# 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
ARPACK
ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.
DoubleConsumer
Double precision matrix element stream consumer.
FloatConsumer
Single precision matrix element stream consumer.
LinearSolver
The interface of the solver of linear system.
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.
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.
BandMatrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
BandMatrix.LU
The LU decomposition.
The biconjugate gradient method is an algorithm to solve systems of linear equations.
DMatrix
Double precision matrix base class.
FloatBandMatrix
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.
FloatBandMatrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
FloatBandMatrix.LU
The LU decomposition.
FloatMatrix
FloatMatrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
FloatMatrix.EVD
Eigenvalue decomposition.
FloatMatrix.LU
The LU decomposition.
FloatMatrix.QR
The QR decomposition.
FloatMatrix.SVD
Singular Value Decomposition.
FloatSparseMatrix
A sparse matrix is a matrix populated primarily with zeros.
FloatSymmMatrix
They symmetric matrix in packed storage.
FloatSymmMatrix.BunchKaufman
The LU decomposition.
FloatSymmMatrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
IMatrix<T>
An abstract interface of 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.
Matrix
Matrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
Matrix.EVD
Eigenvalue decomposition.
Matrix.LU
The LU decomposition.
Matrix.QR
The QR decomposition.
Matrix.SVD
Singular Value Decomposition.
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.
SMatrix
Single precision matrix base class.
SparseMatrix
A sparse matrix is a matrix populated primarily with zeros.
SymmMatrix
They symmetric matrix in packed storage.
SymmMatrix.BunchKaufman
The LU decomposition.
SymmMatrix.Cholesky
The Cholesky decomposition of a symmetric, positive-definite matrix.
• Enum Summary
Enum Description
ARPACK.AsymmOption
Which eigenvalues of asymmetric matrix to compute.
ARPACK.SymmOption
Which eigenvalues of symmetric matrix to compute.

## 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.