Data.Matrix.Banded

Immutable banded matrices.

Banded matrix type

data Banded np e

Immutable banded matrices. The type arguments are as follows:

• np: a phantom type for the shape of the matrix. Most functions will demand that this be specified as a pair. When writing a function signature, you should always prefer Banded (n,p) e to Banded np e.
• e: the element type of the matrix. Only certain element types are supported.

Instances

MatrixShaped Banded

HasMatrixStorage Banded

HasVectorView Banded

BLAS3 e => IMatrix Banded e

Elem e => BaseBanded Banded e

BLAS3 e => MMatrix Banded e IO

BLAS3 e => ReadBanded Banded e IO

BLAS3 e => MMatrix Banded e (ST s)

BLAS3 e => ReadBanded Banded e (ST s)

Shaped Banded (Int, Int)

BLAS3 e => ITensor Banded (Int, Int) e

(BLAS3 e, Monad m) => ReadTensor Banded (Int, Int) e m

BLAS3 e => IMatrix (Herm Banded) e

BLAS3 e => IMatrix (Tri Banded) e

BLAS3 e => ISolve (Tri Banded) e

BLAS3 e => MSolve (Tri Banded) e IO

BLAS3 e => MMatrix (Herm Banded) e IO

BLAS3 e => MMatrix (Tri Banded) e IO

BLAS3 e => MSolve (Tri Banded) e (ST s)

BLAS3 e => MMatrix (Herm Banded) e (ST s)

BLAS3 e => MMatrix (Tri Banded) e (ST s)

(BLAS3 e, Eq e) => Eq (Banded (n, p) e)

BLAS3 e => Show (Banded (n, p) e)

(BLAS3 e, AEq e) => AEq (Banded (n, p) e)

Overloaded interface for banded matrices

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

Common functionality for all banded matrix types.

Methods

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

Get the number of lower diagonals in the banded matrix.

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

Get the number of upper diagonals in the banded matrix

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

Get the range of valid diagonals in the banded matrix. bandwidthds a is equal to (numLower a, numUpper a).

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

Get the leading dimension of the underlying storage of the banded matrix.

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

Get the storage type of the banded matrix.

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

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

coerceBanded :: a np e -> a np' e

Cast the shape type of the banded matrix.

maybeMatrixStorageFromBanded :: a (n, p) e -> Maybe (MatrixStorage a (k, p) e)

Get a matrix with the underlying storage of the banded matrix. This will fail if the banded matrix is hermed.

maybeBandedFromMatrixStorage :: (Int, Int) -> (Int, Int) -> MatrixStorage a (k, p) e -> Maybe (a (n, p) e)

Given a shape and bandwidths, possibly view the elements stored in a dense matrix as a banded matrix. This will if the matrix storage is hermed. An error will be called if the number of rows in the matrix does not equal the desired number of diagonals or if the number of columns in the matrix does not equal the desired number of columns.

Instances

Elem e => BaseBanded IOBanded e

Elem e => BaseBanded Banded e

Elem e => BaseBanded (STBanded s) e

Overloaded interface for matrices

module Data.Matrix.Class

module Data.Matrix.Class.IMatrix

Creating banded matrices

banded :: BLAS3 e => (Int, Int) -> (Int, Int) -> [((Int, Int), e)] -> Banded (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.

listsBanded :: BLAS3 e => (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.

Special banded matrices

zeroBanded :: BLAS3 e => (Int, Int) -> (Int, Int) -> Banded (n, p) e

Create a zero banded matrix with the specified shape and bandwidths.

constantBanded :: BLAS3 e => (Int, Int) -> (Int, Int) -> e -> Banded (n, p) e

Create a constant banded matrix of the specified shape and bandwidths.

Conversions between vectors and banded matrices

bandedFromVector :: Elem e => (Int, Int) -> Vector k 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.

diagBandedFromVector :: Elem e => Vector n e -> Banded (n, n) e

Create a diagonal banded matrix from a vector.

maybeVectorFromBanded :: Elem e => Banded (n, p) e -> Maybe (Vector k e)

Convert a diagonal banded matrix to a vector. Fail if the banded matrix has more than one diagonal

Vector views

diagBanded :: BLAS1 e => Banded (n, p) e -> Int -> Vector k e

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

Overloaded interface for reading banded matrix elements

module Data.Tensor.Class

module Data.Tensor.Class.ITensor