From 81b49377edf2d5b08dca4b5ff3132499861244ea Mon Sep 17 00:00:00 2001 From: Arun Isaac Date: Sat, 8 Jan 2022 12:44:52 +0530 Subject: Bunch of unfinished experiments These experiments were in progress towards the end, and never properly finished. I leave the code here in case it turns out to be useful. --- src/sample-on-ellipsoid.sc | 154 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 154 insertions(+) create mode 100644 src/sample-on-ellipsoid.sc (limited to 'src/sample-on-ellipsoid.sc') diff --git a/src/sample-on-ellipsoid.sc b/src/sample-on-ellipsoid.sc new file mode 100644 index 0000000..a3012ed --- /dev/null +++ b/src/sample-on-ellipsoid.sc @@ -0,0 +1,154 @@ +(sc-include "macros/macros") + +(pre-include "gsl/gsl_blas.h") +(pre-include "gsl/gsl_cblas.h") +(pre-include "gsl/gsl_eigen.h") +(pre-include "extent-sampling.h") +(pre-include "nd-random.h") +(pre-include "oracles.h") +(pre-include "utils.h") + +(pre-define ECCENTRICITY 2) +(pre-define DIMENSION 4) + +(pre-define COVARIANCE_SAMPLES 1000) +(pre-define SAMPLES 10000) + +;; We are generalizing ellipsoid sampling with estimation of +;; covariance matrix. +;; +;; We need a fw(alpha) for a non-diagonal but symmetric A. With that, +;; we will know how to normalize the volume estimate. This new +;; fw(alpha) must involve some simple rotation to the eigen basis of +;; A. + +(declare covariance-accumulator + (type (struct (square gsl-matrix*) + (sum gsl-vector*) + (n int)))) + +(define (covariance-accumulator-alloc dimension) (covariance-accumulator int) + (declare accumulator covariance-accumulator) + (set (struct-get accumulator square) (gsl-matrix-alloc dimension dimension)) + (set (struct-get accumulator sum) (gsl-vector-alloc dimension)) + (set (struct-get accumulator n) 0) + (return accumulator)) + +(define (covariance-accumulator-add accumulator sample) (void covariance-accumulator* gsl-vector*) + (define square gsl-matrix* (: accumulator square)) + (cblas-dsyr CblasRowMajor CblasLower (: sample size) 1 + (: sample data) (: sample stride) + (: square data) (: square tda)) + (gsl-vector-add (: accumulator sum) sample) + (incr (: accumulator n))) + +(define (covariance-accumulator-covariance accumulator result) (void covariance-accumulator gsl-matrix*) + (let* ((dim int (: (struct-get accumulator sum) size)) + (n int (struct-get accumulator n)) + (sum gsl-vector* (struct-get accumulator sum)) + (square gsl-matrix* (struct-get accumulator square))) + (gsl-matrix-memcpy result square) + (gsl-matrix-scale result (/ 1.0 (- n 1))) + (cblas-dsyr CblasRowMajor CblasLower dim (/ -1.0 n n) + (: sum data) (: sum stride) + (: result data) (: result tda)))) + +(define (covariance-accumulator-free accumulator) (void covariance-accumulator) + (gsl-matrix-free (struct-get accumulator square)) + (gsl-vector-free (struct-get accumulator sum))) + +(sc-define-syntax (with-covariance-accumulator var dimension body ...) + (with-alloc var covariance-accumulator + (covariance-accumulator-alloc dimension) + covariance-accumulator-free + body ...)) + +(define (matrix-vector-multiply A x y) + (void (const gsl-matrix*) (const gsl-vector*) gsl-vector*) + (cblas-dgemv CblasRowMajor CblasNoTrans (: A size1) (: A size2) + 1 (: A data) (: A tda) + (: x data) (: x stride) 0 (: y data) (: y stride))) + +;; (define (product-of-diagonal-entries mat) +;; (double (const gsl-matrix*)) +;; (define result double 1) +;; ;; TODO: Do not assume matrix is square. +;; (for-i i (: mat size1) +;; (set* result (gsl-matrix-get mat i i))) +;; (return result)) + +(define (product-of-entries vec) (double (const gsl-vector*)) + (define result double 1) + (for-i i (: vec size) + (set* result (gsl-vector-get vec i))) + (return result)) + +(sc-define-syntax (with-eigen-symmv workspace dimension body ...) + (with-alloc workspace gsl-eigen-symmv-workspace* + (gsl-eigen-symmv-alloc dimension) + gsl-eigen-symmv-free + body ...)) + +(define (eigen-symmetric A eval evec) (void gsl-matrix* gsl-vector* gsl-matrix*) + (with-eigen-symmv workspace (: A size1) + (gsl-eigen-symmv A eval evec workspace))) + +(sc-define-syntax (invoke-extent-oracle extent-oracle r x) + ((: extent-oracle oracle) r x (: extent-oracle params))) + +(define (print-vector x) (void gsl-vector*) + (for-i i (: x size) + (printf "%g\t" (gsl-vector-get x i))) + (printf "\n")) + +(define (print-matrix A) (void gsl-matrix*) + (for-i i (: A size1) + (for-i j (: A size2) + (printf "%g\t" (gsl-matrix-get A i j))) + (printf "\n"))) + +(define (volume-by-ellipsoid extent-oracle rng dimension stats) + (void (const extent-oracle-t*) (const gsl-rng*) (unsigned int) gsl-rstat-workspace*) + (let* ((vn double (ln-volume-of-ball dimension))) + (with-square-matrix transform dimension + (with-covariance-accumulator accumulator dimension + (with-vector x dimension + (for-i i COVARIANCE-SAMPLES + (random-direction-vector rng x) + (gsl-vector-scale x (invoke-extent-oracle extent-oracle rng x)) + (covariance-accumulator-add (address-of accumulator) x))) + (covariance-accumulator-covariance accumulator transform)) + (with-vector eval dimension + (with-square-matrix evec dimension + (eigen-symmetric transform eval evec) + (print-vector eval) + (printf "\n") + (print-matrix evec)) + ;; (gsl-matrix-set-identity transform) + ;; (gsl-matrix-set transform 0 0 (* 0.5 ECCENTRICITY)) + (let* ((ln-determinant double (log (product-of-entries eval)))) + (with-vector x dimension + (with-vector y dimension + (for-i i SAMPLES + (random-direction-vector rng x) + (matrix-vector-multiply transform x y) + (let* ((norm double (gsl-blas-dnrm2 y))) + (gsl-vector-scale y (/ norm)) + (gsl-rstat-add (exp (+ vn + (* dimension (- (log (invoke-extent-oracle extent-oracle rng y)) + (log norm))) + ln-determinant)) + stats)))))))))) + +(define (main) (int) + (declare params (struct-variable spheroid-params + (eccentricity ECCENTRICITY))) + (declare oracle (struct-variable extent-oracle-t + (oracle spheroid-extent-oracle) + (params (address-of params)))) + (printf "True volume: %g\n" (spheroid-true-volume DIMENSION (address-of params))) + (with-rng rng + (with-rstats stats + (volume-by-ellipsoid (address-of oracle) rng DIMENSION stats) + (printf "Estimated volume: %g\n" (gsl-rstat-mean stats)))) + (return 0)) -- cgit v1.2.3