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
IMatrix	An abstract interface of matrix.

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.
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'.
EigenValueDecomposition	Eigen decomposition of a real matrix.
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.
Matrix	A matrix is a rectangular array of numbers.
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.
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.

Author:

Haifeng Li