Add cpp math functions to calc normalization arrays

Add math funcs to reconstruct FET

src/math_functions.cpp

@@ -103,17 +103,36 @@ void calc_pn_c(int n, double x, double pnx[]) {
 }
 
 
-double evaluate_legendre_c(int n, const double data[], double x) {
+double evaluate_legendre_c(int n, const double data[], double x, int flag) {
   double pnx[n + 1];
   double val = 0.0;
   calc_pn_c(n, x, pnx);
-  for (int l = 0; l <= n; l++) {
-    val += (l + 0.5) * data[l] * pnx[l];
+
+  if (flag == 1) {
+    for (int l = 0; l <= n; l++) {
+      val += (l + 0.5) * data[l] * pnx[l];
+    }
+  } else if (flag == 2) {
+    for (int l = 0; l <= n; l++) {
+      val += data[l] * pnx[l];
+    }
   }
+
   return val;
 }
 
 
+void calc_norm_pn_c(int l, double zmin, double zmax, double norm_vec[]) {
+  // ===========================================================================
+  // Set up the normalization vector for FET Pn reconstruction
+  double d = zmax - zmin;
+
+  for (int i = 0; i <= l; i++) {
+    norm_vec[i] = (2 * i + 1)/d;
+  }
+}
+
+
 void calc_rn_c(int n, const double uvw[3], double rn[]){
   // rn[] is assumed to have already been allocated to the correct size
 
@@ -615,6 +634,33 @@ void calc_zn_rad_c(int n, double rho, double zn_rad[]) {
 }
 
 
+void calc_norm_zn_rad_c(int n, double r, double norm_vec[]) {
+  // ===========================================================================
+  // Set up the normalization vector for FET Zn Radial only reconstruction
+  int index;
+
+  for (int i = 0; i <= n; i+=2) {
+    index = int(i/2);
+    norm_vec[index] = (i + 1)/(PI * r * r);
+  }
+}
+
+
+double evaluate_zernike_rad_c(int n, const double data[], double r) {
+  double rnr[n / 2 + 1];
+  double val = 0.0;
+  calc_zn_rad_c(n, r, rnr);
+  int index;
+
+  for (int i = 0; i <= n; i+ = 2) {
+    index = int(i/2);
+    val += data[index] * rnr[index];
+  }
+
+  return val;
+}
+
+
 void rotate_angle_c(double uvw[3], double mu, double* phi) {
   // Copy original directional cosines
   double u0 = uvw[0]; // original cosine in x direction

src/math_functions.h

@@ -53,11 +53,27 @@ extern "C" void calc_pn_c(int n, double x, double pnx[]);
 //! @param data The polynomial expansion coefficient data; without the (2l+1)/2
 //!   factor.
 //! @param x    The value to evaluate at; x is expected to be within [-1,1]
+//! @param flag A flag of which method to calculate Legendre polynomials. 1 for
+//!   default (2l+1)/2; 2 for custom normalized coefficients
 //! @return The requested Legendre polynomials of order 0 to n (inclusive)
 //!   evaluated at x
 //==============================================================================
 
-extern "C" double evaluate_legendre_c(int n, const double data[], double x);
+extern "C" double evaluate_legendre_c(int n, const double data[], double x, int flag = 1);
+
+//==============================================================================
+//! Evaluate the normalization vector when reconstructing functional expansion
+//! from Legendre polynomials. 
+//!
+//! The normalization is (2 * l + 1)/(zmax - zmin)
+//!
+//! @param l         The maximum order requested
+//! @param zmin      The minimum location of 1-d domain
+//! @param zmax      The maximum location of 1-d domain
+//! @param norm_vec  The requested normalization of order 0 to n (inclusive)
+//==============================================================================
+
+extern "C" void calc_norm_pn_c(int l, double zmin, double zmax, double norm_vec[]);
 
 //==============================================================================
 //! Calculate the n-th order real spherical harmonics for a given angle (in
@@ -69,6 +85,7 @@ extern "C" double evaluate_legendre_c(int n, const double data[], double x);
 //!   evaluated at uvw.
 //==============================================================================
 
+
 extern "C" void calc_rn_c(int n, const double uvw[3], double rn[]);
 
 //==============================================================================
@@ -109,6 +126,33 @@ extern "C" void calc_zn_c(int n, double rho, double phi, double zn[]);
 
 extern "C" void calc_zn_rad_c(int n, double rho, double zn_rad[]);
 
+//==============================================================================
+//! Evaluate the normalization vector when reconstructing functional expansion
+//! from radial only Zernike polynomials. 
+//!
+//! The normalization is (2 * l + 1)/(zmax - zmin)
+//!
+//! @param n         The maximum order requested
+//! @param r      	 The radius of the disk
+//! @param norm_vec  The requested normalization of even orders from 0 to n
+//==============================================================================
+
+extern "C" void calc_norm_zn_rad_c(int n, double r, double norm_vec[]);
+
+//==============================================================================
+//! Find the value of f(x) given a set of even order Zernike coefficients and 
+//! the value of x if there is only radial dependency.
+//!
+//! @param n    The maximum order of the expansion
+//! @param data The overall polynomial expansion coefficient data;
+//!   normalization should be considered by users
+//! @param r    The value to evaluate at; r is expected to be within [0,1]
+//! @return The requested Zernike polynomials of order 0 to n (inclusive)
+//!   evaluated at r
+//==============================================================================
+
+extern "C" double evaluate_zernike_rad_c(int n, const double data[], double r);
+
 //==============================================================================
 //! Rotate the direction cosines through a polar angle whose cosine is mu and
 //! through an azimuthal angle sampled uniformly.