Sparse matrices.
We assume the matrices to be very sparse, so we just implement them as sorted association lists.
- data Matrix i b
- matrixInvariant :: (Num i, Ix i) => Matrix i b -> Bool
- data Size i = Size {}
- sizeInvariant :: (Ord i, Num i) => Size i -> Bool
- data MIx i = MIx {}
- mIxInvariant :: (Ord i, Num i) => MIx i -> Bool
- fromLists :: (Ord i, Num i, Enum i, HasZero b) => Size i -> [[b]] -> Matrix i b
- fromIndexList :: (Ord i, HasZero b) => Size i -> [(MIx i, b)] -> Matrix i b
- toLists :: (Ord i, Integral i, Enum i, HasZero b) => Matrix i b -> [[b]]
- matrix :: (Arbitrary i, Integral i, Arbitrary b, HasZero b) => Size i -> Gen (Matrix i b)
- matrixUsingRowGen :: (Arbitrary i, Integral i, Arbitrary b, HasZero b) => Size i -> (i -> Gen [b]) -> Gen (Matrix i b)
- size :: Matrix i b -> Size i
- square :: Ix i => Matrix i b -> Bool
- isEmpty :: (Num i, Ix i) => Matrix i b -> Bool
- isSingleton :: (Num i, Ix i) => Matrix i b -> Maybe b
- add :: Ord i => (a -> a -> a) -> Matrix i a -> Matrix i a -> Matrix i a
- intersectWith :: Ord i => (a -> a -> a) -> Matrix i a -> Matrix i a -> Matrix i a
- mul :: (Enum i, Num i, Ix i, Eq a) => Semiring a -> Matrix i a -> Matrix i a -> Matrix i a
- transpose :: Ord i => Matrix i b -> Matrix i b
- diagonal :: (Enum i, Num i, Ix i, HasZero b) => Matrix i b -> Array i b
- addRow :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i b
- addColumn :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i b
- tests :: IO Bool
Basic data types
Type of matrices, parameterised on the type of values.
(Eq i, Eq b) => Eq (Matrix i b) | |
(Ord i, Ord b) => Ord (Matrix i b) | |
(Ord i, Integral i, Enum i, Show i, Show b, HasZero b) => Show (Matrix i b) | |
(Arbitrary i, Num i, Integral i, Arbitrary b, HasZero b) => Arbitrary (Matrix i b) | |
(Ord i, Integral i, Enum i, CoArbitrary b, HasZero b) => CoArbitrary (Matrix i b) | |
(Integral i, HasZero b, Pretty b) => Pretty (Matrix i b) |
Size of a matrix.
Type of matrix indices (row, column).
Generating and creating matrices
fromIndexList :: (Ord i, HasZero b) => Size i -> [(MIx i, b)] -> Matrix i bSource
Constructs a matrix from a list of (index, value)-pairs.
toLists :: (Ord i, Integral i, Enum i, HasZero b) => Matrix i b -> [[b]]Source
Converts a matrix to a list of row lists.
matrix :: (Arbitrary i, Integral i, Arbitrary b, HasZero b) => Size i -> Gen (Matrix i b)Source
Generates a matrix of the given size.
:: (Arbitrary i, Integral i, Arbitrary b, HasZero b) | |
=> Size i | |
-> (i -> Gen [b]) | The generator is parameterised on the size of the row. |
-> Gen (Matrix i b) |
Generates a matrix of the given size, using the given generator to generate the rows.
Combining and querying matrices
isSingleton :: (Num i, Ix i) => Matrix i b -> Maybe bSource
Returns 'Just b' iff it is a 1x1 matrix with just one entry b
.
intersectWith :: Ord i => (a -> a -> a) -> Matrix i a -> Matrix i a -> Matrix i aSource
build the pointwise conjunction intersectWith
f m1 m2m1
and m2
.
Uses f
to combine non-zero values.
Modifying matrices
addRow :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i bSource
adds a new row to addRow
x mm
, after the rows already
existing in the matrix. All elements in the new row get set to x
.
addColumn :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i bSource
adds a new column to addColumn
x mm
, after the columns
already existing in the matrix. All elements in the new column get
set to x
.