-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Bindings to the BLAS library -- -- The BLAS (Basic Linear Algebra Subprograms) are routines that provide -- standard building blocks for performing basic vector and matrix -- operations. The Level 1 BLAS perform scalar, vector and vector-vector -- operations, the Level 2 BLAS perform matrix-vector operations, and the -- Level 3 BLAS perform matrix-matrix operations. Because the BLAS are -- efficient, portable, and widely available, they are commonly used in -- the development of high quality linear algebra software, LAPACK for -- example. -- -- For more information, see the Netlib BLAS webpage: -- http://www.netlib.org/blas/ @package blas @version 0.7 -- | Overloaded interface for mutable and immutable tensors. This module -- contains the common functionality for the classes in -- Data.Tensor.Class.ITensor and Data.Tensor.Class.MTensor. module Data.Tensor.Class -- | The base class for objects with shapes and indices (i.e. Vector, -- Matrix, etc.). class (Ix i, Show i) => Shaped x i | x -> i shape :: (Shaped x i) => x n e -> i bounds :: (Shaped x i) => x n e -> (i, i) -- | Overloaded interface for immutable tensors. module Data.Tensor.Class.ITensor -- | A class for immutable tensors. class (Shaped x i) => ITensor x i e size :: (ITensor x i e) => x n e -> Int (//) :: (ITensor x i e) => x n e -> [(i, e)] -> x n e unsafeAt :: (ITensor x i e) => x n e -> i -> e unsafeReplace :: (ITensor x i e) => x n e -> [(i, e)] -> x n e indices :: (ITensor x i e) => x n e -> [i] elems :: (ITensor x i e) => x n e -> [e] assocs :: (ITensor x i e) => x n e -> [(i, e)] tmap :: (ITensor x i e) => (e -> e) -> x n e -> x n e (*>) :: (ITensor x i e, Num e) => e -> x n e -> x n e shift :: (ITensor x i e, Num e) => e -> x n e -> x n e -- | Get the value at the given index. Range-checks the argument. (!) :: (ITensor x i e) => x n e -> i -> e -- | Common functionality for the types defined in -- Data.Matrix.Dense.Class and Data.Matrix.Banded.Class, -- and a base class for the mutable and immutable matrix classes defined -- in the submodules of this one. module Data.Matrix.Class -- | A base class for objects shaped like matrices. class (Shaped a (Int, Int)) => MatrixShaped a herm :: (MatrixShaped a) => a (m, n) e -> a (n, m) e -- | Get the number of rows in the matrix. numRows :: (MatrixShaped a) => a mn e -> Int -- | Get the number of rows in the matrix. numCols :: (MatrixShaped a) => a mn e -> Int -- | Indicate whether or not a matrix has the same number of rows and -- columns. isSquare :: (MatrixShaped a) => a mn e -> Bool -- | Indicate whether or not the number of rows is less than or equal to -- the number of columns. isFat :: (MatrixShaped a) => a mn e -> Bool -- | Indicate whether or not the number of rows is greater than or equal to -- the number of columns. isTall :: (MatrixShaped a) => a mn e -> Bool -- | Replaces (m,n) with (n,m) flipShape :: (Int, Int) -> (Int, Int) -- | A class for matrices with an associated type for row, column, and -- diagonal vector views. class HasVectorView a :: (* -> * -> *) where { type family VectorView a :: * -> * -> *; } -- | A class for matrix types that use a matrix internally for storage, -- Data.Matrix.Banded.Class for example. class HasMatrixStorage a :: (* -> * -> *) where { type family MatrixStorage a :: * -> * -> *; } -- | Matrix element storage order. data OrderEnum RowMajor :: OrderEnum ColMajor :: OrderEnum -- | Transpose type. data TransEnum NoTrans :: TransEnum ConjTrans :: TransEnum -- | Lower or upper triangular storage. data UpLoEnum Upper :: UpLoEnum Lower :: UpLoEnum -- | Diagonal storage. data DiagEnum Unit :: DiagEnum NonUnit :: DiagEnum -- | Multiplication side. data SideEnum LeftSide :: SideEnum RightSide :: SideEnum -- | Exchange RowMajor and ColMajor. flipOrder :: OrderEnum -> OrderEnum -- | Exchange NoTrans and ConjTrans. flipTrans :: TransEnum -> TransEnum -- | Exchange Upper and Lower. flipUpLo :: UpLoEnum -> UpLoEnum -- | Exchange LeftSide and RigthSide. flipSide :: SideEnum -> SideEnum -- | Type classes for elements with BLAS support. module Data.Elem.BLAS -- | The base class for elements. class (AEq e, Storable e, Fractional e) => Elem e conjugate :: (Elem e) => e -> e norm :: (Elem e) => e -> Double norm1 :: (Elem e) => e -> Double fromReal :: (Elem e) => Double -> e maybeToReal :: (Elem e) => e -> Maybe Double -- | Types with vector-vector operations. class (Elem a) => BLAS1 a -- | Types with matrix-vector operations. class (BLAS1 a) => BLAS2 a -- | Types with matrix-matrix operations. class (BLAS2 a) => BLAS3 a -- | Overloaded interface for mutable tensors. This modules includes -- tensors which can be read in a monad, ReadTensor, as -- well as tensors which can be modified in a monad, -- WriteTensor. module Data.Tensor.Class.MTensor -- | Class for mutable read-only tensors. class (Shaped x i, Monad m) => ReadTensor x i e m | x -> i getSize :: (ReadTensor x i e m) => x n e -> m Int unsafeReadElem :: (ReadTensor x i e m) => x n e -> i -> m e getIndices :: (ReadTensor x i e m) => x n e -> m [i] getIndices' :: (ReadTensor x i e m) => x n e -> m [i] getElems :: (ReadTensor x i e m) => x n e -> m [e] getElems' :: (ReadTensor x i e m) => x n e -> m [e] getAssocs :: (ReadTensor x i e m) => x n e -> m [(i, e)] getAssocs' :: (ReadTensor x i e m) => x n e -> m [(i, e)] -- | Gets the value at the specified index after checking that the argument -- is in bounds. readElem :: (ReadTensor x i e m) => x n e -> i -> m e -- | Class for modifiable mutable tensors. class (ReadTensor x i e m) => WriteTensor x i e m | x -> m getMaxSize :: (WriteTensor x i e m) => x n e -> m Int setZero :: (WriteTensor x i e m, Num e) => x n e -> m () setConstant :: (WriteTensor x i e m) => e -> x n e -> m () canModifyElem :: (WriteTensor x i e m) => x n e -> i -> m Bool unsafeWriteElem :: (WriteTensor x i e m) => x n e -> i -> e -> m () unsafeModifyElem :: (WriteTensor x i e m) => x n e -> i -> (e -> e) -> m () modifyWith :: (WriteTensor x i e m) => (e -> e) -> x n e -> m () unsafeSwapElems :: (WriteTensor x i e m) => x n e -> i -> i -> m () doConj :: (WriteTensor x i e m, Elem e) => x n e -> m () scaleBy :: (WriteTensor x i e m, Num e) => e -> x n e -> m () shiftBy :: (WriteTensor x i e m, Num e) => e -> x n e -> m () -- | Set the value of the element at the given index. writeElem :: (WriteTensor x i e m) => x n e -> i -> e -> m () -- | Update the value of the element at the given index. modifyElem :: (WriteTensor x i e m) => x n e -> i -> (e -> e) -> m () -- | Swap the values stored at two positions in the tensor. swapElems :: (WriteTensor x i e m) => x n e -> i -> i -> m () -- | Immutable dense vectors. module Data.Vector.Dense -- | Immutable dense vectors. The type arguments are as follows: -- -- data Vector n e -- | Common functionality for all vector types. class (Shaped x Int, Elem e) => BaseVector x e dim :: (BaseVector x e) => x n e -> Int isConj :: (BaseVector x e) => x n e -> Bool conj :: (BaseVector x e) => x n e -> x n e coerceVector :: (BaseVector x e) => x n e -> x n' e -- | Create a vector with the given dimension and elements. The elements -- given in the association list must all have unique indices, otherwise -- the result is undefined. vector :: (BLAS1 e) => Int -> [(Int, e)] -> Vector n e -- | Create a vector of the given dimension with elements initialized to -- the values from the list. listVector n es is equivalent to -- vector n (zip [0..(n-1)] es), except that the result is -- undefined if length es is less than n. listVector :: (BLAS1 e) => Int -> [e] -> Vector n e -- | zeroVector n creates a vector of dimension n with -- all values set to zero. zeroVector :: (BLAS1 e) => Int -> Vector n e -- | constantVector n e creates a vector of dimension n -- with all values set to e. constantVector :: (BLAS1 e) => Int -> e -> Vector n e -- | basisVector n i creates a vector of dimension n with -- zeros everywhere but position i, where there is a one. basisVector :: (BLAS1 e) => Int -> Int -> Vector n e -- | subvector x o n creates a subvector of x starting at -- index o and having length n. subvector :: (BLAS1 e) => Vector n e -> Int -> Int -> Vector n' e -- | subvectorWithStride s x o n creates a subvector of x -- starting at index o, having length n and stride -- s. subvectorWithStride :: (BLAS1 e) => Int -> Vector n e -> Int -> Int -> Vector n' e -- | Compute the sum of absolute values of entries in the vector. sumAbs :: (BLAS1 e) => Vector n e -> Double -- | Compute the 2-norm of a vector. norm2 :: (BLAS1 e) => Vector n e -> Double -- | Get the index and norm of the element with absulte value. Not valid if -- any of the vector entries are NaN. Raises an exception if the -- vector has length 0. whichMaxAbs :: (BLAS1 e) => Vector n e -> (Int, e) -- | Compute the dot product of two vectors. (<.>) :: (BLAS1 e) => Vector n e -> Vector n e -> e -- | An overloaded interface to mutable dense vectors. For vector types -- than can be used with this interface, see Data.Vector.Dense.IO -- and Data.Vector.Dense.ST. Many of these functions can also be -- used with the immutable type defined in Data.Vector.Dense. module Data.Vector.Dense.Class -- | Common functionality for all vector types. class (Shaped x Int, Elem e) => BaseVector x e dim :: (BaseVector x e) => x n e -> Int stride :: (BaseVector x e) => x n e -> Int isConj :: (BaseVector x e) => x n e -> Bool conj :: (BaseVector x e) => x n e -> x n e coerceVector :: (BaseVector x e) => x n e -> x n' e unsafeVectorToIOVector :: (BaseVector x e) => x n e -> IOVector n e -- | Vectors that can be read in a monad. class (BaseVector x e, BLAS1 e, Monad m, ReadTensor x Int e m) => ReadVector x e m unsafePerformIOWithVector :: (ReadVector x e m) => x n e -> (IOVector n e -> IO a) -> m a freezeVector :: (ReadVector x e m) => x n e -> m (Vector n e) unsafeFreezeVector :: (ReadVector x e m) => x n e -> m (Vector n e) -- | Vectors that can be created or modified in a monad. class (ReadVector x e m, WriteTensor x Int e m) => WriteVector x e m unsafeConvertIOVector :: (WriteVector x e m) => IO (IOVector n e) -> m (x n e) newVector_ :: (WriteVector x e m) => Int -> m (x n e) thawVector :: (WriteVector x e m) => Vector n e -> m (x n e) unsafeThawVector :: (WriteVector x e m) => Vector n e -> m (x n e) -- | Creates a new vector with the given association list. Unspecified -- indices will get initialized to zero. newVector :: (WriteVector x e m) => Int -> [(Int, e)] -> m (x n e) -- | Creates a new vector of the given dimension with the given elements. -- If the list has length less than the passed-in dimenson, the tail of -- the vector will be uninitialized. newListVector :: (WriteVector x e m) => Int -> [e] -> m (x n e) -- | Create a zero vector of the specified length. newZeroVector :: (WriteVector x e m) => Int -> m (x n e) -- | Create a vector with every element initialized to the same value. newConstantVector :: (WriteVector x e m) => Int -> e -> m (x n e) -- | newBasisVector n i creates a vector of length n that -- is all zero except for at position i, where it equal to one. newBasisVector :: (WriteVector x e m) => Int -> Int -> m (x n e) -- | Set every element in the vector to zero. setZeroVector :: (WriteVector x e m) => x n e -> m () -- | Set every element in the vector to a constant. setConstantVector :: (WriteVector x e m) => e -> x n e -> m () -- | setBasis x i sets the ith coordinate of x -- to 1, and all other coordinates to 0. If the vector -- has been scaled, it is possible that readVector x i will not -- return exactly 1. See setElem. setBasisVector :: (WriteVector x e m) => Int -> x n e -> m () -- | Creates a new vector by copying another one. newCopyVector :: (ReadVector x e m, WriteVector y e m) => x n e -> m (y n e) -- | Creates a new vector by copying another one. The returned vector is -- gauranteed not to be a view into another vector. That is, the returned -- vector will have isConj to be False. newCopyVector' :: (ReadVector x e m, WriteVector y e m) => x n e -> m (y n e) -- | copyVector dst src replaces the values in dst with -- those in source. The operands must be the same shape. copyVector :: (WriteVector y e m, ReadVector x e m) => y n e -> x n e -> m () -- | Swap the values stored in two vectors. swapVector :: (WriteVector x e m, WriteVector y e m) => x n e -> y n e -> m () -- | subvectorView x o n creates a subvector view of x -- starting at index o and having length n. subvectorView :: (BaseVector x e) => x n e -> Int -> Int -> x n' e -- | subvectorViewWithStride s x o n creates a subvector view of -- x starting at index o, having length n and -- stride s. subvectorViewWithStride :: (BaseVector x e) => Int -> x n e -> Int -> Int -> x n' e -- | Get a new vector with elements with the conjugates of the elements of -- the given vector getConjVector :: (ReadVector x e m, WriteVector y e m) => x n e -> m (y n e) -- | Get a new vector by scaling the elements of another vector by a given -- value. getScaledVector :: (ReadVector x e m, WriteVector y e m) => e -> x n e -> m (y n e) -- | Get a new vector by shifting the elements of another vector by a given -- value. getShiftedVector :: (ReadVector x e m, WriteVector y e m) => e -> x n e -> m (y n e) -- | Conjugate every element of the vector. doConjVector :: (WriteVector y e m) => y n e -> m () -- | Scale every element by the given value. scaleByVector :: (WriteVector y e m) => e -> y n e -> m () -- | Add the given value to every element. shiftByVector :: (WriteVector y e m) => e -> y n e -> m () -- | getAddVector x y creates a new vector equal to the sum -- x+y. The operands must have the same dimension. getAddVector :: (ReadVector x e m, ReadVector y e m, WriteVector z e m) => x n e -> y n e -> m (z n e) -- | getSubVector x y creates a new tensor equal to the difference -- x-y. The operands must have the same dimension. getSubVector :: (ReadVector x e m, ReadVector y e m, WriteVector z e m) => x n e -> y n e -> m (z n e) -- | getMulVector x y creates a new vector equal to the -- elementwise product x*y. The operands must have the same -- dimensino getMulVector :: (ReadVector x e m, ReadVector y e m, WriteVector z e m) => x n e -> y n e -> m (z n e) -- | getDivVector x y creates a new vector equal to the -- elementwise ratio x/y. The operands must have the same shape. getDivVector :: (ReadVector x e m, ReadVector y e m, WriteVector z e m) => x n e -> y n e -> m (z n e) -- | addVector y x replaces y with y+x. addVector :: (WriteVector y e m, ReadVector x e m) => y n e -> x n e -> m () -- | subVector y x replaces y with y-x. subVector :: (WriteVector y e m, ReadVector x e m) => y n e -> x n e -> m () -- | axpyVector alpha x y replaces y with alpha * x + -- y. axpyVector :: (ReadVector x e m, WriteVector y e m) => e -> x n e -> y n e -> m () -- | mulVector y x replaces y with y*x. mulVector :: (WriteVector y e m, ReadVector x e m) => y n e -> x n e -> m () -- | divVector y x replaces y with y/x. divVector :: (WriteVector y e m, ReadVector x e m) => y n e -> x n e -> m () -- | Gets the sum of the absolute values of the vector entries. getSumAbs :: (ReadVector x e m) => x n e -> m Double -- | Gets the 2-norm of a vector. getNorm2 :: (ReadVector x e m) => x n e -> m Double -- | Gets the index and norm of the element with maximum magnitude. This is -- undefined if any of the elements are NaN. It will throw an -- exception if the dimension of the vector is 0. getWhichMaxAbs :: (ReadVector x e m) => x n e -> m (Int, e) -- | Computes the dot product of two vectors. getDot :: (ReadVector x e m, ReadVector y e m) => x n e -> y n e -> m e -- | Mutable vectors in the ST monad. module Data.Vector.Dense.ST -- | A safe way to create and work with a mutable vector before returning -- an immutable vector for later perusal. This function avoids copying -- the vector before returning it - it uses unsafeFreezeVector -- internally, but this wrapper is a safe interface to that function. runSTVector :: (forall s. ST s (STVector s n e)) -> Vector n e -- | Dense vectors in the ST monad. The type arguments are as -- follows: -- -- data STVector s n e -- | Mutable vectors in the IO monad. module Data.Vector.Dense.IO -- | Dense vectors in the IO monad. The type arguments are as -- follows: -- -- data IOVector n e -- | View an array in memory as a vector. vectorViewArray :: (Elem e) => ForeignPtr e -> Int -> Int -> IOVector n e -- | View an array in memory as a vector, with the given stride. vectorViewArrayWithStride :: (Elem e) => Int -> ForeignPtr e -> Int -> Int -> IOVector n e -- | Execute an IO action with a pointer to the first element in the -- vector. withIOVector :: IOVector n e -> (Ptr e -> IO a) -> IO a -- | Hermitian views of matrices. module Data.Matrix.Herm -- | A hermitian view of an underlying matrix. The view can either be of -- the upper or lower triangular part of the matrix. The type arguments -- are as follows: -- -- data Herm a nn e Herm :: UpLoEnum -> (a nn e) -> Herm a nn e -- | Convert from a base matrix type to a Herm matrix type. hermFromBase :: UpLoEnum -> a (n, n) e -> Herm a (n, n) e -- | Convert from a Herm matrix type to a base matrix type. hermToBase :: Herm a (n, n) e -> (UpLoEnum, a (n, n) e) -- | Apply a function to the unerlying matrix. mapHerm :: (a nn e -> b nn' e) -> Herm a nn e -> Herm b nn' e -- | Construct a lower-triangular hermitian view into a matrix. This also -- checks to see if the base matrix is square. hermL :: (MatrixShaped a) => a (n, n) e -> Herm a (n, n) e -- | Construct an upper-triangular hermitian view into a matrix. This also -- checks to see if the base matrix is square. hermU :: (MatrixShaped a) => a (n, n) e -> Herm a (n, n) e -- | Cast the phantom shape type. coerceHerm :: Herm a mn e -> Herm a mn' e -- | An overloaded interface for mutable matrices. The type class -- associates a matrix with a monad type in which operations can be -- perfomred. The matrices provide access to rows and columns, and can -- operate via multiplication on dense vectors and matrices. module Data.Matrix.Class.MMatrix -- | A type class for mutable matrices associated with a monad. The member -- functions of the type class do not perform any checks on the validity -- of shapes or indices, so in general their safe counterparts should be -- preferred. class (MatrixShaped a, BLAS3 e, Monad m) => MMatrix a e m getRows :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> m [x l e] getCols :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> m [x k e] -- | Get the given row in a matrix. getRow :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> Int -> m (x l e) -- | Get the given column in a matrix. getCol :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> Int -> m (x k e) -- | Get a strict list the row vectors in the matrix. getRows' :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> m [x l e] -- | Get a strict list of the column vectors in the matrix. getCols' :: (MMatrix a e m, WriteVector x e m) => a (k, l) e -> m [x k e] -- | Apply to a vector getApply :: (MMatrix a e m, ReadVector x e m, WriteVector y e m) => a (k, l) e -> x l e -> m (y k e) -- | Scale and apply to a vector getSApply :: (MMatrix a e m, ReadVector x e m, WriteVector y e m) => e -> a (k, l) e -> x l e -> m (y k e) -- | Apply to a matrix getApplyMat :: (MMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (r, s) e -> b (s, t) e -> m (c (r, t) e) -- | Scale and apply to a matrix getSApplyMat :: (MMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => e -> a (r, s) e -> b (s, t) e -> m (c (r, t) e) -- | Apply to a vector and store the result in another vector doApply :: (MMatrix a e m, ReadVector x e m, WriteVector y e m) => a (k, l) e -> x l e -> y k e -> m () -- | 
--   y := alpha a x + beta y
--
doSApplyAdd :: (MMatrix a e m, ReadVector x e m, WriteVector y e m) => e -> a (k, l) e -> x l e -> e -> y k e -> m () -- | 
--   x := a x
--
doApply_ :: (MMatrix a e m, WriteVector y e m) => a (n, n) e -> y n e -> m () -- | 
--   x := alpha a x
--
doSApply_ :: (MMatrix a e m, WriteVector y e m) => e -> a (n, n) e -> y n e -> m () -- | Apply to a matrix and store the result in another matrix doApplyMat :: (MMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (r, s) e -> b (s, t) e -> c (r, t) e -> m () -- | 
--   c := alpha a b + beta c
--
doSApplyAddMat :: (MMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => e -> a (r, s) e -> b (s, t) e -> e -> c (r, t) e -> m () -- | 
--   b := a b
--
doApplyMat_ :: (MMatrix a e m, WriteMatrix b e m) => a (s, s) e -> b (s, t) e -> m () -- | 
--   b := alpha a b
--
doSApplyMat_ :: (MMatrix a e m, WriteMatrix b e m) => e -> a (s, s) e -> b (s, t) e -> m () -- | An overloaded interface for solving matrix systems in a monad. The -- matrices can operate via inverse multiplication on immutable dense -- vectors and matrices. module Data.Matrix.Class.MSolve -- | A type class for mutable matrices with inverses. The member functions -- of the type class do not perform any checks on the validity of shapes -- or indices, so in general their safe counterparts should be preferred. class (MatrixShaped a, BLAS3 e, Monad m) => MSolve a e m -- | Return x such that a x = y. getSolve :: (MSolve a e m, ReadVector y e m, WriteVector x e m) => a (k, l) e -> y k e -> m (x l e) -- | Return b such that a b = c. getSolveMat :: (MSolve a e m, ReadMatrix c e m, WriteMatrix b e m) => a (r, s) e -> c (r, t) e -> m (b (s, t) e) -- | Return x such that a x = alpha y. getSSolve :: (MSolve a e m, ReadVector y e m, WriteVector x e m) => e -> a (k, l) e -> y k e -> m (x l e) -- | Return b such that a b = alpha c. getSSolveMat :: (MSolve a e m, ReadMatrix c e m, WriteMatrix b e m) => e -> a (r, s) e -> c (r, t) e -> m (b (s, t) e) -- | Set x := a^{-1} y. doSolve :: (MSolve a e m, ReadVector y e m, WriteVector x e m) => a (r, s) e -> y r e -> x s e -> m () -- | Set b := a^{-1} c. doSolveMat :: (MSolve a e m, ReadMatrix c e m, WriteMatrix b e m) => a (r, s) e -> c (r, t) e -> b (s, t) e -> m () -- | Set x := a^{-1} (alpha y). doSSolve :: (MSolve a e m, ReadVector y e m, WriteVector x e m) => e -> a (k, l) e -> y k e -> x l e -> m () -- | Set b := a^{-1} (alpha c). doSSolveMat :: (MSolve a e m, ReadMatrix c e m, WriteMatrix b e m) => e -> a (r, s) e -> c (r, t) e -> b (s, t) e -> m () -- | Set x := a^{-1} x. doSolve_ :: (MSolve a e m, ReadVector y e m, WriteVector x e m) => a (k, k) e -> x k e -> m () -- | Set b := a^{-1} b. doSolveMat_ :: (MSolve a e m, WriteMatrix b e m) => a (k, k) e -> b (k, l) e -> m () -- | Set x := a^{-1} (alpha x). doSSolve_ :: (MSolve a e m, WriteVector x e m) => e -> a (k, k) e -> x k e -> m () -- | Set b := a^{-1} (alpha b). doSSolveMat_ :: (MSolve a e m, WriteMatrix b e m) => e -> a (k, k) e -> b (k, l) e -> m () -- | An overloaded interface to mutable dense matrices. For matrix types -- than can be used with this interface, see Data.Matrix.Dense.IO -- and Data.Matrix.Dense.ST. Many of these functions can also be -- used with the immutable type defined in Data.Matrix.Dense. module Data.Matrix.Dense.Class -- | Common functionality for all dense matrix types. class (HasVectorView a, Elem e, MatrixShaped a, BaseVector (VectorView a) e) => BaseMatrix a e ldaMatrix :: (BaseMatrix a e) => a (n, p) e -> Int isHermMatrix :: (BaseMatrix a e) => a (n, p) e -> Bool coerceMatrix :: (BaseMatrix a e) => a np e -> a np' e maybeViewMatrixAsVector :: (BaseMatrix a e) => a (n, p) e -> Maybe (VectorView a np e) maybeViewVectorAsRow :: (BaseMatrix a e) => VectorView a p e -> Maybe (a (one, p) e) maybeViewVectorAsCol :: (BaseMatrix a e) => VectorView a n e -> Maybe (a (n, one) e) maybeViewVectorAsMatrix :: (BaseMatrix a e) => (Int, Int) -> VectorView a np e -> Maybe (a (n, p) e) unsafeMatrixToIOMatrix :: (BaseMatrix a e) => a (n, p) e -> IOMatrix (n, p) e -- | Dense matrices that can be read in a monad. class (BaseMatrix a e, BLAS3 e, ReadTensor a (Int, Int) e m, MMatrix a e m, MMatrix (Herm a) e m, MMatrix (Tri a) e m, MSolve (Tri a) e m, ReadVector (VectorView a) e m) => ReadMatrix a e m unsafePerformIOWithMatrix :: (ReadMatrix a e m) => a (n, p) e -> (IOMatrix (n, p) e -> IO r) -> m r freezeMatrix :: (ReadMatrix a e m) => a (n, p) e -> m (Matrix (n, p) e) unsafeFreezeMatrix :: (ReadMatrix a e m) => a (n, p) e -> m (Matrix (n, p) e) -- | Dense matrices that can be created or modified in a monad. class (ReadMatrix a e m, WriteTensor a (Int, Int) e m, WriteVector (VectorView a) e m) => WriteMatrix a e m newMatrix_ :: (WriteMatrix a e m) => (Int, Int) -> m (a (n, p) e) unsafeConvertIOMatrix :: (WriteMatrix a e m) => IO (IOMatrix (n, p) e) -> m (a (n, p) e) thawMatrix :: (WriteMatrix a e m) => Matrix (n, p) e -> m (a (n, p) e) unsafeThawMatrix :: (WriteMatrix a e m) => Matrix (n, p) e -> m (a (n, p) e) -- | Creates a new matrix with the given association list. Unspecified -- indices will get initialized to zero. newMatrix :: (WriteMatrix a e m) => (Int, Int) -> [((Int, Int), e)] -> m (a (n, p) e) -- | Create a new matrix with the given elements in column-major order. newListMatrix :: (WriteMatrix a e m) => (Int, Int) -> [e] -> m (a (n, p) e) -- | Form a matrix from a list of row vectors. newRowsMatrix :: (ReadVector x e m, WriteMatrix a e m) => (Int, Int) -> [x p e] -> m (a (n, p) e) -- | Form a matrix from a list of column vectors. newColsMatrix :: (ReadVector x e m, WriteMatrix a e m) => (Int, Int) -> [x n e] -> m (a (n, p) e) -- | Create a new matrix from a row vector. newRowMatrix :: (ReadVector x e m, WriteMatrix a e m) => x p e -> m (a (one, p) e) -- | Create a new matrix from a column vector. newColMatrix :: (ReadVector x e m, WriteMatrix a e m) => x n e -> m (a (n, one) e) -- | Create a zero matrix of the specified shape. newZeroMatrix :: (WriteMatrix a e m) => (Int, Int) -> m (a (n, p) e) -- | Set every element in the matrix to zero. setZeroMatrix :: (WriteMatrix a e m) => a (n, p) e -> m () -- | Create a constant matrix of the specified shape. newConstantMatrix :: (WriteMatrix a e m) => (Int, Int) -> e -> m (a (n, p) e) -- | Set every element in the matrix to the given constant. setConstantMatrix :: (WriteMatrix a e m) => e -> a (n, p) e -> m () -- | Create a new matrix of the given shape with ones along the diagonal, -- and zeros everywhere else. newIdentityMatrix :: (WriteMatrix a e m) => (Int, Int) -> m (a (n, p) e) -- | Set diagonal elements to one and all other elements to zero. setIdentityMatrix :: (WriteMatrix a e m) => a (n, p) e -> m () -- | Get a copy of a matrix. newCopyMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => a (n, p) e -> m (b (n, p) e) -- | Get a copy of a matrix and make sure the returned matrix is not a -- view. Specififially, the returned matrix will have -- isHermMatrix equal to False. newCopyMatrix' :: (ReadMatrix a e m, WriteMatrix b e m) => a (n, p) e -> m (b (n, p) e) -- | copyMatrix dst src replaces the values in dst with -- those in source. The operands must be the same shape. copyMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m () -- | swapMatrix x y swaps the values stored in two matrices. swapMatrix :: (WriteMatrix a e m, WriteMatrix b e m) => a (n, p) e -> b (n, p) e -> m () -- | Swap the elements in two rows of a matrix. swapRows :: (WriteMatrix a e m) => a (n, p) e -> Int -> Int -> m () -- | Swap the elements in two columns of a matrix. swapCols :: (WriteMatrix a e m) => a (n, p) e -> Int -> Int -> m () -- | submatrixView a ij mn returns a view of the submatrix of -- a with element (0,0) being element ij in -- a, and having shape mn. submatrixView :: (BaseMatrix a e) => a (n, p) e -> (Int, Int) -> (Int, Int) -> a (n', p') e -- | Divide the rows of a matrix into two blocks and return views into the -- blocks. The integer argument indicates how many rows should be in the -- first block. splitRowsAt :: (BaseMatrix a e) => Int -> a (n, p) e -> (a (n1, p) e, a (n2, p) e) -- | Divide the columns of a matrix into two blocks and return views into -- the blocks. The integer argument indicates how many columns should be -- in the first block. splitColsAt :: (BaseMatrix a e) => Int -> a (n, p) e -> (a (n, p1) e, a (n, p2) e) -- | Get a list of vector views of the rows of the matrix. rowViews :: (BaseMatrix a e) => a (n, p) e -> [VectorView a p e] -- | Get a list of vector views of the columns of the matrix. colViews :: (BaseMatrix a e) => a (n, p) e -> [VectorView a n e] -- | Get a vector view of the given row in a matrix. rowView :: (BaseMatrix a e) => a (n, p) e -> Int -> VectorView a p e -- | Get a vector view of the given column in a matrix. colView :: (BaseMatrix a e) => a (n, p) e -> Int -> VectorView a n e -- | Get a vector view of the given diagonal in a matrix. diagView :: (BaseMatrix a e) => a (n, p) e -> Int -> VectorView a k e -- | Get the given diagonal in a matrix. Negative indices correspond to -- sub-diagonals. getDiag :: (ReadMatrix a e m, WriteVector y e m) => a (n, p) e -> Int -> m (y k e) -- | Get a new matrix with elements with the conjugates of the elements of -- the given matrix. getConjMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => a (n, p) e -> m (b (n, p) e) -- | Get a new matrix by scaling the elements of another matrix by a given -- value. getScaledMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => e -> a (n, p) e -> m (b (n, p) e) -- | Get a new matrix by shifting the elements of another matrix by a given -- value. getShiftedMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => e -> a (n, p) e -> m (b (n, p) e) -- | Conjugate every element of a matrix. doConjMatrix :: (WriteMatrix a e m) => a (n, p) e -> m () -- | Scale every element of a matrix by the given value. scaleByMatrix :: (WriteMatrix a e m) => e -> a (n, p) e -> m () -- | Add a constant to every element in a matrix. shiftByMatrix :: (WriteMatrix a e m) => e -> a (n, p) e -> m () -- | getAddMatrix a b creates a new matrix equal to the sum -- a+b. The operands must have the same shape. getAddMatrix :: (ReadMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (n, p) e -> b (n, p) e -> m (c (n, p) e) -- | getSubMatrix a b creates a new matrix equal to the difference -- a-b. The operands must have the same shape. getSubMatrix :: (ReadMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (n, p) e -> b (n, p) e -> m (c (n, p) e) -- | getMulMatrix a b creates a new matrix equal to the -- elementwise product a*b. The operands must have the same -- shape. getMulMatrix :: (ReadMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (n, p) e -> b (n, p) e -> m (c (n, p) e) -- | getDivMatrix a b creates a new matrix equal to the -- elementwise ratio a/b. The operands must have the same shape. getDivMatrix :: (ReadMatrix a e m, ReadMatrix b e m, WriteMatrix c e m) => a (n, p) e -> b (n, p) e -> m (c (n, p) e) -- | Replace the first argument with the elementwise sum. addMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m () -- | Replace the first argument with the elementwise sum. subMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m () -- | axpyMatrix a x y replaces y := a x + y. axpyMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => e -> a (n, p) e -> b (n, p) e -> m () -- | Replace the first argument with the elementwise product. mulMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m () -- | Replace the first argument with the elementwise quotient. divMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m () -- | Mutable dense matrices in the IO monad. module Data.Matrix.Dense.IO -- | Dense matrix in the IO monad. The type arguments are as -- follows: -- -- data IOMatrix np e -- | Perform an IO action with a pointer to the first element of the -- matrix. withIOMatrix :: IOMatrix (n, p) e -> (Ptr e -> IO a) -> IO a -- | View an array in memory as a matrix. matrixViewArray :: (Elem e) => ForeignPtr e -> Int -> (Int, Int) -> IOMatrix (n, p) e -- | View an array in memory as a matrix, with the given leading dimension -- size. matrixViewArrayWithLda :: (Elem e) => Int -> ForeignPtr e -> Int -> (Int, Int) -> IOMatrix (n, p) e -- | Mutable dense matrices in the ST monad. module Data.Matrix.Dense.ST -- | Dense matrix in the ST monad. The type arguments are as -- follows: -- -- data STMatrix s np e -- | A safe way to create and work with a mutable matrix before returning -- an immutable matrix for later perusal. This function avoids copying -- the matrix before returning it - it uses unsafeFreezeMatrix -- internally, but this wrapper is a safe interface to that function. runSTMatrix :: (forall s. ST s (STMatrix s n e)) -> Matrix n e -- | An overloaded interface for immutable matrices. The matrices provide -- access to rows and columns, and can operate via multiplication on -- immutable dense vectors and matrices. module Data.Matrix.Class.IMatrix -- | A type class for immutable matrices. The member functions of the type -- class do not perform any checks on the validity of shapes or indices, -- so in general their safe counterparts should be preferred. class (MatrixShaped a, BLAS3 e) => IMatrix a e -- | Get the given row in a matrix. row :: (IMatrix a e) => a (m, n) e -> Int -> Vector n e -- | Get the given column in a matrix. col :: (IMatrix a e) => a (m, n) e -> Int -> Vector m e -- | Get a list the row vectors in the matrix. rows :: (IMatrix a e) => a (m, n) e -> [Vector n e] -- | Get a list the column vectors in the matrix. cols :: (IMatrix a e) => a (m, n) e -> [Vector m e] -- | Matrix multiplication by a vector. (<*>) :: (IMatrix a e) => a (m, n) e -> Vector n e -> Vector m e -- | Matrix multiplication by a matrix. (<**>) :: (IMatrix a e) => a (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e -- | Scale and multiply by a vector. sapply k a x is equal to -- a <*> (k *> x), and often it is faster. sapply :: (IMatrix a e) => e -> a (m, n) e -> Vector n e -> Vector m e -- | Scale and multiply by a matrix. sapplyMat k a b is equal to -- a <**> (k *> b), and often it is faster. sapplyMat :: (IMatrix a e) => e -> a (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e -- | Immutable dense matrices. module Data.Matrix.Dense -- | Immutable dense matrices. The type arguments are as follows: -- -- data Matrix np e -- | Common functionality for all dense matrix types. class (HasVectorView a, Elem e, MatrixShaped a, BaseVector (VectorView a) e) => BaseMatrix a e isHermMatrix :: (BaseMatrix a e) => a (n, p) e -> Bool coerceMatrix :: (BaseMatrix a e) => a np e -> a np' e -- | Create a new matrix of the given size and initialize the given -- elements to the given values. All other elements get set to zero. matrix :: (BLAS3 e) => (Int, Int) -> [((Int, Int), e)] -> Matrix (n, p) e -- | Create a new matrix with the given elements in row-major order. listMatrix :: (BLAS3 e) => (Int, Int) -> [e] -> Matrix (n, p) e -- | Create a matrix of the given shape from a list of rows rowsMatrix :: (BLAS3 e) => (Int, Int) -> [Vector p e] -> Matrix (n, p) e -- | Create a matrix of the given shape from a list of columns colsMatrix :: (BLAS3 e) => (Int, Int) -> [Vector n e] -> Matrix (n, p) e -- | Get a new zero of the given shape. zeroMatrix :: (BLAS3 e) => (Int, Int) -> Matrix (n, p) e -- | Get a new constant of the given shape. constantMatrix :: (BLAS3 e) => (Int, Int) -> e -> Matrix (n, p) e -- | Get a new matrix of the given shape with ones along the diagonal and -- zeroes everywhere else. identityMatrix :: (BLAS3 e) => (Int, Int) -> Matrix (n, p) e -- | Get a matrix from a row vector. matrixFromRow :: (BLAS3 e) => Vector p e -> Matrix (one, p) e -- | Get a matrix from a column vector. matrixFromCol :: (BLAS3 e) => Vector n e -> Matrix (n, one) e -- | Get a matrix from the elements stored in columnwise order in the -- vector. matrixFromVector :: (BLAS3 e) => (Int, Int) -> Vector np e -> Matrix (n, p) e -- | Get a vector by concatenating the columns of the matrix. vectorFromMatrix :: (BLAS3 e) => Matrix (n, p) e -> Vector np e -- | submatrix a ij mn returns the submatrix of a with -- element (0,0) being element ij in a, and -- having shape mn. submatrix :: (Elem e) => Matrix (n, p) e -> (Int, Int) -> (Int, Int) -> Matrix (n', p') e -- | Divide the rows of a matrix into two blocks and return views into the -- blocks. The integer argument indicates how many rows should be in the -- first block. splitRowsAt :: (BaseMatrix a e) => Int -> a (n, p) e -> (a (n1, p) e, a (n2, p) e) -- | Divide the columns of a matrix into two blocks and return views into -- the blocks. The integer argument indicates how many columns should be -- in the first block. splitColsAt :: (BaseMatrix a e) => Int -> a (n, p) e -> (a (n, p1) e, a (n, p2) e) -- | Get a the given diagonal in a matrix. Negative indices correspond to -- sub-diagonals. diag :: (Elem e) => Matrix (n, p) e -> Int -> Vector k e -- | An overloaded interface for solving immutable matrix systems. The -- matrices can operate via inverse multiplication on immutable dense -- vectors and matrices. module Data.Matrix.Class.ISolve -- | A type class for immutable matrices with inverses. The member -- functions of the type class do not perform any checks on the validity -- of shapes or indices, so in general their safe counterparts should be -- preferred. class (MatrixShaped a, BLAS3 e) => ISolve a e -- | Solve for a vector. (<\>) :: (ISolve a e) => a (m, n) e -> Vector m e -> Vector n e -- | Solve for a matrix. (<\\>) :: (ISolve a e) => a (m, n) e -> Matrix (m, k) e -> Matrix (n, k) e -- | Solve for a vector and scale. ssolve k a y is equal to a -- <\> (k *> y) but is often faster. ssolve :: (ISolve a e) => e -> a (m, n) e -> Vector m e -> Vector n e -- | Solve for a matrix and scale. ssolveMat k a c is equal to -- a <\\> (k *> c) but is often faster. ssolveMat :: (ISolve a e) => e -> a (m, n) e -> Matrix (m, k) e -> Matrix (n, k) e -- | Triangular views of matrices. module Data.Matrix.Tri -- | A triangular or trapezoidal view of an underlying matrix. The view can -- either be of the upper or lower triangular part of the matrix, and can -- optionally include or exclude the diagonal. If the diagonal enum is -- Unit, the diagonal entries of the underlying matrix are not -- referenced, but are assumed to be 1. The type arguments are -- as follows: -- -- data Tri a np e Tri :: UpLoEnum -> DiagEnum -> (a np e) -> Tri a np e -- | Convert from a base matrix type to a triangular view. triFromBase :: UpLoEnum -> DiagEnum -> a (n, p) e -> Tri a (n, p) e -- | Convert from a triangular view to the base matrix. triToBase :: Tri a (n, p) e -> (UpLoEnum, DiagEnum, a (n, p) e) -- | Apply a function to the base matrix. mapTri :: (a np e -> b np' e) -> Tri a np e -> Tri b np' e -- | Get a lower triangular view of a matrix. lower :: (MatrixShaped a) => a (n, p) e -> Tri a (n, p) e -- | Get a lower triangular view of a matrix, with unit diagonal. lowerU :: (MatrixShaped a) => a (n, p) e -> Tri a (n, p) e -- | Get an upper triangular view of a matrix. upper :: (MatrixShaped a) => a (n, p) e -> Tri a (n, p) e -- | Get an upper triangular view of a matrix, with unit diagonal. upperU :: (MatrixShaped a) => a (n, p) e -> Tri a (n, p) e -- | Cast the phantom shape type. coerceTri :: Tri a np e -> Tri a np' e -- | Immutable banded matrices. module Data.Matrix.Banded -- | Immutable banded matrices. The type arguments are as follows: -- -- data Banded np e -- | Common functionality for all banded matrix types. class (MatrixShaped a, HasVectorView a, HasMatrixStorage a, Elem e, BaseVector (VectorView a) e, BaseMatrix (MatrixStorage a) e) => BaseBanded a e numLower :: (BaseBanded a e) => a (n, p) e -> Int numUpper :: (BaseBanded a e) => a (n, p) e -> Int bandwidths :: (BaseBanded a e) => a (n, p) e -> (Int, Int) coerceBanded :: (BaseBanded a e) => a np e -> a np' e maybeMatrixStorageFromBanded :: (BaseBanded a e) => a (n, p) e -> Maybe (MatrixStorage a (k, p) e) maybeBandedFromMatrixStorage :: (BaseBanded a e) => (Int, Int) -> (Int, Int) -> MatrixStorage a (k, p) e -> Maybe (a (n, p) e) -- | Create a banded matrix with the given shape, bandwidths, and -- associations. The indices in the associations list must all fall in -- the bandwidth of the matrix. Unspecified elements will be set to zero. banded :: (BLAS3 e) => (Int, Int) -> (Int, Int) -> [((Int, Int), e)] -> Banded (n, p) e -- | Create a banded matrix of the given shape and bandwidths by specifying -- its diagonal elements. The lists must all have the same length, equal -- to the number of elements in the main diagonal of the matrix. The -- sub-diagonals are specified first, then the super-diagonals. In -- subdiagonal i, the first i elements of the list are -- ignored. listsBanded :: (BLAS3 e) => (Int, Int) -> (Int, Int) -> [[e]] -> Banded (n, p) e -- | Create a zero banded matrix with the specified shape and bandwidths. zeroBanded :: (BLAS3 e) => (Int, Int) -> (Int, Int) -> Banded (n, p) e -- | Create a constant banded matrix of the specified shape and bandwidths. constantBanded :: (BLAS3 e) => (Int, Int) -> (Int, Int) -> e -> Banded (n, p) e -- | Create a banded matrix from a vector. The vector must have length -- equal to one of the specified dimension sizes. bandedFromVector :: (Elem e) => (Int, Int) -> Vector k e -> Banded (n, p) e -- | Create a diagonal banded matrix from a vector. diagBandedFromVector :: (Elem e) => Vector n e -> Banded (n, n) e -- | Convert a diagonal banded matrix to a vector. Fail if the banded -- matrix has more than one diagonal maybeVectorFromBanded :: (Elem e) => Banded (n, p) e -> Maybe (Vector k e) -- | Get a the given diagonal in a banded matrix. Negative indices -- correspond to sub-diagonals. diagBanded :: (BLAS1 e) => Banded (n, p) e -> Int -> Vector k e -- | Test generators for BLAS types. module Test.QuickCheck.BLAS -- | Element types that can be tested with QuickCheck properties. class (BLAS3 e, Arbitrary e) => TestElem e isTestElemElem :: (TestElem e) => e -> Bool -- | Generate a list of elements suitable for testing with. elements :: (TestElem e) => Int -> Gen [e] -- | Generate a list of elements for testing that have no imaginary part. realElements :: (TestElem e) => Int -> Gen [e] -- | Get an appropriate dimension for a random vector dim :: Gen Int -- | Generate a random vector of the given size. vector :: (TestElem e) => Int -> Gen (Vector n e) -- | Generate an appropriate shape for a random matrix. shape :: Gen (Int, Int) -- | Generate a random matrix of the given shape. matrix :: (TestElem e) => (Int, Int) -> Gen (Matrix (m, n) e) -- | Generate valid bandwidths for the given matrix shape. bandwidths :: (Int, Int) -> Gen (Int, Int) -- | Generate a random banded matrix. banded :: (TestElem e) => (Int, Int) -> (Int, Int) -> Gen (Banded (m, n) e) -- | An overloaded interface to mutable banded matrices. For matrix types -- than can be used with this interface, see Data.Matrix.Banded.IO -- and Data.Matrix.Banded.ST. Many of these functions can also be -- used with the immutable type defined in Data.Matrix.Banded. module Data.Matrix.Banded.Class -- | Common functionality for all banded matrix types. class (MatrixShaped a, HasVectorView a, HasMatrixStorage a, Elem e, BaseVector (VectorView a) e, BaseMatrix (MatrixStorage a) e) => BaseBanded a e numLower :: (BaseBanded a e) => a (n, p) e -> Int numUpper :: (BaseBanded a e) => a (n, p) e -> Int bandwidths :: (BaseBanded a e) => a (n, p) e -> (Int, Int) ldaBanded :: (BaseBanded a e) => a (n, p) e -> Int isHermBanded :: (BaseBanded a e) => a (n, p) e -> Bool coerceBanded :: (BaseBanded a e) => a np e -> a np' e maybeMatrixStorageFromBanded :: (BaseBanded a e) => a (n, p) e -> Maybe (MatrixStorage a (k, p) e) maybeBandedFromMatrixStorage :: (BaseBanded a e) => (Int, Int) -> (Int, Int) -> MatrixStorage a (k, p) e -> Maybe (a (n, p) e) viewVectorAsBanded :: (BaseBanded a e) => (Int, Int) -> VectorView a k e -> a (n, p) e viewVectorAsDiagBanded :: (BaseBanded a e) => VectorView a n e -> a (n, n) e maybeViewBandedAsVector :: (BaseBanded a e) => a (n, p) e -> Maybe (VectorView a k e) unsafeBandedToIOBanded :: (BaseBanded a e) => a (n, p) e -> IOBanded (n, p) e -- | Banded matrices that can be read in a monad. class (BaseBanded a e, BLAS2 e, ReadTensor a (Int, Int) e m, MMatrix a e m, MMatrix (Herm a) e m, MMatrix (Tri a) e m, MSolve (Tri a) e m, ReadVector (VectorView a) e m, ReadMatrix (MatrixStorage a) e m) => ReadBanded a e m unsafePerformIOWithBanded :: (ReadBanded a e m) => a (n, p) e -> (IOBanded (n, p) e -> IO r) -> m r freezeBanded :: (ReadBanded a e m) => a (n, p) e -> m (Banded (n, p) e) unsafeFreezeBanded :: (ReadBanded a e m) => a (n, p) e -> m (Banded (n, p) e) -- | Banded matrices that can be created or modified in a monad. class (ReadBanded a e m, WriteTensor a (Int, Int) e m, WriteVector (VectorView a) e m, WriteMatrix (MatrixStorage a) e m) => WriteBanded a e m newBanded_ :: (WriteBanded a e m) => (Int, Int) -> (Int, Int) -> m (a (n, p) e) unsafeConvertIOBanded :: (WriteBanded a e m) => IO (IOBanded (n, p) e) -> m (a (n, p) e) thawBanded :: (WriteBanded a e m) => Banded (n, p) e -> m (a (n, p) e) unsafeThawBanded :: (WriteBanded a e m) => Banded (n, p) e -> m (a (n, p) e) -- | Create a banded matrix with the given shape, bandwidths, and -- associations. The indices in the associations list must all fall in -- the bandwidth of the matrix. Unspecified elements will be set to zero. newBanded :: (WriteBanded a e m) => (Int, Int) -> (Int, Int) -> [((Int, Int), e)] -> m (a (n, p) e) -- | Create a banded matrix of the given shape and bandwidths by specifying -- its diagonal elements. The lists must all have the same length, equal -- to the number of elements in the main diagonal of the matrix. The -- sub-diagonals are specified first, then the super-diagonals. In -- subdiagonal i, the first i elements of the list are -- ignored. newListsBanded :: (WriteBanded a e m) => (Int, Int) -> (Int, Int) -> [[e]] -> m (a (n, p) e) -- | Create a zero banded matrix with the specified shape and bandwidths. newZeroBanded :: (WriteBanded a e m) => (Int, Int) -> (Int, Int) -> m (a (n, p) e) -- | Set every element of a banded matrix to zero. setZeroBanded :: (WriteBanded a e m) => a (n, p) e -> m () -- | Create a constant banded matrix of the specified shape and bandwidths. newConstantBanded :: (WriteBanded a e m) => (Int, Int) -> (Int, Int) -> e -> m (a (n, p) e) -- | Set every element of a banded matrix to a constant. setConstantBanded :: (WriteBanded a e m) => e -> a (n, p) e -> m () -- | Create a new banded matrix by taking a copy of another one. newCopyBanded :: (ReadBanded a e m, WriteBanded b e m) => a (n, p) e -> m (b (n, p) e) -- | Copy the elements of one banded matrix into another. The two matrices -- must have the same shape and badwidths. copyBanded :: (WriteBanded b e m, ReadBanded a e m) => b (n, p) e -> a (n, p) e -> m () -- | Get a view into the partial row of the banded matrix, along with the -- number of zeros to pad before and after the view. rowViewBanded :: (BaseBanded a e) => a (n, p) e -> Int -> (Int, VectorView a k e, Int) -- | Get a view into the partial column of the banded matrix, along with -- the number of zeros to pad before and after the view. colViewBanded :: (BaseBanded a e) => a (n, p) e -> Int -> (Int, VectorView a k e, Int) -- | Get a view of a diagonal of the banded matrix. This will fail if the -- index is outside of the bandwidth. diagViewBanded :: (BaseBanded a e) => a (n, p) e -> Int -> VectorView a k e -- | Get a copy of the given diagonal of a banded matrix. getDiagBanded :: (ReadBanded a e m, WriteVector y e m) => a (n, p) e -> Int -> m (y k e) -- | Mutable banded matrices in the IO monad. module Data.Matrix.Banded.IO -- | Banded matrix in the IO monad. The type arguments are as -- follows: -- -- data IOBanded np e -- | Execute an IO action with a pointer to the first element in the -- banded matrix. withIOBanded :: IOBanded (n, p) e -> (Ptr e -> IO a) -> IO a -- | Mutable dense matrices in the ST monad. module Data.Matrix.Banded.ST -- | Banded matrix in the ST monad. The type arguments are as -- follows: -- -- data STBanded s np e -- | A safe way to create and work with a mutable banded matrix before -- returning an immutable one for later perusal. This function avoids -- copying the matrix before returning it - it uses unsafeFreezeBanded -- internally, but this wrapper is a safe interface to that function. runSTBanded :: (forall s. ST s (STBanded s n e)) -> Banded n e