Math.LinearAlgebra.Sparse.Matrix

Sparse matrix datatype

type SMx α = SVec (SVec α)

Internal storage of matrix

data SparseMatrix α

Sparse matrix is indexed map of non-zero rows,

Constructors

SM

Fields

dims :: (Int, Int)

real height and width of filled matrix

mx :: SMx α

IntMap (IntMap α) representing non-zero values

Instances

Functor SparseMatrix

fmap applies given function on all non-zero values

Eq α => Eq (SparseMatrix α)

(Eq α, Num α) => Num (SparseMatrix α)

All Num work on sparse matrices the same way as on SparseVector (see documentation there)

(Show α, Eq α, Num α) => Show (SparseMatrix α)

Shows size and filled matrix (but without zeroes)

Monoid (SparseMatrix α)

mempty is just emptyMx

mappend is horisontal concatenation

Basic functions

height, width :: SparseMatrix α -> Int

Matrix real height and width

setSize :: Num α => (Int, Int) -> SparseMatrix α -> SparseMatrix α

Sets height and width of matrix

emptyMx :: SparseMatrix α

Matrix of zero size with no values

zeroMx :: Num α => (Int, Int) -> SparseMatrix α

Zero matrix of given size

isZeroMx, isNotZeroMx :: SparseMatrix α -> Bool

Checks if matrix has no non-zero values (i.e. is empty)

idMx :: (Num α, Eq α) => Int -> SparseMatrix α

Identity matrix of given size

Combining matrices

(//) :: SparseMatrix α -> SparseMatrix α -> SparseMatrix α

Vertical concatenation

hconcat, vconcat :: [SparseMatrix α] -> SparseMatrix α

Batch horisontal/vertical concatenation

sizedBlockMx :: Num α => (Int, Int) -> [[SparseMatrix α]] -> SparseMatrix α

Takes size of each block and matrix of sparse matrices and constructs sparse matrix from this blocks

sizedBlockSMx :: (Eq α, Num α) => (Int, Int) -> SparseMatrix (SparseMatrix α) -> SparseMatrix α

Fills sparse matrix of blocks and then applies sizedBlockMx

blockMx :: [[SparseMatrix α]] -> SparseMatrix α

blockSMx :: (Eq α, Num α) => SparseMatrix (SparseMatrix α) -> SparseMatrix α

Addingdeleting rowcolumns

addRow :: Num α => SparseVector α -> Index -> SparseMatrix α -> SparseMatrix α

Adds row at given index, increasing matrix height by 1 and shifting indexes after it

addCol :: Num α => SparseVector α -> Index -> SparseMatrix α -> SparseMatrix α

Adds column at given index, increasing matrix width by 1 and shifting indexes after it

addZeroRow :: Num α => Index -> SparseMatrix α -> SparseMatrix α

Just adds zero row at given index

addZeroCol :: Num α => Index -> SparseMatrix α -> SparseMatrix α

Just adds zero column at given index

delRow :: Num α => Index -> SparseMatrix α -> SparseMatrix α

Deletes row at given index, decreasing matrix height by 1 and shifting indexes after it

delCol :: Num α => Index -> SparseMatrix α -> SparseMatrix α

Deletes column at given index, decreasing matrix width by 1 and shifting indexes after it

delRowCol :: Num α => Index -> Index -> SparseMatrix α -> SparseMatrix α

Deletes row and column at given indexes

separateMx :: Num α => (SparseVector α -> Bool) -> SparseMatrix α -> (SparseMatrix α, SparseMatrix α)

Separates matrix, using pedicate on rows and returns two matrices of the same size, one only with rows satisfying predicate, and another with the rest rows

Lookup/update

(#) :: Num α => SparseMatrix α -> (Index, Index) -> α

Looks up an element in the matrix (if not found, zero is returned)

row :: Num α => SparseMatrix α -> Index -> SparseVector α

Returns row of matrix at given index

col :: (Num α, Eq α) => SparseMatrix α -> Index -> SparseVector α

Returns column of matrix at given index

updRow :: Num α => (SparseVector α -> SparseVector α) -> Index -> SparseMatrix α -> SparseMatrix α

Updates values in row using given function

eraseRow :: Num α => Index -> SparseMatrix α -> SparseMatrix α

Fills row with zeroes (i.e. deletes it, but size of matrix doesn't change)

erase :: Num α => SparseMatrix α -> (Index, Index) -> SparseMatrix α

Erases matrix element at given index

ins :: (Num α, Eq α) => SparseMatrix α -> ((Index, Index), α) -> SparseMatrix α

Inserts new element to the sparse matrix (replaces old value)

findRowIndices :: (SparseVector α -> Bool) -> SparseMatrix α -> [Int]

Finds indices of rows, that satisfy given predicate. Searches from left to right (in ascending order of indices)

findRowIndicesR :: (SparseVector α -> Bool) -> SparseMatrix α -> [Int]

Finds indices of rows, that satisfy given predicate. Searches from right to left (in descending order of indices)

popRow :: Num α => Index -> SparseMatrix α -> (SparseVector α, SparseMatrix α)

Returns a row at given index and matrix without it

(|>) :: Num α => SparseVector α -> SparseMatrix α -> SparseMatrix α

Adds row to matrix at the top

(<|) :: Num α => SparseMatrix α -> SparseVector α -> SparseMatrix α

Adds row to matrix at the bottom

replaceRow :: Num α => SparseVector α -> Index -> SparseMatrix α -> SparseMatrix α

Replaces row at given index with given vector

exchangeRows :: Num α => Index -> Index -> SparseMatrix α -> SparseMatrix α

Exchanges positions of two rows

mapOnRows :: (SparseVector α -> SparseVector β) -> SparseMatrix α -> SparseMatrix β

Applies vector-function on matrix rows

To/from list

diagonalMx :: (Num α, Eq α) => [α] -> SparseMatrix α

Constructs square matrix with given elements on diagonal

mainDiag :: (Eq α, Num α) => SparseMatrix α -> SparseVector α

Collects main diagonal of matrix

fromRows :: Num α => [SparseVector α] -> SparseMatrix α

Constructs matrix from a list of rows

toAssocList :: (Num α, Eq α) => SparseMatrix α -> [((Index, Index), α)]

Converts sparse matrix to associative list, adding fake zero element, to save real size for inverse conversion

fromAssocListWithSize :: (Num α, Eq α) => (Int, Int) -> [((Index, Index), α)] -> SparseMatrix α

Converts associative list to sparse matrix, of given size

fromAssocList :: (Num α, Eq α) => [((Index, Index), α)] -> SparseMatrix α

Converts associative list to sparse matrix, using maximal index as matrix size

fillMx :: Num α => SparseMatrix α -> [[α]]

Converts sparse matrix to plain list-matrix with all zeroes restored

sparseMx :: (Num α, Eq α) => [[α]] -> SparseMatrix α

Converts plain list-matrix to sparse matrix, throwing out all zeroes

Transposition

trans :: (Num α, Eq α) => SparseMatrix α -> SparseMatrix α

Transposes matrix (rows become columns)

Multiplications

mulMV :: (Num α, Eq α) => SparseMatrix α -> SparseVector α -> SparseVector α

Matrix-by-vector multiplication

(×·) :: (Num α, Eq α) => SparseMatrix α -> SparseVector α -> SparseVector α

Unicode alias for mulMV

mulVM :: (Num α, Eq α) => SparseVector α -> SparseMatrix α -> SparseVector α

Vector-by-matrix multiplication

·× :: (Num α, Eq α) => SparseVector α -> SparseMatrix α -> SparseVector α

Unicode alias for mulVM

mul :: (Num α, Eq α) => SparseMatrix α -> SparseMatrix α -> SparseMatrix α

Sparse matrices multiplication

(×) :: (Num α, Eq α) => SparseMatrix α -> SparseMatrix α -> SparseMatrix α

Unicode alias for mul