{-# LANGUAGE ViewPatterns #-}

-- |

module ArrayFire.LAPACK where

import ArrayFire.Internal.LAPACK

import ArrayFire.FFI

import ArrayFire.Types

import ArrayFire.Internal.Types

-- | Singular Value Decomposition

svd

:: AFType a

=> Array a

-- ^ the input Matrix

-> (Array a, Array a, Array a)

-- ^ Output 'Array' containing (U, diagonal values of sigma, V^H)

svd = (`op3p` af_svd)

-- | Singular Value Decomposition (in-place)

svdInPlace

:: AFType a

=> Array a

-- ^ the input matrix

-> (Array a, Array a, Array a)

-- ^ Output 'Array' containing (U, diagonal values of sigma, V^H)

svdInPlace = (`op3p` af_svd_inplace)

-- | Perform LU decomposition

lu

:: AFType a

=> Array a

-- ^ is the input matrix

-> (Array a, Array a, Array a)

-- ^ Returns the output 'Array's (lower, upper, pivot)

lu = (`op3p` af_lu)

-- | Perform LU decomposition (in-place).

luInPlace

:: AFType a

=> Array a

-- ^ contains the input on entry, the packed LU decomposition on exit.

-> Bool

-- ^ specifies if the pivot is returned in original LAPACK compliant format

-> Array a

-- ^ will contain the permutation indices to map the input to the decomposition

luInPlace a (fromIntegral . fromEnum -> b) = a `op1` (\x y -> af_lu_inplace x y b)

-- | Perform QR decomposition

qr

:: AFType a

=> Array a

-- ^ the input matrix

-> (Array a, Array a, Array a)

-- ^ Returns (q, r, tau) 'Array's

-- /q/ is the orthogonal matrix from QR decomposition

-- /r/ is the upper triangular matrix from QR decomposition

-- /tau/ will contain additional information needed for solving a least squares problem using /q/ and /r/

qr = (`op3p` af_qr)

-- | Perform QR decomposition

qrInPlace

:: AFType a

=> Array a

-- ^ is the input matrix on entry. It contains packed QR decomposition on exit

-> Array a

-- ^ will contain additional information needed for unpacking the data

qrInPlace = (`op1` af_qr_inplace)

-- | Perform Cholesky Decomposition

cholesky

:: AFType a

=> Array a

-- ^ input 'Array'

-> Bool

-- ^ a boolean determining if out is upper or lower triangular

-> (Int, Array a)

-- ^ contains the triangular matrix. Multiply 'Int' with its conjugate transpose reproduces the input array.

-- is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

cholesky a (fromIntegral . fromEnum -> b) = do

let (x',y') = op1b a (\x y z -> af_cholesky x y z b)

(fromIntegral x', y')

-- | Perform Cholesky Decomposition

choleskyInplace

:: AFType a

=> Array a

-- ^ is the input matrix on entry. It contains the triangular matrix on exit.

-> Bool

-- ^ a boolean determining if in is upper or lower triangular

-> Int

-- ^ is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

choleskyInplace a (fromIntegral . fromEnum -> b) =

fromIntegral $ infoFromArray a (\x y -> af_cholesky_inplace x y b)

-- | Solve a system of equations

solve

:: AFType a

=> Array a

-- ^ is the coefficient matrix

-> Array a

-- ^ is the measured values

-> MatProp

-- ^ determining various properties of matrix a

-> Array a

-- ^ is the matrix of unknown variables

solve a b m =

op2 a b (\x y z -> af_solve x y z (toMatProp m))

-- | Solve a system of equations.

solveLU

:: AFType a

=> Array a

-- ^ is the output matrix from packed LU decomposition of the coefficient matrix

-> Array a

-- ^ is the pivot array from packed LU decomposition of the coefficient matrix

-> Array a

-- ^ is the matrix of measured values

-> MatProp

-- ^ determining various properties of matrix a

-> Array a

-- ^ will contain the matrix of unknown variables

solveLU a b c m =

op3 a b c (\x y z w -> af_solve_lu x y z w (toMatProp m))

-- | Invert a matrix.

inverse

:: AFType a

=> Array a

-- ^ is input matrix

-> MatProp

-- ^ determining various properties of matrix in

-> Array a

-- ^ will contain the inverse of matrix in

inverse a m =

a `op1` (\x y -> af_inverse x y (toMatProp m))

-- | Find the rank of the input matrix

rank

:: AFType a

=> Array a

-- ^ is input matrix

-> Double

-- ^ is the tolerance value

-> Int

-- ^ will contain the rank of in

rank a b =

fromIntegral (a `infoFromArray` (\x y -> af_rank x y b))

-- | Find the determinant of a Matrix

det

:: AFType a

=> Array a

-- ^ is input matrix

-> (Double,Double)

-- ^ will contain the real and imaginary part of the determinant of in

det = (`infoFromArray2` af_det)

-- | Find the norm of the input matrix.

norm

:: AFType a

=> Array a

-- ^ is the input matrix

-> NormType

-- ^ specifies the 'NormType'

-> Double

-- ^ specifies the value of P when type is one of AF_NORM_VECTOR_P, AF_NORM_MATRIX_L_PQ is used. It is ignored for other values of type

-> Double

-- ^ specifies the value of Q when type is AF_NORM_MATRIX_L_PQ. This parameter is ignored if type is anything else

-> Double

-- ^ will contain the norm of in

norm arr (fromNormType -> a) b c =

arr `infoFromArray` (\w y -> af_norm w y a b c)

-- | Is LAPACK available

isLAPACKAvailable

:: Bool

-- ^ Returns if LAPACK is available

isLAPACKAvailable =

toEnum . fromIntegral $ afCall1' af_is_lapack_available