Safe Haskell	None
Language	Haskell98

Data.Eigen.Matrix

Contents

Matrix type
Matrix conversions
Standard matrices and special cases
Accessing matrix data
Matrix properties
Generic reductions
Boolean reductions
Basic matrix algebra
Mapping over elements
Matrix transformations
Matrix serialization
Mutable matrices
Raw pointers

Synopsis

Matrix type

Matrix aliases follows Eigen naming convention

data Matrix a b where Source

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

Constructors

Matrix :: Elem a b => !Int -> !Int -> !(Vector b) -> Matrix a b

Instances

Elem a b => Num (Matrix a b) Source	Basic matrix math exposed through Num instance: `(*)`, `(+)`, `(-)`, `fromInteger`, `signum`, `abs`, `negate`
(Elem a b, Show a) => Show (Matrix a b) Source	Pretty prints the matrix
Elem a b => Binary (Matrix a b) Source	Matrix binary serialization

type MatrixXf = Matrix Float CFloat Source

Alias for single precision matrix

type MatrixXd = Matrix Double CDouble Source

Alias for double precision matrix

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

class (Num a, Cast a b, Cast b a, Storable b, Code b) => Elem a b | a -> b Source

Instances

Elem Double CDouble Source
Elem Float CFloat Source
Elem (Complex Double) (CComplex CDouble) Source
Elem (Complex Float) (CComplex CFloat) Source

data CComplex a Source

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

Instances

Storable a => Storable (CComplex a) Source
Elem (Complex Double) (CComplex CDouble) Source
Elem (Complex Float) (CComplex CFloat) Source

valid :: Elem a b => Matrix a b -> Bool Source

Verify matrix dimensions and memory layout

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

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

Convert matrix to a list of rows

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

empty :: Elem a b => Matrix a b Source

Empty 0x0 matrix

null :: Elem a b => Matrix a b -> Bool Source

Is matrix empty?

square :: Elem a b => Matrix a b -> Bool Source

Is matrix square?

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

Matrix where all coeff are 0

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

Matrix where all coeff are 1

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

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

The random matrix of a given size

Accessing matrix data

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

Number of columns for the matrix

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

Number of rows for the matrix

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

Mtrix size as (rows, cols) pair

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

Matrix coefficient at specific row and col

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

Matrix coefficient at specific row and col

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

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

col :: Elem a b => Int -> Matrix a b -> [a] Source

List of coefficients for the given col

row :: Elem a b => Int -> Matrix a b -> [a] Source

List of coefficients for the given row

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

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

Top N rows of matrix

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

Bottom N rows of matrix

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

Left N columns of matrix

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

Right N columns of matrix

Matrix properties

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

The sum of all coefficients of the matrix

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

The product of all coefficients of the matrix

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

The mean of all coefficients of the matrix

minCoeff :: (Elem a b, Ord a) => Matrix a b -> a Source

The minimum coefficient of the matrix

maxCoeff :: (Elem a b, Ord a) => Matrix a b -> a Source

The maximum coefficient of the matrix

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

>>> a
Matrix 2x2
1.0 2.0
3.0 4.0

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

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

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

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

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

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

Diagonal of the matrix

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

Transpose of the matrix

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

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

Adjoint of the matrix

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

Conjugate of the matrix

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

Constructors

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.

Instances

Enum TriangularMode Source
Eq TriangularMode Source
Read TriangularMode Source
Show TriangularMode Source

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.

Raw pointers

unsafeWith :: Elem a b => Matrix a b -> (Ptr b -> CInt -> CInt -> IO c) -> IO c Source

Pass a pointer to the matrix's data to the IO action. The data may not be modified through the pointer.