Changeset 3595 in Sophya for trunk/Cosmo/SimLSS/geneutils.cc

Timestamp:

Apr 19, 2009, 2:47:10 PM (16 years ago)

Author:

cmv

Message:

improve DL precison and tests main routine, cmv 19/04/2009

File:

• trunk/Cosmo/SimLSS/geneutils.cc (modified) (4 diffs)

trunk/Cosmo/SimLSS/geneutils.cc

@@ -296 +296 @@
 double SinXsX(double x,bool app)
 // Calcul de sin(x)/x
-// Approx: dernier terme x^6/(6*20*42) ~ 1e-13 -> x^2 ~ 1.7e-4
+// Le Dl est en O[x]^10  (cad on va jusqu'au terme en x^8 compris)
+// Approx: terme en x^6/(6*20*42) ~ 1e-13 -> x^2 ~ 1.7e-4
 {
   double x2 = x*x;
-  if(app || x2<1.7e-4) return 1. - x2/6.*(1. - x2/20.*(1. - x2/42.));
+  if(app || x2<1.7e-4) return 1.-x2/6.*(1.-x2/20.*(1.-x2/42.*(1.-x2/72.)));
   return sin(x)/x;
 }
@@ -305 +306 @@
 double SinXsX_Sqr(double x,bool app)
 // Calcul de (sin(x)/x)^2
-// Approx: dernier terme 2*x^6/(3*15*14) ~ 1e-13 -> x^2 ~ 6.8e-5
+// Le Dl est en O[x]^10  (cad on va jusqu'au terme en x^8 compris)
+// Approx: terme 2*x^6/(3*15*14) ~ 1e-13 -> x^2 ~ 6.8e-5
 {
   double x2 = x*x;
-  if(app || x2<6.8e-5) return 1. - x2/3.*(1. - 2.*x2/15.*(1. - x2/14.));
+  if(app || x2<6.8e-5) return 1.-x2/3.*(1.-2.*x2/15.*(1.-x2/14.*(1.-2.*x2/45.)));
   x2 = sin(x)/x;
   return x2*x2;
@@ -343 +345 @@
 // Calcul de [sin(N*x)/sin(x)]^2  avec N entier positif
 // ATTENTION: cf remarque pour N entier dans SinNXsX
+//            maximum de la fonction: N^2
 // Approx: dernier terme x^4*2*N^4/45 ~ 1e-13 -> x^2 ~ 1.5e-6/N^2
 {
@@ -349 +352 @@
   if(app || sx*sx<1.5e-6/N2) {
     double x2 = asin(sx); x2 *= x2;
-    return N2*(1. - (N-1.)*(N+1.)/3.*x2*(1. - (2.*N2-3.)/15.*x2));
+    //return N2*(1.-(N*N-1.)/3.*x2);
+    return N2*(1.-(N-1.)*(N+1.)/3.*x2*(1.-(2.*N2-3.)/15.*x2));
   }
   sx = sin((double)N*x)/sx;