Include header for FFTW3 library for its complex type. More...

Macros
#define	NFFT_SWAP_complex(x, y)
	Swapping of two vectors.
#define	NFFT_SWAP_double(x, y)
	Swapping of two vectors.
#define	PI 3.141592653589793238462643383279502884197169399375105820974944592
	Formerly known to be an irrational number.
#define	PI2 6.283185307179586476925286766559005768394338798750211641949889185
#define	PI4 12.56637061435917295385057353311801153678867759750042328389977837
#define	NFFT_MAX(a, b) ((a)>(b)? (a) : (b))
	Maximum of its two arguments.
#define	NFFT_MIN(a, b) ((a)<(b)? (a) : (b))
	Mimimum of its two arguments.

Functions
double	nfft_bspline_old (int k, double x, double *A)
	To test the new one.
double	nfft_bspline (int k, double x, double *scratch)
	Computes the B-spline $M_{k,0}\left(x\right)$ , scratch is used for de Boor's scheme.
int	nfft_prod_int (int *vec, int d)
	Computes integer $\prod_{t=0}^{d-1} v_t$ .
int	nfst_prod_minus_a_int (int *vec, int a, int d)
	Computes integer $\prod_{t=0}^{d-1} v_t-a$ .
int	nfft_plain_loop (int idx, int N, int d)
	Computes $\sum_{t=0}^{d-1} i_t \prod_{t'=t+1}^{d-1} N_{t'}$ .
double	nfft_prod_real (double *vec, int d)
	Computes double $\prod_{t=0}^{d-1} v_t$ .
double	nfft_dot_complex (fftw_complex *x, int n)
	Computes the inner/dot product .
double	nfft_dot_double (double *x, int n)
	Computes the inner/dot product .
double	nfft_dot_w_complex (fftw_complex x, double w, int n)
	Computes the weighted inner/dot product $x^H (w \odot x)$ .
double	nfft_dot_w_double (double x, double w, int n)
	Computes the weighted inner/dot product $x^H (w \odot x)$ .
double	nfft_dot_w_w2_complex (fftw_complex x, double w, double *w2, int n)
	Computes the weighted inner/dot product $x^H (w1\odot w2\odot w2 \odot x)$ .
double	nfft_dot_w2_complex (fftw_complex x, double w2, int n)
	Computes the weighted inner/dot product $x^H (w2\odot w2 \odot x)$ .
void	nfft_cp_complex (fftw_complex x, fftw_complex y, int n)
	Copies $x \leftarrow y$ .
void	nfft_cp_double (double x, double y, int n)
	Copies $x \leftarrow y$ .
void	nfft_cp_a_complex (fftw_complex x, double a, fftw_complex y, int n)
	Copies $x \leftarrow a y$ .
void	nfft_cp_a_double (double x, double a, double y, int n)
	Copies $x \leftarrow a y$ .
void	nfft_cp_w_complex (fftw_complex x, double w, fftw_complex *y, int n)
	Copies $x \leftarrow w\odot y$ .
void	nfft_cp_w_double (double x, double w, double *y, int n)
	Copies $x \leftarrow w\odot y$ .
void	nfft_upd_axpy_complex (fftw_complex x, double a, fftw_complex y, int n)
	Updates $x \leftarrow a x + y$ .
void	nfft_upd_axpy_double (double x, double a, double y, int n)
	Updates $x \leftarrow a x + y$ .
void	nfft_upd_xpay_complex (fftw_complex x, double a, fftw_complex y, int n)
	Updates $x \leftarrow x + a y$ .
void	nfft_upd_xpay_double (double x, double a, double y, int n)
	Updates $x \leftarrow x + a y$ .
void	nfft_upd_axpby_complex (fftw_complex x, double a, fftw_complex y, double b, int n)
	Updates $x \leftarrow a x + b y$ .
void	nfft_upd_axpby_double (double x, double a, double y, double b, int n)
	Updates $x \leftarrow a x + b y$ .
void	nfft_upd_xpawy_complex (fftw_complex x, double a, double w, fftw_complex *y, int n)
	Updates $x \leftarrow x + a w\odot y$ .
void	nfft_upd_xpawy_double (double x, double a, double w, double *y, int n)
	Updates $x \leftarrow x + a w\odot y$ .
void	nfft_upd_axpwy_complex (fftw_complex x, double a, double w, fftw_complex *y, int n)
	Updates $x \leftarrow a x + w\odot y$ .
void	nfft_upd_axpwy_double (double x, double a, double w, double *y, int n)
	Updates $x \leftarrow a x + w\odot y$ .
void	nfft_fftshift_complex (fftw_complex x, int d, int N)
	Swaps each half over N[d]/2.
void	nfft_vpr_int (int x, int n, char text)
	Prints a vector of integer numbers.
void	nfft_vpr_double (double x, int n, const char text)
	Prints a vector of doubles numbers.
void	nfft_vpr_complex (fftw_complex x, int n, const char text)
	Prints a vector of complex numbers.
void	nfft_vrand_unit_complex (fftw_complex *x, int n)
	Inits a vector of random complex numbers in $[0,1]\times[0,1]{\rm i}$ .
void	nfft_vrand_shifted_unit_double (double *x, int n)
	Inits a vector of random double numbers in .
void	nfft_voronoi_weights_1d (double w, double x, int M)
	Computes non periodic voronoi weights, assumes ordered nodes .
void	nfft_voronoi_weights_S2 (double w, double xi, int M)
	Computes voronoi weights for nodes on the sphere S^2.
double	nfft_modified_fejer (int N, int kk)
	Computes the damping factor for the modified Fejer kernel, ie $\frac{2}{N}\left(1-\frac{\left\|2k+1\right\|}{N}\right)$ .
double	nfft_modified_jackson2 (int N, int kk)
	Computes the damping factor for the modified Jackson kernel.
double	nfft_modified_jackson4 (int N, int kk)
	Computes the damping factor for the modified generalised Jackson kernel.
double	nfft_modified_sobolev (double mu, int kk)
	Computes the damping factor for the modified Sobolev kernel.
double	nfft_modified_multiquadric (double mu, double c, int kk)
	Computes the damping factor for the modified multiquadric kernel.
int	nfft_smbi (const double x, const double alpha, const int nb, const int ize, double *b)
	Calculates the modified bessel function $I_{n+\alpha}(x)$ , possibly scaled by $\mathrm{e}^{-x}$ , for real non-negative with $0 \le \alpha < 1$ , and $n=0,1,\ldots,nb-1$ .
double	nfft_drand48 (void)
void	nfft_srand48 (long int seed)
void	nfft_sort_node_indices_radix_lsdf (int n, int keys0, int keys1, int rhigh)
	Radix sort for node indices.
void	nfft_sort_node_indices_radix_msdf (int n, int keys0, int keys1, int rhigh)
	Radix sort for node indices.
int	nfft_get_num_threads (void)

Detailed Description

Include header for FFTW3 library for its complex type.

This module implements frequently used utility functions. In particular, this includes simple measurement of resources, evaluation of window functions, vector routines for basic linear algebra tasks, and computation of weights for the inverse transforms.

Macro Definition Documentation

#define NFFT_SWAP_complex	(	x,
		y
	)

Value:

{fftw_complex* NFFT_SWAP_temp__; \

NFFT_SWAP_temp__=(x); (x)=(y); (y)=NFFT_SWAP_temp__;}

Swapping of two vectors.

Definition at line 52 of file nfft3util.h.

Referenced by fgt_test_andersson(), fgt_test_error(), fgt_test_error_p(), fgt_test_simple(), glacier_cv(), main(), solver_loop_one_step_cgnr_complex(), solver_loop_one_step_landweber_complex(), solver_loop_one_step_steepest_descent_complex(), and taylor_time_accuracy().

#define NFFT_SWAP_double	(	x,
		y
	)

Value:

{double* NFFT_SWAP_temp__; NFFT_SWAP_temp__=(x); \

(x)=(y); (y)=NFFT_SWAP_temp__;}

Swapping of two vectors.

Definition at line 57 of file nfft3util.h.

Referenced by solver_loop_one_step_cgnr_double(), solver_loop_one_step_landweber_double(), and solver_loop_one_step_steepest_descent_double().

Function Documentation

void nfft_voronoi_weights_S2	(	double *	w,
		double *	xi,
		int	M
	)

Computes voronoi weights for nodes on the sphere S^2.

Definition at line 581 of file util.c.

References nfft_free(), nfft_malloc(), and PI.

Referenced by main().

int nfft_smbi	(	const R	x,
		const R	alpha,
		const int	nb,
		const int	ize,
		R *	b
	)

Calculates the modified bessel function $I_{n+\alpha}(x)$ , possibly scaled by $\mathrm{e}^{-x}$ , for real non-negative $x,alpha$ with $0 \le \alpha < 1$ , and $n=0,1,\ldots,nb-1$ .

[in] x non-negative real number in $I_{n+\alpha}(x)$
[in] alpha non-negative real number with $0 \le \alpha < 1$ in $I_{n+\alpha}(x)$
[in] nb number of functions to be calculated
[in] ize switch between no scaling (ize = 1) and exponential scaling (ize = 2)
[out] b real output vector to contain ,
Returns:
error indicator. Only if this value is identical to nb, then all values in b have been calculated to full accuracy. If not, errors are indicated using the following scheme:
- ncalc < 0: At least one of the arguments was out of range (e.g. nb <= 0, ize neither equals 1 nor 2, $|x| \ge exparg$ ). In this case, the output vector b is not calculated and ncalc is set to $\min(nb,0)-1$ .
- 0 < ncalc < nb: Not all requested functions could be calculated to full accuracy. This can occur when nb is much larger than |x|. in this case, the values $I_{n+\alpha}(x)$ are calculated to full accuracy for $n=0,1,\ldots,ncalc$ . The rest of the values up to $n=0,1,\ldots,nb-1$ is calculated to a lower accuracy.

This program is based on a program written by David J. Sookne [2] that computes values of the Bessel functions $J_{\nu}(x)$ or $I_{\nu}(x)$ for real argument $x$ and integer order $\nu$ . modifications include the restriction of the computation to the Bessel function $I_{\nu}(x)$ for non-negative real argument, the extension of the computation to arbitrary non-negative orders $\nu$ , and the elimination of most underflow.

References: [1] F. W. J. Olver and D. J. Sookne, A note on backward recurrence algorithms", Math. Comput. (26), 1972, pp 125 – 132. [2] D. J. Sookne, "Bessel functions of real argument and int order", NBS Jour. of Res. B. (77B), 1973, pp. 125 – 132.

Modified by W. J. Cody, Applied Mathematics Division, Argonne National Laboratory, Argonne, IL, 60439, USA

Modified by Jens Keiner, Institute of Mathematics, University of Lübeck, 23560 Lübeck, Germany

Definition at line 950 of file util.c.

References nfsft_wisdom::alpha.

Referenced by main().

void nfft_sort_node_indices_radix_lsdf	(	int	n,
		int *	keys0,
		int *	keys1,
		int	rhigh
	)

Radix sort for node indices.

Author:: Michael Hofmann

Definition at line 1301 of file util.c.

void nfft_sort_node_indices_radix_msdf	(	int	n,
		int *	keys0,
		int *	keys1,
		int	rhigh
	)

Radix sort for node indices.

Author:: Michael Hofmann

Definition at line 1383 of file util.c.

References nfft_sort_node_indices_radix_msdf().

Referenced by nfft_sort_node_indices_radix_msdf().

Macros

Functions

Detailed Description

Macro Definition Documentation

Function Documentation