Safe Haskell | None |
---|---|

Language | Haskell98 |

- data Matrix a b where
- type MatrixXf = Matrix Float CFloat
- type MatrixXd = Matrix Double CDouble
- type MatrixXcf = Matrix (Complex Float) (CComplex CFloat)
- type MatrixXcd = Matrix (Complex Double) (CComplex CDouble)
- class (Num a, Cast a b, Cast b a, Storable b, Code b) => Elem a b | a -> b
- data CComplex a
- valid :: Elem a b => Matrix a b -> Bool
- fromList :: Elem a b => [[a]] -> Matrix a b
- toList :: Elem a b => Matrix a b -> [[a]]
- generate :: Elem a b => Int -> Int -> (Int -> Int -> a) -> Matrix a b
- empty :: Elem a b => Matrix a b
- null :: Elem a b => Matrix a b -> Bool
- square :: Elem a b => Matrix a b -> Bool
- zero :: Elem a b => Int -> Int -> Matrix a b
- ones :: Elem a b => Int -> Int -> Matrix a b
- identity :: Elem a b => Int -> Int -> Matrix a b
- constant :: Elem a b => Int -> Int -> a -> Matrix a b
- random :: Elem a b => Int -> Int -> IO (Matrix a b)
- cols :: Elem a b => Matrix a b -> Int
- rows :: Elem a b => Matrix a b -> Int
- dims :: Elem a b => Matrix a b -> (Int, Int)
- (!) :: Elem a b => Matrix a b -> (Int, Int) -> a
- coeff :: Elem a b => Int -> Int -> Matrix a b -> a
- unsafeCoeff :: Elem a b => Int -> Int -> Matrix a b -> a
- col :: Elem a b => Int -> Matrix a b -> [a]
- row :: Elem a b => Int -> Matrix a b -> [a]
- block :: Elem a b => Int -> Int -> Int -> Int -> Matrix a b -> Matrix a b
- topRows :: Elem a b => Int -> Matrix a b -> Matrix a b
- bottomRows :: Elem a b => Int -> Matrix a b -> Matrix a b
- leftCols :: Elem a b => Int -> Matrix a b -> Matrix a b
- rightCols :: Elem a b => Int -> Matrix a b -> Matrix a b
- sum :: Elem a b => Matrix a b -> a
- prod :: Elem a b => Matrix a b -> a
- mean :: Elem a b => Matrix a b -> a
- minCoeff :: (Elem a b, Ord a) => Matrix a b -> a
- maxCoeff :: (Elem a b, Ord a) => Matrix a b -> a
- trace :: Elem a b => Matrix a b -> a
- norm :: Elem a b => Matrix a b -> a
- squaredNorm :: Elem a b => Matrix a b -> a
- blueNorm :: Elem a b => Matrix a b -> a
- hypotNorm :: Elem a b => Matrix a b -> a
- determinant :: Elem a b => Matrix a b -> a
- fold :: Elem a b => (c -> a -> c) -> c -> Matrix a b -> c
- fold' :: Elem a b => (c -> a -> c) -> c -> Matrix a b -> c
- ifold :: Elem a b => (Int -> Int -> c -> a -> c) -> c -> Matrix a b -> c
- ifold' :: Elem a b => (Int -> Int -> c -> a -> c) -> c -> Matrix a b -> c
- fold1 :: Elem a b => (a -> a -> a) -> Matrix a b -> a
- fold1' :: Elem a b => (a -> a -> a) -> Matrix a b -> a
- all :: Elem a b => (a -> Bool) -> Matrix a b -> Bool
- any :: Elem a b => (a -> Bool) -> Matrix a b -> Bool
- count :: Elem a b => (a -> Bool) -> Matrix a b -> Int
- add :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b
- sub :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b
- mul :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b
- map :: Elem a b => (a -> a) -> Matrix a b -> Matrix a b
- imap :: Elem a b => (Int -> Int -> a -> a) -> Matrix a b -> Matrix a b
- filter :: Elem a b => (a -> Bool) -> Matrix a b -> Matrix a b
- ifilter :: Elem a b => (Int -> Int -> a -> Bool) -> Matrix a b -> Matrix a b
- diagonal :: Elem a b => Matrix a b -> Matrix a b
- transpose :: Elem a b => Matrix a b -> Matrix a b
- inverse :: Elem a b => Matrix a b -> Matrix a b
- adjoint :: Elem a b => Matrix a b -> Matrix a b
- conjugate :: Elem a b => Matrix a b -> Matrix a b
- normalize :: Elem a b => Matrix a b -> Matrix a b
- modify :: Elem a b => (forall s. MMatrix a b s -> ST s ()) -> Matrix a b -> Matrix a b
- convert :: (Elem a b, Elem c d) => (a -> c) -> Matrix a b -> Matrix c d
- data TriangularMode
- triangularView :: Elem a b => TriangularMode -> Matrix a b -> Matrix a b
- lowerTriangle :: Elem a b => Matrix a b -> Matrix a b
- upperTriangle :: Elem a b => Matrix a b -> Matrix a b
- encode :: Elem a b => Matrix a b -> ByteString
- decode :: Elem a b => ByteString -> Matrix a b
- thaw :: Elem a b => PrimMonad m => Matrix a b -> m (MMatrix a b (PrimState m))
- freeze :: Elem a b => PrimMonad m => MMatrix a b (PrimState m) -> m (Matrix a b)
- unsafeThaw :: Elem a b => PrimMonad m => Matrix a b -> m (MMatrix a b (PrimState m))
- unsafeFreeze :: Elem a b => PrimMonad m => MMatrix a b (PrimState m) -> m (Matrix a b)
- unsafeWith :: Elem a b => Matrix a b -> (Ptr b -> CInt -> CInt -> IO c) -> IO c

# Matrix type

Matrix aliases follows Eigen naming convention

Matrix to be used in pure computations, uses column major memory layout, features copy-free FFI with C++ Eigen library.

type MatrixXcf = Matrix (Complex Float) (CComplex CFloat) Source

Alias for single previsiom matrix of complex numbers

type MatrixXcd = Matrix (Complex Double) (CComplex CDouble) Source

Alias for double prevision matrix of complex numbers

Complex number for FFI with the same memory layout as std::complex<T>

# Matrix conversions

fromList :: Elem a b => [[a]] -> Matrix a b Source

Construct matrix from a list of rows, column count is detected as maximum row length. Missing values are filled with 0

generate :: Elem a b => Int -> Int -> (Int -> Int -> a) -> Matrix a b Source

- generate rows cols (λ row col -> val)

Create matrix using generator function `λ row col -> val`

# Standard matrices and special cases

identity :: Elem a b => Int -> Int -> Matrix a b Source

The identity matrix (not necessarily square).

constant :: Elem a b => Int -> Int -> a -> Matrix a b Source

Matrix where all coeffs are filled with given value

# Accessing matrix data

unsafeCoeff :: Elem a b => Int -> Int -> Matrix a b -> a Source

Unsafe version of coeff function. No bounds check performed so SEGFAULT possible

block :: Elem a b => Int -> Int -> Int -> Int -> Matrix a b -> Matrix a b Source

Extract rectangular block from matrix defined by startRow startCol blockRows blockCols

# Matrix properties

trace :: Elem a b => Matrix a b -> a Source

The trace of a matrix is the sum of the diagonal coefficients and can also be computed as sum (diagonal m)

norm :: Elem a b => Matrix a b -> a Source

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 => Matrix a b -> a Source

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 => Matrix a b -> a Source

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.

hypotNorm :: Elem a b => Matrix a b -> a Source

The l2 norm of the matrix avoiding undeflow and overflow. This version use a concatenation of hypot calls, and it is very slow.

determinant :: Elem a b => Matrix a b -> a Source

The determinant of the matrix

# Generic reductions

fold :: Elem a b => (c -> a -> c) -> c -> Matrix a b -> c Source

Reduce matrix using user provided function applied to each element.

fold' :: Elem a b => (c -> a -> c) -> c -> Matrix a b -> c Source

Reduce matrix using user provided function applied to each element. This is strict version of `fold`

ifold :: Elem a b => (Int -> Int -> c -> a -> c) -> c -> Matrix a b -> c Source

Reduce matrix using user provided function applied to each element and it's index

ifold' :: Elem a b => (Int -> Int -> c -> a -> c) -> c -> Matrix a b -> c Source

Reduce matrix using user provided function applied to each element and it's index. This is strict version of `ifold`

fold1 :: Elem a b => (a -> a -> a) -> Matrix a b -> a Source

Reduce matrix using user provided function applied to each element.

fold1' :: Elem a b => (a -> a -> a) -> Matrix a b -> a Source

Reduce matrix using user provided function applied to each element. This is strict version of `fold`

# Boolean reductions

all :: Elem a b => (a -> Bool) -> Matrix a b -> Bool Source

Applied to a predicate and a matrix, all determines if all elements of the matrix satisfies the predicate

any :: Elem a b => (a -> Bool) -> Matrix a b -> Bool Source

Applied to a predicate and a matrix, any determines if any element of the matrix satisfies the predicate

count :: Elem a b => (a -> Bool) -> Matrix a b -> Int Source

Returns the number of coefficients in a given matrix that evaluate to true

# Basic matrix algebra

add :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b Source

Adding two matrices by adding the corresponding entries together. You can use `(+)`

function as well.

sub :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b Source

Subtracting two matrices by subtracting the corresponding entries together. You can use `(-)`

function as well.

mul :: Elem a b => Matrix a b -> Matrix a b -> Matrix a b Source

Matrix multiplication. You can use `(*)`

function as well.

# Mapping over elements

map :: Elem a b => (a -> a) -> Matrix a b -> Matrix a b Source

Apply a given function to each element of the matrix.

Here is an example how to implement scalar matrix multiplication:

`>>>`

`let a = fromList [[1,2],[3,4]] :: MatrixXf`

`>>>`

Matrix 2x2 1.0 2.0 3.0 4.0`a`

`>>>`

Matrix 2x2 10.0 20.0 30.0 40.0`map (*10) a`

imap :: Elem a b => (Int -> Int -> a -> a) -> Matrix a b -> Matrix a b Source

Apply a given function to each element of the matrix.

Here is an example how upper triangular matrix can be implemented:

`>>>`

`let a = fromList [[1,2,3],[4,5,6],[7,8,9]] :: MatrixXf`

`>>>`

Matrix 3x3 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0`a`

`>>>`

Matrix 3x3 1.0 2.0 3.0 0.0 5.0 6.0 0.0 0.0 9.0`imap (\row col val -> if row <= col then val else 0) a`

filter :: Elem a b => (a -> Bool) -> Matrix a b -> Matrix a b Source

Filter elements in the matrix. Filtered elements will be replaced by 0

ifilter :: Elem a b => (Int -> Int -> a -> Bool) -> Matrix a b -> Matrix a b Source

Filter elements in the matrix. Filtered elements will be replaced by 0

# Matrix transformations

inverse :: Elem a b => Matrix a b -> Matrix a b Source

Inverse of the matrix

For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses PartialPivLU decomposition

normalize :: Elem a b => Matrix a b -> Matrix a b Source

Nomalize the matrix by deviding it on its `norm`

modify :: Elem a b => (forall s. MMatrix a b s -> ST s ()) -> Matrix a b -> Matrix a b Source

Apply a destructive operation to a matrix. The operation will be performed in place if it is safe to do so and will modify a copy of the matrix otherwise.

convert :: (Elem a b, Elem c d) => (a -> c) -> Matrix a b -> Matrix c d Source

Convert matrix to different type using user provided element converter

data TriangularMode Source

Lower | View matrix as a lower triangular matrix. |

Upper | View matrix as an upper triangular matrix. |

StrictlyLower | View matrix as a lower triangular matrix with zeros on the diagonal. |

StrictlyUpper | View matrix as an upper triangular matrix with zeros on the diagonal. |

UnitLower | View matrix as a lower triangular matrix with ones on the diagonal. |

UnitUpper | View matrix as an upper triangular matrix with ones on the diagonal. |

triangularView :: Elem a b => TriangularMode -> Matrix a b -> Matrix a b Source

Triangular view extracted from the current matrix

lowerTriangle :: Elem a b => Matrix a b -> Matrix a b Source

Lower trinagle of the matrix. Shortcut for `triangularView Lower`

upperTriangle :: Elem a b => Matrix a b -> Matrix a b Source

Upper trinagle of the matrix. Shortcut for `triangularView Upper`

# Matrix serialization

encode :: Elem a b => Matrix a b -> ByteString Source

Encode the matrix as a lazy byte string

decode :: Elem a b => ByteString -> Matrix a b Source

Decode matrix from the lazy byte string

# Mutable matrices

thaw :: Elem a b => PrimMonad m => Matrix a b -> m (MMatrix a b (PrimState m)) Source

Yield a mutable copy of the immutable matrix

freeze :: Elem a b => PrimMonad m => MMatrix a b (PrimState m) -> m (Matrix a b) Source

Yield an immutable copy of the mutable matrix

unsafeThaw :: Elem a b => PrimMonad m => Matrix a b -> m (MMatrix a b (PrimState m)) Source

Unsafely convert an immutable matrix to a mutable one without copying. The immutable matrix may not be used after this operation.

unsafeFreeze :: Elem a b => PrimMonad m => MMatrix a b (PrimState m) -> m (Matrix a b) Source

Unsafe convert a mutable matrix to an immutable one without copying. The mutable matrix may not be used after this operation.