Stability	experimental
Maintainer	Patrick Perry <patperry@stanford.edu>

Data.Matrix.Dense

Contents

Dense matrix type
Overloaded interface for dense matrices
Overloaded interface for matrices
Creating matrices
Special matrices
Conversions between vectors and matrices
Matrix views
Vector views
Overloaded interface for reading matrix elements

Description

Immutable dense matrices.

Synopsis

Dense matrix type

data Matrix np e Source

Immutable dense 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 Matrix (n,p) e to Matrix np e.
e: the element type of the matrix. Only certain element types are supported.

Instances

MatrixShaped Matrix
HasVectorView Matrix
Elem e => BaseMatrix Matrix e
BLAS3 e => IMatrix Matrix e
BLAS3 e => MMatrix Matrix e IO
BLAS3 e => ReadMatrix Matrix e IO
BLAS3 e => MMatrix Matrix e (ST s)
BLAS3 e => ReadMatrix Matrix e (ST s)
Shaped Matrix (Int, Int)
BLAS3 e => ITensor Matrix (Int, Int) e
(BLAS3 e, Monad m) => ReadTensor Matrix (Int, Int) e m
BLAS3 e => IMatrix (Herm Matrix) e
BLAS3 e => IMatrix (Tri Matrix) e
BLAS3 e => ISolve (Tri Matrix) e
BLAS3 e => MSolve (Tri Matrix) e IO
BLAS3 e => MMatrix (Herm Matrix) e IO
BLAS3 e => MMatrix (Tri Matrix) e IO
BLAS3 e => MSolve (Tri Matrix) e (ST s)
BLAS3 e => MMatrix (Herm Matrix) e (ST s)
BLAS3 e => MMatrix (Tri Matrix) e (ST s)
(BLAS3 e, Eq e) => Eq (Matrix (n, p) e)
(BLAS3 e, Floating e) => Floating (Matrix (m, n) e)
BLAS3 e => Fractional (Matrix (n, p) e)
BLAS3 e => Num (Matrix (n, p) e)
(BLAS3 e, Show e) => Show (Matrix (n, p) e)
(BLAS3 e, AEq e) => AEq (Matrix (n, p) e)

Overloaded interface for dense matrices

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

Common functionality for all dense matrix types.

Methods

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

Get the leading dimension of the storage of the matrix.

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

Get the storage type of the matrix.

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

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

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

Cast the shape type of the matrix.

Instances

Elem e => BaseMatrix IOMatrix e
Elem e => BaseMatrix Matrix e
Elem e => BaseMatrix (STMatrix s) e

Overloaded interface for matrices

module Data.Matrix.Class

module Data.Matrix.Class.IMatrix

Creating matrices

matrix :: BLAS3 e => (Int, Int) -> [((Int, Int), e)] -> Matrix (n, p) eSource

Create a new matrix of the given size and initialize the given elements to the given values. All other elements get set to zero.

listMatrix :: BLAS3 e => (Int, Int) -> [e] -> Matrix (n, p) eSource

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

rowsMatrix :: BLAS3 e => (Int, Int) -> [Vector p e] -> Matrix (n, p) eSource

Create a matrix of the given shape from a list of rows

colsMatrix :: BLAS3 e => (Int, Int) -> [Vector n e] -> Matrix (n, p) eSource

Create a matrix of the given shape from a list of columns

Special matrices

zeroMatrix :: BLAS3 e => (Int, Int) -> Matrix (n, p) eSource

Get a new zero of the given shape.

constantMatrix :: BLAS3 e => (Int, Int) -> e -> Matrix (n, p) eSource

Get a new constant of the given shape.

identityMatrix :: BLAS3 e => (Int, Int) -> Matrix (n, p) eSource

Get a new matrix of the given shape with ones along the diagonal and zeroes everywhere else.

Conversions between vectors and matrices

matrixFromRow :: BLAS3 e => Vector p e -> Matrix (one, p) eSource

Get a matrix from a row vector.

matrixFromCol :: BLAS3 e => Vector n e -> Matrix (n, one) eSource

Get a matrix from a column vector.

matrixFromVector :: BLAS3 e => (Int, Int) -> Vector np e -> Matrix (n, p) eSource

Get a matrix from the elements stored in columnwise order in the vector.

vectorFromMatrix :: BLAS3 e => Matrix (n, p) e -> Vector np eSource

Get a vector by concatenating the columns of the matrix.

Matrix views

submatrix :: Elem e => Matrix (n, p) e -> (Int, Int) -> (Int, Int) -> Matrix (n', p') eSource

submatrix a ij mn returns 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)Source

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)Source

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.

Vector views

diag :: Elem e => Matrix (n, p) e -> Int -> Vector k eSource

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

Overloaded interface for reading matrix elements

module Data.Tensor.Class

module Data.Tensor.Class.ITensor