add documentation

GX-AnalyticContinuation/README.md

@@ -0,0 +1,69 @@
+## GreenX library - Analytic Continuation 
+
+The analytic continuation component provides routines to interpolate functions using the thiele pade interpolant.
+
+> [!Note]
+> **Key Features**
+> - basic thiele pade algorithm
+> - greedy algorithm for thiele pade to enhance numerical stability
+> - arbitrary precision arithmetic using the GMP library for even more numerical stability
+
+## Usage 
+
+### Basic usage pade interpolation
+
+> **Default**:
+> - use the greedy algorithm
+> - use 64 bit float precision (double precision) when GMP is not linked
+> - use 128 bit float precision (quadrupel precision) when linked against GMP
+
+```fortran
+use gx_ac, only: create_thiele_pade, evaluate_thiele_pade_at, & 
+                 free_params, params
+
+
+complex(dp), allocatable :: x_ref(:), y_ref(:)
+
+type(params)          :: params_thiele
+complex(dp), dimension(:), allocatable :: x_query
+complex(dp), dimension(:), allocatable :: y_return
+integer                                :: n_par         ! number of pade parameters
+
+allocate(x_ref(npar), y_ref(npar))
+allocate(x_query(10), y_return(10)) 
+
+! initialize x_ref, y_ref and x_quer
+
+! create the interpolation model and store it in struct
+params_thiele = create_thiele_pade(n_par, x_ref, y_ref)
+
+! evaluate the interpolation model at given x points
+y_return(1:10) =  evaluate_thiele_pade_at(params_thiele, x_query)
+
+! Clean-up
+call free_params(params_thiele)
+```
+
+### Advanced usage pade interpolation
+e.g. to use the plain thiele pade algorithm (non-greedy) with 10 fold float precision: 
+```fortran
+params_thiele = create_thiele_pade(n_par, x_ref, y_ref, do_greedy=.false., precision=320)
+```
+e.g. to use the greedy algorithm with the faster double precision fortran implementation (doesn't make use of GMP even if it is linked) :
+```fortran
+params_thiele = create_thiele_pade(n_par, x_ref, y_ref, do_greedy=.true., precision=64)
+```
+
+### Availability of GMP at runtime
+
+It is possible to check whether GMP is linked against GreenX at runtime:
+```fortran
+use gx_ac, only: arbitrary_precision_available, create_thiele_pade
+
+if (arbitrary_precision_available) then
+    ! this will succeed
+    params_thiele = create_thiele_pade(n_par, x_ref, y_ref, do_greedy=.false., precision=320)
+else if (.not. arbitrary_precision_available) then 
+    ! this will result in an error
+    params_thiele = create_thiele_pade(n_par, x_ref, y_ref, do_greedy=.false., precision=320)
+end if 

GX-AnalyticContinuation/api/gx_ac.F90

@@ -33,6 +33,12 @@ module gx_ac
        complex(kind=dp), dimension(:), allocatable :: a_par
    end type params 
 
+#ifdef GMPXX_FOUND
+   logical, parameter :: arbitrary_precision_available = .true.
+#else
+   logical, parameter :: arbitrary_precision_available = .false.
+#endif
+
 #ifdef GMPXX_FOUND
    interface