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Anthony Wang 2022-02-11 15:25:23 -06:00
parent 0f1a894cfb
commit 484a9fcbdb
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9 changed files with 312 additions and 66 deletions
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21
libraries/CurveFitting/LICENSE Normal file
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MIT License
Copyright (c) 2019 Andrey Fedorov
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# arduinoCurveFitting
Fit polynomial curves to given points using least squares regression. The max order of polynomial fitting is 20, this should be more than enough to fit most practical problems. All values are kept as double for precision, this works well on a Teensy due to its floating point unit and large (64 bit) double precision. the numbers required increase exponentially as the number of points or order increases.
This library solves the least squares problem using Cramer's rule and a small function to calculate the determinant of each matrix.
More explained in this article
https://medium.com/@rowaner111/fitting-curves-to-data-on-an-arduino-part-1-how-to-use-arduinocurvefitting-a3173c6dd4ef

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libraries/CurveFitting/examples/fitCurve/fitCurve.ino Normal file
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#include <curveFitting.h>
void setup(){
Serial.begin(9600);
while(!Serial);
Serial.println("Starting");
char buf[100];
int xpower = 3;
int order = 3;
snprintf(buf, 100, "Fitting curve of order %i to data of power %i...\n", order, xpower);
Serial.print(buf);
double x[26];
double t[26];
for (int i = 0; i < sizeof(x)/sizeof(double); i++){
t[i] = i;
x[i] = pow(i, xpower);
}
double coeffs[order+1];
int ret = fitCurve(order, sizeof(x)/sizeof(double), t, x, sizeof(coeffs)/sizeof(double), coeffs);
if (ret == 0){ //Returned value is 0 if no error
uint8_t c = 'a';
Serial.println("Coefficients are");
for (int i = 0; i < sizeof(coeffs)/sizeof(double); i++){
snprintf(buf, 100, "%c=",c++);
Serial.print(buf);
Serial.print(coeffs[i]);
Serial.print('\t');
}
}
}
void loop(){
}

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libraries/CurveFitting/keywords.txt Normal file
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fitCurve KEYWORD2

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libraries/CurveFitting/library.properties Normal file
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name=CurveFitting
version=1.0.6
author=Rotario <rotarioner@gmail.com>
maintainer=Rotario <rotarioner@gmail.com>
sentence=Fits polynomial curves to given datapoints
paragraph=Fit polynomial curves to given points using least squares regression. The max order of polynomial fitting is 20, this should be more than enough to fit most practical problems. All values are kept as double for precision, this works well on a Teensy due to its floating point unit and large (64 bit) double precision. the numbers required increase exponentially as the number of points or order increases.
url=https://github.com/Rotario/arduinoCurveFitting
includes=curveFitting.h
category=Data Processing
architectures=*

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libraries/CurveFitting/src/curveFitting.cpp Normal file
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/*
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;
}

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/*
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.
*/
#ifndef curveFit_h
#define curveFit_h
#include <Arduino.h>
#define MAX_ORDER 20
#ifndef CURVE_FIT_DEBUG
#define CURVE_FIT_DEBUG 0
#endif
/* Enum for error messages */
enum curveFitERROR{
ORDER_AND_NCOEFFS_DO_NOT_MATCH = -1,
ORDER_INCORRECT = -2,
NPOINTS_INCORRECT = -3
};
/* Matrix Helper Functions */
void printMat(const char *s, double*m, int n);
void showmat(const char *s, double **m, int n);
void cpyArray(double *src, double*dest, int n);
void subCol(double *mat, double* sub, uint8_t coln, uint8_t n);
double curveFitPower(double base, int exponent);
/* Determinant matrix functions */
int trianglize(double **m, int n);
double det(double *in, int n, uint8_t prnt);
/* Curve fitting functions */
int fitCurve (int order, int nPoints, double py[], int nCoeffs, double *coeffs);
int fitCurve (int order, int nPoints, double px[], double py[], int nCoeffs, double *coeffs);
#endif

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For information on installing libraries, see: http://www.arduino.cc/en/Guide/Libraries

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main.ino
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/*
____ __________________________________ ____
/ __ \/ ____/_ __/ ____/ ____/_ __/ __ \/ __ \
/ / / / __/ / / / __/ / / / / / / / / /_/ /
/ /_/ / /___ / / / /___/ /___ / / / /_/ / _, _/
/___________/ __________/\____/ _____\__________|
/ __ )/ / / / _/ / / __ \/ _/ | / / ____/
/ __ / / / // // / / / / // // |/ / / __
/ /_/ / /_/ // // /___/ /_/ // // /| / /_/ /
/_____/\____/___/_____/_____/___/_/ |_/\____/
Ladue Horton Watkins High School Science Olympiad
Licensed under the Parity Public License
*/
#include <curveFitting.h>
using ld = long double;
const int LED_R = 8, LED_G = 10, LED_B = 12, THERM = 0; // Device component pins
const ld R_k = 10000, V_in = 5, analog_max = 1023; // Device constants
// Analog to digital conversion
ld a2d(int a) { return V_in * a / analog_max; }
int d2a(ld d) { return d * analog_max / V_in; }
// Voltage to resistance conversion
ld v2r(ld V_out) { return R_k * (V_in / V_out - 1); }
ld vol[100];
int con[100];
const int order = 2;
int coeff[order + 1];
void setup() {
Serial.begin(9600);
Serial.println("Starting calibration")
Serial.println("Place sensor in water and enter the concentration into the console")
Serial.println("When you are finished, type c to continue")
int n = 0;
while (1) {
String s = Serial.readString();
if (s == "c") break;
vol[n] = a2d(analogRead(THERM));
con[n] = toInt(s);
Serial.println(n);
Serial.println(vol[n]);
Serial.println(con[n]);
++n;
}
fitCurve(order, n, vol, con, coeff);
}
void loop() {
v = a2d(analogRead(THERM));
c = 0;
for (int i = order; i >= 0; --i) c = v*c + coeff[i];
Serial.println(c);
}