MFI

Modern Fortran interfaces to BLAS and LAPACK

This project aims to be a collection of modern fortran interfaces to commonly used procedure, for now BLAS and LAPACK. The main goal is to reduce the pain of using such libraries, providing a generic interface to the intrinsic supported types and identifying the optional or reconstructible arguments of a given procedure. The code uses fypp, to generate the interfaces automatically to all supported types and kinds.

Example $C = AB$

program main
use mfi_blas, only: mfi_gemm
use f77_blas, only: f77_gemm
use iso_fortran_env
implicit none
! ... variables and other boilerplate code here ...
! Original interface: type and precision dependent
call cgemm('N','N', N, N, N, alpha, A, N, B, N, beta, C, N)
! Improved F77 interface: still a lot of arguments
call f77_gemm('N','N', N, N, N, alpha, A, N, B, N, beta, C, N)
! Modern fortran interface: less arguments and more readable 
call mfi_gemm(A,B,C)
end program

Getting Started

FPM

This project supports the Fortran Package Manager. Follow the directions on that page to install FPM if you haven't already.

Using as a dependency in FPM

Add a entry in the "dependencies" section of your project's fpm.toml

# fpm.toml
[ dependencies ]
mfi = { git="https://github.com/14NGiestas/mfi.git", branch="mfi-fpm" }

Manual building

First get the code, by cloning the repo:

git clone https://github.com/14NGiestas/mfi.git
cd mfi/

Dependencies

Install the fypp using the command:

sudo pip install fypp

Install lapack and blas (use the static versions). This can be tricky, if you run into any problem, please open an issue.

Arch Linux

• aur/openblas-lapack-static

Ubuntu

• lapack-dev

Usually you can do the following:

make
fpm test

By default, the lapack-dev package (which provides the reference blas) do not provide the i?amin implementation (among other extensions) in such cases you can use blas extensions with:

make FYPPFLAGS=-DMFI_EXTENSIONS
fpm test

Or if you have support to such extensions in your blas provider you can:

make FYPPFLAGS="-DMFI_EXTENSIONS -DMFI_LINK_EXTERNAL"
fpm test

which will generate the code linking extensions to the external library

Support

Please note that this project is experimental, is missing a test suite and errors may occur (in which case open an issue). If you want a specific routine to be featured here feel free to open a PR or open an issue providing a test case, a link to an specification (docs) and it's datatype variants.

BLAS

Level 1

Most of BLAS level 1 routines can be replaced by intrinsincs and other features in modern fortran.

done?	name	description	modern alternative
	asum	Sum of vector magnitudes	sum
👍	axpy	Scalar-vector product	a*x + b
👍	copy	Copy vector	x = b
	dot	Dot product	dot_product
	sdsdot	Dot product with double precision
👍	dotc	Dot product conjugated
👍	dotu	Dot product unconjugated
	nrm2	Vector 2-norm (Euclidean norm)	norm2
	rot	Plane rotation of points
	rotg	Generate Givens rotation of points
👍	rotm	Modified Givens plane rotation of points
👍	rotmg	Generate modified Givens plane rotation of points
	scal	Vector-scalar product	a*x + b
👍	swap	Vector-vector swap

Level 2

done?	name	description
👍	gbmv	Matrix-vector product using a general band matrix
👍	gemv	Matrix-vector product using a general matrix
👍	ger	Rank-1 update of a general matrix
👍	gerc	Rank-1 update of a conjugated general matrix
👍	geru	Rank-1 update of a general matrix, unconjugated
👍	hbmv	Matrix-vector product using a Hermitian band matrix
👍	hemv	Matrix-vector product using a Hermitian matrix
👍	her	Rank-1 update of a Hermitian matrix
👍	her2	Rank-2 update of a Hermitian matrix
👍	hpmv	Matrix-vector product using a Hermitian packed matrix
👍	hpr	Rank-1 update of a Hermitian packed matrix
👍	hpr2	Rank-2 update of a Hermitian packed matrix
👍	sbmv	Matrix-vector product using symmetric band matrix
👍	spmv	Matrix-vector product using a symmetric packed matrix
👍	spr	Rank-1 update of a symmetric packed matrix
👍	spr2	Rank-2 update of a symmetric packed matrix
👍	symv	Matrix-vector product using a symmetric matrix
👍	syr	Rank-1 update of a symmetric matrix
👍	syr2	Rank-2 update of a symmetric matrix
👍	tbmv	Matrix-vector product using a triangular band matrix
👍	tbsv	Solution of a linear system of equations with a triangular band matrix
👍	tpmv	Matrix-vector product using a triangular packed matrix
👍	tpsv	Solution of a linear system of equations with a triangular packed matrix
👍	trmv	Matrix-vector product using a triangular matrix
👍	trsv	Solution of a linear system of equations with a triangular matrix

Level 3

done?	name	description
👍	gemm	Computes a matrix-matrix product with general matrices.
👍	hemm	Computes a matrix-matrix product where one input matrix is Hermitian and one is general.
👍	herk	Performs a Hermitian rank-k update.
👍	her2k	Performs a Hermitian rank-2k update.
👍	symm	Computes a matrix-matrix product where one input matrix is symmetric and one matrix is general.
👍	syrk	Performs a symmetric rank-k update.
👍	syr2k	Performs a symmetric rank-2k update.
👍	trmm	Computes a matrix-matrix product where one input matrix is triangular and one input matrix is general.
👍	trsm	Solves a triangular matrix equation (forward or backward solve).

Utils / Extensions

Level 1

Here are some extensions that may be useful. Again, BLAS level 1 routines can be replaced by intrinsincs and other features in modern fortran.

done?	name	description	modern alternative
👍	iamax	Index of the maximum absolute value element of a vector	maxval, maxloc
👍	iamin	Index of the minimum absolute value element of a vector	minval, minloc

LAPACK

Linear Equation Routines

done?	name	description
👍	geqrf	Computes the QR factorization of a general m-by-n matrix.
👍	gerqf	Computes the RQ factorization of a general m-by-n matrix.
👍	getrf	Computes the LU factorization of a general m-by-n matrix.
👍	getri	Computes the inverse of an LU-factored general matrix.
👍	getrs	Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.
👍	hetrf	Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.
	orgqr	Generates the real orthogonal matrix Q of the QR factorization formed by geqrf.
	ormqr	Multiplies a real matrix by the orthogonal matrix Q of the QR factorization formed by geqrf.
	ormrq	Multiplies a real matrix by the orthogonal matrix Q of the RQ factorization formed by gerqf.
👍	potrf	Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
👍	potri	Computes the inverse of a Cholesky-factored symmetric (Hermitian) positive-definite matrix.
👍	potrs	Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix, with multiple right-hand sides.
	sytrf	Computes the Bunch-Kaufman factorization of a symmetric matrix.
	trtrs	Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides.
	ungqr	Generates the complex unitary matrix Q of the QR factorization formed by geqrf.
	unmqr	Multiplies a complex matrix by the unitary matrix Q of the QR factorization formed by geqrf.
	unmrq	Multiplies a complex matrix by the unitary matrix Q of the RQ factorization formed by gerqf.

Singular Value and Eigenvalue Problem Routines

done?	name	description
	gebrd	Reduces a general matrix to bidiagonal form.
👍	gesvd	Computes the singular value decomposition of a general rectangular matrix.
👍	heevd	Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm.
👍	hegvd	Computes all eigenvalues and, optionally, all eigenvectors of a complex generalized Hermitian definite eigenproblem using divide and conquer algorithm.
	hetrd	Reduces a complex Hermitian matrix to tridiagonal form.
	orgbr	Generates the real orthogonal matrix Q or PT determined by gebrd.
	orgtr	Generates the real orthogonal matrix Q determined by sytrd.
	ormtr	Multiplies a real matrix by the orthogonal matrix Q determined by sytrd.
	syevd	Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm.
	sygvd	Computes all eigenvalues and, optionally, all eigenvectors of a real generalized symmetric definite eigenproblem using divide and conquer algorithm.
	sytrd	Reduces a real symmetric matrix to tridiagonal form.
	ungbr	Generates the complex unitary matrix Q or PT determined by gebrd.
	ungtr	Generates the complex unitary matrix Q determined by hetrd.
	unmtr	Multiplies a complex matrix by the unitary matrix Q determined by hetrd.

Other Auxiliary Routines

There are some other auxiliary lapack routines around, that may apear here:

name	Data Types	Description
mfi_lartg	s, d, c, z	Generates a plane rotation with real cosine and real/complex sine.