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Software library for numerical linear algebra
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations
LAPACK
The ScaLAPACK (or Scalable LAPACK) library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently
ScaLAPACK
C++ software for numerical linear algebra
Free and open-source software portal LAPACK++, the Linear Algebra PACKage in C++, is a computer software library of algorithms for numerical linear algebra
LAPACK++
American computer scientist (born 1950)
Basic Linear Algebra Subprograms (BLAS), Linear Algebra Package (LAPACK), ScaLAPACK, Parallel Virtual Machine (PVM), Message Passing Interface (MPI),
Jack_Dongarra
Routines for performing common linear algebra operations
links to BLAS/ATLAS and LAPACK. It is sponsored by NICTA (in Australia) and is licensed under a free license. LAPACK LAPACK is a higher level Linear
Basic Linear Algebra Subprograms
Basic_Linear_Algebra_Subprograms
Optimized math routines developed by Intel
engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. The library
Math_Kernel_Library
is written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. Intel IPP
List_of_numerical_libraries
Software library for linear algebra
implementation of the BLAS APIs as well as some additional functions from LAPACK, a higher-level library built on top of BLAS. In BLAS, functionality is
Automatically Tuned Linear Algebra Software
Automatically_Tuned_Linear_Algebra_Software
Linear Algebra PACKage (LAPACK), Automatically Tuned Linear Algebra Software (ATLAS), and ARPACK. High-performance BLAS/LAPACK replacement libraries such
Armadillo_(C++_library)
List of notable software written in or for the C++ programming language
uBLAS CGAL Class Library for Numbers deal.II Eigen GetFEM++ IML++ IT++ LAPACK++ Matrix Template Library MFEM Multiple Precision Integers and Rationals
List of C++ software and tools
List_of_C++_software_and_tools
LAPACK Users' guide. SIAM. Anderson, E., Bai, Z., Dongarra, J., Greenbaum, A., McKenney, A., Du Croz, J., ... & Sorensen, D. (1990, November). LAPACK:
Comparison of linear algebra libraries
Comparison_of_linear_algebra_libraries
Open-source linear algebra library
unrolling and vectorization. Eigen itself can provide BLAS and a subset of LAPACK interfaces. Free and open-source software portal Mathematics portal List
Eigen_(C++_library)
General-purpose programming language
Integer set library LAPACK Libfixmath Lis (linear algebra library) LOBPCG Math Kernel Library Mathomatic OpenBLAS PARI/GP ScaLAPACK PETSc SLEPc UMFPACK
C_(programming_language)
free and open source libraries, especially BLAS, LAPACK and FFTW libraries. Instead of BLAS and LAPACK, some optimized platform-specific libraries can
IT++
General-purpose programming language
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
C++
Mathematical software
supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which runs more efficiently on modern architectures. LINPACK makes use
LINPACK
Upper bound on rounding error in floating-point arithmetic
floating-point formats. According to formal definition — used by Prof. Demmel, LAPACK and Scilab. It represents the largest relative rounding error in round-to-nearest
Machine_epsilon
Software documentation on Unix systems
trailing-edge.com. Archived from the original on 2020-08-03. Retrieved 2020-05-06. "lapack (l) - Linux Man Pages". www.systutorials.com. Archived from the original
Man_page
Matrix decomposition method
partial port of the LAPACK to C++, C#, Delphi, Visual Basic, etc. (spdmatrixcholesky, hpdmatrixcholesky) libflame is a C library with LAPACK functionality.
Cholesky_decomposition
Storage method in computer memory
which stores all the elements for a given row contiguously in memory. LAPACK defines various matrix representations in memory. There is also Sparse matrix
Matrix_representation
algorithms and utilizes the functionality of software interfaces such as BLAS, LAPACK, and MPI. In 2004, Trilinos received an R&D100 Award. Several supercomputing
Trilinos
Linear algebra library
created by Mikio Braun, for the Java programming language built upon BLAS and LAPACK. Unlike most other Java linear algebra libraries, jblas is designed to be
Jblas: Linear Algebra for Java
Jblas:_Linear_Algebra_for_Java
Mono, written in C# and F#. It features functionality similar to BLAS and LAPACK. Math.NET Numerics started 2009 by merging code and teams of dnAnalytics
Math.NET_Numerics
List of software related to the MATLAB programming language
https://github.com/mathworks/MATLAB-Coder-integration-for-BLAS-LAPACK https://www.netlib.org/lapack/lapwrapmw/ https://www.mathworks.com/matlabcentral/filee
List of MATLAB software and tools
List_of_MATLAB_software_and_tools
architectures. It provides a computational backbone for ScaLAPACK, a parallel implementation of LAPACK. It depends on Level 1 sequential BLAS operations for
PBLAS
General-purpose programming language
hydrological modeling, numerical linear algebra and numerical libraries (LAPACK, IMSL and NAG), optimization, satellite simulation, structural engineering
Fortran
American mathematician
six years, he moved to Berkeley in 1990. Demmel is known for his work on LAPACK, a software library for numerical linear algebra and more generally for
James_Demmel
Python library for numerical programming
scipy.sparse library. Internally, both MATLAB and NumPy rely on BLAS and LAPACK for efficient linear algebra computations. Python bindings of the widely
NumPy
Branch of mathematics
Consequently, linear algebra algorithms have been highly optimized. BLAS and LAPACK are the best known implementations. For improving efficiency, some of them
Linear_algebra
Open-source software
open-source implementation of the BLAS (Basic Linear Algebra Subprograms) and LAPACK APIs with many hand-crafted optimizations for specific processor types.
OpenBLAS
Matrix with nonzero elements on the main diagonal and the diagonals above and below it
than a general matrix by using a special storage scheme. For instance, the LAPACK Fortran package stores an unsymmetric tridiagonal matrix of order n in three
Tridiagonal_matrix
uBLAS CGAL Class Library for Numbers deal.II Eigen GetFEM++ IML++ IT++ LAPACK++ Matrix Template Library MFEM Multiple Precision Integers and Rationals
List of free and open-source software packages
List_of_free_and_open-source_software_packages
m-file-script syntax providing some compatibility with MATLAB and its clones. LAPACK has Fortran 90 routines for solving systems of simultaneous linear equations
List of numerical-analysis software
List_of_numerical-analysis_software
example, matrix multiplication). TNT is analogous to the BLAS library used by LAPACK. Higher level algorithms, such as LU decomposition and singular value decomposition
Template_Numerical_Toolkit
Software library of numerical-analysis algorithms
In 1992, the Library incorporated LAPACK routines for the first time; NAG had been a collaborator in the LAPACK project since 1987. The first release
NAG_Numerical_Library
team as an undergraduate intern at Argonne, and later went on to create LAPACK, which has largely superseded EISPACK and LINPACK. Smith, Brian; Boyle,
EISPACK
American software company
levels 0 through 5. Absoft offers support for MPI (MPICH2 and Open MPI). ScaLAPACK and BLACS is shipped with all platforms. IMSL 7.0, integrated but available
Absoft
French mathematician
PhD (Numerical Analysis) in 1997. She has contributed software to LAPACK, ScaLAPACK, and the MATLAB distribution. Tisseur is a member of the editorial
Françoise_Tisseur
CAPD library deal.II Class Library for Numbers Eigen GetFEM++ IML++ IT++ LAPACK++ Matrix Template Library Multiple Precision Integers and Rationals MFEM
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
belongs to R n {\displaystyle \mathbb {R} ^{n}} . Here are some of the LAPACK routines that apply to block reflectors "*larft" forms the triangular vector
Block_reflector
Set of rules defining correctly structured C++ program
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
C++_syntax
Computer approximation for real numbers
Fortran Compiler)". gcc.gnu.org. "Bug in zheevd · Issue #43 · Reference-LAPACK/lapack". GitHub. Becker, Heiko; Darulova, Eva; Myreen, Magnus O.; Tatlock,
Floating-point_arithmetic
Gradient boosting machine learning library
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
XGBoost
Computer vision library
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
OpenCV
Java library for linear algebra
standard linear algebra operations for dense matrices based on BLAS and LAPACK code. Partial set of sparse operations is provided through the Templates
Matrix_Toolkit_Java
Fortran software and development tools
programming model introduced in Fortran 2008 ScaLAPACK — parallel linear algebra package built on top of LAPACK FUnit — open-source unit testing framework
List of Fortran software and tools
List_of_Fortran_software_and_tools
in binary form. This external library contains open-source software like lapack and C++ Mathematical Expression Toolkit Library. But also free software
Radioss
optimized open source forks of various projects including BLIS, libFLAME, ScaLAPACK, and FFTW. It also offers various new open source solutions including AOCL-Sparse
AMD_Core_Math_Library
Parallel computing platform: GPGPU libraries and application programming interface
uses the library Tensile privately. This pair of libraries constitutes the LAPACK implementation for ROCm and is strongly coupled to rocBLAS. ROCm developer
ROCm
Institute of Standards and Technology in 1998 similar in functionality to LAPACK. The main capabilities provided by JAMA are: Eigensystem solving LU decomposition
JAMA (numerical linear algebra library)
JAMA_(numerical_linear_algebra_library)
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
Blitz++
Software used in mathematical applications
uBLAS CGAL Class Library for Numbers deal.II Eigen GetFEM++ IML++ IT++ LAPACK++ Matrix Template Library MFEM Multiple Precision Integers and Rationals
Mathematical_software
Collection of C++ libraries
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
Boost_(C++_libraries)
Matrix decomposition
ISBN 978-0-521-88068-8 Online Matrix Calculator Performs QR decomposition of matrices. LAPACK users manual gives details of subroutines to calculate the QR decomposition
QR_decomposition
Book by Brian Kernighan and Dennis Ritchie
Integer set library LAPACK Libfixmath Lis (linear algebra library) LOBPCG Math Kernel Library Mathomatic OpenBLAS PARI/GP ScaLAPACK PETSc SLEPc UMFPACK
The_C_Programming_Language
Form of a matrix storage
for Cholesky for banded matrices (available for banded matrices, e.g. in LAPACK; for a prototype skyline code, see ). Before storing a matrix in skyline
Skyline_matrix
Object-oriented framework for software development
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
Qt_(software)
Matrix factorisation in mathematics
Hammarling, S; McKenny, A; Sorensen, D (1995). "Nonsymmetric Eigenproblems". LAPACK Users guide. Philadelphia, PA: Society for Industrial and Applied Mathematics
Schur_decomposition
Fortran compiler
Software BLAS BLIS EISPACK Harwell Subroutine Library IMSL Numerical Libraries LAPACK Librsb LINPACK Lis Math Kernel Library MINPACK NAG Fortran Library Netlib
GNU_Fortran
Field of mathematics
optimisation; C and Fortran have packages like Basic Linear Algebra Subprograms and LAPACK, Python has the library NumPy, and Perl has the Perl Data Language. Many
Numerical_linear_algebra
Algorithm that estimates unknowns from a series of measurements over time
with the LU decomposition as implemented in the Linear Algebra PACKage (LAPACK). These results are further factored into the L·D·LT structure with methods
Kalman_filter
in C and Java translations. Fastest Fourier Transform in the West (FFTW) LAPACK List of open-source mathematical libraries Official website Swarztrauber
FFTPACK
Concept in numerical linear algebra
end if return end Furthermore, as Edward Anderson discovered in improving LAPACK, a previously overlooked numerical consideration is continuity. To achieve
Givens_rotation
Matrix in which most of the elements are zero
their solution. Armadillo provides a user-friendly C++ wrapper for BLAS and LAPACK. SciPy provides support for several sparse matrix formats, linear algebra
Sparse_matrix
Generalization of the one-dimensional normal distribution to higher dimensions
well known. If a rank-revealing (pivoted) Cholesky decomposition such as LAPACK's dpstrf() is available, it can be used in the general positive-semidefinite
Multivariate normal distribution
Multivariate_normal_distribution
Matrix with non-zero elements only in a diagonal band
original on 2016-03-04, retrieved 2011-08-08. Information pertaining to LAPACK and band matrices A tutorial on banded matrices and other sparse matrix
Band_matrix
American computer scientist
Software BLAS BLIS EISPACK Harwell Subroutine Library IMSL Numerical Libraries LAPACK Librsb LINPACK Lis Math Kernel Library MINPACK NAG Fortran Library Netlib
John_Backus
application development. ILNumerics added interfaces to popular codes (LAPACK, FFTW), complex numbers and generic mult-dimensional array classes. In 2010
ILNumerics
Open source software
OpenMP application programming interface. It makes use of the BLAS, LAPACK, ScaLAPACK, FFTW and Apache Xerces libraries. Qbox was designed for operation
Qbox
Wayne W.; Bredeweg, Robert A.; Chauvel, Jean Paul.; Harner, Richard S.; LaPack, Mark.; Leugers, Anne.; Martin, Daniel P.; Wright, Larry G.; Yalvac, E.
Process_analytical_chemistry
Most widely known generalized inverse of a matrix
multiplication, even if a state-of-the art implementation (such as that of LAPACK) is used. The above procedure shows why taking the pseudoinverse is not
Moore–Penrose_inverse
is written in Fortran 90 with parallelism by MPI and it uses BLAS and ScaLAPACK kernels for dense matrix computations. Since 1999, MUMPS has been supported
MUMPS_(software)
Type of programming language
Used for performance-critical applications with libraries such as BLAS and LAPACK. Java Broad Sense Supports scientific computing via libraries like Apache
Scientific programming language
Scientific_programming_language
Matrix decomposition
eigenvalues, which was first described by Golub and Kahan in 1965. The LAPACK subroutine DBDSQR implements this iterative method, with some modifications
Singular_value_decomposition
Vectors mapped to 0 by a linear map
homogeneous systems. A state of the art software for this purpose is the Lapack library.[citation needed] Kernel (algebra) Zero set System of linear equations
Kernel_(linear_algebra)
National laboratory in Albuquerque, New Mexico
density-functional theory. It utilizes libraries such as MPI, BLAS, and LAPACK and is developed under the GNU General Public License. Titan Informatics
Sandia_National_Laboratories
(Open Numerical Algorithm Language) implementation—including an official LAPACK translation—with NumPy/MATLAB-style multidimensional arrays, broadcasting
List of .NET libraries and frameworks
List_of_.NET_libraries_and_frameworks
Several equations of degree 1 to be solved simultaneously
improve accuracy of numerical solutions to systems of linear equations LAPACK – Software library for numerical linear algebra Linear equation over a ring
System_of_linear_equations
Type of matrix factorization
Computer code LAPACK is a collection of FORTRAN subroutines for solving dense linear algebra problems ALGLIB includes a partial port of the LAPACK to C++, C#
LU_decomposition
were unavailable or expensive. Several large Fortran libraries, such as LAPACK, were made available as C libraries via conversion with f2c. The f2c program
F2c
Kind of square matrix in linear algebra
and Tridiagonal Matrices. SIAM. "Computational Routines (eigenvalues) in LAPACK". sites.science.oregonstate.edu. Retrieved 2020-05-24. Horn, Roger A.; Johnson
Hessenberg_matrix
Java software and development tools
Linear Algebra for Java (Jblas) – linear algebra library using native BLAS/LAPACK bindings Java Astrodynamics Toolkit – numerical library of software components
List of Java software and tools
List_of_Java_software_and_tools
Computer algebra system
FriCAS Combinatorics Symmetrica, Sage-Combinat Linear algebra ATLAS, BLAS, LAPACK, NumPy, LinBox, IML, GSL Graph theory NetworkX Group theory GAP Numerical
SageMath
OpenCL port of the MAGMA project, a linear algebra library similar to LAPACK CP2K: molecular simulations Geostack, a high-performance geospatial processing
List_of_OpenCL_applications
COIN-OR Bonmin, COIN-OR Cgl, Interior Point OPTimizer (IPOPT)) and outside (LAPACK, Basic Linear Algebra Subprograms (BLAS), MUltifrontal Massively Parallel
Couenne
include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. OpenBLAS – Linear algebra library for BLAS and LAPACK APIs PARI/GP
List_of_C_software_and_tools
Matrix equation in control theory
{O}}(n^{3})} arithmetical operations,[citation needed] is used, among others, by LAPACK and the lyap function in GNU Octave. See also the sylvester function in
Sylvester_equation
Applying operations to whole sets of values simultaneously
benefits from quite efficient linear algebra libraries such as ATLAS or LAPACK. Returning to the previous quotation of Iverson, the rationale behind it
Array_programming
threads for intra-node parallelization. Other libraries used are Lapack, ScaLAPACK, FFTW, libxc and spglib. RMG runs on laptops, desktops, workstations
RMG_(program)
Matrix Algebra on GPU and Multicore Architectures (MAGMA) and NVIDIA CUDA. LAPACK, software library based on matrix transformations for dense matrices. List
ARPACK
Measure of a systems floating point architecture
in 2010, he said he expects running times of 2.5 days in "a few years". LAPACK "The Linpack Benchmark, TOP500 Supercomputing Sites". Retrieved 2015-02-10
LINPACK_benchmarks
Specialist field of computer science
variation of C or Fortran and optimized algebra libraries such as BLAS or LAPACK. In addition, parallel computing is heavily used in scientific computing
Computational_science
Container for a set of identifiers
collisions. Likewise, many packages originally written in Fortran (e.g., BLAS, LAPACK) reserve the first few letters of a function's name to indicate the group
Namespace
Software library for the C++ programming language
Class Library for Numbers deal.II Dune Eigen GetFEM++ GiNaC IML++ IT++ JAMA LAPACK++ LEMON Math Kernel Library Matrix Template Library MFEM Netlib Number Theory
Standard_Template_Library
Optimizing C/C++ and Fortran compiler suite
Library, AMD Secure RNG Library, AOCL-Sparse, BLIS, FFTW, libFLAME, and ScaLAPACK that are tuned for the Zen processors. AMD also offers AMD μProf, a performance
AMD_Optimizing_C/C++_Compiler
Generic title of a series of books on algorithms and numerical analysis
for the "black box" side, yielding important libraries such as BLAS and LAPACK, and integrated environments like MATLAB and Mathematica. By the early 1990s
Numerical_Recipes
computations (matrix-matrix multiplication, LU solve) and works with ScaLAPACK. Sparse matrices are available but the implementation is not optimal yet
Global_Arrays
Tennessee Jack Dongarra, computer science professor; creator of LINPACK and LAPACK; 2021 Turing Award recipient Gertrude Ehrlich, professor of mathematics
List of University of Tennessee people
List_of_University_of_Tennessee_people
Topics referred to by the same term
for performing common linear algebra operations Linear Algebra Package (LAPACK), a standard software library for numerical linear algebra Linear amplifier
Linear_(disambiguation)
Name of two different techniques based on the singular value decomposition
_{1}X^{*},\\A_{2}&=U_{2}\Sigma _{2}X^{*}.\end{aligned}}} LAPACK (ggsvd3): A 1 = U 1 Σ 1 [ 0 , R ] Q ^ ∗ , A 2 = U 2 Σ 2 [ 0 , R ] Q ^ ∗
Generalized singular value decomposition
Generalized_singular_value_decomposition
LAPACK
LAPACK
LAPACK
LAPACK
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Bejewelled, With beautiful smile
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Sun Rays
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Feminine form of Italian Florentino, FLORENTINA means "blossoming."
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one that draws water; poverty; cloud; death
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LAPACK
LAPACK
LAPACK
LAPACK
LAPACK