úξ‹     Matrix-matrix multiply. Strict complex doubles. (Take the magnitude of a complex number. FTake the argument (phase) of a complex number, in the range [-pi .. pi]. 4Calculate roots of unity for the forward transform. &Length of lowest dimension of result. 4Calculate roots of unity for the inverse transform. &Length of lowest dimension of result. ;Compute the DFT along the low order dimension of an array. CCompute the inverse DFT along the low order dimension of an array. <Generic function for computation of forward or inverse DFT. R This function is also useful if you transform many arrays with the same extent,  and don',t want to recompute the roots for each one. H The extent of the given roots must match that of the input array, else . Roots of unity.  Input array. #Compute a single value of the DFT. H The extent of the given roots must match that of the input array, else . Roots of unity.  Input array. Index of the value we want.     +Apply the centering transform to a vector. +Apply the centering transform to a matrix.    ;Compute the DFT along the low order dimension of an array. CCompute the inverse DFT along the low order dimension of an array. $Compute the DFT of a square matrix. $ If the matrix is not square then . -Compute the inverse DFT of a square matrix. Compute the DFT of a 3d cube. # If the array is not a cube then . &Compute the inverse DFT of a 3d cube. # If the array is not a cube then . TGeneric function for computation of forward or inverse Discrete Fourier Transforms. < Computation is along the low order dimension of the array. Roots of unity. Input values.        !repa-algorithms-1.1.0.0"Data.Array.Repa.Algorithms.Complex!Data.Array.Repa.Algorithms.Matrix$Data.Array.Repa.Algorithms.DFT.RootsData.Array.Repa.Algorithms.DFT%Data.Array.Repa.Algorithms.DFT.CenterData.Array.Repa.Algorithms.FFTdph-base-0.4.0$Data.Array.Parallel.Base.Hyperstrict:*: multiplyMMComplexmagargcalcRootsOfUnitycalcInverseRootsOfUnitydftidft dftWithRootsdftWithRootsSingle centerVector centerMatrixfftifftfft2difft2dfft3difft3d fftWithRootsbaseGHC.Errerror fftWithRoots'