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add: C implementation, 

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Daniel Kapla 2019-09-16 11:15:51 +02:00
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CVE_C/DESCRIPTION Normal file
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Package: CVE
Type: Package
Title: Conditional Variance Estimator for Sufficient Dimension Reduction
Version: 0.1
Date: 2019-08-29
Author: Loki
Maintainer: Loki <loki@no.mail>
Description: Implementation of the Conditional Variance Estimation (CVE) method. This package version is writen in pure R.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 6.1.1

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# Generated by roxygen2: do not edit by hand
S3method(plot,cve)
S3method(summary,cve)
export(cve)
export(cve.call)
export(cve.grid.search)
export(cve_linesearch)
export(cve_sgd)
export(cve_simple)
export(dataset)
export(elem.pairs)
export(estimate.bandwidth)
export(grad)
export(null)
export(rStiefl)
import(stats)
importFrom(graphics,lines)
importFrom(graphics,plot)
importFrom(graphics,points)
importFrom(stats,model.frame)
importFrom(stats,rbinom)
importFrom(stats,rnorm)
useDynLib(CVE, .registration = TRUE)

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#' Conditional Variance Estimator (CVE)
#'
#' Conditional Variance Estimator for Sufficient Dimension
#' Reduction
#'
#' TODO: And some details
#'
#'
#' @references Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
#'
#' @docType package
#' @author Loki
#' @useDynLib CVE, .registration = TRUE
"_PACKAGE"
#' Implementation of the CVE method.
#'
#' Conditional Variance Estimator (CVE) is a novel sufficient dimension
#' reduction (SDR) method assuming a model
#' \deqn{Y \sim g(B'X) + \epsilon}{Y ~ g(B'X) + epsilon}
#' where B'X is a lower dimensional projection of the predictors.
#'
#' @param formula Formel for the regression model defining `X`, `Y`.
#' See: \code{\link{formula}}.
#' @param data data.frame holding data for formula.
#' @param method The different only differe in the used optimization.
#' All of them are Gradient based optimization on a Stiefel manifold.
#' \itemize{
#' \item "simple" Simple reduction of stepsize.
#' \item "sgd" stocastic gradient decent.
#' \item TODO: further
#' }
#' @param ... Further parameters depending on the used method.
#' @examples
#' library(CVE)
#'
#' # sample dataset
#' ds <- dataset("M5")
#'
#' # call ´cve´ with default method (aka "simple")
#' dr.simple <- cve(ds$Y ~ ds$X, k = ncol(ds$B))
#' # plot optimization history (loss via iteration)
#' plot(dr.simple, main = "CVE M5 simple")
#'
#' # call ´cve´ with method "linesearch" using ´data.frame´ as data.
#' data <- data.frame(Y = ds$Y, X = ds$X)
#' # Note: ´Y, X´ are NOT defined, they are extracted from ´data´.
#' dr.linesearch <- cve(Y ~ ., data, method = "linesearch", k = ncol(ds$B))
#' plot(dr.linesearch, main = "CVE M5 linesearch")
#'
#' @references Fertl L., Bura E. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
#'
#' @seealso \code{\link{formula}}. For a complete parameters list (dependent on
#' the method) see \code{\link{cve_simple}}, \code{\link{cve_sgd}}
#' @import stats
#' @importFrom stats model.frame
#' @export
cve <- function(formula, data, method = "simple", max.dim = 10, ...) {
# check for type of `data` if supplied and set default
if (missing(data)) {
data <- environment(formula)
} else if (!is.data.frame(data)) {
stop('Parameter `data` must be a `data.frame` or missing.')
}
# extract `X`, `Y` from `formula` with `data`
model <- stats::model.frame(formula, data)
X <- as.matrix(model[,-1, drop = FALSE])
Y <- as.matrix(model[, 1, drop = FALSE])
# pass extracted data on to [cve.call()]
dr <- cve.call(X, Y, method = method, ...)
# overwrite `call` property from [cve.call()]
dr$call <- match.call()
return(dr)
}
#' @param nObs as describet in the Paper.
#' @param X Data
#' @param Y Responces
#' @param nObs Like in the paper.
#' @param k guess for SDR dimension.
#' @param ... Method specific parameters.
#' @rdname cve
#' @export
cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5,
min.dim = 1, max.dim = 10, k, ...) {
# parameter checking
if (!is.matrix(X)) {
stop('X should be a matrices.')
}
if (is.matrix(Y)) {
Y <- as.vector(Y)
}
if (nrow(X) != length(Y)) {
stop('Rows of X and number of Y elements are not compatible.')
}
if (ncol(X) < 2) {
stop('X is one dimensional, no need for dimension reduction.')
}
if (!missing(k)) {
min.dim <- as.integer(k)
max.dim <- as.integer(k)
} else {
min.dim <- as.integer(min.dim)
max.dim <- as.integer(min(max.dim, ncol(X) - 1L))
}
if (min.dim > max.dim) {
stop('`min.dim` bigger `max.dim`.')
}
if (max.dim >= ncol(X)) {
stop('`max.dim` must be smaller than `ncol(X)`.')
}
# Call specified method.
method <- tolower(method)
call <- match.call()
dr <- list()
for (k in min.dim:max.dim) {
if (method == 'simple') {
dr.k <- cve_simple(X, Y, k, nObs = nObs, ...)
} else if (method == 'linesearch') {
dr.k <- cve_linesearch(X, Y, k, nObs = nObs, ...)
} else if (method == 'sgd') {
dr.k <- cve_sgd(X, Y, k, nObs = nObs, ...)
} else {
stop('Got unknown method.')
}
dr.k$k <- k
class(dr.k) <- "cve.k"
dr[[k]] <- dr.k
}
# augment result information
dr$method <- method
dr$call <- call
class(dr) <- "cve"
return(dr)
}
# TODO: write summary
# summary.cve <- function() {
# # code #
# }
#' Ploting helper for objects of class \code{cve}.
#'
#' @param x Object of class \code{cve} (result of [cve()]).
#' @param content Specifies what to plot:
#' \itemize{
#' \item "history" Plots the loss history from stiefel optimization
#' (default).
#' \item ... TODO: add (if there are any)
#' }
#' @param ... Pass through parameters to [plot()] and [lines()]
#'
#' @usage ## S3 method for class 'cve'
#' plot(x, content = "history", ...)
#' @seealso see \code{\link{par}} for graphical parameters to pass through
#' as well as \code{\link{plot}} for standard plot utility.
#' @importFrom graphics plot lines points
#' @method plot cve
#' @export
plot.cve <- function(x, ...) {
# H <- x$history
# H_1 <- H[!is.na(H[, 1]), 1]
# defaults <- list(
# main = "History",
# xlab = "Iterations i",
# ylab = expression(loss == L[n](V^{(i)})),
# xlim = c(1, nrow(H)),
# ylim = c(0, max(H)),
# type = "l"
# )
# call.plot <- match.call()
# keys <- names(defaults)
# keys <- keys[match(keys, names(call.plot)[-1], nomatch = 0) == 0]
# for (key in keys) {
# call.plot[[key]] <- defaults[[key]]
# }
# call.plot[[1L]] <- quote(plot)
# call.plot$x <- quote(1:length(H_1))
# call.plot$y <- quote(H_1)
# eval(call.plot)
# if (ncol(H) > 1) {
# for (i in 2:ncol(H)) {
# H_i <- H[H[, i] > 0, i]
# lines(1:length(H_i), H_i)
# }
# }
# x.ends <- apply(H, 2, function(h) { length(h[!is.na(h)]) })
# y.ends <- apply(H, 2, function(h) { tail(h[!is.na(h)], n=1) })
# points(x.ends, y.ends)
}
#' Prints a summary of a \code{cve} result.
#' @param object Instance of 'cve' as return of \code{cve}.
#' @method summary cve
#' @export
summary.cve <- function(object, ...) {
cat('Summary of CVE result - Method: "', object$method, '"\n',
'\n',
'Dataset size: ', nrow(object$X), '\n',
'Data Dimension: ', ncol(object$X), '\n',
'SDR Dimension: ', object$k, '\n',
'loss: ', object$loss, '\n',
'\n',
'Called via:\n',
' ',
sep='')
print(object$call)
}

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#' Implementation of the CVE method using curvilinear linesearch with Armijo-Wolfe
#' conditions.
#'
#' @keywords internal
#' @export
cve_linesearch <- function(X, Y, k,
nObs = sqrt(nrow(X)),
h = NULL,
tau = 1.0,
tol = 1e-3,
rho1 = 0.1,
rho2 = 0.9,
slack = 0,
epochs = 50L,
attempts = 10L,
max.linesearch.iter = 10L,
logger = NULL
) {
# Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables
# from within `grad`.
environment(grad) <- environment()
# Get dimensions.
n <- nrow(X)
p <- ncol(X)
q <- p - k
# Save initial learning rate `tau`.
tau.init <- tau
# Addapt tolearance for break condition.
tol <- sqrt(2 * q) * tol
# Estaimate bandwidth if not given.
if (missing(h) | !is.numeric(h)) {
h <- estimate.bandwidth(X, k, nObs)
}
# Compute persistent data.
# Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization.
pair.index <- elem.pairs(seq(n))
i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Matrix of vectorized indices. (vec(index) -> seq)
index <- matrix(seq(n * n), n, n)
lower <- index[lower.tri(index)]
upper <- t(index)[lower]
# Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F]
# Identity matrix.
I_p <- diag(1, p)
# Init tracking of current best (according multiple attempts).
V.best <- NULL
loss.best <- Inf
# Start loop for multiple attempts.
for (attempt in 1:attempts) {
# Sample a `(p, q)` dimensional matrix from the stiefel manifold as
# optimization start value.
V <- rStiefl(p, q)
# Initial loss and gradient.
loss <- Inf
G <- grad(X, Y, V, h, loss.out = TRUE, persistent = TRUE)
# Set last loss (aka, loss after applying the step).
loss.last <- loss
# Call logger with initial values before starting optimization.
if (is.function(logger)) {
epoch <- 0 # Set epoch count to 0 (only relevant for logging).
error <- NA
logger(environment())
}
## Start optimization loop.
for (epoch in 1:epochs) {
# Cayley transform matrix `A`
A <- (G %*% t(V)) - (V %*% t(G))
# Directional derivative of the loss at current position, given
# as `Tr(G^T \cdot A \cdot V)`.
loss.prime <- -0.5 * norm(A, type = 'F')^2
# Linesearch
tau.upper <- Inf
tau.lower <- 0
tau <- tau.init
for (iter in 1:max.linesearch.iter) {
# Apply learning rate `tau`.
A.tau <- (tau / 2) * A
# Parallet transport (on Stiefl manifold) into direction of `G`.
inv <- solve(I_p + A.tau)
V.tau <- inv %*% ((I_p - A.tau) %*% V)
# Loss at position after a step.
loss <- Inf # aka loss.tau
G.tau <- grad(X, Y, V.tau, h, loss.out = TRUE, persistent = TRUE)
# Armijo condition.
if (loss > loss.last + (rho1 * tau * loss.prime)) {
tau.upper <- tau
tau <- (tau.lower + tau.upper) / 2
next()
}
V.prime.tau <- -0.5 * inv %*% A %*% (V + V.tau)
loss.prime.tau <- sum(G * V.prime.tau) # Tr(grad(tau)^T \cdot Y^'(tau))
# Wolfe condition.
if (loss.prime.tau < rho2 * loss.prime) {
tau.lower <- tau
if (tau.upper == Inf) {
tau <- 2 * tau.lower
} else {
tau <- (tau.lower + tau.upper) / 2
}
} else {
break()
}
}
# Compute error.
error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F")
# Check break condition (epoch check to skip ignored gradient calc).
# Note: the devision by `sqrt(2 * k)` is included in `tol`.
if (error < tol | epoch >= epochs) {
# take last step and stop optimization.
V <- V.tau
# Final call to the logger before stopping optimization
if (is.function(logger)) {
G <- G.tau
logger(environment())
}
break()
}
# Perform the step and remember previous loss.
V <- V.tau
loss.last <- loss
G <- G.tau
# Log after taking current step.
if (is.function(logger)) {
logger(environment())
}
}
# Check if current attempt improved previous ones
if (loss < loss.best) {
loss.best <- loss
V.best <- V
}
}
return(list(
loss = loss.best,
V = V.best,
B = null(V.best),
h = h
))
}

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#' Simple implementation of the CVE method. 'Simple' means that this method is
#' a classic GD method unsing no further tricks.
#'
#' @keywords internal
#' @export
cve_sgd <- function(X, Y, k,
nObs = sqrt(nrow(X)),
h = NULL,
tau = 0.01,
tol = 1e-3,
epochs = 50L,
batch.size = 16L,
attempts = 10L,
logger = NULL
) {
# Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables
# from within `grad`.
environment(grad) <- environment()
# Get dimensions.
n <- nrow(X) # Number of samples.
p <- ncol(X) # Data dimensions
q <- p - k # Complement dimension of the SDR space.
# Save initial learning rate `tau`.
tau.init <- tau
# Addapt tolearance for break condition.
tol <- sqrt(2 * q) * tol
# Estaimate bandwidth if not given.
if (missing(h) || !is.numeric(h)) {
h <- estimate.bandwidth(X, k, nObs)
}
# Compute persistent data.
# Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization.
pair.index <- elem.pairs(seq(n))
i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Index of vectorized matrix, for lower and upper triangular part.
lower <- ((i - 1) * n) + j
upper <- ((j - 1) * n) + i
# Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F]
# Identity matrix.
I_p <- diag(1, p)
# Init a list of data indices (shuffled for batching).
indices <- seq(n)
# Init tracking of current best (according multiple attempts).
V.best <- NULL
loss.best <- Inf
# Start loop for multiple attempts.
for (attempt in 1:attempts) {
# Reset learning rate `tau`.
tau <- tau.init
# Sample a `(p, q)` dimensional matrix from the stiefel manifold as
# optimization start value.
V <- rStiefl(p, q)
# Keep track of last `V` for computing error after an epoch.
V.last <- V
if (is.function(logger)) {
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
error <- NA
epoch <- 0
logger(environment())
}
# Repeat `epochs` times
for (epoch in 1:epochs) {
# Shuffle batches
batch.shuffle <- sample(indices)
# Make a step for each batch.
for (batch.start in seq(1, n, batch.size)) {
# Select batch data indices.
batch.end <- min(batch.start + batch.size - 1, length(batch.shuffle))
batch <- batch.shuffle[batch.start:batch.end]
# Compute batch gradient.
loss <- NULL
G <- grad(X[batch, ], Y[batch], V, h, loss.out = TRUE)
# Cayley transform matrix.
A <- (G %*% t(V)) - (V %*% t(G))
# Apply learning rate `tau`.
A.tau <- tau * A
# Parallet transport (on Stiefl manifold) into direction of `G`.
V <- solve(I_p + A.tau) %*% ((I_p - A.tau) %*% V)
}
# And the error for the history.
error <- norm(V.last %*% t(V.last) - V %*% t(V), type = "F")
V.last <- V
if (is.function(logger)) {
# Compute loss at end of epoch for logging.
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
logger(environment())
}
# Check break condition.
if (error < tol) {
break()
}
}
# Compute actual loss after finishing for comparing multiple attempts.
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
# After each attempt, check if last attempt reached a better result.
if (loss < loss.best) {
loss.best <- loss
V.best <- V
}
}
return(list(
loss = loss.best,
V = V.best,
B = null(V.best),
h = h
))
}

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#' Simple implementation of the CVE method. 'Simple' means that this method is
#' a classic GD method unsing no further tricks.
#'
#' @keywords internal
#' @export
cve_simple <- function(X, Y, k,
nObs = sqrt(nrow(X)),
h = NULL,
tau = 1.0,
tol = 1e-3,
slack = 0,
epochs = 50L,
attempts = 10L,
logger = NULL
) {
# Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables
# from within `grad`.
environment(grad) <- environment()
# Get dimensions.
n <- nrow(X) # Number of samples.
p <- ncol(X) # Data dimensions
q <- p - k # Complement dimension of the SDR space.
# Save initial learning rate `tau`.
tau.init <- tau
# Addapt tolearance for break condition.
tol <- sqrt(2 * q) * tol
# Estaimate bandwidth if not given.
if (missing(h) || !is.numeric(h)) {
h <- estimate.bandwidth(X, k, nObs)
}
# Compute persistent data.
# Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization.
pair.index <- elem.pairs(seq(n))
i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Index of vectorized matrix, for lower and upper triangular part.
lower <- ((i - 1) * n) + j
upper <- ((j - 1) * n) + i
# Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F]
# Identity matrix.
I_p <- diag(1, p)
# Init tracking of current best (according multiple attempts).
V.best <- NULL
loss.best <- Inf
# Start loop for multiple attempts.
for (attempt in 1:attempts) {
# Reset learning rate `tau`.
tau <- tau.init
# Sample a `(p, q)` dimensional matrix from the stiefel manifold as
# optimization start value.
V <- rStiefl(p, q)
# Initial loss and gradient.
loss <- Inf
G <- grad(X, Y, V, h, loss.out = TRUE, persistent = TRUE)
# Set last loss (aka, loss after applying the step).
loss.last <- loss
# Cayley transform matrix `A`
A <- (G %*% t(V)) - (V %*% t(G))
# Call logger with initial values before starting optimization.
if (is.function(logger)) {
epoch <- 0 # Set epoch count to 0 (only relevant for logging).
error <- NA
logger(environment())
}
## Start optimization loop.
for (epoch in 1:epochs) {
# Apply learning rate `tau`.
A.tau <- tau * A
# Parallet transport (on Stiefl manifold) into direction of `G`.
V.tau <- solve(I_p + A.tau) %*% ((I_p - A.tau) %*% V)
# Loss at position after a step.
loss <- grad(X, Y, V.tau, h, loss.only = TRUE, persistent = TRUE)
# Check if step is appropriate, iff not reduce learning rate.
if ((loss - loss.last) > slack * loss.last) {
tau <- tau / 2
next() # Keep position and try with smaller `tau`.
}
# Compute error.
error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F")
# Check break condition (epoch check to skip ignored gradient calc).
# Note: the devision by `sqrt(2 * k)` is included in `tol`.
if (error < tol || epoch >= epochs) {
# take last step and stop optimization.
V <- V.tau
# Call logger last time befor stoping.
if (is.function(logger)) {
logger(environment())
}
break()
}
# Perform the step and remember previous loss.
V <- V.tau
loss.last <- loss
# Call logger after taking a step.
if (is.function(logger)) {
logger(environment())
}
# Compute gradient at new position.
G <- grad(X, Y, V, h, persistent = TRUE)
# Cayley transform matrix `A`
A <- (G %*% t(V)) - (V %*% t(G))
}
# Check if current attempt improved previous ones
if (loss < loss.best) {
loss.best <- loss
V.best <- V
}
}
return(list(
loss = loss.best,
V = V.best,
B = null(V.best),
h = h
))
}

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#' Generates test datasets.
#'
#' Provides sample datasets. There are 5 different datasets named
#' M1, M2, M3, M4 and M5 describet in the paper references below.
#' The general model is given by:
#' \deqn{Y ~ g(B'X) + \epsilon}
#'
#' @param name One of \code{"M1"}, \code{"M2"}, \code{"M3"}, \code{"M4"} or \code{"M5"}
#' @param n nr samples
#' @param p Dim. of random variable \code{X}.
#' @param p.mix Only for \code{"M4"}, see: below.
#' @param lambda Only for \code{"M4"}, see: below.
#'
#' @return List with elements
#' \itemize{
#' \item{X}{data}
#' \item{Y}{response}
#' \item{B}{Used dim-reduction matrix}
#' \item{name}{Name of the dataset (name parameter)}
#' }
#'
#' @section M1:
#' The data follows \eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} for a subspace
#' dimension of \eqn{k = 2} with a default of \eqn{n = 200} data points.
#' The link function \eqn{g} is given as
#' \deqn{g(x) = \frac{x_1}{0.5 + (x_2 + 1.5)^2} + 0.5\epsilon}{g(x) = x_1 / (0.5 + (x_2 + 1.5)^2) + 0.5 epsilon}
#' @section M2:
#' \eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} with \eqn{k = 2} with a default of \eqn{n = 200} data points.
#' The link function \eqn{g} is given as
#' \deqn{g(x) = x_1 x_2^2 + 0.5\epsilon}{g(x) = x_1 x_2^2 + 0.5 epsilon}
#' @section M3:
#' TODO:
#' @section M4:
#' TODO:
#' @section M5:
#' TODO:
#'
#' @import stats
#' @importFrom stats rnorm rbinom
#' @export
dataset <- function(name = "M1", n, B, p.mix = 0.3, lambda = 1.0) {
# validate parameters
stopifnot(name %in% c("M1", "M2", "M3", "M4", "M5"))
# set default values if not supplied
if (missing(n)) {
n <- if (name %in% c("M1", "M2")) 200 else if (name != "M5") 100 else 42
}
if (missing(B)) {
p <- 12
if (name == "M1") {
B <- cbind(
c( 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0),
c( 1,-1, 1,-1, 1,-1, 0, 0, 0, 0, 0, 0)
) / sqrt(6)
} else if (name == "M2") {
B <- cbind(
c(c(1, 0), rep(0, 10)),
c(c(0, 1), rep(0, 10))
)
} else {
B <- matrix(c(rep(1 / sqrt(6), 6), rep(0, 6)), 12, 1)
}
} else {
p <- dim(B)[1]
# validate col. nr to match dataset `k = dim(B)[2]`
stopifnot(
name %in% c("M1", "M2") && dim(B)[2] == 2,
name %in% c("M3", "M4", "M5") && dim(B)[2] == 1
)
}
# set link function `g` for model `Y ~ g(B'X) + epsilon`
if (name == "M1") {
g <- function(BX) { BX[1] / (0.5 + (BX[2] + 1.5)^2) }
} else if (name == "M2") {
g <- function(BX) { BX[1] * BX[2]^2 }
} else if (name %in% c("M3", "M4")) {
g <- function(BX) { cos(BX[1]) }
} else { # name == "M5"
g <- function(BX) { 2 * log(abs(BX[1]) + 1) }
}
# compute X
if (name != "M4") {
# compute root of the covariance matrix according the dataset
if (name %in% c("M1", "M3")) {
# Variance-Covariance structure for `X ~ N_p(0, \Sigma)` with
# `\Sigma_{i, j} = 0.5^{|i - j|}`.
Sigma <- matrix(0.5^abs(kronecker(1:p, 1:p, '-')), p, p)
# decompose Sigma to Sigma.root^T Sigma.root = Sigma for usage in creation of `X`
Sigma.root <- chol(Sigma)
} else { # name %in% c("M2", "M5")
Sigma.root <- diag(rep(1, p)) # d-dim identity
}
# data `X` as multivariate random normal variable with
# variance matrix `Sigma`.
X <- replicate(p, rnorm(n, 0, 1)) %*% Sigma.root
} else { # name == "M4"
X <- t(replicate(100, rep((1 - 2 * rbinom(1, 1, p.mix)) * lambda, p) + rnorm(p, 0, 1)))
}
# responce `y ~ g(B'X) + epsilon` with `epsilon ~ N(0, 1 / 2)`
Y <- apply(X, 1, function(X_i) {
g(t(B) %*% X_i) + rnorm(1, 0, 0.5)
})
return(list(X = X, Y = Y, B = B, name = name))
}

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#' Estimated bandwidth for CVE.
#'
#' Estimates a propper bandwidth \code{h} according
#' \deqn{%
#' h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
#' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
#'
#' @param X data matrix of dimension (n x p) with n data points X_i of dimension
#' q. Therefor each row represents a datapoint of dimension p.
#' @param k Guess for rank(B).
#' @param nObs Ether numeric of a function. If specified as numeric value
#' its used in the computation of the bandwidth directly. If its a function
#' `nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
#' supplied at all is to use \code{nObs <- nrow(x)^0.5}.
#'
#' @seealso [\code{\link{qchisq}}]
#' @export
estimate.bandwidth <- function(X, k, nObs) {
n <- nrow(X)
p <- ncol(X)
X_centered <- scale(X, center=TRUE, scale=FALSE)
Sigma <- (1 / n) * t(X_centered) %*% X_centered
quantil <- qchisq((nObs - 1) / (n - 1), k)
return(2 * quantil * sum(diag(Sigma)) / p)
}

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#' Compute get gradient of `L(V)` given a dataset `X`.
#'
#' @param X Data matrix.
#' @param Y Responce.
#' @param V Position to compute the gradient at, aka point on Stiefl manifold.
#' @param h Bandwidth
#' @param loss.out Iff \code{TRUE} loss will be written to parent environment.
#' @param loss.only Boolean to only compute the loss, of \code{TRUE} a single
#' value loss is returned and \code{envir} is ignored.
#' @param persistent Determines if data indices and dependent calculations shall
#' be reused from the parent environment. ATTENTION: Do NOT set this flag, only
#' intended for internal usage by carefully aligned functions!
#' @keywords internal
#' @export
grad <- function(X, Y, V, h,
loss.out = FALSE,
loss.only = FALSE,
persistent = FALSE) {
# Get number of samples and dimension.
n <- nrow(X)
p <- ncol(X)
if (!persistent) {
# Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization.
pair.index <- elem.pairs(seq(n))
i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Index of vectorized matrix, for lower and upper triangular part.
lower <- ((i - 1) * n) + j
upper <- ((j - 1) * n) + i
# Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F]
}
out <- .Call("grad_c", PACKAGE = "CVE",
X, X_diff, as.double(Y), V, as.double(h));
if (loss.only) {
return(out$loss)
}
if (loss.out) {
loss <<- out$loss
}
return(out$G)
}

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#' Performs a grid search for parameters over a parameter grid.
#' @examples
#' args <- list(
#' h = c(0.05, 0.1, 0.2),
#' method = c("simple", "sgd"),
#' tau = c(0.5, 0.1, 0.01)
#' )
#' cve.grid.search(args)
#' @export
cve.grid.search <- function(X, Y, k, args) {
args$stringsAsFactors = FALSE
args$KEEP.OUT.ATTRS = FALSE
grid <- do.call(expand.grid, args)
grid.length <- length(grid[[1]])
print(grid)
for (i in 1:grid.length) {
arguments <- as.list(grid[i, ])
# Set required arguments
arguments$X <- X
arguments$Y <- Y
arguments$k <- k
# print(arguments)
dr <- do.call(cve.call, arguments)
print(dr$loss)
}
}
# ds <- dataset()
# X <- ds$X
# Y <- ds$Y
# (k <- ncol(ds$B))
# args <- list(
# h = c(0.05, 0.1, 0.2),
# method = c("simple", "sgd"),
# tau = c(0.5, 0.1, 0.01),
# attempts = c(1L)
# )
# cve.grid.search(X, Y, k, args)

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#' Samples uniform from the Stiefel Manifold
#'
#' @param p row dim.
#' @param q col dim.
#' @return `(p, q)` semi-orthogonal matrix
#' @examples
#' V <- rStiefel(6, 4)
#' @export
rStiefl <- function(p, q) {
return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
}
#' Null space basis of given matrix `V`
#'
#' @param V `(p, q)` matrix
#' @return Semi-orthogonal `(p, p - q)` matrix spaning the null space of `V`.
#' @keywords internal
#' @export
null <- function(V) {
tmp <- qr(V)
set <- if(tmp$rank == 0L) seq_len(ncol(V)) else -seq_len(tmp$rank)
return(qr.Q(tmp, complete=TRUE)[, set, drop=FALSE])
}
#' Creates a (numeric) matrix where each column contains
#' an element to element matching.
#' @param elements numeric vector of elements to match
#' @return matrix of size `(2, n * (n - 1) / 2)` for a argument of lenght `n`.
#' @keywords internal
#' @examples
#' elem.pairs(seq.int(2, 5))
#' @export
elem.pairs <- function(elements) {
# Number of elements to match.
n <- length(elements)
# Create all combinations.
pairs <- rbind(rep(elements, each=n), rep(elements, n))
# Select unique combinations without self interaction.
return(pairs[, pairs[1, ] < pairs[2, ]])
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\docType{package}
\name{CVE-package}
\alias{CVE}
\alias{CVE-package}
\title{Conditional Variance Estimator (CVE)}
\description{
Conditional Variance Estimator for Sufficient Dimension
Reduction
}
\details{
TODO: And some details
}
\references{
Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
}
\author{
Loki
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{cve}
\alias{cve}
\alias{cve.call}
\title{Implementation of the CVE method.}
\usage{
cve(formula, data, method = "simple", max.dim = 10, ...)
cve.call(X, Y, method = "simple", nObs = nrow(X)^0.5, min.dim = 1,
max.dim = 10, k, ...)
}
\arguments{
\item{formula}{Formel for the regression model defining `X`, `Y`.
See: \code{\link{formula}}.}
\item{data}{data.frame holding data for formula.}
\item{method}{The different only differe in the used optimization.
All of them are Gradient based optimization on a Stiefel manifold.
\itemize{
\item "simple" Simple reduction of stepsize.
\item "sgd" stocastic gradient decent.
\item TODO: further
}}
\item{...}{Further parameters depending on the used method.}
\item{X}{Data}
\item{Y}{Responces}
\item{nObs}{as describet in the Paper.}
\item{k}{guess for SDR dimension.}
\item{nObs}{Like in the paper.}
\item{...}{Method specific parameters.}
}
\description{
Conditional Variance Estimator (CVE) is a novel sufficient dimension
reduction (SDR) method assuming a model
\deqn{Y \sim g(B'X) + \epsilon}{Y ~ g(B'X) + epsilon}
where B'X is a lower dimensional projection of the predictors.
}
\examples{
library(CVE)
# sample dataset
ds <- dataset("M5")
# call ´cve´ with default method (aka "simple")
dr.simple <- cve(ds$Y ~ ds$X, k = ncol(ds$B))
# plot optimization history (loss via iteration)
plot(dr.simple, main = "CVE M5 simple")
# call ´cve´ with method "linesearch" using ´data.frame´ as data.
data <- data.frame(Y = ds$Y, X = ds$X)
# Note: ´Y, X´ are NOT defined, they are extracted from ´data´.
dr.linesearch <- cve(Y ~ ., data, method = "linesearch", k = ncol(ds$B))
plot(dr.linesearch, main = "CVE M5 linesearch")
}
\references{
Fertl L., Bura E. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
}
\seealso{
\code{\link{formula}}. For a complete parameters list (dependent on
the method) see \code{\link{cve_simple}}, \code{\link{cve_sgd}}
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/gridSearch.R
\name{cve.grid.search}
\alias{cve.grid.search}
\title{Performs a grid search for parameters over a parameter grid.}
\usage{
cve.grid.search(X, Y, k, args)
}
\description{
Performs a grid search for parameters over a parameter grid.
}
\examples{
args <- list(
h = c(0.05, 0.1, 0.2),
method = c("simple", "sgd"),
tau = c(0.5, 0.1, 0.01)
)
cve.grid.search(args)
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cve_linesearch.R
\name{cve_linesearch}
\alias{cve_linesearch}
\title{Implementation of the CVE method using curvilinear linesearch with Armijo-Wolfe
conditions.}
\usage{
cve_linesearch(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1,
tol = 0.001, rho1 = 0.1, rho2 = 0.9, slack = 0, epochs = 50L,
attempts = 10L, max.linesearch.iter = 10L, logger = NULL)
}
\description{
Implementation of the CVE method using curvilinear linesearch with Armijo-Wolfe
conditions.
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cve_sgd.R
\name{cve_sgd}
\alias{cve_sgd}
\title{Simple implementation of the CVE method. 'Simple' means that this method is
a classic GD method unsing no further tricks.}
\usage{
cve_sgd(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 0.01,
tol = 0.001, epochs = 50L, batch.size = 16L, attempts = 10L,
logger = NULL)
}
\description{
Simple implementation of the CVE method. 'Simple' means that this method is
a classic GD method unsing no further tricks.
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cve_simple.R
\name{cve_simple}
\alias{cve_simple}
\title{Simple implementation of the CVE method. 'Simple' means that this method is
a classic GD method unsing no further tricks.}
\usage{
cve_simple(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1,
tol = 0.001, slack = 0, epochs = 50L, attempts = 10L,
logger = NULL)
}
\description{
Simple implementation of the CVE method. 'Simple' means that this method is
a classic GD method unsing no further tricks.
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/datasets.R
\name{dataset}
\alias{dataset}
\title{Generates test datasets.}
\usage{
dataset(name = "M1", n, B, p.mix = 0.3, lambda = 1)
}
\arguments{
\item{name}{One of \code{"M1"}, \code{"M2"}, \code{"M3"}, \code{"M4"} or \code{"M5"}}
\item{n}{nr samples}
\item{p.mix}{Only for \code{"M4"}, see: below.}
\item{lambda}{Only for \code{"M4"}, see: below.}
\item{p}{Dim. of random variable \code{X}.}
}
\value{
List with elements
\itemize{
\item{X}{data}
\item{Y}{response}
\item{B}{Used dim-reduction matrix}
\item{name}{Name of the dataset (name parameter)}
}
}
\description{
Provides sample datasets. There are 5 different datasets named
M1, M2, M3, M4 and M5 describet in the paper references below.
The general model is given by:
\deqn{Y ~ g(B'X) + \epsilon}
}
\section{M1}{
The data follows \eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} for a subspace
dimension of \eqn{k = 2} with a default of \eqn{n = 200} data points.
The link function \eqn{g} is given as
\deqn{g(x) = \frac{x_1}{0.5 + (x_2 + 1.5)^2} + 0.5\epsilon}{g(x) = x_1 / (0.5 + (x_2 + 1.5)^2) + 0.5 epsilon}
}
\section{M2}{
\eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} with \eqn{k = 2} with a default of \eqn{n = 200} data points.
The link function \eqn{g} is given as
\deqn{g(x) = x_1 x_2^2 + 0.5\epsilon}{g(x) = x_1 x_2^2 + 0.5 epsilon}
}
\section{M3}{
TODO:
}
\section{M4}{
TODO:
}
\section{M5}{
TODO:
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{elem.pairs}
\alias{elem.pairs}
\title{Creates a (numeric) matrix where each column contains
an element to element matching.}
\usage{
elem.pairs(elements)
}
\arguments{
\item{elements}{numeric vector of elements to match}
}
\value{
matrix of size `(2, n * (n - 1) / 2)` for a argument of lenght `n`.
}
\description{
Creates a (numeric) matrix where each column contains
an element to element matching.
}
\examples{
elem.pairs(seq.int(2, 5))
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/estimateBandwidth.R
\name{estimate.bandwidth}
\alias{estimate.bandwidth}
\title{Estimated bandwidth for CVE.}
\usage{
estimate.bandwidth(X, k, nObs)
}
\arguments{
\item{X}{data matrix of dimension (n x p) with n data points X_i of dimension
q. Therefor each row represents a datapoint of dimension p.}
\item{k}{Guess for rank(B).}
\item{nObs}{Ether numeric of a function. If specified as numeric value
its used in the computation of the bandwidth directly. If its a function
`nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
supplied at all is to use \code{nObs <- nrow(x)^0.5}.}
}
\description{
Estimates a propper bandwidth \code{h} according
\deqn{%
h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
}
\seealso{
[\code{\link{qchisq}}]
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/gradient.R
\name{grad}
\alias{grad}
\title{Compute get gradient of `L(V)` given a dataset `X`.}
\usage{
grad(X, Y, V, h, loss.out = FALSE, loss.only = FALSE,
persistent = FALSE)
}
\arguments{
\item{X}{Data matrix.}
\item{Y}{Responce.}
\item{V}{Position to compute the gradient at, aka point on Stiefl manifold.}
\item{h}{Bandwidth}
\item{loss.out}{Iff \code{TRUE} loss will be written to parent environment.}
\item{loss.only}{Boolean to only compute the loss, of \code{TRUE} a single
value loss is returned and \code{envir} is ignored.}
\item{persistent}{Determines if data indices and dependent calculations shall
be reused from the parent environment. ATTENTION: Do NOT set this flag, only
intended for internal usage by carefully aligned functions!}
}
\description{
Compute get gradient of `L(V)` given a dataset `X`.
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{null}
\alias{null}
\title{Null space basis of given matrix `V`}
\usage{
null(V)
}
\arguments{
\item{V}{`(p, q)` matrix}
}
\value{
Semi-orthogonal `(p, p - q)` matrix spaning the null space of `V`.
}
\description{
Null space basis of given matrix `V`
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{plot.cve}
\alias{plot.cve}
\title{Ploting helper for objects of class \code{cve}.}
\usage{
## S3 method for class 'cve'
plot(x, content = "history", ...)
}
\arguments{
\item{x}{Object of class \code{cve} (result of [cve()]).}
\item{...}{Pass through parameters to [plot()] and [lines()]}
\item{content}{Specifies what to plot:
\itemize{
\item "history" Plots the loss history from stiefel optimization
(default).
\item ... TODO: add (if there are any)
}}
}
\description{
Ploting helper for objects of class \code{cve}.
}
\seealso{
see \code{\link{par}} for graphical parameters to pass through
as well as \code{\link{plot}} for standard plot utility.
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{rStiefl}
\alias{rStiefl}
\title{Samples uniform from the Stiefel Manifold}
\usage{
rStiefl(p, q)
}
\arguments{
\item{p}{row dim.}
\item{q}{col dim.}
}
\value{
`(p, q)` semi-orthogonal matrix
}
\description{
Samples uniform from the Stiefel Manifold
}
\examples{
V <- rStiefel(6, 4)
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{summary.cve}
\alias{summary.cve}
\title{Prints a summary of a \code{cve} result.}
\usage{
\method{summary}{cve}(object, ...)
}
\arguments{
\item{object}{Instance of 'cve' as return of \code{cve}.}
}
\description{
Prints a summary of a \code{cve} result.
}

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## With R 3.1.0 or later, you can uncomment the following line to tell R to
## enable compilation with C++11 (where available)
##
## Also, OpenMP support in Armadillo prefers C++11 support. However, for wider
## availability of the package we do not yet enforce this here. It is however
## recommended for client packages to set it.
##
## And with R 3.4.0, and RcppArmadillo 0.7.960.*, we turn C++11 on as OpenMP
## support within Armadillo prefers / requires it
CXX_STD = CXX11
PKG_CXXFLAGS = $(SHLIB_OPENMP_CXXFLAGS)
PKG_LIBS = $(SHLIB_OPENMP_CXXFLAGS) $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS)

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## With R 3.1.0 or later, you can uncomment the following line to tell R to
## enable compilation with C++11 (where available)
##
## Also, OpenMP support in Armadillo prefers C++11 support. However, for wider
## availability of the package we do not yet enforce this here. It is however
## recommended for client packages to set it.
##
## And with R 3.4.0, and RcppArmadillo 0.7.960.*, we turn C++11 on as OpenMP
## support within Armadillo prefers / requires it
CXX_STD = CXX11
PKG_CXXFLAGS = $(SHLIB_OPENMP_CXXFLAGS)
PKG_LIBS = $(SHLIB_OPENMP_CXXFLAGS) $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS)

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#ifndef CVE_INCLUDE_GUARD_CONFIG_
#define CVE_INCLUDE_GUARD_CONFIG_
#define CVE_MEM_CHUNK_SIZE 2032
#define CVE_MEM_CHUNK_SMALL 1016
#endif /* CVE_INCLUDE_GUARD_CONFIG_ */

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#include <Rinternals.h>
void grad(const int n, const int p, const int q,
const double *X,
const double *X_diff,
const double *Y,
const double *V,
const double h,
double *G, double *loss);
SEXP grad_c(SEXP X, SEXP X_diff, SEXP Y, SEXP V, SEXP h) {
SEXP G = PROTECT(allocMatrix(REALSXP, nrows(V), ncols(V)));
SEXP loss = PROTECT(ScalarReal(0.0));
grad(nrows(X), ncols(X), ncols(V),
REAL(X), REAL(X_diff), REAL(Y), REAL(V), *REAL(h),
REAL(G), REAL(loss));
SEXP out = PROTECT(allocVector(VECSXP, 2));
SET_VECTOR_ELT(out, 0, G);
SET_VECTOR_ELT(out, 1, loss);
SEXP names = PROTECT(allocVector(STRSXP, 2));
SET_STRING_ELT(names, 0, mkChar("G"));
SET_STRING_ELT(names, 1, mkChar("loss"));
setAttrib(out, install("names"), names);
UNPROTECT(4);
return out;
}

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#include <stdlib.h>
#include <math.h>
#include "sums.h"
#include "sweep.h"
#include "matrix.h"
#include "indexing.h"
// TODO: clarify
static inline double gaussKernel(const double x, const double scale) {
return exp(scale * x * x);
}
// TODO: mutch potential for optimization!!!
static void weightedYandLoss(const int n,
const double *Y,
const double *vecD,
const double *vecW,
const double *colSums,
double *y1, double *L, double *vecS,
double *loss) {
int i, j, k, N = n * (n - 1) / 2;
double l;
for (i = 0; i < n; ++i) {
y1[i] = Y[i] / colSums[i];
L[i] = Y[i] * Y[i] / colSums[i];
}
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
y1[i] += Y[j] * vecW[k] / colSums[i];
y1[j] += Y[i] * vecW[k] / colSums[j];
L[i] += Y[j] * Y[j] * vecW[k] / colSums[i];
L[j] += Y[i] * Y[i] * vecW[k] / colSums[j];
}
}
l = 0.0;
for (i = 0; i < n; ++i) {
l += (L[i] -= y1[i] * y1[i]);
}
*loss = l / (double)n;
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
l = Y[j] - y1[i];
vecS[k] = (L[i] - (l * l)) / colSums[i];
l = Y[i] - y1[j];
vecS[k] += (L[j] - (l * l)) / colSums[j];
}
}
for (k = 0; k < N; ++k) {
vecS[k] *= vecW[k] * vecD[k];
}
}
void grad(const int n, const int p, const int q,
const double *X,
const double *X_diff,
const double *Y,
const double *V,
const double h,
double *G, double *loss) {
// Number of X_i to X_j not trivial pairs.
int i, N = (n * (n - 1)) / 2;
double scale = -0.5 / h;
if (X_diff == (void*)0) {
// TODO: ...
}
// Allocate and compute projection matrix `Q = I_p - V * V^T`
double *Q = (double*)malloc(p * p * sizeof(double));
nullProj(V, p, q, Q);
// allocate and compute vectorized distance matrix with a temporary
// projection of `X_diff`.
double *vecD = (double*)malloc(N * sizeof(double));
double *X_proj;
if (p < 5) { // TODO: refine that!
X_proj = (double*)malloc(N * 5 * sizeof(double));
} else {
X_proj = (double*)malloc(N * p * sizeof(double));
}
matrixprod(X_diff, N, p, Q, p, p, X_proj);
rowSquareSums(X_proj, N, p, vecD);
// Apply kernel to distence vector for weights computation.
double *vecW = X_proj; // reuse memory area, no longer needed.
for (i = 0; i < N; ++i) {
vecW[i] = gaussKernel(vecD[i], scale);
}
double *colSums = X_proj + N; // still allocated!
rowSumsSymVec(vecW, n, 1.0, colSums); // rowSums = colSums cause Sym
// compute weighted responces of first end second momontum, aka y1, y2.
double *y1 = X_proj + N + n;
double *L = X_proj + N + (2 * n);
// Allocate X_diff scaling vector `vecS`, not in `X_proj` mem area because
// used symultanious to X_proj in final gradient computation.
double *vecS = (double*)malloc(N * sizeof(double));
weightedYandLoss(n, Y, vecD, vecW, colSums, y1, L, vecS, loss);
// compute the gradient using X_proj for intermidiate scaled X_diff.
rowSweep(X_diff, N, p, "*", vecS, X_proj);
// reuse Q which has the required dim (p, p).
crossprod(X_diff, N, p, X_proj, N, p, Q);
// Product with V
matrixprod(Q, p, p, V, p, q, G);
// And final scaling (TODO: move into matrixprod!)
scale = -2.0 / (((double)n) * h * h);
N = p * q;
for (i = 0; i < N; ++i) {
G[i] *= scale;
}
free(vecS);
free(X_proj);
free(vecD);
free(Q);
}

12
CVE_C/src/indexing.c Normal file
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@ -0,0 +1,12 @@
#include "indexing.h"
void rangePairs(const int from, const int to, int *pairs) {
int i, j, k;
for (k = 0, i = from; i < to; ++i) {
for (j = i + 1; j < to; ++j, k += 2) {
pairs[k] = i;
pairs[k + 1] = j;
}
}
}

8
CVE_C/src/indexing.h Normal file
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@ -0,0 +1,8 @@
/* Include Guard */
#ifndef CVE_INCLUDE_GUARD_INDEXING_
#define CVE_INCLUDE_GUARD_INDEXING_
void rangePairs(const int from, const int to, int *pairs);
#endif /* CVE_INCLUDE_GUARD_INDEXING_ */

23
CVE_C/src/init.c Normal file
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@ -0,0 +1,23 @@
#include <R.h>
#include <Rinternals.h>
#include <stdlib.h> // for NULL
#include <R_ext/Rdynload.h>
/* FIXME:
Check these declarations against the C/Fortran source code.
*/
/* .Call calls */
extern SEXP grad_c(SEXP, SEXP, SEXP, SEXP, SEXP);
static const R_CallMethodDef CallEntries[] = {
{"grad_c", (DL_FUNC) &grad_c, 5},
{NULL, NULL, 0}
};
/* Restrict C entrypoints to registered routines. */
void R_initCVE(DllInfo *dll)
{
R_registerRoutines(dll, NULL, CallEntries, NULL, NULL);
R_useDynamicSymbols(dll, FALSE);
}

71
CVE_C/src/matrix.c Normal file
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@ -0,0 +1,71 @@
#include <string.h> // for `mem*` functions.
#include "config.h"
#include "matrix.h"
#include <R_ext/BLAS.h>
void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C) {
const double one = 1.0;
const double zero = 0.0;
// DGEMM with parameterization:
// C <- A %*% B
F77_NAME(dgemm)("N", "N", &nrowA, &ncolB, &ncolA,
&one, A, &nrowA, B, &nrowB,
&zero, C, &nrowA);
}
void crossprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C) {
const double one = 1.0;
const double zero = 0.0;
// DGEMM with parameterization:
// C <- t(A) %*% B
F77_NAME(dgemm)("T", "N", &ncolA, &ncolB, &nrowA,
&one, A, &nrowA, B, &nrowB,
&zero, C, &ncolA);
}
void nullProj(const double *B, const int nrowB, const int ncolB,
double *Q) {
const double minusOne = -1.0;
const double one = 1.0;
// Initialize as identity matrix.
memset(Q, 0, sizeof(double) * nrowB * nrowB);
double *Q_diag, *Q_end = Q + nrowB * nrowB;
for (Q_diag = Q; Q_diag < Q_end; Q_diag += nrowB + 1) {
*Q_diag = 1.0;
}
// DGEMM with parameterization:
// C <- (-1.0 * B %*% t(B)) + C
F77_NAME(dgemm)("N", "T", &nrowB, &nrowB, &ncolB,
&minusOne, B, &nrowB, B, &nrowB,
&one, Q, &nrowB);
}
// A dence skwe-symmetric rank 2 update.
// Perform the update
// C := alpha (A * B^T - B * A^T) + beta C
void skewSymRank2k(const int nrow, const int ncol,
double alpha, const double *A, const double *B,
double beta,
double *C) {
F77_NAME(dgemm)("N", "T",
&nrow, &nrow, &ncol,
&alpha, A, &nrow, B, &nrow,
&beta, C, &nrow);
alpha *= -1.0;
beta = 1.0;
F77_NAME(dgemm)("N", "T",
&nrow, &nrow, &ncol,
&alpha, B, &nrow, A, &nrow,
&beta, C, &nrow);
}

25
CVE_C/src/matrix.h Normal file
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@ -0,0 +1,25 @@
/* Include Guard */
#ifndef CVE_INCLUDE_GUARD_MATRIX_
#define CVE_INCLUDE_GUARD_MATRIX_
void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C);
void crossprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C);
void nullProj(const double *B, const int nrowB, const int ncolB,
double *Q);
// A dence skwe-symmetric rank 2 update.
// Perform the update
// C := alpha (A * B^T - B * A^T) + beta C
void skewSymRank2k(const int nrow, const int ncol,
double alpha, const double *A, const double *B,
double beta,
double *C);
#endif /* CVE_INCLUDE_GUARD_MATRIX_ */

113
CVE_C/src/sums.c Normal file
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@ -0,0 +1,113 @@
#include <string.h> // for `mem*` functions.
#include "config.h"
#include "sums.h"
void rowSums(const double *A, const int nrow, const int ncol,
double *sum) {
int i, j, block_size, block_size_i;
const double *A_block = A;
const double *A_end = A + nrow * ncol;
if (nrow > CVE_MEM_CHUNK_SIZE) {
block_size = CVE_MEM_CHUNK_SIZE;
} else {
block_size = nrow;
}
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Reset `A` to new block beginning.
A = A_block;
// Take block size of eveything left and reduce to max size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Compute first blocks column,
for (j = 0; j < block_size_i; ++j) {
sum[j] = A[j];
}
// and sum the following columns to the first one.
for (A += nrow; A < A_end; A += nrow) {
for (j = 0; j < block_size_i; ++j) {
sum[j] += A[j];
}
}
// Step one block forth.
A_block += block_size_i;
sum += block_size_i;
}
}
void colSums(const double *A, const int nrow, const int ncol,
double *sum) {
int j;
double *sum_end = sum + ncol;
memset(sum, 0, sizeof(double) * ncol);
for (; sum < sum_end; ++sum) {
for (j = 0; j < nrow; ++j) {
*sum += A[j];
}
A += nrow;
}
}
void rowSquareSums(const double *A, const int nrow, const int ncol,
double *sum) {
int i, j, block_size, block_size_i;
const double *A_block = A;
const double *A_end = A + nrow * ncol;
if (nrow < CVE_MEM_CHUNK_SIZE) {
block_size = nrow;
} else {
block_size = CVE_MEM_CHUNK_SIZE;
}
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Reset `A` to new block beginning.
A = A_block;
// Take block size of eveything left and reduce to max size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Compute first blocks column,
for (j = 0; j < block_size_i; ++j) {
sum[j] = A[j] * A[j];
}
// and sum the following columns to the first one.
for (A += nrow; A < A_end; A += nrow) {
for (j = 0; j < block_size_i; ++j) {
sum[j] += A[j] * A[j];
}
}
// Step one block forth.
A_block += block_size_i;
sum += block_size_i;
}
}
void rowSumsSymVec(const double *Avec, const int nrow,
const double diag,
double *sum) {
int i, j;
if (diag == 0.0) {
memset(sum, 0, nrow * sizeof(double));
} else {
for (i = 0; i < nrow; ++i) {
sum[i] = diag;
}
}
for (j = 0; j < nrow; ++j) {
for (i = j + 1; i < nrow; ++i, ++Avec) {
sum[j] += *Avec;
sum[i] += *Avec;
}
}
}

19
CVE_C/src/sums.h Normal file
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@ -0,0 +1,19 @@
/* Include Guard */
#ifndef CVE_INCLUDE_GUARD_SUMS_
#define CVE_INCLUDE_GUARD_SUMS_
void rowSums(const double *A, const int nrow, const int ncol,
double *sum);
void colSums(const double *A, const int nrow, const int ncol,
double *sum);
void rowSquareSums(const double *A, const int nrow, const int ncol,
double *sum);
void rowSumsSymVec(const double *Avec, const int nrow,
const double diag,
double *sum);
#endif /* CVE_INCLUDE_GUARD_SUMS_ */

113
CVE_C/src/sweep.c Normal file
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@ -0,0 +1,113 @@
#include <R_ext/Error.h> // for `error`.
#include "config.h"
#include "sweep.h"
/* C[, j] = A[, j] * v for each j = 1 to ncol */
void rowSweep(const double *A, const int nrow, const int ncol,
const char* op,
const double *v, // vector of length nrow
double *C) {
int i, j, block_size, block_size_i;
const double *A_block = A;
double *C_block = C;
const double *A_end = A + nrow * ncol;
if (nrow > CVE_MEM_CHUNK_SMALL) { // small because 3 vectors in cache
block_size = CVE_MEM_CHUNK_SMALL;
} else {
block_size = nrow;
}
if (*op == '+') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] + v[j]; // FUN = '+'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '-') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] - v[j]; // FUN = '-'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '*') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] * v[j]; // FUN = '*'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '/') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] / v[j]; // FUN = '/'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else {
error("Got unknown 'op' (opperation) argument.");
}
}

11
CVE_C/src/sweep.h Normal file
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@ -0,0 +1,11 @@
/* Include Guard */
#ifndef CVE_INCLUDE_GUARD_SWEEP_
#define CVE_INCLUDE_GUARD_SWEEP_
void rowSweep(const double *A, const int nrow, const int ncol,
const char* op,
const double *v, // vector of length nrow
double *C);
#endif /* CVE_INCLUDE_GUARD_SWEEP_ */

29
notes.md
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@ -6,6 +6,35 @@ grep --include=*\.{c,h,R} -rnw '.' -e "sweep"
``` ```
searches in all `C` source and header fils as well as `R` source files for the term _sweep_. searches in all `C` source and header fils as well as `R` source files for the term _sweep_.
## Recursive dir. compair with colored sructure (more or less).
```bash
diff -r CVE_R/ CVE_C/ | grep -E "^([<>]|[^<>].*)"
```
## Parsing `bash` script parameters.
```bash
usage="$0 [-v|--verbose] [-n|--dry-run] [(-s|--stack-size) <size>] [-h|--help] [-- [p1, [p2, ...]]]"
verbose=false
help=false
dry_run=false
stack_size=0
while [ $# -gt 0 ]; do
case "$1" in
-v | --verbose ) verbose=true; shift ;;
-n | --dry-run ) dry_run=true; shift ;;
-s | --stack-size ) stack_size="$2"; shift; shift ;;
-h | --help ) echo $usage; exit ;; # On help print usage and exit.
-- ) shift; break ;; # Break param "parsing".
* ) echo $usage >&2; exit 1 ;; # Print usage and exit with failure.
esac
done
echo verbose=$verbose
echo dry_run=$dry_run
echo stack_size=$stack_size
```
# Development # Development
## Build and install. ## Build and install.
To build the package the `devtools` package is used. This also provides `roxygen2` which is used for documentation and authomatic creaton of the `NAMESPACE` file. To build the package the `devtools` package is used. This also provides `roxygen2` which is used for documentation and authomatic creaton of the `NAMESPACE` file.

21
wip.R
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@ -118,6 +118,17 @@ microbenchmark(
) )
## Matrix-Matrix opperation .call --------------------------------------------- ## Matrix-Matrix opperation .call ---------------------------------------------
transpose.c <- function(A) {
stopifnot(
is.matrix(A), is.numeric(A)
)
if (!is.double(A)) {
A <- matrix(as.double(A), nrow(A), ncol(A))
}
.Call('R_transpose', PACKAGE = 'wip', A)
}
matrixprod.c <- function(A, B) { matrixprod.c <- function(A, B) {
stopifnot( stopifnot(
is.matrix(A), is.numeric(A), is.matrix(A), is.numeric(A),
@ -174,6 +185,14 @@ m <- 300
A <- matrix(runif(n * k), n, k) A <- matrix(runif(n * k), n, k)
B <- matrix(runif(k * m), k, m) B <- matrix(runif(k * m), k, m)
stopifnot(
all.equal(t(A), transpose.c(A))
)
microbenchmark(
t(A),
transpose.c(A)
)
stopifnot( stopifnot(
all.equal(A %*% B, matrixprod.c(A, B)) all.equal(A %*% B, matrixprod.c(A, B))
) )
@ -326,4 +345,4 @@ stopifnot(all.equal(
microbenchmark( microbenchmark(
grad = grad(X, Y, V, h), grad = grad(X, Y, V, h),
gradient.c = gradient.c(X, X_diff, Y, V, h) gradient.c = gradient.c(X, X_diff, Y, V, h)
) )

22
wip.c
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@ -1,4 +1,5 @@
#include <stdlib.h> #include <stdlib.h>
#include <string.h> // for `mem*` functions.
#include <R_ext/BLAS.h> #include <R_ext/BLAS.h>
#include <R_ext/Lapack.h> #include <R_ext/Lapack.h>
@ -99,15 +100,15 @@ static inline void rowSquareSums(const double *A,
} }
static inline void rowSumsSymVec(const double *Avec, const int nrow, static inline void rowSumsSymVec(const double *Avec, const int nrow,
const double *diag, const double diag,
double *sum) { double *sum) {
int i, j; int i, j;
if (*diag == 0.0) { if (diag == 0.0) {
memset(sum, 0, nrow * sizeof(double)); memset(sum, 0, nrow * sizeof(double));
} else { } else {
for (i = 0; i < nrow; ++i) { for (i = 0; i < nrow; ++i) {
sum[i] = *diag; sum[i] = diag;
} }
} }
@ -228,6 +229,18 @@ static void rowSweep(const double *A, const int nrow, const int ncol,
} }
} }
void transpose(const double *A, const int nrow, const int ncol, double* T) {
int i, j, len = nrow * ncol;
// Filling column-wise and accessing row-wise.
for (i = 0, j = 0; i < len; ++i, j += nrow) {
if (j >= len) {
j -= len - 1;
}
T[i] = A[j];
}
}
static inline void matrixprod(const double *A, const int nrowA, const int ncolA, static inline void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB, const double *B, const int nrowB, const int ncolB,
double *C) { double *C) {
@ -363,7 +376,6 @@ static void gradient(const int n, const int p, const int q,
// Number of X_i to X_j not trivial pairs. // Number of X_i to X_j not trivial pairs.
int i, N = (n * (n - 1)) / 2; int i, N = (n * (n - 1)) / 2;
double scale = -0.5 / h; double scale = -0.5 / h;
const double one = 1.0;
if (X_diff == (void*)0) { if (X_diff == (void*)0) {
// TODO: ... // TODO: ...
@ -391,7 +403,7 @@ static void gradient(const int n, const int p, const int q,
vecW[i] = gaussKernel(vecD[i], scale); vecW[i] = gaussKernel(vecD[i], scale);
} }
double *colSums = X_proj + N; // still allocated! double *colSums = X_proj + N; // still allocated!
rowSumsSymVec(vecW, n, &one, colSums); // rowSums = colSums cause Sym rowSumsSymVec(vecW, n, 1.0, colSums); // rowSums = colSums cause Sym
// compute weighted responces of first end second momontum, aka y1, y2. // compute weighted responces of first end second momontum, aka y1, y2.
double *y1 = X_proj + N + n; double *y1 = X_proj + N + n;

20
wip.h
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@ -1,5 +1,5 @@
#ifndef _CVE_INCLUDE_GUARD_ #ifndef CVE_INCLUDE_GUARD_
#define _CVE_INCLUDE_GUARD_ #define CVE_INCLUDE_GUARD_
#include <Rinternals.h> #include <Rinternals.h>
@ -41,12 +41,12 @@ SEXP R_rowSquareSums(SEXP A) {
} }
static inline void rowSumsSymVec(const double *Avec, const int nrow, static inline void rowSumsSymVec(const double *Avec, const int nrow,
const double *diag, const double diag,
double *sum); double *sum);
SEXP R_rowSumsSymVec(SEXP Avec, SEXP nrow, SEXP diag) { SEXP R_rowSumsSymVec(SEXP Avec, SEXP nrow, SEXP diag) {
SEXP sum = PROTECT(allocVector(REALSXP, *INTEGER(nrow))); SEXP sum = PROTECT(allocVector(REALSXP, *INTEGER(nrow)));
rowSumsSymVec(REAL(Avec), *INTEGER(nrow), REAL(diag), REAL(sum)); rowSumsSymVec(REAL(Avec), *INTEGER(nrow), *REAL(diag), REAL(sum));
UNPROTECT(1); UNPROTECT(1);
return sum; return sum;
@ -67,6 +67,16 @@ SEXP R_rowSweep(SEXP A, SEXP v, SEXP op) {
return C; return C;
} }
void transpose(const double *A, const int nrow, const int ncol, double* T);
SEXP R_transpose(SEXP A) {
SEXP T = PROTECT(allocMatrix(REALSXP, ncols(A), nrows(A)));
transpose(REAL(A), nrows(A), ncols(A), REAL(T));
UNPROTECT(1); /* T */
return T;
}
static inline void matrixprod(const double *A, const int nrowA, const int ncolA, static inline void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB, const double *B, const int nrowB, const int ncolB,
double *C); double *C);
@ -156,4 +166,4 @@ SEXP R_gradient(SEXP X, SEXP X_diff, SEXP Y, SEXP V, SEXP h) {
return G; return G;
} }
#endif /* _CVE_INCLUDE_GUARD_ */ #endif /* CVE_INCLUDE_GUARD_ */