BORIS - Borel Resummation with conformal mapping

Compilation and running

Clone the repository and compile with

git clone https://github.com/apik/boris.git
cd boris
cargo build --release

To check installation we provided number of internal tests available from

cargo test

To install produced binaries to working directory use

cargo install --path . --root INSTALL_DIR

Two binaries will be available INSTALL_DIR/bin/point and INSTALL_DIR/bin/scan

Description of implemented operation modes

Single parameter mode

cargo run --release --bin point -- input/point.toml

or with

INSTALL_DIR/bin/point input/point.toml

Example config file should contain information about original series coefficients, target resummation point(ep), resummation algorithm parameters(a,b,lam,q)

# info string
info = "Single point mode"
# # series
f = [ 2.0, -0.25, -0.0859375, 0.11442530392291644, -0.2875129509289455, 0.9561331447210607, -3.855754549203757 ]
# ep
ep=1
# a
a=0.375
# b
b   = 10.0
# lambda
lam = 1.42
# q
q=0.04

info is arbitrry text string passed directly to the output

Scan parameter mode

cargo run --release --bin scan -- -w [WORKERS] input/scan.toml

or with

INSTALL_DIR/bin/scan -w [WORKERS] input/scan.toml

In the scan mode parallel execution implemented with rayon is supported. Parameter [WORKERS] sets number of parallel threads and default value is equal to the number of CPU cores.

Sample config file is the following:

###
# Info string to be printed during program run
info = "nu^-1(n=0) = 1.70251"

###
# Series to be resumed, starts with constant term
f   = [2.0, -0.25, -0.0859375, 0.11442530392291644, -0.2875129509289455, 0.9561331447210607, -3.855754549203757]

### Fixed resummation parameters
# ep - final point
ep = 1
#  a - general fixed by symmetry considerations
a   = 0.375

### Resummation parameters to be scanned
# b [min, max, subdivisions]
b   = [0.0, 40.0, 80]
# lambda
lam = [0.0, 4.5, 225]
# q = q/2
q   = [0.0, 0.4, 40]


### Scan plateaus parameters in number of subdivisions units 
deltab   = 40
deltalam = 50
deltaq   = 1


### If provided results are saved in <dump> as .tsv file: b,lam,q,f(l),f(l-1),f(l-2)
# dump = gridNU

### Save final results
# output file name
out = "nuInvN0.m"


### Integration order
# set order of untegration rules, default 20
#n = 40

Now resummation parameters b,lam,q are defined on a grid with syntax [min,max,divisions].

After resummation in all grid points total error estimated and point minimaly sensitive to the resummation parameter detected. Parameters controling are deltab,deltalam,deltaq and are in units of grid steps.

Resummation results on all grid points can be dumped with dump= FILENAME and final result is saved in out=OUTFILE in the form {res_min, res_mean, sigma_mean}