use the notation from the paper in the code

Prog/splittings.f90

@@ -52,20 +52,20 @@ subroutine init_splittings(split)
     nrofsplits = 41
     Allocate(splits(nrofsplits))
 
-    ! V-T Euler
+    ! V-T Euler / NS_1 1
     call createsplit(splits(1), 1, 1)
     splits(1)%Tcoeffs(1) = 1.0
 
     splits(1)%Vcoeffs(1) = 1.0
 
-    ! T - V  Euler
+    ! T - V  Euler 
     call createsplit(splits(2), 2, 1)
     splits(2)%Tcoeffs(1) = 0.0
     splits(2)%Tcoeffs(2) = 1.0
 
     splits(2)%Vcoeffs(1) = 1.0
 
-    !T-V-T leapfrog
+    !T-V-T leapfrog S_1 2
     call createsplit(splits(3), 2, 2)
     splits(3)%Tcoeffs(1) = 0.5
     splits(3)%Tcoeffs(2) = 0.5
@@ -82,7 +82,7 @@ subroutine init_splittings(split)
     splits(4)%Vcoeffs(2) = 0.5
 
 
-    ! The MacLachlan/Omelyan Integrator. A derivation can be found here https://www.massey.ac.nz/~rmclachl/sisc95.pdf
+    ! The MacLachlan/Omelyan Integrator, S_2 2. A derivation can be found here https://www.massey.ac.nz/~rmclachl/sisc95.pdf
     call createsplit(splits(5), 3, 3)
     splits(5)%Tcoeffs(1) = 0.1931833275037836
     splits(5)%Tcoeffs(2) = (1.0 - 2*0.1931833275037836)
@@ -159,7 +159,7 @@ subroutine init_splittings(split)
 
 
     ! Symmetric from symmetric
-    ! This corresponds to the classical Forest/Ruth algorithm
+    ! S_3 4 This corresponds to the classical Forest/Ruth algorithm
     call createsplit(splits(10), 4, 4)
     alpha = 1/(2-2**(1.D0/3.D0) )
     beta = 1.D0-2.D0*alpha
@@ -173,7 +173,7 @@ subroutine init_splittings(split)
     splits(10)%Vcoeffs(3) = beta
     splits(10)%Vcoeffs(4) = alpha
 
-    ! Another variant of symmetric with symmetric by Suzuki
+    ! SS_5 4 Another variant of symmetric with symmetric by Suzuki
     call createsplit(splits(11), 6, 6)
     alpha = 1.D0/(4-4**(1.D0/3.D0) )
     beta = 1 - 4*alpha
@@ -192,7 +192,7 @@ subroutine init_splittings(split)
     splits(11)%Vcoeffs(6) = splits(11)%Vcoeffs(2)
 
 
-    ! fourth order method from Omelyan, 2001, previously discovered by McLachlan 1995
+    ! S_5 4 fourth order method from Omelyan, 2001, previously discovered by McLachlan 1995
     call createsplit(splits(12), 5, 5)
     xi = 0.1720865590295143
     lam = -0.09156203075515678
@@ -255,7 +255,7 @@ subroutine init_splittings(split)
         splits(beg + n)%Vcoeffs(tmpint) = 0
     enddo
 
-    ! the variant with m=2 optimized for large step sizes in Blanes 2014, 2. order
+    ! SE_2 2 the variant with m=2 optimized for large step sizes in Blanes 2014, 2. order
     call createsplit(splits(23), 3, 3)
     splits(23)%Tcoeffs(1) = 0.21178
     splits(23)%Tcoeffs(2) = (1.0 - 2.0*splits(23)%Tcoeffs(1))
@@ -264,7 +264,7 @@ subroutine init_splittings(split)
     splits(23)%Vcoeffs = 0.5
     splits(23)%Vcoeffs(1) = 0.0
 
-    ! the variant with m=3 optimized for large step sizes in Blanes 2014, 2. Order
+    ! SE_3 2 the variant with m=3 optimized for large step sizes in Blanes 2014, 2. Order
     call createsplit(splits(24), 4, 4)
     alpha = 0.11888010966548
     beta = 0.29619504261126
@@ -278,7 +278,7 @@ subroutine init_splittings(split)
     splits(24)%Vcoeffs(3) = 1.D0 - 2.D0*beta
     splits(24)%Vcoeffs(4) = beta
 
-    ! the variant with m=4 optimized for large step sizes in Blanes 2014, 2. Order
+    ! SE_4 2 the variant with m=4 optimized for large step sizes in Blanes 2014, 2. Order
     call createsplit(splits(25), 5, 5)
     xi = 0.071353913450279725904
     lam = 0.268548791161230105820
@@ -296,8 +296,9 @@ subroutine init_splittings(split)
     splits(25)%Vcoeffs(4) = splits(25)%Vcoeffs(3)
     splits(25)%Vcoeffs(5) = splits(25)%Vcoeffs(2)
 
-    call createsplit(splits(26), 3, 3) !hermitian third order method with entirely complex coefficients
-!   , originally found by Suzuki 1990. Can be found in Blanes 2010
+    ! CH_2 3 hermitian third order method with entirely complex coefficients,
+    ! originally found by Suzuki 1990. Can be found in Blanes 2010
+    call createsplit(splits(26), 3, 3) 
     alpha = CMPLX(1.D0/2.D0, Sqrt(3.D0)/6.D0, kind=kind(0.D0))
     splits(26)%Tcoeffs(1) = alpha/2.D0
     splits(26)%Tcoeffs(2) = 1.D0/2.D0
@@ -322,7 +323,7 @@ subroutine init_splittings(split)
     splits(27)%Vcoeffs(4) = 1.D0/4.D0
     splits(27)%Vcoeffs(5) = 1.D0/4.D0
 
-    ! The optimized Order-4 method from here: http://www.gicas.uji.es/Research/splitting-complex.html
+    ! CSR_4 4, The optimized Order-4 method from here: http://www.gicas.uji.es/Research/splitting-complex.html
     call createsplit(splits(28), 5, 5)
 
     splits(28)%Tcoeffs(1) = CMPLX(0.060078275263542357774, -0.060314841253378523039, kind=kind(0.D0))
@@ -351,7 +352,7 @@ subroutine init_splittings(split)
     splits(29)%Vcoeffs(3) = 0.2992014902086648372346181686254076026253
     splits(29)%Vcoeffs(4) = 0.2007985097913351627653818313745923973747
     
-    ! The order 6 method: http://www.gicas.uji.es/Research/splitting-complex.html
+    ! CSR_16 6 The order 6 method: http://www.gicas.uji.es/Research/splitting-complex.html
     call createsplit(splits(30), 17, 17)
     splits(30)%Vcoeffs = 1.D0/16
     splits(30)%Vcoeffs(1) = 0
@@ -388,7 +389,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(31)%Vcoeffs(4) = beta
 
 
-    ! My first own third order method, designed to be a hermitian sequence of Operators
+    ! CHR_3 3 My first own third order method, designed to be a hermitian sequence of Operators
     call createsplit(splits(32), 4, 4)
     beta = 1.D0/3.D0
     splits(32)%Tcoeffs(1) = 1.D0/24.D0*CMPLX(3.D0, -Sqrt(3.D0), dp)
@@ -411,7 +412,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(33)%Vcoeffs(1) = 0.5
     splits(33)%Vcoeffs(2) = 0.5
 
-    ! H_5 4 hermitian splitting with positive b's designed by me
+    ! CHR_5 4 hermitian splitting with positive b's designed by me
 
     call createsplit(splits(34), 6, 6)
     splits(34)%Tcoeffs(1) = CMPLX(0.077032770903379296850,-0.018324799648727332496, dp)
@@ -428,7 +429,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(34)%Vcoeffs(5) = splits(34)%Vcoeffs(3)
     splits(34)%Vcoeffs(6) = splits(34)%Vcoeffs(2)
 
-    ! A hermitian fourth order method as given in Suzuki 1990
+    ! CH_4 4 A hermitian fourth order method as given in Suzuki 1990
     call createsplit(splits(35), 5, 5)
     alpha = CMPLX(1.D0/2.D0, Sqrt(3.D0)/6.D0, kind=kind(0.D0))
     beta =  CMPLX(1.D0/2.D0, 0.2071067811865, dp)
@@ -444,7 +445,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(35)%Vcoeffs(4) = beta*conjg(alpha)
     splits(35)%Vcoeffs(5) = beta*alpha
 
-    ! The real sixth order method from Blanes 2002
+    ! S_10 6 The real sixth order method from Blanes 2002
     call createsplit(splits(36), 11, 11)
     splits(36)%Tcoeffs(1) = 0.0502627644003922
     splits(36)%Tcoeffs(2) = 0.413514300428344
@@ -475,7 +476,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(36)%Vcoeffs(10) = splits(36)%Vcoeffs(3)
     splits(36)%Vcoeffs(11) = splits(36)%Vcoeffs(2)
 
-    ! The phi(1,3) method in Hansen 2009
+    ! CS_3 4 The phi(1,3) method in Hansen 2009
     call createsplit(splits(37), 6, 6)
     alpha = cmplx(0.3243964040201712, 0.1345862724908067, dp)
     beta = 1.D0 - 2.D0*alpha
@@ -521,7 +522,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(39)%Vcoeffs(4) = conjg(splits(39)%Vcoeffs(3))
     splits(39)%Vcoeffs(5) = conjg(splits(39)%Vcoeffs(2))
     
-    ! The hermitian fifth order method
+    ! CHR_9 5 The hermitian fifth order method
     call createsplit(splits(40), 10, 10)
     splits(40)%Tcoeffs(1)=CMPLX(0.048475520387300861784614942150004872732496275960676605704430, &
     & 0.004320853677325454041666651926455479652308652682908398349854853, dp)
@@ -553,7 +554,7 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     
     
     
-    ! The hermitian sixth order method
+    ! CHR_15 6 The hermitian sixth order method
     call createsplit(splits(41), 16, 16)
     splits(41)%Tcoeffs(1)=CMPLX(0.095194656759747098611056828381842973876432181037008757210040895, &
     &-0.03705839851161959800834474467108207397222103451188259084113901385692675627401, dp)