Create Release 1.12 (#5)

* Turn off the executable file permissions

* Save work in progress

* Save work in progress: resolving code issues

* Save work in progress towards addressing all code issues.

* Save work in progress towards addressing all code issues.

* Resolve outstanding code issues

* Add eq_histogram to info.ins

* Change mylookup to lookup_table

* Repair formatting

* Repair description. Tidy up.

* Add description. Add trailing semicolons.

* Move lookup_table.m to the private directory

* Save work in progress

* Save work in progress

* Make lookup_s2_region private

* Add some help documentation

* Improve help documentation

* Clean up trailing blanks

* Debug. Improve help documentation.

* Add eq_histogram/Contents.m

* Update documentation for Release 1.12

* Correct the examples. Add missing semicolons.

* Correct the examples

* Improve help comments

* Move eq_area_error.m out of eq_test

* Improve help comments

* Improve help comments

* Move haslight function to eq_illustrations

* Move illustrate_eq_algorithm function to eq_illustrations

* Correct Contents.m files

* Add tests

* Move illustrate_eq_algorithm back to eq_partitions

* Do not use a cell array for movie_frame

* Remove the initial blank frame

* Close figures between tests

* Add test logs

* Add a script to create a test from the help text in a Matlab file

* Function changed name from s2x to polar2cart

* Remove the OpenGL warning message from the log

* Function changed name from s2x to polar2cart

* Correct the help text

* Trim trailing blanks

* Trim trailing blanks

* Bring up to date. Use consistent formatting.

* Bring up to date

* Bring up to date. Delete trailing blanks.

* Update the help text

* Repair savepathonly by using verLessThan

* Set the toolbox installation state to be uninstalled by default

* Rename txt files

* Update the installation instructions

* Update the installation instructions

* Update the README file

---------

Co-authored-by: Paul <[email protected]>

Author: penguian

AUTHORS

@@ -1,4 +1,6 @@
 Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox.
+Release 1.12 2024-10-20
+Copyright 2024 Paul Leopardi
 Release 1.10 2005-06-26
 Copyright 2004-2005 Paul Leopardi for the University of New South Wales.
 AUTHORS
@@ -15,71 +17,84 @@ References
 ----------
  [Dahl78] B. E. J. Dahlberg,
  "On the distribution of Fekete points",
- Duke Math. J. 45 (1978), no. 3, pp. 537--542.
+  Duke Math. J. 45 (1978), no. 3, pp. 537--542.
 
  [KuiS98]: A. B. J. Kuijlaars,  E. B. Saff,
  "Asymptotics for minimal discrete energy on the sphere",
   Transactions of the American Mathematical Society, v. 350 no. 2 (Feb 1998)
   pp. 523--538.
 
  [KuiSS04]: A. B. J. Kuijlaars,  E. B. Saff, X. Sun,
- "Minimum separation f the minimal energy points on spheres in Euclidean 
- spaces", (preprint) 2004-11-30.
- 
+ "On separation of minimal Riesz energy points on spheres in Euclidean spaces."
+  Journal of computational and applied mathematics 199.1 (2007): 172-180.
+
  [LeGS01]: T. Le Gia, I. H. Sloan,
  "The uniform norm of hyperinterpolation on the unit sphere in an arbitrary
   number of dimensions", Constructive Approximation (2001) 17: p249-265.
- 
- [Leo05]: P. Leopardi,
+
+ [Leo06]: P. Leopardi,
  "A partition of the unit sphere into regions of equal area and small diameter",
- Applied Maths Report AMR05/18, May, 2005, submitted to
- Electronic Transactions on Numerical Analysis.
- http://www.maths.unsw.edu.au/applied/files/2005/amr05_18.pdf
+  Electronic Transactions on Numerical Analysis, Volume 25, 2006, pp. 309-327.
+
+ [Leo07]: P. Leopardi,
+ "Distributing points on the sphere: Partitions, separation, quadrature and energy",
+  PhD thesis, UNSW, 2007.
+
+ [Leo09]: P. Leopardi,
+ "Diameter bounds for equal area partitions of the unit sphere",
+  Electronic Transactions on Numerical Analysis, Volume 35, 2009, pp. 1-16.
+
+ [Leo24]: P. Leopardi,
+ "The applicability of equal area partitions of the unit sphere",
+  Journal of Approximation Software, 1(2), 2024.
 
- [Mue98]: C. Mueller, "Analysis of spherical symmetries in Euclidean spaces",
+ [Mue98]: C. Mueller,
+ "Analysis of spherical symmetries in Euclidean spaces",
   Springer, 1998.
- 
+
  [RakSZ94]: E. A. Rakhmanov, E. B. Saff, Y. M. Zhou,
  "Minimal discrete energy on the sphere",
- Mathematics Research Letters, 1 (1994), pp. 647--662.
- 
+  Mathematics Research Letters, 1 (1994), pp. 647--662.
+
  [RakSZ95]: E. A. Rakhmanov, E. B. Saff, Y. M. Zhou,
  "Electrons on the sphere",
- Computational methods and function theory 1994 (Penang), pp. 293--309, 
- Ser. Approx. Decompos., 5, World Sci. Publishing, River Edge, NJ, 1995.
- 
+  Computational methods and function theory 1994 (Penang), pp. 293--309,
+  Ser. Approx. Decompos., 5, World Sci. Publishing, River Edge, NJ, 1995.
+
  [SafK97]: E. B. Saff, A. B. J. Kuijlaars,
  "Distributing many points on a sphere",
   Mathematical Intelligencer, v19 no1 (1997), pp. 5--11.
- 
- [SafSP]: E. B. Saff, "Sphere Points,"
+
+ [SafSP]: E. B. Saff,
+ "Sphere Points,"
   http://www.math.vanderbilt.edu/~esaff/sphere_points.html
 
- [Saf03]: Ed Saff, "Equal-area partitions of sphere",
+ [Saf03]: Ed Saff,
+ "Equal-area partitions of sphere",
   Presentation at UNSW, 2003-07-28.
- 
+
  [Slo03]: Ian Sloan, "Equal area partition of S^3", Notes, 2003-07-29.
 
- [WeiMW]: E. W. Weisstein, 
+ [WeiMW]: E. W. Weisstein,
  "Hypersphere." From MathWorld--A Wolfram Web Resource.
   http://mathworld.wolfram.com/Hypersphere.html
 
- [Zho95]: Y. M. Zhou, "Arrangement of points on the sphere",
-  Thesis, University of South Florida, 1995.
+ [Zho95]: Y. M. Zhou,
+ "Arrangement of points on the sphere",
+  PhD thesis, University of South Florida, 1995.
 
- [Zho98]: Y. M. Zhou, "Equidistribution and extremal energy of N points on
-  the sphere",  Modelling and computation for applications in mathematics,
+ [Zho98]: Y. M. Zhou,
+ "Equidistribution and extremal energy of N points on the sphere",
+  Modelling and computation for applications in mathematics,
   science, and engineering (Evanston, IL, 1996), pp. 39--57,
   Numer. Math. Sci. Comput., Oxford Univ. Press, New York, 1998.
 
 Installation and Utilities
 --------------------------
-Toolbox Installer 2.2, 2003-07-22 by B. Rasmus Anthin.
+Toolbox Installer 2.2, 2003-07-22 by Rasmus Anthin.
 Matlab Central File Exchange
-http://www.mathworks.com/matlabcentral/fileexchange/
-Home page of B. Rasmus Anthin
-http://www.etek.chalmers.se/~e8rasmus/
+https://au.mathworks.com/matlabcentral/fileexchange/3726-toolbox-installer-2-2
 
-Files modified and relicenced with permission of B. Rasmus Anthin:
+Files modified and relicenced with permission of Rasmus Anthin:
 ./private
 install.m       uninstall.m

CHANGELOG

@@ -1,11 +1,27 @@
 Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox.
+Release 1.12 2024-10-20
+Copyright 2024 Paul Leopardi
 Release 1.10 2005-06-26
 Copyright 2004-2005 Paul Leopardi for the University of New South Wales.
 CHANGELOG
 
 For licensing, see COPYING
 For references, see AUTHORS
 
+Changes between Release 1.10 and Release 1.12 as at 2024-10-20
+==============================================================
+
+1) Bring the installer up-to-date with respect to current Matlab.
+
+2) Bring the code up-to-date with respect to current Matlab.
+
+3) Complete the histogram utilities in the eq_histogram directory.
+
+4) Add tests to the eq_test directory.
+
+* Note * The histogram utilities as at Revision 1.11 of 2012-2013
+were incomplete, untested, and incorrect.
+
 Changes between Revision 1.02 and Release 1.10 as at 2005-06-26
 ===============================================================
 
@@ -337,7 +353,7 @@ point_set_props/point_set_energy_dist.m
 o r^(-s) energy and minimum distance of a point set
 
 point_set_props/point_set_min_dist.m
-o Minimum distance between points of a point set 
+o Minimum distance between points of a point set
 
 point_set_props/point_set_packing_density.m
 o  Density of packing given by min dist of a point set
@@ -349,7 +365,7 @@ point_set_props/eq_energy_coeff.m
 o Coefficient in expansion of energy of an RZ point set
 
 point_set_props/eq_min_dist.m
-o Minimum distance between points of an RZ point set 
+o Minimum distance between points of an RZ point set
 
 point_set_props/eq_packing_density.m
 o  Density of packing given by minimum distance of RZ point set
@@ -395,24 +411,24 @@ dist_matrix.m, sphere_dist_matrix.m
 o Out of scope.
 
 minus_dist.m, minus_dist_sq.m
-o No longer needed. 
-  Were used in constrained nonlinear optimization to estimate diameter. 
+o No longer needed.
+  Were used in constrained nonlinear optimization to estimate diameter.
 
 r2s.m, s2r.m
 o Duplicates of e2s.m and s2e.m.
 
 region_is_cap.m, region_is_sphere.m
-o No longer needed. 
-  Were used to estimate diameter. 
+o No longer needed.
+  Were used to estimate diameter.
 
 run_diam_bound_coeff_from.m,   run_vertex_diam_bound_coeff_from.m
 run_vertex_diam_bound_coeff.m, run_vertex_diam_coeff.m
-o Out of scope. 
+o Out of scope.
   Were used for batch jobs run from Linux shell scripts.
 
 5) Use of subfunctions.
 
-The following M files now contain the subfunctions as listed. 
+The following M files now contain the subfunctions as listed.
 As a consequence, the subfunctions no longer exist as separate M files.
 
 illustrations/illustration_options.m:
@@ -428,7 +444,7 @@ illustrations/show_s2_partition.m:
  SHOW_S2_REGION
 
 partitions/illustrate_eq_algorithm.m:
- OPTION_ARGUMENTS, ILLUSTRATE_STEPS_1_2, 
+ OPTION_ARGUMENTS, ILLUSTRATE_STEPS_1_2,
  ILLUSTRATE_STEPS_3_5, ILLUSTRATE_STEPS_6_7
 
 partitions/partition_options.m:
@@ -572,14 +588,14 @@ Now uses normalized font sizes.
 o Now use illustrations/illustrate_point_set.m
 o Removed unnecessary calls to PACK
 
-10.3) illustrations/show_s2_partition.m, illustrations/show_r3_point_set.m, 
+10.3) illustrations/show_s2_partition.m, illustrations/show_r3_point_set.m,
 o Now use new function SURF_JET to set up extreme values for COLARMAP JET.
   Also, SURF_JET uses HASLIGHT to determine if a light already exists,
   and only calls CAMLIGHT if there is no existing light.
 o Now use new function SHOW_S2_SPHERE to draw the unit sphere S^2.
   Also, SHOW_S2_SPHERE sets specular reflection of the unit sphere to 0.
-o show_s2_partition now uses PAUSE(0) to build up the illustration 
-  collar-by-collar rather than region-by-region. This is faster.  
+o show_s2_partition now uses PAUSE(0) to build up the illustration
+  collar-by-collar rather than region-by-region. This is faster.
 
 10.4) partitions/eq_caps.m
 Check for integer dim and N removed.
@@ -625,7 +641,7 @@ area_error.m:
   2004-03-23
   Simplify by removing options.
   2004-01-20
-  Ensure that routine works whether N is a number or range specified by a row matrix 
+  Ensure that routine works whether N is a number or range specified by a row matrix
 .
   2004-01-19
   Started.
@@ -928,7 +944,7 @@ partsphere.m:
 
 part_to_caps.m:
   2004-08-14
-  Make dim==1 consistent with dim>1 by 
+  Make dim==1 consistent with dim>1 by
   returning the longitude of a sector enclosing the
   cumulative sum of arc lengths given by summing n_regions.
   2004-03-23
@@ -1153,7 +1169,7 @@ Maple revision history
             euclidean_dist functions.
             Clean up conversions s2x and s2r.
 2003-09-26: Plot energy coefficients.
-            Fix functions which list energy and energy coefficients: 
+            Fix functions which list energy and energy coefficients:
             they had incorrect array assignments.
             Gram determinant for S^2 points.
 2003-09-25: Use Euclidean diameters as well as spherical diameters.

COPYING

@@ -1,11 +1,12 @@
 Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox.
-Release 1.10 2005-06-26
+Release 1.12 2024-10-20
 COPYING
 
 For references, see AUTHORS.
 For revision history, see CHANGELOG.
 
-Copyright (c) 2004, 2005, University of New South Wales
+Copyright 2024 Paul Leopardi
+Copyright 2004, 2005, University of New South Wales
 
 Permission is hereby granted, free of charge, to any person obtaining
 a copy of this software and associated documentation files (the

Contents.m

@@ -1,5 +1,5 @@
 % Recursive Zonal Equal Area Sphere Partitioning Toolbox.
-% Release 1.10 2005-06-26
+% Release 1.12 2024-10-14
 %
 %Functions by category
 %=====================
@@ -18,9 +18,9 @@
 %  eq_regions             Recursive zonal equal area (EQ) partition of sphere
 %
 % Point sets
-%  eq_point_set           Center points of regions of EQ partition, 
+%  eq_point_set           Center points of regions of EQ partition,
 %                             in Cartesian coordinates
-%  eq_point_set_polar     Center points of regions of an EQ partition, 
+%  eq_point_set_polar     Center points of regions of an EQ partition,
 %                             in spherical polar coordinates
 %
 % Partition options
@@ -29,6 +29,10 @@
 %Properties of recursive zonal equal area sphere partitions
 %----------------------------------------------------------
 %
+% Area
+%  eq_area_error          Total area error and max area error per region of an
+%                             EQ partition
+%
 % Diameter
 %  eq_diam_bound          Maximum per-region diameter bound of EQ partition
 %  eq_vertex_diam         Maximum vertex diameter of EQ partition
@@ -53,7 +57,7 @@
 %  calc_energy_coeff      Coefficient of second term in expansion of energy
 %
 % Minimum distance
-%  eq_min_dist            Minimum distance between center points of an 
+%  eq_min_dist            Minimum distance between center points of an
 %                             EQ partition
 %  point_set_min_dist     Minimum distance between points of a point set
 %
@@ -62,38 +66,46 @@
 %  calc_dist_coeff        Coefficient of minimum distance
 %
 % Spherical cap packing density
-%  eq_packing_density     Density of packing given by minimum distance of 
+%  eq_packing_density     Density of packing given by minimum distance of
 %                             EQ point set
-%  point_set_packing_density  Density of packing given by minimum distance of 
+%  point_set_packing_density  Density of packing given by minimum distance of
 %                             a point set
 %  calc_packing_density   Density of packing given by minimum distance
 %
 % Hook for user-defined properties
 %  eq_point_set_property  Property of an EQ point set
 %
+%Histogram utilities for S^2
+%---------------------------
+%
+%  eq_count_points_by_s2_region  Given a set of points, count points in each of N regions of S^2
+%  eq_find_s2_region      Given a set of points, partition S^2 into N regions
+%                             and find the index of the region of containing each point
+%  in_s2_region           Test that each of a set of points on S^2 is within a given region
+%
 %Illustrations
 %-------------
 %
+% Illustration of algorithms
+%  illustrate_eq_algorithm  Illustrate the EQ partition algorithm
+%
 % Illustration of EQ Partitions of S^2 or S^3
 %  show_s2_partition      3D illustration of an EQ partition of S^2
 %  project_s2_partition   Use projection to illustrate an EQ partition of S^2
 %  project_s3_partition   Use projection to illustrate an EQ partition of S^3
 %
 % Illustration of point sets on S^2 or S^3
 %  show_r3_point_set      3D illustration of a point set
-%  project_point_set      Use projection to illustrate a point set of 
+%  project_point_set      Use projection to illustrate a point set of
 %                             S^2 or S^3
 % Illustration of a recursive zonal equal area sphere partition algorithm
 %  illustrate_eq_algorithm  Illustrate the EQ partition algorithm
 %
 % Illustration options
 %  illustration_options   Options for illustrations of EQ partitions
 %
-%Tests
-%-----
-%
-%  eq_area_error          Total area error and max area error per region of an
-%                             EQ partition
+% Illustration utilities
+%  haslight               Check if axis handle has a light attached
 %
 %Utilities
 %---------
@@ -106,19 +118,23 @@
 %  euc2sph_dist           Convert Euclidean to spherical distance
 %  euclidean_dist         Euclidean distance between two points
 %  fatcurve               Create a parameterized cylindrical surface
-%  haslight               Check if axis handle has a light attached
 %  ideal_collar_angle     Ideal angle for spherical collars of an EQ partition
-%  illustration_options   Options for illustrations of EQ partitions
-%  partition_options      Options for EQ partition
 %  polar2cart             Convert spherical polar to Cartesian coordinates
 %  sph2euc_dist           Convert spherical to Euclidean distance
 %  spherical_dist         Spherical distance between two points on the sphere
 %  sradius_of_cap         Spherical radius of spherical cap of given area
 %  volume_of_ball         Volume of the unit ball
 %
+%Tests
+%-----
+%
+%  Tests of all functions.
+%
 % If the previous text scrolled off the screen, try
 % more on; help eq_sphere_partitions; more off;
 
+% Copyright 2024 Paul Leopardi
+% $Revision 1.12 $ $Date 2024-10-14 $
 % Copyright 2004-2005 Paul Leopardi for the University of New South Wales.
 % $Revision 1.10 $ $Date 2005-06-26 $
 % Function changed name from e2s to euc2sph_dist