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add: directions, predict,

add: momentum, weighted, slack, ...
fix: estimate.bandwidth, typos, ...
This commit is contained in:
Daniel Kapla 2019-11-20 19:03:21 +01:00
parent 0670bb976e
commit 063c4d638b
36 changed files with 1967 additions and 819 deletions

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@ -2,10 +2,10 @@ Package: CVE
Type: Package
Title: Conditional Variance Estimator for Sufficient Dimension Reduction
Version: 0.2
Date: 2019-10-24
Author: Loki
Maintainer: Loki <loki@no.mail>
Description: Implementation of the Conditional Variance Estimation (CVE) method. This package version is writen in pure R.
Date: 2019-11-13
Author: Daniel Kapla <daniel@kapla.at>, Lukas Fertl <lukas.fertl@chello.at>
Maintainer: Daniel Kapla <daniel@kapla.at>
Description: Implementation of the Conditional Variance Estimation (CVE) method.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 6.1.1

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@ -1,17 +1,23 @@
# Generated by roxygen2: do not edit by hand
S3method(basis,cve)
S3method(directions,cve)
S3method(plot,cve)
S3method(predict,cve)
S3method(predict.dim,cve)
S3method(summary,cve)
export(basis)
export(cve)
export(cve.call)
export(cve.grid.search)
export(dataset)
export(directions)
export(elem.pairs)
export(estimate.bandwidth)
export(null)
export(projTangentStiefl)
export(rStiefl)
export(retractStiefl)
export(predict.dim)
export(projTangentStiefel)
export(rStiefel)
export(retractStiefel)
export(skew)
export(sym)
import(stats)

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@ -48,6 +48,17 @@
#' \item "weighted" variation with addaptive weighting of slices.
#' }
#' @param ... Parameters passed on to \code{cve.call}.
#'
#' @return dr is a S3 object of class \code{cve} with named properties:
#' \itemize{
#' \item X: Original training data,
#' \item Y: Responce of original training data,
#' \item method: Name of used method,
#' \item call: The method call
#' }
#' as well as indexed entries \code{dr[[k]]} storing the k-dimensional SDR
#' projection matrices.
#'
#' @examples
#' library(CVE)
#'
@ -61,7 +72,7 @@
#'
#' # Call the CVE method.
#' dr <- cve(Y ~ X)
#' round(dr[[2]]$B, 1)
#' (B <- basis(dr, 2))
#'
#' @seealso For a detailed description of \code{formula} see
#' [\code{\link{formula}}].
@ -91,24 +102,60 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
#' \code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).
#' @param X data matrix with samples in its rows.
#' @param Y Responses (1 dimensional).
#' @param k Dimension of lower dimensional projection, if \code{k} is given only the specified dimension \code{B} matrix is estimated.
#' @param k Dimension of lower dimensional projection, if \code{k} is given
#' only the specified dimension \code{B} matrix is estimated.
#' @param min.dim lower bounds for \code{k}, (ignored if \code{k} is supplied).
#' @param max.dim upper bounds for \code{k}, (ignored if \code{k} is supplied).
#' @param tau Initial step-size.
#' @param tol Tolerance for break condition.
#' @param epochs maximum number of optimization steps.
#' @param attempts number of arbitrary different starting points.
#' @param logger a logger function (only for advanced user, significantly slows down the computation).
#' @param logger a logger function (only for advanced user, significantly slows
#' down the computation).
#'
#' @return dr is a list which contains:
#' \itemize{
#' \item dir: dir[[d]] is the central space with d-dimension
#' d = 1, 2, ..., p reduced direction of different dimensions
#' \item y: the value of response
#' \item idx: the index of variables which survives after screening
#' \item max.dim: the largest dimensions of CS or CMS which have been calculated in mave function
#' \item ky: parameter used for DIM for selection
#' \item x: the original training data
#' }
#'
#' @rdname cve
#' @export
cve.call <- function(X, Y, method = "simple",
nObs = sqrt(nrow(X)), h = NULL,
min.dim = 1L, max.dim = 10L, k = NULL,
tau = 1.0, tol = 1e-3,
momentum = 0.0, tau = 1.0, tol = 1e-3,
slack = 0.0, gamma = 0.5,
V.init = NULL,
epochs = 50L, attempts = 10L,
logger = NULL) {
# get method bitmask
methods <- list(
"simple" = 0L,
"weighted" = 1L
)
method <- tolower(method)
if (!(method %in% names(methods))) {
stop('Got unknown method.')
}
method_bitmask <- methods[[method]]
# parameter checking
if (!is.numeric(momentum) || length(momentum) > 1L) {
stop("Momentum must be a number.")
}
if (!is.double(momentum)) {
momentum <- as.double(momentum)
}
if (momentum < 0.0 || momentum >= 1.0) {
stop("Momentum must be in [0, 1).")
}
if (!(is.matrix(X) && is.numeric(X))) {
stop("Parameter 'X' should be a numeric matrices.")
}
@ -125,12 +172,23 @@ cve.call <- function(X, Y, method = "simple",
stop("'X' is one dimensional, no need for dimension reduction.")
}
if (missing(k) || is.null(k)) {
if (!is.null(V.init)) {
if (!is.matrix(V.init)) {
stop("'V.init' must be a matrix.")
}
if (!all.equal(crossprod(V.init), diag(1, ncol(V.init)))) {
stop("'V.init' must be semi-orthogonal.")
}
if (ncol(X) != nrow(V.init) || ncol(X) <= ncol(V.init)) {
stop("Dimension missmatch of 'V.init' and 'X'")
}
min.dim <- max.dim <- ncol(X) - ncol(V.init)
attempts <- 0L
} else if (missing(k) || is.null(k)) {
min.dim <- as.integer(min.dim)
max.dim <- as.integer(min(max.dim, ncol(X) - 1L))
} else {
min.dim <- as.integer(k)
max.dim <- as.integer(k)
min.dim <- max.dim <- as.integer(k)
}
if (min.dim > max.dim) {
stop("'min.dim' bigger 'max.dim'.")
@ -161,6 +219,16 @@ cve.call <- function(X, Y, method = "simple",
} else {
tol <- as.double(tol)
}
if (!is.numeric(slack) || length(slack) > 1L || slack < 0.0) {
stop("Break condition slack 'slack' must be not negative number.")
} else {
slack <- as.double(slack)
}
if (!is.numeric(gamma) || length(gamma) > 1L || gamma <= 0.0 || gamma >= 1.0) {
stop("Stepsize reduction 'gamma' must be between 0 and 1.")
} else {
gamma <- as.double(gamma)
}
if (!is.numeric(epochs) || length(epochs) > 1L) {
stop("Parameter 'epochs' must be positive integer.")
@ -170,6 +238,8 @@ cve.call <- function(X, Y, method = "simple",
if (epochs < 1L) {
stop("Parameter 'epochs' must be at least 1L.")
}
if (is.null(V.init)) {
if (!is.numeric(attempts) || length(attempts) > 1L) {
stop("Parameter 'attempts' must be positive integer.")
} else if (!is.integer(attempts)) {
@ -178,6 +248,7 @@ cve.call <- function(X, Y, method = "simple",
if (attempts < 1L) {
stop("Parameter 'attempts' must be at least 1L.")
}
}
if (is.function(logger)) {
loggerEnv <- environment(logger)
@ -189,40 +260,28 @@ cve.call <- function(X, Y, method = "simple",
method <- tolower(method)
call <- match.call()
dr <- list()
dr$res <- list()
for (k in min.dim:max.dim) {
if (estimate) {
h <- estimate.bandwidth(X, k, nObs)
}
if (method == 'simple') {
dr.k <- .Call('cve_simple', PACKAGE = 'CVE',
dr.k <- .Call('cve', PACKAGE = 'CVE',
X, Y, k, h,
tau, tol,
method_bitmask,
V.init,
momentum, tau, tol,
slack, gamma,
epochs, attempts,
logger, loggerEnv)
# 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 == 'rcg') {
# dr.k <- cve_rcg(X, Y, k, nObs = nObs, ...)
# } else if (method == 'momentum') {
# dr.k <- cve_momentum(X, Y, k, nObs = nObs, ...)
# } else if (method == 'rmsprob') {
# dr.k <- cve_rmsprob(X, Y, k, nObs = nObs, ...)
# } else if (method == 'sgdrmsprob') {
# dr.k <- cve_sgdrmsprob(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$B <- null(dr.k$V)
dr.k$loss <- mean(dr.k$L)
dr.k$h <- h
dr.k$k <- k
class(dr.k) <- "cve.k"
dr[[k]] <- dr.k
dr$res[[as.character(k)]] <- dr.k
}
# augment result information
@ -236,22 +295,23 @@ cve.call <- function(X, Y, method = "simple",
#' Loss distribution elbow plot.
#'
#' Boxplots of the loss from \code{min.dim} to \code{max.dim} \code{k} values.
#'
#' @param x Object of class \code{"cve"} (result of [\code{\link{cve}}]).
#' @param ... Pass through parameters to [\code{\link{plot}}] and
#' [\code{\link{lines}}]
#'
#' @seealso see \code{\link{par}} for graphical parameters to pass through
#' as well as \code{\link{plot}}, the standard plot utility.
#' @importFrom graphics plot lines points
#' @method plot cve
#' Boxplots of the loss from \code{min.dim} to \code{max.dim} \code{k} values.
#' @importFrom graphics plot lines points
#' @export
plot.cve <- function(x, ...) {
L <- c()
k <- c()
for (dr.k in x) {
for (dr.k in x$res) {
if (class(dr.k) == 'cve.k') {
k <- c(k, paste0(dr.k$k))
k <- c(k, as.character(dr.k$k))
L <- c(L, dr.k$L)
}
}
@ -260,11 +320,10 @@ plot.cve <- function(x, ...) {
xlab = "SDR dimension",
ylab = "Sample loss distribution",
names = k)
# lines(apply(L, 2, mean)) # TODO: ?
}
#' Prints a summary of a \code{cve} result.
#' @param object Instance of 'cve' as return of \code{cve}.
#' @param object Instance of 'cve' as returned by \code{cve}.
#' @method summary cve
#' @export
summary.cve <- function(object, ...) {
@ -272,11 +331,151 @@ summary.cve <- function(object, ...) {
'\n',
'Dataset size: ', nrow(object$X), '\n',
'Data Dimension: ', ncol(object$X), '\n',
'SDR Dimension: ', object$k, '\n',
'loss: ', object$loss, '\n',
# 'SDR Dimension: ', object$k, '\n',
# 'loss: ', object$loss, '\n',
'\n',
'Called via:\n',
' ',
sep='')
print(object$call)
L <- c()
k <- c()
for (dr.k in object$res) {
if (class(dr.k) == 'cve.k') {
k <- c(k, as.character(dr.k$k))
L <- c(L, dr.k$L)
}
}
L <- matrix(L, ncol = length(k))
S <- apply(L, 2, summary)
colnames(S) <- k
cat('\n')
print(S)
}
#' @export
directions <- function(dr, k) {
UseMethod("directions")
}
#' Computes projected training data \code{X} for given dimension `k`.
#'
#' @param dr Instance of 'cve' as returned by \code{cve}.
#' @param k SDR dimension to use for projection.
#'
#' @method directions cve
#' @aliases directions directions.cve
#' @export
directions.cve <- function(dr, k) {
if (!(k %in% names(dr$res))) {
stop("SDR directions for requested dimension `k` not computed.")
}
return(dr$X %*% dr$res[[as.character(k)]]$B)
}
#' @export
basis <- function(dr, k) {
UseMethod("basis")
}
#' Gets estimated SDR basis.
#'
#' @param dr Instance of 'cve' as returned by \code{cve}.
#' @param k SDR dimension of requested basis, if not given a list of all
#' computed basis is returned.
#'
#' @return List of basis matrices, or the SDR basis for supplied dimension `k`.
#'
#' @method basis cve
#' @aliases basis basis.cve
#' @export
basis.cve <- function(dr, k) {
if (missing(k)) {
Bs <- list()
for (k in names(dr$res)) {
Bs[[k]] <- dr$res[[k]]$B
}
return(Bs)
} else if (k %in% names(dr$res)) {
return(dr$res[[as.character(k)]]$B)
} else {
stop("Requested dimenion `k` not computed.")
}
}
#' Predict method for CVE Fits.
#'
#' Predict responces using reduced data with \code{\link{mars}}.
#'
#' @param object instance of class \code{cve} (result of \code{cve},
#' \code{cve.call}).
#' @param X.new Matrix of the new data to be predicted.
#' @param dim dimension of SDR space to be used for data projecition.
#' @param ... further arguments passed to \code{\link{mars}}.
#'
#' @return prediced response of data \code{X.new}.
#'
#' @seealso \code{\link{cve}}, \code{\link{cve.call}} or \pkg{\link{mars}}.
#'
#' @examples
#' TODO:
#'
#' @aliases predict.cve
#' @rdname predict.cve
#'
#' @method predict cve
#' @export
predict.cve <- function(object, X.new, dim = NULL, ...) {
library(mda)
if (!is.matrix(X.new)) {
X.new <- matrix(X.new, nrow = 1L)
}
B <- dr$res[[as.character(dim)]]$B
model <- mars(object$X %*% B, object$Y)
predict(model, X.new %*% B)
}
#' @export
predict.dim <- function(dr) {
UseMethod("predict.dim")
}
#' @method predict.dim cve
#' @export
predict.dim.cve <- function(dr) {
library(mda)
# Get centered training data and dimensions
X <- scale(dr$X, center = TRUE, scale = FALSE)
n <- nrow(dr$X) # umber of training data samples
Sigma <- (1 / n) * crossprod(X, X)
eig <- eigen(Sigma)
Sigma_root <- eig$vectors %*% tcrossprod(diag(sqrt(eig$values)), eig$vectors)
X <- X %*% solve(Sigma_root)
pred <- matrix(0, n, length(dr$res))
colnames(pred) <- names(dr$res)
for (dr.k in dr$res) {
# get "name" of current dimension
k <- as.character(dr.k$k)
# Project dataset with current SDR basis
X.proj <- X %*% dr.k$B
for (i in 1:n) {
model <- mars(X.proj[-i, ], dr$Y[-i])
pred[i, k] <- predict(model, X.proj[i, , drop = F])
}
}
MSE <- colMeans((pred - dr$Y)^2)
return(list(
MSE = MSE,
k = as.integer(names(which.min(MSE)))
))
}

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@ -2,8 +2,8 @@
#'
#' Estimates a bandwidth \code{h} according
#' \deqn{%
#' h = \chi_{k}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
#' h = qchisq( (nObs - 1)/(n - 1), k ) * (2 tr(\Sigma) / p)}
#' h = (2 * tr(\Sigma) / p) * (1.2 * n^{-1 / (4 + k)})^2}{%
#' h = (2 * tr(Sigma) / p) * (1.2 * n^(-1 / (4 + k)))^2}
#' with \eqn{n} the sample size, \eqn{p} its dimension
#' (\code{n <- nrow(X); p <- ncol(X)}) and the covariance-matrix \eqn{\Sigma}
#' which is \code{(n-1)/n} times the sample covariance estimate.
@ -12,15 +12,15 @@
#' @param k Dimension of lower dimensional projection.
#' @param nObs number of points in a slice, see \eqn{nObs} in CVE paper.
#'
#' @seealso [\code{\link{qchisq}}]
#' @return Estimated bandwidth \code{h}.
#'
#' @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
Sigma <- crossprod(X_centered, X_centered) / n
quantil <- qchisq((nObs - 1) / (n - 1), k)
return(2 * quantil * sum(diag(Sigma)) / p)
return((2 * sum(diag(Sigma)) / p) * (1.2 * n^(-1 / (4 + k)))^2)
}

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@ -1,43 +0,0 @@
#' 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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@ -6,17 +6,17 @@
#' @examples
#' V <- rStiefel(6, 4)
#' @export
rStiefl <- function(p, q) {
rStiefel <- function(p, q) {
return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
}
#' Retraction to the manifold.
#'
#' @param A matrix.
#' @return `(p, q)` semi-orthogonal matrix, aka element of the Stiefl manifold.
#' @return `(p, q)` semi-orthogonal matrix, aka element of the Stiefel manifold.
#' @keywords internal
#' @export
retractStiefl <- function(A) {
retractStiefel <- function(A) {
return(qr.Q(qr(A)))
}
@ -40,14 +40,14 @@ sym <- function(A) {
0.5 * (A + t(A))
}
#' Orthogonal Projection onto the tangent space of the stiefl manifold.
#' Orthogonal Projection onto the tangent space of the stiefel manifold.
#'
#' @param V Point on the stiefl manifold.
#' @param V Point on the stiefel manifold.
#' @param G matrix to be projected onto the tangent space at `V`.
#' @return `(p, q)` matrix as element of the tangent space at `V`.
#' @keywords internal
#' @export
projTangentStiefl <- function(V, G) {
projTangentStiefel <- function(V, G) {
Q <- diag(1, nrow(V)) - V %*% t(V)
return(Q %*% G + V %*% skew(t(V) %*% G))
}

21
CVE_C/man/basis.cve.Rd Normal file
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@ -0,0 +1,21 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{basis.cve}
\alias{basis.cve}
\alias{basis}
\title{Gets estimated SDR basis.}
\usage{
\method{basis}{cve}(dr, k)
}
\arguments{
\item{dr}{Instance of 'cve' as returned by \code{cve}.}
\item{k}{SDR dimension of requested basis, if not given a list of all
computed basis is returned.}
}
\value{
List of basis matrices, or the SDR basis for supplied dimension `k`.
}
\description{
Gets estimated SDR basis.
}

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@ -8,7 +8,8 @@
cve(formula, data, method = "simple", max.dim = 10L, ...)
cve.call(X, Y, method = "simple", nObs = sqrt(nrow(X)), h = NULL,
min.dim = 1L, max.dim = 10L, k = NULL, tau = 1, tol = 0.001,
min.dim = 1L, max.dim = 10L, k = NULL, momentum = 0, tau = 1,
tol = 0.001, slack = 0, gamma = 0.5, V.init = NULL,
epochs = 50L, attempts = 10L, logger = NULL)
}
\arguments{
@ -31,15 +32,15 @@ supplied.}
\item{X}{data matrix with samples in its rows.}
\item{Y}{Responces (1 dimensional).}
\item{Y}{Responses (1 dimensional).}
\item{nObs}{parameter for choosing bandwidth \code{h} using
\code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).}
\item{min.dim}{lower bounds for \code{k}, (ignored if \code{k} is supplied).}
\item{k}{Dimension of lower dimensional projection, if given only the
specified dimension is estimated.}
\item{k}{Dimension of lower dimensional projection, if \code{k} is given
only the specified dimension \code{B} matrix is estimated.}
\item{tau}{Initial step-size.}
@ -49,7 +50,30 @@ specified dimension is estimated.}
\item{attempts}{number of arbitrary different starting points.}
\item{logger}{a logger function (only for addvanced user).}
\item{logger}{a logger function (only for advanced user, significantly slows
down the computation).}
}
\value{
dr is a S3 object of class \code{cve} with named properties:
\itemize{
\item X: Original training data,
\item Y: Responce of original training data,
\item method: Name of used method,
\item call: The method call
}
as well as indexed entries \code{dr[[k]]} storing the k-dimensional SDR
projection matrices.
dr is a list which contains:
\itemize{
\item dir: dir[[d]] is the central space with d-dimension
d = 1, 2, ..., p reduced direction of different dimensions
\item y: the value of response
\item idx: the index of variables which survives after screening
\item max.dim: the largest dimensions of CS or CMS which have been calculated in mave function
\item ky: parameter used for DIM for selection
\item x: the original training data
}
}
\description{
TODO: reuse of package description and details!!!!
@ -67,10 +91,10 @@ Y <- Y[, 1L]^2 + Y[, 2L]^2 + rnorm(n, 0, 0.3)
# Call the CVE method.
dr <- cve(Y ~ X)
round(dr[[2]]$B, 1)
(B <- basis(dr, 2))
}
\seealso{
For a detailed description of the formula parameter see
For a detailed description of \code{formula} see
[\code{\link{formula}}].
}

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@ -1,19 +0,0 @@
% 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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@ -0,0 +1,17 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{directions.cve}
\alias{directions.cve}
\alias{directions}
\title{Computes projected training data \code{X} for given dimension `k`.}
\usage{
\method{directions}{cve}(dr, k)
}
\arguments{
\item{dr}{Instance of 'cve' as returned by \code{cve}.}
\item{k}{SDR dimension to use for projection.}
}
\description{
Computes projected training data \code{X} for given dimension `k`.
}

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@ -11,17 +11,17 @@ estimate.bandwidth(X, k, nObs)
\item{k}{Dimension of lower dimensional projection.}
\item{nObs}{Expected number of points in a slice, see paper.}
\item{nObs}{number of points in a slice, see \eqn{nObs} in CVE paper.}
}
\value{
Estimated bandwidth \code{h}.
}
\description{
Estimates a propper bandwidth \code{h} according
Estimates a bandwidth \code{h} according
\deqn{%
h = \chi_{k}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
h = qchisq( (nObs - 1)/(n - 1), k ) * (2 tr(\Sigma) / p)}
with \eqn{n} the number of sample and \eqn{p} its dimension
h = (2 * tr(\Sigma) / p) * (1.2 * n^{-1 / (4 + k)})^2}{%
h = (2 * tr(Sigma) / p) * (1.2 * n^(-1 / (4 + k)))^2}
with \eqn{n} the sample size, \eqn{p} its dimension
(\code{n <- nrow(X); p <- ncol(X)}) and the covariance-matrix \eqn{\Sigma}
which is given by the standard maximum likelihood estimate.
}
\seealso{
[\code{\link{qchisq}}]
which is \code{(n-1)/n} times the sample covariance estimate.
}

View File

@ -13,7 +13,7 @@
[\code{\link{lines}}]}
}
\description{
Loss distribution elbow plot.
Boxplots of the loss from \code{min.dim} to \code{max.dim} \code{k} values.
}
\seealso{
see \code{\link{par}} for graphical parameters to pass through

31
CVE_C/man/predict.cve.Rd Normal file
View File

@ -0,0 +1,31 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{predict.cve}
\alias{predict.cve}
\title{Predict method for CVE Fits.}
\usage{
\method{predict}{cve}(object, X.new, dim = NULL, ...)
}
\arguments{
\item{object}{instance of class \code{cve} (result of \code{cve},
\code{cve.call}).}
\item{X.new}{Matrix of the new data to be predicted.}
\item{dim}{dimension of SDR space to be used for data projecition.}
\item{...}{further arguments passed to \code{\link{mars}}.}
}
\value{
prediced response of data \code{X.new}.
}
\description{
Predict responces using reduced data with \code{\link{mars}}.
}
\examples{
TODO:
}
\seealso{
\code{\link{cve}}, \code{\link{cve.call}} or \pkg{\link{mars}}.
}

View File

@ -1,13 +1,13 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{projTangentStiefl}
\alias{projTangentStiefl}
\title{Orthogonal Projection onto the tangent space of the stiefl manifold.}
\name{projTangentStiefel}
\alias{projTangentStiefel}
\title{Orthogonal Projection onto the tangent space of the stiefel manifold.}
\usage{
projTangentStiefl(V, G)
projTangentStiefel(V, G)
}
\arguments{
\item{V}{Point on the stiefl manifold.}
\item{V}{Point on the stiefel manifold.}
\item{G}{matrix to be projected onto the tangent space at `V`.}
}
@ -15,6 +15,6 @@ projTangentStiefl(V, G)
`(p, q)` matrix as element of the tangent space at `V`.
}
\description{
Orthogonal Projection onto the tangent space of the stiefl manifold.
Orthogonal Projection onto the tangent space of the stiefel manifold.
}
\keyword{internal}

22
CVE_C/man/rStiefel.Rd Normal file
View File

@ -0,0 +1,22 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{rStiefel}
\alias{rStiefel}
\title{Draws a sample from the invariant measure on the Stiefel manifold \eqn{S(p, q)}.}
\usage{
rStiefel(p, q)
}
\arguments{
\item{p}{row dimension}
\item{q}{col dimension}
}
\value{
\code{p} times \code{q} semi-orthogonal matrix.
}
\description{
Draws a sample from the invariant measure on the Stiefel manifold \eqn{S(p, q)}.
}
\examples{
V <- rStiefel(6, 4)
}

View File

@ -1,22 +0,0 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{rStiefl}
\alias{rStiefl}
\title{Samples uniform from the Stiefl 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 Stiefl Manifold.
}
\examples{
V <- rStiefel(6, 4)
}

View File

@ -1,16 +1,16 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{retractStiefl}
\alias{retractStiefl}
\name{retractStiefel}
\alias{retractStiefel}
\title{Retraction to the manifold.}
\usage{
retractStiefl(A)
retractStiefel(A)
}
\arguments{
\item{A}{matrix.}
}
\value{
`(p, q)` semi-orthogonal matrix, aka element of the Stiefl manifold.
`(p, q)` semi-orthogonal matrix, aka element of the Stiefel manifold.
}
\description{
Retraction to the manifold.

View File

@ -7,7 +7,7 @@
\method{summary}{cve}(object, ...)
}
\arguments{
\item{object}{Instance of 'cve' as return of \code{cve}.}
\item{object}{Instance of 'cve' as returned by \code{cve}.}
}
\description{
Prints a summary of a \code{cve} result.

View File

@ -5,17 +5,22 @@ static inline double gaussKernel(const double x, const double scale) {
return exp(scale * x * x);
}
void cve_simple_sub(const int n, const int p, const int q,
void cve_sub(const int n, const int p, const int q,
const double *X, const double *Y, const double h,
const unsigned int method,
const double momentum,
const double tau_init, const double tol_init,
const double slack, const double gamma,
const int epochs, const int attempts,
double *V, double *L,
SEXP logger, SEXP loggerEnv) {
int attempt, epoch, i, nn = (n * (n - 1)) / 2;
int attempt = 0, epoch, i, nn = (n * (n - 1)) / 2;
double loss, loss_last, loss_best, err, tau;
double tol = tol_init * sqrt((double)(2 * q));
double gKscale = -0.5 / h;
double agility = -2.0 * (1.0 - momentum) / (h * h);
double c;
/* Create further intermediate or internal variables. */
double *Q = (double*)R_alloc(p * p, sizeof(double));
@ -23,8 +28,8 @@ void cve_simple_sub(const int n, const int p, const int q,
double *L_best = (double*)R_alloc(n, sizeof(double));
double *V_tau = (double*)R_alloc(p * q, sizeof(double));
double *X_diff = (double*)R_alloc(nn * p, sizeof(double));
double *X_proj = (double*)R_alloc(nn * p, sizeof(double)); // TODO: needed?
double *y1 = (double*)R_alloc(n , sizeof(double)); // TODO: needed?
double *X_proj = (double*)R_alloc(nn * p, sizeof(double));
double *y1 = (double*)R_alloc(n, sizeof(double));
double *vecD = (double*)R_alloc(nn, sizeof(double));
double *vecK = (double*)R_alloc(nn, sizeof(double));
double *vecS = (double*)R_alloc(nn, sizeof(double));
@ -32,6 +37,12 @@ void cve_simple_sub(const int n, const int p, const int q,
double *G = (double*)R_alloc(p * q, sizeof(double));
double *A = (double*)R_alloc(p * p, sizeof(double));
double *V_init = (void*)0;
if (attempts < 1) {
V_init = (double*)R_alloc(p * q, sizeof(double));
memcpy(V_init, V, p * q * sizeof(double));
}
/* Determine size of working memory used by subroutines. */
const int workLen = getWorkLen(n, p, q);
double *workMem = (double*)R_alloc(workLen, sizeof(double));
@ -39,14 +50,20 @@ void cve_simple_sub(const int n, const int p, const int q,
/* Compute X_diff, this is static for the entire algorithm. */
rowDiffs(X, n, p, X_diff);
for (attempt = 0; attempt < attempts; ++attempt) {
do {
/* (Re)set learning rate. */
tau = tau_init;
/* Sample start value from stiefl manifold. */
rStiefl(p, q, V, workMem, workLen);
/* Check if start value for `V` was supplied. */
if (V_init == (void*)0) {
/* Sample start value from stiefel manifold. */
rStiefel(p, q, V, workMem, workLen);
} else {
/* (Re)Set start value of `V` to `V_init`. */
memcpy(V, V_init, p * q * sizeof(double));
}
/* Create projection matrix for initial `V`. */
/* Create projection matrix `Q <- I - V V^T` for initial `V`. */
nullProj(V, p, q, Q);
/* Compute Distance vector. */
@ -65,7 +82,7 @@ void cve_simple_sub(const int n, const int p, const int q,
/* Compute loss given the kernel vector and its column sums.
* Additionally the first momentum `y1` is computed and stored in
* the working memory (only intermidiate result, needed for `vecS`). */
loss_last = cost(n, Y, vecK, colSums, y1, L);
loss_last = cost(method, n, Y, vecK, colSums, y1, L);
if (logger) {
callLogger(logger, loggerEnv,
@ -74,16 +91,27 @@ void cve_simple_sub(const int n, const int p, const int q,
}
/* Calc the scaling vector used for final computation of grad. */
scaling(n, Y, y1, L, vecD, vecK, colSums, vecS);
scaling(method, n, Y, y1, L, vecD, vecK, colSums, vecS);
/* Compute the eucledian gradient `G`. */
rowSweep(X_diff, nn, p, "*", vecS, X_proj);
crossprod(X_diff, nn, p, X_proj, nn, p, workMem);
matrixprod(workMem, p, p, V, p, q, G);
scale(-2. / (((double)n) * h * h), G, p * q); // in-place
if (method == CVE_METHOD_WEIGHTED) {
/* Compute summ of all kernel applied distances by summing the
* colSums of the kernel matrix. */
c = -(double)n; // to scale with sum(K) - n
for (i = 0; i < n; ++i) {
c += colSums[i];
}
// TODO: check for division by zero, but should not happen!!!
} else {
c = n; // TODO: move (init) up cause always the same ^^ ...
}
scale(agility / c, G, p * q); // in-place
/* Compute Skew-Symmetric matrix `A` used in Cayley transform.
+ `A <- tau * (G V^T - V G^T) + 0 * A`*/
* `A <- tau * (G V^T - V G^T) + 0 * A`*/
skew(p, q, tau, G, V, 0.0, A);
for (epoch = 0; epoch < epochs; ++epoch) {
@ -108,13 +136,13 @@ void cve_simple_sub(const int n, const int p, const int q,
/* Compute loss given the kernel vector and its column sums.
* Additionally the first momentum `y1` is computed and stored in
* the working memory (only intermidiate result, needed for `vecS`). */
loss = cost(n, Y, vecK, colSums, y1, L);
* the working memory (only intermidiate result, needed for vecS).*/
loss = cost(method, n, Y, vecK, colSums, y1, L);
/* Check if step is appropriate, iff not reduce learning rate. */
if ((loss - loss_last) > 0.0) {
tau *= 0.5;
scale(0.5, A, p * p);
if ((loss - loss_last) > loss_last * slack) {
tau *= gamma;
scale(gamma, A, p * p);
continue;
}
@ -139,16 +167,34 @@ void cve_simple_sub(const int n, const int p, const int q,
/* Continue computing the gradient. */
/* Calc the scaling vector used for final computation of grad. */
scaling(n, Y, y1, L, vecD, vecK, colSums, vecS);
scaling(method, n, Y, y1, L, vecD, vecK, colSums, vecS);
/* Compute the eucledian gradient `G`. */
rowSweep(X_diff, nn, p, "*", vecS, X_proj);
crossprod(X_diff, nn, p, X_proj, nn, p, workMem);
matrixprod(workMem, p, p, V, p, q, G);
scale(-2. / (((double)n) * h * h), G, p * q); // in-place
// /* Update without momentum */
// matrixprod(workMem, p, p, V, p, q, G);
// scale(-2. / (((double)n) * h * h), G, p * q); // in-place
/* G <- momentum * G + agility * workMem V */
if (method == CVE_METHOD_WEIGHTED) {
/* Compute summ of all kernel applied distances by summing the
* colSums of the kernel matrix. */
c = -(double)n; // to scale with sum(K) - n
for (i = 0; i < n; ++i) {
c += colSums[i];
}
c = agility / c;
// TODO: check for division by zero, but should not happen!!!
} else {
c = agility / n;
}
F77_NAME(dgemm)("N", "N", &p, &q, &p,
&c, workMem, &p, V, &p,
&momentum, G, &p);
/* Compute Skew-Symmetric matrix `A` used in Cayley transform.
+ `A <- tau * (G V^T - V G^T) + 0 * A`*/
* `A <- tau * (G V^T - V G^T) + 0 * A`*/
skew(p, q, tau, G, V, 0.0, A);
}
@ -158,7 +204,7 @@ void cve_simple_sub(const int n, const int p, const int q,
memcpy(V_best, V, p * q * sizeof(double));
memcpy(L_best, L, n * sizeof(double));
}
}
} while (++attempt < attempts);
memcpy(V, V_best, p * q * sizeof(double));
memcpy(L, L_best, n * sizeof(double));

View File

@ -13,10 +13,25 @@
#define CVE_MEM_CHUNK_SIZE 2032
#define CVE_MEM_CHUNK_SMALL 1016
void cve_simple_sub(const int n, const int p, const int q,
/* Bis masks for method types */
#define CVE_METHOD_WEIGHTED 1
// typedef struct {
// unsigned int nrow;
// unsigned int ncol;
// unsigned int memsize;
// double *data;
// } mat;
// mat* Matrix(const unsigned int nrow, const unsigned int ncol);
void cve_sub(const int n, const int p, const int q,
const double *X, const double *Y, const double h,
const unsigned int method,
const double momentum,
const double tau_init, const double tol_init,
const int epochs, const int attempts,
const double slack, const double gamma,
const int epochs, int attempts,
double *V, double *L,
SEXP logger, SEXP loggerEnv);
@ -28,19 +43,21 @@ void callLogger(SEXP logger, SEXP env,
/* CVE sub-routines */
int getWorkLen(const int n, const int p, const int q);
double cost(const int n,
double cost(const unsigned int method,
const int n,
const double *Y,
const double *vecK,
const double *colSums,
double *y1, double *L);
void scaling(const int n,
void scaling(const unsigned int method,
const int n,
const double *Y, const double *y1, const double *L,
const double *vecD, const double *vecK,
const double *colSums,
double *vecS);
/* rStiefl */
void rStiefl(const int p, const int q, double *V,
/* rStiefel */
void rStiefel(const int p, const int q, double *V,
double *workMem, int workLen);
/* MATRIX */

View File

@ -16,13 +16,14 @@ int getWorkLen(const int n, const int p, const int q) {
}
}
double cost(const int n,
double cost(const unsigned int method,
const int n,
const double *Y,
const double *vecK,
const double *colSums,
double *y1, double *L) {
int i, j, k;
double tmp;
double tmp, sum;
for (i = 0; i < n; ++i) {
y1[i] = Y[i];
@ -44,13 +45,23 @@ double cost(const int n,
}
tmp = 0.0;
if (method == CVE_METHOD_WEIGHTED) {
sum = 0.0;
for (i = 0; i < n; ++i) {
tmp += (colSums[i] - 1.0) * (L[i] -= y1[i] * y1[i]);
sum += colSums[i];
}
return tmp / (sum - (double)n); // TODO: check for division by zero!
} else {
for (i = 0; i < n; ++i) {
tmp += (L[i] -= y1[i] * y1[i]);
}
return tmp / (double)n;
}
}
void scaling(const int n,
void scaling(const unsigned int method,
const int n,
const double *Y, const double *y1, const double *L,
const double *vecD, const double *vecK,
const double *colSums,
@ -58,6 +69,16 @@ void scaling(const int n,
int i, j, k, nn = (n * (n - 1)) / 2;
double tmp;
if (method == CVE_METHOD_WEIGHTED) {
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
tmp = Y[j] - y1[i];
vecS[k] = (L[i] - (tmp * tmp));
tmp = Y[i] - y1[j];
vecS[k] += (L[j] - (tmp * tmp));
}
}
} else {
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
tmp = Y[j] - y1[i];
@ -66,6 +87,7 @@ void scaling(const int n,
vecS[k] += (L[j] - (tmp * tmp)) / colSums[j];
}
}
}
for (k = 0; k < nn; ++k) {
vecS[k] *= vecK[k] * vecD[k];

View File

@ -1,6 +1,6 @@
#include "cve.h"
// SEXP rStiefl_c(SEXP pin, SEXP qin) {
// SEXP rStiefel_c(SEXP pin, SEXP qin) {
// int p = asInteger(pin);
// int q = asInteger(qin);
@ -9,19 +9,22 @@
// int workLen = 2 * (p + 1) * q;
// double *workMem = (double*)R_alloc(workLen, sizeof(double));
// rStiefl(p, q, REAL(Vout), workMem, workLen);
// rStiefel(p, q, REAL(Vout), workMem, workLen);
// UNPROTECT(1);
// return Vout;
// }
SEXP cve_simple(SEXP X, SEXP Y, SEXP k, SEXP h,
SEXP tau, SEXP tol,
SEXP cve(SEXP X, SEXP Y, SEXP k, SEXP h,
SEXP method,
SEXP V, // initial
SEXP momentum, SEXP tau, SEXP tol,
SEXP slack, SEXP gamma,
SEXP epochs, SEXP attempts,
SEXP logger, SEXP loggerEnv) {
/* Handle logger parameter, set to NULL pointer if not a function. */
if (!(isFunction(logger) && isEnvironment(loggerEnv))) {
logger = (SEXP)0;
logger = (void*)0;
}
/* Get dimensions. */
@ -30,20 +33,31 @@ SEXP cve_simple(SEXP X, SEXP Y, SEXP k, SEXP h,
int q = p - asInteger(k);
/* Convert types if needed. */
// TODO:
// TODO: implement! (or leave in calling R code?)
/* Create output list. */
SEXP Vout = PROTECT(allocMatrix(REALSXP, p, q));
SEXP Lout = PROTECT(allocVector(REALSXP, n));
/* Check `attempts`, if not positive use passed values of `V` as
* optimization start value without further attempts.
* Therefor, copy from `V` to `Vout`. */
if (asInteger(attempts) < 1L) {
// TODO: Check for
memcpy(REAL(Vout), REAL(V), p * q * sizeof(double));
}
/* Call CVE simple subroutine. */
cve_simple_sub(n, p, q,
cve_sub(n, p, q,
REAL(X), REAL(Y), asReal(h),
asReal(tau), asReal(tol),
asInteger(method),
asReal(momentum), asReal(tau), asReal(tol),
asReal(slack), asReal(gamma),
asInteger(epochs), asInteger(attempts),
REAL(Vout), REAL(Lout),
logger, loggerEnv);
/* Build output list object with names "V", "L" */
SEXP out = PROTECT(allocVector(VECSXP, 2));
SET_VECTOR_ELT(out, 0, Vout);
SET_VECTOR_ELT(out, 1, Lout);

View File

@ -3,25 +3,22 @@
#include <stdlib.h> // for NULL
#include <R_ext/Rdynload.h>
/* FIXME:
Check these declarations against the C/Fortran source code.
*/
/* .Call calls */
extern SEXP cve_simple(SEXP X, SEXP Y, SEXP k,
SEXP h,
SEXP tau, SEXP tol,
extern SEXP cve(SEXP X, SEXP Y, SEXP k, SEXP h,
SEXP method,
SEXP V, // initial
SEXP momentum, SEXP tau, SEXP tol,
SEXP slack, SEXP gamma,
SEXP epochs, SEXP attempts,
SEXP logger, SEXP loggerEnv);
static const R_CallMethodDef CallEntries[] = {
{"cve_simple", (DL_FUNC) &cve_simple, 10},
{"cve", (DL_FUNC) &cve, 15},
{NULL, NULL, 0}
};
/* Restrict C entrypoints to registered routines. */
void R_initCVE(DllInfo *dll)
{
void R_initCVE(DllInfo *dll) {
R_registerRoutines(dll, NULL, CallEntries, NULL, NULL);
R_useDynamicSymbols(dll, FALSE);
}

View File

@ -1,5 +1,15 @@
#include "cve.h"
// mat* Matrix(const unsigned int nrow, const unsigned int ncol) {
// mat* newMat = (mat*)R_alloc(1, sizeof(mat));
// newMat->nrow = nrow;
// newMat->ncol = ncol;
// newMat->memsize = nrow * ncol;
// newMat->data = (double*)R_alloc(nrow * ncol, sizeof(double));
// return newMat;
// }
double norm(const double *A, const int nrow, const int ncol,
const char *type) {
int i, nelem = nrow * ncol;
@ -86,7 +96,7 @@ void scale(const double s, double *A, const int nelem) {
}
}
// A dence skwe-symmetric rank 2 update.
// A dence skew-symmetric rank 2 update.
// Perform the update
// C := alpha (A * B^T - B * A^T) + beta C
void skew(const int nrow, const int ncol,

View File

@ -49,7 +49,15 @@
// return Qout;
// }
void rStiefl(const int p, const int q, double *V,
/**
* Draws a sample from invariant measure on the Stiefel manifold \eqn{S(p, q)}.
*
* @param p row dimension
* @param q col dimension
* @return \code{p} times \code{q} semi-orthogonal matrix.
* `V <- qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q)))`
*/
void rStiefel(const int p, const int q, double *V,
double *workMem, int workLen) {
int i, j, info;
int pq = p * q;

View File

@ -1,6 +1,29 @@
#include "cve.h"
/* C[, j] = A[, j] * v for each j = 1 to ncol */
#define ROW_SWEEP_ALG(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]) op (v[j]); \
} \
} \
/* Step one block forth. */ \
A_block += block_size_i; \
C_block += block_size_i; \
v += block_size_i; \
}
/* C[, j] = A[, j] op v for each j = 1 to ncol with op as one of +, -, *, / */
void rowSweep(const double *A, const int nrow, const int ncol,
const char* op,
const double *v, // vector of length nrow
@ -17,92 +40,12 @@ void rowSweep(const double *A, const int nrow, const int ncol,
}
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;
}
ROW_SWEEP_ALG(+)
} 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;
}
ROW_SWEEP_ALG(-)
} 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;
}
ROW_SWEEP_ALG(*)
} 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;
}
ROW_SWEEP_ALG(/)
}
}

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library("mda") #library for mars
local_linear<-function(x,h,dat,beta){
Y<-dat[,1]
X<-dat[,-1]
N<-length(Y)
X<-X%*%beta
x<-x%*%beta#beta%*%x
D_mat<-cbind(rep(1,N),X)
if (is.vector(X)){
dim<-1
d<-abs(X-rep(x,N))
}
else{
dim<-length(X[1,])
d<-sqrt(apply(X-t(matrix(rep(x,N),dim,N)),1,norm2))
}
K<-diag(dnorm(d/h)/dnorm(0))
pred<-c(1,x)%*%solve(t(D_mat)%*%K%*%D_mat)%*%t(D_mat)%*%K%*%Y
return(pred)
}
##### performs estimation of small dimesnion by CV with local linear forward regression
est_dim_CV<-function(Blist,dat,h_loclin=NULL,dim.max,median_use=F,method_mars=F){
#standardize regressors by symmetric root of inverse covariance mat
Sig<-est_varmat(dat[,-1])
eig_dec<-eigen(Sig)
Sroot_inv<-eig_dec$vectors%*%((diag(eig_dec$values^(-1/2))))%*%t(eig_dec$vectors)
dat[,-1]<-as.matrix(dat[,-1])%*%Sroot_inv
N<-length(dat[,1])
dim<-length(dat[1,-1])
MSE<-mat.or.vec(N,dim.max)
for(u in 1:dim.max){
beta<-Blist[[u]]
if(is.null(h_loclin)){
#h_loclin<-(1/N)^(1/(3+2*u))
h_loclin<-1.2*N^(-1/(4+u))#(1/N)^(1/(3+2*j))
}
for(i in 1:N){
x<-dat[i,-1]
if(method_mars==F){MSE[i,u]<-(dat[i,1]-local_linear(x,h_loclin,as.matrix(dat[-i,]),beta))^2} #predict with local linear
if(method_mars==T){
dat_fit<-dat[-i,-1]%*%beta
X_new<-dat[i,-1]%*%beta
mars_mod<-mars(dat_fit,dat[-i,1]) #fit mars model
MSE[i,u]<-(dat[i,1]-predict(mars_mod,X_new))^2 #predict with mars model
}#predict with mars
}
}
if(median_use){MSE_ave<-apply(MSE,2,median)}
else{MSE_ave<-colMeans(MSE)}
#apply(MSE,2,median)
est_dim<-which.min(MSE_ave)
ret<-list(est_dim = est_dim, MSE_ave = MSE_ave, MSE = MSE)
return(ret)
}
###########
test_for_dim<-function(Lmat,dim.max=NULL,alpha=0.1,method='greater'){
#Lmat... matrix with dimension N times dim.max with columns corresponding to aov_dat for dim 1,2,3,....,max.dim
if(is.null(dim.max)){dim.max<-length(Lmat[1,])}
pval<-mat.or.vec(dim.max-1,1)
est_dim<-dim.max
# for (j in 1:(dim.max-1)){
j<-1
while(est_dim==dim.max&j<dim.max){
if (method=='greater'){
pval[(j)]<-t.test(Lmat[,(j)],Lmat[,(j+1)],alternative = 'greater',paired=T)$p.value#mod[[1]][,5][1]
if(pval[j]<alpha){est_dim<-j}
}
if (method=='lower'){
pval[(j)]<-t.test(Lmat[,(j)],Lmat[,(j+1)],alternative = 'less',paired=F)$p.value#mod[[1]][,5][1]
if(pval[j]>alpha){est_dim<-j}
}
j<-j+1
}
ret<-list(est_dim,pval)
names(ret)<-c('estdim','pval')
return(ret)
}
####
##
test_for_dim_elbow<-function(Lmat){
dim.max<-length(Lmat[1,])
ave<-colMeans(Lmat)
boxplot(Lmat,xlab='k')
lines(seq(1,dim.max),ave,col='red')
# tmp<-cbind(ave,seq(1,dim.max))
# colnames(tmp)<-c('response','k')
# diff<-lm(response~k,data=as.data.frame(tmp))$coefficients[2]
#
# est_dim<-dim.max
# i<-1
# while(i<dim.max&est_dim==dim.max){
# if(ave[i+1]-ave[i]>diff){est_dim<-i}
# i<-i+1
# }
return(which.min(ave))
}
######
#Small simulation example for truedim =1
set.seed(21)
dim<-6
truedim<-1
N<-50
b<-c(1,0,0,0,0,0)
m<-20
est_dim<-mat.or.vec(m,7)
dim.max<-4
for(i in 1:m){
dat<-creat_sample(b,N,fsquare,0.5)
Blist<-list()
Lmat<-mat.or.vec(N,dim.max)
for(u in 1:dim.max){ #calculate B for different possible truedim's
m1<-stiefl_opt(dat,k=(dim-u)) #original bandwidth selection rule used that controlls number of points in a slice!!!!!!, also choose_h_2
Blist[[u]]<-fill_base(m1$est_base)[,1:u]
Lmat[,u]<-m1$aov_dat
}
#estimate truedim with different methods
est_dim[i,1]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = T)$est_dim
est_dim[i,2]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = F)$est_dim
est_dim[i,3]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = F,method_mars = T)$est_dim
est_dim[i,4]<-test_for_dim(Lmat)$estdim
est_dim[i,5]<-test_for_dim(Lmat,method = 'lower')$estdim
est_dim[i,6]<-test_for_dim_elbow(cbind((dat[,1]-mean(dat[,1]))^2,Lmat))-1
mod_t<-mave(Y~.,data=as.data.frame(dat),method = 'meanMAVE')
est_dim[i,7]<-which.min(mave.dim(mod_t)$cv)
print(i)
}
length(which(est_dim[,1]==truedim))/m #fraction of where dimension is estimated correctly with mwthod 1 (CV with median)
#0.5
length(which(est_dim[,2]==truedim))/m #fraction of where dimension is estimated correctly with mwthod 1 (CV with mean)
#0.9
length(which(est_dim[,3]==truedim))/m #fraction of where dimension is estimated correctly with mwthod 1 (CV with mars and mean)
#0.8
length(which(est_dim[,4]==truedim))/m #fraction of where dimension is estimated correctly with mwthod 1 (t.test method='greater')
#0.0
length(which(est_dim[,5]==truedim))/m #fraction of where dimension is estimated correctly with mwthod 1 (t.test method='lower')
#0.05
length(which(est_dim[,6]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (elbow)
#1
length(which(est_dim[,7]==truedim))/m #fraction of where dimension is estimated correctly with mave
#0.95
##########
#Small simulation example for truedim =2
set.seed(21)
dim<-6
truedim<-2
N<-100
b<-cbind(c(1,rep(0,dim-1)),c(0,1,rep(0,dim-2)))
m<-20
est_dim<-mat.or.vec(m,7)
dim.max<-4
for(i in 1:m){
dat<-creat_sample(b,N,function(x){return(x[1]*x[2])},0.5)
Blist<-list()
Lmat<-mat.or.vec(N,dim.max)
for(u in 1:dim.max){
m1<-stiefl_opt(dat,k=(dim-u)) #original bandwidth selection used !!!!!!!!!!!!!!!!!!!!!, also choose_h_2
Blist[[u]]<-fill_base(m1$est_base)[,1:u]
Lmat[,u]<-m1$aov_dat
}
est_dim[i,1]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = T)$est_dim
est_dim[i,2]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = F)$est_dim
est_dim[i,3]<-est_dim_CV(Blist,dat,dim.max = dim.max,median_use = F,method_mars = T)$est_dim
est_dim[i,4]<-test_for_dim(Lmat)$estdim
est_dim[i,5]<-test_for_dim(Lmat,method = 'lower')$estdim
est_dim[i,6]<-test_for_dim_elbow(cbind((dat[,1]-mean(dat[,1]))^2,Lmat))-1
mod_t<-mave(Y~.,data=as.data.frame(dat),method = 'meanMAVE')
est_dim[i,7]<-which.min(mave.dim(mod_t)$cv)
print(i)
}
length(which(est_dim[,1]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (CV with median)
length(which(est_dim[,2]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (CV with mean)
length(which(est_dim[,3]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (CV with mars and mean)
length(which(est_dim[,4]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (t.test method='greater')
length(which(est_dim[,5]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (t.test method='lower')
length(which(est_dim[,6]==truedim))/m #fraction of where dimension is estimated correctly with mwthod (elbow)

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LV_weight_partial<-function(V,Xl,dtemp,h,q,Y,grad=T){
N<-length(Y)
if(is.vector(V)){k<-1}
else{k<-length(V[1,])}
Xlv<-Xl%*%V
d<-dtemp-((Xlv^2)%*%rep(1,k))
w<-exp(-0.5*(d/h)^2)
w<-matrix(w,N,q)
wn<-apply(w,2,sum)-rep(1,q)#new
w<-apply(w,2,column_normalize)
mY<-t(w)%*%Y
sig<-t(w)%*%(Y^2)-(mY)^2
W<-(kronecker(t(wn),rep(1,N)))##new
if(grad==T){
grad<-mat.or.vec(dim,k)
tmp1<-(kronecker(sig,rep(1,N))-(as.vector(kronecker(rep(1,q),Y))-kronecker(mY,rep(1,N)))^2)
if(k==1){
grad_d<- -2*Xl*as.vector(Xlv)
grad<-(1/h^2)*(1/sum(wn))*t(grad_d*as.vector(d)*as.vector(w)*as.vector(W))%*%tmp1 #new
# wn_grad<-(-1/h^2)*t(grad_d*as.vector(d)*as.vector(w))%*%kronecker(diag(rep(1,q)),rep(1,N))
# grad<- wn_grad%*%(sig-rep(var1[2],q))/(sum(wn))+grad
}
else{
for (j in 1:(k)){
grad_d<- -2*Xl*as.vector(Xlv[,j])
grad[,j]<- (1/h^2)*(1/sum(wn))*t(grad_d*as.vector(d)*as.vector(w)*as.vector(W))%*%tmp1#new
# wn_grad<-(-1/h^2)*t(grad_d*as.vector(d)*as.vector(w))%*%kronecker(diag(rep(1,q)),rep(1,N))
# grad[,j]<- wn_grad%*%(sig-rep(var1[2],q))/(sum(wn))+grad
}
}
ret<-list(t(wn)%*%sig/sum(wn),sig,grad)#new
names(ret)<-c('var','sig','grad')
}
else{
ret<-list(t(wn)%*%sig/sum(wn),sig)#new
names(ret)<-c('var','sig')
}
return(ret)
}
################
stiefl_weight_partial_opt<-function(dat,h=NULL,k,k0=30,p=1,maxit=50,nObs=sqrt(length(dat[,1])),lambda_0=1,tol=10^(-3),sclack_para=0){
Y<-dat[,1]
X<-dat[,-1]
N<-length(Y)
dim<-length(X[1,])
if(p<1){
S<-est_varmat(X)
tmp1<-q_ind(X,S,p)
q<-tmp1$q
ind<-tmp1$ind
}
else{
q<-N
ind<-1:N
}
Xl<-(kronecker(rep(1,q),X)-kronecker(X[ind,],rep(1,N)))
dtemp<-apply(Xl,1,norm2)
if(is.null(h)){
S<-est_varmat(X)
tr<-var_tr(S)
h<-choose_h_2(dim,k,N,nObs,tr)
}
best<-exp(10000)
Vend<-mat.or.vec(dim,k)
sig<-mat.or.vec(q,1)
for(u in 1:k0){
Vnew<-Vold<-stiefl_startval(dim,k)
#print(Vold)
#print(LV(Vold,Xl,dtemp,h,q,Y)$var)
Lnew<-Lold<-exp(10000)
lambda<-lambda_0
err<-10
count<-0
count2<-0
while(err>tol&count<maxit){
#print(Vold)
tmp2<-LV_weight_partial(Vold,Xl,dtemp,h,q,Y)
G<-tmp2$grad
Lold<-tmp2$var
W<-G%*%t(Vold)-Vold%*%t(G)
stepsize<-lambda#/(2*sqrt(count+1))
Vnew<-solve(diag(1,dim)+stepsize*W)%*%(diag(1,dim)-stepsize*W)%*%Vold
# print(Vnew)
tmp3<-LV_weight_partial(Vnew,Xl,dtemp,h,q,Y,grad=F)
Lnew<-tmp3$var
err<-sqrt(sum((Vold%*%t(Vold)-Vnew%*%t(Vnew))^2))/sqrt(2*k)#sqrt(sum(tmp3$grad^2))/(dim*k)#
#print(err)
if(((Lnew-Lold)/Lold) > sclack_para){#/(count+1)^(0.5)
lambda=lambda/2
err<-10
count2<-count2+1
count<-count-1
Vnew<-Vold #!!!!!
}
Vold<-Vnew
count<-count+1
#print(count)
}
if(best>Lnew){
best<-Lnew
Vend<-Vnew
sig<-tmp3$sig
}
}
ret<-list(Vend,best,sig,count,h,count2)
names(ret)<-c('est_base','var','aov_dat','count','h','count2')
return(ret)
}
#################MAVE, OPG, rMAVE, rOPG from Bing Li book
opg=function(x,y,d){
p=dim(x)[2];
n=dim(x)[1]
c0=2.34;
p0=max(p,3);
rn=n^(-1/(2*(p0+6)));
h=c0*n^(-(1/(p0+6)))
sig=diag(var(x));
x=apply(x,2,standvec)
kmat=kern(x,h);
bmat=numeric()
for(i in 1:dim(x)[1]){
wi=kmat[,i];
xi=cbind(1,t(t(x)-x[i,]))
bmat=cbind(bmat,wls(xi,y,wi)$b)}
beta=eigen(bmat%*%t(bmat))$vectors[,1:d]
return(diag(sig^(-1/2))%*%beta)
}
######################
wls=function(x,y,w){
n=dim(x)[1];
p=dim(x)[2]-1
out=c(solve(t(x*w)%*%x/n)%*%apply(x*y*w,2,mean))
return(list(a=out[1],b=out[2:(p+1)]))
}
#################
kern=function(x,h){
x=as.matrix(x);
n=dim(x)[1]
k2=x%*%t(x);
k1=t(matrix(diag(k2),n,n));
k3=t(k1);
k=k1-2*k2+k3
return(exp(-(1/(2*h^2))*(k1-2*k2+k3)))
}
###############
standvec=function(x) return((x-mean(x))/sd(x))
##############
mave2=function(x,y,h,d,nit){
sig=diag(var(x));
n=dim(x)[1];
p=dim(x)[2]
x=apply(x,2,standvec);
beta=opg(x,y,d);#beta=opg(x,y,h,d);
kermat=kern(x,h)
for(iit in 1:nit){
b=numeric();
a=numeric();
for(i in 1:n){
wi=kermat[,i]/(apply(kermat,2,mean)[i])
ui=cbind(1,t(t(x)-x[i,])%*%beta)
out=wls(ui,y,wi);
a=c(a,out$a);b=cbind(b,out$b)}
out=0;out1=0;
for(i in 1:n){
xi=kronecker(t(t(x)-x[i,]),t(b[,i]))
yi=y-a[i];
wi=kermat[,i]/apply(kermat,2,mean)[i]
out=out+apply(xi*yi*wi,2,mean)
out1=out1+t(xi*wi)%*%xi/n}
beta=t(matrix(solve(out1)%*%out,d,p))
}
return(diag(sig^(-1/2))%*%beta)
}
######################
rmave=function(x,y,d,nit){
sig=diag(var(x));
n=dim(x)[1];
p=dim(x)[2]
x=apply(x,2,standvec)
c0=2.34;
p0=max(p,3);
h=c0*n^(-(1/(p0+6)));
rn=n^(-1/(2*(p0+6)))
beta=opg(x,y,d)
for(iit in 1:nit){
kermat=kern(x%*%beta,h);
mkermat=apply(kermat,2,mean)
b=numeric();a=numeric()
for(i in 1:n){
wi=kermat[,i]/mkermat[i];
ui=cbind(1,t(t(x)-x[i,])%*%beta)
out=wls(ui,y,wi);
a=c(a,out$a);b=cbind(b,out$b)
}
out=0;
out1=0
for(i in 1:n) {
xi=kronecker(t(t(x)-x[i,]),t(b[,i]));
yi=y-a[i]
wi=kermat[,i]/mkermat[i]
out=out+apply(xi*yi*wi,2,mean)
out1=out1+t(xi*wi)%*%xi/n}
beta=t(matrix(solve(out1)%*%out,d,p))
h=max(rn*h,c0*n^((-1/(d+4))))
}
return(diag(sig^(-1/2))%*%beta)
}
#########################
ropg=function(x,y,d,nit){
sig=diag(var(x));
x=apply(x,2,standvec);
p=dim(x)[2];
n=dim(x)[1]
c0=2.34;
p0=max(p,3);
rn=n^(-1/(2*(p0+6)));
h=c0*n^(-(1/(p0+6)))
beta=diag(p)
for(iit in 1:nit){
kmat=kern(x%*%beta,h);
bmat=numeric()
for(i in 1:dim(x)[1]){
wi=kmat[,i];
xi=cbind(1,t(t(x)-x[i,]))
bmat=cbind(bmat,wls(xi,y,wi)$b)
}
beta=eigen(bmat%*%t(bmat))$vectors[,1:d]
h=max(rn*h,c0*n^((-1/(d+4))))
}
beta.final=diag(sig^(-1/2))%*%beta
return(beta.final)
}

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LV_weight_partial<-function(V,Xl,dtemp,h,q,Y,grad=T){
N<-length(Y)
if(is.vector(V)){k<-1}
else{k<-length(V[1,])}
Xlv<-Xl%*%V
d<-dtemp-((Xlv^2)%*%rep(1,k))
w<-exp(-0.5*(d/h)^2)
w<-matrix(w,N,q)
wn<-apply(w,2,sum)-rep(1,q)#new
w<-apply(w,2,column_normalize)
mY<-t(w)%*%Y
sig<-t(w)%*%(Y^2)-(mY)^2
W<-(kronecker(t(wn),rep(1,N)))##new
if(grad==T){
grad<-mat.or.vec(dim,k)
tmp1<-(kronecker(sig,rep(1,N))-(as.vector(kronecker(rep(1,q),Y))-kronecker(mY,rep(1,N)))^2)
if(k==1){
grad_d<- -2*Xl*as.vector(Xlv)
grad<-(1/h^2)*(1/sum(wn))*t(grad_d*as.vector(d)*as.vector(w)*as.vector(W))%*%tmp1 #new
# wn_grad<-(-1/h^2)*t(grad_d*as.vector(d)*as.vector(w))%*%kronecker(diag(rep(1,q)),rep(1,N))
# grad<- wn_grad%*%(sig-rep(var1[2],q))/(sum(wn))+grad
}
else{
for (j in 1:(k)){
grad_d<- -2*Xl*as.vector(Xlv[,j])
grad[,j]<- (1/h^2)*(1/sum(wn))*t(grad_d*as.vector(d)*as.vector(w)*as.vector(W))%*%tmp1#new
# wn_grad<-(-1/h^2)*t(grad_d*as.vector(d)*as.vector(w))%*%kronecker(diag(rep(1,q)),rep(1,N))
# grad[,j]<- wn_grad%*%(sig-rep(var1[2],q))/(sum(wn))+grad
}
}
ret<-list(t(wn)%*%sig/sum(wn),sig,grad)#new
names(ret)<-c('var','sig','grad')
}
else{
ret<-list(t(wn)%*%sig/sum(wn),sig)#new
names(ret)<-c('var','sig')
}
return(ret)
}
################
stiefl_weight_partial_opt<-function(dat,h=NULL,k,k0=30,p=1,maxit=50,nObs=sqrt(length(dat[,1])),lambda_0=1,tol=10^(-3),sclack_para=0){
Y<-dat[,1]
X<-dat[,-1]
N<-length(Y)
dim<-length(X[1,])
if(p<1){
S<-est_varmat(X)
tmp1<-q_ind(X,S,p)
q<-tmp1$q
ind<-tmp1$ind
}
else{
q<-N
ind<-1:N
}
Xl<-(kronecker(rep(1,q),X)-kronecker(X[ind,],rep(1,N)))
dtemp<-apply(Xl,1,norm2)
if(is.null(h)){
S<-est_varmat(X)
tr<-var_tr(S)
h<-choose_h_2(dim,k,N,nObs,tr)
}
best<-exp(10000)
Vend<-mat.or.vec(dim,k)
sig<-mat.or.vec(q,1)
for(u in 1:k0){
Vnew<-Vold<-stiefl_startval(dim,k)
#print(Vold)
#print(LV(Vold,Xl,dtemp,h,q,Y)$var)
Lnew<-Lold<-exp(10000)
lambda<-lambda_0
err<-10
count<-0
count2<-0
while(err>tol&count<maxit){
#print(Vold)
tmp2<-LV_weight_partial(Vold,Xl,dtemp,h,q,Y)
G<-tmp2$grad
Lold<-tmp2$var
W<-G%*%t(Vold)-Vold%*%t(G)
stepsize<-lambda#/(2*sqrt(count+1))
Vnew<-solve(diag(1,dim)+stepsize*W)%*%(diag(1,dim)-stepsize*W)%*%Vold
# print(Vnew)
tmp3<-LV_weight_partial(Vnew,Xl,dtemp,h,q,Y,grad=F)
Lnew<-tmp3$var
err<-sqrt(sum((Vold%*%t(Vold)-Vnew%*%t(Vnew))^2))/sqrt(2*k)#sqrt(sum(tmp3$grad^2))/(dim*k)#
#print(err)
if(((Lnew-Lold)/Lold) > sclack_para){#/(count+1)^(0.5)
lambda=lambda/2
err<-10
count2<-count2+1
count<-count-1
Vnew<-Vold #!!!!!
}
Vold<-Vnew
count<-count+1
#print(count)
}
if(best>Lnew){
best<-Lnew
Vend<-Vnew
sig<-tmp3$sig
}
}
ret<-list(Vend,best,sig,count,h,count2)
names(ret)<-c('est_base','var','aov_dat','count','h','count2')
return(ret)
}
#################MAVE, OPG, rMAVE, rOPG from Bing Li book
opg=function(x,y,d){
p=dim(x)[2];
n=dim(x)[1]
c0=2.34;
p0=max(p,3);
rn=n^(-1/(2*(p0+6)));
h=c0*n^(-(1/(p0+6)))
sig=diag(var(x));
x=apply(x,2,standvec)
kmat=kern(x,h);
bmat=numeric()
for(i in 1:dim(x)[1]){
wi=kmat[,i];
xi=cbind(1,t(t(x)-x[i,]))
bmat=cbind(bmat,wls(xi,y,wi)$b)}
beta=eigen(bmat%*%t(bmat))$vectors[,1:d]
return(diag(sig^(-1/2))%*%beta)
}
#######################
stiefl_opt_momentum<-function(dat,h=NULL,k,k0=30,p=1,maxit=50,nObs=sqrt(length(dat[,1])),lambda_0=1,tol=10^(-3),sclack_para=0,momentum_para=0.8){
Y<-dat[,1]
X<-dat[,-1]
N<-length(Y)
dim<-length(X[1,])
if(p<1){
S<-est_varmat(X)
tmp1<-q_ind(X,S,p)
q<-tmp1$q
ind<-tmp1$ind
}
else{
q<-N
ind<-1:N
}
Xl<-(kronecker(rep(1,q),X)-kronecker(X[ind,],rep(1,N)))
dtemp<-apply(Xl,1,norm2)
if(is.null(h)){
S<-est_varmat(X)
tr<-var_tr(S)
h<-choose_h_2(dim,k,N,nObs,tr)
}
best<-exp(10000)
Vend<-mat.or.vec(dim,k)
sig<-mat.or.vec(q,1)
for(u in 1:k0){
Vold<-stiefl_startval(dim,k)
#print(Vold)
#print(LV(Vold,Xl,dtemp,h,q,Y)$var)
Lnew<-Lold<-exp(10000)
lambda<-lambda_0
err<-10
count<-0
count2<-0
Lnew<-LV(Vold,Xl,dtemp,h,q,Y)$var
#print(Lnew)
if(best>Lnew){
best<-Lnew
Vend<-Vold
#sig<-tmp3$sig
}
}
Vnew<-Vold<-Vend
G<-matrix(rep(0,dim*k),dim,k)
while(err>tol&count<maxit){
#print(Vold)
tmp2<-LV(Vold,Xl,dtemp,h,q,Y)
#G<-tmp2$grad
G<-(1-momentum_para)*G + momentum_para*tmp2$grad
Lold<-tmp2$var
W<-G%*%t(Vold)-Vold%*%t(G)
stepsize<-lambda#/(2*sqrt(count+1))
Vnew<-solve(diag(1,dim)+stepsize*W)%*%(diag(1,dim)-stepsize*W)%*%Vold
# print(Vnew)
tmp3<-LV(Vnew,Xl,dtemp,h,q,Y,grad=F)
Lnew<-tmp3$var
err<-sqrt(sum((Vold%*%t(Vold)-Vnew%*%t(Vnew))^2))/sqrt(2*k)#sqrt(sum(tmp3$grad^2))/(dim*k)#
#print(err)
if(((Lnew-Lold)/Lold) > sclack_para){#/(count+1)^(0.5)
lambda=lambda/2
err<-10
count2<-count2+1
count<-count-1
Vnew<-Vold #!!!!!
Lnew<-Lold
}
Vold<-Vnew
count<-count+1
#print(count)
}
ret<-list(Vnew,Lnew,count,h,count2)
names(ret)<-c('est_base','var','count','h','count2')
return(ret)
}
######################
wls=function(x,y,w){
n=dim(x)[1];
p=dim(x)[2]-1
out=c(solve(t(x*w)%*%x/n)%*%apply(x*y*w,2,mean))
return(list(a=out[1],b=out[2:(p+1)]))
}
#################
kern=function(x,h){
x=as.matrix(x);
n=dim(x)[1]
k2=x%*%t(x);
k1=t(matrix(diag(k2),n,n));
k3=t(k1);
k=k1-2*k2+k3
return(exp(-(1/(2*h^2))*(k1-2*k2+k3)))
}
###############
standvec=function(x) return((x-mean(x))/sd(x))
##############
mave2=function(x,y,h,d,nit){
sig=diag(var(x));
n=dim(x)[1];
p=dim(x)[2]
x=apply(x,2,standvec);
beta=opg(x,y,d);#beta=opg(x,y,h,d);
kermat=kern(x,h)
for(iit in 1:nit){
b=numeric();
a=numeric();
for(i in 1:n){
wi=kermat[,i]/(apply(kermat,2,mean)[i])
ui=cbind(1,t(t(x)-x[i,])%*%beta)
out=wls(ui,y,wi);
a=c(a,out$a);b=cbind(b,out$b)}
out=0;out1=0;
for(i in 1:n){
xi=kronecker(t(t(x)-x[i,]),t(b[,i]))
yi=y-a[i];
wi=kermat[,i]/apply(kermat,2,mean)[i]
out=out+apply(xi*yi*wi,2,mean)
out1=out1+t(xi*wi)%*%xi/n}
beta=t(matrix(solve(out1)%*%out,d,p))
}
return(diag(sig^(-1/2))%*%beta)
}
######################
rmave=function(x,y,d,nit){
sig=diag(var(x));
n=dim(x)[1];
p=dim(x)[2]
x=apply(x,2,standvec)
c0=2.34;
p0=max(p,3);
h=c0*n^(-(1/(p0+6)));
rn=n^(-1/(2*(p0+6)))
beta=opg(x,y,d)
for(iit in 1:nit){
kermat=kern(x%*%beta,h);
mkermat=apply(kermat,2,mean)
b=numeric();a=numeric()
for(i in 1:n){
wi=kermat[,i]/mkermat[i];
ui=cbind(1,t(t(x)-x[i,])%*%beta)
out=wls(ui,y,wi);
a=c(a,out$a);b=cbind(b,out$b)
}
out=0;
out1=0
for(i in 1:n) {
xi=kronecker(t(t(x)-x[i,]),t(b[,i]));
yi=y-a[i]
wi=kermat[,i]/mkermat[i]
out=out+apply(xi*yi*wi,2,mean)
out1=out1+t(xi*wi)%*%xi/n}
beta=t(matrix(solve(out1)%*%out,d,p))
h=max(rn*h,c0*n^((-1/(d+4))))
}
return(diag(sig^(-1/2))%*%beta)
}
#########################
ropg=function(x,y,d,nit){
sig=diag(var(x));
x=apply(x,2,standvec);
p=dim(x)[2];
n=dim(x)[1]
c0=2.34;
p0=max(p,3);
rn=n^(-1/(2*(p0+6)));
h=c0*n^(-(1/(p0+6)))
beta=diag(p)
for(iit in 1:nit){
kmat=kern(x%*%beta,h);
bmat=numeric()
for(i in 1:dim(x)[1]){
wi=kmat[,i];
xi=cbind(1,t(t(x)-x[i,]))
bmat=cbind(bmat,wls(xi,y,wi)$b)
}
beta=eigen(bmat%*%t(bmat))$vectors[,1:d]
h=max(rn*h,c0*n^((-1/(d+4))))
}
beta.final=diag(sig^(-1/2))%*%beta
return(beta.final)
}

412
README.md
View File

@ -1,10 +1,42 @@
# TODOs
Doc:
- [x] Stiefel (instead of Stiefl)
- [x] Return value description (`@returs`)
- [x] DESCRIPTION
- [x] Maintainer
- [x] Author
- [x] Volume
- [x] Description (from Paper) and Ref.
- [x] Ref paper in doc
- [ ] Data set descriptions and augmentations.
- [x] Demonstration of the `Logger` function usage (Demo file or so, ...)
# Overview
- **CVE/**: Contains actual `R` package.
- **CVE_legacy/**: Contains original (first) `R` implementatin of the CVE method.
The `*.R` and `*.cpp` files in the root directory are _development_ and _test_ files.
Methods to be implemented:
- [x] simple
- [x] weighted
- [x] momentum
- [x] weighted with momentum
## TODO: README.md
Performance:
- [x] Pure C implementation.
- [NOT Feasible] Stochastic Version
- [NOT Feasible] Gradient Approximations (using Algebraic Software for alternative Loss function formulations and gradient optimizations)
- [NOT Sufficient] Alternative Kernels for reducing samples
- [ ] (To Be further investigated) "Kronecker" optimization
Features (functions):
- [x] Initial `V.init` parameter (only ONE try, ignore number of `attempts` parameter)
- [x] `basis.cve` list of estimated `B`s (with `k` supplied, only `B`)
- [x] `directions.cve` Projected `X` given `k`
- [ ] `predict.cve` using `mars` for predicting responses given new data.
- [ ] `predict.dim.cve` Cross-validation or `aov` (in stats package) or "elbow" estimation
- [x] `plot.elbow`
- [x] `summary`
Changes:
- [-] New `estimate.bandwidth` implementation.
(h = 2 * (tr(\Sigma) / p) * (6/5 * n^(-1 / (4 + k)))^2,
\Sigma = 1/n * (X-mean)'(X-mean))
# Package Structure
@ -31,3 +63,373 @@ the demo file. You can add pauses by adding:
**Note**: Demos are not automatically tested by `R CMD check`. This means that they
can easily break without your knowledge.
# General Notes for Source Code analysis
## Search in multiple files.
Using the Linux `grep` program with the parameters `-rnw` and specifying a include files filter like the following example.
```bash
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_.
## 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
## 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.
```R
setwd("./CVE_R") # Set path to the package root.
library(devtools) # Load required `devtools` package.
document() # Create `.Rd` files and write `NAMESPACE`.
```
Next the package needs to be build, therefore (if pure `R` package, aka. `C/C++`, `Fortran`, ... code) just do the following.
```bash
R CMD build CVE_R
R CMD INSTALL CVE_0.1.tar.gz
```
Then we are ready for using the package.
```R
library(CVE)
help(package = "CVE")
```
## Build and install from within `R`.
An alternative approach is the following.
```R
setwd('./CVE_R')
getwd()
library(devtools)
document()
# No vignettes to build but "inst/doc/" is required!
(path <- build(vignettes = FALSE))
install.packages(path, repos = NULL, type = "source")
```
**Note: I only recommend this approach during development.**
# Analysing
## Logging (a `cve` run).
To log `loss`, `error` (estimated) the true error (error of current estimated `B` against the true `B`) or even the stepsize one can use the `logger` parameter. A `logger` is a function that gets the current `environment` of the CVE optimization methods (__do not alter this environment, only read from it__). This can be used to create logs like in the following example.
```R
library(CVE)
# Setup histories.
(epochs <- 50)
(attempts <- 10)
loss.history <- matrix(NA, epochs + 1, attempts)
error.history <- matrix(NA, epochs + 1, attempts)
tau.history <- matrix(NA, epochs + 1, attempts)
true.error.history <- matrix(NA, epochs + 1, attempts)
# Create a dataset
ds <- dataset("M1")
X <- ds$X
Y <- ds$Y
B <- ds$B # the true `B`
(k <- ncol(ds$B))
# True projection matrix.
P <- B %*% solve(t(B) %*% B) %*% t(B)
# Define the logger for the `cve()` method.
logger <- function(env) {
# Note the `<<-` assignement!
loss.history[env$epoch + 1, env$attempt] <<- env$loss
error.history[env$epoch + 1, env$attempt] <<- env$error
tau.history[env$epoch + 1, env$attempt] <<- env$tau
# Compute true error by comparing to the true `B`
B.est <- null(env$V) # Function provided by CVE
P.est <- B.est %*% solve(t(B.est) %*% B.est) %*% t(B.est)
true.error <- norm(P - P.est, 'F') / sqrt(2 * k)
true.error.history[env$epoch + 1, env$attempt] <<- true.error
}
# Performa SDR
dr <- cve(Y ~ X, k = k, logger = logger, epochs = epochs, attempts = attempts)
# Plot history's
par(mfrow = c(2, 2))
matplot(loss.history, type = 'l', log = 'y', xlab = 'iter',
main = 'loss', ylab = expression(L(V[iter])))
matplot(error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'error', ylab = 'error')
matplot(tau.history, type = 'l', log = 'y', xlab = 'iter',
main = 'tau', ylab = 'tau')
matplot(true.error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'true error', ylab = 'true error')
```
## Reading log files.
The runtime tests (upcomming further tests) are creating log files saved in `tmp/`. These log files are `CSV` files (actualy `TSV`) with a header storing the test results. Depending on the test the files may contain differnt data. As an example we use the runtime test logs which store in each line the `dataset`, the used `method` as well as the `error` (actual error of estimated `B` against real `B`) and the `time`. For reading and analysing the data see the following example.
```R
# Load log as `data.frame`
log <- read.csv('tmp/test0.log', sep = '\t')
# Create a error boxplot grouped by dataset.
boxplot(error ~ dataset, log)
# Overview
for (ds.name in paste0('M', seq(5))) {
ds <- subset(log, dataset == ds.name, select = c('method', 'dataset', 'time', 'error'))
print(summary(ds))
}
```
## Environments and variable lookup.
In the following a view simple examples of how `R` searches for variables.
In addition we manipulate funciton closures to alter the search path in variable lookup and outer scope variable manipulation.
```R
droids <- "These aren't the droids you're looking for."
search <- function() {
print(droids)
}
trooper.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
search()
}
jedi.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
environment(search) <- environment()
search()
}
trooper.seeks()
# [1] "These aren't the droids you're looking for."
jedi.seeks()
# [1] "R2-D2", "C-3PO"
```
The next example ilustrates how to write (without local copies) to variables outside the functions local environment.
```R
counting <- function() {
count <<- count + 1 # Note the `<<-` assignment.
}
(function() {
environment(counting) <- environment()
count <- 0
for (i in 1:10) {
counting()
}
return(count)
})()
(function () {
closure <- new.env()
environment(counting) <- closure
assign("count", 0, envir = closure)
for (i in 1:10) {
counting()
}
return(closure$count)
})()
```
Another example for the usage of `do.call` where the evaluation of parameters is illustated (example taken (and altered) from `?do.call`).
```R
## examples of where objects will be found.
A <- "A.Global"
f <- function(x) print(paste("f.new", x))
env <- new.env()
assign("A", "A.new", envir = env)
assign("f", f, envir = env)
f <- function(x) print(paste("f.Global", x))
f(A) # f.Global A.Global
do.call("f", list(A)) # f.Global A.Global
do.call("f", list(A), envir = env) # f.new A.Global
do.call(f, list(A), envir = env) # f.Global A.Global
do.call("f", list(quote(A)), envir = env) # f.new A.new
do.call(f, list(quote(A)), envir = env) # f.Global A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
```
# Performance benchmarks
In this section alternative implementations of simple algorithms are compared for there performance.
### Computing the trace of a matrix multiplication.
```R
library(microbenchmark)
A <- matrix(runif(120), 12, 10)
# Check correctnes and benckmark performance.
stopifnot(
all.equal(
sum(diag(t(A) %*% A)), sum(diag(crossprod(A, A)))
),
all.equal(
sum(diag(t(A) %*% A)), sum(A * A)
)
)
microbenchmark(
MM = sum(diag(t(A) %*% A)),
cross = sum(diag(crossprod(A, A))),
elem = sum(A * A)
)
# Unit: nanoseconds
# expr min lq mean median uq max neval
# MM 4232 4570.0 5138.81 4737 4956.0 40308 100
# cross 2523 2774.5 2974.93 2946 3114.5 5078 100
# elem 582 762.5 973.02 834 964.0 12945 100
```
```R
n <- 200
M <- matrix(runif(n^2), n, n)
dnorm2 <- function(x) exp(-0.5 * x^2) / sqrt(2 * pi)
stopifnot(
all.equal(dnorm(M), dnorm2(M))
)
microbenchmark(
dnorm = dnorm(M),
dnorm2 = dnorm2(M),
exp = exp(-0.5 * M^2) # without scaling -> irrelevant for usage
)
# Unit: microseconds
# expr min lq mean median uq max neval
# dnorm 841.503 843.811 920.7828 855.7505 912.4720 2405.587 100
# dnorm2 543.510 580.319 629.5321 597.8540 607.3795 2603.763 100
# exp 502.083 535.943 577.2884 548.3745 561.3280 2113.220 100
```
### Using `crosspord()`
```R
p <- 12
q <- 10
V <- matrix(runif(p * q), p, q)
stopifnot(
all.equal(V %*% t(V), tcrossprod(V)),
all.equal(V %*% t(V), tcrossprod(V, V))
)
microbenchmark(
V %*% t(V),
tcrossprod(V),
tcrossprod(V, V)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# V %*% t(V) 2.293 2.6335 2.94673 2.7375 2.9060 19.592 100
# tcrossprod(V) 1.148 1.2475 1.86173 1.3440 1.4650 30.688 100
# tcrossprod(V, V) 1.003 1.1575 1.28451 1.2400 1.3685 2.742 100
```
### Recycling vs. Sweep
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
stopifnot(
all.equal((X_diff %*% V) * rep(vecS, q),
sweep(X_diff %*% V, 1, vecS, `*`)),
all.equal((X_diff %*% V) * rep(vecS, q),
(X_diff %*% V) * vecS)
)
microbenchmark(
rep = (X_diff %*% V) * rep(vecS, q),
sweep = sweep(X_diff %*% V, 1, vecS, `*`, check.margin = FALSE),
recycle = (X_diff %*% V) * vecS
)
# Unit: microseconds
# expr min lq mean median uq max neval
# rep 851.723 988.3655 1575.639 1203.6385 1440.578 18999.23 100
# sweep 1313.177 1522.4010 2355.269 1879.2605 2065.399 18783.24 100
# recycle 719.001 786.1265 1157.285 881.8825 1163.202 19091.79 100
```
### Scaled `crossprod` with matmul order.
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
ref <- crossprod(X_diff, X_diff * vecS) %*% V
stopifnot(
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS)),
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS))
)
microbenchmark(
inner = crossprod(X_diff, X_diff * vecS) %*% V,
outer = crossprod(X_diff, (X_diff %*% V) * vecS)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# inner 789.065 867.939 1683.812 987.9375 1290.055 16800.265 100
# outer 1141.479 1216.929 1404.702 1317.7315 1582.800 2531.766 100
```
### Fast dist matrix computation (aka. row sum of squares).
```R
library(microbenchmark)
library(CVE)
(n <- 200)
(N <- n * (n - 1) / 2)
(p <- 12)
M <- matrix(runif(N * p), N, p)
stopifnot(
all.equal(rowSums(M^2), rowSums.c(M^2)),
all.equal(rowSums(M^2), rowSquareSums.c(M))
)
microbenchmark(
sums = rowSums(M^2),
sums.c = rowSums.c(M^2),
sqSums.c = rowSquareSums.c(M)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# sums 666.311 1051.036 1612.3100 1139.0065 1547.657 13940.97 100
# sums.c 342.647 672.453 1009.9109 740.6255 1224.715 13765.90 100
# sqSums.c 115.325 142.128 175.6242 153.4645 169.678 759.87 100
```
## Using `Rprof()` for performance.
The standart method for profiling where an algorithm is spending its time is with `Rprof()`.
```R
path <- '../tmp/R.prof' # path to profiling file
Rprof(path)
cve.res <- cve.call(X, Y, k = k)
Rprof(NULL)
(prof <- summaryRprof(path)) # Summarise results
```
**Note: considure to run `gc()` before measuring**, aka cleaning up by explicitely calling the garbage collector.

View File

@ -205,6 +205,21 @@ crossprod.c <- function(A, B) {
.Call('R_crossprod', PACKAGE = 'benchmark', A, B)
}
kronecker.c <- function(A, B, op = '*') {
stopifnot(
is.matrix(A), is.numeric(A),
is.matrix(B), is.numeric(B),
is.character(op), op %in% c('*', '+', '/', '-')
)
if (!is.double(A)) {
A <- matrix(as.double(A), nrow = nrow(A))
}
if (!is.double(B)) {
B <- matrix(as.double(B), nrow = nrow(B))
}
.Call('R_kronecker', PACKAGE = 'benchmark', A, B, op)
}
skewSymRank2k.c <- function(A, B, alpha = 1, beta = 0) {
stopifnot(
is.matrix(A), is.numeric(A),
@ -269,6 +284,22 @@ microbenchmark(
crossprod.c = crossprod.c(A, B)
)
n <- 100L
m <- 12L
p <- 11L
q <- 10L
A <- matrix(runif(n * m), n, m)
B <- matrix(runif(p * q), p, q)
stopifnot(all.equal(
kronecker(A, B),
kronecker.c(A, B)
))
microbenchmark(
kronecker = kronecker(A, B),
kronecker.c = kronecker.c(A, B)
)
n <- 12
k <- 11
A <- matrix(runif(n * k), n, k)
@ -307,6 +338,50 @@ microbenchmark(
nullProj.c = nullProj.c(V)
)
# ## Kronecker optimizations ----------------------------------------------------
# library(microbenchmark)
# dist.1 <- function(X_diff, Q) {
# rowSums((X_diff %*% Q)^2)
# }
# dist.2 <- function(X, Q) {
# ones <- rep(1, nrow(X))
# proj <- X %*% Q
# rowSums((kronecker(proj, ones) - kronecker(ones, proj))^2)
# }
# n <- 400L
# p <- 12L
# k <- 2L
# q <- p - k
# X <- matrix(rnorm(n * p), n, p)
# Q <- diag(1, p) - tcrossprod(rnorm(p))
# ones <- rep(1, n)
# X_diff <- kronecker(X, ones) - kronecker(ones, X)
# stopifnot(all.equal(dist.1(X_diff, Q), dist.2(X, Q)))
# microbenchmark(
# dist.1(X_diff, Q),
# dist.2(X, Q),
# times = 10L
# )
# # if (!persistent) {
# # 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
# # lower <- ((i - 1) * n) + j
# # upper <- ((j - 1) * n) + i
# # X_diff <- X[i, , drop = F] - X[j, , drop = F]
# # }
# # # Projection matrix onto `span(V)`
# # Q <- diag(1, p) - tcrossprod(V, V)
# # # Vectorized distance matrix `D`.
# # vecD <- rowSums((X_diff %*% Q)^2)
# ## WIP for gradient. ----------------------------------------------------------
@ -374,7 +449,7 @@ grad <- function(X, Y, V, h, persistent = TRUE) {
G <- (-2 / (n * h^2)) * G
return(G)
}
rStiefl <- function(p, q) {
rStiefel <- function(p, q) {
return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
}
@ -384,7 +459,7 @@ q <- 10
X <- matrix(runif(n * p), n, p)
Y <- runif(n)
V <- rStiefl(p, q)
V <- rStiefel(p, q)
h <- 0.1
pair.index <- elem.pairs(seq(n))

View File

@ -204,6 +204,29 @@ void rowSumsSymVec(const double *Avec, const int nrow,
}
}
#define ROW_SWEEP_ALG(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]) op (v[j]); \
} \
} \
/* Step one block forth. */ \
A_block += block_size_i; \
C_block += block_size_i; \
v += block_size_i; \
}
/* 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,
@ -221,93 +244,13 @@ void rowSweep(const double *A, const int nrow, const int ncol,
}
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;
}
ROW_SWEEP_ALG(+)
} 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;
}
ROW_SWEEP_ALG(-)
} 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;
}
ROW_SWEEP_ALG(*)
} 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;
}
ROW_SWEEP_ALG(/)
} else {
error("Got unknown 'op' (opperation) argument.");
}
@ -364,12 +307,45 @@ void crossprod(const double *A, const int nrowA, const int ncolA,
&zero, C, &ncolA);
}
#define KRONECKER_ALG(op) \
for (j = 0; j < ncolA; ++j) { \
for (l = 0; l < ncolB; ++l) { \
colB = B + (l * nrowB); \
for (i = 0; i < nrowA; ++i) { \
for (k = 0; k < nrowB; ++k) { \
*(C++) = (A[i]) op (colB[k]); \
} \
} \
} \
A += nrowA; \
}
void kronecker(const double * restrict A, const int nrowA, const int ncolA,
const double * restrict B, const int nrowB, const int ncolB,
const char* op,
double * restrict C) {
int i, j, k, l;
const double *colB;
if (*op == '+') {
KRONECKER_ALG(+)
} else if (*op == '-') {
KRONECKER_ALG(-)
} else if (*op == '*') {
KRONECKER_ALG(*)
} else if (*op == '/') {
KRONECKER_ALG(/)
} else {
error("Got unknown 'op' (opperation) argument.");
}
}
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.
// Initialize Q 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) {
@ -377,7 +353,7 @@ void nullProj(const double *B, const int nrowB, const int ncolB,
}
// DGEMM with parameterization:
// C <- (-1.0 * B %*% t(B)) + C
// Q <- (-1.0 * B %*% t(B)) + Q
F77_NAME(dgemm)("N", "T", &nrowB, &nrowB, &ncolB,
&minusOne, B, &nrowB, B, &nrowB,
&one, Q, &nrowB);

View File

@ -137,6 +137,24 @@ SEXP R_crossprod(SEXP A, SEXP B) {
return C;
}
void kronecker(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
const char *op,
double *C);
SEXP R_kronecker(SEXP A, SEXP B, SEXP op) {
SEXP C = PROTECT(allocMatrix(REALSXP,
nrows(A) * nrows(B),
ncols(A) * ncols(B)));
kronecker(REAL(A), nrows(A), ncols(A),
REAL(B), nrows(B), ncols(B),
CHAR(STRING_ELT(op, 0)),
REAL(C));
UNPROTECT(1);
return C;
}
void skewSymRank2k(const int n, const int k,
double alpha, const double *A, const double *B,
double beta,

368
notes.md
View File

@ -1,368 +0,0 @@
# General Notes for Souce Code analysis
## Search in multiple files.
Using the Linux `grep` program with the parameters `-rnw` and specifying a include files filter like the following example.
```bash
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_.
## 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
## 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.
```R
setwd("./CVE_R") # Set path to the package root.
library(devtools) # Load required `devtools` package.
document() # Create `.Rd` files and write `NAMESPACE`.
```
Next the package needs to be build, therefore (if pure `R` package, aka. `C/C++`, `Fortran`, ... code) just do the following.
```bash
R CMD build CVE_R
R CMD INSTALL CVE_0.1.tar.gz
```
Then we are ready for using the package.
```R
library(CVE)
help(package = "CVE")
```
## Build and install from within `R`.
An alternative approach is the following.
```R
setwd('./CVE_R')
getwd()
library(devtools)
document()
# No vignettes to build but "inst/doc/" is required!
(path <- build(vignettes = FALSE))
install.packages(path, repos = NULL, type = "source")
```
**Note: I only recommend this approach during development.**
# Analysing
## Logging (a `cve` run).
To log `loss`, `error` (estimated) the true error (error of current estimated `B` against the true `B`) or even the stepsize one can use the `logger` parameter. A `logger` is a function that gets the current `environment` of the CVE optimization methods (__do not alter this environment, only read from it__). This can be used to create logs like in the following example.
```R
library(CVE)
# Setup histories.
(epochs <- 50)
(attempts <- 10)
loss.history <- matrix(NA, epochs + 1, attempts)
error.history <- matrix(NA, epochs + 1, attempts)
tau.history <- matrix(NA, epochs + 1, attempts)
true.error.history <- matrix(NA, epochs + 1, attempts)
# Create a dataset
ds <- dataset("M1")
X <- ds$X
Y <- ds$Y
B <- ds$B # the true `B`
(k <- ncol(ds$B))
# True projection matrix.
P <- B %*% solve(t(B) %*% B) %*% t(B)
# Define the logger for the `cve()` method.
logger <- function(env) {
# Note the `<<-` assignement!
loss.history[env$epoch + 1, env$attempt] <<- env$loss
error.history[env$epoch + 1, env$attempt] <<- env$error
tau.history[env$epoch + 1, env$attempt] <<- env$tau
# Compute true error by comparing to the true `B`
B.est <- null(env$V) # Function provided by CVE
P.est <- B.est %*% solve(t(B.est) %*% B.est) %*% t(B.est)
true.error <- norm(P - P.est, 'F') / sqrt(2 * k)
true.error.history[env$epoch + 1, env$attempt] <<- true.error
}
# Performa SDR
dr <- cve(Y ~ X, k = k, logger = logger, epochs = epochs, attempts = attempts)
# Plot history's
par(mfrow = c(2, 2))
matplot(loss.history, type = 'l', log = 'y', xlab = 'iter',
main = 'loss', ylab = expression(L(V[iter])))
matplot(error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'error', ylab = 'error')
matplot(tau.history, type = 'l', log = 'y', xlab = 'iter',
main = 'tau', ylab = 'tau')
matplot(true.error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'true error', ylab = 'true error')
```
## Reading log files.
The runtime tests (upcomming further tests) are creating log files saved in `tmp/`. These log files are `CSV` files (actualy `TSV`) with a header storing the test results. Depending on the test the files may contain differnt data. As an example we use the runtime test logs which store in each line the `dataset`, the used `method` as well as the `error` (actual error of estimated `B` against real `B`) and the `time`. For reading and analysing the data see the following example.
```R
# Load log as `data.frame`
log <- read.csv('tmp/test0.log', sep = '\t')
# Create a error boxplot grouped by dataset.
boxplot(error ~ dataset, log)
# Overview
for (ds.name in paste0('M', seq(5))) {
ds <- subset(log, dataset == ds.name, select = c('method', 'dataset', 'time', 'error'))
print(summary(ds))
}
```
## Environments and variable lookup.
In the following a view simple examples of how `R` searches for variables.
In addition we manipulate funciton closures to alter the search path in variable lookup and outer scope variable manipulation.
```R
droids <- "These aren't the droids you're looking for."
search <- function() {
print(droids)
}
trooper.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
search()
}
jedi.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
environment(search) <- environment()
search()
}
trooper.seeks()
# [1] "These aren't the droids you're looking for."
jedi.seeks()
# [1] "R2-D2", "C-3PO"
```
The next example ilustrates how to write (without local copies) to variables outside the functions local environment.
```R
counting <- function() {
count <<- count + 1 # Note the `<<-` assignment.
}
(function() {
environment(counting) <- environment()
count <- 0
for (i in 1:10) {
counting()
}
return(count)
})()
(function () {
closure <- new.env()
environment(counting) <- closure
assign("count", 0, envir = closure)
for (i in 1:10) {
counting()
}
return(closure$count)
})()
```
Another example for the usage of `do.call` where the evaluation of parameters is illustated (example taken (and altered) from `?do.call`).
```R
## examples of where objects will be found.
A <- "A.Global"
f <- function(x) print(paste("f.new", x))
env <- new.env()
assign("A", "A.new", envir = env)
assign("f", f, envir = env)
f <- function(x) print(paste("f.Global", x))
f(A) # f.Global A.Global
do.call("f", list(A)) # f.Global A.Global
do.call("f", list(A), envir = env) # f.new A.Global
do.call(f, list(A), envir = env) # f.Global A.Global
do.call("f", list(quote(A)), envir = env) # f.new A.new
do.call(f, list(quote(A)), envir = env) # f.Global A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
```
# Performance benchmarks
In this section alternative implementations of simple algorithms are compared for there performance.
### Computing the trace of a matrix multiplication.
```R
library(microbenchmark)
A <- matrix(runif(120), 12, 10)
# Check correctnes and benckmark performance.
stopifnot(
all.equal(
sum(diag(t(A) %*% A)), sum(diag(crossprod(A, A)))
),
all.equal(
sum(diag(t(A) %*% A)), sum(A * A)
)
)
microbenchmark(
MM = sum(diag(t(A) %*% A)),
cross = sum(diag(crossprod(A, A))),
elem = sum(A * A)
)
# Unit: nanoseconds
# expr min lq mean median uq max neval
# MM 4232 4570.0 5138.81 4737 4956.0 40308 100
# cross 2523 2774.5 2974.93 2946 3114.5 5078 100
# elem 582 762.5 973.02 834 964.0 12945 100
```
```R
n <- 200
M <- matrix(runif(n^2), n, n)
dnorm2 <- function(x) exp(-0.5 * x^2) / sqrt(2 * pi)
stopifnot(
all.equal(dnorm(M), dnorm2(M))
)
microbenchmark(
dnorm = dnorm(M),
dnorm2 = dnorm2(M),
exp = exp(-0.5 * M^2) # without scaling -> irrelevant for usage
)
# Unit: microseconds
# expr min lq mean median uq max neval
# dnorm 841.503 843.811 920.7828 855.7505 912.4720 2405.587 100
# dnorm2 543.510 580.319 629.5321 597.8540 607.3795 2603.763 100
# exp 502.083 535.943 577.2884 548.3745 561.3280 2113.220 100
```
### Using `crosspord()`
```R
p <- 12
q <- 10
V <- matrix(runif(p * q), p, q)
stopifnot(
all.equal(V %*% t(V), tcrossprod(V)),
all.equal(V %*% t(V), tcrossprod(V, V))
)
microbenchmark(
V %*% t(V),
tcrossprod(V),
tcrossprod(V, V)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# V %*% t(V) 2.293 2.6335 2.94673 2.7375 2.9060 19.592 100
# tcrossprod(V) 1.148 1.2475 1.86173 1.3440 1.4650 30.688 100
# tcrossprod(V, V) 1.003 1.1575 1.28451 1.2400 1.3685 2.742 100
```
### Recycling vs. Sweep
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
stopifnot(
all.equal((X_diff %*% V) * rep(vecS, q),
sweep(X_diff %*% V, 1, vecS, `*`)),
all.equal((X_diff %*% V) * rep(vecS, q),
(X_diff %*% V) * vecS)
)
microbenchmark(
rep = (X_diff %*% V) * rep(vecS, q),
sweep = sweep(X_diff %*% V, 1, vecS, `*`, check.margin = FALSE),
recycle = (X_diff %*% V) * vecS
)
# Unit: microseconds
# expr min lq mean median uq max neval
# rep 851.723 988.3655 1575.639 1203.6385 1440.578 18999.23 100
# sweep 1313.177 1522.4010 2355.269 1879.2605 2065.399 18783.24 100
# recycle 719.001 786.1265 1157.285 881.8825 1163.202 19091.79 100
```
### Scaled `crossprod` with matmul order.
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
ref <- crossprod(X_diff, X_diff * vecS) %*% V
stopifnot(
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS)),
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS))
)
microbenchmark(
inner = crossprod(X_diff, X_diff * vecS) %*% V,
outer = crossprod(X_diff, (X_diff %*% V) * vecS)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# inner 789.065 867.939 1683.812 987.9375 1290.055 16800.265 100
# outer 1141.479 1216.929 1404.702 1317.7315 1582.800 2531.766 100
```
### Fast dist matrix computation (aka. row sum of squares).
```R
library(microbenchmark)
library(CVE)
(n <- 200)
(N <- n * (n - 1) / 2)
(p <- 12)
M <- matrix(runif(N * p), N, p)
stopifnot(
all.equal(rowSums(M^2), rowSums.c(M^2)),
all.equal(rowSums(M^2), rowSquareSums.c(M))
)
microbenchmark(
sums = rowSums(M^2),
sums.c = rowSums.c(M^2),
sqSums.c = rowSquareSums.c(M)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# sums 666.311 1051.036 1612.3100 1139.0065 1547.657 13940.97 100
# sums.c 342.647 672.453 1009.9109 740.6255 1224.715 13765.90 100
# sqSums.c 115.325 142.128 175.6242 153.4645 169.678 759.87 100
```
## Using `Rprof()` for performance.
The standart method for profiling where an algorithm is spending its time is with `Rprof()`.
```R
path <- '../tmp/R.prof' # path to profiling file
Rprof(path)
cve.res <- cve.call(X, Y, k = k)
Rprof(NULL)
(prof <- summaryRprof(path)) # Summarise results
```
**Note: considure to run `gc()` before measuring**, aka cleaning up by explicitely calling the garbage collector.

View File

@ -9,12 +9,19 @@ tell.user <- function(name, start.time, i, length) {
i, "/", length,
" - elapsed:", format(Sys.time() - start.time), "\033[K")
}
#' Computes "distance" of spanned subspaces.
#' @param B1 Semi-orthonormal basis matrix
#' @param B2 Semi-orthonormal basis matrix
#' @return Frobenius norm of subspace projection matrix diff.
subspace.dist <- function(B1, B2){
P1 <- B1 %*% solve(t(B1) %*% B1) %*% t(B1)
P2 <- B2 %*% solve(t(B2) %*% B2) %*% t(B2)
P1 <- tcrossprod(B1, B1)
P2 <- tcrossprod(B2, B2)
return(norm(P1 - P2, type = 'F'))
}
# Set random seed
set.seed(437)
# Number of simulations
SIM.NR <- 50
# maximal number of iterations in curvilinear search algorithm
@ -70,10 +77,12 @@ for (sim in 1:SIM.NR) {
for (method in methods) {
if (tolower(method) == "legacy") {
dr.time <- system.time(
dr <- stiefl_opt(data,
dr <- stiefel_opt(data,
k = dim - truedim,
k0 = ATTEMPTS,
h = estimate.bandwidth(X, k = truedim, nObs = sqrt(nrow(X))),
h = estimate.bandwidth(X,
k = truedim,
nObs = sqrt(nrow(X))),
maxit = MAXIT
)
)
@ -86,7 +95,7 @@ for (sim in 1:SIM.NR) {
attempts = ATTEMPTS
)
)
dr <- dr[[truedim]]
dr$B <- basis(dr, truedim)
}
key <- paste0(name, '-', method)
@ -104,22 +113,19 @@ for (sim in 1:SIM.NR) {
}
}
cat("\n\n## Time [sec] Means:\n")
print(colMeans(time))
cat("\n## Error Means:\n")
print(colMeans(error))
cat("\n\n## Time [sec] Summary:\n")
print(summary(time))
cat("\n## Error Summary:\n")
print(summary(error))
at <- seq(ncol(error)) + rep(seq(ncol(error) / length(methods)) - 1, each = length(methods))
boxplot(error,
main = paste0("Error (Nr of simulations ", SIM.NR, ")"),
ylab = "Error",
las = 2,
at = at
las = 2
)
boxplot(time,
main = paste0("Time (Nr of simulations ", SIM.NR, ")"),
ylab = "Time [sec]",
las = 2,
at = at
las = 2
)

8
test.R
View File

@ -1,10 +1,15 @@
args <- commandArgs(TRUE)
if (length(args) > 0) {
if (length(args) > 0L) {
method <- args[1]
} else {
method <- "simple"
}
if (length((args) > 1L)) {
momentum <- as.double(args[2])
} else {
momentum <- 0.0
}
epochs <- 50L
attempts <- 25L
@ -56,6 +61,7 @@ for (name in paste0("M", seq(5))) {
true.error.history <- matrix(NA, epochs + 1, attempts)
dr <- cve(Y ~ X, k = k, method = method,
momentum = momentum,
epochs = epochs, attempts = attempts,
logger = logger)