1 files changed, 195 insertions, 0 deletions
diff --git a/Arduino/libraries/arduinoCurveFitting-master/src/curveFitting.cpp b/Arduino/libraries/arduinoCurveFitting-master/src/curveFitting.cpp
new file mode 100644
index 0000000..5e526c0
--- /dev/null
+++ b/Arduino/libraries/arduinoCurveFitting-master/src/curveFitting.cpp
@@ -0,0 +1,195 @@
+/*
+  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;
+}