Data.Eigen.Matrix

Matrix type

data Matrix

constant Matrix class to be used in pure computations, uses the same column major memory layout as Eigen MatrixXd

Constructors

Matrix

Fields

m_rows :: Int

m_cols :: Int

m_vals :: Vector CDouble

Instances

Num Matrix

Nm instance for the matrix

Show Matrix

Pretty prints the matrix

valid :: Matrix -> Bool

Verify matrix dimensions and memory layout

Matrix conversions

fromList :: [[Double]] -> Matrix

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

toList :: Matrix -> [[Double]]

Convert matrix to a list of rows

generate :: Int -> Int -> (Int -> Int -> Double) -> Matrix

Create matrix using generator function f :: row -> col -> val

Standard matrices and special cases

empty :: Matrix

Empty 0x0 matrix

zero :: Int -> Int -> Matrix

Matrix where all coeff are 0

ones :: Int -> Int -> Matrix

Matrix where all coeff are 1

identity :: Int -> Matrix

Square matrix with 1 on main diagonal and 0 elsewhere

constant :: Int -> Int -> Double -> Matrix

Matrix where all coeffs are filled with given value

Accessing matrix data

cols :: Matrix -> Int

Number of columns for the matrix

rows :: Matrix -> Int

Number of rows for the matrix

(!) :: Matrix -> (Int, Int) -> Double

Matrix coefficient at specific row and col

coeff :: Int -> Int -> Matrix -> Double

Matrix coefficient at specific row and col

unsafeCoeff :: Int -> Int -> Matrix -> Double

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

minCoeff :: Matrix -> Double

The minimum of all coefficients of matrix

maxCoeff :: Matrix -> Double

The maximum of all coefficients of matrix

col :: Int -> Matrix -> [Double]

List of coefficients for the given col

row :: Int -> Matrix -> [Double]

List of coefficients for the given row

block :: Int -> Int -> Int -> Int -> Matrix -> Matrix

Extract rectangular block from matrix defined by startRow startCol blockRows blockCols

topRows :: Int -> Matrix -> Matrix

Top n rows of matrix

bottomRows :: Int -> Matrix -> Matrix

Bottom n rows of matrix

leftCols :: Int -> Matrix -> Matrix

Left n columns of matrix

rightCols :: Int -> Matrix -> Matrix

Right n columns of matrix

Matrix properties

norm :: Matrix -> Double

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 :: Matrix -> Double

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.

determinant :: Matrix -> Double

The determinant of the matrix

Matrix operations

add :: Matrix -> Matrix -> Matrix

Return a - b

sub :: Matrix -> Matrix -> Matrix

Return a + b

mul :: Matrix -> Matrix -> Matrix

Return a * b

Matrix transformations

inverse :: Matrix -> Matrix

Inverse of the matrix

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

adjoint :: Matrix -> Matrix

Adjoint of the matrix

conjugate :: Matrix -> Matrix

Conjugate of the matrix

transpose :: Matrix -> Matrix

Transpose of the matrix

normalize :: Matrix -> Matrix

Nomalize the matrix by deviding it on its norm

modify :: (forall s. MMatrix s -> ST s ()) -> Matrix -> Matrix

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.

Mutable matrices

thaw :: PrimMonad m => Matrix -> m (MMatrix (PrimState m))

Yield a mutable copy of the immutable matrix

freeze :: PrimMonad m => MMatrix (PrimState m) -> m Matrix

Yield an immutable copy of the mutable matrix

unsafeThaw :: PrimMonad m => Matrix -> m (MMatrix (PrimState m))

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

unsafeFreeze :: PrimMonad m => MMatrix (PrimState m) -> m Matrix

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