ArrayFire.LAPACK

Documentation

svd

Arguments

:: AFType a

=> Array a

the input Matrix

-> (Array a, Array a, Array a)

Output Array containing (U, diagonal values of sigma, V^H)

Singular Value Decomposition

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The arrayfire function only returns the non zero diagonal elements of S.

svdInPlace

Arguments

:: AFType a

=> Array a

the input matrix

-> (Array a, Array a, Array a)

Output Array containing (U, diagonal values of sigma, V^H)

Singular Value Decomposition (in-place)

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The arrayfire function only returns the non zero diagonal elements of S.

lu

Arguments

:: AFType a

=> Array a

is the input matrix

-> (Array a, Array a, Array a)

Returns the output Arrays (lower, upper, pivot)

Perform LU decomposition

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C Interface for LU decomposition.

luInPlace

Arguments

:: AFType a

=> Array a

contains the input on entry, the packed LU decomposition on exit.

-> Bool

specifies if the pivot is returned in original LAPACK compliant format

-> Array a

will contain the permutation indices to map the input to the decomposition

Perform LU decomposition (in-place).

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C Interface for in place LU decomposition.

qr

Arguments

:: AFType a

=> Array a

the input matrix

-> (Array a, Array a, Array a)

Returns (q, r, tau) Arrays q is the orthogonal matrix from QR decomposition r is the upper triangular matrix from QR decomposition tau will contain additional information needed for solving a least squares problem using q and r

Perform QR decomposition

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C Interface for QR decomposition.

qrInPlace

Arguments

:: AFType a

=> Array a

is the input matrix on entry. It contains packed QR decomposition on exit

-> Array a

will contain additional information needed for unpacking the data

Perform QR decomposition

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C Interface for QR decomposition.

cholesky

Arguments

:: AFType a

=> Array a

input Array

-> Bool

a boolean determining if out is upper or lower triangular

-> (Int, Array a)

contains the triangular matrix. Multiply Int with its conjugate transpose reproduces the input array. is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

Perform Cholesky Decomposition

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This function decomposes a positive definite matrix A into two triangular matrices.

choleskyInplace

Arguments

:: AFType a

=> Array a

is the input matrix on entry. It contains the triangular matrix on exit.

-> Bool

a boolean determining if in is upper or lower triangular

-> Int

is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

Perform Cholesky Decomposition

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C Interface for in place cholesky decomposition.

solve

Arguments

:: AFType a

=> Array a

is the coefficient matrix

-> Array a

is the measured values

-> MatProp

determining various properties of matrix a

-> Array a

is the matrix of unknown variables

Solve a system of equations

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solveLU

Arguments

:: AFType a

=> Array a

is the output matrix from packed LU decomposition of the coefficient matrix

-> Array a

is the pivot array from packed LU decomposition of the coefficient matrix

-> Array a

is the matrix of measured values

-> MatProp

determining various properties of matrix a

-> Array a

will contain the matrix of unknown variables

Solve a system of equations.

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inverse

Arguments

:: AFType a

=> Array a

is input matrix

-> MatProp

determining various properties of matrix in

-> Array a

will contain the inverse of matrix in

Invert a matrix.

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C Interface for inverting a matrix.

rank

Arguments

:: AFType a

=> Array a

is input matrix

-> Double

is the tolerance value

-> Int

will contain the rank of in

Pseudo-inverse

Not implemented in 3.6.4

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pinverse :: AFType a => Array a -> Double -> MatProp -> Array a pinverse a d m = a op1 (x y -> af_pinverse x y d (toMatProp m))

Find the rank of the input matrix

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This function uses af::qr to find the rank of the input matrix within the given tolerance.

det

Arguments

:: AFType a

=> Array a

is input matrix

-> (Double, Double)

will contain the real and imaginary part of the determinant of in

Find the determinant of a Matrix

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C Interface for finding the determinant of a matrix.

norm

Arguments

:: AFType a

=> Array a

is the input matrix

-> NormType

specifies the NormType

-> Double

specifies the value of P when type is one of AF_NORM_VECTOR_P, AF_NORM_MATRIX_L_PQ is used. It is ignored for other values of type

-> Double

specifies the value of Q when type is AF_NORM_MATRIX_L_PQ. This parameter is ignored if type is anything else

-> Double

will contain the norm of in

Find the norm of the input matrix.

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This function can return the norm using various metrics based on the type paramter.

isLAPACKAvailable

Arguments

:: Bool

Returns if LAPACK is available

Is LAPACK available

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