Numerical Libraries

Naming: first letter = precision (s single, d double, c complex, z double complex), next two = matrix type (ge general, sy symmetric, po positive-definite, tr triangular), rest = operation.

32.1 BLAS & LAPACK

daxpy, ddot, dnrm2, dscal BLAS level 1 (vector) BLAS level 2 (matrix–vector)

BLAS level 3 (matrix–matrix) — the most optimized kernel in computing dgesv, dgetrf/dgetrs general linear systems (LU) dposv, dpotrf symmetric positive-definite (Cholesky) dsyev, dsyevd, dgeev dgesvd, dgesdd singular value decomposition

Naming: first letter = precision (s single, d double, c complex, z double complex), next two = matrix type (ge general, sy symmetric, po positive-definite, tr triangular), rest = operation. Optimized implementations: OpenBLAS, Intel MKL, AOCL (AMD), Apple Accelerate, BLIS, cuBLAS (GPU).

program lapack_demo
  implicit none
  integer, parameter :: n = 3
  real(8) :: A(n, n), b(n)
  integer :: ipiv(n), info
  A = reshape([4d0, 2d0, 1d0, 2d0, 5d0, 3d0, 1d0, 3d0, 6d0], [n, n])
  b = [1d0, 2d0, 3d0]
  call dgesv(n, 1, A, n, ipiv, b, n, info)     ! solve Ax = b (LU with partial pivoting)
  if (info /= 0) error stop "dgesv failed"
  print '(3f12.6)', b
end program lapack_demo

gfortran lapack_demo.f90 -llapack -lblas -o lapack_demo     # or link OpenBLAS / Intel MKL

32.2 Other classic & modern libraries

Fortran stdlib (fortran-lang/stdlib) community standard library: strings, sorting, stats, linalg, hashmaps, I/O, logging, quadrature, random FFTW (fftw3.f03) fast Fourier transforms

ScaLAPACK, PETSc, Trilinos (ForTrilinos), hypre, MUMPS parallel linear algebra & solvers large sparse eigenproblems SUNDIALS (Fortran interfaces) ODE/DAE solvers

MINPACK, QUADPACK, ODEPACK, SLATEC (modernized versions on GitHub) nonlinear equations, quadrature, ODEs NetCDF-Fortran, HDF5 scientific data I/O json-fortran, toml-f config/data formats NAG Library, IMSL commercial numerical libraries GNU Scientific Library bindings

32.3 Using stdlib with fpm

# fpm.toml
[dependencies]
stdlib = "*"

use stdlib_sorting, only: sort
use stdlib_stats, only: mean, var
use stdlib_linalg, only: eye, diag, solve, det
use stdlib_strings, only: to_string, starts_with
call sort(x)
print *, mean(x), var(x), to_string(3.14_dp)