# Using the good old Fortran L-BFGS-B code

This post is a sequel to the previous article on how to use the old Fortran code to solve optimization problems in C++ applications. This time we consider the L-BFGS-B algorithm for solving smooth and box-constrained optimization problems of the form \begin{align*} \min_{x}\quad & f(x)\\ \text{subject to}\quad & l\le x\le u, \end{align*} where $l$ and $u$ are simple bounds for $x\in\mathbb{R}^n$, and can take $-\infty$ and $+\infty$ values.

# Using the good old Fortran L-BFGS code

L-BFGS is a well-known and widely-used optimization algorithm for smooth and unconstrained optimization problems. It was originally implemented in Fortran, and also has some more recent implementations including libLBFGS and my own LBFGS++. The Fortran code was written more than 30 years ago, and looks a bit exotic from today’s perspective. However, it is still one of the most stable and mature implementations of the L-BFGS algorithm, and is typically used as a baseline in testing and benchmarking.

# Updates on RSpectra: new "center" and "scale" parameters for svds()

Per the suggestion by @robmaz, RSpectra::svds() now has two new parameters center and scale, to support implicit centering and scaling of matrices in partial SVD. The minimum version for this new feature is RSpectra >= 0.16-0. These two parameters are very useful for principal component analysis (PCA) based on the covariance or correlation matrix, without actually forming them. Below we simulate a random data matrix, and use both R’s built-in prcomp() and the svds() function in RSpectra to compute PCA.

# RcppNumerical: numerical integration and optimization with Rcpp

Introduction I have seen several conversations in Rcpp-devel mailing list asking how to compute numerical integration or optimization in Rcpp. While R in fact has the functions Rdqags, Rdqagi, nmmin, vmmin etc. in its API to accomplish such tasks, it is not so straightforward to use them with Rcpp. For my own research projects I need to do a lot of numerical integration, root finding and optimization, so to make my life a little bit easier, I just created the RcppNumerical package that simplifies these procedures.

# Large scale eigenvalue decomposition and SVD with rARPACK

In January 2016, I was honored to receive an “Honorable Mention” of the John Chambers Award 2016. This article was written for R-bloggers, whose builder, Tal Galili, kindly invited me to write an introduction to the rARPACK package. A Short Story of rARPACK Eigenvalue decomposition is a commonly used technique in numerous statistical problems. For example, principal component analysis (PCA) basically conducts eigenvalue decomposition on the sample covariance of a data matrix: the eigenvalues are the component variances, and eigenvectors are the variable loadings.

# An overview of linear algebra libraries in Scala/Java

This semester I’m taking a course in big data computing using Scala/Spark, and we are asked to finish a course project related to big data analysis. Since statistical modeling heavily relies on linear algebra, I investigated some existing libraries in Scala/Java that deal with matrix and linear algebra algorithms. 1. Set-up Scala/Java libraries are usually distributed as *.jar files. To use them in Scala, we can create a directory to hold them and set up the environment variable to let Scala know about this path.

# Using system fonts in R graphs

This is a pretty old topic in R graphics. A classical article in R NEWS, Non-standard fonts in PostScript and PDF graphics, describes how to use and embed system fonts in the PDF/PostScript device. More recently, Winston Chang developed the extrafont package, which makes the procedure much easier. A useful introduction article can be found in the readme page of extrafont, and also from the Revolution blog. Now, we have another choice: the showtext package.
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#### Yixuan Qiu

Statistics, Data, and Programming

Associate Professor

Shanghai