Ryacas version 1.1.0 publised in Journal of Open Source Software and released to CRAN

It is with great pleasure that I can announce that Ryacas version 1.1.0 has now been accepted into Journal of Open Source Software and same version released to CRAN. (The source code is available at https://github.com/mikldk/ryacas/.)

I already wrote about Ryacas many times before. I will refer you to the “Getting started” and “The high-level (symbol) interface” vignettes or one of the others available at the CRAN page or the package’s website.

It means that you can install the package by (possible after binaries have been built):

install.packages("Ryacas")

Followed by:

library(Ryacas)

A small demo case (with a Rosenbrock function):

x <- yac_symbol("x")
y <- yac_symbol("y")
f <- 100 * (y - x^2)^2 + (1 - x)^2 
f # also yac_symbol
## [1] 100*(y-x^2)^2+(1-x)^2
as_r(f) # as R expression
## expression(100 * (y - x^2)^2 + (1 - x)^2)

We can now find the gradient:

g <- deriv(f, c("x", "y"))
g # yac_symbol
## [1] {(-400)*x*(y-x^2)-2*(1-x),200*(y-x^2)}
as_r(g) # as R expression
## expression(c(-400 * x * (y - x^2) - 2 * (1 - x), 200 * (y - x^2)))
eval(as_r(g), list(x = 3, y = 2)) # get value for a point
## [1]  8404 -1400

Or the Hessian:

H <- Hessian(f, c("x", "y"))
H # yac_symbol
## {{(-400)*(y-x^2-2*x^2)+2,               (-400)*x},
##  {              (-400)*x,                    200}}
as_r(H) # as R expression
## expression(rbind(c(-400 * (y - x^2 - 2 * x^2) + 2, -400 * x), 
##     c(-400 * x, 200)))
eval(as_r(H), list(x = 3, y = 2)) # get value for a point
##       [,1]  [,2]
## [1,] 10002 -1200
## [2,] -1200   200

We can even get these in \(\LaTeX\) format:

tex(g)
## [1] "\\left( -400 x \\left( y - x ^{2}\\right)  - 2 \\left( 1 - x\\right) , 200 \\left( y - x ^{2}\\right) \\right) "

\[ \nabla f(x, y) = \left( -400 x \left( y - x ^{2}\right) - 2 \left( 1 - x\right) , 200 \left( y - x ^{2}\right) \right) \]

tex(H)
## [1] "\\left( \\begin{array}{cc} -400 \\left( y - x ^{2} - 2 x ^{2}\\right)  + 2 & -400 x \\\\ -400 x & 200 \\end{array} \\right) "

\[ \nabla^2 f(x, y) = \left( \begin{array}{cc} -400 \left( y - x ^{2} - 2 x ^{2}\right) + 2 & -400 x \\ -400 x & 200 \end{array} \right) \]