# Package smile.math.matrix

package smile.math.matrix
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.

• Class
Description
ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.
Which eigenvalues of asymmetric matrix to compute.
Which eigenvalues of symmetric matrix to compute.
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.
The Cholesky decomposition of a symmetric, positive-definite matrix.
The LU decomposition.
Big dense matrix of double precision values for more than 2 billion elements.
The Cholesky decomposition of a symmetric, positive-definite matrix.
Eigenvalue decomposition.
The LU decomposition.
The QR decomposition.
Singular Value Decomposition.
Double precision matrix element stream consumer.
Matrix base class.
The preconditioner matrix.
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.
Dense matrix of double precision values.
The Cholesky decomposition of a symmetric, positive-definite matrix.
Eigenvalue decomposition.
The LU decomposition.
The QR decomposition.
Singular Value Decomposition.
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.
A sparse matrix is a matrix populated primarily with zeros.
The symmetric matrix in packed storage.
The LU decomposition.
The Cholesky decomposition of a symmetric, positive-definite matrix.