Mercurial > octave
view liboctave/numeric/randpoisson.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 796f54d4ddbf |
children | aac27ad79be6 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2006-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// /* Original version written by Paul Kienzle distributed as free software in the in the public domain. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cmath> #include <cstddef> #include "f77-fcn.h" #include "lo-error.h" #include "lo-ieee.h" #include "randmtzig.h" #include "randpoisson.h" OCTAVE_BEGIN_NAMESPACE(octave) static double xlgamma (double x) { return std::lgamma (x); } /* ---- pprsc.c from Stadloeber's winrand --- */ /* flogfak(k) = ln(k!) */ static double flogfak (double k) { #define C0 9.18938533204672742e-01 #define C1 8.33333333333333333e-02 #define C3 -2.77777777777777778e-03 #define C5 7.93650793650793651e-04 #define C7 -5.95238095238095238e-04 static double logfak[30L] = { 0.00000000000000000, 0.00000000000000000, 0.69314718055994531, 1.79175946922805500, 3.17805383034794562, 4.78749174278204599, 6.57925121201010100, 8.52516136106541430, 10.60460290274525023, 12.80182748008146961, 15.10441257307551530, 17.50230784587388584, 19.98721449566188615, 22.55216385312342289, 25.19122118273868150, 27.89927138384089157, 30.67186010608067280, 33.50507345013688888, 36.39544520803305358, 39.33988418719949404, 42.33561646075348503, 45.38013889847690803, 48.47118135183522388, 51.60667556776437357, 54.78472939811231919, 58.00360522298051994, 61.26170176100200198, 64.55753862700633106, 67.88974313718153498, 71.25703896716800901 }; double r, rr; if (k >= 30.0) { r = 1.0 / k; rr = r * r; return ((k + 0.5)*std::log (k) - k + C0 + r*(C1 + rr*(C3 + rr*(C5 + rr*C7)))); } else return (logfak[static_cast<int> (k)]); } /****************************************************************** * * * Poisson Distribution - Patchwork Rejection/Inversion * * * ****************************************************************** * * * For parameter my < 10, Tabulated Inversion is applied. * * For my >= 10, Patchwork Rejection is employed: * * The area below the histogram function f(x) is rearranged in * * its body by certain point reflections. Within a large center * * interval variates are sampled efficiently by rejection from * * uniform hats. Rectangular immediate acceptance regions speed * * up the generation. The remaining tails are covered by * * exponential functions. * * * ****************************************************************** * * * FUNCTION : - pprsc samples a random number from the Poisson * * distribution with parameter my > 0. * * REFERENCE : - H. Zechner (1994): Efficient sampling from * * continuous and discrete unimodal distributions, * * Doctoral Dissertation, 156 pp., Technical * * University Graz, Austria. * * SUBPROGRAM : - drand(seed) ... (0,1)-Uniform generator with * * unsigned long integer *seed. * * * * Implemented by H. Zechner, January 1994 * * Revised by F. Niederl, July 1994 * * * ******************************************************************/ static double f (double k, double l_nu, double c_pm) { return exp (k * l_nu - flogfak (k) - c_pm); } static double pprsc (double my) { static double my_last = -1.0; static double m, k2, k4, k1, k5; static double dl, dr, r1, r2, r4, r5, ll, lr, l_my, c_pm, f1, f2, f4, f5, p1, p2, p3, p4, p5, p6; double Dk, X, Y; double Ds, U, V, W; if (my != my_last) { /* set-up */ my_last = my; /* approximate deviation of reflection points k2, k4 from my - 1/2 */ Ds = std::sqrt (my + 0.25); /* mode m, reflection points k2 and k4, and points k1 and k5, */ /* which delimit the centre region of h(x) */ m = std::floor (my); k2 = ceil (my - 0.5 - Ds); k4 = std::floor (my - 0.5 + Ds); k1 = k2 + k2 - m + 1L; k5 = k4 + k4 - m; /* range width of the critical left and right centre region */ dl = (k2 - k1); dr = (k5 - k4); /* recurrence constants r(k)=p(k)/p(k-1) at k = k1, k2, k4+1, k5+1 */ r1 = my / k1; r2 = my / k2; r4 = my / (k4 + 1.0); r5 = my / (k5 + 1.0); /* reciprocal values of the scale parameters of exp. tail envelope */ ll = std::log (r1); /* expon. tail left */ lr = -std::log (r5); /* expon. tail right*/ /* Poisson constants, necessary for computing function values f(k) */ l_my = std::log (my); c_pm = m * l_my - flogfak (m); /* function values f(k) = p(k)/p(m) at k = k2, k4, k1, k5 */ f2 = f (k2, l_my, c_pm); f4 = f (k4, l_my, c_pm); f1 = f (k1, l_my, c_pm); f5 = f (k5, l_my, c_pm); /* area of the two centre and the two exponential tail regions */ /* area of the two immediate acceptance regions between k2, k4 */ p1 = f2 * (dl + 1.0); /* immed. left */ p2 = f2 * dl + p1; /* centre left */ p3 = f4 * (dr + 1.0) + p2; /* immed. right */ p4 = f4 * dr + p3; /* centre right */ p5 = f1 / ll + p4; /* exp. tail left */ p6 = f5 / lr + p5; /* exp. tail right*/ } for (;;) { /* generate uniform number U -- U(0, p6) */ /* case distinction corresponding to U */ if ((U = rand_uniform<double> () * p6) < p2) { /* centre left */ /* immediate acceptance region R2 = [k2, m) *[0, f2), X = k2, ... m -1 */ if ((V = U - p1) < 0.0) return (k2 + std::floor (U/f2)); /* immediate acceptance region R1 = [k1, k2)*[0, f1), X = k1, ... k2-1 */ if ((W = V / dl) < f1 ) return (k1 + std::floor (V/f1)); /* computation of candidate X < k2, and its counterpart Y > k2 */ /* either squeeze-acceptance of X or acceptance-rejection of Y */ Dk = std::floor (dl * rand_uniform<double> ()) + 1.0; if (W <= f2 - Dk * (f2 - f2/r2)) { /* quick accept of */ return (k2 - Dk); /* X = k2 - Dk */ } if ((V = f2 + f2 - W) < 1.0) { /* quick reject of Y*/ Y = k2 + Dk; if (V <= f2 + Dk * (1.0 - f2)/(dl + 1.0)) { /* quick accept of */ return (Y); /* Y = k2 + Dk */ } if (V <= f (Y, l_my, c_pm)) return (Y); /* final accept of Y*/ } X = k2 - Dk; } else if (U < p4) { /* centre right */ /* immediate acceptance region R3 = [m, k4+1)*[0, f4), X = m, ... k4 */ if ((V = U - p3) < 0.0) return (k4 - std::floor ((U - p2)/f4)); /* immediate acceptance region R4 = [k4+1, k5+1)*[0, f5) */ if ((W = V / dr) < f5 ) return (k5 - std::floor (V/f5)); /* computation of candidate X > k4, and its counterpart Y < k4 */ /* either squeeze-acceptance of X or acceptance-rejection of Y */ Dk = std::floor (dr * rand_uniform<double> ()) + 1.0; if (W <= f4 - Dk * (f4 - f4*r4)) { /* quick accept of */ return (k4 + Dk); /* X = k4 + Dk */ } if ((V = f4 + f4 - W) < 1.0) { /* quick reject of Y*/ Y = k4 - Dk; if (V <= f4 + Dk * (1.0 - f4)/ dr) { /* quick accept of */ return (Y); /* Y = k4 - Dk */ } if (V <= f (Y, l_my, c_pm)) return (Y); /* final accept of Y*/ } X = k4 + Dk; } else { W = rand_uniform<double> (); if (U < p5) { /* expon. tail left */ Dk = std::floor (1.0 - std::log (W)/ll); if ((X = k1 - Dk) < 0L) continue; /* 0 <= X <= k1 - 1 */ W *= (U - p4) * ll; /* W -- U(0, h(x)) */ if (W <= f1 - Dk * (f1 - f1/r1)) return (X); /* quick accept of X*/ } else { /* expon. tail right*/ Dk = std::floor (1.0 - std::log (W)/lr); X = k5 + Dk; /* X >= k5 + 1 */ W *= (U - p5) * lr; /* W -- U(0, h(x)) */ if (W <= f5 - Dk * (f5 - f5*r5)) return (X); /* quick accept of X*/ } } /* acceptance-rejection test of candidate X from the original area */ /* test, whether W <= f(k), with W = U*h(x) and U -- U(0, 1)*/ /* log f(X) = (X - m)*log(my) - log X! + log m! */ if (std::log (W) <= X * l_my - flogfak (X) - c_pm) return (X); } } /* ---- pprsc.c end ------ */ /* The remainder of the file is by Paul Kienzle */ /* Table size is predicated on the maximum value of lambda * we want to store in the table, and the maximum value of * returned by the uniform random number generator on [0,1). * With lambda==10 and u_max = 1 - 1/(2^32+1), we * have poisson_pdf(lambda,36) < 1-u_max. If instead our * generator uses more bits of mantissa or returns a value * in the range [0,1], then for lambda==10 we need a table * size of 46 instead. For long doubles, the table size * will need to be longer still. */ #define TABLESIZE 46 /* Given uniform u, find x such that CDF(L,x)==u. Return x. */ template <typename T> static void poisson_cdf_lookup (double lambda, T *p, std::size_t n) { double t[TABLESIZE]; /* Precompute the table for the u up to and including 0.458. * We will almost certainly need it. */ int intlambda = static_cast<int> (std::floor (lambda)); double P; int tableidx; std::size_t i = n; t[0] = P = exp (-lambda); for (tableidx = 1; tableidx <= intlambda; tableidx++) { P = P*lambda/static_cast<double> (tableidx); t[tableidx] = t[tableidx-1] + P; } while (i-- > 0) { double u = rand_uniform<double> (); /* If u > 0.458 we know we can jump to floor(lambda) before * comparing (this observation is based on Stadlober's winrand * code). For lambda >= 1, this will be a win. Lambda < 1 * is already fast, so adding an extra comparison is not a * problem. */ int k = (u > 0.458 ? intlambda : 0); /* We aren't using a for loop here because when we find the * right k we want to jump to the next iteration of the * outer loop, and the continue statement will only work for * the inner loop. */ nextk: if (u <= t[k]) { p[i] = static_cast<T> (k); continue; } if (++k < tableidx) goto nextk; /* We only need high values of the table very rarely so we * don't automatically compute the entire table. */ while (tableidx < TABLESIZE) { P = P*lambda/static_cast<double> (tableidx); t[tableidx] = t[tableidx-1] + P; /* Make sure we converge to 1.0 just in case u is uniform * on [0,1] rather than [0,1). */ if (t[tableidx] == t[tableidx-1]) t[tableidx] = 1.0; tableidx++; if (u <= t[tableidx-1]) break; } /* We are assuming that the table size is big enough here. * This should be true even if rand_uniform is returning values in * the range [0,1] rather than [0,1). */ p[i] = static_cast<T> (tableidx-1); } } /* From Press, et al., Numerical Recipes */ template <typename T> static void poisson_rejection (double lambda, T *p, std::size_t n) { double sq = std::sqrt (2.0*lambda); double alxm = std::log (lambda); double g = lambda*alxm - xlgamma (lambda+1.0); std::size_t i; for (i = 0; i < n; i++) { double y, em, t; do { do { y = tan (M_PI*rand_uniform<double> ()); em = sq * y + lambda; } while (em < 0.0); em = std::floor (em); t = 0.9*(1.0+y*y)*exp (em*alxm-flogfak (em)-g); } while (rand_uniform<double> () > t); p[i] = em; } } /* The cutoff of L <= 1e8 in the following two functions before using * the normal approximation is based on: * > L=1e8; x=floor(linspace(0,2*L,1000)); * > max(abs(normal_pdf(x,L,L)-poisson_pdf(x,L))) * ans = 1.1376e-28 * For L=1e7, the max is around 1e-9, which is within the step size of * rand_uniform. For L>1e10 the pprsc function breaks down, as I saw * from the histogram of a large sample, so 1e8 is both small enough * and large enough. */ /* Generate a set of poisson numbers with the same distribution */ template <typename T> void rand_poisson (T L_arg, octave_idx_type n, T *p) { double L = L_arg; octave_idx_type i; if (L < 0.0 || lo_ieee_isinf (L)) { for (i=0; i<n; i++) p[i] = numeric_limits<T>::NaN (); } else if (L <= 10.0) { poisson_cdf_lookup<T> (L, p, n); } else if (L <= 1e8) { for (i=0; i<n; i++) p[i] = pprsc (L); } else { /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ const double sqrtL = std::sqrt (L); for (i = 0; i < n; i++) { p[i] = std::floor (rand_normal<T> () * sqrtL + L + 0.5); if (p[i] < 0.0) p[i] = 0.0; /* will probably never happen */ } } } template void rand_poisson<double> (double, octave_idx_type, double *); template void rand_poisson<float> (float, octave_idx_type, float *); /* Generate one poisson variate */ template <typename T> T rand_poisson (T L_arg) { double L = L_arg; T ret; if (L < 0.0) ret = numeric_limits<T>::NaN (); else if (L <= 12.0) { /* From Press, et al. Numerical recipes */ double g = exp (-L); int em = -1; double t = 1.0; do { ++em; t *= rand_uniform<T> (); } while (t > g); ret = em; } else if (L <= 1e8) { /* numerical recipes */ poisson_rejection<T> (L, &ret, 1); } else if (lo_ieee_isinf (L)) { /* FIXME: R uses NaN, but the normal approximation suggests that * limit should be Inf. Which is correct? */ ret = numeric_limits<T>::NaN (); } else { /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ ret = std::floor (rand_normal<T> () * std::sqrt (L) + L + 0.5); if (ret < 0.0) ret = 0.0; /* will probably never happen */ } return ret; } template OCTAVE_API double rand_poisson<double> (double); template OCTAVE_API float rand_poisson<float> (float); OCTAVE_END_NAMESPACE(octave)