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
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
/**********************************************************************
* File: quadlsq.cpp (Formerly qlsq.c)
* Description: Code for least squares approximation of quadratics.
* Author: Ray Smith
* Created: Wed Oct 6 15:14:23 BST 1993
*
* (C) Copyright 1993, Hewlett-Packard Ltd.
** Licensed under the Apache License, Version 2.0 (the "License");
** you may not use this file except in compliance with the License.
** You may obtain a copy of the License at
** http://www.apache.org/licenses/LICENSE-2.0
** Unless required by applicable law or agreed to in writing, software
** distributed under the License is distributed on an "AS IS" BASIS,
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
** See the License for the specific language governing permissions and
** limitations under the License.
*
**********************************************************************/
#include "mfcpch.h"
#include <stdio.h>
#include <math.h>
#include "errcode.h"
#include "quadlsq.h"
const ERRCODE EMPTY_QLSQ = "Can't delete from an empty QLSQ";
#define EXTERN
/**********************************************************************
* QLSQ::clear
*
* Function to initialize a QLSQ.
**********************************************************************/
void QLSQ::clear() { //initialize
a = 0;
b = 0;
c = 0;
n = 0; //no elements
sigx = 0; //update accumulators
sigy = 0;
sigxx = 0;
sigxy = 0;
sigyy = 0;
sigxxx = 0;
sigxxy = 0;
sigxxxx = 0;
}
/**********************************************************************
* QLSQ::add
*
* Add an element to the accumulator.
**********************************************************************/
void QLSQ::add( //add an element
double x, //xcoord
double y //ycoord
) {
n++; //count elements
sigx += x; //update accumulators
sigy += y;
sigxx += x * x;
sigxy += x * y;
sigyy += y * y;
sigxxx += (long double) x *x * x;
sigxxy += (long double) x *x * y;
sigxxxx += (long double) x *x * x * x;
}
/**********************************************************************
* QLSQ::remove
*
* Delete an element from the acculuator.
**********************************************************************/
void QLSQ::remove( //delete an element
double x, //xcoord
double y //ycoord
) {
if (n <= 0)
//illegal
EMPTY_QLSQ.error ("QLSQ::remove", ABORT, NULL);
n--; //count elements
sigx -= x; //update accumulators
sigy -= y;
sigxx -= x * x;
sigxy -= x * y;
sigyy -= y * y;
sigxxx -= (long double) x *x * x;
sigxxy -= (long double) x *x * y;
sigxxxx -= (long double) x *x * x * x;
}
/**********************************************************************
* QLSQ::fit
*
* Fit the given degree of polynomial and store the result.
**********************************************************************/
void QLSQ::fit( //fit polynomial
int degree //degree to fit
) {
long double cubetemp; //intermediates
long double squaretemp;
long double top96, bottom96; /*accurate top & bottom */
if (n >= 4 && degree >= 2) {
cubetemp = sigxxx * n - (long double) sigxx *sigx;
top96 =
cubetemp * ((long double) sigxy * n - (long double) sigx * sigy);
squaretemp = (long double) sigxx *n - (long double) sigx *sigx;
top96 += squaretemp * ((long double) sigxx * sigy - sigxxy * n);
bottom96 = cubetemp * cubetemp;
bottom96 -= squaretemp * (sigxxxx * n - (long double) sigxx * sigxx);
a = top96 / bottom96;
top96 = ((long double) sigxx * sigx - sigxxx * n) * a
+ (long double) sigxy *n - (long double) sigx *sigy;
bottom96 = (long double) sigxx *n - (long double) sigx *sigx;
b = top96 / bottom96;
c = (sigy - a * sigxx - b * sigx) / n;
}
else if (n == 0 || degree < 0) {
a = b = c = 0;
}
else {
a = 0;
if (n > 1 && degree > 0) {
b = (sigxy * n - sigx * sigy) / (sigxx * n - sigx * sigx);
}
else
b = 0;
c = (sigy - b * sigx) / n;
}
}
|
