Package elki.math.linearalgebra
Some 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:
 Cholesky Decomposition of symmetric, positive definite matrices.
 LU Decomposition of rectangular matrices.
 QR Decomposition of rectangular matrices.
 Singular Value Decomposition of rectangular matrices.
 Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
Solve a linear system \(Ax=b\) and compute the residual norm, \(bAx\).
double[][] matrix = { {1.,2.,3}, {4.,5.,6.}, {7.,8.,10.} };
double[] b = MathUtil.randomDoubleArray(3, new Random());
double[] x = VMath.solve(matrix, b);
double[] r = VMath.minusEquals(VMath.times(matrix, x), b);
double norm = VMath.euclideanLength(r);
The original Jamapackage has been developed by the MathWorks and NIST and can be found at math.nist.gov.
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 codingstyle was subtly changed to a more Javatypical style.

Class Summary Class Description AffineTransformation Affine transformations implemented using homogeneous coordinates.Centroid Class to compute the centroid of some data.CholeskyDecomposition Cholesky Decomposition.ConstrainedQuadraticProblemSolver Solve a constrained quadratic equation in the form \( \tfrac12 x^T A x + b^T x + c \) constrained by a bounding box.ConstrainedQuadraticProblemSolver.ProblemData Contains arrays for a specific size needed for the problem calculation using this object saves the creation of all those arrays, because we can just reuse them.CovarianceMatrix Class for computing covariance matrixes using stable mean and variance computations.EigenvalueDecomposition Eigenvalues and eigenvectors of a real matrix.LinearEquationSystem Class for systems of linear equations.LUDecomposition LU Decomposition.ProjectedCentroid Centroid only using a subset of dimensions.QRDecomposition QR Decomposition.SingularValueDecomposition Singular Value Decomposition.VMath Class providing basic vector mathematics, for lowlevel vectors stored asdouble[]
. 
Enum Summary Enum Description ConstrainedQuadraticProblemSolver.DimensionState Describes the calculation state of a Dimension