Data.Number.Flint.Support.D.Mat

Double precision matrices

data DMat

Constructors

DMat !(ForeignPtr CDMat)

Instances

Show DMat

Defined in Data.Number.Flint.Support.D.Mat.Instances

Methods

showsPrec :: Int -> DMat -> ShowS

show :: DMat -> String

showList :: [DMat] -> ShowS

data CDMat

Constructors

CDMat (Ptr CDouble) CLong CLong (Ptr (Ptr CDouble))

Instances

Storable CDMat

Defined in Data.Number.Flint.Support.D.Mat.FFI

Methods

sizeOf :: CDMat -> Int

alignment :: CDMat -> Int

peekElemOff :: Ptr CDMat -> Int -> IO CDMat

pokeElemOff :: Ptr CDMat -> Int -> CDMat -> IO ()

peekByteOff :: Ptr b -> Int -> IO CDMat

pokeByteOff :: Ptr b -> Int -> CDMat -> IO ()

peek :: Ptr CDMat -> IO CDMat

poke :: Ptr CDMat -> CDMat -> IO ()

Smart constructors

newDMat :: CLong -> CLong -> IO DMat

newDMat rows cols

Construct new DMat with rows rows and cols columns.

withDMat :: DMat -> (Ptr CDMat -> IO a) -> IO (DMat, a)

withDMat mat f

Apply f to a mat.

withNewDMat :: CLong -> CLong -> (Ptr CDMat -> IO a) -> IO (DMat, a)

withNewDMat rows cols f

Apply f to a new DMat with rows rows and cols columns.

Memory management

d_mat_init :: Ptr CDMat -> CLong -> CLong -> IO ()

d_mat_init mat rows cols

Initialises a matrix with the given number of rows and columns for use.

d_mat_clear :: Ptr CDMat -> IO ()

d_mat_clear mat

Clears the given matrix.

Basic assignment and manipulation

d_mat_set :: Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_set mat1 mat2

Sets mat1 to a copy of mat2. The dimensions of mat1 and mat2 must be the same.

d_mat_swap :: Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_swap mat1 mat2

Swaps two matrices. The dimensions of mat1 and mat2 are allowed to be different.

d_mat_swap_entrywise :: Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_swap_entrywise mat1 mat2

Swaps two matrices by swapping the individual entries rather than swapping the contents of the structs.

d_mat_entry :: Ptr CDMat -> CLong -> CLong -> IO CDouble

d_mat_entry mat i j

Returns the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix. This function is implemented as a macro.

d_mat_get_entry :: Ptr CDMat -> CLong -> CLong -> IO CDouble

d_mat_get_entry mat i j

Returns the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix.

d_mat_entry_ptr :: Ptr CDMat -> CLong -> CLong -> IO (Ptr CDouble)

d_mat_entry_ptr mat i j

Returns a pointer to the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix.

d_mat_zero :: Ptr CDMat -> IO ()

d_mat_zero mat

Sets all entries of mat to 0.

d_mat_one :: Ptr CDMat -> IO ()

d_mat_one mat

Sets mat to the unit matrix, having ones on the main diagonal and zeroes elsewhere. If mat is nonsquare, it is set to the truncation of a unit matrix.

Random matrix generation

d_mat_randtest :: Ptr CDMat -> Ptr CFRandState -> CLong -> CLong -> IO ()

d_mat_randtest mat state minexp maxexp

Sets the entries of mat to random signed numbers with exponents between minexp and maxexp or zero.

Input and output

d_mat_get_str :: Ptr CDMat -> IO CString

d_mat_get_str mat

Returns a string representation of the given matrix.

d_mat_fprint :: Ptr CFile -> Ptr CDMat -> IO ()

d_mat_fprint file mat

Prints the given matrix to the stream stdout.

d_mat_print :: Ptr CDMat -> IO ()

d_mat_print mat

Prints the given matrix to the stream stdout.

Comparison

d_mat_equal :: Ptr CDMat -> Ptr CDMat -> IO CInt

d_mat_equal mat1 mat2

Returns a non-zero value if mat1 and mat2 have the same dimensions and entries, and zero otherwise.

d_mat_approx_equal :: Ptr CDMat -> Ptr CDMat -> CDouble -> IO CInt

d_mat_approx_equal mat1 mat2 eps

Returns a non-zero value if mat1 and mat2 have the same dimensions and entries within eps of each other, and zero otherwise.

d_mat_is_zero :: Ptr CDMat -> IO CInt

d_mat_is_zero mat

Returns a non-zero value if all entries mat are zero, and otherwise returns zero.

d_mat_is_approx_zero :: Ptr CDMat -> CDouble -> IO CInt

d_mat_is_approx_zero mat eps

Returns a non-zero value if all entries mat are zero to within eps and otherwise returns zero.

d_mat_is_empty :: Ptr CDMat -> IO CInt

d_mat_is_empty mat

Returns a non-zero value if the number of rows or the number of columns in mat is zero, and otherwise returns zero.

d_mat_is_square :: Ptr CDMat -> IO CInt

d_mat_is_square mat

Returns a non-zero value if the number of rows is equal to the number of columns in mat, and otherwise returns zero.

Transpose

d_mat_transpose :: Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_transpose B A

Sets \(B\) to \(A^T\), the transpose of \(A\). Dimensions must be compatible. \(A\) and \(B\) are allowed to be the same object if \(A\) is a square matrix.

Matrix multiplication

d_mat_mul_classical :: Ptr CDMat -> Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_mul_classical C A B

Sets C to the matrix product \(C = A B\). The matrices must have compatible dimensions for matrix multiplication (an exception is raised otherwise). Aliasing is allowed.

Gram-Schmidt Orthogonalisation and QR Decomposition

d_mat_gso :: Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_gso B A

Takes a subset of \(R^m\) \(S = {a_1, a_2, \ldots, a_n}\) (as the columns of a \(m x n\) matrix A) and generates an orthonormal set \(S' = {b_1, b_2, \ldots, b_n}\) (as the columns of the \(m x n\) matrix B) that spans the same subspace of \(R^m\) as \(S\).

This uses an algorithm of Schwarz-Rutishauser. See pp. 9 of https://people.inf.ethz.ch/gander/papers/qrneu.pdf

d_mat_qr :: Ptr CDMat -> Ptr CDMat -> Ptr CDMat -> IO ()

d_mat_qr Q R A

Computes the \(QR\) decomposition of a matrix A using the Gram-Schmidt process. (Sets Q and R such that \(A = QR\) where R is an upper triangular matrix and Q is an orthogonal matrix.)

This uses an algorithm of Schwarz-Rutishauser. See pp. 9 of https://people.inf.ethz.ch/gander/papers/qrneu.pdf