Data.Eigen.SparseMatrix

SparseMatrix type

SparseMatrix aliases follows Eigen naming convention

data SparseMatrix a b where

A versatible sparse matrix representation.

This class implements a more versatile variants of the common compressed row/column storage format. Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index. All the non zeros are stored in a single large buffer. Unlike the compressed format, there might be extra space inbetween the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero can be done with limited memory reallocation and copies.

The results of Eigen's operations always produces compressed sparse matrices. On the other hand, the insertion of a new element into a SparseMatrix converts this later to the uncompressed mode.

A call to the function compress turns the matrix into the standard compressed format compatible with many library.

Implementation deails of SparseMatrix are intentionally hidden behind ForeignPtr bacause Eigen doesn't provide mapping over plain data for sparse matricies.

For more infomration please see Eigen documentation page: http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html

Constructors

SparseMatrix :: Elem a b => !(ForeignPtr (CSparseMatrix a b)) -> SparseMatrix a b

Instances

Elem a b => Num (SparseMatrix a b)

Shortcuts for basic matrix math

(Elem a b, Show a) => Show (SparseMatrix a b)

Pretty prints the sparse matrix

type SparseMatrixXf = SparseMatrix Float CFloat

Alias for single precision sparse matrix

type SparseMatrixXd = SparseMatrix Double CDouble

Alias for double precision sparse matrix

type SparseMatrixXcf = SparseMatrix (Complex Float) (CComplex CFloat)

Alias for single previsiom sparse matrix of complex numbers

type SparseMatrixXcd = SparseMatrix (Complex Double) (CComplex CDouble)

Alias for double prevision sparse matrix of complex numbers

Accessing matrix data

cols :: Elem a b => SparseMatrix a b -> Int

Number of columns for the sparse matrix

rows :: Elem a b => SparseMatrix a b -> Int

Number of rows for the sparse matrix

coeff :: Elem a b => Int -> Int -> SparseMatrix a b -> a

Matrix coefficient at given row and col

(!) :: Elem a b => SparseMatrix a b -> (Int, Int) -> a

Matrix coefficient at given row and col

Matrix conversions

fromList :: Elem a b => Int -> Int -> [(Int, Int, a)] -> SparseMatrix a b

Construct sparse matrix of given size from the list of triplets (row, col, val)

toList :: Elem a b => SparseMatrix a b -> [(Int, Int, a)]

Convert sparse matrix to the list of triplets (row, col, val). Compressed elements will not be included

fromDenseList :: (Elem a b, Eq a) => [[a]] -> SparseMatrix a b

Construct sparse matrix of two-dimensional list of values. Matrix dimensions will be detected automatically. Zero values will be compressed.

toDenseList :: Elem a b => SparseMatrix a b -> [[a]]

Convert sparse matrix to (rows X cols) dense list of values

fromMatrix :: Elem a b => Matrix a b -> SparseMatrix a b

Construct sparse matrix from dense matrix. Zero elements will be compressed

toMatrix :: Elem a b => SparseMatrix a b -> Matrix a b

Construct dense matrix from sparse matrix

Matrix properties

norm :: Elem a b => SparseMatrix a b -> a

For vectors, the l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of this with itself.

squaredNorm :: Elem a b => SparseMatrix a b -> a

For vectors, the squared l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of this with itself.

blueNorm :: Elem a b => SparseMatrix a b -> a

The l2 norm of the matrix using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

block :: Elem a b => Int -> Int -> Int -> Int -> SparseMatrix a b -> SparseMatrix a b

Extract rectangular block from sparse matrix defined by startRow startCol blockRows blockCols

compress :: Elem a b => SparseMatrix a b -> SparseMatrix a b

Turns the matrix into the compressed format

uncompress :: Elem a b => SparseMatrix a b -> SparseMatrix a b

not exposed currently

compressed :: Elem a b => SparseMatrix a b -> Bool

not exposed currently

nonZeros :: Elem a b => SparseMatrix a b -> Int

Number of non-zeros elements in the sparse matrix

innerSize :: Elem a b => SparseMatrix a b -> Int

Minor dimension with respect to the storage order

outerSize :: Elem a b => SparseMatrix a b -> Int

Major dimension with respect to the storage order

Basic matrix algebra

add :: Elem a b => SparseMatrix a b -> SparseMatrix a b -> SparseMatrix a b

Adding two sparse matrices by adding the corresponding entries together. You can use (+) function as well.

sub :: Elem a b => SparseMatrix a b -> SparseMatrix a b -> SparseMatrix a b

Subtracting two sparse matrices by subtracting the corresponding entries together. You can use (-) function as well.

mul :: Elem a b => SparseMatrix a b -> SparseMatrix a b -> SparseMatrix a b

Matrix multiplication. You can use (*) function as well.

Matrix transformations

pruned :: Elem a b => a -> SparseMatrix a b -> SparseMatrix a b

Suppresses all nonzeros which are much smaller than reference under the tolerence epsilon

scale :: Elem a b => a -> SparseMatrix a b -> SparseMatrix a b

Multiply matrix on a given scalar

transpose :: Elem a b => SparseMatrix a b -> SparseMatrix a b

Transpose of the sparse matrix

adjoint :: Elem a b => SparseMatrix a b -> SparseMatrix a b

Adjoint of the sparse matrix

Matrix serialization

encode :: Elem a b => SparseMatrix a b -> ByteString

Encode the sparse matrix as a lazy byte string

decode :: forall a b. Elem a b => ByteString -> SparseMatrix a b

Decode sparse matrix from the lazy byte string