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Package de.lmu.ifi.dbs.elki.math.linearalgebra

Linear Algebra package provides classes and computational methods for operations on matrices.


Class Summary
AffineTransformation Affine transformations implemented using homogeneous coordinates.
CholeskyDecomposition Cholesky Decomposition.
EigenPair Helper class which encapsulates an eigenvector and its corresponding eigenvalue.
EigenvalueDecomposition Eigenvalues and eigenvectors of a real matrix.
LinearEquationSystem Class for systems of linear equations.
LUDecomposition LU Decomposition.
Matrix The Matrix Class represents real-valued matrices.
QRDecomposition QR Decomposition.
SingularValueDecomposition Singular Value Decomposition.
SortedEigenPairs Helper class which encapsulates an array of eigenpairs (i.e. an array of eigenvectors and their corresponding eigenvalues).
Vector Provides a vector object that encapsulates an m x 1 - matrix object.

Package de.lmu.ifi.dbs.elki.math.linearalgebra Description

Linear Algebra package provides classes and computational methods for operations on matrices.

The content of this package is adapted from the Jama package.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:

Example of use:

Solve a linear system A x = b and compute the residual norm, ||b - A x||.

      double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
      Matrix A = new Matrix(vals);
      Matrix b = Matrix.random(3,1);
      Matrix x = A.solve(b);
      Matrix r = A.times(x).minus(b);
      double rnorm = r.normInf();

The original Jama-package has been developed by the MathWorks and NIST and can be found at http://math.nist.gov/javanumerics/jama/. Here, for the adaption some classes and methods convenient for data mining applications within ELKI were added. Furthermore some erroneous comments were corrected and the coding-style was subtly changed to a more Java-typical style.

Release 0.2 (2009-07-06_1820)