Chapter IX.1. Introduction

Chapter IX.1. Introduction
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All the transforms that belong neither to the I/O nor the the wavelet library should be documented here. They have been classified as follows:

Fast Fourier transforms based on the "Fastest Fourier transform in the west" (FFTW) library. Should also include a crude homemade FFT, currently not yet implemented.
Statistics currently includes only moments and histograms computations.
Thresholding algorithms : global and scale by scale iterative thresholding, as well as simple fixed threshold and decimation.
Curvilinear interpolation of 2D datasets. Based either on bicubic splines (code taken from alglib), or on direct summation of Fourier series.
Reduction : Partial summation of multidimensional datasets that reduce the number of dimensions, for example radial average, vertical average, etc. Also includes complete reduction to scalar quantities : summing, checking for NaN values, etc.
Others : Finite differences in time and in space Normalization Transforms based on algebraic expressions.

We provide a table of all documented transforms that summarizes some of their main characteristics. Transforms with names appearing in italics have not been implemented or tested yet.

directory	name	source	target	cost	MPI	OpenMP	test name
algebraic	expression_transform	coefs a	coefs b	N	yes	yes	expression_transform
	generate_grid	coefs a	coefs b	N	yes	yes	N/A
	renormalize	coefs a	coefs b	N	yes	yes	N/A
difference	space_difference	grid_coefs a	grid_coefs b	N	no	yes	zigzag_burgers/zigzag_derivative
	time_difference	coefs a	coefs b	N	yes	yes	time_derivative
fftw	dealias	fourier_coefs	fourier_coefs	N	yes	yes	functors
	fftw_c2r	fourier_coefs	grid_coefs	NlnN	d>=2	yes	fftw
	fftw_r2c	grid_coefs	fourier_coefs	NlnN	d>=2	yes	fftw
	fourier_spectrum	fourier_coefs	fourier_spectrum	N	yes	no	fourier_spectrum
interpolation	bicubic_spline_curve_interp	grid_coefs	curve_coefs	N	no	yes	interpolation
	direct_fourier_curve_interp	fourier_coefs	curve_coefs	N^(3/2)	no	yes	interpolation
	direct_fourier_interp	fourier_coefs	scalar	N	no	yes	interpolation
io	ascii_reader	ascii_file	coefs	N	no	no	wt
	ascii_writer	coefs	ascii_file	N	no	no	wt,zigzag_adapt,zigzag_array,zigag_burgers
	hdf5_reader	hdf5_file	coefs	N	yes	no	hdf5
	hdf5_writer	coefs	hdf5_file	N	yes	no	hdf5
reduction	one_d_average	coefs1	coefs2	N	yes	no	one_d_average
	peek_for_nan	coefs	scalar<bool>	1	N/A	N/A	scalar_reduction
	scalar_reduction	coefs	scalar	N	yes	yes	scalar_reduction
	weighted_scalar_reduction	coefs	scalar	N	no	yes	scalar_reduction
stats	cumulant	coefs	scalar	N	?	?	N/A
	histogram	coefs	histogram	N	yes	no	histogram
	scale_dependent_flatness	coefs	scale_dependent_moment	N	yes	yes	scale_dependent_moments
	scale_dependent_moment	source	scale_dependent_moment	N	yes	yes	scale_dependent_moments
thresholding	adapt_zigzag_structure	wt_coefs a	wt_coefs a	M	no	no	zigzag_adapt
	decimator	wt_coefs a	wt_coefs a	<N	yes	yes	decimator
	iterative_thresholder	coefs a	coefs a	Nf(N)	yes	yes	thresholding
	sbs_iterative_thresholder	wt_coefs a	wt_coefs a	Nf(N)	yes	yes	sbs_thresholding
	thresholder	coefs a	coefs a	N	yes	yes	thresholding
wavelets	complex_to_wt	complex_coefs	wt_coefs	?	yes	d>=2	N/A
	grid_to_wt	grid_coefs	wt_coefs	N	yes	d>=2	wt
	select_wt_coefs	wt_coefs	scale_wt_coefs	1	yes	d>=2	N/A
	wt_anisotropic	wt_coefs a	wt_coefs a	N	yes	d>=2	wt
	wt_derivating_inverse	wt_coefs a	wt_coefs a	N	yes	d>=2	wt
	wt_derivative_refilter	wt_coefs a	wt_coefs a	N	no	no	wt
	wt_forward	wt_coefs a	wt_coefs a	N	yes	d>=2	wt
	wt_inverse	wt_coefs a	wt_coefs a	N	yes	d>=2	wt
	wt_to_complex	wt_coefs	complex_coefs	?	yes	d>=2	N/A
	wt_to_grid	wt_coefs	grid_coefs	N	yes	d>=2	wt