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.
---
 CMakeLists.txt             |   6 ++
 src/centroid.sc            |  66 +++++++++++++++++++
 src/extent-sampling.sc     |  22 +++++++
 src/macros/macros.sc       |  15 +++++
 src/sample-on-ellipsoid.sc | 154 +++++++++++++++++++++++++++++++++++++++++++++
 src/whitening.sc           | 145 ++++++++++++++++++++++++++++++++++++++++++
 6 files changed, 408 insertions(+)
 create mode 100644 src/centroid.sc
 create mode 100644 src/sample-on-ellipsoid.sc
 create mode 100644 src/whitening.sc

diff --git a/CMakeLists.txt b/CMakeLists.txt
index b4fae28..6701515 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -75,6 +75,12 @@ add_executable(integral integral.c)
 target_link_libraries(integral nsmc -lm)
 add_executable(spheroid spheroid.c)
 target_link_libraries(spheroid nsmc)
+add_executable(centroid centroid.c)
+target_link_libraries(centroid nsmc)
+add_executable(whitening whitening.c)
+target_link_libraries(whitening nsmc -lm)
+add_executable(sample-on-ellipsoid sample-on-ellipsoid.c)
+target_link_libraries(sample-on-ellipsoid nsmc -lm)
 
 # Build and install scheme wrapper.
 if(${GUILE_FOUND})
diff --git a/src/centroid.sc b/src/centroid.sc
new file mode 100644
index 0000000..64f2df3
--- /dev/null
+++ b/src/centroid.sc
@@ -0,0 +1,66 @@
+(sc-include "macros/macros")
+
+(pre-include "gsl/gsl_blas.h")
+(pre-include "gsl/gsl_vector.h")
+(pre-include "extent-sampling.h")
+(pre-include "nd-random.h")
+(pre-include "oracles.h")
+
+(pre-define DIMENSION 100)
+(pre-define CUBE-EDGE 1.0)
+(pre-define ELLIPSOID-AXES-START 0.25)
+(pre-define ELLIPSOID-AXES-END 0.5)
+
+(pre-define SAMPLES-PER-ITERATION 5000)
+(pre-define ITERATIONS 10)
+
+(sc-define-syntax (invoke-extent-oracle extent-oracle r x)
+  ((struct-get extent-oracle oracle) r x (struct-get extent-oracle params)))
+
+(define (find-centroid oracle center filename) (void extent-oracle-t gsl-vector* (const char*))
+  (with-rng rng
+    (with-vector new-center DIMENSION
+      (with-vector x DIMENSION
+        (with-file fp filename "w"
+          (fprintf fp "%g\n" (gsl-blas-dnrm2 center))
+          (for-i iteration ITERATIONS
+            (gsl-vector-set-zero new-center)
+            (for-i trial SAMPLES-PER-ITERATION
+              (random-direction-vector rng x)
+              (gsl-vector-scale x (invoke-extent-oracle oracle rng x))
+              (gsl-vector-add new-center x)
+
+              (gsl-vector-scale x (/ -1.0 (gsl-blas-dnrm2 x)))
+              (gsl-vector-scale x (invoke-extent-oracle oracle rng x))
+              (gsl-vector-add new-center x))
+            (gsl-vector-scale new-center (/ 1.0 2 SAMPLES-PER-ITERATION))
+            (gsl-vector-memcpy center new-center)
+            (fprintf fp "%g\n" (gsl-blas-dnrm2 center))))))))
+
+(define (main) (int)
+  (with-vector center DIMENSION
+    (gsl-vector-set-basis center 0)
+    (gsl-vector-scale center (* 0.25 CUBE-EDGE))
+    (declare cube-params (struct-variable cube-params
+                                          (edge CUBE-EDGE)
+                                          (center center)))
+    (declare cube-oracle (struct-variable extent-oracle-t
+                                          (oracle cube-extent-oracle-with-center)
+                                          (params (address-of cube-params))))
+    (find-centroid cube-oracle center "cube.dat")
+
+    (gsl-vector-set-basis center 0)
+    (gsl-vector-scale center (* 0.5 ELLIPSOID-AXES-START))
+    (with-vector axes DIMENSION
+      (for-i i DIMENSION
+        (gsl-vector-set axes i (+ ELLIPSOID-AXES-START (* i (/ (- ELLIPSOID-AXES-END
+                                                                  ELLIPSOID-AXES-START)
+                                                               (- DIMENSION 1))))))
+      (declare ellipsoid-params (struct-variable ellipsoid-params
+                                                 (axes axes)
+                                                 (center center)))
+      (declare ellipsoid-oracle (struct-variable extent-oracle-t
+                                                 (oracle ellipsoid-extent-oracle-with-center)
+                                                 (params (address-of ellipsoid-params))))
+      (find-centroid ellipsoid-oracle center "ellipsoid.dat")))
+  (return 0))
diff --git a/src/extent-sampling.sc b/src/extent-sampling.sc
index d46f31d..b74051f 100644
--- a/src/extent-sampling.sc
+++ b/src/extent-sampling.sc
@@ -52,6 +52,28 @@
            (else
             (set accurate-estimates 0))))))))
 
+;; (pre-let* (WINDOW-LENGTH 1000 COVARIANCE-SAMPLES 1000 HARDCODED-ECCENTRICITY 2)
+;;   (define (volume-whitening extent-oracle true-volume r dimension rtol stats)
+;;     (void (const extent-oracle-t*) double (const gsl-rng*) (unsigned int) double gsl-rstat-workspace*)
+;;     (define accurate-estimates int 0)
+;;     (let* ((vn double (ln-volume-of-ball dimension)))
+;;       (with-square-matrix transform dimension
+;;         (gsl-matrix-set-identity transform)
+;;         ;; TODO: Replace hardcoded eccentricity.
+;;         (gsl-matrix-set transform 0 0 HARDCODED-ECCENTRICITY)
+;;         (with-vector x dimension
+;;           (with-vector y dimension
+;;             (do-while (< accurate-estimates WINDOW-LENGTH)
+;;               (random-direction-vector r x)
+;;               (cblas-dgemv CblasRowMajor CblasNoTrans dimension dimension 1 transform dimension x 1 0 y 1)
+;;               (gsl-rstat-add (exp (+ vn (* dimension (log (gsl-blas-dnrm2 y)))))
+;;                              stats)
+;;               (cond
+;;                ((rtol? (gsl-rstat-mean stats) true-volume rtol)
+;;                 (set+ accurate-estimates 1))
+;;                (else
+;;                 (set accurate-estimates 0))))))))))
+
 (sc-define-syntax (invoke-integrand integrand r x)
   ((: integrand integrand) r x (: integrand params)))
 
diff --git a/src/macros/macros.sc b/src/macros/macros.sc
index 1ccfeab..4832887 100644
--- a/src/macros/macros.sc
+++ b/src/macros/macros.sc
@@ -26,6 +26,9 @@
   (when (not condition)
     body ...))
 
+(sc-define-syntax (incr var)
+  (set+ var 1))
+
 (sc-define-syntax (for-i index limit body ...)
   (for ((define index int 0)
         (< index limit)
@@ -49,6 +52,18 @@
               gsl-vector-free
               body ...))
 
+(sc-define-syntax (with-matrix var m n body ...)
+  (with-alloc var gsl-matrix*
+              (gsl-matrix-alloc m n)
+              gsl-matrix-free
+              body ...))
+
+(sc-define-syntax (with-square-matrix var n body ...)
+  (with-alloc var gsl-matrix*
+              (gsl-matrix-alloc n n)
+              gsl-matrix-free
+              body ...))
+
 (sc-define-syntax (with-rng var body ...)
   (with-alloc var gsl-rng*
               (gsl-rng-alloc gsl-rng-default) gsl-rng-free
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))
diff --git a/src/whitening.sc b/src/whitening.sc
new file mode 100644
index 0000000..c330ed4
--- /dev/null
+++ b/src/whitening.sc
@@ -0,0 +1,145 @@
+(sc-include "macros/macros")
+
+(pre-include "gsl/gsl_blas.h")
+(pre-include "gsl/gsl_cblas.h")
+(pre-include "gsl/gsl_eigen.h")
+(pre-include "gsl/gsl_matrix.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 2)
+
+(pre-define SAMPLES 100)
+
+(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)
+  (set+ (: accumulator n) 1))
+
+(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)))
+
+(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")))
+
+(pre-let* (COVARIANCE-SAMPLES 10000)
+  (define (volume-whitening 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)))
+        ;; TODO: Replace hardcoded eccentricity.
+        (gsl-matrix-set-identity transform)
+        (gsl-matrix-set transform 0 0 (/ 1.0 ECCENTRICITY))
+        ;; find surface vector as usual using the extent function
+        ;; transform this surface vector to a virtual body
+        ;; find the volume of this virtual body as usual
+        ;; use this volume to find the volume of the real body
+        ;;
+        ;; The idea is to transform the real body to a virtual body
+        ;; whose volume can be estimated very accurately. Then, scale
+        ;; up the virtual volume to get the real volume. Hopefully,
+        ;; the enlargement of error will be small.
+
+        ;; So, the simple determinant relation between the volumes of
+        ;; the real and virtual bodies is incorrect. What then is
+        ;; correct?
+        (with-vector x dimension
+          (with-vector y dimension
+            (for-i i SAMPLES
+              (random-direction-vector rng x)
+              (gsl-vector-scale x (invoke-extent-oracle extent-oracle rng x))
+              (matrix-vector-multiply transform x y)
+              (gsl-rstat-add (exp (+ vn (* dimension (log (gsl-blas-dnrm2 y)))))
+                             stats)
+              (printf "%g (%g/%g)\t" (gsl-rstat-mean stats)
+                      (gsl-blas-dnrm2 x)
+                      (gsl-blas-dnrm2 y)))))))
+    (printf "\n")))
+
+(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-whitening (address-of oracle) rng DIMENSION stats)))
+  (return 0))
-- 
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