) = 0.
call dgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
Memd[vector], COEFF(GS_COEFF(sf)+offset))
default:
call error (0, "GSSOLVE1: Illegal surface type.")
}
call sfree (sp)
end
|
