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 programGetting 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 fyppInstall lapack and blas (use the static versions). This can be tricky, if you run into any problem, please open an issue.
Arch Linux
Ubuntu
Usually you can do the following:
make
fpm testBy 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 testOr if you have support to such extensions in your blas provider you can:
make FYPPFLAGS="-DMFI_EXTENSIONS -DMFI_LINK_EXTERNAL"
fpm testwhich 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. |