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authorJoel Sherrill <joel.sherrill@OARcorp.com>2011-04-08 17:33:11 +0000
committerJoel Sherrill <joel.sherrill@OARcorp.com>2011-04-08 17:33:11 +0000
commit73f643f3f4a55310b2c8c1a9858906b2dd676e72 (patch)
treeb1df97f18dace4a5702b0bc7aafdfee8a2f25ada /gsl-1.9/monte/vegas.c
parentee523abdace8337d05ec4a179fcdf5de3fe0f634 (diff)
2011-04-08 Joel Sherrill <joel.sherrill@oarcorp.com>
* AUTHORS, BUGS, COPYING, ChangeLog, INSTALL, Makefile.am, Makefile.in, NEWS, README, SUPPORT, THANKS, TODO, acconfig.h, aclocal.m4, autogen.sh, config.guess, config.h.in, config.sub, configure, configure.ac, gsl-config.in, gsl-histogram.c, gsl-randist.c, gsl.m4, gsl.pc.in, gsl.spec.in, gsl_machine.h, gsl_math.h, gsl_mode.h, gsl_nan.h, gsl_pow_int.h, gsl_precision.h, gsl_types.h, gsl_version.h.in, install-sh, ltmain.sh, mdate-sh, missing, mkinstalldirs, templates_off.h, templates_on.h, test_gsl_histogram.sh, version.c, blas/ChangeLog, blas/Makefile.am, blas/Makefile.in, blas/TODO, blas/blas.c, blas/gsl_blas.h, blas/gsl_blas_types.h, block/ChangeLog, block/Makefile.am, block/Makefile.in, block/block.c, block/block_source.c, block/file.c, block/fprintf_source.c, block/fwrite_source.c, block/gsl_block.h, block/gsl_block_char.h, block/gsl_block_complex_double.h, block/gsl_block_complex_float.h, block/gsl_block_complex_long_double.h, block/gsl_block_double.h, block/gsl_block_float.h, block/gsl_block_int.h, block/gsl_block_long.h, block/gsl_block_long_double.h, block/gsl_block_short.h, block/gsl_block_uchar.h, block/gsl_block_uint.h, block/gsl_block_ulong.h, block/gsl_block_ushort.h, block/gsl_check_range.h, block/init.c, block/init_source.c, block/test.c, block/test_complex_io.c, block/test_complex_source.c, block/test_io.c, block/test_source.c, bspline/ChangeLog, bspline/Makefile.am, bspline/Makefile.in, bspline/TODO, bspline/bspline.c, bspline/gsl_bspline.h, bspline/test.c, cblas/ChangeLog, cblas/Makefile.am, cblas/Makefile.in, cblas/TODO, cblas/caxpy.c, cblas/cblas.h, cblas/ccopy.c, cblas/cdotc_sub.c, cblas/cdotu_sub.c, cblas/cgbmv.c, cblas/cgemm.c, cblas/cgemv.c, cblas/cgerc.c, cblas/cgeru.c, cblas/chbmv.c, cblas/chemm.c, cblas/chemv.c, cblas/cher.c, cblas/cher2.c, cblas/cher2k.c, cblas/cherk.c, cblas/chpmv.c, cblas/chpr.c, cblas/chpr2.c, cblas/cscal.c, cblas/csscal.c, cblas/cswap.c, cblas/csymm.c, cblas/csyr2k.c, cblas/csyrk.c, cblas/ctbmv.c, cblas/ctbsv.c, cblas/ctpmv.c, cblas/ctpsv.c, cblas/ctrmm.c, cblas/ctrmv.c, cblas/ctrsm.c, cblas/ctrsv.c, cblas/dasum.c, cblas/daxpy.c, cblas/dcopy.c, cblas/ddot.c, cblas/dgbmv.c, cblas/dgemm.c, cblas/dgemv.c, cblas/dger.c, cblas/dnrm2.c, cblas/drot.c, cblas/drotg.c, cblas/drotm.c, cblas/drotmg.c, cblas/dsbmv.c, cblas/dscal.c, cblas/dsdot.c, cblas/dspmv.c, cblas/dspr.c, cblas/dspr2.c, cblas/dswap.c, cblas/dsymm.c, cblas/dsymv.c, cblas/dsyr.c, cblas/dsyr2.c, cblas/dsyr2k.c, cblas/dsyrk.c, cblas/dtbmv.c, cblas/dtbsv.c, cblas/dtpmv.c, cblas/dtpsv.c, cblas/dtrmm.c, cblas/dtrmv.c, cblas/dtrsm.c, cblas/dtrsv.c, cblas/dzasum.c, cblas/dznrm2.c, cblas/gsl_cblas.h, cblas/hypot.c, cblas/icamax.c, cblas/idamax.c, cblas/isamax.c, cblas/izamax.c, cblas/sasum.c, cblas/saxpy.c, cblas/scasum.c, cblas/scnrm2.c, cblas/scopy.c, cblas/sdot.c, cblas/sdsdot.c, cblas/sgbmv.c, cblas/sgemm.c, cblas/sgemv.c, cblas/sger.c, cblas/snrm2.c, cblas/source_asum_c.h, cblas/source_asum_r.h, cblas/source_axpy_c.h, cblas/source_axpy_r.h, cblas/source_copy_c.h, cblas/source_copy_r.h, cblas/source_dot_c.h, cblas/source_dot_r.h, cblas/source_gbmv_c.h, cblas/source_gbmv_r.h, cblas/source_gemm_c.h, cblas/source_gemm_r.h, cblas/source_gemv_c.h, cblas/source_gemv_r.h, cblas/source_ger.h, cblas/source_gerc.h, cblas/source_geru.h, cblas/source_hbmv.h, cblas/source_hemm.h, cblas/source_hemv.h, cblas/source_her.h, cblas/source_her2.h, cblas/source_her2k.h, cblas/source_herk.h, cblas/source_hpmv.h, cblas/source_hpr.h, cblas/source_hpr2.h, cblas/source_iamax_c.h, cblas/source_iamax_r.h, cblas/source_nrm2_c.h, cblas/source_nrm2_r.h, cblas/source_rot.h, cblas/source_rotg.h, cblas/source_rotm.h, cblas/source_rotmg.h, cblas/source_sbmv.h, cblas/source_scal_c.h, cblas/source_scal_c_s.h, cblas/source_scal_r.h, cblas/source_spmv.h, cblas/source_spr.h, cblas/source_spr2.h, cblas/source_swap_c.h, cblas/source_swap_r.h, cblas/source_symm_c.h, cblas/source_symm_r.h, cblas/source_symv.h, cblas/source_syr.h, cblas/source_syr2.h, cblas/source_syr2k_c.h, cblas/source_syr2k_r.h, cblas/source_syrk_c.h, cblas/source_syrk_r.h, cblas/source_tbmv_c.h, cblas/source_tbmv_r.h, cblas/source_tbsv_c.h, cblas/source_tbsv_r.h, cblas/source_tpmv_c.h, cblas/source_tpmv_r.h, cblas/source_tpsv_c.h, cblas/source_tpsv_r.h, cblas/source_trmm_c.h, cblas/source_trmm_r.h, cblas/source_trmv_c.h, cblas/source_trmv_r.h, cblas/source_trsm_c.h, cblas/source_trsm_r.h, cblas/source_trsv_c.h, cblas/source_trsv_r.h, cblas/srot.c, cblas/srotg.c, cblas/srotm.c, cblas/srotmg.c, cblas/ssbmv.c, cblas/sscal.c, cblas/sspmv.c, cblas/sspr.c, cblas/sspr2.c, cblas/sswap.c, cblas/ssymm.c, cblas/ssymv.c, cblas/ssyr.c, cblas/ssyr2.c, cblas/ssyr2k.c, cblas/ssyrk.c, cblas/stbmv.c, cblas/stbsv.c, cblas/stpmv.c, cblas/stpsv.c, cblas/strmm.c, cblas/strmv.c, cblas/strsm.c, cblas/strsv.c, cblas/test.c, cblas/test_amax.c, cblas/test_asum.c, cblas/test_axpy.c, cblas/test_copy.c, cblas/test_dot.c, cblas/test_gbmv.c, cblas/test_gemm.c, cblas/test_gemv.c, cblas/test_ger.c, cblas/test_hbmv.c, cblas/test_hemm.c, cblas/test_hemv.c, cblas/test_her.c, cblas/test_her2.c, cblas/test_her2k.c, cblas/test_herk.c, cblas/test_hpmv.c, cblas/test_hpr.c, cblas/test_hpr2.c, cblas/test_nrm2.c, cblas/test_rot.c, cblas/test_rotg.c, cblas/test_rotm.c, cblas/test_rotmg.c, cblas/test_sbmv.c, cblas/test_scal.c, cblas/test_spmv.c, cblas/test_spr.c, cblas/test_spr2.c, cblas/test_swap.c, cblas/test_symm.c, cblas/test_symv.c, cblas/test_syr.c, cblas/test_syr2.c, cblas/test_syr2k.c, cblas/test_syrk.c, cblas/test_tbmv.c, cblas/test_tbsv.c, cblas/test_tpmv.c, cblas/test_tpsv.c, cblas/test_trmm.c, cblas/test_trmv.c, cblas/test_trsm.c, cblas/test_trsv.c, cblas/tests.c, cblas/tests.h, cblas/xerbla.c, cblas/zaxpy.c, cblas/zcopy.c, cblas/zdotc_sub.c, cblas/zdotu_sub.c, cblas/zdscal.c, cblas/zgbmv.c, cblas/zgemm.c, cblas/zgemv.c, cblas/zgerc.c, cblas/zgeru.c, cblas/zhbmv.c, cblas/zhemm.c, cblas/zhemv.c, cblas/zher.c, cblas/zher2.c, cblas/zher2k.c, cblas/zherk.c, cblas/zhpmv.c, cblas/zhpr.c, cblas/zhpr2.c, cblas/zscal.c, cblas/zswap.c, cblas/zsymm.c, cblas/zsyr2k.c, cblas/zsyrk.c, cblas/ztbmv.c, cblas/ztbsv.c, cblas/ztpmv.c, cblas/ztpsv.c, cblas/ztrmm.c, cblas/ztrmv.c, cblas/ztrsm.c, cblas/ztrsv.c, cdf/ChangeLog, cdf/Makefile.am, cdf/Makefile.in, cdf/beta.c, cdf/beta_inc.c, cdf/betainv.c, cdf/binomial.c, cdf/cauchy.c, cdf/cauchyinv.c, cdf/chisq.c, cdf/chisqinv.c, cdf/error.h, cdf/exponential.c, cdf/exponentialinv.c, cdf/exppow.c, cdf/fdist.c, cdf/fdistinv.c, cdf/flat.c, cdf/flatinv.c, cdf/gamma.c, cdf/gammainv.c, cdf/gauss.c, cdf/gaussinv.c, cdf/geometric.c, cdf/gsl_cdf.h, cdf/gumbel1.c, cdf/gumbel1inv.c, cdf/gumbel2.c, cdf/gumbel2inv.c, cdf/hypergeometric.c, cdf/laplace.c, cdf/laplaceinv.c, cdf/logistic.c, cdf/logisticinv.c, cdf/lognormal.c, cdf/lognormalinv.c, cdf/nbinomial.c, cdf/pareto.c, cdf/paretoinv.c, cdf/pascal.c, cdf/poisson.c, cdf/rat_eval.h, cdf/rayleigh.c, cdf/rayleighinv.c, cdf/tdist.c, cdf/tdistinv.c, cdf/test.c, cdf/test_auto.c, cdf/weibull.c, cdf/weibullinv.c, cheb/ChangeLog, cheb/Makefile.am, cheb/Makefile.in, cheb/deriv.c, cheb/eval.c, cheb/gsl_chebyshev.h, cheb/init.c, cheb/integ.c, cheb/test.c, combination/ChangeLog, combination/Makefile.am, combination/Makefile.in, combination/combination.c, combination/file.c, combination/gsl_combination.h, combination/init.c, combination/test.c, complex/ChangeLog, complex/Makefile.am, complex/Makefile.in, complex/TODO, complex/gsl_complex.h, complex/gsl_complex_math.h, complex/math.c, complex/results.h, complex/results1.h, complex/results_real.h, complex/test.c, const/ChangeLog, const/Makefile.am, const/Makefile.in, const/TODO, const/gsl_const.h, const/gsl_const_cgs.h, const/gsl_const_cgsm.h, const/gsl_const_mks.h, const/gsl_const_mksa.h, const/gsl_const_num.h, const/test.c, deriv/ChangeLog, deriv/Makefile.am, deriv/Makefile.in, deriv/deriv.c, deriv/gsl_deriv.h, deriv/test.c, dht/ChangeLog, dht/Makefile.am, dht/Makefile.in, dht/dht.c, dht/gsl_dht.h, dht/test.c, diff/ChangeLog, diff/Makefile.am, diff/Makefile.in, diff/diff.c, diff/gsl_diff.h, diff/test.c, doc/12-cities.eps, doc/ChangeLog, doc/Makefile.am, doc/Makefile.in, doc/algorithm.sty, doc/algorithmic.sty, doc/autoconf.texi, doc/blas.texi, doc/bspline.eps, doc/bspline.texi, doc/calc.sty, doc/cblas.texi, doc/cheb.eps, doc/cheb.texi, doc/combination.texi, doc/complex.texi, doc/const.texi, doc/debug.texi, doc/dht.texi, doc/diff.texi, doc/dwt-orig.eps, doc/dwt-samp.eps, doc/dwt.texi, doc/eigen.texi, doc/err.texi, doc/fdl.texi, doc/fft-complex-radix2-f.eps, doc/fft-complex-radix2-t.eps, doc/fft-complex-radix2.eps, doc/fft-real-mixedradix.eps, doc/fft.texi, doc/fftalgorithms.bib, doc/fftalgorithms.tex, doc/final-route.eps, doc/fit-exp.eps, doc/fit-wlinear.eps, doc/fit-wlinear2.eps, doc/fitting.texi, doc/freemanuals.texi, doc/gpl.texi, doc/gsl-config.1, doc/gsl-design.texi, doc/gsl-histogram.1, doc/gsl-randist.1, doc/gsl-ref.info, doc/gsl-ref.info-1, doc/gsl-ref.info-2, doc/gsl-ref.info-3, doc/gsl-ref.info-4, doc/gsl-ref.info-5, doc/gsl-ref.info-6, doc/gsl-ref.texi, doc/gsl.3, doc/histogram.eps, doc/histogram.texi, doc/histogram2d.eps, doc/ieee754.texi, doc/initial-route.eps, doc/integration.texi, doc/interp.texi, doc/interp2.eps, doc/interpp2.eps, doc/intro.texi, doc/landau.dat, doc/linalg.texi, doc/math.texi, doc/mdate-sh, doc/min-interval.eps, doc/min.texi, doc/montecarlo.texi, doc/multifit.texi, doc/multimin.eps, doc/multimin.texi, doc/multiroots.texi, doc/ntuple.eps, doc/ntuple.texi, doc/ode-initval.texi, doc/permutation.texi, doc/poly.texi, doc/qrng.eps, doc/qrng.texi, doc/rand-bernoulli.tex, doc/rand-beta.tex, doc/rand-binomial.tex, doc/rand-bivariate-gaussian.tex, doc/rand-cauchy.tex, doc/rand-chisq.tex, doc/rand-erlang.tex, doc/rand-exponential.tex, doc/rand-exppow.tex, doc/rand-fdist.tex, doc/rand-flat.tex, doc/rand-gamma.tex, doc/rand-gaussian-tail.tex, doc/rand-gaussian.tex, doc/rand-geometric.tex, doc/rand-gumbel.tex, doc/rand-gumbel1.tex, doc/rand-gumbel2.tex, doc/rand-hypergeometric.tex, doc/rand-landau.tex, doc/rand-laplace.tex, doc/rand-levy.tex, doc/rand-levyskew.tex, doc/rand-logarithmic.tex, doc/rand-logistic.tex, doc/rand-lognormal.tex, doc/rand-nbinomial.tex, doc/rand-pareto.tex, doc/rand-pascal.tex, doc/rand-poisson.tex, doc/rand-rayleigh-tail.tex, doc/rand-rayleigh.tex, doc/rand-tdist.tex, doc/rand-weibull.tex, doc/randist.texi, doc/random-walk.tex, doc/randplots.gnp, doc/rng.texi, doc/roots-bisection.eps, doc/roots-false-position.eps, doc/roots-newtons-method.eps, doc/roots-secant-method.eps, doc/roots.texi, doc/siman-energy.eps, doc/siman-test.eps, doc/siman.texi, doc/sort.texi, doc/specfunc-airy.texi, doc/specfunc-bessel.texi, doc/specfunc-clausen.texi, doc/specfunc-coulomb.texi, doc/specfunc-coupling.texi, doc/specfunc-dawson.texi, doc/specfunc-debye.texi, doc/specfunc-dilog.texi, doc/specfunc-elementary.texi, doc/specfunc-ellint.texi, doc/specfunc-elljac.texi, doc/specfunc-erf.texi, doc/specfunc-exp.texi, doc/specfunc-expint.texi, doc/specfunc-fermi-dirac.texi, doc/specfunc-gamma.texi, doc/specfunc-gegenbauer.texi, doc/specfunc-hyperg.texi, doc/specfunc-laguerre.texi, doc/specfunc-lambert.texi, doc/specfunc-legendre.texi, doc/specfunc-log.texi, doc/specfunc-mathieu.texi, doc/specfunc-pow-int.texi, doc/specfunc-psi.texi, doc/specfunc-synchrotron.texi, doc/specfunc-transport.texi, doc/specfunc-trig.texi, doc/specfunc-zeta.texi, doc/specfunc.texi, doc/stamp-vti, doc/statistics.texi, doc/sum.texi, doc/texinfo.tex, doc/usage.texi, doc/vdp.eps, doc/vectors.texi, doc/version-ref.texi, doc/examples/blas.c, doc/examples/blas.out, doc/examples/block.c, doc/examples/block.out, doc/examples/bspline.c, doc/examples/cblas.c, doc/examples/cblas.out, doc/examples/cdf.c, doc/examples/cdf.out, doc/examples/cheb.c, doc/examples/combination.c, doc/examples/combination.out, doc/examples/const.c, doc/examples/const.out, doc/examples/demo_fn.c, doc/examples/demo_fn.h, doc/examples/diff.c, doc/examples/diff.out, doc/examples/dwt.c, doc/examples/dwt.dat, doc/examples/ecg.dat, doc/examples/eigen.c, doc/examples/eigen_nonsymm.c, doc/examples/expfit.c, doc/examples/fft.c, doc/examples/fftmr.c, doc/examples/fftreal.c, doc/examples/fitting.c, doc/examples/fitting2.c, doc/examples/fitting3.c, doc/examples/histogram.c, doc/examples/histogram2d.c, doc/examples/ieee.c, doc/examples/ieeeround.c, doc/examples/integration.c, doc/examples/integration.out, doc/examples/interp.c, doc/examples/interpp.c, doc/examples/intro.c, doc/examples/intro.out, doc/examples/linalglu.c, doc/examples/linalglu.out, doc/examples/matrix.c, doc/examples/matrixw.c, doc/examples/min.c, doc/examples/min.out, doc/examples/monte.c, doc/examples/nlfit.c, doc/examples/ntupler.c, doc/examples/ntuplew.c, doc/examples/ode-initval.c, doc/examples/odefixed.c, doc/examples/permseq.c, doc/examples/permshuffle.c, doc/examples/polyroots.c, doc/examples/polyroots.out, doc/examples/qrng.c, doc/examples/randpoisson.2.out, doc/examples/randpoisson.c, doc/examples/randpoisson.out, doc/examples/randwalk.c, doc/examples/rng.c, doc/examples/rng.out, doc/examples/rngunif.2.out, doc/examples/rngunif.c, doc/examples/rngunif.out, doc/examples/rootnewt.c, doc/examples/roots.c, doc/examples/siman.c, doc/examples/sortsmall.c, doc/examples/sortsmall.out, doc/examples/specfun.c, doc/examples/specfun.out, doc/examples/specfun_e.c, doc/examples/specfun_e.out, doc/examples/stat.c, doc/examples/stat.out, doc/examples/statsort.c, doc/examples/statsort.out, doc/examples/sum.c, doc/examples/sum.out, doc/examples/vector.c, doc/examples/vectorr.c, doc/examples/vectorview.c, doc/examples/vectorview.out, doc/examples/vectorw.c, eigen/ChangeLog, eigen/Makefile.am, eigen/Makefile.in, eigen/TODO, eigen/francis.c, eigen/gsl_eigen.h, eigen/herm.c, eigen/hermv.c, eigen/jacobi.c, eigen/nonsymm.c, eigen/nonsymmv.c, eigen/qrstep.c, eigen/schur.c, eigen/schur.h, eigen/sort.c, eigen/symm.c, eigen/symmv.c, eigen/test.c, err/ChangeLog, 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statistics/wskew_source.c, statistics/wvariance.c, statistics/wvariance_source.c, sum/ChangeLog, sum/Makefile.am, sum/Makefile.in, sum/gsl_sum.h, sum/levin_u.c, sum/levin_utrunc.c, sum/test.c, sum/work_u.c, sum/work_utrunc.c, sys/ChangeLog, sys/Makefile.am, sys/Makefile.in, sys/coerce.c, sys/expm1.c, sys/fcmp.c, sys/fdiv.c, sys/gsl_sys.h, sys/hypot.c, sys/infnan.c, sys/invhyp.c, sys/ldfrexp.c, sys/log1p.c, sys/minmax.c, sys/pow_int.c, sys/prec.c, sys/test.c, test/ChangeLog, test/Makefile.am, test/Makefile.in, test/gsl_test.h, test/results.c, utils/Makefile.am, utils/Makefile.in, utils/README, utils/memcpy.c, utils/memmove.c, utils/placeholder.c, utils/strdup.c, utils/strtol.c, utils/strtoul.c, utils/system.h, vector/ChangeLog, vector/Makefile.am, vector/Makefile.in, vector/TODO, vector/copy.c, vector/copy_source.c, vector/file.c, vector/file_source.c, vector/gsl_vector.h, vector/gsl_vector_char.h, vector/gsl_vector_complex.h, vector/gsl_vector_complex_double.h, vector/gsl_vector_complex_float.h, vector/gsl_vector_complex_long_double.h, vector/gsl_vector_double.h, vector/gsl_vector_float.h, vector/gsl_vector_int.h, vector/gsl_vector_long.h, vector/gsl_vector_long_double.h, vector/gsl_vector_short.h, vector/gsl_vector_uchar.h, vector/gsl_vector_uint.h, vector/gsl_vector_ulong.h, vector/gsl_vector_ushort.h, vector/init.c, vector/init_source.c, vector/minmax.c, vector/minmax_source.c, vector/oper.c, vector/oper_source.c, vector/prop.c, vector/prop_source.c, vector/reim.c, vector/reim_source.c, vector/subvector.c, vector/subvector_source.c, vector/swap.c, vector/swap_source.c, vector/test.c, vector/test_complex_source.c, vector/test_source.c, vector/test_static.c, vector/vector.c, vector/vector_source.c, vector/view.c, vector/view.h, vector/view_source.c, wavelet/ChangeLog, wavelet/Makefile.am, wavelet/Makefile.in, wavelet/TODO, wavelet/bspline.c, wavelet/daubechies.c, wavelet/dwt.c, wavelet/gsl_wavelet.h, wavelet/gsl_wavelet2d.h, wavelet/haar.c, wavelet/test.c, wavelet/wavelet.c: New files.
Diffstat (limited to 'gsl-1.9/monte/vegas.c')
-rw-r--r--gsl-1.9/monte/vegas.c864
1 files changed, 864 insertions, 0 deletions
diff --git a/gsl-1.9/monte/vegas.c b/gsl-1.9/monte/vegas.c
new file mode 100644
index 0000000..1a3eb21
--- /dev/null
+++ b/gsl-1.9/monte/vegas.c
@@ -0,0 +1,864 @@
+/* monte/vegas.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Michael Booth
+ *
+ * This program 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 2 of the License, or (at
+ * your option) any later version.
+ *
+ * This program 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 this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author: MJB */
+/* Modified by: Brian Gough, 12/2000 */
+
+/* This is an implementation of the adaptive Monte-Carlo algorithm
+ of G. P. Lepage, originally described in J. Comp. Phys. 27, 192(1978).
+ The current version of the algorithm was described in the Cornell
+ preprint CLNS-80/447 of March, 1980.
+
+ This code follows most closely the c version by D.R.Yennie, coded
+ in 1984.
+
+ The input coordinates are x[j], with upper and lower limits xu[j]
+ and xl[j]. The integration length in the j-th direction is
+ delx[j]. Each coordinate x[j] is rescaled to a variable y[j] in
+ the range 0 to 1. The range is divided into bins with boundaries
+ xi[i][j], where i=0 corresponds to y=0 and i=bins to y=1. The grid
+ is refined (ie, bins are adjusted) using d[i][j] which is some
+ variation on the squared sum. A third parameter used in defining
+ the real coordinate using random numbers is called z. It ranges
+ from 0 to bins. Its integer part gives the lower index of the bin
+ into which a call is to be placed, and the remainder gives the
+ location inside the bin.
+
+ When stratified sampling is used the bins are grouped into boxes,
+ and the algorithm allocates an equal number of function calls to
+ each box.
+
+ The variable alpha controls how "stiff" the rebinning algorithm is.
+ alpha = 0 means never change the grid. Alpha is typically set between
+ 1 and 2.
+
+ */
+
+/* configuration headers */
+#include <config.h>
+
+/* standard headers */
+#include <math.h>
+#include <stdio.h>
+
+/* gsl headers */
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_monte_vegas.h>
+
+/* lib-specific headers */
+#define BINS_MAX 50 /* even integer, will be divided by two */
+
+/* A separable grid with coordinates and values */
+#define COORD(s,i,j) ((s)->xi[(i)*(s)->dim + (j)])
+#define NEW_COORD(s,i) ((s)->xin[(i)])
+#define VALUE(s,i,j) ((s)->d[(i)*(s)->dim + (j)])
+
+/* predeclare functions */
+
+typedef int coord;
+
+static void init_grid (gsl_monte_vegas_state * s, double xl[], double xu[],
+ size_t dim);
+static void reset_grid_values (gsl_monte_vegas_state * s);
+static void init_box_coord (gsl_monte_vegas_state * s, coord box[]);
+static int change_box_coord (gsl_monte_vegas_state * s, coord box[]);
+static void accumulate_distribution (gsl_monte_vegas_state * s, coord bin[],
+ double y);
+static void random_point (double x[], coord bin[], double *bin_vol,
+ const coord box[],
+ const double xl[], const double xu[],
+ gsl_monte_vegas_state * s, gsl_rng * r);
+static void resize_grid (gsl_monte_vegas_state * s, unsigned int bins);
+static void refine_grid (gsl_monte_vegas_state * s);
+
+static void print_lim (gsl_monte_vegas_state * state,
+ double xl[], double xu[], unsigned long dim);
+static void print_head (gsl_monte_vegas_state * state,
+ unsigned long num_dim, unsigned long calls,
+ unsigned int it_num,
+ unsigned int bins, unsigned int boxes);
+static void print_res (gsl_monte_vegas_state * state,
+ unsigned int itr, double res, double err,
+ double cum_res, double cum_err,
+ double chi_sq);
+static void print_dist (gsl_monte_vegas_state * state, unsigned long dim);
+static void print_grid (gsl_monte_vegas_state * state, unsigned long dim);
+
+int
+gsl_monte_vegas_integrate (gsl_monte_function * f,
+ double xl[], double xu[],
+ size_t dim, size_t calls,
+ gsl_rng * r,
+ gsl_monte_vegas_state * state,
+ double *result, double *abserr)
+{
+ double cum_int, cum_sig;
+ size_t i, k, it;
+
+ if (dim != state->dim)
+ {
+ GSL_ERROR ("number of dimensions must match allocated size", GSL_EINVAL);
+ }
+
+ for (i = 0; i < dim; i++)
+ {
+ if (xu[i] <= xl[i])
+ {
+ GSL_ERROR ("xu must be greater than xl", GSL_EINVAL);
+ }
+
+ if (xu[i] - xl[i] > GSL_DBL_MAX)
+ {
+ GSL_ERROR ("Range of integration is too large, please rescale",
+ GSL_EINVAL);
+ }
+ }
+
+ if (state->stage == 0)
+ {
+ init_grid (state, xl, xu, dim);
+
+ if (state->verbose >= 0)
+ {
+ print_lim (state, xl, xu, dim);
+ }
+ }
+
+ if (state->stage <= 1)
+ {
+ state->wtd_int_sum = 0;
+ state->sum_wgts = 0;
+ state->chi_sum = 0;
+ state->it_num = 1;
+ state->samples = 0;
+ }
+
+ if (state->stage <= 2)
+ {
+ unsigned int bins = state->bins_max;
+ unsigned int boxes = 1;
+
+ if (state->mode != GSL_VEGAS_MODE_IMPORTANCE_ONLY)
+ {
+ /* shooting for 2 calls/box */
+
+ boxes = floor (pow (calls / 2.0, 1.0 / dim));
+ state->mode = GSL_VEGAS_MODE_IMPORTANCE;
+
+ if (2 * boxes >= state->bins_max)
+ {
+ /* if bins/box < 2 */
+ int box_per_bin = GSL_MAX (boxes / state->bins_max, 1);
+
+ bins = GSL_MIN(boxes / box_per_bin, state->bins_max);
+ boxes = box_per_bin * bins;
+
+ state->mode = GSL_VEGAS_MODE_STRATIFIED;
+ }
+ }
+
+ {
+ double tot_boxes = pow ((double) boxes, (double) dim);
+ state->calls_per_box = GSL_MAX (calls / tot_boxes, 2);
+ calls = state->calls_per_box * tot_boxes;
+ }
+
+ /* total volume of x-space/(avg num of calls/bin) */
+ state->jac = state->vol * pow ((double) bins, (double) dim) / calls;
+
+ state->boxes = boxes;
+
+ /* If the number of bins changes from the previous invocation, bins
+ are expanded or contracted accordingly, while preserving bin
+ density */
+
+ if (bins != state->bins)
+ {
+ resize_grid (state, bins);
+
+ if (state->verbose > 1)
+ {
+ print_grid (state, dim);
+ }
+ }
+
+ if (state->verbose >= 0)
+ {
+ print_head (state,
+ dim, calls, state->it_num, state->bins, state->boxes);
+ }
+ }
+
+ state->it_start = state->it_num;
+
+ cum_int = 0.0;
+ cum_sig = 0.0;
+
+ state->chisq = 0.0;
+
+ for (it = 0; it < state->iterations; it++)
+ {
+ double intgrl = 0.0, intgrl_sq = 0.0;
+ double sig = 0.0;
+ double wgt;
+ size_t calls_per_box = state->calls_per_box;
+ double jacbin = state->jac;
+ double *x = state->x;
+ coord *bin = state->bin;
+
+ state->it_num = state->it_start + it;
+
+ reset_grid_values (state);
+ init_box_coord (state, state->box);
+
+ do
+ {
+ double m = 0, q = 0;
+ double f_sq_sum = 0.0;
+
+ for (k = 0; k < calls_per_box; k++)
+ {
+ double fval, bin_vol;
+
+ random_point (x, bin, &bin_vol, state->box, xl, xu, state, r);
+
+ fval = jacbin * bin_vol * GSL_MONTE_FN_EVAL (f, x);
+
+ /* recurrence for mean and variance */
+
+ {
+ double d = fval - m;
+ m += d / (k + 1.0);
+ q += d * d * (k / (k + 1.0));
+ }
+
+ if (state->mode != GSL_VEGAS_MODE_STRATIFIED)
+ {
+ double f_sq = fval * fval;
+ accumulate_distribution (state, bin, f_sq);
+ }
+ }
+
+ intgrl += m * calls_per_box;
+
+ f_sq_sum = q * calls_per_box ;
+
+ sig += f_sq_sum ;
+
+ if (state->mode == GSL_VEGAS_MODE_STRATIFIED)
+ {
+ accumulate_distribution (state, bin, f_sq_sum);
+ }
+ }
+ while (change_box_coord (state, state->box));
+
+ /* Compute final results for this iteration */
+
+ sig = sig / (calls_per_box - 1.0) ;
+
+ if (sig > 0)
+ {
+ wgt = 1.0 / sig;
+ }
+ else if (state->sum_wgts > 0)
+ {
+ wgt = state->sum_wgts / state->samples;
+ }
+ else
+ {
+ wgt = 0.0;
+ }
+
+ intgrl_sq = intgrl * intgrl;
+
+ state->result = intgrl;
+ state->sigma = sqrt(sig);
+
+ if (wgt > 0.0)
+ {
+ state->samples++ ;
+ state->sum_wgts += wgt;
+ state->wtd_int_sum += intgrl * wgt;
+ state->chi_sum += intgrl_sq * wgt;
+
+ cum_int = state->wtd_int_sum / state->sum_wgts;
+ cum_sig = sqrt (1 / state->sum_wgts);
+
+ if (state->samples > 1)
+ {
+ state->chisq = (state->chi_sum - state->wtd_int_sum * cum_int) /
+ (state->samples - 1.0);
+ }
+ }
+ else
+ {
+ cum_int += (intgrl - cum_int) / (it + 1.0);
+ cum_sig = 0.0;
+ }
+
+
+ if (state->verbose >= 0)
+ {
+ print_res (state,
+ state->it_num, intgrl, sqrt (sig), cum_int, cum_sig,
+ state->chisq);
+ if (it + 1 == state->iterations && state->verbose > 0)
+ {
+ print_grid (state, dim);
+ }
+ }
+
+ if (state->verbose > 1)
+ {
+ print_dist (state, dim);
+ }
+
+ refine_grid (state);
+
+ if (state->verbose > 1)
+ {
+ print_grid (state, dim);
+ }
+
+ }
+
+ /* By setting stage to 1 further calls will generate independent
+ estimates based on the same grid, although it may be rebinned. */
+
+ state->stage = 1;
+
+ *result = cum_int;
+ *abserr = cum_sig;
+
+ return GSL_SUCCESS;
+}
+
+
+
+gsl_monte_vegas_state *
+gsl_monte_vegas_alloc (size_t dim)
+{
+ gsl_monte_vegas_state *s =
+ (gsl_monte_vegas_state *) malloc (sizeof (gsl_monte_vegas_state));
+
+ if (s == 0)
+ {
+ GSL_ERROR_VAL ("failed to allocate space for vegas state struct",
+ GSL_ENOMEM, 0);
+ }
+
+ s->delx = (double *) malloc (dim * sizeof (double));
+
+ if (s->delx == 0)
+ {
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for delx", GSL_ENOMEM, 0);
+ }
+
+ s->d = (double *) malloc (BINS_MAX * dim * sizeof (double));
+
+ if (s->d == 0)
+ {
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for d", GSL_ENOMEM, 0);
+ }
+
+ s->xi = (double *) malloc ((BINS_MAX + 1) * dim * sizeof (double));
+
+ if (s->xi == 0)
+ {
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for xi", GSL_ENOMEM, 0);
+ }
+
+ s->xin = (double *) malloc ((BINS_MAX + 1) * sizeof (double));
+
+ if (s->xin == 0)
+ {
+ free (s->xi);
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for xin", GSL_ENOMEM, 0);
+ }
+
+ s->weight = (double *) malloc (BINS_MAX * sizeof (double));
+
+ if (s->weight == 0)
+ {
+ free (s->xin);
+ free (s->xi);
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for xin", GSL_ENOMEM, 0);
+ }
+
+ s->box = (coord *) malloc (dim * sizeof (coord));
+
+ if (s->box == 0)
+ {
+ free (s->weight);
+ free (s->xin);
+ free (s->xi);
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for box", GSL_ENOMEM, 0);
+ }
+
+ s->bin = (coord *) malloc (dim * sizeof (coord));
+
+ if (s->bin == 0)
+ {
+ free (s->box);
+ free (s->weight);
+ free (s->xin);
+ free (s->xi);
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for bin", GSL_ENOMEM, 0);
+ }
+
+ s->x = (double *) malloc (dim * sizeof (double));
+
+ if (s->x == 0)
+ {
+ free (s->bin);
+ free (s->box);
+ free (s->weight);
+ free (s->xin);
+ free (s->xi);
+ free (s->d);
+ free (s->delx);
+ free (s);
+ GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
+ }
+
+ s->dim = dim;
+ s->bins_max = BINS_MAX;
+
+ gsl_monte_vegas_init (s);
+
+ return s;
+}
+
+/* Set some default values and whatever */
+int
+gsl_monte_vegas_init (gsl_monte_vegas_state * state)
+{
+ state->stage = 0;
+ state->alpha = 1.5;
+ state->verbose = -1;
+ state->iterations = 5;
+ state->mode = GSL_VEGAS_MODE_IMPORTANCE;
+ state->chisq = 0;
+ state->bins = state->bins_max;
+ state->ostream = stdout;
+
+ return GSL_SUCCESS;
+}
+
+void
+gsl_monte_vegas_free (gsl_monte_vegas_state * s)
+{
+ free (s->x);
+ free (s->delx);
+ free (s->d);
+ free (s->xi);
+ free (s->xin);
+ free (s->weight);
+ free (s->box);
+ free (s->bin);
+ free (s);
+}
+
+static void
+init_box_coord (gsl_monte_vegas_state * s, coord box[])
+{
+ size_t i;
+
+ size_t dim = s->dim;
+
+ for (i = 0; i < dim; i++)
+ {
+ box[i] = 0;
+ }
+}
+
+/* change_box_coord steps through the box coord like
+ {0,0}, {0, 1}, {0, 2}, {0, 3}, {1, 0}, {1, 1}, {1, 2}, ...
+*/
+static int
+change_box_coord (gsl_monte_vegas_state * s, coord box[])
+{
+ int j = s->dim - 1;
+
+ int ng = s->boxes;
+
+ while (j >= 0)
+ {
+ box[j] = (box[j] + 1) % ng;
+
+ if (box[j] != 0)
+ {
+ return 1;
+ }
+
+ j--;
+ }
+
+ return 0;
+}
+
+static void
+init_grid (gsl_monte_vegas_state * s, double xl[], double xu[], size_t dim)
+{
+ size_t j;
+
+ double vol = 1.0;
+
+ s->bins = 1;
+
+ for (j = 0; j < dim; j++)
+ {
+ double dx = xu[j] - xl[j];
+ s->delx[j] = dx;
+ vol *= dx;
+
+ COORD (s, 0, j) = 0.0;
+ COORD (s, 1, j) = 1.0;
+ }
+
+ s->vol = vol;
+}
+
+
+static void
+reset_grid_values (gsl_monte_vegas_state * s)
+{
+ size_t i, j;
+
+ size_t dim = s->dim;
+ size_t bins = s->bins;
+
+ for (i = 0; i < bins; i++)
+ {
+ for (j = 0; j < dim; j++)
+ {
+ VALUE (s, i, j) = 0.0;
+ }
+ }
+}
+
+static void
+accumulate_distribution (gsl_monte_vegas_state * s, coord bin[], double y)
+{
+ size_t j;
+ size_t dim = s->dim;
+
+ for (j = 0; j < dim; j++)
+ {
+ int i = bin[j];
+ VALUE (s, i, j) += y;
+ }
+}
+
+static void
+random_point (double x[], coord bin[], double *bin_vol,
+ const coord box[], const double xl[], const double xu[],
+ gsl_monte_vegas_state * s, gsl_rng * r)
+{
+ /* Use the random number generator r to return a random position x
+ in a given box. The value of bin gives the bin location of the
+ random position (there may be several bins within a given box) */
+
+ double vol = 1.0;
+
+ size_t j;
+
+ size_t dim = s->dim;
+ size_t bins = s->bins;
+ size_t boxes = s->boxes;
+
+ DISCARD_POINTER(xu); /* prevent warning about unused parameter */
+
+ for (j = 0; j < dim; ++j)
+ {
+ /* box[j] + ran gives the position in the box units, while z
+ is the position in bin units. */
+
+ double z = ((box[j] + gsl_rng_uniform_pos (r)) / boxes) * bins;
+
+ int k = z;
+
+ double y, bin_width;
+
+ bin[j] = k;
+
+ if (k == 0)
+ {
+ bin_width = COORD (s, 1, j);
+ y = z * bin_width;
+ }
+ else
+ {
+ bin_width = COORD (s, k + 1, j) - COORD (s, k, j);
+ y = COORD (s, k, j) + (z - k) * bin_width;
+ }
+
+ x[j] = xl[j] + y * s->delx[j];
+
+ vol *= bin_width;
+ }
+
+ *bin_vol = vol;
+}
+
+
+static void
+resize_grid (gsl_monte_vegas_state * s, unsigned int bins)
+{
+ size_t j, k;
+ size_t dim = s->dim;
+
+ /* weight is ratio of bin sizes */
+
+ double pts_per_bin = (double) s->bins / (double) bins;
+
+ for (j = 0; j < dim; j++)
+ {
+ double xold;
+ double xnew = 0;
+ double dw = 0;
+ int i = 1;
+
+ for (k = 1; k <= s->bins; k++)
+ {
+ dw += 1.0;
+ xold = xnew;
+ xnew = COORD (s, k, j);
+
+ for (; dw > pts_per_bin; i++)
+ {
+ dw -= pts_per_bin;
+ NEW_COORD (s, i) = xnew - (xnew - xold) * dw;
+ }
+ }
+
+ for (k = 1 ; k < bins; k++)
+ {
+ COORD(s, k, j) = NEW_COORD(s, k);
+ }
+
+ COORD (s, bins, j) = 1;
+ }
+
+ s->bins = bins;
+}
+
+static void
+refine_grid (gsl_monte_vegas_state * s)
+{
+ size_t i, j, k;
+ size_t dim = s->dim;
+ size_t bins = s->bins;
+
+ for (j = 0; j < dim; j++)
+ {
+ double grid_tot_j, tot_weight;
+ double * weight = s->weight;
+
+ double oldg = VALUE (s, 0, j);
+ double newg = VALUE (s, 1, j);
+
+ VALUE (s, 0, j) = (oldg + newg) / 2;
+ grid_tot_j = VALUE (s, 0, j);
+
+ /* This implements gs[i][j] = (gs[i-1][j]+gs[i][j]+gs[i+1][j])/3 */
+
+ for (i = 1; i < bins - 1; i++)
+ {
+ double rc = oldg + newg;
+ oldg = newg;
+ newg = VALUE (s, i + 1, j);
+ VALUE (s, i, j) = (rc + newg) / 3;
+ grid_tot_j += VALUE (s, i, j);
+ }
+ VALUE (s, bins - 1, j) = (newg + oldg) / 2;
+
+ grid_tot_j += VALUE (s, bins - 1, j);
+
+ tot_weight = 0;
+
+ for (i = 0; i < bins; i++)
+ {
+ weight[i] = 0;
+
+ if (VALUE (s, i, j) > 0)
+ {
+ oldg = grid_tot_j / VALUE (s, i, j);
+ /* damped change */
+ weight[i] = pow (((oldg - 1) / oldg / log (oldg)), s->alpha);
+ }
+
+ tot_weight += weight[i];
+
+#ifdef DEBUG
+ printf("weight[%d] = %g\n", i, weight[i]);
+#endif
+ }
+
+ {
+ double pts_per_bin = tot_weight / bins;
+
+ double xold;
+ double xnew = 0;
+ double dw = 0;
+ i = 1;
+
+ for (k = 0; k < bins; k++)
+ {
+ dw += weight[k];
+ xold = xnew;
+ xnew = COORD (s, k + 1, j);
+
+ for (; dw > pts_per_bin; i++)
+ {
+ dw -= pts_per_bin;
+ NEW_COORD (s, i) = xnew - (xnew - xold) * dw / weight[k];
+ }
+ }
+
+ for (k = 1 ; k < bins ; k++)
+ {
+ COORD(s, k, j) = NEW_COORD(s, k);
+ }
+
+ COORD (s, bins, j) = 1;
+ }
+ }
+}
+
+
+static void
+print_lim (gsl_monte_vegas_state * state,
+ double xl[], double xu[], unsigned long dim)
+{
+ unsigned long j;
+
+ fprintf (state->ostream, "The limits of integration are:\n");
+ for (j = 0; j < dim; ++j)
+ fprintf (state->ostream, "\nxl[%lu]=%f xu[%lu]=%f", j, xl[j], j, xu[j]);
+ fprintf (state->ostream, "\n");
+ fflush (state->ostream);
+}
+
+static void
+print_head (gsl_monte_vegas_state * state,
+ unsigned long num_dim, unsigned long calls,
+ unsigned int it_num, unsigned int bins, unsigned int boxes)
+{
+ fprintf (state->ostream,
+ "\nnum_dim=%lu, calls=%lu, it_num=%d, max_it_num=%d ",
+ num_dim, calls, it_num, state->iterations);
+ fprintf (state->ostream,
+ "verb=%d, alph=%.2f,\nmode=%d, bins=%d, boxes=%d\n",
+ state->verbose, state->alpha, state->mode, bins, boxes);
+ fprintf (state->ostream,
+ "\n single.......iteration ");
+ fprintf (state->ostream, "accumulated......results \n");
+
+ fprintf (state->ostream,
+ "iteration integral sigma integral ");
+ fprintf (state->ostream, " sigma chi-sq/it\n\n");
+ fflush (state->ostream);
+
+}
+
+static void
+print_res (gsl_monte_vegas_state * state,
+ unsigned int itr,
+ double res, double err,
+ double cum_res, double cum_err,
+ double chi_sq)
+{
+ fprintf (state->ostream,
+ "%4d %6.4e %10.2e %6.4e %8.2e %10.2e\n",
+ itr, res, err, cum_res, cum_err, chi_sq);
+ fflush (state->ostream);
+}
+
+static void
+print_dist (gsl_monte_vegas_state * state, unsigned long dim)
+{
+ unsigned long i, j;
+ int p = state->verbose;
+ if (p < 1)
+ return;
+
+ for (j = 0; j < dim; ++j)
+ {
+ fprintf (state->ostream, "\n axis %lu \n", j);
+ fprintf (state->ostream, " x g\n");
+ for (i = 0; i < state->bins; i++)
+ {
+ fprintf (state->ostream, "weight [%11.2e , %11.2e] = ",
+ COORD (state, i, j), COORD(state,i+1,j));
+ fprintf (state->ostream, " %11.2e\n", VALUE (state, i, j));
+
+ }
+ fprintf (state->ostream, "\n");
+ }
+ fprintf (state->ostream, "\n");
+ fflush (state->ostream);
+
+}
+
+static void
+print_grid (gsl_monte_vegas_state * state, unsigned long dim)
+{
+ unsigned long i, j;
+ int p = state->verbose;
+ if (p < 1)
+ return;
+
+ for (j = 0; j < dim; ++j)
+ {
+ fprintf (state->ostream, "\n axis %lu \n", j);
+ fprintf (state->ostream, " x \n");
+ for (i = 0; i <= state->bins; i++)
+ {
+ fprintf (state->ostream, "%11.2e", COORD (state, i, j));
+ if (i % 5 == 4)
+ fprintf (state->ostream, "\n");
+ }
+ fprintf (state->ostream, "\n");
+ }
+ fprintf (state->ostream, "\n");
+ fflush (state->ostream);
+
+}
+