### Example FIRep Input

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

This example demonstrates the required format for FIRep input, including data specifications and flags. Ensure flags are compatible with bigrade orientations.

```bash
--datatype firep
--xlabel parameter 1
--ylabel parameter 2

# data
2 3 3
1 0 ; 0 1 2
0 1 ; 0 1 2
0 0 ; 1 2
0 0 ; 0 2
0 0 ; 0 1


```

--------------------------------

### Bifiltration Data Input Example

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

This example demonstrates the format for specifying a bifiltration, including vertex definitions and their appearance bigrades. Ensure the `--datatype bifiltration` flag is used.

```bash
--datatype bifiltration
--xlabel time of appearance
--ylabel network distance

#data
0 ; 0 0
1 ; 0 0
2 ; 0 0
3 ; 0 0
0 1 ; 0 0
0 2 ; 0 0
1 2 ; 0 0
0 1 2 ; 0 1 1 0
1 3 ; 1 1
2 3 ; 1 1

```

--------------------------------

### Install RIVET Dependencies on Ubuntu

Source: https://rivet.readthedocs.io/en/latest/installing.html

Installs CMake, Qt5, and Boost libraries required for building RIVET on Ubuntu systems.

```bash
sudo apt-get update
sudo apt-get install cmake qt5-default qt5-qmake qtbase5-dev-tools libboost-all-dev

```

--------------------------------

### Install RIVET Dependencies on Mac OS X

Source: https://rivet.readthedocs.io/en/latest/installing.html

Installs CMake, Qt5, and Boost using Homebrew on Mac OS X.

```bash
brew install cmake qt5 boost

```

--------------------------------

### Install Xcode Command Line Tools

Source: https://rivet.readthedocs.io/en/latest/installing.html

Installs the Xcode Command Line Tools necessary for development on Mac OS X. This is a prerequisite for building RIVET.

```bash
# only needed if you've never run it before, (running it again doesn't hurt anything)
# installs XCode Command Line Tools
xcode-select --install

```

--------------------------------

### Minimal Presentation Output Format

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

This example illustrates the expected output format when computing a minimal presentation. It includes x- and y-grades, row and column bigrades, and a sparse matrix representation.

```text
x-grades
3
7/2
4

y-grades
0
1
2

MINIMAL PRESENTATION:
Number of rows:2
Row bigrades:
| (1,0) (0,1) |
Number of columns:3
Column bigrades:
| (1,1) (2,1) (1,2) |
0 1
1
0

```

```text
1 0 1
1 1 0

```

--------------------------------

### Configure Qt Base Path for RIVET Build on Mac

Source: https://rivet.readthedocs.io/en/latest/installing.html

Sets the QT_BASE environment variable to the installation path of Qt5, which is needed for qmake to find the correct Qt version.

```bash
export QT_BASE=`brew info qt5 | grep Cellar | cut -d' ' -f1`

```

--------------------------------

### Compute Module Invariants File with Options

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

Example of computing a module invariants file using specific options. Use --datatype to specify input format, --homology for degree, and --xbins/--ybins for Betti number grid resolution.

```bash
rivet_console input.txt output.rivet --datatype metric --homology 1 --xbins 100 --ybins 100
```

--------------------------------

### Hilbert Function and Bigraded Betti Numbers Output Format

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

This example shows the output structure for Hilbert function and bigraded Betti numbers. It includes x- and y-grades, non-zero Hilbert function points (x-index, y-index, value), and non-zero Betti number points for each Betti number.

```text
x-grades
3
7/2
4

y-grades
0
1
2

Dimensions > 0:

(0, 1, 1)
(0, 2, 1)

(1, 0, 1)
(1, 1, 1)
(1, 1, 1)

(2, 0, 1)


Betti numbers:
xi_0:
(1, 0, 1)
(0, 1, 1)
xi_1:
(1, 1, 1)
(1, 2, 1)
(2, 1, 1)
xi_2:
(2, 2, 1)


```

--------------------------------

### Metric Space with Function Data Type Example

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

This example demonstrates the file format for the 'metric_fn' data type, including required and optional flags, function values, and the distance matrix. It's used when points in a metric space have associated function values.

```bash
#required flag:
--datatype metric_fn

#optional flags:
--xlabel birth time
--ylabel geodesic distance

#function values
1,1.1,-2
# distance matrix, given in upper triangular format
2,3.2
1.25

```

--------------------------------

### Install Homebrew Package Manager

Source: https://rivet.readthedocs.io/en/latest/installing.html

Installs the Homebrew package manager on Mac OS X, used for installing development tools like CMake, Qt5, and Boost.

```bash
/usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"

```

--------------------------------

### Install RIVET Dependencies on WSL

Source: https://rivet.readthedocs.io/en/latest/installing.html

Installs essential build tools and libraries for RIVET on a Linux distribution within WSL. Run this command in your Linux console.

```bash
sudo apt-get update
sudo apt-get install cmake build-essential qt5-default qt5-qmake qtbase5-dev-tools libboost-all-dev

```

--------------------------------

### Example CSV Point Cloud Data

Source: https://rivet.readthedocs.io/en/latest/gettingstarted.html

This snippet shows the first five lines of a CSV file representing a point cloud in R2. Each line contains two comma-separated coordinates for a point.

```csv
1.57,2.40
1.21,2.70
0.79,-2.44
-2.44,-2.24
-2.54,-1.25

```

--------------------------------

### Sample Line File Format

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

This file specifies a list of affine lines in R2R2 with non-negative slope. Each line is defined by its angle (degrees, 0-90) and offset (signed distance from origin). Lines starting with '#' and blank lines are ignored.

```plaintext
#A line that starts with a # character will be ignored, as will blank lines
23 -0.22
67 1.88
10 0.92
#100 0.92   <-- will error if uncommented, 100 > 90

```

--------------------------------

### Sample Barcode Output

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

The output provides barcode information for each specified line. It includes the query parameters (angle and offset) followed by barcode data, which is a multiset of intervals. For example, '88.1838 inf x1' represents a single interval [88.1838, infinity).

```plaintext
23 -0.22: 88.1838 inf x1, 88.1838 91.2549 x5, 88.1838 89.7194 x12
67 0.88: 23.3613 inf x1
10 0.92: 11.9947 inf x1, 11.9947 19.9461 x2, 11.9947 16.4909 x1, 11.9947 13.0357 x4

```

--------------------------------

### Troubleshoot qmake SDK Path Error on Mac

Source: https://rivet.readthedocs.io/en/latest/installing.html

Resolves the 'Project ERROR: Could not resolve SDK Path for 'macosx'' error by setting the Xcode SDK path.

```bash
sudo xcode-select --switch /Applications/Xcode.app/Contents/Developer

```

--------------------------------

### Access RIVET Console Help

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

Use this command to display the help information for the rivet_console executable, which includes syntax and technical details.

```bash
rivet_console (-h | --help)
```

--------------------------------

### Accept Xcode License

Source: https://rivet.readthedocs.io/en/latest/installing.html

Accepts the Xcode license agreement from the command line, which is required before using Xcode tools.

```bash
sudo xcodebuild -license

```

--------------------------------

### Compute Hilbert Function and Betti Numbers with rivet_console

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

Execute this command to compute both the Hilbert function and bigraded Betti numbers for a bipersistence module. Use the `--betti` flag with the input file. Note that these cannot be printed separately or combined with the minimal presentation in the current version.

```bash
rivet_console <input_file> --betti [command-line flags]
```

--------------------------------

### Basic rivet_console Syntax

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

This is the general syntax for using the rivet_console command. Specify input and output files, and optional flags to control the computation.

```bash
rivet_console <input> <output> [options]
```

--------------------------------

### Build RIVET on Ubuntu

Source: https://rivet.readthedocs.io/en/latest/installing.html

Compiles RIVET using CMake and Make after cloning the repository. Includes steps to create executables and symlink the console.

```bash
cd $RIVET_DIR
mkdir build
cd build
cmake ..
make
cd ..
qmake
make

```

```bash
ln -s build/rivet_console

```

--------------------------------

### Configure RIVET Project File for Boost on Mac

Source: https://rivet.readthedocs.io/en/latest/installing.html

Modifies the RIVET.pro file to specify Boost library paths and include directories, ensuring qmake can locate Boost during the build process.

```qmake
CONFIG += c++11
QMAKE_CFLAGS += -std=c++11 -stdlib=libc++ -mmacosx-version-min=10.9
QMAKE_CXXFLAGS += -std=c++11 -stdlib=libc++ -mmacosx-version-min=10.9

LIBS += -L"/usr/local/Cellar/boost/1.63.0/lib"
INCLUDEPATH += "/usr/local/Cellar/boost/1.63.0/include"

LIBS += -L"/usr/local/Cellar/boost/1.63.0/lib" -lboost_random

```

--------------------------------

### Compute Minimal Presentation with rivet_console

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

Use this command to compute and print the minimal presentation of a bipersistence module. Specify the input file and use the `--minpres` flag. Additional command-line flags can be appended.

```bash
rivet_console <input_file> --minpres [command-line flags]
```

--------------------------------

### Build RIVET on Mac OS X

Source: https://rivet.readthedocs.io/en/latest/installing.html

Compiles RIVET using CMake and Make, utilizing the specified Qt5 path. Includes steps to create executables and symlink the console.

```bash
cd $RIVET_DIR
mkdir build
cd build
cmake ..
make
cd ..
$QT_BASE/bin/qmake
make

```

```bash
cd rivet_GUI.app/Contents/MacOS
ln -s ../../../build/rivet_console

```

--------------------------------

### Format C++ Source Code

Source: https://rivet.readthedocs.io/en/latest/about.html

Format all .cpp and .h files in the RIVET project using clang-format. Ensure this is run before submitting code for review.

```shell
clang-format -i **/*.cpp **/*.h

```

--------------------------------

### Compute Barcodes with rivet_console

Source: https://rivet.readthedocs.io/en/latest/rivetconsole.html

Use this command to compute barcodes for 1-D slices. Specify the input module invariants file and a file containing the lines for which to compute barcodes.

```bash
rivet_console <module_invariants_file> --barcodes <line_file>
```

--------------------------------

### Set DISPLAY Environment Variable for RIVET Viewer

Source: https://rivet.readthedocs.io/en/latest/installing.html

Sets the DISPLAY environment variable to enable the RIVET viewer to connect to an X server. This is necessary when running graphical applications from within WSL.

```bash
export DISPLAY=:0

```

--------------------------------

### Point Cloud with Function Data Format for RIVET

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

Use this format when providing points in Euclidean n-space along with a function defined on these points. RIVET constructs a function-Rips bifiltration by default. The first line lists function values, followed by point coordinates.

```plaintext
#required flag (can be given instead on the command line)
--datatype points_fn

#optional flags
--xlabel birth time
--xreverse

#function
3,0.5,4

#data
0,0
1.1,2
-2,3

```

--------------------------------

### Point Cloud Data Format for RIVET

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

Use this format for specifying a set of points in Euclidean n-space. RIVET constructs a degree-Rips bifiltration by default. Ensure points are listed with coordinates separated by whitespace or commas.

```plaintext
#the following flag is optional, because "points" is the default value of datatype
#however, it is not a bad idea to include the flag for readability
--datatype points

#optional flags
--maxdist 0.5

#data
0,0
1.1,2
-2,3

```

--------------------------------

### Metric Space Data: Full Matrix Format

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

Provides a 3x3 symmetric distance matrix with zeros on the diagonal. This format is explicitly provided, one row per line, with numbers separated by whitespace or commas. Use the `--datatype metric` flag.

```plaintext
#required flag:
--datatype metric

#optional flags:
--xlabel birth time
--ylabel geodesic distance

# distance matrix (symmetric matrix, with zeros on the diagonal)
0,2,3.2
2,0,1.25
3.2,1.25,0

```

--------------------------------

### RIVET BibTex Citation

Source: https://rivet.readthedocs.io/en/latest/about.html

Use this BibTex entry to cite the RIVET software in your publications. Ensure the version and year are up-to-date.

```bibtex
@software{rivet,
        author = {{The RIVET Developers}},
        title = {RIVET},
        url = {https://github.com/rivetTDA/rivet/},
        version = {1.1.0},
        year = {2020}
}

```

--------------------------------

### Metric Space Data: Upper Triangular Format

Source: https://rivet.readthedocs.io/en/latest/inputdata.html

Provides the same 3x3 distance data in an upper triangular format. This format specifies only the entries above the diagonal, reducing the amount of data required. Use the `--datatype metric` flag.

```plaintext
# distance matrix (upper triangular format)
2,3.2
1.25

```

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