blas-0.4: Bindings to the BLAS library Source code Contents Index

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

Contents Dense matrix type Creating matrices Special matrices Rows and columns Diagonals Augmenting matrices Matrix multiplication Matrix arithmetic Casting matrices Converting between vectors and matrices Unsafe operations

Description

Synopsis

type Matrix = DMatrix Imm module BLAS.Matrix.Base module BLAS.Matrix.Immutable module BLAS.Tensor.Base module BLAS.Tensor.Dense.Immutable module BLAS.Tensor.Immutable module BLAS.Tensor.Scalable matrix :: BLAS1 e => (Int, Int) -> [((Int, Int), e)] -> Matrix (m, n) e listMatrix :: Elem e => (Int, Int) -> [e] -> Matrix (m, n) e fromCols :: BLAS1 e => (Int, Int) -> [Vector m e] -> Matrix (m, n) e fromRows :: BLAS1 e => (Int, Int) -> [Vector n e] -> Matrix (m, n) e identity :: BLAS1 e => (Int, Int) -> Matrix (m, n) e row :: Elem e => DMatrix t (m, n) e -> Int -> DVector t n e col :: Elem e => DMatrix t (m, n) e -> Int -> DVector t m e rows :: Elem e => DMatrix t (m, n) e -> [DVector t n e] cols :: Elem e => DMatrix t (m, n) e -> [DVector t m e] diag :: Elem e => DMatrix t (m, n) e -> Int -> DVector t k e submatrix :: Elem e => DMatrix t (m, n) e -> (Int, Int) -> (Int, Int) -> DMatrix t (k, l) e apply :: BLAS2 e => Matrix (m, n) e -> Vector n e -> Vector m e applyMat :: BLAS3 e => Matrix (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e sapply :: BLAS2 e => e -> Matrix (m, n) e -> Vector n e -> Vector m e sapplyMat :: BLAS3 e => e -> Matrix (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e shift :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e scale :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e invScale :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e coerceMatrix :: DMatrix t mn e -> DMatrix t kl e fromRow :: BLAS1 e => Vector n e -> Matrix (one, n) e fromCol :: BLAS1 e => Vector m e -> Matrix (m, one) e unsafeMatrix :: BLAS1 e => (Int, Int) -> [((Int, Int), e)] -> Matrix (m, n) e unsafeRow :: Elem e => DMatrix t (m, n) e -> Int -> DVector t n e unsafeCol :: Elem e => DMatrix t (m, n) e -> Int -> DVector t m e unsafeDiag :: Elem e => DMatrix t (m, n) e -> Int -> DVector t k e unsafeSubmatrix :: Elem e => DMatrix t (m, n) e -> (Int, Int) -> (Int, Int) -> DMatrix t (k, l) e

Dense matrix type

type Matrix = DMatrix Imm Source

module BLAS.Matrix.Base

module BLAS.Matrix.Immutable

module BLAS.Tensor.Base

module BLAS.Tensor.Dense.Immutable

module BLAS.Tensor.Immutable

module BLAS.Tensor.Scalable

Creating matrices

matrix :: BLAS1 e => (Int, Int) -> [((Int, Int), e)] -> Matrix (m, n) e Source

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 :: Elem e => (Int, Int) -> [e] -> Matrix (m, n) e Source

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

fromCols :: BLAS1 e => (Int, Int) -> [Vector m e] -> Matrix (m, n) e Source

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

fromRows :: BLAS1 e => (Int, Int) -> [Vector n e] -> Matrix (m, n) e Source

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

Special matrices

identity :: BLAS1 e => (Int, Int) -> Matrix (m, n) e Source

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

Rows and columns

row :: Elem e => DMatrix t (m, n) e -> Int -> DVector t n e Source

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

col :: Elem e => DMatrix t (m, n) e -> Int -> DVector t m e Source

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

rows :: Elem e => DMatrix t (m, n) e -> [DVector t n e] Source

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

cols :: Elem e => DMatrix t (m, n) e -> [DVector t m e] Source

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

Diagonals

diag :: Elem e => DMatrix t (m, n) e -> Int -> DVector t k e Source

diag a 0 gets a vector view of the main diagonal of a. diag a k for k positive gets a view of the kth superdiagonal. For k negative, it gets a view of the (-k)th subdiagonal.

Augmenting matrices

submatrix :: Elem e => DMatrix t (m, n) e -> (Int, Int) -> (Int, Int) -> DMatrix t (k, l) e Source

submatrix a ij mn returns a view of the submatrix of a with element (0,0) being element ij in a, and having shape mn.

Matrix multiplication

apply :: BLAS2 e => Matrix (m, n) e -> Vector n e -> Vector m e Source

Multiply a matrix by a vector.

applyMat :: BLAS3 e => Matrix (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e Source

Multiply a matrix by a matrix.

sapply :: BLAS2 e => e -> Matrix (m, n) e -> Vector n e -> Vector m e Source

Multiply a scaled matrix by a vector.

sapplyMat :: BLAS3 e => e -> Matrix (m, k) e -> Matrix (k, n) e -> Matrix (m, n) e Source

Multiply a scaled matrix by a matrix.

Matrix arithmetic

shift :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e Source

Form a new matrix by adding a value to every element in a matrix.

scale :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e Source

Create a new matrix by scaling another matrix by the given value.

invScale :: BLAS1 e => e -> Matrix (m, n) e -> Matrix (m, n) e Source

Form a new matrix by dividing every element by a value.

Casting matrices

coerceMatrix :: DMatrix t mn e -> DMatrix t kl e Source

Coerce the phantom shape type from one type to another.

Converting between vectors and matrices

fromRow :: BLAS1 e => Vector n e -> Matrix (one, n) e Source

Get a matrix from a row vector.

fromCol :: BLAS1 e => Vector m e -> Matrix (m, one) e Source

Get a matrix from a column vector.

Unsafe operations

unsafeMatrix :: BLAS1 e => (Int, Int) -> [((Int, Int), e)] -> Matrix (m, n) e Source

Same as matrix but does not do any bounds checking.

unsafeRow :: Elem e => DMatrix t (m, n) e -> Int -> DVector t n e Source

Same as row, but does not do any bounds checking.

unsafeCol :: Elem e => DMatrix t (m, n) e -> Int -> DVector t m e Source

Same as col, but does not do any bounds checking.

unsafeDiag :: Elem e => DMatrix t (m, n) e -> Int -> DVector t k e Source

Same as diag, but does not do any bounds checking.

unsafeSubmatrix :: Elem e => DMatrix t (m, n) e -> (Int, Int) -> (Int, Int) -> DMatrix t (k, l) e Source

Same as submatrix but does not do any bounds checking.

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