Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman
Macros
randmt: Samplers using the global generator

Macros

#define init_randmt(seed)   (init_randmt_r(&__randmt_global_generator, seed))
 Initialize the global generator with a seed. More...
 
#define init_randmt_auto()   (init_randmt_auto_r(&__randmt_global_generator))
 Initialize the global generator with the current time. More...
 
#define rand_uint32()   (rand_uint32_r(&__randmt_global_generator))
 Generate a random 32-bit unsigned integer (nonreentrant) More...
 
#define rand_unif()   (rand_unif_r(&__randmt_global_generator))
 Generate a uniform random number on (0,1) (nonreentrant) More...
 
#define rand_normal()   (rand_normal_r(&__randmt_global_generator))
 Generate a standard normal distributed random number (nonreentrant) More...
 
#define rand_exp(mu)   (rand_exp_r(&__randmt_global_generator, mu))
 Generate an exponentially-distributed number (nonreentrant) More...
 
#define rand_gamma(a, b)   (rand_gamma_r(&__randmt_global_generator, a, b))
 Generate a Gamma-distributed number (nonreentrant) More...
 
#define rand_poisson(mu)   (rand_poisson_r(&__randmt_global_generator, mu))
 Generate a Poisson-distributed number (nonreentrant) More...
 
#define rand_geometric(p)   (rand_geometric_r(&__randmt_global_generator, p))
 Generate a geometrically-distributed number (nonreentrant) More...
 

Detailed Description

These functions use the global pseudorandom number generator.

Macro Definition Documentation

#define init_randmt (   seed)    (init_randmt_r(&__randmt_global_generator, seed))

Initialize the global generator with a seed.

Parameters
seedthe seed value
See Also
init_randmt_auto()
init_randmt_r()

This routine seeds the global random number generator with an unsigned 32-bit integer value.

A constant seed can be used to reproduce the same pseudorandom numbers.

int i;
printf("Ten numbers:\n");
for(i = 0; i < 10; i++)
printf("%f\n", rand_unif());
printf("The same ten numbers:\n");
for(i = 0; i < 10; i++)
printf("%f\n", rand_unif());

Definition at line 314 of file randmt.h.

#define init_randmt_auto ( )    (init_randmt_auto_r(&__randmt_global_generator))

Initialize the global generator with the current time.

See Also
init_randmt()
init_randmt_auto_r()

This function seeds the global generator with the current time. It should be called once at the beginning of the program so that different pseudorandom values are produced on different runs.

This function only needs to be called once. Seeding multiple times does not improve the statistical quality of the generator.

Definition at line 328 of file randmt.h.

#define rand_exp (   mu)    (rand_exp_r(&__randmt_global_generator, mu))

Generate an exponentially-distributed number (nonreentrant)

Parameters
mumean parameter of the distribution (positive value)
Returns
Pseudo-random exponentially-distibuted value with mean mu
See Also
rand_exp_r()

Generates a pseudo-random value distributed with probability density

\[ f(x;\mu) = \begin{cases} \frac{1}{\mu} \mathrm{e}^{-x/\mu}, & x \ge 0, \\ 0, & x < 0, \end{cases} \]

generated by inversion. The global generator is used to generate the value.

Distribution properties:

  • CDF: $ 1 - \exp(-x/\mu) $
  • Mean: $ \mu $
  • Variance: $ \mu^2 $

Definition at line 395 of file randmt.h.

#define rand_gamma (   a,
 
)    (rand_gamma_r(&__randmt_global_generator, a, b))

Generate a Gamma-distributed number (nonreentrant)

Parameters
ashape parameter (positive value)
bscale parameter (positive value)
Returns
Pseudo-random Gamma-distibuted value
See Also
rand_gamma_r()

Generates a Gamma-distributed random value with density

\[ f(x;a,b) = x^{a-1} \frac{\exp(-x/b)}{\Gamma(a)b^k}, \quad x \ge 0, \]

where $ \Gamma(a) $ is the Gamma function, using the method of Marsaglia and Tsang, 2000. The global generator is used to generate the value.

Distribution properties:

  • CDF: $ \gamma(a,x/b)/\Gamma(a) $, where $ \gamma $ is the lower incomplete gamma function
  • Mean: $ ab $
  • Variance: $ ab^2 $

Definition at line 416 of file randmt.h.

#define rand_geometric (   p)    (rand_geometric_r(&__randmt_global_generator, p))

Generate a geometrically-distributed number (nonreentrant)

Parameters
pprobability of success
Returns
Pseudo-random geometrically-distibuted value
See Also
rand_geometric_r()

Generates a pseudo-random value distributed with probability mass fuction

\[ \mathrm{P}(X = k) = (1 - p)^{k-1} p, \quad k = 1, 2, \ldots, \]

where $ 0 < p \le 1 $, generated by inversion. The global generator is used to generate the value.

Distribution properties:

  • CDF: $ 1 - (1 - p)^{\lfloor k \rfloor} $
  • Mean: $ 1/p $
  • Variance: $ (1 - p)/p^2 $

Definition at line 460 of file randmt.h.

#define rand_normal ( )    (rand_normal_r(&__randmt_global_generator))

Generate a standard normal distributed random number (nonreentrant)

Returns
Pseudo-random double value with standard normal distribution
See Also
rand_normal_r()

A pseudo-random normally distributed number with density

\[ f(x) = \frac{1}{\sqrt{2\pi}} \mathrm{e}^{-x^2/2}, \]

generated by the Box-Muller transform. The global generator is used to generate the value.

Distribution properties:

  • CDF: $ \frac{1}{2}\bigl( 1 + \mathrm{erf}(x/\sqrt{2})\bigr) $
  • Mean: 0
  • Variance: 1

Definition at line 374 of file randmt.h.

#define rand_poisson (   mu)    (rand_poisson_r(&__randmt_global_generator, mu))

Generate a Poisson-distributed number (nonreentrant)

Parameters
muthe mean parameter of the distribution (positive value)
Returns
Pseudo-random Poisson-distibuted value
See Also
rand_poisson_r()

A pseudo-random normally distributed number with probability mass function

\[ \mathrm{P}(X = k) = \frac{\mu^k \mathrm{e}^{-\mu}}{k!}, \quad k = 0, 1,\ldots, \]

using a simple direct algorthm for mu < 10 and the "PTRS" algorthm of Hormann for larger mu. The global generator is used to generate the value.

Reference: Wolfgang Hormann, "The transformed rejection method for generating Poisson random variables," Insurance: Mathematics and Economics 12, pp. 39-45, 1993.

Distribution properties:

  • CDF: $ 1 - \gamma(\lfloor k+1 \rfloor, \mu)/\lfloor k \rfloor ! $, where $ \gamma $ is the lower incomplete Gamma function
  • Mean: $ \mu $
  • Variance: $ \mu $

Definition at line 442 of file randmt.h.

#define rand_uint32 ( )    (rand_uint32_r(&__randmt_global_generator))

Generate a random 32-bit unsigned integer (nonreentrant)

Returns
Pseudo-random integer value uniformly between 0 and 0xFFFFFFFF
See Also
rand_uint32_r()
rand_unif()

The global generator is used to generate the value.

Definition at line 338 of file randmt.h.

#define rand_unif ( )    (rand_unif_r(&__randmt_global_generator))

Generate a uniform random number on (0,1) (nonreentrant)

Returns
Pseudo-random double value in the open interval (0,1)
See Also
rand_unif_r()
rand_uint32()

This routine generates a random number uniformly on the open interval (0,1) with 53-bit resolution. The formula used to generate the number is

\[ \mathtt{rand\_unif} = (a 2^{26} + b + 0.5 - \epsilon) / 2^{53}, \]

where a = integer of 27 random bits, b = integer of 26 random bits. The global generator is used to generate the value.

Distribution properties:

  • CDF: $ \min(\max(x,0),1) $
  • Mean: $ \frac{1}{2} $
  • Variance: $ \frac{1}{12} $

Definition at line 357 of file randmt.h.