# mtrand.pyx -- A Pyrex wrapper of Jean-Sebastien Roy's RandomKit # # Copyright 2005 Robert Kern (robert.kern@gmail.com) # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the # "Software"), to deal in the Software without restriction, including # without limitation the rights to use, copy, modify, merge, publish, # distribute, sublicense, and/or sell copies of the Software, and to # permit persons to whom the Software is furnished to do so, subject to # the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF # MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. # IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY # CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE # SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. include "Python.pxi" include "numpy.pxi" cdef extern from "math.h": double exp(double x) double log(double x) double floor(double x) double sin(double x) double cos(double x) cdef extern from "randomkit.h": ctypedef struct rk_state: unsigned long key[624] int pos int has_gauss double gauss ctypedef enum rk_error: RK_NOERR = 0 RK_ENODEV = 1 RK_ERR_MAX = 2 char *rk_strerror[2] # 0xFFFFFFFFUL unsigned long RK_MAX void rk_seed(unsigned long seed, rk_state *state) rk_error rk_randomseed(rk_state *state) unsigned long rk_random(rk_state *state) long rk_long(rk_state *state) unsigned long rk_ulong(rk_state *state) unsigned long rk_interval(unsigned long max, rk_state *state) double rk_double(rk_state *state) void rk_fill(void *buffer, size_t size, rk_state *state) rk_error rk_devfill(void *buffer, size_t size, int strong) rk_error rk_altfill(void *buffer, size_t size, int strong, rk_state *state) double rk_gauss(rk_state *state) cdef extern from "distributions.h": double rk_normal(rk_state *state, double loc, double scale) double rk_standard_exponential(rk_state *state) double rk_exponential(rk_state *state, double scale) double rk_uniform(rk_state *state, double loc, double scale) double rk_standard_gamma(rk_state *state, double shape) double rk_gamma(rk_state *state, double shape, double scale) double rk_beta(rk_state *state, double a, double b) double rk_chisquare(rk_state *state, double df) double rk_noncentral_chisquare(rk_state *state, double df, double nonc) double rk_f(rk_state *state, double dfnum, double dfden) double rk_noncentral_f(rk_state *state, double dfnum, double dfden, double nonc) double rk_standard_cauchy(rk_state *state) double rk_standard_t(rk_state *state, double df) double rk_vonmises(rk_state *state, double mu, double kappa) double rk_pareto(rk_state *state, double a) double rk_weibull(rk_state *state, double a) double rk_power(rk_state *state, double a) double rk_laplace(rk_state *state, double loc, double scale) double rk_gumbel(rk_state *state, double loc, double scale) double rk_logistic(rk_state *state, double loc, double scale) double rk_lognormal(rk_state *state, double mode, double sigma) double rk_rayleigh(rk_state *state, double mode) double rk_wald(rk_state *state, double mean, double scale) double rk_triangular(rk_state *state, double left, double mode, double right) long rk_binomial(rk_state *state, long n, double p) long rk_binomial_btpe(rk_state *state, long n, double p) long rk_binomial_inversion(rk_state *state, long n, double p) long rk_negative_binomial(rk_state *state, long n, double p) long rk_poisson(rk_state *state, double lam) long rk_poisson_mult(rk_state *state, double lam) long rk_poisson_ptrs(rk_state *state, double lam) long rk_zipf(rk_state *state, double a) long rk_geometric(rk_state *state, double p) long rk_hypergeometric(rk_state *state, long good, long bad, long sample) long rk_logseries(rk_state *state, double p) ctypedef double (* rk_cont0)(rk_state *state) ctypedef double (* rk_cont1)(rk_state *state, double a) ctypedef double (* rk_cont2)(rk_state *state, double a, double b) ctypedef double (* rk_cont3)(rk_state *state, double a, double b, double c) ctypedef long (* rk_disc0)(rk_state *state) ctypedef long (* rk_discnp)(rk_state *state, long n, double p) ctypedef long (* rk_discnmN)(rk_state *state, long n, long m, long N) ctypedef long (* rk_discd)(rk_state *state, double a) cdef extern from "initarray.h": void init_by_array(rk_state *self, unsigned long *init_key, unsigned long key_length) # Initialize numpy import_array() import numpy as _sp cdef object cont0_array(rk_state *state, rk_cont0 func, object size): cdef double *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state) else: array = _sp.empty(size, _sp.float64) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state) return array cdef object cont1_array_sc(rk_state *state, rk_cont1 func, object size, double a): cdef double *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, a) else: array = _sp.empty(size, _sp.float64) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, a) return array cdef object cont1_array(rk_state *state, rk_cont1 func, object size, ndarray oa): cdef double *array_data cdef double *oa_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef flatiter itera cdef broadcast multi if size is None: array = PyArray_SimpleNew(oa.nd, oa.dimensions, NPY_DOUBLE) length = PyArray_SIZE(array) array_data = array.data itera = PyArray_IterNew(oa) for i from 0 <= i < length: array_data[i] = func(state, ((itera.dataptr))[0]) PyArray_ITER_NEXT(itera) else: array = _sp.empty(size, _sp.float64) array_data = array.data multi = PyArray_MultiIterNew(2, array, oa) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 1) array_data[i] = func(state, oa_data[0]) PyArray_MultiIter_NEXTi(multi, 1) return array cdef object cont2_array_sc(rk_state *state, rk_cont2 func, object size, double a, double b): cdef double *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, a, b) else: array = _sp.empty(size, _sp.float64) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, a, b) return array cdef object cont2_array(rk_state *state, rk_cont2 func, object size, ndarray oa, ndarray ob): cdef double *array_data cdef double *oa_data cdef double *ob_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef broadcast multi if size is None: multi = PyArray_MultiIterNew(2, oa, ob) array = PyArray_SimpleNew(multi.nd, multi.dimensions, NPY_DOUBLE) array_data = array.data for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 0) ob_data = PyArray_MultiIter_DATA(multi, 1) array_data[i] = func(state, oa_data[0], ob_data[0]) PyArray_MultiIter_NEXT(multi) else: array = _sp.empty(size, _sp.float64) array_data = array.data multi = PyArray_MultiIterNew(3, array, oa, ob) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 1) ob_data = PyArray_MultiIter_DATA(multi, 2) array_data[i] = func(state, oa_data[0], ob_data[0]) PyArray_MultiIter_NEXTi(multi, 1) PyArray_MultiIter_NEXTi(multi, 2) return array cdef object cont3_array_sc(rk_state *state, rk_cont3 func, object size, double a, double b, double c): cdef double *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, a, b, c) else: array = _sp.empty(size, _sp.float64) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, a, b, c) return array cdef object cont3_array(rk_state *state, rk_cont3 func, object size, ndarray oa, ndarray ob, ndarray oc): cdef double *array_data cdef double *oa_data cdef double *ob_data cdef double *oc_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef broadcast multi if size is None: multi = PyArray_MultiIterNew(3, oa, ob, oc) array = PyArray_SimpleNew(multi.nd, multi.dimensions, NPY_DOUBLE) array_data = array.data for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 0) ob_data = PyArray_MultiIter_DATA(multi, 1) oc_data = PyArray_MultiIter_DATA(multi, 2) array_data[i] = func(state, oa_data[0], ob_data[0], oc_data[0]) PyArray_MultiIter_NEXT(multi) else: array = _sp.empty(size, _sp.float64) array_data = array.data multi = PyArray_MultiIterNew(4, array, oa, ob, oc) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 1) ob_data = PyArray_MultiIter_DATA(multi, 2) oc_data = PyArray_MultiIter_DATA(multi, 3) array_data[i] = func(state, oa_data[0], ob_data[0], oc_data[0]) PyArray_MultiIter_NEXT(multi) return array cdef object disc0_array(rk_state *state, rk_disc0 func, object size): cdef long *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state) else: array = _sp.empty(size, int) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state) return array cdef object discnp_array_sc(rk_state *state, rk_discnp func, object size, long n, double p): cdef long *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, n, p) else: array = _sp.empty(size, int) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, n, p) return array cdef object discnp_array(rk_state *state, rk_discnp func, object size, ndarray on, ndarray op): cdef long *array_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef double *op_data cdef long *on_data cdef broadcast multi if size is None: multi = PyArray_MultiIterNew(2, on, op) array = PyArray_SimpleNew(multi.nd, multi.dimensions, NPY_LONG) array_data = array.data for i from 0 <= i < multi.size: on_data = PyArray_MultiIter_DATA(multi, 0) op_data = PyArray_MultiIter_DATA(multi, 1) array_data[i] = func(state, on_data[0], op_data[0]) PyArray_MultiIter_NEXT(multi) else: array = _sp.empty(size, int) array_data = array.data multi = PyArray_MultiIterNew(3, array, on, op) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: on_data = PyArray_MultiIter_DATA(multi, 1) op_data = PyArray_MultiIter_DATA(multi, 2) array_data[i] = func(state, on_data[0], op_data[0]) PyArray_MultiIter_NEXTi(multi, 1) PyArray_MultiIter_NEXTi(multi, 2) return array cdef object discnmN_array_sc(rk_state *state, rk_discnmN func, object size, long n, long m, long N): cdef long *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, n, m, N) else: array = _sp.empty(size, int) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, n, m, N) return array cdef object discnmN_array(rk_state *state, rk_discnmN func, object size, ndarray on, ndarray om, ndarray oN): cdef long *array_data cdef long *on_data cdef long *om_data cdef long *oN_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef broadcast multi if size is None: multi = PyArray_MultiIterNew(3, on, om, oN) array = PyArray_SimpleNew(multi.nd, multi.dimensions, NPY_LONG) array_data = array.data for i from 0 <= i < multi.size: on_data = PyArray_MultiIter_DATA(multi, 0) om_data = PyArray_MultiIter_DATA(multi, 1) oN_data = PyArray_MultiIter_DATA(multi, 2) array_data[i] = func(state, on_data[0], om_data[0], oN_data[0]) PyArray_MultiIter_NEXT(multi) else: array = _sp.empty(size, int) array_data = array.data multi = PyArray_MultiIterNew(4, array, on, om, oN) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: on_data = PyArray_MultiIter_DATA(multi, 1) om_data = PyArray_MultiIter_DATA(multi, 2) oN_data = PyArray_MultiIter_DATA(multi, 3) array_data[i] = func(state, on_data[0], om_data[0], oN_data[0]) PyArray_MultiIter_NEXT(multi) return array cdef object discd_array_sc(rk_state *state, rk_discd func, object size, double a): cdef long *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if size is None: return func(state, a) else: array = _sp.empty(size, int) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = func(state, a) return array cdef object discd_array(rk_state *state, rk_discd func, object size, ndarray oa): cdef long *array_data cdef double *oa_data cdef ndarray array "arrayObject" cdef npy_intp length cdef npy_intp i cdef broadcast multi cdef flatiter itera if size is None: array = PyArray_SimpleNew(oa.nd, oa.dimensions, NPY_LONG) length = PyArray_SIZE(array) array_data = array.data itera = PyArray_IterNew(oa) for i from 0 <= i < length: array_data[i] = func(state, ((itera.dataptr))[0]) PyArray_ITER_NEXT(itera) else: array = _sp.empty(size, int) array_data = array.data multi = PyArray_MultiIterNew(2, array, oa) if (multi.size != PyArray_SIZE(array)): raise ValueError("size is not compatible with inputs") for i from 0 <= i < multi.size: oa_data = PyArray_MultiIter_DATA(multi, 1) array_data[i] = func(state, oa_data[0]) PyArray_MultiIter_NEXTi(multi, 1) return array cdef double kahan_sum(double *darr, long n): cdef double c, y, t, sum cdef long i sum = darr[0] c = 0.0 for i from 1 <= i < n: y = darr[i] - c t = sum + y c = (t-sum) - y sum = t return sum cdef class RandomState: """Container for the Mersenne Twister PRNG. Constructor ----------- RandomState(seed=None): initializes the PRNG with the given seed. See the seed() method for details. Distribution Methods ----------------- RandomState exposes a number of methods for generating random numbers drawn from a variety of probability distributions. In addition to the distribution-specific arguments, each method takes a keyword argument size=None. If size is None, then a single value is generated and returned. If size is an integer, then a 1-D numpy array filled with generated values is returned. If size is a tuple, then a numpy array with that shape is filled and returned. """ cdef rk_state *internal_state def __init__(self, seed=None): self.internal_state = PyMem_Malloc(sizeof(rk_state)) self.seed(seed) def __dealloc__(self): if self.internal_state != NULL: PyMem_Free(self.internal_state) self.internal_state = NULL def seed(self, seed=None): """Seed the generator. seed(seed=None) seed can be an integer, an array (or other sequence) of integers of any length, or None. If seed is None, then RandomState will try to read data from /dev/urandom (or the Windows analogue) if available or seed from the clock otherwise. """ cdef rk_error errcode cdef ndarray obj "arrayObject_obj" if seed is None: errcode = rk_randomseed(self.internal_state) elif type(seed) is int: rk_seed(seed, self.internal_state) elif isinstance(seed, _sp.integer): iseed = int(seed) rk_seed(iseed, self.internal_state) else: obj = PyArray_ContiguousFromObject(seed, NPY_LONG, 1, 1) init_by_array(self.internal_state, (obj.data), obj.dimensions[0]) def get_state(self): """Return a tuple representing the internal state of the generator. get_state() -> ('MT19937', int key[624], int pos, int has_gauss, float cached_gaussian) """ cdef ndarray state "arrayObject_state" state = _sp.empty(624, _sp.uint) memcpy((state.data), (self.internal_state.key), 624*sizeof(long)) state = _sp.asarray(state, _sp.uint32) return ('MT19937', state, self.internal_state.pos, self.internal_state.has_gauss, self.internal_state.gauss) def set_state(self, state): """Set the state from a tuple. state = ('MT19937', int key[624], int pos, int has_gauss, float cached_gaussian) For backwards compatibility, the following form is also accepted although it is missing some information about the cached Gaussian value. state = ('MT19937', int key[624], int pos) set_state(state) """ cdef ndarray obj "arrayObject_obj" cdef int pos algorithm_name = state[0] if algorithm_name != 'MT19937': raise ValueError("algorithm must be 'MT19937'") key, pos = state[1:3] if len(state) == 3: has_gauss = 0 cached_gaussian = 0.0 else: has_gauss, cached_gaussian = state[3:5] try: obj = PyArray_ContiguousFromObject(key, NPY_ULONG, 1, 1) except TypeError: # compatibility -- could be an older pickle obj = PyArray_ContiguousFromObject(key, NPY_LONG, 1, 1) if obj.dimensions[0] != 624: raise ValueError("state must be 624 longs") memcpy((self.internal_state.key), (obj.data), 624*sizeof(long)) self.internal_state.pos = pos self.internal_state.has_gauss = has_gauss self.internal_state.gauss = cached_gaussian # Pickling support: def __getstate__(self): return self.get_state() def __setstate__(self, state): self.set_state(state) def __reduce__(self): return (_sp.random.__RandomState_ctor, (), self.get_state()) # Basic distributions: def random_sample(self, size=None): """Return random floats in the half-open interval [0.0, 1.0). random_sample(size=None) -> random values """ return cont0_array(self.internal_state, rk_double, size) def tomaxint(self, size=None): """Returns random integers x such that 0 <= x <= sys.maxint. tomaxint(size=None) -> random values """ return disc0_array(self.internal_state, rk_long, size) def randint(self, low, high=None, size=None): """Return random integers x such that low <= x < high. randint(low, high=None, size=None) -> random values If high is None, then 0 <= x < low. """ cdef long lo, hi, diff cdef long *array_data cdef ndarray array "arrayObject" cdef long length cdef long i if high is None: lo = 0 hi = low else: lo = low hi = high diff = hi - lo - 1 if diff < 0: raise ValueError("low >= high") if size is None: return rk_interval(diff, self.internal_state) + lo else: array = _sp.empty(size, int) length = PyArray_SIZE(array) array_data = array.data for i from 0 <= i < length: array_data[i] = lo + rk_interval(diff, self.internal_state) return array def bytes(self, unsigned int length): """Return random bytes. bytes(length) -> str """ cdef void *bytes bytestring = PyString_FromStringAndSize(NULL, length) bytes = PyString_AS_STRING(bytestring) rk_fill(bytes, length, self.internal_state) return bytestring def uniform(self, low=0.0, high=1.0, size=None): """Uniform distribution over [low, high). uniform(low=0.0, high=1.0, size=None) -> random values """ cdef ndarray olow, ohigh, odiff cdef double flow, fhigh cdef object temp flow = PyFloat_AsDouble(low) fhigh = PyFloat_AsDouble(high) if not PyErr_Occurred(): return cont2_array_sc(self.internal_state, rk_uniform, size, flow, fhigh-flow) PyErr_Clear() olow = PyArray_FROM_OTF(low, NPY_DOUBLE, NPY_ALIGNED) ohigh = PyArray_FROM_OTF(high, NPY_DOUBLE, NPY_ALIGNED) temp = _sp.subtract(ohigh, olow) Py_INCREF(temp) # needed to get around Pyrex's automatic reference-counting # rules because EnsureArray steals a reference odiff = PyArray_EnsureArray(temp) return cont2_array(self.internal_state, rk_uniform, size, olow, odiff) def rand(self, *args): """Return an array of the given dimensions which is initialized to random numbers from a uniform distribution in the range [0,1). rand(d0, d1, ..., dn) -> random values Note: This is a convenience function. If you want an interface that takes a tuple as the first argument use numpy.random.random_sample(shape_tuple). """ if len(args) == 0: return self.random_sample() else: return self.random_sample(size=args) def randn(self, *args): """Returns zero-mean, unit-variance Gaussian random numbers in an array of shape (d0, d1, ..., dn). randn(d0, d1, ..., dn) -> random values Note: This is a convenience function. If you want an interface that takes a tuple as the first argument use numpy.random.standard_normal(shape_tuple). """ if len(args) == 0: return self.standard_normal() else: return self.standard_normal(args) def random_integers(self, low, high=None, size=None): """Return random integers x such that low <= x <= high. random_integers(low, high=None, size=None) -> random values. If high is None, then 1 <= x <= low. """ if high is None: high = low low = 1 return self.randint(low, high+1, size) # Complicated, continuous distributions: def standard_normal(self, size=None): """Standard Normal distribution (mean=0, stdev=1). standard_normal(size=None) -> random values """ return cont0_array(self.internal_state, rk_gauss, size) def normal(self, loc=0.0, scale=1.0, size=None): """Normal distribution (mean=loc, stdev=scale). normal(loc=0.0, scale=1.0, size=None) -> random values """ cdef ndarray oloc, oscale cdef double floc, fscale floc = PyFloat_AsDouble(loc) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_normal, size, floc, fscale) PyErr_Clear() oloc = PyArray_FROM_OTF(loc, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0)): raise ValueError("scale <= 0") return cont2_array(self.internal_state, rk_normal, size, oloc, oscale) def beta(self, a, b, size=None): """Beta distribution over [0, 1]. beta(a, b, size=None) -> random values """ cdef ndarray oa, ob cdef double fa, fb fa = PyFloat_AsDouble(a) fb = PyFloat_AsDouble(b) if not PyErr_Occurred(): if fa <= 0: raise ValueError("a <= 0") if fb <= 0: raise ValueError("b <= 0") return cont2_array_sc(self.internal_state, rk_beta, size, fa, fb) PyErr_Clear() oa = PyArray_FROM_OTF(a, NPY_DOUBLE, NPY_ALIGNED) ob = PyArray_FROM_OTF(b, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oa, 0)): raise ValueError("a <= 0") if _sp.any(_sp.less_equal(ob, 0)): raise ValueError("b <= 0") return cont2_array(self.internal_state, rk_beta, size, oa, ob) def exponential(self, scale=1.0, size=None): """Exponential distribution. exponential(scale=1.0, size=None) -> random values """ cdef ndarray oscale cdef double fscale fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont1_array_sc(self.internal_state, rk_exponential, size, fscale) PyErr_Clear() oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0") return cont1_array(self.internal_state, rk_exponential, size, oscale) def standard_exponential(self, size=None): """Standard exponential distribution (scale=1). standard_exponential(size=None) -> random values """ return cont0_array(self.internal_state, rk_standard_exponential, size) def standard_gamma(self, shape, size=None): """Standard Gamma distribution. standard_gamma(shape, size=None) -> random values """ cdef ndarray oshape cdef double fshape fshape = PyFloat_AsDouble(shape) if not PyErr_Occurred(): if fshape <= 0: raise ValueError("shape <= 0") return cont1_array_sc(self.internal_state, rk_standard_gamma, size, fshape) PyErr_Clear() oshape = PyArray_FROM_OTF(shape, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oshape, 0.0)): raise ValueError("shape <= 0") return cont1_array(self.internal_state, rk_standard_gamma, size, oshape) def gamma(self, shape, scale=1.0, size=None): """Gamma distribution. gamma(shape, scale=1.0, size=None) -> random values """ cdef ndarray oshape, oscale cdef double fshape, fscale fshape = PyFloat_AsDouble(shape) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fshape <= 0: raise ValueError("shape <= 0") if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_gamma, size, fshape, fscale) PyErr_Clear() oshape = PyArray_FROM_OTF(shape, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oshape, 0.0)): raise ValueError("shape <= 0") if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0") return cont2_array(self.internal_state, rk_gamma, size, oshape, oscale) def f(self, dfnum, dfden, size=None): """F distribution. f(dfnum, dfden, size=None) -> random values """ cdef ndarray odfnum, odfden cdef double fdfnum, fdfden fdfnum = PyFloat_AsDouble(dfnum) fdfden = PyFloat_AsDouble(dfden) if not PyErr_Occurred(): if fdfnum <= 0: raise ValueError("shape <= 0") if fdfden <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_f, size, fdfnum, fdfden) PyErr_Clear() odfnum = PyArray_FROM_OTF(dfnum, NPY_DOUBLE, NPY_ALIGNED) odfden = PyArray_FROM_OTF(dfden, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(odfnum, 0.0)): raise ValueError("dfnum <= 0") if _sp.any(_sp.less_equal(odfden, 0.0)): raise ValueError("dfden <= 0") return cont2_array(self.internal_state, rk_f, size, odfnum, odfden) def noncentral_f(self, dfnum, dfden, nonc, size=None): """Noncentral F distribution. noncentral_f(dfnum, dfden, nonc, size=None) -> random values """ cdef ndarray odfnum, odfden, ononc cdef double fdfnum, fdfden, fnonc fdfnum = PyFloat_AsDouble(dfnum) fdfden = PyFloat_AsDouble(dfden) fnonc = PyFloat_AsDouble(nonc) if not PyErr_Occurred(): if fdfnum <= 1: raise ValueError("dfnum <= 1") if fdfden <= 0: raise ValueError("dfden <= 0") if fnonc < 0: raise ValueError("nonc < 0") return cont3_array_sc(self.internal_state, rk_noncentral_f, size, fdfnum, fdfden, fnonc) PyErr_Clear() odfnum = PyArray_FROM_OTF(dfnum, NPY_DOUBLE, NPY_ALIGNED) odfden = PyArray_FROM_OTF(dfden, NPY_DOUBLE, NPY_ALIGNED) ononc = PyArray_FROM_OTF(nonc, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(odfnum, 1.0)): raise ValueError("dfnum <= 1") if _sp.any(_sp.less_equal(odfden, 0.0)): raise ValueError("dfden <= 0") if _sp.any(_sp.less(ononc, 0.0)): raise ValueError("nonc < 0") return cont3_array(self.internal_state, rk_noncentral_f, size, odfnum, odfden, ononc) def chisquare(self, df, size=None): """Chi^2 distribution. chisquare(df, size=None) -> random values """ cdef ndarray odf cdef double fdf fdf = PyFloat_AsDouble(df) if not PyErr_Occurred(): if fdf <= 0: raise ValueError("df <= 0") return cont1_array_sc(self.internal_state, rk_chisquare, size, fdf) PyErr_Clear() odf = PyArray_FROM_OTF(df, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(odf, 0.0)): raise ValueError("df <= 0") return cont1_array(self.internal_state, rk_chisquare, size, odf) def noncentral_chisquare(self, df, nonc, size=None): """Noncentral Chi^2 distribution. noncentral_chisquare(df, nonc, size=None) -> random values """ cdef ndarray odf, ononc cdef double fdf, fnonc fdf = PyFloat_AsDouble(df) fnonc = PyFloat_AsDouble(nonc) if not PyErr_Occurred(): if fdf <= 1: raise ValueError("df <= 0") if fnonc <= 0: raise ValueError("nonc <= 0") return cont2_array_sc(self.internal_state, rk_noncentral_chisquare, size, fdf, fnonc) PyErr_Clear() odf = PyArray_FROM_OTF(df, NPY_DOUBLE, NPY_ALIGNED) ononc = PyArray_FROM_OTF(nonc, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(odf, 0.0)): raise ValueError("df <= 1") if _sp.any(_sp.less_equal(ononc, 0.0)): raise ValueError("nonc < 0") return cont2_array(self.internal_state, rk_noncentral_chisquare, size, odf, ononc) def standard_cauchy(self, size=None): """Standard Cauchy with mode=0. standard_cauchy(size=None) """ return cont0_array(self.internal_state, rk_standard_cauchy, size) def standard_t(self, df, size=None): """Standard Student's t distribution with df degrees of freedom. standard_t(df, size=None) """ cdef ndarray odf cdef double fdf fdf = PyFloat_AsDouble(df) if not PyErr_Occurred(): if fdf <= 0: raise ValueError("df <= 0") return cont1_array_sc(self.internal_state, rk_standard_t, size, fdf) PyErr_Clear() odf = PyArray_FROM_OTF(df, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(odf, 0.0)): raise ValueError("df <= 0") return cont1_array(self.internal_state, rk_standard_t, size, odf) def vonmises(self, mu, kappa, size=None): """von Mises circular distribution with mode mu and dispersion parameter kappa on [-pi, pi]. vonmises(mu, kappa, size=None) """ cdef ndarray omu, okappa cdef double fmu, fkappa fmu = PyFloat_AsDouble(mu) fkappa = PyFloat_AsDouble(kappa) if not PyErr_Occurred(): if fkappa < 0: raise ValueError("kappa < 0") return cont2_array_sc(self.internal_state, rk_vonmises, size, fmu, fkappa) PyErr_Clear() omu = PyArray_FROM_OTF(mu, NPY_DOUBLE, NPY_ALIGNED) okappa = PyArray_FROM_OTF(kappa, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less(okappa, 0.0)): raise ValueError("kappa < 0") return cont2_array(self.internal_state, rk_vonmises, size, omu, okappa) def pareto(self, a, size=None): """Pareto distribution. pareto(a, size=None) """ cdef ndarray oa cdef double fa fa = PyFloat_AsDouble(a) if not PyErr_Occurred(): if fa <= 0: raise ValueError("a <= 0") return cont1_array_sc(self.internal_state, rk_pareto, size, fa) PyErr_Clear() oa = PyArray_FROM_OTF(a, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oa, 0.0)): raise ValueError("a <= 0") return cont1_array(self.internal_state, rk_pareto, size, oa) def weibull(self, a, size=None): """Weibull distribution. weibull(a, size=None) """ cdef ndarray oa cdef double fa fa = PyFloat_AsDouble(a) if not PyErr_Occurred(): if fa <= 0: raise ValueError("a <= 0") return cont1_array_sc(self.internal_state, rk_weibull, size, fa) PyErr_Clear() oa = PyArray_FROM_OTF(a, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oa, 0.0)): raise ValueError("a <= 0") return cont1_array(self.internal_state, rk_weibull, size, oa) def power(self, a, size=None): """Power distribution. power(a, size=None) """ cdef ndarray oa cdef double fa fa = PyFloat_AsDouble(a) if not PyErr_Occurred(): if fa <= 0: raise ValueError("a <= 0") return cont1_array_sc(self.internal_state, rk_power, size, fa) PyErr_Clear() oa = PyArray_FROM_OTF(a, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oa, 0.0)): raise ValueError("a <= 0") return cont1_array(self.internal_state, rk_power, size, oa) def laplace(self, loc=0.0, scale=1.0, size=None): """Laplace distribution. laplace(loc=0.0, scale=1.0, size=None) """ cdef ndarray oloc, oscale cdef double floc, fscale floc = PyFloat_AsDouble(loc) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_laplace, size, floc, fscale) PyErr_Clear() oloc = PyArray_FROM_OTF(loc, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0") return cont2_array(self.internal_state, rk_laplace, size, oloc, oscale) def gumbel(self, loc=0.0, scale=1.0, size=None): """Gumbel distribution. gumbel(loc=0.0, scale=1.0, size=None) """ cdef ndarray oloc, oscale cdef double floc, fscale floc = PyFloat_AsDouble(loc) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_gumbel, size, floc, fscale) PyErr_Clear() oloc = PyArray_FROM_OTF(loc, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0") return cont2_array(self.internal_state, rk_gumbel, size, oloc, oscale) def logistic(self, loc=0.0, scale=1.0, size=None): """Logistic distribution. logistic(loc=0.0, scale=1.0, size=None) """ cdef ndarray oloc, oscale cdef double floc, fscale floc = PyFloat_AsDouble(loc) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_logistic, size, floc, fscale) PyErr_Clear() oloc = PyArray_FROM_OTF(loc, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0") return cont2_array(self.internal_state, rk_logistic, size, oloc, oscale) def lognormal(self, mean=0.0, sigma=1.0, size=None): """Log-normal distribution. Note that the mean parameter is not the mean of this distribution, but the underlying normal distribution. lognormal(mean, sigma) <=> exp(normal(mean, sigma)) lognormal(mean=0.0, sigma=1.0, size=None) """ cdef ndarray omean, osigma cdef double fmean, fsigma fmean = PyFloat_AsDouble(mean) fsigma = PyFloat_AsDouble(sigma) if not PyErr_Occurred(): if fsigma <= 0: raise ValueError("sigma <= 0") return cont2_array_sc(self.internal_state, rk_lognormal, size, fmean, fsigma) PyErr_Clear() omean = PyArray_FROM_OTF(mean, NPY_DOUBLE, NPY_ALIGNED) osigma = PyArray_FROM_OTF(sigma, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(osigma, 0.0)): raise ValueError("sigma <= 0.0") return cont2_array(self.internal_state, rk_lognormal, size, omean, osigma) def rayleigh(self, scale=1.0, size=None): """Rayleigh distribution. rayleigh(scale=1.0, size=None) """ cdef ndarray oscale cdef double fscale fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fscale <= 0: raise ValueError("scale <= 0") return cont1_array_sc(self.internal_state, rk_rayleigh, size, fscale) PyErr_Clear() oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oscale, 0.0)): raise ValueError("scale <= 0.0") return cont1_array(self.internal_state, rk_rayleigh, size, oscale) def wald(self, mean, scale, size=None): """Wald (inverse Gaussian) distribution. wald(mean, scale, size=None) """ cdef ndarray omean, oscale cdef double fmean, fscale fmean = PyFloat_AsDouble(mean) fscale = PyFloat_AsDouble(scale) if not PyErr_Occurred(): if fmean <= 0: raise ValueError("mean <= 0") if fscale <= 0: raise ValueError("scale <= 0") return cont2_array_sc(self.internal_state, rk_wald, size, fmean, fscale) PyErr_Clear() omean = PyArray_FROM_OTF(mean, NPY_DOUBLE, NPY_ALIGNED) oscale = PyArray_FROM_OTF(scale, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(omean,0.0)): raise ValueError("mean <= 0.0") elif _sp.any(_sp.less_equal(oscale,0.0)): raise ValueError("scale <= 0.0") return cont2_array(self.internal_state, rk_wald, size, omean, oscale) def triangular(self, left, mode, right, size=None): """Triangular distribution starting at left, peaking at mode, and ending at right (left <= mode <= right). triangular(left, mode, right, size=None) """ cdef ndarray oleft, omode, oright cdef double fleft, fmode, fright fleft = PyFloat_AsDouble(left) fright = PyFloat_AsDouble(right) fmode = PyFloat_AsDouble(mode) if not PyErr_Occurred(): if fleft > fmode: raise ValueError("left > mode") if fmode > fright: raise ValueError("mode > right") if fleft == fright: raise ValueError("left == right") return cont3_array_sc(self.internal_state, rk_triangular, size, fleft, fmode, fright) PyErr_Clear() oleft = PyArray_FROM_OTF(left, NPY_DOUBLE, NPY_ALIGNED) omode = PyArray_FROM_OTF(mode, NPY_DOUBLE, NPY_ALIGNED) oright = PyArray_FROM_OTF(right, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.greater(oleft, omode)): raise ValueError("left > mode") if _sp.any(_sp.greater(omode, oright)): raise ValueError("mode > right") if _sp.any(_sp.equal(oleft, oright)): raise ValueError("left == right") return cont3_array(self.internal_state, rk_triangular, size, oleft, omode, oright) # Complicated, discrete distributions: def binomial(self, n, p, size=None): """Binomial distribution of n trials and p probability of success. binomial(n, p, size=None) -> random values """ cdef ndarray on, op cdef long ln cdef double fp fp = PyFloat_AsDouble(p) ln = PyInt_AsLong(n) if not PyErr_Occurred(): if ln <= 0: raise ValueError("n <= 0") if fp < 0: raise ValueError("p < 0") elif fp > 1: raise ValueError("p > 1") return discnp_array_sc(self.internal_state, rk_binomial, size, ln, fp) PyErr_Clear() on = PyArray_FROM_OTF(n, NPY_LONG, NPY_ALIGNED) op = PyArray_FROM_OTF(p, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(n, 0)): raise ValueError("n <= 0") if _sp.any(_sp.less(p, 0)): raise ValueError("p < 0") if _sp.any(_sp.greater(p, 1)): raise ValueError("p > 1") return discnp_array(self.internal_state, rk_binomial, size, on, op) def negative_binomial(self, n, p, size=None): """Negative Binomial distribution. negative_binomial(n, p, size=None) -> random values """ cdef ndarray on cdef ndarray op cdef long ln cdef double fp fp = PyFloat_AsDouble(p) ln = PyInt_AsLong(n) if not PyErr_Occurred(): if ln <= 0: raise ValueError("n <= 0") if fp < 0: raise ValueError("p < 0") elif fp > 1: raise ValueError("p > 1") return discnp_array_sc(self.internal_state, rk_negative_binomial, size, ln, fp) PyErr_Clear() on = PyArray_FROM_OTF(n, NPY_LONG, NPY_ALIGNED) op = PyArray_FROM_OTF(p, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(n, 0)): raise ValueError("n <= 0") if _sp.any(_sp.less(p, 0)): raise ValueError("p < 0") if _sp.any(_sp.greater(p, 1)): raise ValueError("p > 1") return discnp_array(self.internal_state, rk_negative_binomial, size, on, op) def poisson(self, lam=1.0, size=None): """Poisson distribution. poisson(lam=1.0, size=None) -> random values """ cdef ndarray olam cdef double flam flam = PyFloat_AsDouble(lam) if not PyErr_Occurred(): if lam < 0: raise ValueError("lam < 0") return discd_array_sc(self.internal_state, rk_poisson, size, flam) PyErr_Clear() olam = PyArray_FROM_OTF(lam, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less(olam, 0)): raise ValueError("lam < 0") return discd_array(self.internal_state, rk_poisson, size, olam) def zipf(self, a, size=None): """Zipf distribution. zipf(a, size=None) """ cdef ndarray oa cdef double fa fa = PyFloat_AsDouble(a) if not PyErr_Occurred(): if fa <= 1.0: raise ValueError("a <= 1.0") return discd_array_sc(self.internal_state, rk_zipf, size, fa) PyErr_Clear() oa = PyArray_FROM_OTF(a, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less_equal(oa, 1.0)): raise ValueError("a <= 1.0") return discd_array(self.internal_state, rk_zipf, size, oa) def geometric(self, p, size=None): """Geometric distribution with p being the probability of "success" on an individual trial. geometric(p, size=None) """ cdef ndarray op cdef double fp fp = PyFloat_AsDouble(p) if not PyErr_Occurred(): if fp < 0.0: raise ValueError("p < 0.0") if fp > 1.0: raise ValueError("p > 1.0") return discd_array_sc(self.internal_state, rk_geometric, size, fp) PyErr_Clear() op = PyArray_FROM_OTF(p, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less(op, 0.0)): raise ValueError("p < 0.0") if _sp.any(_sp.greater(op, 1.0)): raise ValueError("p > 1.0") return discd_array(self.internal_state, rk_geometric, size, op) def hypergeometric(self, ngood, nbad, nsample, size=None): """Hypergeometric distribution. Consider an urn with ngood "good" balls and nbad "bad" balls. If one were to draw nsample balls from the urn without replacement, then the hypergeometric distribution describes the distribution of "good" balls in the sample. hypergeometric(ngood, nbad, nsample, size=None) """ cdef ndarray ongood, onbad, onsample cdef long lngood, lnbad, lnsample lngood = PyInt_AsLong(ngood) lnbad = PyInt_AsLong(nbad) lnsample = PyInt_AsLong(nsample) if not PyErr_Occurred(): if ngood < 1: raise ValueError("ngood < 1") if nbad < 1: raise ValueError("nbad < 1") if nsample < 1: raise ValueError("nsample < 1") if ngood + nbad < nsample: raise ValueError("ngood + nbad < nsample") return discnmN_array_sc(self.internal_state, rk_hypergeometric, size, lngood, lnbad, lnsample) PyErr_Clear() ongood = PyArray_FROM_OTF(ngood, NPY_LONG, NPY_ALIGNED) onbad = PyArray_FROM_OTF(nbad, NPY_LONG, NPY_ALIGNED) onsample = PyArray_FROM_OTF(nsample, NPY_LONG, NPY_ALIGNED) if _sp.any(_sp.less(ongood, 1)): raise ValueError("ngood < 1") if _sp.any(_sp.less(onbad, 1)): raise ValueError("nbad < 1") if _sp.any(_sp.less(onsample, 1)): raise ValueError("nsample < 1") if _sp.any(_sp.less(_sp.add(ongood, onbad),onsample)): raise ValueError("ngood + nbad < nsample") return discnmN_array(self.internal_state, rk_hypergeometric, size, ongood, onbad, onsample) def logseries(self, p, size=None): """Logarithmic series distribution. logseries(p, size=None) """ cdef ndarray op cdef double fp fp = PyFloat_AsDouble(p) if not PyErr_Occurred(): if fp < 0.0: raise ValueError("p < 0.0") if fp > 1.0: raise ValueError("p > 1.0") return discd_array_sc(self.internal_state, rk_logseries, size, fp) PyErr_Clear() op = PyArray_FROM_OTF(p, NPY_DOUBLE, NPY_ALIGNED) if _sp.any(_sp.less(op, 0.0)): raise ValueError("p < 0.0") if _sp.any(_sp.greater(op, 1.0)): raise ValueError("p > 1.0") return discd_array(self.internal_state, rk_logseries, size, op) # Multivariate distributions: def multivariate_normal(self, mean, cov, size=None): """Return an array containing multivariate normally distributed random numbers with specified mean and covariance. multivariate_normal(mean, cov) -> random values multivariate_normal(mean, cov, [m, n, ...]) -> random values mean must be a 1 dimensional array. cov must be a square two dimensional array with the same number of rows and columns as mean has elements. The first form returns a single 1-D array containing a multivariate normal. The second form returns an array of shape (m, n, ..., cov.shape[0]). In this case, output[i,j,...,:] is a 1-D array containing a multivariate normal. """ # Check preconditions on arguments mean = _sp.array(mean) cov = _sp.array(cov) if size is None: shape = [] else: shape = size if len(mean.shape) != 1: raise ValueError("mean must be 1 dimensional") if (len(cov.shape) != 2) or (cov.shape[0] != cov.shape[1]): raise ValueError("cov must be 2 dimensional and square") if mean.shape[0] != cov.shape[0]: raise ValueError("mean and cov must have same length") # Compute shape of output if isinstance(shape, int): shape = [shape] final_shape = list(shape[:]) final_shape.append(mean.shape[0]) # Create a matrix of independent standard normally distributed random # numbers. The matrix has rows with the same length as mean and as # many rows are necessary to form a matrix of shape final_shape. x = self.standard_normal(_sp.multiply.reduce(final_shape)) x.shape = (_sp.multiply.reduce(final_shape[0:len(final_shape)-1]), mean.shape[0]) # Transform matrix of standard normals into matrix where each row # contains multivariate normals with the desired covariance. # Compute A such that dot(transpose(A),A) == cov. # Then the matrix products of the rows of x and A has the desired # covariance. Note that sqrt(s)*v where (u,s,v) is the singular value # decomposition of cov is such an A. from numpy.dual import svd # XXX: we really should be doing this by Cholesky decomposition (u,s,v) = svd(cov) x = _sp.dot(x*_sp.sqrt(s),v) # The rows of x now have the correct covariance but mean 0. Add # mean to each row. Then each row will have mean mean. _sp.add(mean,x,x) x.shape = tuple(final_shape) return x def multinomial(self, long n, object pvals, size=None): """Multinomial distribution. multinomial(n, pvals, size=None) -> random values pvals is a sequence of probabilities that should sum to 1 (however, the last element is always assumed to account for the remaining probability as long as sum(pvals[:-1]) <= 1). """ cdef long d cdef ndarray parr "arrayObject_parr", mnarr "arrayObject_mnarr" cdef double *pix cdef long *mnix cdef long i, j, dn cdef double Sum d = len(pvals) parr = PyArray_ContiguousFromObject(pvals, NPY_DOUBLE, 1, 1) pix = parr.data if kahan_sum(pix, d-1) > (1.0 + 1e-12): raise ValueError("sum(pvals[:-1]) > 1.0") if size is None: shape = (d,) elif type(size) is int: shape = (size, d) else: shape = size + (d,) multin = _sp.zeros(shape, int) mnarr = multin mnix = mnarr.data i = 0 while i < PyArray_SIZE(mnarr): Sum = 1.0 dn = n for j from 0 <= j < d-1: mnix[i+j] = rk_binomial(self.internal_state, dn, pix[j]/Sum) dn = dn - mnix[i+j] if dn <= 0: break Sum = Sum - pix[j] if dn > 0: mnix[i+d-1] = dn i = i + d return multin def dirichlet(self, object alpha, size=None): """dirichlet(alpha, size=None) Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference. :Parameters: alpha : array parameter of the distribution (k dimension for sample of dimension k). size : array number of samples to draw. $X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i}$ Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape alpha_i, then X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, ..., y_n) is Dirichlet distributed. Reference: - David Mc Kay : Information Theory, inference and Learning algorithms, chapter 23. the book is available for free at http://www.inference.phy.cam.ac.uk/mackay/ """ #================= # Pure python algo #================= #alpha = N.atleast_1d(alpha) #k = alpha.size #if n == 1: # val = N.zeros(k) # for i in range(k): # val[i] = sgamma(alpha[i], n) # val /= N.sum(val) #else: # val = N.zeros((k, n)) # for i in range(k): # val[i] = sgamma(alpha[i], n) # val /= N.sum(val, axis = 0) # val = val.T #return val cdef long k cdef long totsize cdef ndarray alpha_arr, val_arr cdef double *alpha_data, *val_data cdef long i, j cdef double acc, invacc k = len(alpha) alpha_arr = PyArray_ContiguousFromObject(alpha, NPY_DOUBLE, 1, 1) alpha_data = alpha_arr.data if size is None: shape = (k,) elif type(size) is int: shape = (size, k) else: shape = size + (k,) diric = _sp.zeros(shape, _sp.float64) val_arr = diric val_data= val_arr.data i = 0 totsize = PyArray_SIZE(val_arr) while i < totsize: acc = 0.0 for j from 0 <= j < k: val_data[i+j] = rk_standard_gamma(self.internal_state, alpha_data[j]) acc = acc + val_data[i+j] invacc = 1/acc for j from 0 <= j < k: val_data[i+j] = val_data[i+j] * invacc i = i + k return diric # Shuffling and permutations: def shuffle(self, object x): """Modify a sequence in-place by shuffling its contents. shuffle(x) """ cdef long i, j cdef int copy i = len(x) - 1 try: j = len(x[0]) except: j = 0 if (j == 0): # adaptation of random.shuffle() while i > 0: j = rk_interval(i, self.internal_state) x[i], x[j] = x[j], x[i] i = i - 1 else: # make copies copy = hasattr(x[0], 'copy') if copy: while(i > 0): j = rk_interval(i, self.internal_state) x[i], x[j] = x[j].copy(), x[i].copy() i = i - 1 else: while(i > 0): j = rk_interval(i, self.internal_state) x[i], x[j] = x[j][:], x[i][:] i = i - 1 def permutation(self, object x): """Given an integer, return a shuffled sequence of integers >= 0 and < x; given a sequence, return a shuffled array copy. permutation(x) """ if isinstance(x, (int, _sp.integer)): arr = _sp.arange(x) else: arr = _sp.array(x) self.shuffle(arr) return arr _rand = RandomState() seed = _rand.seed get_state = _rand.get_state set_state = _rand.set_state random_sample = _rand.random_sample randint = _rand.randint bytes = _rand.bytes uniform = _rand.uniform rand = _rand.rand randn = _rand.randn random_integers = _rand.random_integers standard_normal = _rand.standard_normal normal = _rand.normal beta = _rand.beta exponential = _rand.exponential standard_exponential = _rand.standard_exponential standard_gamma = _rand.standard_gamma gamma = _rand.gamma f = _rand.f noncentral_f = _rand.noncentral_f chisquare = _rand.chisquare noncentral_chisquare = _rand.noncentral_chisquare standard_cauchy = _rand.standard_cauchy standard_t = _rand.standard_t vonmises = _rand.vonmises pareto = _rand.pareto weibull = _rand.weibull power = _rand.power laplace = _rand.laplace gumbel = _rand.gumbel logistic = _rand.logistic lognormal = _rand.lognormal rayleigh = _rand.rayleigh wald = _rand.wald triangular = _rand.triangular binomial = _rand.binomial negative_binomial = _rand.negative_binomial poisson = _rand.poisson zipf = _rand.zipf geometric = _rand.geometric hypergeometric = _rand.hypergeometric logseries = _rand.logseries multivariate_normal = _rand.multivariate_normal multinomial = _rand.multinomial dirichlet = _rand.dirichlet shuffle = _rand.shuffle permutation = _rand.permutation