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.