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(sc-include "macros/macros")
(pre-include "gsl/gsl_poly.h")
(pre-include "gsl/gsl_sf.h")
(pre-include "extent-sampling.h")
(pre-include "oracles.h")
(pre-include "integrands.h")
(pre-include "utils.h")
(pre-define TRIALS 1000)
(pre-define MAX-EXTENT 1.0)
(sc-define-syntax* (define-polynomial var)
(let ((coefficients (list -0.09375 0.6875 -1.5 1))
(coeff (sc-gensym)))
`(begin
(declare ,coeff (array double ,(length coefficients)))
(array-set* ,coeff ,@coefficients)
(declare ,var (struct-variable polynomial-integrand-params
(coefficients ,coeff)
(degree ,(1- (length coefficients))))))))
(sc-define-syntax (polynomial-map! polynomial i coeff form)
(for-i i (+ 1 (struct-get polynomial degree))
(let* ((coeff double (array-get (struct-get polynomial coefficients)
i)))
(array-set (convert-type (struct-get polynomial coefficients)
double*)
i form))))
(define (polyval polynomial value) (double polynomial-integrand-params double)
(return (gsl-poly-eval (struct-get polynomial coefficients)
(+ 1 (struct-get polynomial degree))
value)))
(sc-define-syntax* (define-polynomial-integrand integrand)
(let ((params (sc-gensym)))
`(begin
(define-polynomial ,params)
(declare ,integrand (struct-variable (const integrand-t)
(integrand polynomial-integrand)
(params (address-of ,params)))))))
(sc-define-syntax* (define-uniform-extent-oracle oracle a b)
(let ((oracle-params (sc-gensym)))
`(begin
(declare ,oracle-params (struct-variable uniform-params
(a ,a)
(b ,b)))
(declare ,oracle (struct-variable extent-oracle-t
(oracle uniform-extent-oracle)
(params (address-of ,oracle-params)))))))
(sc-define-syntax* (experiment integrand true-integral filename)
(let ((rtols (list 0.2 0.1 0.05)))
`(begin
,@(map (lambda (i rtol)
`(begin
(with-data-file fp ,(format #f "integral-~a-~a.dat" filename rtol) "w"
(fprintf fp "dimension\tsamples\n"))))
(iota (length rtols))
rtols)
(for-i-step dimension 10 100 10
(printf "Dimension %d: " dimension)
(with-rstats* samples ,(length rtols)
(for-i trial TRIALS
(with-rstats stats
,@(map (lambda (i rtol)
`(begin
(integral (address-of ,integrand)
(address-of oracle)
(,true-integral dimension)
rng
dimension
,rtol
stats)
(gsl-rstat-add (gsl-rstat-n stats)
(array-get samples ,i))))
(iota (length rtols))
rtols))
(when (= (modulo trial (/ TRIALS 10)) 0)
(printf "%d " trial))
(fflush NULL))
(printf "\n")
,@(map (lambda (i rtol)
`(with-data-file fp ,(format #f "integral-~a-~a.dat" filename rtol) "a"
(fprintf fp "%d\t%g\n" dimension (gsl-rstat-mean (array-get samples ,i)))))
(iota (length rtols))
rtols))))))
(define (true-polynomial-integral dimension)
(double (unsigned int))
(define-polynomial polynomial)
(polynomial-map! polynomial k coeff
(/ coeff (+ dimension k) (+ dimension k 1)))
(return (* (surface-area-of-ball dimension)
(gsl-pow-uint MAX-EXTENT dimension)
(polyval polynomial MAX-EXTENT))))
(define (lower-incomplete-gamma s x)
(double double double)
(return (* (gsl-sf-gamma s)
(gsl-sf-gamma-inc-P s x))))
(define (true-gaussian-integral dimension)
(double (unsigned int))
(return (/ (* (pow 2.0 (- (* dimension 0.5) 1))
(surface-area-of-ball dimension)
(- (* MAX-EXTENT
(lower-incomplete-gamma (* 0.5 dimension)
(* 0.5 (gsl-pow-2 MAX-EXTENT))))
(* (sqrt 2.0)
(lower-incomplete-gamma (* 0.5 (+ dimension 1))
(* 0.5 (gsl-pow-2 MAX-EXTENT))))))
MAX-EXTENT)))
(define (true-x-coordinate-integral dimension)
(double (unsigned int))
(return (/ (* (gsl-pow-uint MAX-EXTENT (1+ dimension))
(surface-area-of-ball (+ dimension 3)))
2.0
(pow M-PI 2)
(+ dimension 2))))
(define (main) (int)
(define-polynomial-integrand -polynomial-integrand)
(declare -gaussian-integrand (struct-variable (const integrand-t)
gaussian-integrand
NULL))
(declare -x-coordinate-integrand (struct-variable (const integrand-t)
x-coordinate-integrand
NULL))
(define-uniform-extent-oracle oracle 0 MAX-EXTENT)
(with-rng rng
(experiment -polynomial-integrand true-polynomial-integral "polynomial")
(experiment -gaussian-integrand true-gaussian-integral "gaussian")
(experiment -x-coordinate-integrand true-x-coordinate-integral "x-coordinate"))
(with-data-file fp "integral-parameters.tex" "w"
(fprintf fp "\\\\newcommand{\\\\integraltrials}{%d}\n" TRIALS))
(return 0))
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