Package smile.math.matrix

Matrix interface, dense and sparse (band or irregular) matrix encapsulation classes, LU, QR, Cholesky, SVD and eigen decompositions, etc.

See: Description

Interface Summary

Interface	Description
DenseMatrix	An abstract interface of dense matrix.
LinearSolver	The interface of the solver of linear system.
Matrix	An abstract interface of matrix.
MatrixMultiplication<A,B>	Matrix multiplication interface.
Preconditioner	The preconditioner matrix in the biconjugate gradient method.

Class Summary

Class	Description
BandMatrix	A band matrix is a sparse matrix, whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
BiconjugateGradient	The biconjugate gradient method is an algorithm to solve systems of linear equations.
CholeskyDecomposition	Cholesky decomposition is a decomposition of a symmetric, positive-definite matrix into a lower triangular matrix L and the transpose of the lower triangular matrix such that A = L*L'.
ColumnMajorMatrix	A dense matrix whose data is stored in a single 1D array of doubles in column major order.
EigenValueDecomposition	Eigen decomposition of a real matrix.
Lanczos	The Lanczos algorithm is a direct algorithm devised by Cornelius Lanczos that is an adaptation of power methods to find the most useful eigenvalues and eigenvectors of an nth order linear system with a limited number of operations, m, where m is much smaller than n.
LUDecomposition	For an m-by-n matrix A with m ≥ n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U.
NaiveMatrix	Naive implementation of Matrix interface.
PageRank	PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set.
PowerIteration	The power iteration (also known as power method) is an eigenvalue algorithm that will produce the greatest (in absolute value) eigenvalue and a nonzero vector the corresponding eigenvector.
QRDecomposition	For an m-by-n matrix A with m ≥ n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R such that A = Q*R.
RowMajorMatrix	A dense matrix whose data is stored in a single 1D array of doubles in row major order.
SingularValueDecomposition	Singular Value Decomposition.
SparseMatrix	A sparse matrix is a matrix populated primarily with zeros.

Package smile.math.matrix Description

Matrix interface, dense and sparse (band or irregular) matrix encapsulation classes, LU, QR, Cholesky, SVD and eigen decompositions, etc. A matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries.

One of most important matrix operations is the matrix vector multiplication, which is the only operation needed in many iterative matrix algorithms, e.g. biconjugate gradient method for solving linear equations and power iteration and Lanczos algorithm for eigen decomposition, which are usually very efficient for very large and sparse matrices.