simplify normalisation for derivatives

libsharp/sharp.c

@@ -405,8 +405,7 @@ static void alm2almtmp (sharp_job *job, int lmax, int mi)
     for (int l=job->ainfo->mval[mi]; l<=lmax; ++l)
       {
       ptrdiff_t aidx = sharp_alm_index(job->ainfo,l,mi);
-      double fct = (job->type==ALM2MAP) ? job->norm_l[l] :
+      double fct = job->norm_l[l];
-                    fabs(job->norm_l[l])*sqrt(l*(l+1.));
       for (int i=0; i<job->ntrans*job->nalm; ++i)
         if (job->fde==DOUBLE)
           job->almtmp[job->ntrans*job->nalm*l+i]
@@ -464,7 +463,9 @@ void sharp_execute_job (sharp_job *job)
   int lmax = job->ainfo->lmax,
       mmax=sharp_get_mmax(job->ainfo->mval, job->ainfo->nm);
 
-  job->norm_l = sharp_Ylmgen_get_norm (lmax, job->spin);
+  job->norm_l = (job->type==ALM2MAP_DERIV1) ?
+     sharp_Ylmgen_get_d1norm (lmax) :
+     sharp_Ylmgen_get_norm (lmax, job->spin);
 
 /* clear output arrays if requested */
   init_output (job);

libsharp/sharp_ylmgen_c.c

@@ -205,3 +205,13 @@ double *sharp_Ylmgen_get_norm (int lmax, int spin)
     res[l] = (l<spin) ? 0. : spinsign*0.5*sqrt((2*l+1)/(4*pi));
   return res;
   }
+
+double *sharp_Ylmgen_get_d1norm (int lmax)
+  {
+  const double pi = 3.141592653589793238462643383279502884197;
+  double *res=RALLOC(double,lmax+1);
+
+  for (int l=0; l<=lmax; ++l)
+    res[l] = (l<1) ? 0. : 0.5*sqrt(l*(l+1.)*(2*l+1.)/(4*pi));
+  return res;
+  }

libsharp/sharp_ylmgen_c.h

@@ -85,6 +85,12 @@ void sharp_Ylmgen_prepare (sharp_Ylmgen_C *gen, int m);
     \a spin. The array must be deallocated (using free()) by the user. */
 double *sharp_Ylmgen_get_norm (int lmax, int spin);
 
+/*! Returns a pointer to an array with \a lmax+1 entries containing
+    normalisation factors that must be applied to Y_lm values computed for
+    first derivatives. The array must be deallocated (using free()) by the
+    user. */
+double *sharp_Ylmgen_get_d1norm (int lmax);
+
 #ifdef __cplusplus
 }
 #endif