Linear Algebra Module Documentation

Documentation for BELFEM's backend-agnostic linear algebra API.

Contents

Guides

• linalg_usage_guide.md - Comprehensive usage guide for BELFEM linear algebra
  • Overview of backend abstraction (Armadillo vs. Blaze)
  • Vector and Matrix API reference
  • 26 free functions (solvers, decompositions, utilities)
  • Performance tips and common patterns
  • Backend selection and interoperability
• lapack_usage_guide.md - Maintainer guide for the unified LAPACK wrappers (src/linalg/lapack/)
  • gesv, posv, getrf/getri, gels, gemm, gesvd, geev, gees — one body, both backends, four datatypes
  • Shared contracts: AbortOnError/info error model, pivot policy, the three Work-buffer models
  • Design pillars: int_t = LAPACK integer, complex glue, leading dimensions, hidden Fortran char lengths
  • Checklist for adding a new routine, pitfalls table

Quick Reference

Core Types

Type	Description	File
Vector<T>	Column vector (n×1)	cl_Vector.hpp
Matrix<T>	Dense matrix (m×n)	cl_Matrix.hpp

Categories of Free Functions

Category	Functions
Linear Algebra	dot, cross, crossmat, norm, trans
Solvers	gesv, posv, inv, inv2, inv3, det, eigen
Utilities	linspace, append, combine, reverse, sort, unique
Aggregates	sum, max, min
Polynomials	polyval, dpolyval, ddpolyval, polyfit
Statistics	r2

Backend Selection

# Armadillo (default on Linux; Blaze is the default on Apple)
cmake -DUSE_MATRIX_ARMADILLO=ON -DUSE_MATRIX_BLAZE=OFF ..
 
# Blaze
cmake -DUSE_MATRIX_BLAZE=ON -DUSE_MATRIX_ARMADILLO=OFF ..

See Also

• Source code - header files in src/linalg/
• Armadillo backend - Armadillo-specific implementations
• Blaze backend - Blaze-specific implementations
• Sparse module - Sparse matrix solvers
• Root documentation - General BELFEM documentation