Code Catalog

A one-page catalog of working scripts and quickstarts for np, npRmpi, and crs.

Keywords

np, npRmpi, crs, code examples, scripts, quickstart

This page is meant to be the quickest route to working scripts. It groups the existing code by package, task, and runtime mode so that you can scan, copy, and then drill down only if you need more context.

How to use this page

• If you want only the smallest starter scripts, go first to Quickstarts.
• If you want something you can paste into R immediately, start with the short blocks below.
• If you want a fuller script, use the tables further down.
• If you know a function name, use the site search box or the Reference page.

Minimal starters you can copy immediately

np: kernel regression

Source file: np_regression_quickstart.R

rm(list = ls())

## Minimal np regression example.
##
## The intended workflow is:
## 1. compute a bandwidth object,
## 2. fit the regression estimator,
## 3. inspect the result and a simple fitted curve.

library(np)
options(np.messages = FALSE)

data(cps71, package = "np")
dat <- cps71[, c("logwage", "age")]

bw <- npregbw(logwage ~ age, data = dat, regtype = "ll", bwmethod = "cv.aic")
fit <- npreg(bws = bw, data = dat)

summary(bw)
summary(fit)

plot(dat$age, dat$logwage, cex = 0.25, col = "grey")
o <- order(dat$age)
lines(dat$age[o], fitted(fit)[o], col = 2, lwd = 2)

Start here if you want the core np workflow in its simplest form. For more context, see Kernel Primer or Quickstarts.

np: density estimation

Source file: np_density_quickstart.R

rm(list = ls())

## Minimal np density-estimation example.
##
## The intended workflow is:
## 1. compute a bandwidth object,
## 2. fit the density estimator,
## 3. inspect the result.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- data.frame(waiting = faithful$waiting)

bw <- npudensbw(~ waiting, data = dat, bwmethod = "cv.ml")
fhat <- npudens(bws = bw, data = dat)

summary(bw)
summary(fhat)

Start here if the object of interest is a density rather than a regression mean. For distribution, conditional-density, conditional-distribution, and quantile starters, see Quickstarts and Density, Distribution, Quantiles.

npRmpi: same workflow, MPI initialized once

Source file: nprmpi_session_quickstart.R

rm(list = ls())

## Minimal modern npRmpi example.
##
## The intended workflow is:
## 1. initialize MPI once in session/spawn mode,
## 2. write ordinary np-style code,
## 3. quit cleanly at the end.

library(npRmpi)

npRmpi.init(mode = "spawn", nslaves = 1)
on.exit(npRmpi.quit(), add = TRUE)

options(npRmpi.autodispatch = TRUE, np.messages = FALSE)

set.seed(1)
x <- runif(200)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
dat <- data.frame(y, x)

bw <- npregbw(y ~ x, regtype = "ll", bwmethod = "cv.ls", data = dat)
fit <- npreg(bws = bw, data = dat)

summary(bw)
summary(fit)

plot(dat$x, dat$y, cex = 0.35, col = "grey")
o <- order(dat$x)
lines(dat$x[o], fitted(fit)[o], col = 2, lwd = 2)

This is the modern default instructional path for npRmpi: initialize MPI once, then write ordinary np-style code. For mode details, see MPI and Large Data.

crs: spline regression

Source file: crs_quickstart.R

rm(list = ls())

## Minimal crs spline-regression example.
##
## This is the smallest useful workflow:
## 1. fit a spline model,
## 2. inspect the summary,
## 3. optionally move on to plotting or tighter search control.

library(crs)
options(crs.messages = FALSE)

set.seed(42)
n <- 250
x1 <- runif(n)
x2 <- runif(n)
y <- sin(2 * pi * x1) + x2 + rnorm(n, sd = 0.2)
dat <- data.frame(y, x1, x2)

fit <- crs(y ~ x1 + x2, data = dat)

summary(fit)

Use this when regression splines are the natural first tool. For the conceptual route, see Spline Primer.

np: kernel methods in serial

Script	Main topic	Functions/features	Start reading here
np_regression_quickstart.R	Minimal kernel-regression workflow	npregbw, npreg	Kernel Primer
np_density_quickstart.R	Minimal density-estimation workflow	npudensbw, npudens	Density, Distribution, Quantiles
np_distribution_quickstart.R	Minimal distribution-estimation workflow	npudistbw, npudist	Density, Distribution, Quantiles
np_conditional_density_quickstart.R	Minimal conditional-density workflow	npcdensbw, npcdens	Density, Distribution, Quantiles
np_conditional_distribution_quickstart.R	Minimal conditional-distribution workflow	npcdistbw, npcdist	Density, Distribution, Quantiles
np_quantile_quickstart.R	Minimal quantile-regression workflow	npcdistbw, npqreg	Density, Distribution, Quantiles
np_classification_quickstart.R	Minimal classification / conditional-mode workflow	npconmode	Classification and Modes
np_plotting_quickstart.R	Minimal plotting and interval workflow	npreg, plot, predict	Plotting and Intervals
np_entropy_quickstart.R	Minimal entropy/testing workflow	npunitest	Entropy and Testing
np_semiparametric_quickstart.R	Minimal semiparametric workflow	npplreg	Semiparametric Models
np_significance_quickstart.R	Minimal significance-testing workflow	npreg, npsigtest	Significance and Specification
np_specification_quickstart.R	Minimal model-specification workflow	lm, npcmstest	Significance and Specification

Additional serial scripts

Script	Main topic	Functions/features	Start reading here
regression_intro_a.R	Univariate regression and plotting	npreg, local constant, local linear	Kernel Primer
regression_intro_b.R	Derivative estimation	npreg, derivative output	Plotting and Intervals
regression_intro_c.R	Plotting fitted objects and intervals	plot(), asymptotic and bootstrap error handling	Plotting and Intervals
regression_multivar_a.R	Multivariate regression	mixed predictors, multivariate fit	Multivariate Regression and Prediction
demo_poly.R	Generalized local polynomial comparison	npglpreg, crs, local polynomial comparison	Worked Examples

npRmpi: modern session-mode quick start

If you want one current downloadable script before anything else, start here.

Script	Main topic	Functions/features	Start reading here
nprmpi_session_quickstart.R	Modern session / spawn workflow	npRmpi.init, npregbw, npreg, autodispatch	MPI and Large Data
nprmpi_attach_quickstart.R	Modern attach-mode workflow	npRmpi.init(mode = \attach\), npregbw, npreg	MPI and Large Data
nprmpi_profile_quickstart.R	Modern profile/manual-broadcast workflow	mpi.bcast.cmd, np.mpi.initialize, npregbw, npreg	MPI and Large Data

Inline source for common scripts

The blocks below are pulled directly from the script files in www/, so they stay aligned with the downloadable versions.

Notenp: Kernel regression

Source file: np_regression_quickstart.R

rm(list = ls())

## Minimal np regression example.
##
## The intended workflow is:
## 1. compute a bandwidth object,
## 2. fit the regression estimator,
## 3. inspect the result and a simple fitted curve.

library(np)
options(np.messages = FALSE)

data(cps71, package = "np")
dat <- cps71[, c("logwage", "age")]

bw <- npregbw(logwage ~ age, data = dat, regtype = "ll", bwmethod = "cv.aic")
fit <- npreg(bws = bw, data = dat)

summary(bw)
summary(fit)

plot(dat$age, dat$logwage, cex = 0.25, col = "grey")
o <- order(dat$age)
lines(dat$age[o], fitted(fit)[o], col = 2, lwd = 2)

Notenp: Density estimation

Source file: np_density_quickstart.R

rm(list = ls())

## Minimal np density-estimation example.
##
## The intended workflow is:
## 1. compute a bandwidth object,
## 2. fit the density estimator,
## 3. inspect the result.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- data.frame(waiting = faithful$waiting)

bw <- npudensbw(~ waiting, data = dat, bwmethod = "cv.ml")
fhat <- npudens(bws = bw, data = dat)

summary(bw)
summary(fhat)

Notenp: Distribution estimation

Source file: np_distribution_quickstart.R

rm(list = ls())

## Minimal np distribution example.
##
## This mirrors the usual density workflow but targets the
## unconditional distribution function instead.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- data.frame(waiting = faithful$waiting)

bw <- npudistbw(~ waiting, data = dat, nmulti = 1)
Fhat <- npudist(bws = bw, data = dat)

summary(bw)
summary(Fhat)

Notenp: Conditional density estimation

Source file: np_conditional_density_quickstart.R

rm(list = ls())

## Minimal np conditional-density example.
##
## This keeps the first run small enough to be practical while still
## showing the standard two-step workflow:
## 1. compute a bandwidth object,
## 2. fit the conditional-density estimator.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- faithful[seq_len(120), c("eruptions", "waiting")]

bw <- npcdensbw(eruptions ~ waiting, data = dat, nmulti = 1)
fhat <- npcdens(bws = bw, data = dat)

summary(bw)
summary(fhat)

Notenp: Conditional distribution estimation

Source file: np_conditional_distribution_quickstart.R

rm(list = ls())

## Minimal np conditional-distribution example.
##
## This uses a small first run so the standard two-step workflow stays
## copyable and practical.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- faithful[seq_len(120), c("eruptions", "waiting")]

bw <- npcdistbw(eruptions ~ waiting, data = dat, nmulti = 1)
Fhat <- npcdist(bws = bw, data = dat)

summary(bw)
summary(Fhat)

Notenp: Conditional quantiles

Source file: np_quantile_quickstart.R

rm(list = ls())

## Minimal np quantile-regression example.
##
## The key idea is to compute a conditional-distribution bandwidth once
## and then reuse it for more than one quantile.

library(np)
options(np.messages = FALSE)

data(faithful, package = "datasets")
dat <- faithful[seq_len(120), c("eruptions", "waiting")]

bw <- npcdistbw(eruptions ~ waiting, data = dat, nmulti = 1)
q25 <- npqreg(bws = bw, tau = 0.25)
q50 <- npqreg(bws = bw, tau = 0.50)
q75 <- npqreg(bws = bw, tau = 0.75)

summary(bw)
summary(q50)

plot(dat$waiting, dat$eruptions, cex = 0.35, col = "grey")
o <- order(dat$waiting)
lines(dat$waiting[o], q25$quantile[o], col = 2, lty = 2, lwd = 2)
lines(dat$waiting[o], q50$quantile[o], col = 4, lty = 1, lwd = 2)
lines(dat$waiting[o], q75$quantile[o], col = 2, lty = 3, lwd = 2)

Notenp: Classification and conditional mode

Source file: np_classification_quickstart.R

rm(list = ls())

## Minimal np classification / conditional-mode example.
##
## This keeps the first run compact while still showing the basic
## nonparametric classification route.

library(np)
data(birthwt, package = "MASS")

birthwt$low <- factor(birthwt$low)
birthwt$smoke <- factor(birthwt$smoke)
birthwt$race <- factor(birthwt$race)

fit <- npconmode(low ~ smoke + race + age + lwt, data = birthwt, nmulti = 1)

summary(fit)
fit$confusion.matrix

Notenp: Plotting and asymptotic intervals

Source file: np_plotting_quickstart.R

rm(list = ls())

## Minimal np plotting and interval example.
##
## This fits a simple model, saves one asymptotic-interval plot, and
## shows the prediction route on a small evaluation grid.

library(np)
options(np.messages = FALSE)

data(cps71, package = "np")

fit <- npreg(
  logwage ~ age,
  regtype = "ll",
  bwmethod = "cv.aic",
  gradients = TRUE,
  data = cps71
)

plot_path <- file.path(tempdir(), "np_plotting_quickstart.png")
png(plot_path, width = 700, height = 500)
plot(fit, plot.errors.method = "asymptotic", plot.errors.style = "band")
dev.off()

pred_grid <- data.frame(age = seq(20, 60, by = 10))
predict(fit, newdata = pred_grid)

cat("Saved plot to:", plot_path, "\n")

Notenp: Entropy and testing

Source file: np_entropy_quickstart.R

rm(list = ls())

## Minimal np entropy/testing example.
##
## This uses the univariate density-equality test because it is a
## compact, fast first run.

library(np)
options(np.messages = FALSE)

set.seed(1234)
n <- 300
x <- rnorm(n)
y <- rnorm(n)

test_out <- npunitest(x, y, bootstrap = FALSE)

summary(test_out)

Notenp: Semiparametric models

Source file: np_semiparametric_quickstart.R

rm(list = ls())

## Minimal np semiparametric example.
##
## This uses a partially linear model because it is the clearest
## lightweight entry point into the semiparametric family.

library(np)
options(np.messages = FALSE)

set.seed(42)
n <- 200
x1 <- rnorm(n)
z <- runif(n)
y <- 1 + 2 * x1 + sin(2 * pi * z) + rnorm(n, sd = 0.2)
dat <- data.frame(y, x1, z)

fit <- npplreg(y ~ x1 | z, data = dat)

summary(fit)

Notenp: Significance testing

Source file: np_significance_quickstart.R

rm(list = ls())

## Minimal np significance-testing example.
##
## The idea is to fit a model with one irrelevant regressor and then
## ask whether the nonparametric significance test detects that.

library(np)
options(np.messages = FALSE)

set.seed(42)
n <- 200
z <- factor(rbinom(n, 1, 0.5))
x1 <- rnorm(n)
x2 <- runif(n, -2, 2)
y <- x1 + x2 + rnorm(n)
dat <- data.frame(z, x1, x2, y)

fit <- npreg(
  y ~ z + x1 + x2,
  regtype = "ll",
  bwmethod = "cv.aic",
  data = dat
)

test_out <- npsigtest(fit)

summary(fit)
summary(test_out)

Notenp: Model specification testing

Source file: np_specification_quickstart.R

rm(list = ls())

## Minimal np model-specification test example.
##
## The idea is to fit a simple linear model to nonlinear data and then
## ask whether the parametric specification looks too restrictive.

library(np)
options(np.messages = FALSE)

set.seed(42)
n <- 120
x <- runif(n, -2, 2)
y <- x + x^2 + rnorm(n, sd = 0.25)

model_ols <- lm(y ~ x, x = TRUE, y = TRUE)
X <- data.frame(x = x)

test_out <- npcmstest(
  model = model_ols,
  xdat = X,
  ydat = y,
  nmulti = 1
)

summary(model_ols)
summary(test_out)

Notenp: univariate regression starter

Source file: regression_intro_a.R

rm(list=ls())

## Here is a simple illustration to help you get started with
## univariate kernel regression.

## First, let's grab some data from the np package

## Load the np package

library(np)

## Load the cps71 dataset contained in the np package

data(cps71)

## Attach the data so that the variables `logwage' and `age' can be
## called directly

attach(cps71)

## Plot the data (note it is sorted on age already which helps when
## plotting the lines below, and note the cex=0.25 uses circles that
## are 1/4 the standard size that are grey not black which is the
## default)

plot(age,logwage,cex=0.25,col="grey")

## Fit a (default) local constant model (since we do not explicitly
## call npregbw() which conducts least-squares cross-validated
## bandwidth selection by default it is automatically invoked when we
## call npreg())

model.lc <- npreg(logwage~age)

## Plot the fitted values (the colors and linetypes allow us to
## distinguish different plots on the same figure)

lines(age,fitted(model.lc),col=1,lty=1)

## Fit a local linear model (we use the arguments regtype="ll" to do
## this)

model.ll <- npreg(logwage~age,regtype="ll")

## Plot the fitted values with a different color and linetype

lines(age,fitted(model.ll),col=2,lty=2)

## Add a legend

legend("topleft",
       c("Local Constant","Local Linear"),
       lty=c(1,2),
       col=c(1,2),
       bty="n")

Notenp: multivariate regression and plotting

Source file: regression_multivar_a.R

rm(list=ls())

## Here is a simple illustration to help you get started with
## multivariate kernel regression and plotting via R's `plot' function
## (which calls the np function `npplot')

## First, let's grab some data from the np package

## Load the np package

library(np)

## Load the wage1 dataset contained in the np package

data(wage1)

## Attach the data so that the variables `lwage', `female', `educ' and
## `exper' can be called directly

attach(wage1)

## Fit a local linear model (since we do not explicitly call npregbw()
## which conducts least-squares cross-validated bandwidth selection by
## default it is automatically invoked when we call npreg()). Here we
## have a `factor' (female) and two `numeric' predictors (educ and
## exper - see ?wage1 for details)

model <- npreg(lwage~female+educ+exper,regtype="ll")

## model will be an object of class `npreg'. The generic R function
## `plot' will call `npplot' when it is deployed on an object of this
## type (see ?npplot for details on supported npplot
## arguments). Calling plot on a npreg object allows you to do some
## tedious things without having to write code such as including
## confidence intervals as the following example demonstrates. Note
## also that we do not explicitly have to specify `gradients=TRUE' in
## the call to npreg() as plot (npplot) will take care of this for
## us. Below we use the asymptotic standard error estimates and then
## take +- 1.96 standard error)

plot(model,plot.errors.method="asymptotic",plot.errors.style="band")

## We might also wish to use bootstrapping instead (here we bootstrap
## the standard errors and then take +- 1.96 standard error)

plot(model,plot.errors.method="bootstrap",plot.errors.style="band")

## Alternately, we might compute true nonparametric confidence
## intervals using (by default) the 0.025 and 0.975 percentiles of the
## pointwise bootstrap distributions

plot(model,plot.errors.method="bootstrap",plot.errors.type="quantiles",plot.errors.style="band")

## Note that adding the argument `gradients=TRUE' to the plot call
## will automatically plot the derivatives instead

plot(model,plot.errors.method="bootstrap",plot.errors.type="quantiles",plot.errors.style="band",gradients=TRUE)

NotenpRmpi: Session / spawn mode

Source file: nprmpi_session_quickstart.R

rm(list = ls())

## Minimal modern npRmpi example.
##
## The intended workflow is:
## 1. initialize MPI once in session/spawn mode,
## 2. write ordinary np-style code,
## 3. quit cleanly at the end.

library(npRmpi)

npRmpi.init(mode = "spawn", nslaves = 1)
on.exit(npRmpi.quit(), add = TRUE)

options(npRmpi.autodispatch = TRUE, np.messages = FALSE)

set.seed(1)
x <- runif(200)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
dat <- data.frame(y, x)

bw <- npregbw(y ~ x, regtype = "ll", bwmethod = "cv.ls", data = dat)
fit <- npreg(bws = bw, data = dat)

summary(bw)
summary(fit)

plot(dat$x, dat$y, cex = 0.35, col = "grey")
o <- order(dat$x)
lines(dat$x[o], fitted(fit)[o], col = 2, lwd = 2)

NotenpRmpi: Attach mode

Source file: nprmpi_attach_quickstart.R

rm(list = ls())

## Minimal attach-mode npRmpi example.
##
## Launch with a pre-created MPI world, for example:
##   mpiexec -env R_PROFILE_USER "" -env R_PROFILE "" -n 2 \
##     Rscript --no-save nprmpi_attach_quickstart.R

library(npRmpi)

npRmpi.init(mode = "attach", comm = 1, autodispatch = TRUE)
options(np.messages = FALSE)

if (mpi.comm.rank(0L) == 0L) {
  set.seed(1)
  x <- runif(200)
  y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
  dat <- data.frame(y, x)

  bw <- npregbw(y ~ x, regtype = "ll", bwmethod = "cv.ls", data = dat)
  fit <- npreg(bws = bw, data = dat)

  summary(bw)
  summary(fit)

  npRmpi.quit(mode = "attach", comm = 1)
}

NotenpRmpi: Profile / manual-broadcast mode

Source file: nprmpi_profile_quickstart.R

rm(list = ls())

## Minimal profile/manual-broadcast npRmpi example.
##
## Launch with an explicit profile source, for example:
##   RPROFILE=$(Rscript --no-save -e 'cat(system.file("Rprofile", package="npRmpi"))')
##   mpiexec -env R_PROFILE_USER "$RPROFILE" -env R_PROFILE "" -n 2 \
##     Rscript --no-save nprmpi_profile_quickstart.R

invisible(mpi.bcast.cmd(np.mpi.initialize(), caller.execute = TRUE))
invisible(mpi.bcast.cmd(options(np.messages = FALSE), caller.execute = TRUE))

set.seed(1)
x <- runif(200)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
dat <- data.frame(y, x)

invisible(mpi.bcast.Robj2slave(dat))

invisible(mpi.bcast.cmd(
  bw <- npregbw(y ~ x, regtype = "ll", bwmethod = "cv.ls", data = dat),
  caller.execute = TRUE
))

invisible(mpi.bcast.cmd(
  fit <- npreg(bws = bw, data = dat),
  caller.execute = TRUE
))

summary(bw)
summary(fit)

invisible(mpi.bcast.cmd(mpi.quit(), caller.execute = TRUE))

npRmpi: serial and MPI comparison scripts

These are older comparison scripts, but still useful if you want to see side-by-side serial and MPI routes. For new work, start with the session / spawn example above and then come back to these when you want route parity or legacy comparison.

Task	Serial	MPI	Start reading here
Conditional density estimation	npcdensls_serial.R	npcdensls_npRmpi.R	Density, Distribution, Quantiles
Model specification test	npcmstest_serial.R	npcmstest_npRmpi.R	Significance and Specification
Conditional mode estimation	npconmode_serial.R	npconmode_npRmpi.R	Classification and Modes
Density equality test	npdeneqtest_serial.R	npdeneqtest_npRmpi.R	Entropy and Testing
Single index estimation	npindexich_serial.R	npindexich_npRmpi.R	Semiparametric Models
Partially linear regression	npplreg_serial.R	npplreg_npRmpi.R	Semiparametric Models
Local linear AIC bandwidth selection	npregllaic_serial.R	npregllaic_npRmpi.R	Kernel Primer
Serial dependence test	npsdeptest_serial.R	npsdeptest_npRmpi.R	Entropy and Testing
Significance test	npsigtest_serial.R	npsigtest_npRmpi.R	Significance and Specification
Unconditional density estimation	npudensml_serial.R	npudensml_npRmpi.R	Density, Distribution, Quantiles

npRmpi: local polynomial / constrained examples

Script	Main topic
lp_k1_prodfunc.R	Production-function style local polynomial example
lp_k1.R	Local polynomial example
lp_radial_mean.R	Constrained radial mean example
lp_radial_deriv.R	Constrained radial derivative example

crs: spline examples

Script	Main topic	Notes
crs_quickstart.R	Minimal spline-regression workflow	modern quickstart
radial_rgl.R	Bivariate radial spline surface	requires rgl
sine_rgl.R	Bivariate sine spline surface	requires rgl
radial_constrained_mean.R	Constrained spline mean estimation	uses quadprog
radial_constrained_first_partial.R	Constrained first derivative	uses quadprog
radial_constrained_second_partial.R	Constrained second derivative	uses quadprog

Notecrs: Spline regression

Source file: crs_quickstart.R

rm(list = ls())

## Minimal crs spline-regression example.
##
## This is the smallest useful workflow:
## 1. fit a spline model,
## 2. inspect the summary,
## 3. optionally move on to plotting or tighter search control.

library(crs)
options(crs.messages = FALSE)

set.seed(42)
n <- 250
x1 <- runif(n)
x2 <- runif(n)
y <- sin(2 * pi * x1) + x2 + rnorm(n, sd = 0.2)
dat <- data.frame(y, x1, x2)

fit <- crs(y ~ x1 + x2, data = dat)

summary(fit)

Interactive demos for teaching and exploration

Script	Main topic	Notes
manipulate_density.R	Univariate density with sliders	RStudio + manipulate
manipulate_eruptions.R	Old Faithful density	RStudio + manipulate
manipulate_distribution.R	Univariate distribution	RStudio + manipulate
manipulate_bivariate_density.R	Bivariate density	RStudio + manipulate
manipulate_faithful_density.R	Old Faithful bivariate density	RStudio + manipulate
manipulate_bivariate_distribution.R	Bivariate distribution	RStudio + manipulate
manipulate_wage1.R	Multivariate regression partial plots	RStudio + manipulate
manipulate_npglpreg.R	Generalized local polynomial regression	RStudio + manipulate
manipulate_npglpreg_sin.R	Sinusoidal GLP illustration	RStudio + manipulate
manipulate_constrained_local_polynomial.R	Constrained local polynomial regression	requires quadprog
manipulate_constrained_local_polynomial_production.R	Constrained production function	requires quadprog
manipulate_constrained_spline.R	Constrained spline surface	requires quadprog
manipulate_constrained_spline_derivative.R	Constrained spline derivative	requires quadprog
manipulate_copula.R	Copula plots	requires mnormt
manipulate_socco.R	SOCCO nonlinear-system demo	requires data.RData and figures.R

Notes

• The gallery still preserves the original scripts, but the site now aims to route you to them more directly.
• The short blocks near the top are there so you can copy a minimal working pattern without downloading anything first.
• For MPI-specific launch semantics, see MPI and Large Data.
• For short copyable code blocks rather than full scripts, start with Worked Examples.