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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, ld*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, ld **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(ld *src, ld*dest, int n){
for (int i = 0; i < n*n; i++){
dest[i] = src[i];
}
}
void subCol(ld *mat, ld* 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(ld **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;
ld *tmp = m[i];
m[i] = m[max], m[max] = tmp;
}
if (!m[i][i]) return 0;
for (int row = i + 1; row < n; row++) {
ld 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;
}
ld det(ld *in, int n, uint8_t prnt)
{
ld *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);
ld p = 1;
for (int i = 0; i < n; i++)
p *= m[i][i];
return p * sign;
}
/*End of Determinant algorithm*/
//Raise x to power
ld curveFitPower(ld base, int exponent){
if (exponent == 0){
return 1;
} else {
ld val = base;
for (int i = 1; i < exponent; i++){
val = val * base;
}
return val;
}
}
int fitCurve (int order, int nPoints, ld py[], int nCoeffs, ld *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;
ld T[MAX_ORDER] = {0}; //Values to generate RHS of linear equation
ld S[MAX_ORDER*2+1] = {0}; //Values for LHS and RHS of linear equation
ld denom; //denominator for Cramer's rule, determinant of LHS linear equation
ld x, y;
ld 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...
}
}
ld 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];
}
}
ld 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, ld px[], ld py[], int nCoeffs, ld *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;
ld T[MAX_ORDER] = {0}; //Values to generate RHS of linear equation
ld S[MAX_ORDER*2+1] = {0}; //Values for LHS and RHS of linear equation
ld denom; //denominator for Cramer's rule, determinant of LHS linear equation
ld 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...
}
}
ld 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];
}
}
ld 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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