Port WAMFF subroutine to C++

src/include/tra_subs.h

 #include <fstream>
+#include <cmath>
 #include <complex>
 
 #ifndef INCLUDE_TRA_SUBS_H_
 #define INCLUDE_TRA_SUBS_H_
 #endif
 
+//Externally defined subroutines
+extern void sphar(
+	   double cosrth, double sinrth, double cosrph, double sinrph,
+	   int ll, std::complex<double> *ylm
+);
+//End of externally defined subroutines
+
+/*! C++ porting of WAMFF
+ *
+ * \param wk: Vector of complex. QUESTION: definition?
+ * \param x: `double`
+ * \param y: `double`
+ * \param z: `double`
+ * \param lm: `int`
+ * \param apfafa: `double` QUESTION: definition?
+ * \param tra: `double` QUESTION: definition?
+ * \param spd: `double` QUESTION: definition?
+ * \param rir: `double` QUESTION: definition?
+ * \param ftcn: `double` QUESTION: definition?
+ * \param lmode: `int` QUESTION: definition?
+ * \param pmf: `double` QUESTION: definition?
+ */
+void wamff(
+	   std::complex<double> *wk, double x, double y, double z, int lm, double apfafa,
+	   double tra, double spd, double rir, double ftcn, int lmode, double pmf
+) {
+  const int nlmm = lm * (lm + 2);
+  const int nlmmt = 2 * nlmm;
+  const int nlmp = nlmm + 2;
+  std::complex<double> **w, *ylm;
+  const std::complex<double> cc0(0.0, 0.0);
+  const std::complex<double> uim(0.0, 1.0);
+  std::complex<double> cfam, cf1, cf2;
+  double rho, cph, sph, cth, sth, r;
+  double ftc1, ftc2;
+  double *up = new double[3];
+  double *un = new double[3];
+  w = new std::complex<double>*[nlmmt];
+  for (int wi = 0; wi < nlmmt; wi++) w[wi] = new std::complex<double>[2]();
+  ylm = new std::complex<double>[nlmp]();
+  bool onx = (y == 0.0);
+  bool ony = (x == 0.0);
+  bool onz = (onx && ony);
+  if (!(onz && onx && ony)) {
+    rho = sqrt(x * x + y * y);
+    cph = x / rho;
+    sph = y = rho;
+  } else {
+    if (onz) { // label 10
+      cph = 1.0;
+      sph = 0.0;
+    } else {
+      if (onx) { // label 12
+	rho = sqrt(x * x);
+	cph = (x < 0.0)? -1.0 : 1.0;
+	sph = 0.0;
+      } else {
+	if (ony) { // label 13
+	  rho = sqrt(y * y);
+	  cph = 0.0;
+	  sph = (y < 0.0)? -1.0: 1.0;
+	}
+      }
+    }
+  }
+  // label 15
+  if (z == 0.0) {
+    if (!onz) {
+      r = rho;
+      cth = 0.0;
+      sth = 1.0;
+    } else { // label 17
+      r = 0.0;
+      cth = 1.0;
+      sth = 0.0;
+    }
+  } else { // label 18
+    if (!onz) {
+      r = sqrt(rho * rho + z * z);
+      cth = z / r;
+      sth = rho / r;
+    } else { // label 20
+      r = sqrt(z * z);
+      cth = (z < 0.0)? -1.0: 1.0;
+      sth = 0.0;
+    }
+  }
+  if (lmode == 0 || sth != 0.0) { // label 25
+    ylm[nlmp - 1] = cc0;
+    sphar(cth, sth, cph, sph, lm, ylm);
+    up[0] = cph * cth;
+    up[1] = sph * cth;
+    up[2] = -sth;
+    un[0] = -sph;
+    un[1] = cph;
+    un[2] = 0.0;
+    // Would call PWMALP(W,UP,UN,YLM,LM)
+    double apfa = sth * apfafa;
+    if (spd > 0.0) {
+      double sthl = sth * rir;
+      double cthl = sqrt(1.0 - sthl * sthl);
+      double arg = spd * (z - (r / rir) * cthl);
+      cfam = (tra * std::exp(-apfa * apfa) / sqrt(cthl)) * std::exp(uim * arg);
+      if (lmode == 0) { // CHECK: Computed GO TO, not sure what happens with LMODE = 0
+	if (sth == 0.0) { // label 45
+	  ftc1 = ftcn;
+	  ftc2 = ftcn;
+	  // goes to 48
+	}
+      } else if (lmode == 1) { // label 46
+	cfam *= ((cph + uim * sph) * sth * pmf);
+	ftc1 = 2.0 * cthl / (cthl * rir + cth);
+	ftc2 = 2.0 * cthl / (cthl + cth * rir);
+	// follows on to 48
+      } else if (lmode == 2) { // label 50
+	ftc1 = 2.0 * cthl / (cthl * rir + cth);
+	cfam *= (sth * pmf * ftc1);
+	for (int i52 = 0; i52 < nlmmt; i52++) wk[i52] = w[i52][0] * cfam;
+	// returns
+      } else if (lmode == 3) { // label 53
+	ftc2 = 2.0 * cthl / (cthl  + cth * rir);
+	cfam *= (sth * pmf * ftc2);
+	for (int i55 = 0; i55 < nlmmt; i55++) wk[i55] = w[i55][1] * cfam;
+	// returns
+      }
+      if (lmode == 0 || lmode == 1) { //label 48
+	cf1 = cph * ftc1 * cfam;
+	cf2 = -sph * ftc2 * cfam;
+	// goes to 62
+      }
+    } else { // label 57
+      double fam = tra * std::exp(-apfa * apfa) / sqrt(cth);
+      if (lmode == 0) {
+	double f1 = cph * fam;
+	double f2 = -sph * fam;
+	for (int i58 = 0; i58 < nlmmt; i58++) wk[i58] = w[i58][0] * f1 + w[i58][1] * f2;
+	// returns
+      } else if (lmode == 1) { // label 60
+	cfam = (pmf * sth * fam) * (cph * uim * sph);
+	cf1 = cph * cfam;
+	cf2 = -sph * cfam;
+	// follows on to 62
+      } else if (lmode == 2) { // label 65
+	fam *= (pmf * sth);
+	for (int i67 = 0; i67 < nlmmt; i67++) wk[i67] = w[i67][0] * fam;
+	// returns
+      } else if (lmode == 3) { // label 68
+	fam *= (pmf * sth);
+	for (int i70 = 0; i70 < nlmmt; i70++) wk[i70] = w[i70][1] * fam;
+	// returns
+      }
+    }
+    if (lmode == 0 || lmode == 1) { // label 62
+      for (int i63 = 0; i63 < nlmmt; i63++) wk[i63] = w[i63][0] * cf1 + w[i63][1] * cf2;
+    }
+  }
+  // Clean up memory
+  delete[] up;
+  delete[] un;
+  for (int wi = nlmmt - 1; wi > -1; wi--) delete[] w[wi];
+  delete[] w;
+  delete[] ylm;
+}
+
 /*! C++ porting of FRFMER
  *
  * \param nkv: `int` QUESTION: definition?
@@ -15,7 +180,7 @@
  * \param tra: `double` QUESTION: definition?
  * \param spd: `double` QUESTION: definition?
  * \param rir: `double` QUESTION: definition?
- * \param fctn: `double` QUESTION: definition?
+ * \param ftcn: `double` QUESTION: definition?
  * \param le: `int` QUESTION: definition?
  * \param lmode: `int` QUESTION: definition?
  * \param pmf: `double` QUESTION: definition?