1 files changed, 177 insertions, 172 deletions
diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README
index c3dd170b..1cd2ca95 100644
--- a/src/Alpha_complex/utilities/README
+++ b/src/Alpha_complex/utilities/README
@@ -1,172 +1,177 @@
-# Alpha_complex #
-
-## `alpha_complex_3d_persistence` ##
-This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:
-
-`p dim b d`
-
-where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
-
-**Usage**
-`alpha_complex_3d_persistence [options] <OFF input file>`
-
-**Allowed options**
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
-
-**Example**
-`alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45`
-
-outputs:
-```
-Simplex_tree dim: 3
-2  0 0 inf
-2  1 0.0682162 1.0001
-2  1 0.0934117 1.00003
-2  2 0.56444 1.03938
-```
-
-Here we retrieve expected Betti numbers on a tore 3D:
-```
-Betti numbers[0] = 1
-Betti numbers[1] = 2
-Betti numbers[2] = 1
-```
-
-N.B.: 
-* `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
-* Filtration values are alpha square values.
-
-
-
-## `exact_alpha_complex_3d_persistence` ##
-Same as `alpha_complex_3d_persistence`, but using exact computation. It is slower, but it is necessary when points are on a grid for instance.
-
-
-
-## `weighted_alpha_complex_3d_persistence` ##
-Same as `alpha_complex_3d_persistence`, but using weighted points.
-
-**Usage**
-`weighted_alpha_complex_3d_persistence [options] <OFF input file> <weights input file>`
-
-**Allowed options**
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
-
-**Example**
-`weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45`
-
-outputs:
-```
-Simplex_tree dim: 3
-2  0 -1 inf
-2  1 -0.931784 0.000103311
-2  1 -0.906588 2.60165e-05
-2  2 -0.43556 0.0393798
-```
-
-N.B.:
-* Weights values are explained on CGAL [Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)
-and [Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.
-* Filtration values are alpha square values.
-
-
-## `periodic_alpha_complex_3d_persistence` ##
-Same as `alpha_complex_3d_persistence`, but using periodic alpha shape 3d.
-
-**Usage**
-`periodic_alpha_complex_3d_persistence <input OFF file> <cuboid file> <p> <min_persistence>`
-where
-`<input OFF file>` is the path to the input point cloud in OFF format.
-`<cuboid file>` is the path to the file describing the periodic domain. It must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).
-`<p>` is the characteristic p of the coefficient field *Z/pZ* for computing homology. It must be a stricly positive integer.
-`<min_persistence>` is the minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
-
-**Usage**
-`./periodic_alpha_complex_3d_persistence [options] input-file cuboid-file`
-
-**Allowed options**
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals
-
-
-**Example**
-`periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0`
-
-outputs:
-```
-Periodic Delaunay computed.
-Simplex_tree dim: 3
-3  0 0 inf
-3  1 0.0025 inf
-3  1 0.0025 inf
-3  1 0.0025 inf
-3  2 0.005 inf
-3  2 0.005 inf
-3  2 0.005 inf
-3  3 0.0075 inf
-```
-
-Here we retrieve expected Betti numbers on an 3D iso-oriented cuboids:
-```
-Betti numbers[0] = 1
-Betti numbers[1] = 3
-Betti numbers[2] = 3
-Betti numbers[3] = 1
-```
-
-N.B.: 
-* Cuboid file must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).
-* Filtration values are alpha square values.
-
-
-
-
-## `alpha_complex_persistence` ##
-This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud. The output diagram contains one bar per line, written with the convention:
-
-`p dim b d`
-
-where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
-
-**Usage**
-`alpha_complex_persistence [options] <OFF input file>`
-
-**Allowed options**
-
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.
-* `-p [ --field-charac ]` (default = 11)     Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
-
-**Example**
-`alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off`
-
-outputs:
-```
-Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
-Simplex_tree dim: 3
-2  0 0 inf 
-2  1 0.0682162 1.0001 
-2  1 0.0934117 1.00003 
-2  2 0.56444 1.03938 
-```
-
-Here we retrieve expected Betti numbers on a tore 3D:
-```
-Betti numbers[0] = 1
-Betti numbers[1] = 2
-Betti numbers[2] = 1
-```
-
-N.B.: 
-* `alpha_complex_persistence` only accepts OFF files in dimension d.
-* Filtration values are alpha square values.
+# Alpha_complex #
+
+## `alpha_complex_3d_persistence` ##
+This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:
+
+`p dim birth death`
+
+where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
+
+**Usage**
+`alpha_complex_3d_persistence [options] <input OFF file>`
+where
+`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+
+**Example**
+`alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45`
+
+outputs:
+```
+Simplex_tree dim: 3
+2  0 0 inf
+2  1 0.0682162 1.0001
+2  1 0.0934117 1.00003
+2  2 0.56444 1.03938
+```
+
+Here we retrieve expected Betti numbers on a tore 3D:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+```
+
+N.B.: 
+* `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
+* Filtration values are alpha square values.
+
+
+
+## `exact_alpha_complex_3d_persistence` ##
+Same as `alpha_complex_3d_persistence`, but using exact computation. It is slower, but it is necessary when points are on a grid for instance.
+
+
+
+## `weighted_alpha_complex_3d_persistence` ##
+Same as `alpha_complex_3d_persistence`, but using weighted points.
+
+**Usage**
+`weighted_alpha_complex_3d_persistence [options] <input OFF file> <weights input file>`
+where
+`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+`<input weights file>` is the path to the file containing the weights of the points (one value per line).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+
+**Example**
+`weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45`
+
+outputs:
+```
+Simplex_tree dim: 3
+2  0 -1 inf
+2  1 -0.931784 0.000103311
+2  1 -0.906588 2.60165e-05
+2  2 -0.43556 0.0393798
+```
+
+N.B.:
+* Weights values are explained on CGAL [Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)
+and [Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.
+* Filtration values are alpha square values.
+
+
+## `periodic_alpha_complex_3d_persistence` ##
+Same as `alpha_complex_3d_persistence`, but using periodic alpha shape 3d.
+Refer to the [CGAL's 3D Periodic Triangulations User Manual](https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html) for more details.
+
+**Usage**
+`periodic_alpha_complex_3d_persistence [options] <input OFF file> <cuboid file>`
+where
+`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+`<cuboid file>` is the path to the file describing the periodic domain. It must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals
+
+
+**Example**
+`periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0`
+
+outputs:
+```
+Periodic Delaunay computed.
+Simplex_tree dim: 3
+3  0 0 inf
+3  1 0.0025 inf
+3  1 0.0025 inf
+3  1 0.0025 inf
+3  2 0.005 inf
+3  2 0.005 inf
+3  2 0.005 inf
+3  3 0.0075 inf
+```
+
+Here we retrieve expected Betti numbers on an 3D iso-oriented cuboids:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 3
+Betti numbers[2] = 3
+Betti numbers[3] = 1
+```
+
+N.B.: 
+* Cuboid file must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).
+* Filtration values are alpha square values.
+
+
+
+
+## `alpha_complex_persistence` ##
+This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud. The output diagram contains one bar per line, written with the convention:
+
+`p dim birth death`
+
+where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
+
+**Usage**
+`alpha_complex_persistence [options] <input OFF file>`
+where
+`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.
+* `-p [ --field-charac ]` (default = 11)     Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+
+**Example**
+`alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off`
+
+outputs:
+```
+Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
+Simplex_tree dim: 3
+2  0 0 inf 
+2  1 0.0682162 1.0001 
+2  1 0.0934117 1.00003 
+2  2 0.56444 1.03938 
+```
+
+Here we retrieve expected Betti numbers on a tore 3D:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+```
+
+N.B.:
+* Filtration values are alpha square values.