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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
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++
The ScaLAPACK (or Scalable LAPACK) library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently
ScaLAPACK
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
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
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
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)
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
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
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
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
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
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
Linear Algebra PACKage (LAPACK), Automatically Tuned Linear Algebra Software (ATLAS), and ARPACK. High-performance BLAS/LAPACK replacement libraries such
Armadillo_(C++_library)
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++
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
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
free and open source libraries, especially BLAS, LAPACK and FFTW libraries. Instead of BLAS and LAPACK, some optimized platform-specific libraries can
IT++
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
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
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
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
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
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
Integer set library LAPACK Libfixmath Lis (linear algebra library) LOBPCG Math Kernel Library Mathomatic OpenBLAS PARI/GP ScaLAPACK PETSc SLEPc UMFPACK
C_(programming_language)
General-purpose programming language
hydrological modeling, numerical linear algebra and numerical libraries (LAPACK, IMSL and NAG), optimization, satellite simulation, structural engineering
Fortran
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
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
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)
Programming language
Integer set library LAPACK Libfixmath Lis (linear algebra library) LOBPCG Math Kernel Library Mathomatic OpenBLAS PARI/GP ScaLAPACK PETSc SLEPc UMFPACK
Outline of the C programming language
Outline_of_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 free and open-source software packages
List_of_free_and_open-source_software_packages
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
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
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
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 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
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)
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
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
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
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
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
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
in C and Java translations. Fastest Fourier Transform in the West (FFTW) LAPACK List of open-source mathematical libraries Official website Swarztrauber
FFTPACK
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
in binary form. This external library contains open-source software like lapack and C++ Mathematical Expression Toolkit Library. But also free software
Radioss
(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
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)
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++
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
Programming term
matrix https://www.netlib.org/lapack/lug/ https://www.netlib.org/blas/ https://github.com/numericalalgorithmsgroup/LAPACK_Examples Golub, Gene H.; Van
Packed_storage_matrix
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
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
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)
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)
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
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
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
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
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
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
MIT Basic Linear Algebra Subprograms (BLAS) Fortran, C, R BSD, GPL, LGPL LAPACK Fortran, C BSD Dart core libraries Dart BSD-3-Clause GORM Go MIT Haskell
List of open-source code libraries
List_of_open-source_code_libraries
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
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
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
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
Collection of classes and functions used in 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
C++_Standard_Library
General purpose C++ 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
POCO_C++_Libraries
COIN-OR Bonmin, COIN-OR Cgl, Interior Point OPTimizer (IPOPT)) and outside (LAPACK, Basic Linear Algebra Subprograms (BLAS), MUltifrontal Massively Parallel
Couenne
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
Open-source library for computing
libraries including Gmsh, PETSc, Trilinos, METIS, SUNDIALS, VTK, p4est, BLAS, LAPACK, HDF5, NetCDF, and Open Cascade Technology. The software started from work
Deal.II
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
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
As http://www.netlib.org/linpack says, LINPACK is largely superseded by LAPACK. Walter H. Vandevender, Karen H. Haskell, The SLATEC mathematical subroutine
SLATEC
Algorithm for matrix multiplication
workspace and overcomes the need for a square 2D grid. It is used by the ScaLAPACK, PLAPACK, and Elemental libraries. When multiplying two n×n matrices A and
Cannon's_algorithm
Technique in compiler construction
common issue that must be dealt with to call Fortran libraries, such as LAPACK, from other languages, such as C. Because of the case insensitivity, the
Name_mangling
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
LAPACK
LAPACK
LAPACK
LAPACK
Surname or Lastname
English
English : from Kene, a short form of the Old English personal name Cēn or Cyne, based on Old English cēne ‘wise’, ‘brave’, ‘proud’.Americanized spelling of German Kühn (see Kuehn).Robert Keayne (d. 1655) was one of the founders of Boston MA, and is buried in the King’s Chapel Burying Ground there.
Boy/Male
Indian, Punjabi, Sikh
One who Loves to Meditate
Boy/Male
American, British, English
From the King's Hall
Female
Japanese
(由美) Japanese short form of names beginning with Yumi-, YUMI means "cause-beauty."
Boy/Male
Irish
Prosperous protector.
Girl/Female
Muslim
One of friendly and likable nature
Girl/Female
Arabic, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Telugu
Beauty; Monsoon Wind
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : patronymic from the personal name Randel (see Randall).
Boy/Male
Swedish
Noble or ready.
Surname or Lastname
English
English : variant of Lippincott.
LAPACK
LAPACK
LAPACK
LAPACK
LAPACK