This module implements frequently used utility functions. More...

Macros
#define	CONCAT(prefix, name) prefix ## name

#define	Y(name) CONCAT(nfft_,name)

#define	FFTW(name) CONCAT(fftw_,name)

#define	NFFT(name) CONCAT(nfft_,name)

#define	NFCT(name) CONCAT(nfct_,name)

#define	NFST(name) CONCAT(nfst_,name)

#define	NFSFT(name) CONCAT(nfsft_,name)

#define	SOLVER(name) CONCAT(solver_,name)

#define	X(name) Y(name)

#define	STRINGIZEx(x) #x

#define	STRINGIZE(x) STRINGIZEx(x)

#define	K(x) ((R) x)

#define	DK(name, value) const R name = K(value)

#define	KPI K(3.1415926535897932384626433832795028841971693993751)

#define	K2PI K(6.2831853071795864769252867665590057683943387987502)

#define	K4PI K(12.5663706143591729538505735331180115367886775975004)

#define	KE K(2.7182818284590452353602874713526624977572470937000)

#define	IF(x, a, b) ((x)?(a):(b))

#define	MIN(a, b) (((a)<(b))?(a):(b))

#define	MAX(a, b) (((a)>(b))?(a):(b))

#define	ABS(x) (((x)>K(0.0))?(x):(-(x)))

#define	SIGN(a) (((a)>=0)?1:-1)

#define	SIGN(a) (((a)>=0)?1:-1)

#define	SIGNF(a) IF((a)<K(0.0),K(-1.0),K(1.0))

#define	SIZE(x) sizeof(x)/sizeof(x[0])

#define	CSWAP(x, y)
	Swap two vectors. More...

#define	RSWAP(x, y)
	Swap two vectors. More...

#define	PHI_HUT(n, k, d) (Y(bessel_i0)((R)(ths->m) * SQRT(ths->b[d] * ths->b[d] - (K(2.0) * KPI * (R)(k) / (R)(n)) * (K(2.0) * KPI * (R)(k) / (R)(n)))))

#define	PHI(n, x, d)

#define	WINDOW_HELP_INIT

#define	WINDOW_HELP_FINALIZE {Y(free)(ths->b);}

#define	WINDOW_HELP_ESTIMATE_m 8

#define	COPYSIGN copysign

#define	NEXTAFTER nextafter

#define	MKNAN nan

#define	CEIL ceil

#define	FLOOR floor

#define	NEARBYINT nearbyint

#define	RINT rint

#define	ROUND round

#define	LRINT lrint

#define	LROUND lround

#define	LLRINT llrint

#define	LLROUND llround

#define	TRUNC trunc

#define	FMOD fmod

#define	REMAINDER remainder

#define	REMQUO remquo

#define	FDIM fdim

#define	FMAX fmax

#define	FMIN fmin

#define	FFMA fma

#define	FABS fabs

#define	SQRT sqrt

#define	CBRT cbrt

#define	HYPOT hypot

#define	EXP exp

#define	EXP2 exp2

#define	EXPM1 expm1

#define	LOG log

#define	LOG2 log2

#define	LOG10 log10

#define	LOG1P log1p

#define	LOGB logb

#define	ILOGB ilogb

#define	MODF modf

#define	FREXP frexp

#define	LDEXP ldexp

#define	SCALBN scalbn

#define	SCALBLN scalbln

#define	POW pow

#define	COS cos

#define	SIN sin

#define	TAN tan

#define	COSH cosh

#define	SINH sinh

#define	TANH tanh

#define	ACOS acos

#define	ASIN asin

#define	ATAN atan

#define	ATAN2 atan2

#define	ACOSH acosh

#define	ASINH asinh

#define	ATANH atanh

#define	TGAMMA tgamma

#define	LGAMMA lgamma

#define	J0 j0

#define	J1 j1

#define	JN jn

#define	Y0 y0

#define	Y1 y1

#define	YN yn

#define	ERF erf

#define	ERFC erfc

#define	CREAL creal

#define	CIMAG cimag

#define	CABS cabs

#define	CARG carg

#define	CONJ conj

#define	CPROJ cproj

#define	CSQRT csqrt

#define	CEXP cexp

#define	CLOG clog

#define	CPOW cpow

#define	CSIN csin

#define	CCOS ccos

#define	CTAN ctan

#define	CASIN casin

#define	CACOS cacos

#define	CATAN catan

#define	CSINH csinh

#define	CCOSH ccosh

#define	CTANH ctanh

#define	CASINH casinh

#define	CACOSH cacosh

#define	CATANH catanh

#define	MANT_DIG DBL_MANT_DIG

#define	MIN_EXP DBL_MIN_EXP

#define	MAX_EXP DBL_MAX_EXP

#define	FLTROUND 0.0

#define	R_RADIX FLT_RADIX

#define	II _Complex_I

#define	__FGS__ "lg"

#define	__FES__ "lE"

#define	__FE__ "% 20.16lE"

#define	__FI__ "%lf"

#define	__FIS__ "lf"

#define	__FR__ "%le"

#define	TRUE 1

#define	FALSE 0

#define	__D__ "%td"

#define	UNUSED(x) (void)x
	Dummy use of unused parameters to silence compiler warnings.

#define	UNUSED(x) (void)x
	Dummy use of unused parameters to silence compiler warnings.

#define	STACK_MALLOC(T, p, x) p = (T)alloca(x)

#define	STACK_FREE(x) /* Nothing. Cleanup done automatically. */

#define	TIC(a)
	Timing, method works since the inaccurate timer is updated mostly in the measured function. More...

#define	TOC(a)

#define	TIC_FFTW(a)

#define	TOC_FFTW(a)

#define	CK(ex) (void)((ex) \|\| (Y(assertion_failed)(#ex, __LINE__, __FILE__), 0))

#define	A(ex) /* nothing */

Typedefs
typedef double	R

typedef double _Complex	C

typedef ptrdiff_t	INT

Enumerations
enum	float_property { NFFT_SAFE__MIN = 1, NFFT_BASE = 2, NFFT_PRECISION = 3, NFFT_MANT_DIG = 4, NFFT_FLTROUND = 5, NFFT_E_MIN = 6, NFFT_R_MIN = 7, NFFT_E_MAX = 8, NFFT_R_MAX = 9 }

Functions
INT	nfft_m2K (const INT m)

R	nfft_elapsed_seconds (ticks t1, ticks t0)
	Return number of elapsed seconds between two time points. More...

R	nfft_sinc (R x)

R	nfft_lambda (R z, R eps)

R	nfft_lambda2 (R mu, R nu)

R	nfft_bessel_i0 (R x)

R	nfft_bsplines (const INT, const R x)

R	nfft_float_property (float_property)

R	nfft_prod_real (R *vec, INT d)

INT	nfft_log2i (const INT m)

void	nfft_next_power_of_2_exp (const INT N, INT N2, INT t)

void	nfft_next_power_of_2_exp_int (const int N, int N2, int t)

R	nfft_error_l_infty_double (const R x, const R y, const INT n)

R	nfft_error_l_infty_1_double (const R x, const R y, const INT n, const R *z, const INT m)

R	nfft_error_l_2_complex (const C x, const C y, const INT n)

R	nfft_error_l_2_double (const R x, const R y, const INT n)

void	nfft_sort_node_indices_radix_msdf (INT n, INT keys0, INT keys1, INT rhigh)

void	nfft_sort_node_indices_radix_lsdf (INT n, INT keys0, INT keys1, INT rhigh)

void	nfft_assertion_failed (const char s, int line, const char file)

R	nfft_dot_double (R *x, INT n)
	Computes the inner/dot product . More...

R	nfft_dot_w_complex (C x, R w, INT n)
	Computes the weighted inner/dot product $x^H (w \odot x)$ . More...

R	nfft_dot_w_double (R x, R w, INT n)
	Computes the weighted inner/dot product $x^H (w \odot x)$ . More...

R	nfft_dot_w_w2_complex (C x, R w, R *w2, INT n)
	Computes the weighted inner/dot product $x^H (w\odot w2\odot w2 \odot x)$ . More...

R	nfft_dot_w2_complex (C x, R w2, INT n)
	Computes the weighted inner/dot product $x^H (w2\odot w2 \odot x)$ . More...

void	nfft_cp_complex (C x, C y, INT n)
	Copies $x \leftarrow y$ . More...

void	nfft_cp_double (R x, R y, INT n)
	Copies $x \leftarrow y$ . More...

void	nfft_cp_a_complex (C x, R a, C y, INT n)
	Copies $x \leftarrow a y$ . More...

void	nfft_cp_a_double (R x, R a, R y, INT n)
	Copies $x \leftarrow a y$ . More...

void	nfft_cp_w_complex (C x, R w, C *y, INT n)
	Copies $x \leftarrow w\odot y$ . More...

void	nfft_cp_w_double (R x, R w, R *y, INT n)
	Copies $x \leftarrow w\odot y$ . More...

void	nfft_upd_axpy_double (R x, R a, R y, INT n)
	Updates $x \leftarrow a x + y$ . More...

void	nfft_upd_xpay_complex (C x, R a, C y, INT n)
	Updates $x \leftarrow x + a y$ . More...

void	nfft_upd_xpay_double (R x, R a, R y, INT n)
	Updates $x \leftarrow x + a y$ . More...

void	nfft_upd_axpby_complex (C x, R a, C y, R b, INT n)
	Updates $x \leftarrow a x + b y$ . More...

void	nfft_upd_axpby_double (R x, R a, R y, R b, INT n)
	Updates $x \leftarrow a x + b y$ . More...

void	nfft_upd_xpawy_complex (C x, R a, R w, C *y, INT n)
	Updates $x \leftarrow x + a w\odot y$ . More...

void	nfft_upd_xpawy_double (R x, R a, R w, R *y, INT n)
	Updates $x \leftarrow x + a w\odot y$ . More...

void	nfft_upd_axpwy_complex (C x, R a, R w, C *y, INT n)
	Updates $x \leftarrow a x + w\odot y$ . More...

void	nfft_upd_axpwy_double (R x, R a, R w, R *y, INT n)
	Updates $x \leftarrow a x + w\odot y$ . More...

void	nfft_voronoi_weights_1d (R w, R x, const INT M)

R	nfft_modified_fejer (const INT N, const INT kk)
	Compute damping factor for modified Fejer kernel: /f${2}{N}(1-{\|2k+1\|}{N})/f$.

R	nfft_modified_jackson2 (const INT N, const INT kk)
	Compute damping factor for modified Jackson kernel. More...

R	nfft_modified_jackson4 (const INT N, const INT kk)
	Compute damping factor for modified generalised Jackson kernel. More...

R	nfft_modified_sobolev (const R mu, const INT kk)
	Compute damping factor for modified Sobolev kernel. More...

R	nfft_modified_multiquadric (const R mu, const R c, const INT kk)
	Comput damping factor for modified multiquadric kernel. More...

Detailed Description

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 CSWAP	(	x,
		y
	)

Value:

{C* NFFT_SWAP_temp__; \

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

Swap two vectors.

Definition at line 139 of file infft.h.

Referenced by 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 RSWAP	(	x,
		y
	)

Value:

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

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

Swap two vectors.

Definition at line 143 of file infft.h.

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

#define PHI	(	n,
		x,
		d
	)

Value:

(  (((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n)) > K(0.0)) \
                      ?   SINH(ths->b[d] * SQRT((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n))) \
                        / (KPI * SQRT((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n))) \
                      :   ((((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n)) < K(0.0)) \
                        ?   SIN(ths->b[d] * SQRT((x) * (R)(n) * (x) * (R)(n) - (R)(ths->m) * (R)(ths->m))) \
                          / (KPI * SQRT((x) * (R)(n) * (x) * (R)(n) - (R)(ths->m) * (R)(ths->m))) \
                        : ths->b[d] / KPI))

Definition at line 209 of file infft.h.

#define WINDOW_HELP_INIT

Value:

{ \
      int WINDOW_idx; \
      ths->b = (R*) Y(malloc)((size_t)(ths->d) * sizeof(R)); \
      for (WINDOW_idx = 0; WINDOW_idx < ths->d; WINDOW_idx++) \
        ths->b[WINDOW_idx] = (KPI * (K(2.0) - K(1.0) / ths->sigma[WINDOW_idx])); \
  }

Definition at line 216 of file infft.h.

#define TIC ( a )

Timing, method works since the inaccurate timer is updated mostly in the measured function.

For small times not every call of the measured function will also produce a 'unit' time step. Measuring the fftw might cause a wrong output vector due to the repeated ffts.

Definition at line 1397 of file infft.h.

Function Documentation

R nfft_elapsed_seconds	(	ticks	t1,
		ticks	t0
	)

Return number of elapsed seconds between two time points.

Referenced by fastsum_precompute_source_nodes(), fastsum_trafo(), main(), nfsft_adjoint(), and nfsft_trafo().

R nfft_dot_double	(	R *	x,
		INT	n
	)

Computes the inner/dot product $x^H x$ .

R nfft_dot_w_complex	(	C *	x,
		R *	w,
		INT	n
	)

Computes the weighted inner/dot product $x^H (w \odot x)$ .

R nfft_dot_w_double	(	R *	x,
		R *	w,
		INT	n
	)

Computes the weighted inner/dot product $x^H (w \odot x)$ .

R nfft_dot_w_w2_complex	(	C *	x,
		R *	w,
		R *	w2,
		INT	n
	)

Computes the weighted inner/dot product $x^H (w\odot w2\odot w2 \odot x)$ .

R nfft_dot_w2_complex	(	C *	x,
		R *	w2,
		INT	n
	)

Computes the weighted inner/dot product $x^H (w2\odot w2 \odot x)$ .

void nfft_cp_complex	(	C *	x,
		C *	y,
		INT	n
	)

Copies $x \leftarrow y$ .

void nfft_cp_double	(	R *	x,
		R *	y,
		INT	n
	)

Copies $x \leftarrow y$ .

void nfft_cp_a_complex	(	C *	x,
		R	a,
		C *	y,
		INT	n
	)

Copies $x \leftarrow a y$ .

void nfft_cp_a_double	(	R *	x,
		R	a,
		R *	y,
		INT	n
	)

Copies $x \leftarrow a y$ .

void nfft_cp_w_complex	(	C *	x,
		R *	w,
		C *	y,
		INT	n
	)

Copies $x \leftarrow w\odot y$ .

void nfft_cp_w_double	(	R *	x,
		R *	w,
		R *	y,
		INT	n
	)

Copies $x \leftarrow w\odot y$ .

void nfft_upd_axpy_double	(	R *	x,
		R	a,
		R *	y,
		INT	n
	)

Updates $x \leftarrow a x + y$ .

void nfft_upd_xpay_complex	(	C *	x,
		R	a,
		C *	y,
		INT	n
	)

Updates $x \leftarrow x + a y$ .

void nfft_upd_xpay_double	(	R *	x,
		R	a,
		R *	y,
		INT	n
	)

Updates $x \leftarrow x + a y$ .

void nfft_upd_axpby_complex	(	C *	x,
		R	a,
		C *	y,
		R	b,
		INT	n
	)

Updates $x \leftarrow a x + b y$ .

void nfft_upd_axpby_double	(	R *	x,
		R	a,
		R *	y,
		R	b,
		INT	n
	)

Updates $x \leftarrow a x + b y$ .

void nfft_upd_xpawy_complex	(	C *	x,
		R	a,
		R *	w,
		C *	y,
		INT	n
	)

Updates $x \leftarrow x + a w\odot y$ .

void nfft_upd_xpawy_double	(	R *	x,
		R	a,
		R *	w,
		R *	y,
		INT	n
	)

Updates $x \leftarrow x + a w\odot y$ .

void nfft_upd_axpwy_complex	(	C *	x,
		R	a,
		R *	w,
		C *	y,
		INT	n
	)

Updates $x \leftarrow a x + w\odot y$ .

void nfft_upd_axpwy_double	(	R *	x,
		R	a,
		R *	w,
		R *	y,
		INT	n
	)

Updates $x \leftarrow a x + w\odot y$ .

R nfft_modified_jackson2	(	const INT	N,
		const INT	kk
	)

Compute damping factor for modified Jackson kernel.

R nfft_modified_jackson4	(	const INT	N,
		const INT	kk
	)

Compute damping factor for modified generalised Jackson kernel.

R nfft_modified_sobolev	(	const R	mu,
		const INT	kk
	)

Compute damping factor for modified Sobolev kernel.

R nfft_modified_multiquadric	(	const R	mu,
		const R	c,
		const INT	kk
	)

Comput damping factor for modified multiquadric kernel.

Macros

Typedefs

Enumerations

Functions

Detailed Description

Macro Definition Documentation

Function Documentation