Added documentation for most modules

Only Spinors and Dirac are missing.

docs/make.jl

@@ -9,6 +9,10 @@ makedocs(sitename="LatticeGPU", modules=[LatticeGPU], doctest=true,
              "LatticeGPU.jl" => "index.md", 
              "Space-time" => "space.md",
              "Groups and algebras" => "groups.md",
-             "Fields" => "fields.md"
+             "Fields" => "fields.md",
+             "Yang-Mills" => "ym.md",
+             "Gradient flow" => "flow.md",
+             "Schrödinger Functional" => "sf.md",
+             "Input Output" => "io.md"
              ], 
          repo = "https://igit.ific.uv.es/alramos/latticegpu.jl")

docs/src/fields.md

@@ -10,10 +10,11 @@ gauge fields `SU3`, for scalar fields `Float64`). We have:
   direction.
 - `N` scalar fields: `N` elemental types at each spacetime point.
 
-For all these fields the spacetime point are ordered in memory
+Fields can have **naturaL indexing**, where the memory layout follows
-according to the point-in-block and block indices (see
+the point-in-block and block indices (see
-[`SpaceParm`](@ref)). An execption is the [`scalar_field_point`](@ref)
+[`SpaceParm`](@ref)). Fields can also have **lexicographic indexing**,
-fields. 
+where points are labelled by a D-dimensional index (see [`scalar_field_point`](@ref)).
+
 
 ## Initialization
 

docs/src/flow.md

@@ -0,0 +1,47 @@
+# Gradient flow
+
+The gradient flow equations can be integrated in two different ways:
+1. Using a fixed step-size integrator. In this approach one fixes the
+   step size $\epsilon$ and the links are evolved from
+   $V_\mu(t)$ to $V_\mu(t +\epsilon)$ using some integration
+   scheme. 
+1. Using an adaptive step-size integrator. In this approach one fixes
+   the tolerance $h$ and the links are evolved for a time $t_{\rm
+   end}$ (i.e. from $V_\mu(t)$ to $V_\mu(t +t_{\rm end})$)
+   with the condition that the maximum error while advancing is not
+   larger than $h$.
+   
+In general adaptive step size integrators are much more efficient, but
+one loses the possibility to measure flow quantities at the
+intermediate times $\epsilon, 2\epsilon, 3\epsilon,...$. Adaptive
+step size integrators are ideal for finite size scaling studies, while
+a mix of both integrators is the most efficient approach in scale
+setting applications. 
+
+## Integration schemes
+
+```@docs
+FlowIntr
+wfl_euler
+zfl_euler
+wfl_rk2
+zfl_rk2
+wfl_rk3
+zfl_rk3
+```
+
+## Integrating the flow equations
+
+```@docs
+flw
+flw_adapt
+```
+
+## Observables
+
+```@docs
+Eoft_plaq
+Eoft_clover
+Qtop
+```
+

docs/src/groups.md

@@ -153,6 +153,10 @@ projalg
 ## Generic `Algebra` methods
 
 ```@docs
+dot
+norm
+norm2
+normalize
 exp
 expm
 alg2mat

docs/src/io.md

@@ -0,0 +1,14 @@
+
+# Input/Output
+
+## Configurations
+
+Routines to read/write and import gauge configurations.
+```@docs
+read_cnfg
+save_cnfg
+import_bsfqcd
+import_lex64
+import_cern64
+```
+

docs/src/sf.md

@@ -0,0 +1,9 @@
+# Schödinger Functional
+
+Specific SF observables and routines
+
+```@docs
+setbndfield
+sfcoupling
+```
+

docs/src/space.md

@@ -3,7 +3,10 @@
 
 D-dimensional lattice points are labeled by two ordered integer
 numbers: the point-in-block index ($$b$$ in the figure below) and the
-block index ($$r$$ in the figure below). The routines [`up`](@ref) and
+block index ($$r$$ in the figure below). This is called **natural
+indexing**, in contrast with the **lexicographic indexing**  where points on
+the lattice are represented by a D-dimensional `CartesianIndex`.
+The routines [`up`](@ref) and
 [`dw`](@ref) allow you to displace to the neighboring points of the
 lattice. 
 ![D dimensional lattice points are labeled by its

docs/src/ym.md

@@ -0,0 +1,59 @@
+
+# Simulating Yang-Mills on the lattice 
+
+```@docs
+GaugeParm
+YMworkspace
+ztwist
+```
+
+## Gauge actions and forces
+
+Routines to compute the gauge action.
+```@docs
+gauge_action
+```
+
+Routines to compute the force derived from gauge actions. 
+
+```@docs
+force_gauge
+```
+
+### Force field refresh
+
+Algebra fields with **natural indexing** can be randomized.
+```@docs
+randomize!
+```
+
+
+## Basic observables
+
+Some basic observable.
+```@docs
+plaquette
+```
+
+## HMC simulations
+
+### Integrating the EOM
+
+```@docs
+IntrScheme
+leapfrog
+omf2
+omf4
+MD!
+```
+
+### HMC algorithm
+
+```@docs
+hamiltonian
+HMC!
+```
+
+
+
+

src/LatticeGPU.jl

@@ -40,6 +40,7 @@ include("YM/YM.jl")
 using .YM
 export ztwist
 export YMworkspace, GaugeParm, force0_wilson!, field, field_pln, randomize!, zero!, norm2
+export force_gauge, MD!
 export gauge_action, hamiltonian, plaquette, HMC!, OMF4!
 export Eoft_clover, Eoft_plaq, Qtop
 export FlowIntr, wfl_euler, zfl_euler, wfl_rk2, zfl_rk2, wfl_rk3, zfl_rk3

src/MD/MD.jl

@@ -24,6 +24,11 @@ const r1omf2 =  0.1931833275037836
 const r2omf2 =  0.5
 const r3omf2 =  1 - 2*r1omf2
 
+"""
+        struct IntrScheme{N, T}
+
+Integrator for the molecular dynamics.
+"""
 struct IntrScheme{N, T}
     r::NTuple{N, T}
     eps::T
@@ -31,8 +36,23 @@ struct IntrScheme{N, T}
 end
 
 
+"""
+        omf2(::Type{T}, eps, ns)
+
+Second order Omelyan integrator with `eps` stepsize and `ns` steps.
+"""
 omf2(::Type{T}, eps, ns) where T = IntrScheme{3,T}((r1omf2,r2omf2,r3omf2), eps, ns)
+"""
+        omf4(::Type{T}, eps, ns)
+
+Fourth order Omelyan integrator with `eps` stepsize and `ns` steps.
+"""
 omf4(::Type{T}, eps, ns) where T = IntrScheme{6,T}((r1omf4,r2omf4,r3omf4,r4omf4,r5omf4,r6omf4), eps, ns)
+"""
+        leapfrog(::Type{T}, eps, ns)
+
+Leapfrog integrator with `eps` stepsize and `ns` steps.
+"""
 leapfrog(::Type{T}, eps, ns) where T = IntrScheme{2,T}((0.5,1.0), eps, ns)
 
 

src/YM/YM.jl

@@ -20,6 +20,19 @@ using ..MD
 
 import Base.show
 
+"""
+        struct GaugeParm{T,G,N}
+
+Structure containning the parameters of a pure gauge simulation. These are:
+- beta: Type `T`. The bare coupling of the simulation
+- c0: Type `T`. LatticeGPU supports the simulation of gauge actions made of 1x1 Wilson Loops and 2x1 Wilson loops. The parameter c0 defines the coefficient on the simulation of the 1x1 loops. Some common choices are:
+  - c0=1: Wilson plaquette action
+  - c0=5/3: Tree-level improved Lüscher-Weisz action.
+  - c0=3.648: Iwasaki gauge action
+- cG: Tuple (`T`, `T`). Boundary improvement parameters.
+- ng: `Int64`. Rank of the gauge group.
+- Ubnd: Boundary field for SF boundary conditions
+"""
 struct GaugeParm{T,G,N}
     beta::T
     c0::T
@@ -63,6 +76,21 @@ function Base.show(io::IO, gp::GaugeParm{T, G, N}) where {T,G,N}
     return nothing
 end
 
+"""
+        struct YMworkspace{T}
+
+Structure containing memory workspace that is resused by different routines in order to avoid allocating/deallocating time.
+The parameter `T` represents the precision of the simulation (i.e. single/double). The structure contains the following components
+- GRP: Group being simulated
+- ALG: Corresponding Algebra 
+- PRC: Precision (i.e. `T`)
+- frc1: Algebra field with natural indexing.
+- frc2: Algebra field with natural indexing.
+- mom:  Algebra field with natural indexing.
+- U1:   Group field with natural indexing.
+- cm:   Complex field with lexicographic indexing.
+- rm:   Real field with lexicographic indexing.
+"""
 struct YMworkspace{T}
     GRP
     ALG
@@ -110,7 +138,11 @@ function Base.show(io::IO, ymws::YMworkspace)
     return nothing
 end
 
+"""
+        function ztwist(gp::GaugeParm{T,G}, lp::SpaceParm{N,M,B,D}[, ipl])
 
+Returns the twist factor. If a plane index is passed, returns the twist factor as a complex{T}. If this is not provided, returns a tuple, containing the factor of each plane.
+"""
 function ztwist(gp::GaugeParm{T,G}, lp::SpaceParm{N,M,B,D}) where {T,G,N,M,B,D}
 
     function plnf(ipl)
@@ -133,10 +165,10 @@ include("YMfields.jl")
 export randomize!, zero!, norm2
 
 include("YMact.jl")
-export krnl_plaq!, force0_wilson!
+export krnl_plaq!, force_gauge, force_wilson
 
 include("YMhmc.jl")
-export gauge_action, hamiltonian, plaquette, HMC!, OMF4!
+export gauge_action, hamiltonian, plaquette, HMC!, MD!
 
 include("YMflow.jl")
 export FlowIntr, flw, flw_adapt

src/YM/YMact.jl

@@ -335,9 +335,9 @@ function krnl_force_impr_pln!(frc1, frc2, U::AbstractArray{T}, c0, c1, Ubnd, cG,
 end
 
 """ 
-    function force_wilson(ymws::YMworkspace, U, lp::SpaceParm)
+    function force_gauge(ymws::YMworkspace, U, gp::GaugeParm, lp::SpaceParm)
 
-Computes the force deriving from the Wilson plaquette action, without
+Computes the force deriving from an improved action with parameter `c0`, without
 the prefactor 1/g0^2, and assign it to the workspace force `ymws.frc1`
 """    
 function force_gauge(ymws::YMworkspace, U, c0, cG, gp::GaugeParm, lp::SpaceParm)
@@ -354,8 +354,15 @@ function force_gauge(ymws::YMworkspace, U, c0, cG, gp::GaugeParm, lp::SpaceParm)
     end
     return nothing
 end
-
 force_gauge(ymws::YMworkspace, U, c0, gp, lp) = force_gauge(ymws, U, c0, gp.cG[1], gp, lp)
+force_gauge(ymws::YMworkspace, U, gp, lp) = force_gauge(ymws, U, gp.c0, gp.cG[1], gp, lp)
+
+""" 
+    function force_wilson(ymws::YMworkspace, U, gp::GaugeParm, lp::SpaceParm)
+
+Computes the force deriving from the Wilson plaquette action, without
+the prefactor 1/g0^2, and assign it to the workspace force `ymws.frc1`
+"""    
 force_wilson(ymws::YMworkspace, U, gp::GaugeParm, lp::SpaceParm) = force_gauge(ymws, U, 1, gp, lp)
 force_wilson(ymws::YMworkspace, U, cG, gp::GaugeParm, lp::SpaceParm) = force_gauge(ymws, U, 1, gp.cG[1], gp, lp)
 

src/YM/YMfields.jl

@@ -9,6 +9,11 @@
 ### created: Thu Jul 15 15:16:47 2021
 ###                               
 
+"""
+        function randomize!(f, lp::SpaceParm, ymws::YMworkspace)
+
+Given an algebra field with natural indexing, this routine sets the components to random Gaussian distributed values. If SF boundary conditions are used, the force at the boundaries is set to zero.
+"""
 function randomize!(f, lp::SpaceParm, ymws::YMworkspace) 
         
     if ymws.ALG == SU2alg

src/YM/YMflow.jl

@@ -10,6 +10,11 @@
 ###                               
 
 
+"""
+        struct FlowIntr{N,T}
+
+Structure containing info about a particular flow integrator
+"""
 struct FlowIntr{N,T}
     r::T
     e0::NTuple{N,T}
@@ -26,11 +31,46 @@ struct FlowIntr{N,T}
 end
 
 # pre-defined integrators
+"""
+        wfl_euler(::Type{T}, eps::T, tol::T)
+
+Euler scheme integrator for the Wilson Flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 wfl_euler(::Type{T}, eps::T, tol::T) where T = FlowIntr{0,T}(one(T),(),(),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
+
+"""
+        zfl_euler(::Type{T}, eps::T, tol::T)
+
+Euler scheme integrator for the Zeuthen flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 zfl_euler(::Type{T}, eps::T, tol::T) where T = FlowIntr{0,T}(one(T),(),(),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
+
+"""
+        wfl_rk2(::Type{T}, eps::T, tol::T)
+
+Second order Runge-Kutta integrator for the Wilson flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 wfl_rk2(::Type{T}, eps::T, tol::T)   where T = FlowIntr{1,T}(one(T)/2,(-one(T)/2,),(one(T),),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
+
+"""
+        zfl_rk2(::Type{T}, eps::T, tol::T)
+
+Second order Runge-Kutta integrator for the Zeuthen flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 zfl_rk2(::Type{T}, eps::T, tol::T)   where T = FlowIntr{1,T}(one(T)/2,(-one(T)/2,),(one(T),),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
+
+"""
+        wfl_rk3(::Type{T}, eps::T, tol::T)
+
+Third order Runge-Kutta integrator for the Wilson flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 wfl_rk3(::Type{T}, eps::T, tol::T)   where T = FlowIntr{2,T}(one(T)/4,(-17/36,-one(T)),(8/9,3/4),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
+
+"""
+        Zfl_rk3(::Type{T}, eps::T, tol::T)
+
+Third order Runge-Kutta integrator for the Zeuthen flow. The fixed step size is given by `eps` and the tolerance for the adaptive integrators by `tol`. 
+"""
 zfl_rk3(::Type{T}, eps::T, tol::T)   where T = FlowIntr{2,T}(one(T)/4,(-17/36,-one(T)),(8/9,3/4),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
 
 function Base.show(io::IO, int::FlowIntr{N,T}) where {N,T}
@@ -122,6 +162,11 @@ function krnl_add_zth!(frc, frc2::AbstractArray{TA}, U::AbstractArray{TG}, lp::S
     return nothing
 end
 
+"""
+        function flw(U, int::FlowIntr{NI,T}, ns::Int64, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)
+
+Integrates the flow equations with the integration scheme defined by `int` performing `ns` steps with fixed step size. The configuration `U` is overwritten.   
+"""
 function flw(U, int::FlowIntr{NI,T}, ns::Int64, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T}    
     @timeit "Integrating flow equations" begin
         for i in 1:ns
@@ -152,6 +197,11 @@ flw(U, int::FlowIntr{NI,T}, ns::Int64, gp::GaugeParm, lp::SpaceParm, ymws::YMwor
 # Adaptive step size integrators
 ##
 
+"""
+        function flw_adapt(U, int::FlowIntr{NI,T}, tend::T, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)
+
+Integrates the flow equations with the integration scheme defined by `int` using the adaptive step size integrator up to `tend` with the tolerance defined in `int`. The configuration `U` is overwritten.   
+"""
 function flw_adapt(U, int::FlowIntr{NI,T}, tend::T, epsini::T, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T}
 
     eps = int.eps_ini
@@ -201,7 +251,7 @@ flw_adapt(U, int::FlowIntr{NI,T}, tend::T, gp::GaugeParm, lp::SpaceParm, ymws::Y
 """
     function Eoft_plaq([Eslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)
 
-Measure the action density `E(t)` using the plaquette discretization. If the argument `Eslc`
+Measure the action density `E(t)` using the plaquette discretization. If the argument `Eslc` is given
 the contribution for each Euclidean time slice and plane are returned.
 """
 function Eoft_plaq(Eslc, U, gp::GaugeParm{T,G,NN}, lp::SpaceParm{N,M,B,D}, ymws::YMworkspace) where {T,G,NN,N,M,B,D}
@@ -277,10 +327,9 @@ function krnl_plaq_pln!(plx, U::AbstractArray{T}, Ubnd, ztw, ipl, lp::SpaceParm{
 end
 
 """
-    Qtop([Qslc,] U, lp, ymws)
+    Qtop([Qslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)
 
-Measure the topological charge `Q` of the configuration `U`. If the argument `Qslc` is present
+Measure the topological charge `Q` of the configuration `U` using the clover definition of the field strength tensor. If the argument `Qslc` is present the contribution for each Euclidean time slice are returned. Only wors in 4D.
-the contribution for each Euclidean time slice are returned.
 """
 function Qtop(Qslc, U, gp::GaugeParm, lp::SpaceParm{4,M,B,D}, ymws::YMworkspace) where {M,B,D}
 

src/YM/YMhmc.jl

@@ -13,7 +13,7 @@
     
     function gauge_action(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)
 
-Returns the value of the gauge plaquette action for the configuration U. The parameters `\beta` and `c0` are taken from the `gp` structure. 
+Returns the value of the gauge action for the configuration U. The parameters `\beta` and `c0` are taken from the `gp` structure. 
 """
 function gauge_action(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace{T}) where T <: AbstractFloat
 
@@ -37,6 +37,11 @@ function gauge_action(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace{T}) whe
     return S
 end
 
+"""
+        function plaquette(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)
+
+Computes the average plaquette for the configuration `U`.
+"""
 function plaquette(U, lp::SpaceParm{N,M,B,D}, gp::GaugeParm, ymws::YMworkspace) where {N,M,B,D}
 
     ztw = ztwist(gp, lp)
@@ -48,7 +53,12 @@ function plaquette(U, lp::SpaceParm{N,M,B,D}, gp::GaugeParm, ymws::YMworkspace)
 
     return CUDA.mapreduce(real, +, ymws.cm)/(prod(lp.iL)*lp.npls)
 end
-    
+
+"""
+        function hamiltonian(mom, U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)
+
+Returns the Energy ``H = \\frac{p^2}{2}+S[U]``, where the momenta field is given by `mom` and the configuration by `U`.
+"""
 function hamiltonian(mom, U, lp, gp, ymws)
     @timeit "Computing Hamiltonian" begin
         K = CUDA.mapreduce(norm2, +, mom)/2 
@@ -58,6 +68,11 @@ function hamiltonian(mom, U, lp, gp, ymws)
     return K+V
 end
 
+"""
+        HMC!(U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace; noacc=false)
+
+Performs a HMC step (molecular dynamics integration and accept/reject step). The configuration `U` is updated ans function returns the energy violation and if the configuration was accepted in a tuple.
+"""
 function HMC!(U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace{T}; noacc=false) where T
 
     @timeit "HMC trayectory" begin
@@ -92,6 +107,11 @@ function HMC!(U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspac
 end
 HMC!(U, eps, ns, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace{T}; noacc=false) where T = HMC!(U, omf4(T, eps, ns), lp, gp, ymws; noacc=noacc)
 
+"""
+        function MD!(mom, U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)
+
+Performs the integration of a molecular dynamics trajectory starting from the momentum field `mom` and the configuration `U` according to the integrator described by `int`.
+"""
 function MD!(mom, U, int::IntrScheme{NI, T}, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace{T}) where {NI, T <: AbstractFloat}
     
     @timeit "MD evolution" begin

src/YM/YMsf.jl

@@ -10,9 +10,9 @@
 ###                               
 
 """ 
-    sfcoupling(U, lp::SpaceParm{N,M,B,D}, gp::GaugeParm, ymws::YMworkspace) where {N,M,B,D}
+    sfcoupling(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace) 
 
-Measures the Schrodinger Functional coupling `ds/d\eta` and `d^2S/d\eta d\nu`. 
+Measures the Schrodinger Functional coupling ``{\\rm d}S/{\\rm d}\\eta`` and ``{\\rm d}^2S/{\\rm d}\\eta d\nu``. 
 """
 function sfcoupling(U, lp::SpaceParm{N,M,B,D}, gp::GaugeParm, ymws::YMworkspace) where {N,M,B,D}
 
@@ -89,7 +89,11 @@ end
     return exp(X)
 end
     
+"""
+        function setbndfield(U, phi, lp::SpaceParm)
 
+Sets abelian boundary fields with phases `phi[1]` and `phi[2]` to the configuration `U` at time salice ``x_0=0``.
+"""
 function setbndfield(U, phi, lp::SpaceParm{N,M,B,D}) where {N,M,B,D}
 
     CUDA.@sync begin