Linear Algebra

arpack-ng

opencollab / arpack-ng

Serial iterative eigensolvers for selected eigenvalues of large matrices.

Matching APIs: DSAUPD / DSEUPD

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D4a1.

D D4 D4a D4a1

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Checked drivers: arpack-poisson-eigenpairs

blas-interface

Sebastian Ehlert (awvwgk) / blas-interface

Explicit generic Fortran interfaces to BLAS vector and matrix operations.

Matching APIs: blas_gemm

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1b6.

D D1 D1b D1b6 D2

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Checked drivers: blas-gemm-reference

dbcsr

CP2K (cp2k) / dbcsr

Serial block-sparse matrix multiplication, checked against MATMUL.

Matching APIs: dbcsr_multiply

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1

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Checked drivers: dbcsr-products-reference

ddpcm

Filippo Lipparini (filippolipparini) / ddPCM

Continuum solvation by domain decomposition; formaldehyde energy and forces checked against author references.

Matching APIs: cosmo / jacobi_diis

Source-supported: pinned procedure evidence; a matching checked driver is still needed.

D D2 Z

Package details · Repository · Open default example

fglm

jordan4ibanez / fglm

Typed vectors and 4-by-4 matrices for geometric transformations.

Matching APIs: add / multiply / translate / rotate_z

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1

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Checked drivers: fglm-transform-reference

fgsl

reinh-bader / fgsl

Fortran bindings to GSL; checked adaptive quadrature with an endpoint singularity.

Uncertain: discovery classification awaiting procedure-level source review.

C D E F G H H2 H2a H2a1 H2a1a H2a1a1 I J K L

Package details · Repository · Open default example

fmm2d

Flatiron Institute (flatironinstitute) / fmm2d

Fast multipole evaluation of two-dimensional Laplace and Helmholtz interactions.

Matching APIs: rfmm2d_t_c_p

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1 I I2

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Checked drivers: fmm2d-laplace-reference

fordot

Ali (gha3mi) / fordot

Selectable dot-product implementations, including BLAS and blocked calculations.

Matching APIs: dot_product

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1

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Checked drivers: fordot-exact-reference

foreig

Ali (gha3mi) / foreig

LAPACK interfaces for eigenvalues and eigenvectors of real matrices.

Matching APIs: eig (SYEV method)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D4a1.

D D4 D4a D4a1

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Checked drivers: foreig-symmetric-reference

forinv

Ali (gha3mi) / forinv

Matrix inverses and singular-value-decomposition pseudoinverses.

Matching APIs: inv (SVD pseudoinverse)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D9c.

D D2 D6 D9 D9c

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Checked drivers: forinv-pseudoinverse-reference

forlab

ZUO Zhihua (zoziha) / forlab

MATLAB/NumPy-style numerical utilities, linear algebra, interpolation and statistics.

Matching APIs: solve (rectangular real system)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D9a1.

D D1 D2 D9 D9a D9a1 E E1 L L1

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Checked drivers: forlab-least-squares-reference

formatmul

Ali (gha3mi) / formatmul

Matrix products with transpose options and selectable multiplication methods.

Matching APIs: matmul

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1

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Checked drivers: formatmul-products-reference

forpca

Ali (gha3mi) / forpca

Principal component directions from eigendecomposition or singular value decomposition.

Matching APIs: tpca%pca (SVD mode)

Source-supported: pinned procedure evidence; a matching checked driver is still needed.

D D4 D6 L L13 L13b

Package details · Repository · Open default example

forsolver

Ali (gha3mi) / forsolver

Linear solvers and Newton-type nonlinear solvers with analytic, finite-difference and complex-step derivatives.

Uncertain: discovery classification awaiting procedure-level source review.

D D2 F F1 F1b F2 H H1

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forsvd

Ali (gha3mi) / forsvd

Singular value decomposition and truncated low-rank matrix approximations.

Matching APIs: svd

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D6.

D D6

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Checked drivers: forsvd-spectrum-reference

fortran-lapack

Federico Perini (perazz) / fortran-lapack

Modern linear algebra: linear systems, eigenvalues, least squares, and matrix factorizations.

Matching APIs: solve; eigh (real symmetric overload); qr; svd; lstsq; syev (real64 overload); gesvd (real64 overload)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2a1.

D D2 D2a D2a1 D4 D4a D4a1 D5 D6 D9 D9a D9a1

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Checked drivers: fortran-lapack-dense-solve · fortran-lapack-least-squares · fortran-lapack-symmetric-eigen · fortran-lapack-qr-decomposition · fortran-lapack-svd-decomposition

fsparse

José Alves (jalvesz) / FSPARSE

Sparse matrix storage, format conversions and matrix-vector products.

Matching APIs: matvec; dense2coo, coo2dense, coo2csr, csr2coo

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1b4.

D D1 D1b D1b4 D1b9

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Checked drivers: fsparse-matvec-reference · fsparse-storage-reference

heatflow

Exeter Quantum Codes (ExeQuantCode) / HeatFlow

Finite-difference models of Fourier and Cattaneo heat transport.

Matching APIs: SRSin / linbcg

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2.

D D2 I I2

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Checked drivers: heatflow-bicg-reference

kiss

Ivan Pribec (ivan-pi) / kiss

Krylov iterative solvers for dense matrices and matrix-free linear operators.

Matching APIs: cg_dense

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2b1b.

D D2 D2b D2b1 D2b1b

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Checked drivers: kiss-positive-definite-solve

libmbd

libMBD (libmbd) / libmbd

Many-body dispersion energies and gradients; checked argon-dimer example.

Matching APIs: mbd_calc_t%evaluate_vdw_method / get_mbd_hamiltonian_energy_real

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D4.

D D4 Z

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Checked drivers: libmbd-dimer-spectrum

lightkrylov

nekStab (nekstab) / LightKrylov

Krylov methods for eigenvalues, linear systems, singular values and matrix exponentials.

Matching APIs: gmres

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2.

D D2 D4 D6

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Checked drivers: lightkrylov-gmres-reference

linalg

Jason Christopherson (jchristopherson) / linalg

Convenient dense and sparse linear algebra interfaces to BLAS, LAPACK and ARPACK.

Matching APIs: lu_factor, solve_lu; eigen (real symmetric overload); qr_factor; svd; solve_least_squares

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D5.

D D1 D2 D2a D2a1 D3 D4 D4a D4a1 D5 D6 D9 D9a D9a1

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Checked drivers: linalg-qr-reference · linalg-eigen-reference · linalg-svd-reference · linalg-least-squares-reference · linalg-lu-reference

linalg_fortran

Euler-37 / linalg_fortran

Typed LAPACK interfaces for matrix inverses, determinants and Hermitian eigenproblems.

Matching APIs: linalg%inv / linalg%det; linalg%eigh

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D4a1.

D D2 D4 D4a D4a1

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Checked drivers: linalg-poisson-eigenpairs · linalg-inverse-factor-reference

lsmr

Jacob Williams (jacobwilliams) / LSMR

Iterative solution of sparse linear equations and least-squares problems.

Matching APIs: lsmr

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D9a1.

D D2 D9 D9a D9a1 K K1

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Checked drivers: lsmr-least-squares-reference

lsqr

Jacob Williams (jacobwilliams) / LSQR

Iterative sparse linear systems and least-squares solver using coordinate storage.

Matching APIs: lsqr_solver_ez%solve

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D9a1.

D D2 D9 D9a D9a1 K K1

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Checked drivers: lsqr-least-squares-reference

lusol

Jacob Williams (jacobwilliams) / lusol

Sparse LU factorization, linear solves and efficient column updates.

Matching APIs: lu1fac / lu6sol / lu8rpc

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2a4.

D D2 D2a D2a4

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Checked drivers: lusol-update-reference

m_la

urbanjost / M_LA

Magic squares, reduced row-echelon forms and other small matrix utilities.

Matching APIs: mat_magic

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1.

D D1

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Checked drivers: m-la-magic-reference

metis-fpm

gnikit / metis-fpm

METIS graph partitioning and sparse matrix ordering through a Fortran interface.

Uncertain: discovery classification awaiting procedure-level source review.

D P

Package details · Repository · Open default example

minres

Will Dickson (willdickson) / minres

Iterative solution of symmetric sparse systems, including indefinite matrices.

Matching APIs: minres_solver

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2b4.

D D2 D2b D2b4

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Checked drivers: minres-indefinite-solve

nafpack

Jules Minard (minard-jules) / NAFPack

Numerical analysis routines for Fourier transforms, linear systems and eigenproblems.

Uncertain: discovery classification awaiting procedure-level source review.

D D2 D4 J J1 J1a J1a2

Package details · Repository · Open default example

ntpoly

william-dawson / NTPoly

Sparse matrix functions and inverse solvers; single-process MPI example.

Matching APIs: SquareRoot / InverseSquareRoot; Invert

Verified: a checked driver demonstrates a capability in this class.

D D2

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Checked drivers: ntpoly-matrix-root-reference · ntpoly-inverse-reference

propack

SciPy (scipy) / PROPACK

Partial singular-value decompositions using the historical SciPy PROPACK sources (double precision).

Matching APIs: dlansvd

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D6.

D D6

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Checked drivers: propack-spectrum-reference

qdldl-fortran

Jacob Williams (jacobwilliams) / qdldl-fortran

Sparse LDL-transpose factorization, orderings and solves for quasi-definite systems.

Matching APIs: qdldl_type%analyze / factor / solve

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2b4.

D D2 D2b D2b4

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Checked drivers: qdldl-quasidefinite-solve

scalapackfx

DFTB+ Project (dftbplus) / scalapackfx

ScaLAPACK wrappers; checked single-process symmetric eigensolver example.

Matching APIs: scalafx_psyev

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D4a1.

D D4 D4a D4a1

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Checked drivers: scalapackfx-eigen-reference

slicot

SLICOT (slicot) / SLICOT-Reference

Numerical methods for systems and control, including matrix equations.

Matching APIs: SB03MD; SB04MD; SB04QD

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D8.

D D8

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Checked drivers: slicot-lyapunov-known-matrix · slicot-continuous-sylvester · slicot-discrete-sylvester

sparse_fortran

Euler-37 / sparse_fortran

Coordinate and compressed-row sparse matrices with matrix-vector products.

Matching APIs: sparse_coo%sparse_product, sparse_csr%sparse_product

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D1b4.

D D1 D1b D1b4

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Checked drivers: sparse-matvec-reference

specialmatrices

Jean-Christophe Loiseau (loiseaujc) / SpecialMatrices

Structured diagonal, circulant, Toeplitz, tridiagonal, and other matrices.

Matching APIs: solve (diagonal matrices)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2.

D D1 D2 D3

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Checked drivers: specialmatrices-diagonal-reference

stdlib

fortran-lang / stdlib

General utilities, statistics, strings, sorting, and numerical routines.

Matching APIs: solve; lstsq (real dense overload)

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2a1.

A C D D1 D2 D2a D2a1 D9 D9a D9a1 L L1 L1a L1a1 L1a1a L1a1b L6 L6c N N3 N4 N5 N6 R R3

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Checked drivers: stdlib-dense-solve · stdlib-least-squares

y12m

Ivan Pribec (ivan-pi) / y12m

Direct sparse LU factorization with pivoting, reordering and reuse for multiple right-hand sides.

Matching APIs: y12mb, y12mc, y12md

Verified: a checked driver demonstrates a capability in this class.

Driver demonstrates the narrower class D2a4.

D D2 D2a D2a4

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Checked drivers: y12m-sparse-reference