## Package org.apache.commons.math3.linear

Linear algebra support.

See:
Description

Interface Summary
AnyMatrix: Interface defining very basic matrix operations.
DecompositionSolver: Interface handling decomposition algorithms that can solve A × X = B.
FieldDecompositionSolver<T extends FieldElement<T>>: Interface handling decomposition algorithms that can solve A × X = B.
FieldMatrix<T extends FieldElement<T>>: Interface defining field-valued matrix with basic algebraic operations.
FieldMatrixChangingVisitor<T extends FieldElement<?>>: Interface defining a visitor for matrix entries.
FieldMatrixPreservingVisitor<T extends FieldElement<?>>: Interface defining a visitor for matrix entries.
FieldVector<T extends FieldElement<T>>: Interface defining a field-valued vector with basic algebraic operations.
RealMatrix: Interface defining a real-valued matrix with basic algebraic operations.
RealMatrixChangingVisitor: Interface defining a visitor for matrix entries.
RealMatrixPreservingVisitor: Interface defining a visitor for matrix entries.
SparseRealMatrix: Marker interface for `RealMatrix` implementations that require sparse backing storage

Class Summary
AbstractFieldMatrix<T extends FieldElement<T>>: Basic implementation of `FieldMatrix` methods regardless of the underlying storage.
AbstractRealMatrix: Basic implementation of RealMatrix methods regardless of the underlying storage.
Array2DRowFieldMatrix<T extends FieldElement<T>>: Implementation of FieldMatrix<T> using a `FieldElement`[][] array to store entries.
Array2DRowRealMatrix: Implementation of `RealMatrix` using a `double[][]` array to store entries.
ArrayFieldVector<T extends FieldElement<T>>: This class implements the `FieldVector` interface with a `FieldElement` array.
ArrayRealVector: This class implements the `RealVector` interface with a double array.
BiDiagonalTransformer: Class transforming any matrix to bi-diagonal shape.
BlockFieldMatrix<T extends FieldElement<T>>: Cache-friendly implementation of FieldMatrix using a flat arrays to store square blocks of the matrix.
BlockRealMatrix: Cache-friendly implementation of RealMatrix using a flat arrays to store square blocks of the matrix.
CholeskyDecomposition: Calculates the Cholesky decomposition of a matrix.
CholeskyDecomposition.Solver: Specialized solver.
ConjugateGradient: This is an implementation of the conjugate gradient method for `RealLinearOperator`.
DefaultFieldMatrixChangingVisitor<T extends FieldElement<T>>: Default implementation of the `FieldMatrixChangingVisitor` interface.
DefaultFieldMatrixPreservingVisitor<T extends FieldElement<T>>: Default implementation of the `FieldMatrixPreservingVisitor` interface.
DefaultIterativeLinearSolverEvent: A default concrete implementation of the abstract class `IterativeLinearSolverEvent`.
DefaultRealMatrixChangingVisitor: Default implementation of the `RealMatrixChangingVisitor` interface.
DefaultRealMatrixPreservingVisitor: Default implementation of the `RealMatrixPreservingVisitor` interface.
EigenDecomposition: Calculates the eigen decomposition of a real symmetric matrix.
EigenDecomposition.Solver: Specialized solver.
FieldLUDecomposition<T extends FieldElement<T>>: Calculates the LUP-decomposition of a square matrix.
FieldLUDecomposition.Solver<T extends FieldElement<T>>: Specialized solver.
IterativeLinearSolver: This abstract class defines an iterative solver for the linear system A · x = b.
IterativeLinearSolverEvent: This is the base class for all events occuring during the iterations of a `IterativeLinearSolver`.
JacobiPreconditioner: This class implements the standard Jacobi (diagonal) preconditioner.
LUDecomposition: Calculates the LUP-decomposition of a square matrix.
LUDecomposition.Solver: Specialized solver.
MatrixUtils: A collection of static methods that operate on or return matrices.
MatrixUtils.BigFractionMatrixConverter: Converter for `FieldMatrix`/`BigFraction`.
MatrixUtils.FractionMatrixConverter: Converter for `FieldMatrix`/`Fraction`.
OpenMapRealMatrix: Sparse matrix implementation based on an open addressed map.
OpenMapRealVector: This class implements the `RealVector` interface with a `OpenIntToDoubleHashMap` backing store.
PreconditionedIterativeLinearSolver: This abstract class defines preconditioned iterative solvers.
QRDecomposition: Calculates the QR-decomposition of a matrix.
QRDecomposition.Solver: Specialized solver.
RealLinearOperator: This class defines a linear operator operating on real (`double`) vector spaces.
RealVector: Class defining a real-valued vector with basic algebraic operations.
RealVectorFormat: Formats a vector in components list format "{v0; v1; ...; vk-1}".
RectangularCholeskyDecomposition: Calculates the rectangular Cholesky decomposition of a matrix.
SingularValueDecomposition: Calculates the compact Singular Value Decomposition of a matrix.
SingularValueDecomposition.Solver: Specialized solver.
SparseFieldMatrix<T extends FieldElement<T>>: Sparse matrix implementation based on an open addressed map.
SparseFieldVector<T extends FieldElement<T>>: This class implements the `FieldVector` interface with a `OpenIntToFieldHashMap` backing store.
SparseRealVector: Marker class for RealVectors that require sparse backing storage
SymmLQ: Implementation of the SYMMLQ iterative linear solver proposed by Paige and Saunders (1975).
SymmLQ.SymmLQEvent: The type of all events fired by this implementation of the SYMMLQ method.
TriDiagonalTransformer: Class transforming a symmetrical matrix to tridiagonal shape.

Exception Summary
IllConditionedOperatorException: An exception to be thrown when the condition number of a `RealLinearOperator` is too high.
MatrixDimensionMismatchException: Exception to be thrown when either the number of rows or the number of columns of a matrix do not match the expected values.
NonPositiveDefiniteMatrixException: Exception to be thrown when a positive definite matrix is expected.
NonPositiveDefiniteOperatorException: Exception to be thrown when a symmetric, definite positive `RealLinearOperator` is expected.
NonSelfAdjointOperatorException: Exception to be thrown when a self-adjoint `RealLinearOperator` is expected.
NonSquareMatrixException: Exception to be thrown when a square matrix is expected.
NonSquareOperatorException: Exception to be thrown when a square linear operator is expected.
NonSymmetricMatrixException: Exception to be thrown when a symmetric matrix is expected.
SingularMatrixException: Exception to be thrown when a non-singular matrix is expected.
SingularOperatorException: Exception to be thrown when trying to invert a singular operator.

## Package org.apache.commons.math3.linear Description

Linear algebra support.

Copyright (c) 2003-2013 Apache Software Foundation