static char rng_module_doc[] = "GSL Random-number generators implemented as C extension types.\n\ \n\ Use rng(Random-number generator types) to create an instance of a new\n\ random generator. All known random generator types are listed below. The\n\ different distributions are methods of the random generator instances.\n\ Consult the GSL manual for full details.\n\ \n\ Random-number generator types\n\ borosh13\n\ cmrg\n\ coveyou\n\ fishman18\n\ fishman20\n\ fishman2x\n\ gfsr4\n\ knuthran\n\ knuthran2\n\ lecuyer21\n\ minstd\n\ mrg\n\ mt19937\n\ mt19937_1999\n\ r250\n\ ran0\n\ ran1\n\ ran2\n\ ran3\n\ rand\n\ rand48\n\ random128_bsd\n\ random128_glibc2\n\ random128_libc5\n\ random256_bsd\n\ random256_glibc2\n\ random256_libc5\n\ random32_bsd\n\ random32_glibc2\n\ random32_libc5\n\ random64_bsd\n\ random64_glibc2\n\ random64_libc5\n\ random8_bsd\n\ random8_glibc2\n\ random8_libc5\n\ random_bsd\n\ random_glibc2\n\ random_libc5\n\ randu\n\ ranf\n\ ranlux\n\ ranlux389\n\ ranlxd1\n\ ranlxd2\n\ ranlxs0\n\ ranlxs1\n\ ranlxs2\n\ ranmar\n\ slatec\n\ taus\n\ taus2\n\ taus113\n\ transputer\n\ tt800\n\ uni\n\ uni32\n\ vax\n\ waterman14\n\ zuf\n"; static char rng_doc[]= "RNG Object Constructor\n\ Usage:\n\ rng(rng_type)\n\ Input:\n\ rng_type ... one of the many rng types GSL provides.\n\ "; static char rng_type_doc[]= "A PyGSL encapsulation of a GSL random number generator\n\ Try help(.method) to get more information about the method\n\ in question.\n\ \n\ \n\ Methods:\n\ Basic methods:\n\ __copy__ returns a copy of this instance\n\ clone \n\ get\n\ max\n\ min\n\ name\n\ set\n\ \n\ Random distributions:\n\ bernoulli\n\ beta\n\ binomial\n\ bivariate_gaussian\n\ cauchy\n\ chisq\n\ dir_2d\n\ dir_2d_trig_method\n\ dir_3d\n\ dir_nd\n\ dirichlet\n\ erlang\n\ exponential\n\ exppow\n\ fdist\n\ flat\n\ gamma\n\ gamma_int\n\ gaussian\n\ gaussian_ratio_method\n\ gaussian_tail\n\ geometric\n\ gumbel1\n\ gumbel2\n\ hypergeometric\n\ landau\n\ laplace\n\ levy\n\ levy_skew\n\ logarithmic\n\ logistic\n\ lognormal\n\ multinomial\n\ negative_binomial\n\ pareto\n\ pascal\n\ poisson\n\ rayleigh\n\ rayleigh_tail\n\ tdist\n\ ugaussian\n\ ugaussian_ratio_method\n\ ugaussian_tail\n\ uniform\n\ uniform_int\n\ uniform_pos\n\ weibull\n"; #define RNG_ARRAY_ITERATE "\n x can be an array. In this case this function\ will iterate over it and\nreturn an array of p(x).\n" #define RNG_ARRAY_INTEGER_ITERATE "\n k can be an array. In this case this function\ will iterate over it and\nreturn an array of p(k).\n" #define RNG_ARRAY "\n If the optional paramter n is given, this method will\ return a sample\nof size n.\n" static char rng_clone_doc [] = "Returns a clone of this instance\n"; static char rng_set_doc[] = "Initalises (seeds) the random number generator.\n\ Usage:\n\ set(seed)\n"; static char rng_get_doc[] = "Returns a random integer.\n\ Usage:\n\ get((n))\n" RNG_ARRAY_ITERATE; static char rng_uniform_doc [] = "Returns a double precision floating point number uniformly distributed\n\ in the range [0,1). The range includes 0.0 but excludes 1.0.\n\ Usage:\n\ uniform((n))\n" RNG_ARRAY_ITERATE; static char rng_uniform_pos_doc [] = "Returns a double precision floating point number uniformly distributed\n\ in the range (0,1). The range excludes 0.0 and 1.0.\n\ Usage:\n\ uniform_pos((n))\n" RNG_ARRAY_ITERATE; static char rng_uniform_int_doc [] = "Returns an integer between 0 and M-1\n\ Usage:\n\ uniform(M, (n))\n" RNG_ARRAY_ITERATE; static char rng_max_doc [] = "Returns the larget value that the get method can return\n"; static char rng_min_doc [] = "Returns the smallest value that the get method can return\n"; static char rng_gaussian_doc[] = "Returns a Gaussian random variate, with mean zero and standard deviation\n\ SIGMA. Use the transformation z =mu + x on the numbers returned by this\n\ method to obtain a Gaussian distribution with mean mu. This function\n\ uses the Box-Mueller algorithm which requires two calls to the random\n\ number generator R.\n\ \n\ Usage:\n\ gaussian(sigma, (n))\n" RNG_ARRAY; static char rng_gaussian_pdf_doc[]= "Computes the probability density p(x) at x for a Gaussian distribution\n\ with standard deviation SIGMA\n\ Usage:\n\ p = gaussian_pdf(x, sigma)\n\ \n" RNG_ARRAY_ITERATE; static char rng_gaussian_ratio_doc [] = "Computes a gaussian random variate using the Kinderman-Monahan ratio\n\ method. See the gaussian method for usage details.\n"; static char rng_ugaussian_ratio_doc [] = "Computes a gaussian random variate using the Kinderman-Monahan ratio\n\ method. See the ugaussian method for usage details.\n"; static char rng_ugaussian_doc[] = "Returns a Gaussian random variate, with mean zero and standard deviation\n\ SIGMA = 1. Use the transformation z =mu + x on the numbers returned by this\n\ method to obtain a Gaussian distribution with mean mu. This function\n\ uses the Box-Mueller algorithm which requires two calls to the random\n\ number generator R.\n\ \n\ Usage:\n\ ugaussian((n))\n" RNG_ARRAY; static char rng_ugaussian_pdf_doc[] = "Computes the probability density p(x) at x for a Gaussian distribution\n\ with standard deviation SIGMA=1\n\ Usage:\n\ p = ugaussian_pdf(x)\n\ \n" RNG_ARRAY_ITERATE; static char rng_gaussian_tail_doc [] = "This method provides random variates from the upper tail of a Gaussian\n\ distribution with standard deviation SIGMA. The values returned are\n\ larger than the lower limit A, which must be positive. The method is\n\ based on Marsaglia's famous rectangle-wedge-tail algorithm.\n\ Usage:\n\ p = gaussian_tail(a, sigma, (n))\n\ \n" RNG_ARRAY; static char rng_ugaussian_tail_doc [] = "This method provides random variates from the upper tail of a Gaussian\n\ distribution with standard deviation SIGMA=1. The values returned are\n\ larger than the lower limit A, which must be positive. The method is\n\ based on Marsaglia's famous rectangle-wedge-tail algorithm.\n\ Usage:\n\ p = gaussian_tail(a, (n))\n\ \n" RNG_ARRAY; static char rng_gaussian_tail_pdf_doc[] = "Computes the probability density p(x) at X for a Gaussian tail\n\ distribution with standard deviation SIGMA and lower limit A\n\ Usage:\n\ p = gaussian_tail_pdf(x, a, sigma)\n\ \n" RNG_ARRAY_ITERATE; static char rng_ugaussian_tail_pdf_doc[] = "Computes the probability density p(x) at X for a Gaussian tail\n\ distribution with standard deviation SIGMA=1 and lower limit A\n\ Usage:\n\ p = gaussian_tail_pdf(x, a, sigma)\n\ \n" RNG_ARRAY_ITERATE; static char rng_bivariate_gaussian_doc [] = "This method generates a pair of correlated gaussian variates,\n\ with mean zero, correlation coefficient RHO and standard deviations\n\ SIGMA_X and SIGMA_Y in the x and y directions.\n\ Usage:\n\ x, y = bivariate_gaussian(sigma_x, sigma_y, rho, (n)\n" RNG_ARRAY_ITERATE; static char rng_bivariate_gaussian_pdf_doc[] = "Computes the probability density p(x,y) at (X,Y) for a bivariate\n\ gaussian distribution with standard deviations SIGMA_X, SIGMA_Y\n\ and correlation coefficient RHO\n\ Usage :\n\ p_x, p_y = bivariate_gaussian_pdf(x, y, sigma_x, sigma_y, rho)\n\ \n\ If x and y are arrays, the function will iterate over them and return\n\ arrays\n"; static char rng_exponential_doc [] = "This method returns a random variate from the exponential distribution\n\ with mean MU.\n\ Usage:\n\ exponential(mu, (n))\n" RNG_ARRAY; static char rng_exponential_pdf_doc [] = "Computes the probability density p(x) at X for an exponential\n\ distribution with mean MU\n\ Usage:\n\ p = exponential_pdf(x, mu)\n" RNG_ARRAY_ITERATE; static char rng_laplace_doc [] = "This method returns a random variate from the laplace distribution\n\ with witdh A.\n\ Usage:\n\ laplace(a, (n))\n" RNG_ARRAY; static char rng_laplace_pdf_doc [] = "Computes the probability density p(x) at X for a Laplace distribution\n\ with mean A\n\ Usage:\n\ p = laplace_pdf(x, a)\n" RNG_ARRAY_ITERATE; static char rng_exppow_doc [] = "This method returns a random variate from the exponential power\n\ distribution with scale parameter A and exponent B.\n\ Usage:\n\ exponential(a, b, (n))\n" RNG_ARRAY; static char rng_exppow_pdf_doc [] = "Computes the probability density p(x) at X for an exponential power\n\ distribution with scale parameter A and exponent B\n\ Usage:\n\ p = exppow_pdf(x, a, b)\n" RNG_ARRAY_ITERATE; static char rng_cauchy_doc [] = "This method returns a random variate from the Cauchy distribution\n\ with scale parameter A.\n\ Usage:\n\ cauchy(a, (n))\n" RNG_ARRAY; static char rng_cauchy_pdf_doc [] = "Computes the probability density p(x) at X for a Cauchy distribution\n\ with scale parameter A\n\ Usage:\n\ p = cauchy_pdf(x, a)\n" RNG_ARRAY_ITERATE; static char rng_rayleigh_doc [] = "This method returns a random variate from the Rayleigh distribution\n\ with scale parameter SIGMA.\n\ Usage:\n\ rayleigh(sigma, (n))\n" RNG_ARRAY; static char rng_rayleigh_pdf_doc [] = "Computes the probability density p(x) at X for a Rayleigh distribution\n\ with scale parameter SIGMA\n\ Usage:\n\ p = rayleigh_pdf(x, a, sigma)\n" RNG_ARRAY_ITERATE; static char rng_rayleigh_tail_doc [] = "This method returns a random variate from the Rayleigh tail\n\ distribution with scale parameter SIGMA and a lower limit A.\n\ Usage:\n\ rayleigh_tail(a, sigma, (n))\n" RNG_ARRAY; static char rng_rayleigh_tail_pdf_doc [] = "Computes the probability density p(x) at X for a Rayleigh tail\n\ distribution with scale parameter SIGMA and lower limit A.\n\ Usage:\n\ p = rayleigh_tail_pdf(x, a, sigma)" RNG_ARRAY_ITERATE; static char rng_landau_doc [] = "This method returns a random variate from the Landau distribution\n\ Usage:\n\ landau((n))\n" RNG_ARRAY; static char rng_landau_pdf_doc [] = "Computes the probability density p(x) at X for the Landau distribution\n\ using an approximation.\n\ Usage:\n\ p = landau_pdf(x)" RNG_ARRAY_ITERATE; static char rng_levy_doc [] = "This method returns a random variate from the Levy symmetric stable\n\ distribution with scale C and exponent ALPHA. The algorithm only works\n\ for 0 < alpha <= 2. There is no 'pdf' implemented\n\ Usage:\n\ levy(c, alpha, (n))\n" RNG_ARRAY; static char rng_levy_skew_doc [] = "This method returns a random variate from the Levy skew stable\n\ distribution with scale C, exponent ALPHA and skewness parameter BETA.\n\ The skewness parameter must lie in the range [-1,1].\n\ Usage:\n\ levy_skew(c, alpha, beta, (n))\n" RNG_ARRAY; static char rng_gamma_doc [] = "This method returns a random variate from the gamma distribution\n\ Usage:\n\ gamma(a, b, (n))\n" RNG_ARRAY; static char rng_gamma_pdf_doc [] = "Computes the probability density p(x) at X for the gamma distribution\n\ Usage:\n\ p = gamma_pdf(x, a, b)" RNG_ARRAY_ITERATE; static char rng_flat_doc [] = "This method returns a random variate from the flat (uniform)\n\ distribution from A to B.\n\ Usage:\n\ flat(a, b, (n))\n" RNG_ARRAY; static char rng_flat_pdf_doc [] = "Computes the probability density p(x) at X for the flat (uniform) distribution\n\ Usage:\n\ p = flat_pdf(x, a, b)" RNG_ARRAY_ITERATE; static char rng_lognormal_doc [] = "This method returns a random variate from the log normal distribution.\n\ Usage:\n\ flat(zeta, sigma, (n))\n" RNG_ARRAY; static char rng_lognormal_pdf_doc [] = "Computes the probability density p(x) at X for the log normal distribution\n\ Usage:\n\ p = lognormal_pdf(x, zeta, sigma)" RNG_ARRAY_ITERATE; static char rng_chisq_doc [] = "This method returns a random variate from the chi-squared distribution\n\ with NU degrees of freedom\n\ Usage:\n\ chisq(nu, (n))\n" RNG_ARRAY; static char rng_chisq_pdf_doc [] = "Computes the probability density p(x) at X for the chisq distribution\n\ Usage:\n\ p = chisq_pdf(x, nu)" RNG_ARRAY_ITERATE; /* Update number of variables !!! */ static char rng_fdist_doc [] = "This method returns a random variate from the F-distribution\n\ distribution with degrees of freedom NU\n\ Usage:\n\ fdist(nu, (n))\n" RNG_ARRAY; static char rng_fdist_pdf_doc [] = "Computes the probability density p(x) at X for the F-distribution\n\ with NU degrees of freedom.\n\ Usage:\n\ p = fdist_pdf(x, nu1)" RNG_ARRAY_ITERATE; static char rng_tdist_doc [] = "This method returns a random variate from the t-distribution\n\ distribution with degrees of freedom NU1 and NU2\n\ Usage:\n\ tdist(nu1, nu2, (n))\n" RNG_ARRAY; static char rng_tdist_pdf_doc [] = "Computes the probability density p(x) at X for the t-distribution\n\ with NU1 and NU2 degrees of freedom.\n\ Usage:\n\ p = tdist_pdf(x, nu1, nu2)" RNG_ARRAY_ITERATE; static char rng_beta_doc [] = "This method returns a random variate from the beta distribution\n\ Usage:\n\ beta(a, b, (n))\n" RNG_ARRAY; static char rng_beta_pdf_doc [] = "Computes the probability density p(x) at X for the beta distribution\n\ Usage:\n\ p = beta_pdf(x, a, b)" RNG_ARRAY_ITERATE; static char rng_logistic_doc [] = "This method returns a random variate from the logistic distribution\n\ Usage:\n\ logistic(a, (n))\n" RNG_ARRAY; static char rng_logistic_pdf_doc [] = "Computes the probability density p(x) at X for the logistic distribution\n\ Usage:\n\ p = logistic_pdf(x, a)" RNG_ARRAY_ITERATE; static char rng_pareto_doc [] = "This method returns a random variate from the pareto distribution\n\ Usage:\n\ pareto(a, b, (n))\n" RNG_ARRAY; static char rng_pareto_pdf_doc [] = "Computes the probability density p(x) at X for the pareto distribution\n\ with exponent a and scale b\n\ Usage:\n\ p = pareto_pdf(x, a)" RNG_ARRAY_ITERATE; static char rng_dir_2d_doc [] = "This method returns a random direction vector v = (X,Y) in two\n\ dimensions.\n\ Usage:\n\ dir_2d((n))\n" RNG_ARRAY; static char rng_dir_2d_trig_method_doc [] = "This method returns a random direction vector v = (X,Y) in two\n\ dimensions using trigonometric functions internally.\n\ Usage:\n\ dir_2d_trig_method((n))\n" RNG_ARRAY; static char rng_dir_3d_doc [] = "This method returns a random direction vector v = (X,Y,Z) in three\n\ dimensions.\n\ Usage:\n\ dir_3d((n))\n" RNG_ARRAY; static char rng_dir_nd_doc [] = "This method returns a random direction vector v = (x1, ..., xn) in three\n\ dimensions.\n\ Usage:\n\ dir_nd((n))\n" RNG_ARRAY; static char rng_weibull_doc [] = "This method returns a random variate from the weibull distribution\n\ with scale a and exponent b\n\ Usage:\n\ weibull(a, b, (n))\n" RNG_ARRAY; static char rng_weibull_pdf_doc [] = "Computes the probability density p(x) at X for the weibull distribution\n\ with scale a and exponent b\n\ Usage:\n\ p = weibull_pdf(x, a)" RNG_ARRAY_ITERATE; static char rng_gumbel1_doc [] = "This method returns a random variate from the gumbel1 distribution\n\ with parametes a and b\n\ Usage:\n\ gumbel1(a, b, (n))\n" RNG_ARRAY; static char rng_gumbel1_pdf_doc [] = "Computes the probability density p(x) at X for the gumbel1 distribution\n\ with parameters a and b \n\ Usage:\n\ p = gumbel1_pdf(x, a, b)" RNG_ARRAY_ITERATE; static char rng_gumbel2_doc [] = "This method returns a random variate from the gumbel2 distribution\n\ with parametes a and b\n\ Usage:\n\ gumbel2(a, b, (n))\n" RNG_ARRAY; static char rng_gumbel2_pdf_doc [] = "Computes the probability density p(x) at X for the gumbel2 distribution\n\ with parameters a and b \n\ Usage:\n\ p = gumbel2_pdf(x, a, b)" RNG_ARRAY_ITERATE; static char rng_dirichlet_doc [] = "This method returns an array of K random variates from a Dirichlet\n\ distribution of order K-1\n\ Usage:\n\ p(theta_1, ..., theta_k) = dirchlet(alpha, (n))\n\ alpha must be of length k" RNG_ARRAY; static char rng_dirichlet_pdf_doc [] = " Computes the probability density p(\theta_1, ... , \theta_K) at\n\ THETA[K] for a Dirichlet distribution with parameters\n\ ALPHA[K]\n\ Usage:\n"; static char rng_dirichlet_lnpdf_doc [] = " Computes logarithmic of the probability density\n\ p(\theta_1, ... , \theta_K) at THETA[K] for a Dirichlet distribution\n\ with parameters ALPHA[K]\n\ Usage:\n"; static char rng_poisson_doc [] = "This method returns a random integer from the poisson distribution\n\ with mean MU\n\ Usage:\n\ poisson(mu, (n))\n" RNG_ARRAY; static char rng_poisson_pdf_doc [] = "Computes the probability density p(k) at k for the poisson distribution\n\ with mean MU \n\ Usage:\n\ p = poisson_pdf(k, mu)" RNG_ARRAY_INTEGER_ITERATE; static char rng_bernoulli_doc [] = "This method returns either 0 or 1, the result of a Bernoulli trial with\n\ probability P.\n\ Usage:\n\ bernoulli(p, (n))\n" RNG_ARRAY; static char rng_bernoulli_pdf_doc [] = "Computes the probability density p(k) at k for the bernoulli\n\ distribution with probability parameter P.\n\ Usage:\n\ p = bernoulli_pdf(k, P)" RNG_ARRAY_INTEGER_ITERATE; static char rng_binomial_doc [] = "This method returns a random integer from the binomial distribution,\n\ the number of successes in N independent trials with probability P\n\ Usage:\n\ binomial(P, N, (n))\n" RNG_ARRAY; static char rng_binomial_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ binomial distribution with parameters P and N\n\ Usage:\n\ p = binomial_pdf(k, P, N)" RNG_ARRAY_INTEGER_ITERATE; static char rng_negative_binomial_doc [] = "This method returns a random integer from the negative binomial\n\ distribution, the number of failures in N independent trials with\n\ probability P. Note: N is not required to be an integer\n\ Usage:\n\ negative_binomial(P, N, (n))\n" RNG_ARRAY; static char rng_negative_binomial_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ negative binomial distribution with parameters P and N.\n\ Usage:\n\ p = negative_binomial_pdf(k, P, N)" RNG_ARRAY_INTEGER_ITERATE; static char rng_pascal_doc [] = "This method returns a random integer from the pascal distribution\n\ Usage:\n\ pascal(P, K, (n))\n" RNG_ARRAY; static char rng_pascal_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ pascal distribution with parameters P and N\n\ Usage:\n\ p = pascal_pdf(k, P, N)" RNG_ARRAY_INTEGER_ITERATE; static char rng_geometric_doc [] = "This method returns a random integer from the geometric distribution\n\ Usage:\n\ geometric(P, (n))\n" RNG_ARRAY; static char rng_geometric_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ geometric distribution with parameters P\n\ Usage:\n\ p = geometric_pdf(k, P)" RNG_ARRAY_INTEGER_ITERATE; static char rng_hypergeometric_doc [] = "This method returns a random integer from the hypergeometric distribution\n\ Usage:\n\ hypergeometric(N1, N2, N3, (n))\n" RNG_ARRAY; static char rng_hypergeometric_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ hypergeometric distribution with parameters N1, N2, N3\n\ Usage:\n\ p = hypergeometric_pdf(k, n1, n2, n3)" RNG_ARRAY_INTEGER_ITERATE; static char rng_logarithmic_doc [] = "This method returns a random integer from the logarithmic distribution\n\ Usage:\n\ logarithmic(P, K, (n))\n" RNG_ARRAY; static char rng_logarithmic_pdf_doc [] = "Computes the probability density p(k) of obtaining K from a\n\ logarithmic distribution with parameters P and N\n\ Usage:\n\ p = logarithmic_pdf(k, P, N)" RNG_ARRAY_INTEGER_ITERATE; static char multinomial_doc [] = "samples from the multinomial distribution parametrized\n\ by 'phi' and 'k'\n\ Usage:\n\ multinomial(phi, k, N)" RNG_ARRAY; static char multinomial_pdf_doc [] = "Computes the probability P(n_1, n_2, ..., n_K) of sampling N[K]\n\ from a multinomial distribution with parameters \n\ P[K].\n\ Usage:\n\ p = multinomial_pdf(phi, n)\n\ \n\ phi ... probability distribution over possible events.\n\ n ... an two dimensional array, where each pdf is stored in one row\n\ ";