Data.Matrix.Dense.Class

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.

Dense matrix type classes

class (HasVectorView a, Elem e, MatrixShaped a, BaseVector (VectorView a) e) => BaseMatrix a e where

Common functionality for all dense matrix types.

Methods

ldaMatrix :: a (n, p) e -> Int

Get the leading dimension of the storage of the matrix.

transEnumMatrix :: a (n, p) e -> TransEnum

Get the storage type of the matrix.

isHermMatrix :: a (n, p) e -> Bool

Indicate whether or not the underlying matrix storage is transposed and conjugated.

coerceMatrix :: a np e -> a np' e

Cast the shape type of the matrix.

maybeViewMatrixAsVector :: a (n, p) e -> Maybe (VectorView a np e)

Possibly create a vector view of a matrix. This will fail if the matrix is hermed or if the lda of the matrix is not equal to the number of rows in the matrix.

maybeViewVectorAsRow :: VectorView a p e -> Maybe (a (one, p) e)

Possibly create a matrix view of a row vector. This will fail if the stride of the vector is not 1 or the vector is conjugated.

maybeViewVectorAsCol :: VectorView a n e -> Maybe (a (n, one) e)

Possibly create a matrix view of a column vector. This will fail if the stride of the vector is not 1 or the vector is not conjugated.

maybeViewVectorAsMatrix :: (Int, Int) -> VectorView a np e -> Maybe (a (n, p) e)

Possible create a matrix view of the vector. This will fail if the stride of the vector is not 1 or the vector is conjugated. An error will be called if the vector does not have the same number of elements as the desired matrix.

unsafeMatrixToIOMatrix :: a (n, p) e -> IOMatrix (n, p) e

Unsafe cast from a matrix to an IOMatrix.

Instances

Elem e => BaseMatrix IOMatrix e

Elem e => BaseMatrix Matrix e

Elem e => BaseMatrix (STMatrix s) e

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 where

Dense matrices that can be read in a monad.

Methods

unsafePerformIOWithMatrix :: a (n, p) e -> (IOMatrix (n, p) e -> IO r) -> m r

Cast the matrix to an IOMatrix, perform an IO action, and convert the IO action to an action in the monad m. This operation is very unsafe.

freezeMatrix :: a (n, p) e -> m (Matrix (n, p) e)

Convert a mutable matrix to an immutable one by taking a complete copy of it.

unsafeFreezeMatrix :: a (n, p) e -> m (Matrix (n, p) e)

Instances

BLAS3 e => ReadMatrix IOMatrix e IO

BLAS3 e => ReadMatrix Matrix e IO

BLAS3 e => ReadMatrix Matrix e (ST s)

BLAS3 e => ReadMatrix (STMatrix s) e (ST s)

class (ReadMatrix a e m, WriteTensor a (Int, Int) e m, WriteVector (VectorView a) e m) => WriteMatrix a e m where

Dense matrices that can be created or modified in a monad.

Methods

newMatrix_ :: (Int, Int) -> m (a (n, p) e)

Creates a new matrix of the given shape. The elements will be uninitialized.

unsafeConvertIOMatrix :: IO (IOMatrix (n, p) e) -> m (a (n, p) e)

Unsafely convert an IO action that creates an IOMatrix into an action in m that creates a matrix.

thawMatrix :: Matrix (n, p) e -> m (a (n, p) e)

Convert an immutable matrix to a mutable one by taking a complete copy of it.

unsafeThawMatrix :: Matrix (n, p) e -> m (a (n, p) e)

Instances

BLAS3 e => WriteMatrix IOMatrix e IO

BLAS3 e => WriteMatrix (STMatrix s) e (ST s)

Overloaded interface for matrices

module Data.Matrix.Class

module Data.Matrix.Class.MMatrix

Creating matrices

newMatrix :: WriteMatrix a e m => (Int, Int) -> [((Int, Int), e)] -> m (a (n, p) e)

Creates a new matrix with the given association list. Unspecified indices will get initialized to zero.

newListMatrix :: WriteMatrix a e m => (Int, Int) -> [e] -> m (a (n, p) e)

Create a new matrix with the given elements in column-major order.

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 row vectors.

newColsMatrix :: (ReadVector x e m, WriteMatrix a e m) => (Int, Int) -> [x n e] -> m (a (n, p) e)

Form a matrix from a list of column vectors.

newRowMatrix :: (ReadVector x e m, WriteMatrix a e m) => x p e -> m (a (one, p) e)

Create a new matrix from a row vector.

newColMatrix :: (ReadVector x e m, WriteMatrix a e m) => x n e -> m (a (n, one) e)

Create a new matrix from a column vector.

Special matrices

newZeroMatrix :: WriteMatrix a e m => (Int, Int) -> m (a (n, p) e)

Create a zero matrix of the specified shape.

setZeroMatrix :: WriteMatrix a e m => a (n, p) e -> m ()

Set every element in the matrix to zero.

newConstantMatrix :: WriteMatrix a e m => (Int, Int) -> e -> m (a (n, p) e)

Create a constant matrix of the specified shape.

setConstantMatrix :: WriteMatrix a e m => e -> a (n, p) e -> m ()

Set every element in the matrix to the given constant.

newIdentityMatrix :: WriteMatrix a e m => (Int, Int) -> m (a (n, p) e)

Create a new matrix of the given shape with ones along the diagonal, and zeros everywhere else.

setIdentityMatrix :: WriteMatrix a e m => a (n, p) e -> m ()

Set diagonal elements to one and all other elements to zero.

Copying matrices

newCopyMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => a (n, p) e -> m (b (n, p) e)

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.

copyMatrix :: (WriteMatrix b e m, ReadMatrix a e m) => b (n, p) e -> a (n, p) e -> m ()

copyMatrix dst src replaces the values in dst with those in source. The operands must be the same shape.

swapMatrix :: (WriteMatrix a e m, WriteMatrix b e m) => a (n, p) e -> b (n, p) e -> m ()

swapMatrix x y swaps the values stored in two matrices.

Swapping rows and columns

swapRows :: WriteMatrix a e m => a (n, p) e -> Int -> Int -> m ()

Swap the elements in two rows of a matrix.

swapCols :: WriteMatrix a e m => a (n, p) e -> Int -> Int -> m ()

Swap the elements in two columns of a matrix.

Matrix views

submatrixView :: BaseMatrix a e => a (n, p) e -> (Int, Int) -> (Int, Int) -> a (n', p') e

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.

splitRowsAt :: BaseMatrix a e => Int -> a (n, p) e -> (a (n1, p) e, a (n2, 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.

splitColsAt :: BaseMatrix a e => Int -> a (n, p) e -> (a (n, p1) e, a (n, p2) 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.

Row and column views

rowViews :: BaseMatrix a e => a (n, p) e -> [VectorView a p e]

Get a list of vector views of the rows of the matrix.

colViews :: BaseMatrix a e => a (n, p) e -> [VectorView a n e]

Get a list of vector views of the columns of the matrix.

rowView :: BaseMatrix a e => a (n, p) e -> Int -> VectorView a p e

Get a vector view of the given row in a matrix.

colView :: BaseMatrix a e => a (n, p) e -> Int -> VectorView a n e

Get a vector view of the given column in a matrix.

diagView :: BaseMatrix a e => a (n, p) e -> Int -> VectorView a k e

Get a vector view of the given diagonal in a matrix.

Conversions between matrices and vectors

liftMatrix :: ReadMatrix a e m => (forall k. VectorView a k e -> m ()) -> a (n, p) e -> m ()

Take a unary elementwise vector operation and apply it to the elements of a matrix.

liftMatrix2 :: (ReadMatrix a e m, ReadMatrix b f m) => (forall k. VectorView a k e -> VectorView b k f -> m ()) -> a (n, p) e -> b (n, p) f -> m ()

Take a binary elementwise vector operation and apply it to the elements of a pair of matrices.

Getting diagonals

getDiag :: (ReadMatrix a e m, WriteVector y e m) => a (n, p) e -> Int -> m (y k e)

Get the given diagonal in a matrix. Negative indices correspond to sub-diagonals.

Overloaded interface for reading and writing matrix elements

module Data.Tensor.Class

module Data.Tensor.Class.MTensor

Matrix operations

Unary

getConjMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => a (n, p) e -> m (b (n, p) e)

Get a new matrix with elements with the conjugates of the elements of the given matrix.

getScaledMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => e -> a (n, p) e -> m (b (n, p) e)

Get a new matrix by scaling 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)

Get a new matrix by shifting the elements of another matrix by a given value.

doConjMatrix :: WriteMatrix a e m => a (n, p) e -> m ()

Conjugate every element of a matrix.

scaleByMatrix :: WriteMatrix a e m => e -> a (n, p) e -> m ()

Scale every element of a matrix by the given value.

shiftByMatrix :: WriteMatrix a e m => e -> a (n, p) e -> m ()

Add a constant to every element in a matrix.

Binary

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)

getAddMatrix a b creates a new matrix equal to the sum 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)

getSubMatrix a b creates a new matrix equal to the difference 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)

getMulMatrix a b creates a new matrix equal to the elementwise product 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)

getDivMatrix a b creates a new matrix equal to the elementwise ratio a/b. The operands must have the same shape.

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 ()

Replace the first argument with the elementwise sum.

axpyMatrix :: (ReadMatrix a e m, WriteMatrix b e m) => e -> a (n, p) e -> b (n, p) e -> m ()

axpyMatrix a x y replaces y := a x + y.

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 product.

divMatrix :: (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.

Conversions between mutable and immutable matrices

Conversions from IOMatrixs