**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# LAPACK

Summary

LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines.
LAPACK was designed as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK, written in the 1970s and 1980s, was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed to effectively exploit the caches on modern cache-based architectures and the instruction-level parallelism of modern superscalar processors, and thus can run orders of magnitude faster than LINPACK on such machines, given a well-tuned BLAS implementation. LAPACK has also been extended to run on distributed memory systems in later packages such as ScaLAPACK and PLAPACK.
Netlib LAPACK is licensed under a three-clause BSD style license, a permissive free software license with few restrictions.
Subroutines in LAPACK have a naming convention which makes the identifiers very compact. This was necessary as the first Fortran standards only supported identifiers up to six characters long, so the names had to be shortened to fit into this limit.
A LAPACK subroutine name is in the form pmmaaa, where:
p is a one-letter code denoting the type of numerical constants used. S, D stand for real floating-point arithmetic respectively in single and double precision, while C and Z stand for complex arithmetic with respectively single and double precision.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (22)

Related concepts (14)

Related units (1)

Related courses (1)

Related people (2)

Ontological neighbourhood

Related lectures (8)

Numerical linear algebra

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.

LINPACK

LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which runs more efficiently on modern architectures. LINPACK makes use of the BLAS (Basic Linear Algebra Subprograms) libraries for performing basic vector and matrix operations.

Tridiagonal matrix

In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this), and the supradiagonal/upper diagonal (the first diagonal above the main diagonal). For example, the following matrix is tridiagonal: The determinant of a tridiagonal matrix is given by the continuant of its elements. An orthogonal transformation of a symmetric (or Hermitian) matrix to tridiagonal form can be done with the Lanczos algorithm.

MATH-611: Scientific programming for Engineers

The students will acquire a solid knowledge on the processes necessary to design, write and use scientific software. Software design techniques will be used to program a multi-usage particles code, ai

Singular Value Decomposition

Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.

Direct Methods for Linear Systems

Covers the solution of linear systems using direct methods and the evolution of matrices.

Eigen Library for Linear Algebra

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Daniel Kressner, Zvonimir Bujanovic

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...

In this thesis we address the computation of a spectral decomposition for symmetric
banded matrices. In light of dealing with large-scale matrices, where classical dense
linear algebra routines are not applicable, it is essential to design alternative tech ...