From 50842cbc95006c8ff1a9066fa9431999025c4688 Mon Sep 17 00:00:00 2001 From: cjamin Date: Wed, 22 Nov 2017 16:34:52 +0000 Subject: b => birth + d => death git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/add_utils_in_gudhi_v2@2943 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 6ec0292942fcc14c1ef53b8ff9d1182b8f07a287 --- src/Alpha_complex/utilities/README | 346 ++++++++++++++++++------------------- 1 file changed, 173 insertions(+), 173 deletions(-) (limited to 'src/Alpha_complex/utilities') diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README index 0d3d6bfc..1cd2ca95 100644 --- a/src/Alpha_complex/utilities/README +++ b/src/Alpha_complex/utilities/README @@ -1,177 +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] ` +# 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] ` where -`` 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] ` +`` 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] ` +where +`` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html). +`` 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] ` where `` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html). -`` 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] ` -where -`` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html). -`` 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 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] ` +`` 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] ` where -`` 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. +`` 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. -- cgit v1.2.3