Merge branch 'dev-improve-polylog'

README.md

@@ -78,9 +78,17 @@ The compilation process creates the following results
       difference between two successive terms at which the series
       expansion (6) is truncated.
 
-   * `integer LiInf = 1000`
+   * `real(kind=prec) :: Lidel = 1e-15`
+
+      difference $`|\delta_i|`$ between two successive terms at which the
+      series expansion for
+
+      ```math
+        {\rm Li}_n(x) = \sum_{i=1}^\infty  \frac{x^i}{i^n}
+                      = \sum_{i=1}^\infty \delta_i
+      ```
+      is truncated.
 
-      number of terms in the expansion of classical polylogarithms.
 
    * `real(kind=prec) :: hCircle = 1.1`
 

checks/test.f90

@@ -456,6 +456,14 @@ CONTAINS
     call test_one_flat( (/ (0._prec,0.), (1._prec,0.), (0.1_prec,-0.1_prec), (-1.3_prec,10.2_prec), (0.4_prec,0._prec) /) , ref, 'F.19')
 
 
+    ref = (0.6492441149301267712849185177612894261440132_prec,2.76692869057070821067245201199781913943_prec)
+    call iprint('  testing GPL G.1 ...',-1)
+    res = G([ toinum( (-1641._prec,4682._prec)/5000. ),&
+              toinum( (-1187._prec,4827._prec)/5000. ),&
+              toinum( 1069._prec/5000., +1_1 ), toinum( 787._prec / 5000., -1_1)], toinum(1._prec) )
+    call check(res,ref, ttol=5.e-9_prec)
+
+
 
   end subroutine do_GPL_tests
   

src/globals.f90

@@ -16,7 +16,7 @@ MODULE globals
 
   ! The following parameters control the accuracy of the evaluation
   real(kind=prec), protected :: MPLdelta = zero          ! if the MPL sum changes less then del it is truncated.
-  integer, protected :: PolylogInfinity = 1000           ! expansion order for Polylogs
+  real(kind=prec), protected ::  Lidelta = zero          ! like MPLdelta but for polylogs
   real(kind=prec), protected :: HoelderCircle = 1.1_prec ! when to apply Hoelder convolution?
   integer, parameter :: PolyLogCacheSize(2) = (/ 5, 100 /)
         ! = (/ mmax, n /). At most n polylogs with weight mmax will be cached
@@ -46,11 +46,10 @@ CONTAINS
   END SUBROUTINE parse_cmd_args
 #endif
 
-  SUBROUTINE SET_OPTIONS(mpldel, liinf, hcircle)
-    real(kind=prec), optional :: hcircle, mpldel
-    integer, optional :: liinf
+  SUBROUTINE SET_OPTIONS(mpldel, lidel, hcircle)
+    real(kind=prec), optional :: hcircle, mpldel, lidel
     if (present(MPLdel)) MPLdelta = mpldel
-    if (present(liinf)) PolyLogInfinity = liinf
+    if (present( Lidel)) LiDelta  =  lidel
     if (present(hcircle)) HoelderCircle = hcircle
   END SUBROUTINE
 

src/maths_functions.f90

@@ -31,14 +31,19 @@ CONTAINS
   FUNCTION naive_polylog(m,x) result(res)
     ! Computes the classical polylogarithm Li_m(x) using series representation up to order n
     integer :: m
-    complex(kind=prec) :: x, res
+    complex(kind=prec) :: x, res, del
     integer(kind=ikin) :: i
     res=0._prec
-    do i=1,PolylogInfinity
+
+    i = 1
+    del = 1._prec
+    do while (abs(del) > zero)
       if(i**m.lt.0) return ! roll over
       if(abs(x**i).lt.1.e-250_prec) return
-      res = res+x**i/i**m
-    enddo
+      del = x**i/i**m
+      res = res+del
+      i = i+1
+    end do
   END FUNCTION naive_polylog
 
   FUNCTION Li2(x)