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Diffstat (limited to 'src/Alpha_complex/utilities/README')
-rw-r--r-- | src/Alpha_complex/utilities/README | 89 |
1 files changed, 56 insertions, 33 deletions
diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README index 6e7d16b7..c3dd170b 100644 --- a/src/Alpha_complex/utilities/README +++ b/src/Alpha_complex/utilities/README @@ -8,22 +8,24 @@ This program computes the persistent homology with coefficient field Z/pZ of the 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 <input OFF file> <p> <min_persistence>` -where -`<input OFF file>` is the path to the input point cloud in OFF format. -`<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. +`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 2 0.45` +`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 +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: @@ -48,21 +50,34 @@ Same as `alpha_complex_3d_persistence`, but using exact computation. It is slowe Same as `alpha_complex_3d_persistence`, but using weighted points. **Usage** -`weighted_alpha_complex_3d_persistence <input OFF file> <input weights file> <p> <min_persistence>` -where -`<input OFF file>` is the path to the input point cloud in OFF format. -`<input weights file>` is the path to the file containing the weights of the points (one value per line). -`<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. +`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` -## `periodic_alpha_complex_3d_persistence` ## -This program computes the persistent homology with coefficient field Z/pZ of the 3D periodic alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention: +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 +``` -`p dim b d` +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. -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). + +## `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>` @@ -72,21 +87,31 @@ where `<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 3 1.0` +`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 +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: @@ -98,14 +123,12 @@ Betti numbers[3] = 1 ``` N.B.: -* `periodic_alpha_complex_3d_persistence` only accepts OFF files in dimension 3. -* In this example, the periodic cube is hard coded to { x = [0,1]; y = [0,1]; z = [0,1] } +* 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: @@ -119,7 +142,7 @@ where `dim` is the dimension of the homological feature, `b` and `d` are respect **Allowed options** * `-h [ --help ]` Produce help message -* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout. +* `-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. |