jacobi: Jacobi polynomials

In dkahle/mpoly: Symbolic Computation and More with Multivariate Polynomials

Jacobi polynomials

Description

Jacobi polynomials as computed by orthopolynom.

Usage

jacobi(
  degree,
  alpha = 1,
  beta = 1,
  kind = "p",
  indeterminate = "x",
  normalized = FALSE
)

Arguments

degree	degree of polynomial
alpha	the first parameter, also called p
beta	the second parameter, also called q
kind	"g" or "p"
indeterminate	indeterminate
normalized	provide normalized coefficients

Value

a mpoly object or mpolyList object

Author(s)

David Kahle calling code from the orthopolynom package

See Also

orthopolynom::jacobi.g.polynomials(), orthopolynom::jacobi.p.polynomials(), http://en.wikipedia.org/wiki/Jacobi_polynomials

Examples

jacobi(0)
jacobi(1)
jacobi(2)
jacobi(3)
jacobi(4)
jacobi(5)
jacobi(6)
jacobi(10, 2, 2, normalized = TRUE)

jacobi(0:5)
jacobi(0:5, normalized = TRUE)
jacobi(0:5, kind = "g")
jacobi(0:5, indeterminate = "t")



# visualize the jacobi polynomials

library(ggplot2); theme_set(theme_classic())
library(tidyr)

s <- seq(-1, 1, length.out = 201)
N <- 5 # number of jacobi polynomials to plot
(jacPolys <- jacobi(0:N, 2, 2))

df <- data.frame(s, as.function(jacPolys)(s))
names(df) <- c("x", paste0("P_", 0:N))
mdf <- gather(df, degree, value, -x)
qplot(x, value, data = mdf, geom = "line", color = degree)

qplot(x, value, data = mdf, geom = "line", color = degree) +
  coord_cartesian(ylim = c(-30, 30))

dkahle/mpoly documentation built on Nov. 21, 2024, 8:27 a.m.