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-rw-r--r--libraries/CurveFitting/src/curveFitting.cpp195
1 files changed, 195 insertions, 0 deletions
diff --git a/libraries/CurveFitting/src/curveFitting.cpp b/libraries/CurveFitting/src/curveFitting.cpp
new file mode 100644
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+++ b/libraries/CurveFitting/src/curveFitting.cpp
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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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