*** WORK IN PROGRESS ***

Current API

Procedure	Type	Description	Optional arguments
solve(A,b)	function	Solve linear systems - one (b(:)) or many (b(:,:))	solve(A,b,overwrite_a,err): option to let A be destroyed, return state handler err
lstsq(A,b)	function	Solve non-square systems in a least squares sense - one (b(:)) or many (b(:,:))	lstsq(A,b,cond,overwrite_a,rank,err): cond is optional SVD cutoff; rank to return matrix rank, err to return state handler
det(A)	function	Determinant of a scalar or square matrix	det(A,overwrite_a,err=err): option to let A be destroyed, return state handler err
inv(A)	function	Inverse of a scalar or square matrix	inv(A,err=err): A is not destroyed; return state handler err
invert(A)	subroutine	In-place inverse of a scalar or square matrix	call invert(A,err=err): A is replaced with $A^{-1}$, return state handler err
.inv.A	operator	Inverse of a scalar or square matrix	A is replaced with $A^{-1}$
svd(A)	subroutine	Singular value decomposition of $A = U S V^t$	call svd(A,s,u,vt,full_matrices=.false.,err=state), all optional arguments but A,s
svdvals(A)	function	Singular values $S$ from $A = U S V^t$	s = svdvals(A), real array with same precision as A
eye(m)	function	Identity matrix of size m	eye(m,n,mold,err): Optional column size n, datatype dtype (default: real64), error handler
eigvals(A)	function	Eigenvalues of matrix $A$	eigvals(A,err): Optional state handler err
eig(A,lambda)	subroutine	Eigenproblem of matrix $A$	eig(A,lambda,left,right,overwrite_a,err): optional output eigenvector matrices (left and/or right)
eigvalsh(A)	function	Eigenvalues of symmetric or hermitian matrix $A$	eigvalsh(A,upper_a,err): Choose to use upper or lower triangle; optional state handler err
eigh(A,lambda)	subroutine	Eigenproblem of symmetric or hermitianmatrix $A$	eigh(A,lambda,vector,upper_a,overwrite_a,err): optional output eigenvectors
diag(n,source)	function	Diagonal matrix from scalar input value	diag(n,source,err): Optional error handler
diag(source)	function	Diagonal matrix from array input values	diag(source,err): Optional error handler
qr(A,Q,R)	subroutine	QR factorization	qr(A,Q,R,storage=work,err=err): Optional pre-allocated working storage, error handler
qr_space(A,lwork)	subroutine	QR Working space size	qr_space(A,lwork,err): Optional error handler

All procedures work with all types (real, complex) and kinds (32, 64, 128-bit floats).

fortran-lapack

This package contains a Modern Fortran implementation of the Reference-LAPACK library. The reference Fortran-77 library is automatically downloaded from its master repository, and processed to create Modern Fortran modules with full explicit typing features. Release 3.10.1 is currently targeted. Function interfaces are unchanged from the original implementation, and allow future extension to handle its usage through external implementations. The following refactorings are applied:

• All datatypes and accuracy constants standardized into a module (stdlib-compatible names)
• Both libraries available for 32, 64 and 128-bit floats
• Free format, lower-case style
• implicit none(type, external) everywhere
• all pure procedures where possible
• intent added to all procedure arguments
• Removed DO 10 .... 10 CONTINUE, replaced with do..end do loops or labelled loop_10: do ... cycle loop_10 ... end do loop_10 in case control statements are present
• BLAS modularized into a single-file module
• LAPACK modularized into a single-file module
• All procedures prefixed (with stdlib_, currently).
• F77-style parameters removed, and numeric constants moved to the top of each module.
• Ambiguity in single vs. double precision constants (0.0, 0.d0, (1.0,0.0)) removed
• preprocessor-based OpenMP directives retained.

The single-source module structure hopefully allows for cross-procedural inlining which is otherwise impossible without link-time optimization.

Building

An automated build is currently available via the Fortran Package Manager. To add fortran-lapack to your project, simply add it as a dependency:

[dependencies]
fortran-lapack = { git="https://github.com/perazz/fortran-lapack.git" }

Extension to external BLAS/LAPACK libraries

This task is in progress. The names of all procedures have been prefixed not to pollute the original BLAS/LAPACK namespace, so that handling of external libraries can be accomplished via a preprocessor flag. For example:

#ifdef EXTERNAL_BLAS
interface 
    pure subroutine saxpy(n, a, x, incx, y, incy)
      import :: ik, sp
      integer, parameter :: wp = sp
      integer(ik), intent(in) :: n
      real(wp), intent(in) :: a
      real(wp), intent(in) :: x(*)
      integer(ik), intent(in) :: incx
      real(wp), intent(inout) :: y(*)
      integer(ik), intent(in) :: incy
    end subroutine saxpy
end interface
#else
interface saxpy
    module procedure stdlib_saxpy
end interface
#endif

Licensing

LAPACK is a freely-available software package. It is available from netlib via anonymous ftp and the World Wide Web. Thus, it can be included in commercial software packages (and has been). Credit for the library should be given to the LAPACK authors. The license used for the software is the modified BSD license. According to the original license, we changed the name of the routines and commented the changes made to the original.

Acknowledgments

The development of this package is supported by the Sovereign Tech Fund.