Math.LinearAlgebra.Sparse.Matrix

Documentation

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)

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

Shows size and filled matrix (but without zeroes)

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

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

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

WARNING: doesn't work with empty rows

Partitions matrix, using pedicate on rows and returns two new matrices, one constructed from rows satisfying predicate, and another from rows that don't

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

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

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

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

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

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

(#) :: 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)

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

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

showSparseMatrix :: (Show α, Eq α, Num α) => [[α]] -> String

column :: (Show α, Eq α, Num α) => [α] -> [String]

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

Transposes matrix (rows become columns)

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