-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Eigen C++ library (linear algebra: matrices, vectors, numerical solvers). -- @package eigen @version 1.2.2 module Data.Eigen.Internal class Cast a b cast :: Cast a b => a -> b performIO :: IO a -> a c_freeString :: CString -> IO () call :: IO CString -> IO () c_setNbThreads :: CInt -> IO () c_getNbThreads :: IO CInt c_random :: Ptr CDouble -> CInt -> CInt -> IO CString c_add :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_sub :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_mul :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_diagonal :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_transpose :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_inverse :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_adjoint :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_conjugate :: Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> IO CString c_normalize :: Ptr CDouble -> CInt -> CInt -> IO CString c_sum :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_prod :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_mean :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_norm :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_trace :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_squaredNorm :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_blueNorm :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_hypotNorm :: Ptr CDouble -> CInt -> CInt -> IO CDouble c_determinant :: Ptr CDouble -> CInt -> CInt -> IO CDouble instance Cast Int CInt instance Cast CInt Int instance Cast Double CDouble instance Cast CDouble Double module Data.Eigen.Matrix.Mutable -- | Mutable matrix. You can modify elements data MMatrix s MMatrix :: Int -> Int -> MVector s CDouble -> MMatrix s mm_rows :: MMatrix s -> Int mm_cols :: MMatrix s -> Int mm_vals :: MMatrix s -> MVector s CDouble type IOMatrix = MMatrix RealWorld type STMatrix s = MMatrix s -- | Create a mutable matrix of the given size and fill it with 0 as an -- initial value. new :: PrimMonad m => Int -> Int -> m (MMatrix (PrimState m)) -- | Create a mutable matrix of the given size and fill it with as an -- initial value. replicate :: PrimMonad m => Int -> Int -> m (MMatrix (PrimState m)) -- | Yield the element at the given position. read :: PrimMonad m => MMatrix (PrimState m) -> Int -> Int -> m Double -- | Replace the element at the given position. write :: PrimMonad m => MMatrix (PrimState m) -> Int -> Int -> Double -> m () -- | Yield the element at the given position. No bounds checks are -- performed. unsafeRead :: PrimMonad m => MMatrix (PrimState m) -> Int -> Int -> m Double -- | Replace the element at the given position. No bounds checks are -- performed. unsafeWrite :: PrimMonad m => MMatrix (PrimState m) -> Int -> Int -> Double -> m () -- | Set all elements of the matrix to the given value set :: PrimMonad m => (MMatrix (PrimState m)) -> Double -> m () -- | Copy a matrix. The two matrices must have the same length and may not -- overlap. copy :: PrimMonad m => (MMatrix (PrimState m)) -> (MMatrix (PrimState m)) -> m () -- | Pass a pointer to the matrix's data to the IO action. Modifying data -- through the pointer is unsafe if the matrix could have been frozen -- before the modification. unsafeWith :: IOMatrix -> (Ptr CDouble -> CInt -> CInt -> IO a) -> IO a -- | Some Eigen's algorithms can exploit the multiple cores present in your -- hardware. To this end, it is enough to enable OpenMP on your compiler, -- for instance: GCC: -fopenmp. You can control the number of thread that -- will be used using either the OpenMP API or Eiegn's API using the -- following priority: OMP_NUM_THREADS=n ./my_program setNbThreads n -- Unless setNbThreads has been called, Eigen uses the number of -- threads specified by OpenMP. You can restore this bahavior by calling -- setNbThreads n -- -- Currently, the following algorithms can make use of multi-threading: -- general matrix - matrix products PartialPivLU module Data.Eigen.Parallel -- | Sets the max number of threads reserved for Eigen setNbThreads :: Int -> IO () -- | Gets the max number of threads reserved for Eigen getNbThreads :: IO Int module Data.Eigen.Matrix -- | Matrix to be used in pure computations, uses column major memory -- layout data Matrix Matrix :: Int -> Int -> Vector CDouble -> Matrix m_rows :: Matrix -> Int m_cols :: Matrix -> Int m_vals :: Matrix -> Vector CDouble -- | Verify matrix dimensions and memory layout valid :: Matrix -> Bool -- | Construct matrix from a list of rows, column count is detected as -- maximum row length. Missing values are filled with 0 fromList :: [[Double]] -> Matrix -- | Convert matrix to a list of rows toList :: Matrix -> [[Double]] -- | Create matrix using generator function f :: row -> col -> val generate :: Int -> Int -> (Int -> Int -> Double) -> Matrix -- | Empty 0x0 matrix empty :: Matrix -- | Is matrix empty? null :: Matrix -> Bool -- | Is matrix square? square :: Matrix -> Bool -- | Matrix where all coeff are 0 zero :: Int -> Int -> Matrix -- | Matrix where all coeff are 1 ones :: Int -> Int -> Matrix -- | Square matrix with 1 on main diagonal and 0 elsewhere identity :: Int -> Matrix -- | Matrix where all coeffs are filled with given value constant :: Int -> Int -> Double -> Matrix -- | The random matrix of a given size random :: Int -> Int -> IO Matrix -- | Number of columns for the matrix cols :: Matrix -> Int -- | Number of rows for the matrix rows :: Matrix -> Int -- | Matrix coefficient at specific row and col (!) :: Matrix -> (Int, Int) -> Double -- | Matrix coefficient at specific row and col coeff :: Int -> Int -> Matrix -> Double -- | Unsafe version of coeff function. No bounds check performed so -- SEGFAULT possible unsafeCoeff :: Int -> Int -> Matrix -> Double -- | List of coefficients for the given col col :: Int -> Matrix -> [Double] -- | List of coefficients for the given row row :: Int -> Matrix -> [Double] -- | Extract rectangular block from matrix defined by startRow startCol -- blockRows blockCols block :: Int -> Int -> Int -> Int -> Matrix -> Matrix -- | Top n rows of matrix topRows :: Int -> Matrix -> Matrix -- | Bottom n rows of matrix bottomRows :: Int -> Matrix -> Matrix -- | Left n columns of matrix leftCols :: Int -> Matrix -> Matrix -- | Right n columns of matrix rightCols :: Int -> Matrix -> Matrix -- | The sum of all coefficients of the matrix sum :: Matrix -> Double -- | The product of all coefficients of the matrix prod :: Matrix -> Double -- | The mean of all coefficients of the matrix mean :: Matrix -> Double -- | The minimum of all coefficients of matrix minCoeff :: Matrix -> Double -- | The maximum of all coefficients of matrix maxCoeff :: Matrix -> Double -- | The trace of a matrix is the sum of the diagonal coefficients and can -- also be computed as sum (diagonal m) trace :: 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. norm :: 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. squaredNorm :: Matrix -> Double -- | 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. blueNorm :: Matrix -> Double -- | The l2 norm of the matrix avoiding undeflow and overflow. This version -- use a concatenation of hypot calls, and it is very slow. hypotNorm :: Matrix -> Double -- | The determinant of the matrix determinant :: Matrix -> Double -- | Returns true if all of the coefficients in a given matrix evaluate to -- true all :: (Double -> Bool) -> Matrix -> Bool -- | Returns true if at least one of the coefficients in a given matrix -- evaluates to true any :: (Double -> Bool) -> Matrix -> Bool -- | Returns the number of coefficients in a given matrix that evaluate to -- true count :: (Double -> Bool) -> Matrix -> Int -- | Adding two matrices by adding the corresponding entries together add :: Matrix -> Matrix -> Matrix -- | Return a + b sub :: Matrix -> Matrix -> Matrix -- | Matrix multiplication -- mul :: Matrix -> Matrix -> Matrix -- | Diagonal of the matrix diagonal :: Matrix -> Matrix -- | Transpose of the matrix transpose :: Matrix -> Matrix -- | Inverse of the matrix -- -- For small fixed sizes up to 4x4, this method uses cofactors. In the -- general case, this method uses PartialPivLU decomposition inverse :: Matrix -> Matrix -- | Adjoint of the matrix adjoint :: Matrix -> Matrix -- | Conjugate of the matrix conjugate :: Matrix -> Matrix -- | Nomalize the matrix by deviding it on its norm normalize :: 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. modify :: (forall s. MMatrix s -> ST s ()) -> Matrix -> Matrix -- | Yield a mutable copy of the immutable matrix thaw :: PrimMonad m => Matrix -> m (MMatrix (PrimState m)) -- | Yield an immutable copy of the mutable matrix freeze :: PrimMonad m => MMatrix (PrimState m) -> m Matrix -- | Unsafely convert an immutable matrix to a mutable one without copying. -- The immutable matrix may not be used after this operation. unsafeThaw :: PrimMonad m => Matrix -> m (MMatrix (PrimState m)) -- | Unsafe convert a mutable matrix to an immutable one without copying. -- The mutable matrix may not be used after this operation. unsafeFreeze :: PrimMonad m => MMatrix (PrimState m) -> m Matrix -- | Pass a pointer to the matrix's data to the IO action. The data may not -- be modified through the pointer. unsafeWith :: Matrix -> (Ptr CDouble -> CInt -> CInt -> IO a) -> IO a instance Num Matrix instance Show Matrix -- | The problem: You have a system of equations, that you have written as -- a single matrix equation -- -- 
--   Ax = b
--
-- -- Where A and b are matrices (b could be a vector, as a special case). -- You want to find a solution x. -- -- The solution: You can choose between various decompositions, depending -- on what your matrix A looks like, and depending on whether you favor -- speed or accuracy. However, let's start with an example that works in -- all cases, and is a good compromise: -- -- 
--   import Data.Eigen.Matrix
--   import Data.Eigen.LA
--   
--   main = do
--       let
--           a = fromList [[1,2,3], [4,5,6], [7,8,10]]
--           b = fromList [[3],[3],[4]]
--           x = solve ColPivHouseholderQR a b
--       putStrLn "Here is the matrix A:" >> print a
--       putStrLn "Here is the vector b:" >> print b
--       putStrLn "The solution is:" >> print x
--
-- -- produces the following output -- -- 
--   Here is the matrix A:
--   Matrix 3x3
--   1.0 2.0 3.0
--   4.0 5.0 6.0
--   7.0 8.0 10.0
--   
--   Here is the vector b:
--   Matrix 3x1
--   3.0
--   3.0
--   4.0
--   
--   The solution is:
--   Matrix 3x1
--   -2.0000000000000004
--   1.0000000000000018
--   0.9999999999999989
--
-- -- Checking if a solution really exists: Only you know what error margin -- you want to allow for a solution to be considered valid. -- -- You can compute relative error using norm (ax - b) / norm b -- formula or use relativeError function which provides the same -- calculation implemented slightly more efficient. module Data.Eigen.LA -- | 
--   Decomposition           Requirements on the matrix          Speed   Accuracy  Rank  Kernel  Image 
--   
--   PartialPivLU            Invertible                          ++      +         -     -       -
--   FullPivLU               None                                -       +++       +     +       +
--   HouseholderQR           None                                ++      +         -     -       -
--   ColPivHouseholderQR     None                                +       ++        +     -       -
--   FullPivHouseholderQR    None                                -       +++       +     -       -
--   LLT                     Positive definite                   +++     +         -     -       -
--   LDLT                    Positive or negative semidefinite   +++     ++        -     -       -
--   JacobiSVD               None                                -       +++       +     -       -
--   
--   The best way to do least squares solving for square matrices is with a SVD decomposition (JacobiSVD)
--
data Decomposition -- | LU decomposition of a matrix with partial pivoting. PartialPivLU :: Decomposition -- | LU decomposition of a matrix with complete pivoting. FullPivLU :: Decomposition -- | Householder QR decomposition of a matrix. HouseholderQR :: Decomposition -- | Householder rank-revealing QR decomposition of a matrix with -- column-pivoting. ColPivHouseholderQR :: Decomposition -- | Householder rank-revealing QR decomposition of a matrix with full -- pivoting. FullPivHouseholderQR :: Decomposition -- | Standard Cholesky decomposition (LL^T) of a matrix. LLT :: Decomposition -- | Robust Cholesky decomposition of a matrix with pivoting. LDLT :: Decomposition -- | Two-sided Jacobi SVD decomposition of a rectangular matrix. JacobiSVD :: Decomposition rank :: Decomposition -> Matrix -> Int -- | Return matrix whose columns form a basis of the null-space of -- A kernel :: Decomposition -> Matrix -> Matrix -- | Return a matrix whose columns form a basis of the column-space of -- A image :: Decomposition -> Matrix -> Matrix -- | solve :: Decomposition -> Matrix -> Matrix -> Matrix -- | relativeError :: Matrix -> Matrix -> Matrix -> Double -- | -- -- -- -- 
--   import Data.Eigen.LA
--   main = print $ linearRegression [
--       [-4.32, 3.02, 6.89],
--       [-3.79, 2.01, 5.39],
--       [-4.01, 2.41, 6.01],
--       [-3.86, 2.09, 5.55],
--       [-4.10, 2.58, 6.32]]
--    
--
-- -- produces the following output -- -- 
--   ([-2.3466569233817127,-0.2534897541434826,-0.1749653335680988],1.8905965120153139e-3)
--
linearRegression :: [[Double]] -> ([Double], Double) instance Show Decomposition instance Enum Decomposition