Stochastic hyperfine interactions modeling library. The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than $A_{22}$ can be neglected.Program summaryProgram title: SHIMLCatalogue identifier: AEIF_v1_0Program summary URL: obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL 3No. of lines in distributed program, including test data, etc.: 8224No. of bytes in distributed program, including test data, etc.: 312 348Distribution format: tar.gzProgramming language: C$Computer:$ AnyOperating system: LINUX, OS X$RAM:$ Varies$Classification: 7$.4External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4]Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), M”ossbauer effect (ME), muon spin rotation ($mu $SR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When interactions fluctuate at rates comparable to the time scale of a hyperfine method, there is a loss in signal coherence, and spectra are damped. The degree of damping can be used to determine fluctuation rates, provided that theoretical expressions for spectra can be derived for relevant physical models of the fluctuations. SHIML provides routines to help researchers quickly develop code to incorporate stochastic models of fluctuating hyperfine interactions in calculations of hyperfine spectra.Solution method: Calculations are based on the method for modeling stochastic hyperfine interactions for PAC by Winkler and Gerdau [5]. The method is extended to include other hyperfine methods following the work of Dattagupta [6]. The code provides routines for reading model information from text files, allowing researchers to develop new models quickly without the need to modify computer code for each new model to be considered.$Restrictions:$ In the present version of the code, only methods that measure the hyperfine interaction on one probe spin state, such as PAC, $mu $SR, and NMR, are supported.