# htnorm
This repo provides a C implementation of a fast and exact sampling algorithm for a
multivariate normal distribution (MVN) truncated on a hyperplane as described [here][1]
This repo implements the following from the paper:
- Efficient sampling from a MVN truncated on a hyperplane:
- Efficient sampling from a MVN with a stuctured precision matrix that is a sum of an invertible matrix and a low rank matrix:
- Efficient sampling from a MVN with a structured precision and mean:
The algorithms implemented have the following practical applications:
- Topic models when unknown parameters can be interpreted as fractions.
- Admixture models
- discrete graphical models
- Sampling from the posterior distribution of an Intrinsic Conditional Autoregressive prior [icar][8]
- Sampling from the posterior conditional distributions of various bayesian regression problems.
## Dependencies
- A C compiler that implements the C99 standard or later
- An installation of `LAPACK`.
## Usage
Building a shared library of `htnorm` can be done with the following:
```bash
# optionally set path to LAPACK shared library
$ export LIBS_DIR="some/path/to/lib/"
$ make lib
```
Afterwards the shared library will be found in a `lib/` directory of the project root,
and the library can be linked dynamically via `-lhtnorm`.
The puplic interface exposes the samplers through the function declarations
```C
int htn_hyperplane_truncated_mvn(rng_t* rng, const ht_config_t* conf, double* out);
int htn_structured_precision_mvn(rng_t* rng, const sp_config_t* conf, double* out);
```
The details of the parameters are documented in ther header files ["htnorm.h"][4].
Random number generation is done using [PCG64][2] or [Xoroshiro128plus][3] bitgenerators.
The interface allows using a custom bitgenerator, and the details are documented in the header file
["rng.h"][5].
## Example
```C
#include "htnorm.h"
int main (void)
{
...
// instantiate a random number generator
rng_t* rng = rng_new_pcg64_seeded(12345);
ht_config_t config;
init_ht_config(&config, ...);
double* out = ...; // array to store the samples
int res = htn_hyperplane_truncated_mvn(rng, &config, out);
// res contains a number that indicates whether sampling failed or not.
...
// finally free the RNG pointer at some point
rng_free(rng);
...
return 0;
}
```
## Python Interface
[![PyPI - Wheel][10]](https://pypi.org/project/pyhtnorm/#files)
[![PyPI][11]](https://pypi.org/project/pyhtnorm/)
[![CI][12]](https://github.com/zoj613/htnorm/actions/workflows/build-and-test.yml)
[![Codecov][13]](https://codecov.io/gh/zoj613/htnorm/)
[![PyPI - License][14]](https://github.com/zoj613/htnorm/blob/main/LICENSE)
### Dependencies
- NumPy >= 1.19.0
A high level python interface to the library is also provided. Linux and MacOS users can
install it using wheels via pip (thus not needing to worry about availability of C libraries).
Windows OS is currently not supported.
```bash
pip install -U pyhtnorm
```
Wheels are not provided for MacOS. To install via pip, one can run the following commands:
```bash
pip install -U pyhtnorm
```
Alternatively, one can install it from source using the following shell commands:
```bash
$ git clone https://github.com/zoj613/htnorm.git
$ cd htnorm/
$ export PYHT_LIBS_DIR=<some directory with blas and lapack shared library files> # this is optional
$ pip install .
```
Below is an example of how to use htnorm in python to sample from a multivariate
gaussian truncated on the hyperplane  (i.e. making sure the sampled values sum to zero). The python
interface is such that the code can be easily integrated into other existing libraries.
Since `v1.0.0`, it supports passing a `numpy.random.Generator` instance as a parameter to aid reproducibility.
```python
from pyhtnorm import hyperplane_truncated_mvnorm, structured_precision_mvnorm
import numpy as np
rng = np.random.default_rng()
# generate example input
k1, k2 = 1000, 1
temp = rng.random((k1, k1))
cov = temp @ temp.T
G = np.ones((k2, k1))
r = np.zeros(k2)
mean = rng.random(k1)
# passing `random_state` is optional. If the argument is not used, a fresh
# random generator state is instantiated internally using system entropy.
o = hyperplane_truncated_mvnorm(mean, cov, G, r, random_state=rng)
print(o.sum()) # verify if sampled values sum to zero
# alternatively one can pass an array to store the results in
hyperplane_truncated_mvnorm(mean, cov, G, r, out=o)
```
For more information about the function's arguments, refer to its docstring.
A pure numpy implementation is demonstrated in this [example script][9].
## R Interface
One can also use the package in R. To install, use one the following commands:
```R
devtools::install_github("zoj613/htnorm")
pak::pkg_install("zoj613/htnorm")
```
Below is an R translation of the above python example:
```R
library(htnorm)
# make dummy data
mean <- rnorm(1000)
cov <- matrix(rnorm(1000 * 1000), ncol=1000)
cov <- cov %*% t(cov)
G <- matrix(rep(1, 1000), ncol=1000)
r <- c(0)
# initialize the Generator instance
rng <- HTNGenerator(seed=12345, gen="pcg64")
samples <- rng$hyperplane_truncated_mvnorm(mean, cov, G, r)
#verify if sampled values sum to zero
sum(samples)
# optionally pass a vector to store the results in
out <- rep(0, 1000)
rng$hyperplane_truncated_mvnorm(mean, cov, G, r, out = out)
sum(out) #verify
out <- rep(0, 1000)
eig <- eigen(cov)
phi <- eig$vectors
omega <- diag(eig$values)
a <- diag(runif(length(mean)))
rng$structured_precision_mvnorm(mean, a, phi, omega, a_type = "diagonal", out = out)
```
## Licensing
`htnorm` is free software made available under the BSD-3 License. For details
see the [LICENSE][6] file.
## References
- Cong, Yulai; Chen, Bo; Zhou, Mingyuan. Fast Simulation of Hyperplane-Truncated
Multivariate Normal Distributions. Bayesian Anal. 12 (2017), no. 4, 1017--1037.
doi:10.1214/17-BA1052.
- Bhattacharya, A., Chakraborty, A., and Mallick, B. K. (2016).
“Fast sampling with Gaussian scale mixture priors in high-dimensional regression.”
Biometrika, 103(4):985.
[1]: https://projecteuclid.org/euclid.ba/1488337478
[2]: https://www.pcg-random.org/
[3]: https://en.wikipedia.org/wiki/Xoroshiro128%2B
[4]: ./include/htnorm.h
[5]: ./include/htnorm_rng.h
[6]: ./LICENSE
[7]: https://python-poetry.org/docs/pyproject/
[8]: https://www.sciencedirect.com/science/article/abs/pii/S2211675317301574
[9]: ./examples/numpy_implementation.py
[10]: https://img.shields.io/pypi/wheel/pyhtnorm?style=flat-square
[11]: https://img.shields.io/pypi/v/pyhtnorm?style=flat-square
[12]: https://img.shields.io/github/workflow/status/zoj613/htnorm/CI/main?style=flat-square
[13]: https://img.shields.io/codecov/c/github/zoj613/htnorm?style=flat-square
[14]: https://img.shields.io/pypi/l/pyhtnorm?style=flat-square
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"description": "# htnorm\n\nThis repo provides a C implementation of a fast and exact sampling algorithm for a \nmultivariate normal distribution (MVN) truncated on a hyperplane as described [here][1]\n\nThis repo implements the following from the paper:\n\n- Efficient sampling from a MVN truncated on a hyperplane: \n\n \n\n- Efficient sampling from a MVN with a stuctured precision matrix that is a sum of an invertible matrix and a low rank matrix: \n\n \n\n- Efficient sampling from a MVN with a structured precision and mean:\n\n \n\nThe algorithms implemented have the following practical applications:\n- Topic models when unknown parameters can be interpreted as fractions.\n- Admixture models\n- discrete graphical models\n- Sampling from the posterior distribution of an Intrinsic Conditional Autoregressive prior [icar][8]\n- Sampling from the posterior conditional distributions of various bayesian regression problems.\n\n\n## Dependencies\n\n- A C compiler that implements the C99 standard or later\n- An installation of `LAPACK`.\n\n## Usage\n\nBuilding a shared library of `htnorm` can be done with the following:\n```bash\n# optionally set path to LAPACK shared library\n$ export LIBS_DIR=\"some/path/to/lib/\"\n$ make lib\n```\nAfterwards the shared library will be found in a `lib/` directory of the project root,\nand the library can be linked dynamically via `-lhtnorm`.\n\nThe puplic interface exposes the samplers through the function declarations\n```C\n int htn_hyperplane_truncated_mvn(rng_t* rng, const ht_config_t* conf, double* out);\n int htn_structured_precision_mvn(rng_t* rng, const sp_config_t* conf, double* out);\n```\n\nThe details of the parameters are documented in ther header files [\"htnorm.h\"][4].\n\nRandom number generation is done using [PCG64][2] or [Xoroshiro128plus][3] bitgenerators. \nThe interface allows using a custom bitgenerator, and the details are documented in the header file \n[\"rng.h\"][5].\n\n## Example\n```C\n#include \"htnorm.h\"\n\nint main (void)\n{\n ...\n // instantiate a random number generator\n rng_t* rng = rng_new_pcg64_seeded(12345);\n ht_config_t config;\n init_ht_config(&config, ...);\n double* out = ...; // array to store the samples\n int res = htn_hyperplane_truncated_mvn(rng, &config, out);\n // res contains a number that indicates whether sampling failed or not.\n ...\n // finally free the RNG pointer at some point\n rng_free(rng);\n ...\n return 0;\n}\n```\n\n## Python Interface\n[![PyPI - Wheel][10]](https://pypi.org/project/pyhtnorm/#files)\n[![PyPI][11]](https://pypi.org/project/pyhtnorm/)\n[![CI][12]](https://github.com/zoj613/htnorm/actions/workflows/build-and-test.yml)\n[![Codecov][13]](https://codecov.io/gh/zoj613/htnorm/)\n[![PyPI - License][14]](https://github.com/zoj613/htnorm/blob/main/LICENSE)\n\n\n### Dependencies\n- NumPy >= 1.19.0\n\nA high level python interface to the library is also provided. Linux and MacOS users can \ninstall it using wheels via pip (thus not needing to worry about availability of C libraries).\nWindows OS is currently not supported.\n```bash\npip install -U pyhtnorm\n```\nWheels are not provided for MacOS. To install via pip, one can run the following commands:\n```bash\npip install -U pyhtnorm\n```\nAlternatively, one can install it from source using the following shell commands:\n\n```bash\n$ git clone https://github.com/zoj613/htnorm.git\n$ cd htnorm/\n$ export PYHT_LIBS_DIR=<some directory with blas and lapack shared library files> # this is optional\n$ pip install .\n```\n\nBelow is an example of how to use htnorm in python to sample from a multivariate\ngaussian truncated on the hyperplane  (i.e. making sure the sampled values sum to zero). The python\ninterface is such that the code can be easily integrated into other existing libraries.\nSince `v1.0.0`, it supports passing a `numpy.random.Generator` instance as a parameter to aid reproducibility.\n\n```python\nfrom pyhtnorm import hyperplane_truncated_mvnorm, structured_precision_mvnorm\nimport numpy as np\n\nrng = np.random.default_rng()\n\n# generate example input\nk1, k2 = 1000, 1\ntemp = rng.random((k1, k1))\ncov = temp @ temp.T\nG = np.ones((k2, k1))\nr = np.zeros(k2)\nmean = rng.random(k1)\n\n# passing `random_state` is optional. If the argument is not used, a fresh\n# random generator state is instantiated internally using system entropy.\no = hyperplane_truncated_mvnorm(mean, cov, G, r, random_state=rng)\nprint(o.sum()) # verify if sampled values sum to zero\n# alternatively one can pass an array to store the results in\nhyperplane_truncated_mvnorm(mean, cov, G, r, out=o)\n```\n\nFor more information about the function's arguments, refer to its docstring.\n\nA pure numpy implementation is demonstrated in this [example script][9].\n\n\n## R Interface\n\nOne can also use the package in R. To install, use one the following commands:\n```R\ndevtools::install_github(\"zoj613/htnorm\")\npak::pkg_install(\"zoj613/htnorm\")\n```\n\nBelow is an R translation of the above python example:\n\n```R\nlibrary(htnorm)\n\n# make dummy data\nmean <- rnorm(1000)\ncov <- matrix(rnorm(1000 * 1000), ncol=1000)\ncov <- cov %*% t(cov)\nG <- matrix(rep(1, 1000), ncol=1000)\nr <- c(0)\n\n# initialize the Generator instance\nrng <- HTNGenerator(seed=12345, gen=\"pcg64\")\n\nsamples <- rng$hyperplane_truncated_mvnorm(mean, cov, G, r)\n#verify if sampled values sum to zero\nsum(samples)\n\n# optionally pass a vector to store the results in\nout <- rep(0, 1000)\nrng$hyperplane_truncated_mvnorm(mean, cov, G, r, out = out)\nsum(out) #verify\n\nout <- rep(0, 1000)\neig <- eigen(cov)\nphi <- eig$vectors\nomega <- diag(eig$values)\na <- diag(runif(length(mean)))\nrng$structured_precision_mvnorm(mean, a, phi, omega, a_type = \"diagonal\", out = out)\n```\n\n## Licensing\n\n`htnorm` is free software made available under the BSD-3 License. For details\nsee the [LICENSE][6] file.\n\n\n## References\n- Cong, Yulai; Chen, Bo; Zhou, Mingyuan. Fast Simulation of Hyperplane-Truncated \n Multivariate Normal Distributions. Bayesian Anal. 12 (2017), no. 4, 1017--1037. \n doi:10.1214/17-BA1052.\n- Bhattacharya, A., Chakraborty, A., and Mallick, B. K. 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