https://github.com/yukai-yang/smfilter
an R package implementing the filtering algorithms for the state-space models on the Stiefel manifold
https://github.com/yukai-yang/smfilter
cran filtering filtering-algorithm nonlinear-dynamics nonlinear-optimization reduced-rank-parameters sampling simulated-data smoothing state-space-models stiefel-manifold time-series-models
Last synced: 7 months ago
JSON representation
an R package implementing the filtering algorithms for the state-space models on the Stiefel manifold
- Host: GitHub
- URL: https://github.com/yukai-yang/smfilter
- Owner: yukai-yang
- License: gpl-3.0
- Created: 2018-11-16T02:59:39.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2025-05-24T21:57:35.000Z (about 1 year ago)
- Last Synced: 2025-10-22T05:50:50.097Z (7 months ago)
- Topics: cran, filtering, filtering-algorithm, nonlinear-dynamics, nonlinear-optimization, reduced-rank-parameters, sampling, simulated-data, smoothing, state-space-models, stiefel-manifold, time-series-models
- Language: R
- Homepage:
- Size: 393 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: NEWS.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
Awesome Lists containing this project
README
SMFilter version 1.0.4 (Red Filter)
===================================
[](https://cran.r-project.org/package=SMFilter)   
The package implements the filtering algorithms for the state-space models on the Stiefel manifold. It also implements sampling algorithms for uniform, vector Langevin-Bingham and matrix Langevin-Bingham distributions on the Stiefel manifold. You can also find the package on CRAN, see
[SMFilter@CRAN](https://CRAN.R-project.org/package=SMFilter)
and the corresponding paper
[State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering](https://www.mdpi.com/2225-1146/6/4/48)
How to install
--------------
You can either install the stable version from CRAN
``` r
install.packages("SMFilter")
```
or install the development version from GitHub
``` r
devtools::install_github("yukai-yang/SMFilter")
```
provided that the package "devtools" has been installed beforehand.
Example
-------
After installing the package, you need to load (attach better say) it by running the code
``` r
library(SMFilter)
```
You can first check the information and the current version number by running
``` r
version()
#> SMFilter version 1.0.3 (Red Filter)
```
Then you can take a look at all the available functions and data in the package
``` r
ls( grep("SMFilter", search()) )
#> [1] "FDist2" "FilterModel1" "FilterModel2" "rmLB_sm"
#> [5] "runif_sm" "rvlb_sm" "SimModel1" "SimModel2"
#> [9] "version"
```
### Type one model
For details, see
``` r
?SimModel1
```
First we can use the package to sample from the type one model. To this end, we shall initialize by running
``` r
set.seed(1) # control the seed
iT = 100 # sample size
ip = 2 # dimension of the dependent variable
ir = 1 # rank number
iqx = 3 # dimension of the independent variable x_t
iqz=0 # dimension of the independent variable z_t
ik = 0 # lag length
method='max_3' # the optimization methond to use, for details, see FilterModel1
Omega = diag(ip)*.1 # covariance of the errors
vD = 50 # diagonal of the D matrix
```
Then we initialize the data and some other parameters
``` r
if(iqx==0) mX=NULL else mX = matrix(rnorm(iT*iqx),iT, iqx)
if(iqz==0) mZ=NULL else mZ = matrix(rnorm(iT*iqz),iT, iqz)
if(ik==0) mY=NULL else mY = matrix(0, ik, ip)
alpha_0 = matrix(c(runif_sm(num=1,ip=ip,ir=ir)), ip, ir)
beta = matrix(c(runif_sm(num=1,ip=ip*ik+iqx,ir=ir)), ip*ik+iqx, ir)
if(ip*ik+iqz==0) mB=NULL else mB = matrix(c(runif_sm(num=1,ip=(ip*ik+iqz)*ip,ir=1)), ip, ip*ik+iqz)
```
Then we can simulate from the model
``` r
ret = SimModel1(iT=iT, mX=mX, mZ=mZ, mY=mY, alpha_0=alpha_0, beta=beta, mB=mB, vD=vD, Omega=Omega)
```
Have a look at the simulated data
``` r
matplot(ret$dData[,1:ip], type="l", ylab="simulated data")
```
Then let's apply the filtering algorithm on the data
``` r
fil = FilterModel1(mY=as.matrix(ret$dData[,1:ip]), mX=mX, mZ=mZ, beta=beta, mB=mB, Omega=Omega, vD=vD, U0=alpha_0, method=method)
```
Then we compare the filtered modal orientations with the true ones in terms of the squared Frobenius norm distance (normalized).
What if we start with a wrongly specified initial value, −**α**0 cannot be worse?
### Type two model
For details, see
``` r
?SimModel2
```
Again, we start with sampling. We initialize the parameters
``` r
iT = 100
ip = 2
ir = 1
iqx = 4
iqz=0
ik = 0
Omega = diag(ip)*.1
vD = 50
```
Then we initialize the data and some other parameters
``` r
if(iqx==0) mX=NULL else mX = matrix(rnorm(iT*iqx),iT, iqx)
if(iqz==0) mZ=NULL else mZ = matrix(rnorm(iT*iqz),iT, iqz)
if(ik==0) mY=NULL else mY = matrix(0, ik, ip)
alpha = matrix(c(runif_sm(num=1,ip=ip,ir=ir)), ip, ir)
beta_0 = matrix(c(runif_sm(num=1,ip=ip*ik+iqx,ir=ir)), ip*ik+iqx, ir)
if(ip*ik+iqz==0) mB=NULL else mB = matrix(c(runif_sm(num=1,ip=(ip*ik+iqz)*ip,ir=1)), ip, ip*ik+iqz)
```
Then we can simulate from the model
``` r
ret = SimModel2(iT=iT, mX=mX, mZ=mZ, mY=mY, alpha=alpha, beta_0=beta_0, mB=mB, vD=vD)
```
And then have a look at the simulated data
``` r
matplot(ret$dData[,1:ip], type="l",ylab="simulated data")
```
Apply the filtering algorithm on the data
``` r
fil = FilterModel2(mY=as.matrix(ret$dData[,1:ip]), mX=mX, mZ=mZ, alpha=alpha, mB=mB, Omega=Omega, vD=vD, U0=beta_0, method=method)
```
Then we compare the filtered modal orientations with the true ones in terms of the squared Frobenius norm distance (normalized).
What if we start with a wrongly specified initial value, −**β**0 cannot be worse?
