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## Package no.uib.cipr.matrix

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

See:
Description

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

Class Summary
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 LU decomposition FIXME: DenseLU is broken! Fix it
DenseMatrix | Dense matrix.
DenseVector | Dense vector.
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
QL | Computes QL decompositions
QR | Computers QR decompositions
QRP | Computes QR decompositions with column pivoting: `P*A = Q*R` where `A(m,n)`, `Q(m,m)`, and `R(m,n)`, more generally: `P*A = [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
Matrix.Norm | Supported matrix-norms.
NotConvergedException.Reason | Possible reasons for lack of convergence
Vector.Norm | Supported vector-norms.

Exception Summary
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.

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