Package no.uib.cipr.matrix

Dense and structured sparse matrices, along with matrix factorisations and solvers.

See: Description

Interface Summary

Interface	Description
Matrix	Basic matrix interface.
MatrixEntry	An entry of a matrix.
Vector	Basic vector interface.
VectorEntry	An entry of a vector.

Class Summary

Class	Description
AbstractMatrix	Partial implementation of Matrix.
AbstractVector	Partial implementation of Vector.
BandCholesky	Banded Cholesky decomposition
BandLU	Banded LU decomposition
BandMatrix	Banded matrix.
DenseCholesky	Dense Cholesky decomposition
DenseLU	Dense Partial Pivot LU decomposition: A = P * L * U.
DenseMatrix	Dense matrix.
DenseVector	Dense vector.
DenseVectorSub	Wraps a DenseVector, allowing easy access to a sub array of the original without taking copies.
EVD	Computes eigenvalue decompositions of general matrices
GivensRotation	Givens plane rotation
LowerSPDBandMatrix	Lower symmetrical positive definite banded matrix.
LowerSPDDenseMatrix	Lower symmetrical positive definite dense matrix.
LowerSPDPackMatrix	Lower symmetrical positive definite packed matrix.
LowerSymmBandMatrix	Lower symmetrical banded matrix.
LowerSymmDenseMatrix	Lower symmetric dense matrix.
LowerSymmPackMatrix	Lower symmetric packed matrix.
LowerTriangBandMatrix	Lower triangular banded matrix.
LowerTriangDenseMatrix	Lower triangular dense matrix.
LowerTriangPackMatrix	Lower triangular packed matrix.
LQ	Computes LQ decompositions
Matrices	Static utility methods for matrices and vectors
PackCholesky	Packed Cholesky decomposition
PermutationMatrix	Matrix that represents a permutation of another matrix's rows / columns.
QL	Computes QL decompositions
QR	Computers QR decompositions
QRP	Computes QR decompositions with column pivoting: A*P = Q*R where A(m,n), Q(m,m), and R(m,n), more generally: A*P = [Q1 Q2] * [R11, R12; 0 R22] and R22 elements are negligible.
RQ	Computes RQ decompositions
SPDTridiagMatrix	Symmetrical positive definite tridiagonal matrix.
SVD	Computes singular value decompositions
SymmBandEVD	Computes eigenvalues of symmetrical, banded matrices
SymmDenseEVD	Computes eigenvalues of symmetrical, dense matrices
SymmPackEVD	Computes eigenvalues of symmetrical, packed matrices
SymmTridiagEVD	Computes eigenvalues of symmetrical, tridiagonal matrices
SymmTridiagMatrix	Symmetrical tridiagonal matrix.
TridiagMatrix	Tridiagonal matrix.
UnitLowerTriangBandMatrix	Unit lower triangular banded matrix.
UnitLowerTriangDenseMatrix	Unit lower triangular dense matrix.
UnitLowerTriangPackMatrix	Unit lower triangular packed matrix.
UnitUpperTriangBandMatrix	Unit upper triangular banded matrix.
UnitUpperTriangDenseMatrix	Unit upper triangular dense matrix.
UnitUpperTriangPackMatrix	Unit upper triangular packed matrix.
UpperSPDBandMatrix	Upper symmetrical positive definite banded matrix.
UpperSPDDenseMatrix	Upper symmetrical positive definite dense matrix.
UpperSPDPackMatrix	Upper symmetrical positive definite packed matrix.
UpperSymmBandMatrix	Upper symmetrical banded matrix.
UpperSymmDenseMatrix	Upper symmetrix dense matrix.
UpperSymmPackMatrix	Upper symmetric packed matrix.
UpperTriangBandMatrix	Upper triangular banded matrix.
UpperTriangDenseMatrix	Upper triangular dense matrix.
UpperTriangPackMatrix	Upper triangular packed matrix.

Enum Summary

Enum	Description
Matrix.Norm	Supported matrix-norms.
NotConvergedException.Reason	Possible reasons for lack of convergence
Vector.Norm	Supported vector-norms.

Exception Summary

Exception	Description
MatrixNotSPDException	Matrix is not symmetrical, positive definite
MatrixSingularException	Matrix is singular
NotConvergedException	Signals lack of convergence of an iterative process

Package no.uib.cipr.matrix Description

Dense and structured sparse matrices, along with matrix factorisations and solvers. The main components are:

• Matrix and vector interfaces
  • Matrix - Linear algebra matrix.
  • Vector - Linear algebra vector.
• Matrix and vector implementations
  • DenseVector - Stores the vector in a dense array.
  • Dense matrices - Stores the data columnwise in a linear array.
    • DenseMatrix - Recommended matrix for general cases.
    • {Lower,Upper}{Symm,SPD}DenseMatrix - Assumes implicit symmetry, and that the matrix is positive definite (SPD). Stores entries in either the upper or lower triangular part.
    • [Unit]{Lower,Upper}TriangDenseMatrix - Only stores in the lower or upper triangular part, and assumes the rest is zero. If the matrix is unit, the main diagonal is implicitly assumes to be one.
  • Packed matrices - Stores either the lower or upper triangular part of the matrix.
    • {Lower,Upper}{Symm,SPD}PackMatrix - Like their dense counterparts, but consumes less memory.
    • [Unit]{Lower,Upper}TriangPackMatrix - Also like their dense counterparts, but consumes less memory.
  • Banded matrices - Stores the matrix in a dense band.
    • BandMatrix - General band matrix with the possibility of different upper and lower triangular bandwidths.
    • {Lower,Upper}{Symm,SPD}BandMatrix - Like their dense counterparts, but consumes less memory by only storing the lower or upper parts.
    • [Unit]{Lower,Upper}TriangBandMatrix - Also like their dense counterparts, but consumes less memory by only storing the lower or upper parts..
  • Tridiagonal matrices - Stores just three diagonals.
    • TridiagMatrix - Standard tridiagonal matrix.
    • {Symm,SPD}TridiagMatrix - Stores only the main diagonal and an off-diagonal. May also assume that the matrix is positive definite.
• Abstract implementations
  • AbstractMatrix - Implements all the matrix operations, but doesn't specify the matrix storage.
  • AbstractVector - Implements all the vector operations, but doesn't specify the vector storage.
• Utility methods and iterators
  • Matrices - Creates submatrices and synchronized matrices. Also has several miscellaneous utility methods.
  • MatrixEntry - Entry returned when iterating over a matrix using the for-each statement.
  • VectorEntry - Entry returned when iterating over a vector using the for-each statement.
• LU decompositions
  • BandLU - LU decomposition of a banded matrix.
  • DenseLU - LU decomposition of a dense matrix.
  • BandCholesky - Cholesky decomposition of a banded matrix.
  • DenseCholesky - Cholesky decomposition of a dense SPD matrix.
  • PackCholesky - Cholesky decomposition of a packed SPD matrix.
• Orthogonal decompositions
  • LQ - LQ decomposition.
  • QL - QL decomposition.
  • QR - QR decomposition.
  • RQ - RQ decomposition.
  • GivensRotation - Givens plane rotation.
• Spectral decompositions
  • EVD - Eigenvalue decomposition of general matrices.
  • SVD - Singular value decomposition
  • SymmBandEVD - Eigenvalue decomposition of symmetrical, banded matrices.
  • SymmDenseEVD - Eigenvalue decomposition of symmetrical, dense matrices.
  • SymmPackEVD - Eigenvalue decomposition of symmetrical, packed matrices.
  • SymmTridiagEVD - Eigenvalue decomposition of symmetrical, tridiagonal matrices.