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Util - Auxiliary functions

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 | 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 . More...
R | nfft_dot_w_double (R *x, R *w, INT n)
| Computes the weighted inner/dot product . More...
R | nfft_dot_w_w2_complex (C *x, R *w, R *w2, INT n)
| Computes the weighted inner/dot product . More...
R | nfft_dot_w2_complex (C *x, R *w2, INT n)
| Computes the weighted inner/dot product . More...
void | nfft_cp_complex (C *x, C *y, INT n)
| Copies . More...
void | nfft_cp_double (R *x, R *y, INT n)
| Copies . More...
void | nfft_cp_a_complex (C *x, R a, C *y, INT n)
| Copies . More...
void | nfft_cp_a_double (R *x, R a, R *y, INT n)
| Copies . More...
void | nfft_cp_w_complex (C *x, R *w, C *y, INT n)
| Copies . More...
void | nfft_cp_w_double (R *x, R *w, R *y, INT n)
| Copies . More...
void | nfft_upd_axpy_double (R *x, R a, R *y, INT n)
| Updates . More...
void | nfft_upd_xpay_complex (C *x, R a, C *y, INT n)
| Updates . More...
void | nfft_upd_xpay_double (R *x, R a, R *y, INT n)
| Updates . More...
void | nfft_upd_axpby_complex (C *x, R a, C *y, R b, INT n)
| Updates . More...
void | nfft_upd_axpby_double (R *x, R a, R *y, R b, INT n)
| Updates . More...
void | nfft_upd_xpawy_complex (C *x, R a, R *w, C *y, INT n)
| Updates . More...
void | nfft_upd_xpawy_double (R *x, R a, R *w, R *y, INT n)
| Updates . More...
void | nfft_upd_axpwy_complex (C *x, R a, R *w, C *y, INT n)
| Updates . More...
void | nfft_upd_axpwy_double (R *x, R a, R *w, R *y, INT n)
| Updates . 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 CONCAT(), nsfft_init_random_nodes_coeffs(), 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(), nfsft_trafo(), and SearchTree().

R nfft_dot_double | ( | R * | x,
|  | INT | n
| ) |  |

Computes the inner/dot product .

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

Computes the weighted inner/dot product .

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

Computes the weighted inner/dot product .

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

Computes the weighted inner/dot product .

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

Computes the weighted inner/dot product .

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

Copies .

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

Copies .

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

Copies .

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

Copies .

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

Copies .

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

Copies .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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

Updates .

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.