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
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
/*
curveFitting.h - Library for fitting curves to given
points using Least Squares method, with Cramer's rule
used to solve the linear equation. Max polynomial order 20.
Created by Rowan Easter-Robinson, August 23, 2018.
Released into the public domain.
*/
#include <Arduino.h>
#include "curveFitting.h"
void printMat(const char *s, double*m, int n){
Serial.println(s);
char buf[40];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
snprintf(buf, 40, "%30.4f\t", m[i*n+j]);
Serial.print(buf);
}
Serial.println();
}
}
void showmat(const char *s, double **m, int n){
Serial.println(s);
char buf[40];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++){
snprintf(buf, 40, "%30.4f\t", m[i][j]);
Serial.print(buf);
}
Serial.println();
}
}
void cpyArray(double *src, double*dest, int n){
for (int i = 0; i < n*n; i++){
dest[i] = src[i];
}
}
void subCol(double *mat, double* sub, uint8_t coln, uint8_t n){
if (coln >= n) return;
for (int i = 0; i < n; i++){
mat[(i*n)+coln] = sub[i];
}
}
/*Determinant algorithm taken from https://codeforwin.org/2015/08/c-program-to-find-determinant-of-matrix.html */
int trianglize(double **m, int n)
{
int sign = 1;
for (int i = 0; i < n; i++) {
int max = 0;
for (int row = i; row < n; row++)
if (fabs(m[row][i]) > fabs(m[max][i]))
max = row;
if (max) {
sign = -sign;
double *tmp = m[i];
m[i] = m[max], m[max] = tmp;
}
if (!m[i][i]) return 0;
for (int row = i + 1; row < n; row++) {
double r = m[row][i] / m[i][i];
if (!r) continue;
for (int col = i; col < n; col ++)
m[row][col] -= m[i][col] * r;
}
}
return sign;
}
double det(double *in, int n, uint8_t prnt)
{
double *m[n];
m[0] = in;
for (int i = 1; i < n; i++)
m[i] = m[i - 1] + n;
if(prnt) showmat("Matrix", m, n);
int sign = trianglize(m, n);
if (!sign)
return 0;
if(prnt) showmat("Upper triangle", m, n);
double p = 1;
for (int i = 0; i < n; i++)
p *= m[i][i];
return p * sign;
}
/*End of Determinant algorithm*/
//Raise x to power
double curveFitPower(double base, int exponent){
if (exponent == 0){
return 1;
} else {
double val = base;
for (int i = 1; i < exponent; i++){
val = val * base;
}
return val;
}
}
int fitCurve (int order, int nPoints, double py[], int nCoeffs, double *coeffs) {
uint8_t maxOrder = MAX_ORDER;
if (nCoeffs != order + 1) return ORDER_AND_NCOEFFS_DO_NOT_MATCH; // no of coefficients is one larger than the order of the equation
if (nCoeffs > maxOrder || nCoeffs < 2) return ORDER_INCORRECT; //matrix memory hard coded for max of 20 order, which is huge
if (nPoints < 1) return NPOINTS_INCORRECT; //Npoints needs to be positive and nonzero
int i, j;
double T[MAX_ORDER] = {0}; //Values to generate RHS of linear equation
double S[MAX_ORDER*2+1] = {0}; //Values for LHS and RHS of linear equation
double denom; //denominator for Cramer's rule, determinant of LHS linear equation
double x, y;
double px[nPoints]; //Generate X values, from 0 to n
for (i=0; i<nPoints; i++){
px[i] = i;
}
for (i=0; i<nPoints; i++) {//Generate matrix elements
x = px[i];
y = py[i];
for (j = 0; j < (nCoeffs*2)-1; j++){
S[j] += curveFitPower(x, j); // x^j iterated , S10 S20 S30 etc, x^0, x^1...
}
for (j = 0; j < nCoeffs; j++){
T[j] += y * curveFitPower(x, j); //y * x^j iterated, S01 S11 S21 etc, x^0*y, x^1*y, x^2*y...
}
}
double masterMat[nCoeffs*nCoeffs]; //Master matrix LHS of linear equation
for (i = 0; i < nCoeffs ;i++){//index by matrix row each time
for (j = 0; j < nCoeffs; j++){//index within each row
masterMat[i*nCoeffs+j] = S[i+j];
}
}
double mat[nCoeffs*nCoeffs]; //Temp matrix as det() method alters the matrix given
cpyArray(masterMat, mat, nCoeffs);
denom = det(mat, nCoeffs, CURVE_FIT_DEBUG);
cpyArray(masterMat, mat, nCoeffs);
//Generate cramers rule mats
for (i = 0; i < nCoeffs; i++){ //Temporary matrix to substitute RHS of linear equation as per Cramer's rule
subCol(mat, T, i, nCoeffs);
coeffs[nCoeffs-i-1] = det(mat, nCoeffs, CURVE_FIT_DEBUG)/denom; //Coefficients are det(M_i)/det(Master)
cpyArray(masterMat, mat, nCoeffs);
}
return 0;
}
int fitCurve (int order, int nPoints, double px[], double py[], int nCoeffs, double *coeffs) {
uint8_t maxOrder = MAX_ORDER;
if (nCoeffs != order + 1) return ORDER_AND_NCOEFFS_DO_NOT_MATCH; //Number of coefficients is one larger than the order of the equation
if(nCoeffs > maxOrder || nCoeffs < 2) return ORDER_INCORRECT; //Matrix memory hard coded for max of 20 order, which is huge
if (nPoints < 1) return NPOINTS_INCORRECT; //Npoints needs to be positive and nonzero
int i, j;
double T[MAX_ORDER] = {0}; //Values to generate RHS of linear equation
double S[MAX_ORDER*2+1] = {0}; //Values for LHS and RHS of linear equation
double denom; //denominator for Cramer's rule, determinant of LHS linear equation
double x, y;
for (i=0; i<nPoints; i++) {//Generate matrix elements
x = px[i];
y = py[i];
for (j = 0; j < (nCoeffs*2)-1; j++){
S[j] += curveFitPower(x, j); // x^j iterated , S10 S20 S30 etc, x^0, x^1...
}
for (j = 0; j < nCoeffs; j++){
T[j] += y * curveFitPower(x, j); //y * x^j iterated, S01 S11 S21 etc, x^0*y, x^1*y, x^2*y...
}
}
double masterMat[nCoeffs*nCoeffs]; //Master matrix LHS of linear equation
for (i = 0; i < nCoeffs ;i++){//index by matrix row each time
for (j = 0; j < nCoeffs; j++){//index within each row
masterMat[i*nCoeffs+j] = S[i+j];
}
}
double mat[nCoeffs*nCoeffs]; //Temp matrix as det() method alters the matrix given
cpyArray(masterMat, mat, nCoeffs);
denom = det(mat, nCoeffs, CURVE_FIT_DEBUG);
cpyArray(masterMat, mat, nCoeffs);
//Generate cramers rule mats
for (i = 0; i < nCoeffs; i++){ //Temporary matrix to substitute RHS of linear equation as per Cramer's rule
subCol(mat, T, i, nCoeffs);
coeffs[nCoeffs-i-1] = det(mat, nCoeffs, CURVE_FIT_DEBUG)/denom; //Coefficients are det(M_i)/det(Master)
cpyArray(masterMat, mat, nCoeffs);
}
return 0;
}
|
