Package 'DiceView'

Apply Functions Over Array Margins, using custom vectorization (possibly using parallel)

Description

Emulate parallel apply on a function, from mclapply. Returns a vector or array or list of values obtained by applying a function to margins of an array or matrix.

Usage

Apply.function(
  FUN,
  X,
  MARGIN = 1,
  .combine = c,
  .lapply = parallel::mclapply,
  ...
)

Arguments

FUN	function to apply on X
X	array of input values for FUN
MARGIN	1 indicates to apply on rows (default), 2 on columns
.combine	how to combine results (default using c(.))
.lapply	how to vectorize FUN call (default is parallel::mclapply)
...	optional arguments to FUN.

Value

array of values taken by FUN on each row/column of X

Examples

X = matrix(runif(10),ncol=2);
  rowSums(X) == apply(X,1,sum)
  apply(X,1,sum) == Apply.function(sum,X)

X = matrix(runif(10),ncol=1)
  rowSums(X) == apply(X,1,sum)
  apply(X,1,sum) == Apply.function(sum,X)

X = matrix(runif(10),ncol=2)
f = function(X) X[1]/X[2]
apply(X,1,f) == Apply.function(f,X)

---

Checks if some points belong to a given mesh

Description

Checks if some points belong to a given mesh

Usage

are_in.mesh(X, mesh)

Arguments

X	points to check
mesh	mesh identifying the set which X may belong

Examples

X = matrix(runif(100),ncol=2);
inside = are_in.mesh(X,mesh=geometry::delaunayn(matrix(c(0,0,1,1,0,0),ncol=2),output.options =TRUE))
print(inside)
plot(X,col=rgb(1-inside,0,0+inside))

---

This is a simple copy of the Branin-Hoo 2-dimensional test function, as provided in DiceKriging package. The Branin-Hoo function is defined here over [0,1] x [0,1], instead of [-5,0] x [10,15] as usual. It has 3 global minima : x1 = c(0.9616520, 0.15); x2 = c(0.1238946, 0.8166644); x3 = c(0.5427730, 0.15)

Description

This is a simple copy of the Branin-Hoo 2-dimensional test function, as provided in DiceKriging package. The Branin-Hoo function is defined here over [0,1] x [0,1], instead of [-5,0] x [10,15] as usual. It has 3 global minima : x1 = c(0.9616520, 0.15); x2 = c(0.1238946, 0.8166644); x3 = c(0.5427730, 0.15)

Usage

branin(x)

Arguments

x	a 2-dimensional vector specifying the location where the function is to be evaluated.

Value

A real number equal to the Branin-Hoo function values at x

---

Generalize expand.grid() for multi-columns data. Build all combinations of lines from X1 and X2. Each line may hold multiple columns.

Description

Generalize expand.grid() for multi-columns data. Build all combinations of lines from X1 and X2. Each line may hold multiple columns.

Usage

combn.design(X1, X2)

Arguments

X1	variable values, possibly with many columns
X2	variable values, possibly with many columns combn.design(matrix(c(10,20),ncol=1),matrix(c(1,2,3,4,5,6),ncol=2)) combn.design(matrix(c(10,20,30,40),ncol=2),matrix(c(1,2,3,4,5,6),ncol=2))

---

Plot a contour view of a prediction model or function, including design points if available.

Description

Plot a contour view of a prediction model or function, including design points if available.

Usage

## S3 method for class ''function''
contourview(
  fun,
  vectorized = FALSE,
  dim = NULL,
  center = NULL,
  lty_center = 2,
  col_center = "black",
  axis = NULL,
  npoints = 21,
  levels = 10,
  lty_levels = 3,
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels - 1) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels - 1),
  col = NULL,
  col_fading_interval = 0.5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'matrix'
contourview(
  X,
  y,
  center = NULL,
  lty_center = 2,
  col_center = "black",
  axis = NULL,
  col_points = if (!is.null(col)) col else "red",
  col = NULL,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'character'
contourview(eval_str, axis = NULL, mfrow = NULL, ...)

## S3 method for class 'km'
contourview(
  km_model,
  type = "UK",
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(km_model@y, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'Kriging'
contourview(
  Kriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(Kriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NuggetKriging'
contourview(
  NuggetKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(NuggetKriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NoiseKriging'
contourview(
  NoiseKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(NoiseKriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'glm'
contourview(
  glm_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(glm_model$fitted.values, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'list'
contourview(
  modelFit_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(modelFit_model$data$Y, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels) else if
    (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels - 1) else
    col.levels("blue", levels),
  col = NULL,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

contourview(...)

Arguments

fun	a function or 'predict()'-like function that returns a simple numeric or mean and standard error: list(mean=...,se=...).
vectorized	is fun vectorized?
dim	input variables dimension of the model or function.
center	optional coordinates (as a list or data frame) of the center of the section view if the model's dimension is > 2.
lty_center	line type for the section center of the plot (if any).
col_center	color for the section center of the plot (if any).
axis	optional matrix of 2-axis combinations to plot, one by row. The value NULL leads to all possible combinations i.e. choose(D, 2).
npoints	an optional number of points to discretize plot of response surface and uncertainties.
levels	(number of) contour levels to display.
lty_levels	contour line type.
col_levels	color for the surface.
col	color of the object (use col_* for specific objects).
col_fading_interval	an optional factor of alpha (color channel) fading used to plot function output intervals (if any).
mfrow	an optional list to force par(mfrow = ...) call. The default value NULL is automatically set for compact view.
Xlab	an optional list of string to overload names for X.
ylab	an optional string to overload name for y.
Xlim	an optional list to force x range for all plots. The default value NULL is automatically set to include all design points.
title	an optional overload of main title.
add	to print graphics on an existing window.
...	arguments of the contourview.km, contourview.glm, contourview.Kriging or contourview.function function
X	the matrix of input design.
y	the array of output values (two columns means an interval).
col_points	color of points.
bg_fading	an optional factor of alpha (color channel) fading used to plot design points outside from this section.
eval_str	the expression to evaluate in each subplot.
km_model	an object of class "km".
type	the kriging type to use for model prediction.
conf_level	confidence hulls to display.
conf_fading	an optional factor of alpha (color channel) fading used to plot confidence hull.
Kriging_model	an object of class "Kriging".
NuggetKriging_model	an object of class "Kriging".
NoiseKriging_model	an object of class "Kriging".
glm_model	an object of class "glm".
modelFit_model	an object returned by DiceEval::modelFit.

Details

If available, experimental points are plotted with fading colors. Points that fall in the specified section (if any) have the color specified col_points while points far away from the center have shaded versions of the same color. The amount of fading is determined using the Euclidean distance between the plotted point and center.

Author(s)

Yann Richet, IRSN

See Also

sectionview.function for a section plot, and sectionview3d.function for a 2D section plot.

sectionview.matrix for a section plot, and sectionview3d.matrix for a 2D section plot.

contourview.matrix for a section plot.

sectionview.km for a section plot, and sectionview3d.km for a 2D section plot.

sectionview.Kriging for a section plot, and sectionview3d.Kriging for a 2D section plot.

sectionview.NuggetKriging for a section plot, and sectionview3d.NuggetKriging for a 2D section plot.

sectionview.NoiseKriging for a section plot, and sectionview3d.NoiseKriging for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

Examples

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2 + rnorm(15)
model <- lm(y ~ x1 + x2)

contourview(function(x) sum(x),
                     dim=2, Xlim=cbind(range(x1),range(x2)), col='black')
points(x1,x2)

contourview(function(x) {
                      x = as.data.frame(x)
                      colnames(x) <- all.vars(model$call)[-1]
                      predict.lm(model, newdata=x, se.fit=FALSE)
                    }, vectorized=TRUE, dim=2,
              Xlim=cbind(range(x1),range(x2)), add=TRUE)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

contourview(X, y)

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2^2 + rnorm(15)
model <- glm(y ~ x1 + I(x2^2))

contourview(model)

contourview("abline(h=0.25,col='red')")
if (requireNamespace("DiceKriging")) { library(DiceKriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- km(design = X, response = y, covtype="matern3_2")

contourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- Kriging(X = X, y = y, kernel="matern3_2")

contourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NuggetKriging(X = X, y = y, kernel="matern3_2")

contourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NoiseKriging(X = X, y = y, kernel="matern3_2", noise=rep(5^2,15))

contourview(model)

}

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2^2 + rnorm(15)
model <- glm(y ~ x1 + I(x2^2))

contourview(model)

if (requireNamespace("DiceEval")) { library(DiceEval)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- modelFit(X, y, type = "StepLinear")

contourview(model)

}

## A 2D example - Branin-Hoo function
contourview(branin, dim=2, levels=30, col='black')

## Not run: 
## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(seq(0, 1, length = 4), seq(0, 1, length = 4))
design.fact <- data.frame(design.fact); names(design.fact) <- c("x1", "x2")
y <- branin(design.fact); names(y) <- "y"

if (requireNamespace("DiceKriging")) { library(DiceKriging)
## model: km
model <- DiceKriging::km(design = design.fact, response = y)
contourview(model, levels=30)
contourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

if (requireNamespace("rlibkriging")) { library(rlibkriging)
## model: Kriging
model <- Kriging(X = as.matrix(design.fact), y = as.matrix(y), kernel="matern3_2")
contourview(model, levels=30)
contourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

## model: glm
model <- glm(y ~ 1+ x1 + x2 + I(x1^2) + I(x2^2) + x1*x2, data=cbind(y,design.fact))
contourview(model, levels=30)
contourview(branin, dim=2, levels=30, col='red', add=TRUE)

if (requireNamespace("DiceEval")) { library(DiceEval)
## model: StepLinear
model <- modelFit(design.fact, y, type = "StepLinear")
contourview(model, levels=30)
contourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

## End(Not run)

---

eval function and cast result to a list of y, y_low, y_up (possibly NA)

Description

eval function and cast result to a list of y, y_low, y_up (possibly NA)

Usage

EvalInterval.function(fun, X, vectorized = FALSE, dim = ncol(X))

Arguments

fun	function to evaluate
X	matrix of input values for fun
vectorized	whether fun is vectorized or not
dim	dimension of input values for fun if

Value

list of y, y_low, y_up

---

Create a Data Frame from all combinations of factor variables

Description

Generalization of base::expand.grid to more than 2 variables.

Usage

expand.grids(d = length(list(...)), ...)

Arguments

d	number of variables (taken in following arguments with modulo)
...	variables to combine, as arrays of values

Value

data frame of all possible combinations of variables values

---

be careful that fade(.., alpha=0) means total fading, while fade(.., alpha=1) means no fading

Description

be careful that fade(.., alpha=0) means total fading, while fade(.., alpha=1) means no fading

Usage

fade(
  color = "red",
  alpha = seq(from = 0, to = 1, length.out = 5),
  plot = FALSE
)

---

Plot a contour view of a prediction model or function, including design points if available.

Description

Plot a contour view of a prediction model or function, including design points if available.

Usage

## S3 method for class ''function''
filledcontourview(
  fun,
  vectorized = FALSE,
  dim = NULL,
  center = NULL,
  lty_center = 2,
  col_center = "black",
  axis = NULL,
  npoints = 21,
  levels = 10,
  lty_levels = 0,
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  col_interval = "white",
  col_fading_interval = 0.5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  add_fading = 0.5,
  ...
)

## S3 method for class 'km'
filledcontourview(
  km_model,
  type = "UK",
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(km_model@y, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'Kriging'
filledcontourview(
  Kriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(Kriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NuggetKriging'
filledcontourview(
  NuggetKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(NuggetKriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NoiseKriging'
filledcontourview(
  NoiseKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(NoiseKriging_model$y(), 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'glm'
filledcontourview(
  glm_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(glm_model$fitted.values, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  conf_level = 0.5,
  conf_fading = 0.5,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'list'
filledcontourview(
  modelFit_model,
  center = NULL,
  axis = NULL,
  npoints = 21,
  levels = pretty(modelFit_model$data$Y, 10),
  col_points = if (!is.null(col) & length(col) == 1) col else "red",
  col_levels = if (!is.null(col) & length(col) == 1) col.levels(col, levels, fill = TRUE)
    else if (!is.null(col) & length(col) == 2) cols.levels(col[1], col[2], levels, fill =
    TRUE) else col.levels("blue", levels, fill = TRUE),
  col = NULL,
  bg_fading = 1,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

filledcontourview(...)

Arguments

fun	a function or 'predict()'-like function that returns a simple numeric or mean and standard error: list(mean=...,se=...).
vectorized	is fun vectorized?
dim	input variables dimension of the model or function.
center	optional coordinates (as a list or data frame) of the center of the section view if the model's dimension is > 2.
lty_center	line type for thesection center of the plot (if any).
col_center	color for the section center of the plot (if any).
axis	optional matrix of 2-axis combinations to plot, one by row. The value NULL leads to all possible combinations i.e. choose(D, 2).
npoints	an optional number of points to discretize plot of response surface and uncertainties.
levels	(number of) contour levels to display.
lty_levels	contour line type.
col_levels	color for the surface.
col	color of the object (use col_* for specific objects).
col_interval	color to display interval width.
col_fading_interval	an optional factor of alpha (color channel) fading used to plot function output intervals (if any).
mfrow	an optional list to force par(mfrow = ...) call. The default value NULL is automatically set for compact view.
Xlab	an optional list of string to overload names for X.
ylab	an optional string to overload name for y.
Xlim	an optional list to force x range for all plots. The default value NULL is automatically set to include all design points.
title	an optional overload of main title.
add	to print graphics on an existing window.
add_fading	an optional factor of alpha (color channel) fading used to plot when add=TRUE.
...	arguments of the filledcontourview.km, filledcontourview.glm, filledcontourview.Kriging or filledcontourview.function function
km_model	an object of class "km".
type	the kriging type to use for model prediction.
col_points	color of points.
conf_level	confidence hulls to display.
conf_fading	an optional factor of alpha (color channel) fading used to plot confidence hull.
bg_fading	an optional factor of alpha (color channel) fading used to plot design points outside from this section.
Kriging_model	an object of class "Kriging".
NuggetKriging_model	an object of class "Kriging".
NoiseKriging_model	an object of class "Kriging".
glm_model	an object of class "glm".
modelFit_model	an object returned by DiceEval::modelFit.

Details

If available, experimental points are plotted with fading colors. Points that fall in the specified section (if any) have the color specified col_points while points far away from the center have shaded versions of the same color. The amount of fading is determined using the Euclidean distance between the plotted point and center.

Author(s)

Yann Richet, IRSN

See Also

sectionview.function for a section plot, and sectionview3d.function for a 2D section plot.

sectionview.km for a section plot, and sectionview3d.km for a 2D section plot.

sectionview.Kriging for a section plot, and sectionview3d.Kriging for a 2D section plot.

sectionview.NuggetKriging for a section plot, and sectionview3d.NuggetKriging for a 2D section plot.

sectionview.NoiseKriging for a section plot, and sectionview3d.NoiseKriging for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

Examples

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2 + rnorm(15)
model <- lm(y ~ x1 + x2)

filledcontourview(function(x) sum(x),
                     dim=2, Xlim=cbind(range(x1),range(x2)), col='black')
points(x1,x2)

filledcontourview(function(x) {
                      x = as.data.frame(x)
                      colnames(x) <- all.vars(model$call)[-1]
                      predict.lm(model, newdata=x, se.fit=FALSE)
                    }, vectorized=TRUE, dim=2,
                  Xlim=cbind(range(x1),range(x2)), add=TRUE)

if (requireNamespace("DiceKriging")) { library(DiceKriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- km(design = X, response = y, covtype="matern3_2")

filledcontourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- Kriging(X = X, y = y, kernel="matern3_2")

filledcontourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NuggetKriging(X = X, y = y, kernel="matern3_2")

filledcontourview(model)

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NoiseKriging(X = X, y = y, kernel="matern3_2", noise=rep(5^2,15))

filledcontourview(model)

}

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2^2 + rnorm(15)
model <- glm(y ~ x1 + I(x2^2))

filledcontourview(model)

if (requireNamespace("DiceEval")) { library(DiceEval)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- modelFit(X, y, type = "StepLinear")

filledcontourview(model)

}

## A 2D example - Branin-Hoo function
filledcontourview(branin, dim=2, levels=30, col='black')

## Not run: 
## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(seq(0, 1, length = 4), seq(0, 1, length = 4))
design.fact <- data.frame(design.fact); names(design.fact) <- c("x1", "x2")
y <- branin(design.fact); names(y) <- "y"

if (requireNamespace("DiceKriging")) { library(DiceKriging)
## model: km
model <- DiceKriging::km(design = design.fact, response = y)
filledcontourview(model, levels=30)
filledcontourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

if (requireNamespace("rlibkriging")) { library(rlibkriging)
## model: Kriging
model <- Kriging(X = as.matrix(design.fact), y = as.matrix(y), kernel="matern3_2")
filledcontourview(model, levels=30)
filledcontourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

## model: glm
model <- glm(y ~ 1+ x1 + x2 + I(x1^2) + I(x2^2) + x1*x2, data=cbind(y,design.fact))
filledcontourview(model, levels=30)
filledcontourview(branin, dim=2, levels=30, col='red', add=TRUE)

if (requireNamespace("DiceEval")) { library(DiceEval)
## model: StepLinear
model <- modelFit(design.fact, y, type = "StepLinear")
filledcontourview(model, levels=30)
filledcontourview(branin, dim=2, levels=30, col='red', add=TRUE)
}

## End(Not run)

---

Checks if some point belongs to a given mesh

Description

Checks if some point belongs to a given mesh

Usage

is_in.mesh(x, mesh)

Arguments

x	point to check
mesh	mesh identifying the set which X may belong

Examples

is_in.mesh(-0.5,mesh=geometry::delaunayn(matrix(c(0,1),ncol=1),output.options =TRUE))
is_in.mesh(0.5,mesh=geometry::delaunayn(matrix(c(0,1),ncol=1),output.options =TRUE))

x =matrix(-.5,ncol=2,nrow=1)
is_in.mesh(x,mesh=geometry::delaunayn(matrix(c(0,0,1,1,0,0),ncol=2),output.options =TRUE))

x =matrix(.5,ncol=2,nrow=1)
is_in.mesh(x,mesh=geometry::delaunayn(matrix(c(0,0,1,1,0,0),ncol=2),output.options =TRUE))

---

Test if points are in a hull

Description

Test if points are in a hull

Usage

is_in.p(x, p, h = NULL)

Arguments

x	points to test
p	points defining the hull
h	hull itself (built from p if given as NULL (default))

Examples

is_in.p(x=-0.5,p=matrix(c(0,1),ncol=1))
is_in.p(x=0.5,p=matrix(c(0,1),ncol=1))
is_in.p(x=matrix(-.5,ncol=2,nrow=1),p=matrix(c(0,0,1,1,0,0),ncol=2))
is_in.p(x=matrix(.25,ncol=2,nrow=1),p=matrix(c(0,0,1,1,0,0),ncol=2))
is_in.p(x=matrix(-.5,ncol=3,nrow=1),p=matrix(c(0,0,0,1,0,0,0,1,0,0,0,1),ncol=3,byrow = TRUE))
is_in.p(x=matrix(.25,ncol=3,nrow=1),p=matrix(c(0,0,0,1,0,0,0,1,0,0,0,1),ncol=3,byrow = TRUE))

---

Checks if a mesh is valid

Description

Checks if a mesh is valid

Usage

is.mesh(x)

Arguments

x	mesh to check

Value

TRUE if mesh is valid

---

Memoize a function

Description

Before each call of a function, check that the cache holds the results and returns it if available. Otherwise, compute f and cache the result for next evluations.

Usage

Memoize.function(fun)

Arguments

fun	function to memoize

Value

a function with same behavior than argument one, but using cache.

Examples

f=function(n) rnorm(n);
F=Memoize.function(f);
F(5); F(6); F(5)

---

Builds a mesh from a design aor set of points

Description

Builds a mesh from a design aor set of points

Usage

mesh(intervals, mesh.type = "seq", mesh.sizes = 11)

Arguments

intervals	bounds to inverse in, each column contains min and max of each dimension
mesh.type	function or "unif" or "seq" (default) or "LHS" to preform interval partition
mesh.sizes	number of parts for mesh (duplicate for each dimension if using "seq")

Value

delaunay mesh (list(p,tri,...) from geometry)

Examples

mesh = mesh(intervals=matrix(c(0,1,0,1),ncol=2),mesh.type="unif",mesh.sizes=10)
plot2d_mesh(mesh)

---

Search excursion set of nD function, sampled by a mesh

Description

Search excursion set of nD function, sampled by a mesh

Usage

mesh_exsets(
  f,
  vectorized = FALSE,
  threshold,
  sign,
  intervals,
  mesh.type = "seq",
  mesh.sizes = 11,
  maxerror_f = 1e-09,
  tol = .Machine$double.eps^0.25,
  ex_filter.tri = all,
  ...
)

Arguments

f	Function to inverse at 'threshold'
vectorized	boolean: is f already vectorized ? (default: FALSE) or if function: vectorized version of f.
threshold	target value to inverse
sign	focus at conservative for above (sign=1) or below (sign=-1) the threshold
intervals	bounds to inverse in, each column contains min and max of each dimension
mesh.type	"unif" or "seq" (default) or "LHS" to preform interval partition
mesh.sizes	number of parts for mesh (duplicate for each dimension if using "seq")
maxerror_f	maximal tolerance on f precision
tol	the desired accuracy (convergence tolerance on f arg).
ex_filter.tri	boolean function to validate a geometry::tri as considered in excursion : 'any' or 'all'
...	parameters to forward to roots_mesh(...) call

Examples

# mesh_exsets(function(x) x, threshold=.51, sign=1, intervals=rbind(0,1),
#   maxerror_f=1E-2,tol=1E-2) # for faster testing
# mesh_exsets(function(x) x, threshold=.50000001, sign=1, intervals=rbind(0,1),
#   maxerror_f=1E-2,tol=1E-2) # for faster testing
# mesh_exsets(function(x) sum(x), threshold=.51,sign=1, intervals=cbind(rbind(0,1),rbind(0,1)),
#   maxerror_f=1E-2,tol=1E-2) # for faster testing
# mesh_exsets(sin,threshold=0,sign="sup",interval=c(pi/2,5*pi/2),
#   maxerror_f=1E-2,tol=1E-2) # for faster testing

if (identical(Sys.getenv("NOT_CRAN"), "true")) { # too long for CRAN on Windows

  e = mesh_exsets(function(x) (0.25+x[1])^2+(0.5+x[2])^2 ,
                threshold =0.25,sign=-1, intervals=matrix(c(-1,1,-1,1),nrow=2),
                maxerror_f=1E-2,tol=1E-2) # for faster testing

  plot(e$p,xlim=c(-1,1),ylim=c(-1,1));
  apply(e$tri,1,function(tri) polygon(e$p[tri,],col=rgb(.4,.4,.4,.4)))

  if (requireNamespace("rgl")) {
    e = mesh_exsets(function(x) (0.5+x[1])^2+(-0.5+x[2])^2+(0.+x[3])^2,
                  threshold = .25,sign=-1, mesh.type="unif",
                  intervals=matrix(c(-1,1,-1,1,-1,1),nrow=2),
                  maxerror_f=1E-2,tol=1E-2) # for faster testing

    rgl::plot3d(e$p,xlim=c(-1,1),ylim=c(-1,1),zlim=c(-1,1));
    apply(e$tri,1,function(tri)rgl::lines3d(e$p[tri,]))
  }
}

---

Mesh level set of function

Description

Mesh level set of function

Usage

mesh_level(f, vectorized = FALSE, level = 0, intervals, mesh, ...)

Arguments

f	function to be evaluated on the mesh
vectorized	logical or function. If TRUE, f is assumed to be vectorized.
level	level/threshold value
intervals	matrix of intervals
mesh	mesh object or type
...	additional arguments passed to f

---

Minimal distance between one point to many points

Description

Minimal distance between one point to many points

Usage

min_dist(x, X, norm = rep(1, ncol(X)))

Arguments

x	one point
X	matrix of points (same number of columns than x)
norm	normalization vecor of distance (same number of columns than x)

Value

minimal distance

Examples

min_dist(runif(3),matrix(runif(30),ncol=3))

---

Title Multi-local optimization wrapper for optim, using (possibly parallel) multistart.

Description

Title Multi-local optimization wrapper for optim, using (possibly parallel) multistart.

Usage

optims(
  pars,
  fn,
  fn.NaN = NaN,
  .apply = "mclapply",
  pars.eps = 1e-05,
  control = list(),
  ...
)

Arguments

pars	starting points for optim
fn	objective function, like in optim().
fn.NaN	replacement value of fn when returns NaN
.apply	loop/parallelization backend for multistart ("mclapply", "lapply" or "foreach")
pars.eps	minimal distance between two solutions to be considered different
control	control parameters for optim()
...	additional arguments passed to optim()

Value

list with best solution and all solutions

Author(s)

Yann Richet, IRSN

Examples

fn = function(x) ifelse(x==0,1,sin(x)/x)
# plot(fn, xlim=c(-20,20))
optim( par=5,                     fn,lower=-20,upper=20,method='L-BFGS-B')
optims(pars=t(t(seq(-20,20,,20))),fn,lower=-20,upper=20,method='L-BFGS-B')

# Branin function (3 local minimas)
f = function (x) {
  x1 <- x[1] * 15 - 5
  x2 <- x[2] * 15
  (x2 - 5/(4 * pi^2) * (x1^2) + 5/pi * x1 - 6)^2 + 10 * (1 - 1/(8 * pi)) * cos(x1) + 10
}
# expect to find 3 local minimas
optims(pars=matrix(runif(100),ncol=2),f,method="L-BFGS-B",lower=c(0,0),upper=c(1,1))

---

Plot a one dimensional mesh

Description

Plot a one dimensional mesh

Usage

plot_mesh(
  mesh,
  y = 0,
  color.nodes = "black",
  color.mesh = "darkgray",
  alpha = 0.4,
  ...
)

Arguments

mesh	1-dimensional mesh to draw
y	ordinate value where to draw the mesh
color.nodes	color of the mesh nodes
color.mesh	color of the mesh elements
alpha	transparency of the mesh elements & nodes
...	optional arguments passed to plot function

Examples

plot_mesh(mesh_exsets(function(x) x, threshold=.51, sign=1, intervals=rbind(0,1)))
plot_mesh(mesh_exsets(function(x) (x-.5)^2, threshold=.1, sign=-1, intervals=rbind(0,1)))

---

Plot a two dimensional mesh

Description

Plot a two dimensional mesh

Usage

plot2d_mesh(
  mesh,
  color.nodes = "black",
  color.mesh = "darkgray",
  alpha = 0.4,
  ...
)

Arguments

mesh	2-dimensional mesh to draw
color.nodes	color of the mesh nodes
color.mesh	color of the mesh elements
alpha	transparency of the mesh elements & nodes
...	optional arguments passed to plot function

Examples

plot2d_mesh(mesh_exsets(f = function(x) sin(pi*x[1])*sin(pi*x[2]),
                        threshold=0,sign=1, mesh.type="unif",mesh.size=11,
                        intervals = matrix(c(1/2,5/2,1/2,5/2),nrow=2)))

---

Plot a three dimensional mesh

Description

Plot a three dimensional mesh

Usage

plot3d_mesh(
  mesh,
  engine3d = NULL,
  color.nodes = "black",
  color.mesh = "darkgray",
  alpha = 0.4,
  ...
)

Arguments

mesh	3-dimensional mesh to draw
engine3d	3d framework to use: 'rgl' if installed or 'scatterplot3d' (default)
color.nodes	color of the mesh nodes
color.mesh	color of the mesh elements
alpha	transparency of the mesh elements & nodes
...	optional arguments passed to plot function

Examples

if (identical(Sys.getenv("NOT_CRAN"), "true")) { # too long for CRAN on Windows

  plot3d_mesh(mesh_exsets(function(x) (0.5+x[1])^2+(-0.5+x[2])^2+(0.+x[3])^2,
                          threshold = .25,sign=-1, mesh.type="unif",
                          maxerror_f=1E-2,tol=1E-2, # faster display
                          intervals=matrix(c(-1,1,-1,1,-1,1),nrow=2)),
                          engine3d='scatterplot3d')

  if (requireNamespace("rgl")) {
    plot3d_mesh(mesh_exsets(function(x) (0.5+x[1])^2+(-0.5+x[2])^2+(0.+x[3])^2,
                            threshold = .25,sign=-1, mesh.type="unif",
                            maxerror_f=1E-2,tol=1E-2, # faster display
                            intervals=matrix(c(-1,1,-1,1,-1,1),nrow=2)),engine3d='rgl')
  }
}

---

Extract points of mesh which belong to the mesh triangulation (may not contain all points)

Description

Extract points of mesh which belong to the mesh triangulation (may not contain all points)

Usage

points_in.mesh(mesh)

Arguments

mesh	mesh (list(p,tri,...) from geometry)

Value

points coordinates inside the mesh triangulation

---

Extract points of mesh which do not belong to the mesh triangulation (may not contain all points)

Description

Extract points of mesh which do not belong to the mesh triangulation (may not contain all points)

Usage

points_out.mesh(mesh)

Arguments

mesh	(list(p,tri,...) from geometry)

Value

points coordinates outside the mesh triangulation

---

One Dimensional Root (Zero) Finding

Description

Search one root with given precision (on y). Iterate over uniroot as long as necessary.

Usage

root(
  f,
  lower,
  upper,
  maxerror_f = 1e-07,
  f_lower = f(lower, ...),
  f_upper = f(upper, ...),
  tol = .Machine$double.eps^0.25,
  convexity = FALSE,
  rec = 0,
  max.rec = NA,
  ...
)

Arguments

f	the function for which the root is sought.
lower	the lower end point of the interval to be searched.
upper	the upper end point of the interval to be searched.
maxerror_f	the maximum error on f evaluation (iterates over uniroot to converge).
f_lower	the same as f(lower).
f_upper	the same as f(upper).
tol	the desired accuracy (convergence tolerance on f arg).
convexity	the learned convexity factor of the function, used to reduce the boundaries for uniroot.
rec	counter of recursive level.
max.rec	maximal number of recursive level before failure (stop).
...	additional named or unnamed arguments to be passed to f.

Author(s)

Yann Richet, IRSN

Examples

f=function(x) {cat("f");1-exp(x)}; f(root(f,lower=-1,upper=2))
f=function(x) {cat("f");exp(x)-1}; f(root(f,lower=-1,upper=2))

.f = function(x) 1-exp(1*x)
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

.f = function(x) exp(10*x)-1
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20);y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

.f = function(x) exp(100*x)-1
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20);y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

f=function(x) {cat("f");exp(100*x)-1}; f(root(f,lower=-1,upper=2))

## Not run: 

  # Quite hard functions to find roots

  ## Increasing function
  ## convex
  n.f=0
  .f = function(x) exp(10*x)-1
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20);y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)
  ## non-convex
  n.f=0
  .f = function(x) 1-exp(-10*x)
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20);y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)

  # ## Decreasing function
  # ## non-convex
  n.f=0
  .f = function(x) 1-exp(10*x)
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)
  # ## convex
  n.f=0
  .f = function(x) exp(-10*x)-1
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)

## End(Not run)

---

One Dimensional Multiple Roots (Zero) Finding

Description

Search multiple roots of 1D function, sampled/splitted by a (1D) mesh

Usage

roots(
  f,
  vectorized = FALSE,
  interval,
  maxerror_f = 1e-07,
  split = "seq",
  split.size = 11,
  tol = .Machine$double.eps^0.25,
  .lapply = parallel::mclapply,
  ...
)

Arguments

f	Function to find roots
vectorized	boolean: is f already vectorized ? (default: FALSE) or if function: vectorized version of f.
interval	bounds to inverse in
maxerror_f	the maximum error on f evaluation (iterates over uniroot to converge).
split	function or "unif" or "seq" (default) to preform interval partition
split.size	number of parts to perform uniroot inside
tol	the desired accuracy (convergence tolerance on f arg).
.lapply	control the loop/vectorization over different roots (defaults to multicore apply).
...	additional named or unnamed arguments to be passed to f.

Value

array of x, so f(x)=target

Examples

roots(sin,interval=c(pi/2,5*pi/2))
roots(sin,interval=c(pi/2,1.5*pi/2))

f=function(x)exp(x)-1;
f(roots(f,interval=c(-1,2)))

f=function(x)exp(1000*x)-1;
f(roots(f,interval=c(-1,2)))

---

Multi Dimensional Multiple Roots (Zero) Finding, sampled by a mesh

Description

Multi Dimensional Multiple Roots (Zero) Finding, sampled by a mesh

Usage

roots_mesh(
  f,
  vectorized = FALSE,
  intervals,
  mesh.type = "seq",
  mesh.sizes = 11,
  maxerror_f = 1e-07,
  tol = .Machine$double.eps^0.25,
  ...
)

Arguments

f	Function (one or more dimensions) to find roots of
vectorized	is f already vectorized ? (default: no)
intervals	bounds to inverse in, each column contains min and max of each dimension
mesh.type	function or "unif" or "seq" (default) to preform interval partition
mesh.sizes	number of parts for mesh (duplicate for each dimension if using "seq")
maxerror_f	the maximum error on f evaluation (iterates over uniroot to converge).
tol	the desired accuracy (convergence tolerance on f arg).
...	Other args for f

Value

matrix of x, so f(x)=0

Examples

roots_mesh(function(x) x-.51, intervals=rbind(0,1))
roots_mesh(function(x) sum(x)-.51, intervals=cbind(rbind(0,1),rbind(0,1)))
roots_mesh(sin,intervals=c(pi/2,5*pi/2))
roots_mesh(f = function(x) sin(pi*x[1])*sin(pi*x[2]),
           intervals = matrix(c(1/2,5/2,1/2,5/2),nrow=2))

r = roots_mesh(f = function(x) (0.25+x[1])^2+(0.5+x[2])^2 - .25,
intervals=matrix(c(-1,1,-1,1),nrow=2), mesh.size=5)
plot(r,xlim=c(-1,1),ylim=c(-1,1))

r = roots_mesh(function(x) (0.5+x[1])^2+(-0.5+x[2])^2+(0.+x[3])^2 - .5,
               mesh.sizes = 11,
               intervals=matrix(c(-1,1,-1,1,-1,1),nrow=2))
scatterplot3d::scatterplot3d(r,xlim=c(-1,1),ylim=c(-1,1),zlim=c(-1,1))

roots_mesh(function(x)exp(x)-1,intervals=c(-1,2))
roots_mesh(function(x)exp(1000*x)-1,intervals=c(-1,2))

---

Plot a section view of a prediction model or function, including design points if available.

Description

Plot a section view of a prediction model or function, including design points if available.

Usage

## S3 method for class ''function''
sectionview(
  fun,
  vectorized = FALSE,
  dim = NULL,
  center = NULL,
  lty_center = 2,
  col_center = "black",
  axis = NULL,
  npoints = 101,
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  col_fading_interval = 0.5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'matrix'
sectionview(
  X,
  y,
  center = NULL,
  lty_center = 2,
  col_center = "black",
  axis = NULL,
  col_points = if (!is.null(col)) col else "red",
  col = NULL,
  col_fading_interval = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'character'
sectionview(eval_str, axis = NULL, mfrow = NULL, ...)

## S3 method for class 'km'
sectionview(
  km_model,
  type = "UK",
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  conf_level = 0.95,
  conf_fading = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'Kriging'
sectionview(
  Kriging_model,
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  conf_level = 0.95,
  conf_fading = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NuggetKriging'
sectionview(
  NuggetKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  conf_level = 0.95,
  conf_fading = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'NoiseKriging'
sectionview(
  NoiseKriging_model,
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  conf_level = 0.95,
  conf_fading = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'glm'
sectionview(
  glm_model,
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  conf_level = 0.95,
  conf_fading = 0.5,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

## S3 method for class 'list'
sectionview(
  modelFit_model,
  center = NULL,
  axis = NULL,
  npoints = 101,
  col_points = if (!is.null(col)) col else "red",
  col_fun = if (!is.null(col)) col else "blue",
  col = NULL,
  bg_fading = 5,
  mfrow = NULL,
  Xlab = NULL,
  ylab = NULL,
  Xlim = NULL,
  ylim = NULL,
  title = NULL,
  add = FALSE,
  ...
)

sectionview(...)

Arguments

fun	a function or 'predict()'-like function that returns a simple numeric, or an interval, or mean and standard error: list(mean=...,se=...).
vectorized	is fun vectorized?
dim	input variables dimension of the model or function.
center	optional coordinates (as a list or data frame) of the center of the section view if the model's dimension is > 2.
lty_center	line type for the section center of the plot (if any).
col_center	color for the section center of the plot (if any).
axis	optional matrix of 2-axis combinations to plot, one by row. The value NULL leads to all possible combinations i.e. choose(D, 2).
npoints	an optional number of points to discretize plot of response surface and uncertainties.
col_fun	color of the function plot.
col	color of the object (use col_* for specific objects).
col_fading_interval	an optional factor of alpha (color channel) fading used to plot confidence intervals.
mfrow	an optional list to force par(mfrow = ...) call. The default value NULL is automatically set for compact view.
Xlab	an optional list of string to overload names for X.
ylab	an optional string to overload name for y.
Xlim	an optional list to force x range for all plots. The default value NULL is automatically set to include all design points.
ylim	an optional list to force y range for all plots.
title	an optional overload of main title.
add	to print graphics on an existing window.
...	arguments of the sectionview.km, sectionview.glm, sectionview.Kriging or sectionview.function function
X	the matrix of input design.
y	the array of output values (two columns means an interval).
col_points	color of points.
bg_fading	an optional factor of alpha (color channel) fading used to plot design points outside from this section.
eval_str	the expression to evaluate in each subplot.
km_model	an object of class "km".
type	the kriging type to use for model prediction.
conf_level	an optional list of confidence intervals to display.
conf_fading	an optional factor of alpha (color channel) fading used to plot confidence intervals.
Kriging_model	an object of class "Kriging".
NuggetKriging_model	an object of class "Kriging".
NoiseKriging_model	an object of class "Kriging".
glm_model	an object of class "glm".
modelFit_model	an object returned by DiceEval::modelFit.

Details

If available, experimental points are plotted with fading colors. Points that fall in the specified section (if any) have the color specified col_points while points far away from the center have shaded versions of the same color. The amount of fading is determined using the Euclidean distance between the plotted point and center.

Author(s)

Yann Richet, IRSN

See Also

sectionview.function for a section plot, and sectionview3d.function for a 2D section plot.

sectionview.matrix for a section plot, and sectionview3d.matrix for a 2D section plot.

sectionview.matrix for a section plot, and sectionview3d.matrix for a 2D section plot.

sectionview.km for a section plot, and sectionview3d.km for a 2D section plot.

sectionview.Kriging for a section plot, and sectionview3d.Kriging for a 2D section plot.

sectionview.NuggetKriging for a section plot, and sectionview3d.NuggetKriging for a 2D section plot.

sectionview.NoiseKriging for a section plot, and sectionview3d.NoiseKriging for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

sectionview.glm for a section plot, and sectionview3d.glm for a 2D section plot.

Examples

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2 + rnorm(15)
model <- lm(y ~ x1 + x2)

sectionview(function(x) sum(x),
                     dim=2, center=c(0,0), Xlim=cbind(range(x1),range(x2)), col='black')

sectionview(function(x) {
                      x = as.data.frame(x)
                      colnames(x) <- all.vars(model$call)[-1]
                      p = predict.lm(model, newdata=x, se.fit=TRUE)
                      cbind(p$fit-1.96 * p$se.fit, p$fit+1.96 * p$se.fit)
                    }, vectorized=TRUE, dim=2, center=c(0,0),
              Xlim=cbind(range(x1),range(x2)), add=TRUE)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

sectionview(X,y, center=c(.5,.5))

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2^2 + rnorm(15)
model <- glm(y ~ x1 + I(x2^2))

sectionview(model, center=c(.5,.5))

sectionview("abline(h=5)")
if (requireNamespace("DiceKriging")) { library(DiceKriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- km(design = X, response = y, covtype="matern3_2")

sectionview(model, center=c(.5,.5))

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- Kriging(X = X, y = y, kernel="matern3_2")

sectionview(model, center=c(.5,.5))

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NuggetKriging(X = X, y = y, kernel="matern3_2")

sectionview(model, center=c(.5,.5))

}

if (requireNamespace("rlibkriging")) { library(rlibkriging)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin) + 5*rnorm(15)

model <- NoiseKriging(X = X, y = y, kernel="matern3_2", noise=rep(5^2,15))

sectionview(model, center=c(.5,.5))

}

x1 <- rnorm(15)
x2 <- rnorm(15)

y <- x1 + x2^2 + rnorm(15)
model <- glm(y ~ x1 + I(x2^2))

sectionview(model, center=c(.5,.5))

if (requireNamespace("DiceEval")) { library(DiceEval)

X = matrix(runif(15*2),ncol=2)
y = apply(X,1,branin)

model <- modelFit(X, y, type = "StepLinear")

sectionview(model, center=c(.5,.5))

}

## A 2D example - Branin-Hoo function
sectionview(branin, center= c(.5,.5), col='black')

## Not run: 
## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(seq(0, 1, length = 4), seq(0, 1, length = 4))
design.fact <- data.frame(design.fact); names(design.fact) <- c("x1", "x2")
y <- branin(design.fact); names(y) <- "y"

if (requireNamespace("DiceKriging")) { library(DiceKriging)
## model: km
model <- DiceKriging::km(design = design.fact, response = y)
sectionview(model, center= c(.5,.5))
sectionview(branin, center= c(.5,.5), col='red', add=TRUE)
}

if (requireNamespace("rlibkriging")) { library(rlibkriging)
## model: Kriging
model <- Kriging(X = as.matrix(design.fact), y = as.matrix(y), kernel="matern3_2")
sectionview(model, center= c(.5,.5))
sectionview(branin, center= c(.5,.5), col='red', add=TRUE)
}

## model: glm
model <- glm(y ~ 1+ x1 + x2 + I(x1^2) + I(x2^2) + x1*x2, data=cbind(y,design.fact))
sectionview(model, center= c(.5,.5))
sectionview(branin, center= c(.5,.5), col='red', add=TRUE)

if (requireNamespace("DiceEval")) { library(DiceEval)
## model: StepLinear
model <- modelFit(design.fact, y, type = "StepLinear")
sectionview(model, center= c(.5,.5))
sectionview(branin, center= c(.5,.5), col='red', add=TRUE)
}

## End(Not run)

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