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wip: writing C gradient version

This commit is contained in:
Daniel Kapla 2019-09-12 18:42:28 +02:00
parent 47917fe0bd
commit 4d2651fe8a
24 changed files with 1414 additions and 285 deletions
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155
CVE/demo/runtime_test.R
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@ -1,88 +1,71 @@
# ----------------------------------------------------------------------------- # Usage:
# Program: runtime_test.R # ~$ Rscript runtime_test.R
# Author: Loki
# Date: 2019.08.12
#
# Purpose:
# Comparing runtime of "MAVE" with "CVE".
#
# RevisionHistory:
# Loki -- 2019.08.12 initial creation
# -----------------------------------------------------------------------------
# load CVE package library(CVE) # load CVE
library(CVE)
# load MAVE package for comparison
library(MAVE)
# set nr of simulations per dataset #' Writes progress to console.
nr.sim <- 10 tell.user <- function(name, start.time, i, length) {
cat("\rRunning Test (", name, "):",
# set names of datasets to run tests on i, "/", length,
dataset.names <- c("M1", "M2", "M3", "M4", "M5") " - elapsed:", format(Sys.time() - start.time), "\033[K")
}
#' Orthogonal projection to sub-space spanned by `B` subspace.dist <- function(B1, B2){
#' P1 <- B1 %*% solve(t(B1) %*% B1) %*% t(B1)
#' @param B Matrix P2 <- B2 %*% solve(t(B2) %*% B2) %*% t(B2)
#' @return Orthogonal Projection Matrix return(norm(P1 - P2, type = 'F'))
proj <- function(B) {
B %*% solve(t(B) %*% B) %*% t(B)
} }
#' Compute nObs given dataset dimension \code{n}. # Number of simulations
#' SIM.NR <- 50
#' @param n Number of samples # maximal number of iterations in curvilinear search algorithm
#' @return Numeric estimate of \code{nObs} MAXIT <- 50
nObs <- function (n) { n^0.5 } # number of arbitrary starting values for curvilinear optimization
ATTEMPTS <- 10
# set names of datasets
dataset.names <- c("M1", "M2", "M3", "M4", "M5")
# Set used CVE method
methods <- c("simple") # c("legacy", "simple", "sgd", "linesearch")
## prepare "logging" # Setup error and time tracking variables
# result error, time, ... data.frame's error <- matrix(NA, SIM.NR, length(methods) * length(dataset.names))
error <- matrix(nrow = nr.sim, ncol = 2 * length(dataset.names)) time <- matrix(NA, SIM.NR, ncol(error))
time <- matrix(nrow = nr.sim, ncol = 2 * length(dataset.names)) colnames(error) <- kronecker(paste0(dataset.names, '-'), methods, paste0)
# convert to data.frames colnames(time) <- colnames(error)
error <- as.data.frame(error)
time <- as.data.frame(time)
# set names
names(error) <- kronecker(c("CVE.", "MAVE."), dataset.names, paste0)
names(time) <- kronecker(c("CVE.", "MAVE."), dataset.names, paste0)
# get current time # only for telling user (to stdout)
count <- 0
start.time <- Sys.time() start.time <- Sys.time()
## main comparison loop (iterate `nr.sim` times for each dataset) # Start simulation loop.
for (i in seq_along(dataset.names)) { for (sim in 1:SIM.NR) {
for (j in 1:nr.sim) { # Repeat for each dataset.
name <- dataset.names[i] for (name in dataset.names) {
# reporting progress count <- count + 1
cat("\rRunning Test (", name, j , "):", tell.user(name, start.time, count, SIM.NR * length(dataset.names))
(i - 1) * nr.sim + j, "/", length(dataset.names) * nr.sim,
" - Time since start:", format(Sys.time() - start.time), "\033[K") # Create a new dataset
# sample new dataset
ds <- dataset(name) ds <- dataset(name)
k <- ncol(ds$B) # real dim # Prepare X, Y and combine to data matrix
data <- data.frame(X = ds$X, Y = ds$Y) Y <- ds$Y
# call CVE X <- ds$X
cve.time <- system.time( data <- cbind(Y, X)
cve.res <- cve(Y ~ ., # get dimensions
data = data, dim <- ncol(X)
method = "simple", truedim <- ncol(ds$B)
k = k)
) for (method in methods) {
# call MAVE dr.time <- system.time(
mave.time <- system.time( dr <- cve.call(X, Y,
mave.res <- mave(Y ~ ., method = method,
data = data, k = truedim,
method = "meanMAVE") attempts = ATTEMPTS
) )
# compute real and approximated sub-space projections )
P <- proj(ds$B) # real dr <- dr[[truedim]]
P.cve <- proj(cve.res$B)
P.mave <- proj(mave.res$dir[[k]]) key <- paste0(name, '-', method)
# compute (and store) errors error[sim, key] <- subspace.dist(dr$B, ds$B) / sqrt(2 * truedim)
error[j, paste0("CVE.", name)] <- norm(P - P.cve, 'F') / sqrt(2 * k) time[sim, key] <- dr.time["elapsed"]
error[j, paste0("MAVE.", name)] <- norm(P - P.mave, 'F') / sqrt(2 * k) }
# store run-times
time[j, paste0("CVE.", name)] <- cve.time["elapsed"]
time[j, paste0("MAVE.", name)] <- mave.time["elapsed"]
} }
} }
@ -91,16 +74,16 @@ print(colMeans(time))
cat("\n## Error Means:\n") cat("\n## Error Means:\n")
print(colMeans(error)) print(colMeans(error))
len <- length(dataset.names) at <- seq(ncol(error)) + rep(seq(ncol(error) / length(methods)) - 1, each = length(methods))
boxplot(as.matrix(error), boxplot(error,
main = paste0("Error (nr.sim = ", nr.sim, ")"), main = paste0("Error (Nr of simulations ", SIM.NR, ")"),
ylab = expression(error == group("||", P[B] - P[hat(B)], "||")[F] / sqrt(2*k)), ylab = "Error",
las = 2, las = 2,
at = c(1:len, 1:len + len + 1) at = at
) )
boxplot(as.matrix(time), boxplot(time,
main = paste0("Time (nr.sim = ", nr.sim, ")"), main = paste0("Time (Nr of simulations ", SIM.NR, ")"),
ylab = "time [sec]", ylab = "Time [sec]",
las = 2, las = 2,
at = c(1:len, 1:len + len + 1) at = at
) )

2
CVE_R/DESCRIPTION
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@ -1,4 +1,4 @@
Package: CVE Package: CVEpureR
Type: Package Type: Package
Title: Conditional Variance Estimator for Sufficient Dimension Reduction Title: Conditional Variance Estimator for Sufficient Dimension Reduction
Version: 0.1 Version: 0.1

2
CVE_R/NAMESPACE
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@ -2,7 +2,6 @@
S3method(plot,cve) S3method(plot,cve)
S3method(summary,cve) S3method(summary,cve)
export(col.pair.apply)
export(cve) export(cve)
export(cve.call) export(cve.call)
export(cve.grid.search) export(cve.grid.search)
@ -15,7 +14,6 @@ export(estimate.bandwidth)
export(grad) export(grad)
export(null) export(null)
export(rStiefl) export(rStiefl)
export(row.pair.apply)
import(stats) import(stats)
importFrom(graphics,lines) importFrom(graphics,lines)
importFrom(graphics,plot) importFrom(graphics,plot)

124
CVE_R/R/CVE.R
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@ -1,3 +1,17 @@
#' Conditional Variance Estimator (CVE)
#'
#' Conditional Variance Estimator for Sufficient Dimension
#' Reduction
#'
#' TODO: And some details
#'
#'
#' @references Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
#'
#' @docType package
#' @author Loki
"_PACKAGE"
#' Implementation of the CVE method. #' Implementation of the CVE method.
#' #'
#' Conditional Variance Estimator (CVE) is a novel sufficient dimension #' Conditional Variance Estimator (CVE) is a novel sufficient dimension
@ -40,7 +54,7 @@
#' @import stats #' @import stats
#' @importFrom stats model.frame #' @importFrom stats model.frame
#' @export #' @export
cve <- function(formula, data, method = "simple", ...) { cve <- function(formula, data, method = "simple", max.dim = 10, ...) {
# check for type of `data` if supplied and set default # check for type of `data` if supplied and set default
if (missing(data)) { if (missing(data)) {
data <- environment(formula) data <- environment(formula)
@ -69,12 +83,8 @@ cve <- function(formula, data, method = "simple", ...) {
#' @param ... Method specific parameters. #' @param ... Method specific parameters.
#' @rdname cve #' @rdname cve
#' @export #' @export
cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5, k, ...) { cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5,
min.dim = 1, max.dim = 10, k, ...) {
# TODO: replace default value of `k` by `max.dim` when fast enough
if (missing(k)) {
stop("TODO: parameter `k` (rank(B)) is required, replace by `max.dim`.")
}
# parameter checking # parameter checking
if (!is.matrix(X)) { if (!is.matrix(X)) {
@ -90,21 +100,42 @@ cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5, k, ...) {
stop('X is one dimensional, no need for dimension reduction.') stop('X is one dimensional, no need for dimension reduction.')
} }
if (!missing(k)) {
min.dim <- as.integer(k)
max.dim <- as.integer(k)
} else {
min.dim <- as.integer(min.dim)
max.dim <- as.integer(min(max.dim, ncol(X) - 1L))
}
if (min.dim > max.dim) {
stop('`min.dim` bigger `max.dim`.')
}
if (max.dim >= ncol(X)) {
stop('`max.dim` must be smaller than `ncol(X)`.')
}
# Call specified method. # Call specified method.
method <- tolower(method) method <- tolower(method)
if (method == 'simple') { call <- match.call()
dr <- cve_simple(X, Y, k, nObs = nObs, ...) dr <- list()
} else if (method == 'linesearch') { for (k in min.dim:max.dim) {
dr <- cve_linesearch(X, Y, k, nObs = nObs, ...) if (method == 'simple') {
} else if (method == 'sgd') { dr.k <- cve_simple(X, Y, k, nObs = nObs, ...)
dr <- cve_sgd(X, Y, k, nObs = nObs, ...) } else if (method == 'linesearch') {
} else { dr.k <- cve_linesearch(X, Y, k, nObs = nObs, ...)
stop('Got unknown method.') } else if (method == 'sgd') {
dr.k <- cve_sgd(X, Y, k, nObs = nObs, ...)
} else {
stop('Got unknown method.')
}
dr.k$k <- k
class(dr.k) <- "cve.k"
dr[[k]] <- dr.k
} }
# augment result information # augment result information
dr$method <- method dr.k$method <- method
dr$call <- match.call() dr.k$call <- call
class(dr) <- "cve" class(dr) <- "cve"
return(dr) return(dr)
} }
@ -134,41 +165,42 @@ cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5, k, ...) {
#' @export #' @export
plot.cve <- function(x, ...) { plot.cve <- function(x, ...) {
H <- x$history
H_1 <- H[!is.na(H[, 1]), 1]
defaults <- list( # H <- x$history
main = "History", # H_1 <- H[!is.na(H[, 1]), 1]
xlab = "Iterations i",
ylab = expression(loss == L[n](V^{(i)})),
xlim = c(1, nrow(H)),
ylim = c(0, max(H)),
type = "l"
)
call.plot <- match.call() # defaults <- list(
keys <- names(defaults) # main = "History",
keys <- keys[match(keys, names(call.plot)[-1], nomatch = 0) == 0] # xlab = "Iterations i",
# ylab = expression(loss == L[n](V^{(i)})),
# xlim = c(1, nrow(H)),
# ylim = c(0, max(H)),
# type = "l"
# )
for (key in keys) { # call.plot <- match.call()
call.plot[[key]] <- defaults[[key]] # keys <- names(defaults)
} # keys <- keys[match(keys, names(call.plot)[-1], nomatch = 0) == 0]
call.plot[[1L]] <- quote(plot) # for (key in keys) {
call.plot$x <- quote(1:length(H_1)) # call.plot[[key]] <- defaults[[key]]
call.plot$y <- quote(H_1) # }
eval(call.plot) # call.plot[[1L]] <- quote(plot)
# call.plot$x <- quote(1:length(H_1))
# call.plot$y <- quote(H_1)
if (ncol(H) > 1) { # eval(call.plot)
for (i in 2:ncol(H)) {
H_i <- H[H[, i] > 0, i] # if (ncol(H) > 1) {
lines(1:length(H_i), H_i) # for (i in 2:ncol(H)) {
} # H_i <- H[H[, i] > 0, i]
} # lines(1:length(H_i), H_i)
x.ends <- apply(H, 2, function(h) { length(h[!is.na(h)]) }) # }
y.ends <- apply(H, 2, function(h) { tail(h[!is.na(h)], n=1) }) # }
points(x.ends, y.ends) # x.ends <- apply(H, 2, function(h) { length(h[!is.na(h)]) })
# y.ends <- apply(H, 2, function(h) { tail(h[!is.na(h)], n=1) })
# points(x.ends, y.ends)
} }
#' Prints a summary of a \code{cve} result. #' Prints a summary of a \code{cve} result.

38
CVE_R/R/cve_linesearch.R
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@ -13,18 +13,14 @@ cve_linesearch <- function(X, Y, k,
slack = 0, slack = 0,
epochs = 50L, epochs = 50L,
attempts = 10L, attempts = 10L,
max.linesearch.iter = 10L max.linesearch.iter = 10L,
logger = NULL
) { ) {
# Set `grad` functions environment to enable if to find this environments # Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables # local variabels, needed to enable the manipulation of this local variables
# from within `grad`. # from within `grad`.
environment(grad) <- environment() environment(grad) <- environment()
# Setup histories.
loss.history <- matrix(NA, epochs, attempts)
error.history <- matrix(NA, epochs, attempts)
tau.history <- matrix(NA, epochs, attempts)
# Get dimensions. # Get dimensions.
n <- nrow(X) n <- nrow(X)
p <- ncol(X) p <- ncol(X)
@ -44,8 +40,8 @@ cve_linesearch <- function(X, Y, k,
# Compute lookup indexes for symmetrie, lower/upper # Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization. # triangular parts and vectorization.
pair.index <- elem.pairs(seq(n)) pair.index <- elem.pairs(seq(n))
i <- pair.index[, 1] # `i` indices of `(i, j)` pairs i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[, 2] # `j` indices of `(i, j)` pairs j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Matrix of vectorized indices. (vec(index) -> seq) # Matrix of vectorized indices. (vec(index) -> seq)
index <- matrix(seq(n * n), n, n) index <- matrix(seq(n * n), n, n)
lower <- index[lower.tri(index)] lower <- index[lower.tri(index)]
@ -73,6 +69,13 @@ cve_linesearch <- function(X, Y, k,
# Set last loss (aka, loss after applying the step). # Set last loss (aka, loss after applying the step).
loss.last <- loss loss.last <- loss
# Call logger with initial values before starting optimization.
if (is.function(logger)) {
epoch <- 0 # Set epoch count to 0 (only relevant for logging).
error <- NA
logger(environment())
}
## Start optimization loop. ## Start optimization loop.
for (epoch in 1:epochs) { for (epoch in 1:epochs) {
@ -124,16 +127,16 @@ cve_linesearch <- function(X, Y, k,
# Compute error. # Compute error.
error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F") error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F")
# Write history.
loss.history[epoch, attempt] <- loss
error.history[epoch, attempt] <- error
tau.history[epoch, attempt] <- tau
# Check break condition (epoch check to skip ignored gradient calc). # Check break condition (epoch check to skip ignored gradient calc).
# Note: the devision by `sqrt(2 * k)` is included in `tol`. # Note: the devision by `sqrt(2 * k)` is included in `tol`.
if (error < tol | epoch >= epochs) { if (error < tol | epoch >= epochs) {
# take last step and stop optimization. # take last step and stop optimization.
V <- V.tau V <- V.tau
# Final call to the logger before stopping optimization
if (is.function(logger)) {
G <- G.tau
logger(environment())
}
break() break()
} }
@ -141,6 +144,12 @@ cve_linesearch <- function(X, Y, k,
V <- V.tau V <- V.tau
loss.last <- loss loss.last <- loss
G <- G.tau G <- G.tau
# Log after taking current step.
if (is.function(logger)) {
logger(environment())
}
} }
# Check if current attempt improved previous ones # Check if current attempt improved previous ones
@ -152,9 +161,6 @@ cve_linesearch <- function(X, Y, k,
} }
return(list( return(list(
loss.history = loss.history,
error.history = error.history,
tau.history = tau.history,
loss = loss.best, loss = loss.best,
V = V.best, V = V.best,
B = null(V.best), B = null(V.best),

49
CVE_R/R/cve_sgd.R
View File

@ -10,17 +10,14 @@ cve_sgd <- function(X, Y, k,
tol = 1e-3, tol = 1e-3,
epochs = 50L, epochs = 50L,
batch.size = 16L, batch.size = 16L,
attempts = 10L attempts = 10L,
logger = NULL
) { ) {
# Set `grad` functions environment to enable if to find this environments # Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables # local variabels, needed to enable the manipulation of this local variables
# from within `grad`. # from within `grad`.
environment(grad) <- environment() environment(grad) <- environment()
# Setup histories.
loss.history <- matrix(NA, epochs, attempts)
error.history <- matrix(NA, epochs, attempts)
# Get dimensions. # Get dimensions.
n <- nrow(X) # Number of samples. n <- nrow(X) # Number of samples.
p <- ncol(X) # Data dimensions p <- ncol(X) # Data dimensions
@ -32,7 +29,7 @@ cve_sgd <- function(X, Y, k,
tol <- sqrt(2 * q) * tol tol <- sqrt(2 * q) * tol
# Estaimate bandwidth if not given. # Estaimate bandwidth if not given.
if (missing(h) | !is.numeric(h)) { if (missing(h) || !is.numeric(h)) {
h <- estimate.bandwidth(X, k, nObs) h <- estimate.bandwidth(X, k, nObs)
} }
@ -40,12 +37,11 @@ cve_sgd <- function(X, Y, k,
# Compute lookup indexes for symmetrie, lower/upper # Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization. # triangular parts and vectorization.
pair.index <- elem.pairs(seq(n)) pair.index <- elem.pairs(seq(n))
i <- pair.index[, 1] # `i` indices of `(i, j)` pairs i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[, 2] # `j` indices of `(i, j)` pairs j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Matrix of vectorized indices. (vec(index) -> seq) # Index of vectorized matrix, for lower and upper triangular part.
index <- matrix(seq(n * n), n, n) lower <- ((i - 1) * n) + j
lower <- index[lower.tri(index)] upper <- ((j - 1) * n) + i
upper <- t(index)[lower]
# Create all pairewise differences of rows of `X`. # Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F] X_diff <- X[i, , drop = F] - X[j, , drop = F]
@ -69,17 +65,23 @@ cve_sgd <- function(X, Y, k,
# Keep track of last `V` for computing error after an epoch. # Keep track of last `V` for computing error after an epoch.
V.last <- V V.last <- V
if (is.function(logger)) {
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
error <- NA
epoch <- 0
logger(environment())
}
# Repeat `epochs` times # Repeat `epochs` times
for (epoch in 1:epochs) { for (epoch in 1:epochs) {
# Shuffle batches # Shuffle batches
batch.shuffle <- sample(indices) batch.shuffle <- sample(indices)
# Make a step for each batch. # Make a step for each batch.
for (start in seq(1, n, batch.size)) { for (batch.start in seq(1, n, batch.size)) {
# Select batch data indices. # Select batch data indices.
batch <- batch.shuffle[start:(start + batch.size - 1)] batch.end <- min(batch.start + batch.size - 1, length(batch.shuffle))
# Remove `NA`'s (when `n` isn't a multiple of `batch.size`). batch <- batch.shuffle[batch.start:batch.end]
batch <- batch[!is.na(batch)]
# Compute batch gradient. # Compute batch gradient.
loss <- NULL loss <- NULL
@ -93,21 +95,24 @@ cve_sgd <- function(X, Y, k,
# Parallet transport (on Stiefl manifold) into direction of `G`. # Parallet transport (on Stiefl manifold) into direction of `G`.
V <- solve(I_p + A.tau) %*% ((I_p - A.tau) %*% V) V <- solve(I_p + A.tau) %*% ((I_p - A.tau) %*% V)
} }
# Compute actuall loss after finishing optimization.
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
# And the error for the history. # And the error for the history.
error <- norm(V.last %*% t(V.last) - V %*% t(V), type = "F") error <- norm(V.last %*% t(V.last) - V %*% t(V), type = "F")
V.last <- V V.last <- V
# Finaly write history. if (is.function(logger)) {
loss.history[epoch, attempt] <- loss # Compute loss at end of epoch for logging.
error.history[epoch, attempt] <- error loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
logger(environment())
}
# Check break condition. # Check break condition.
if (error < tol) { if (error < tol) {
break() break()
} }
} }
# Compute actual loss after finishing for comparing multiple attempts.
loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
# After each attempt, check if last attempt reached a better result. # After each attempt, check if last attempt reached a better result.
if (loss < loss.best) { if (loss < loss.best) {
loss.best <- loss loss.best <- loss
@ -116,8 +121,6 @@ cve_sgd <- function(X, Y, k,
} }
return(list( return(list(
loss.history = loss.history,
error.history = error.history,
loss = loss.best, loss = loss.best,
V = V.best, V = V.best,
B = null(V.best), B = null(V.best),

55
CVE_R/R/cve_simple.R
View File

@ -10,21 +10,18 @@ cve_simple <- function(X, Y, k,
tol = 1e-3, tol = 1e-3,
slack = 0, slack = 0,
epochs = 50L, epochs = 50L,
attempts = 10L attempts = 10L,
logger = NULL
) { ) {
# Set `grad` functions environment to enable if to find this environments # Set `grad` functions environment to enable if to find this environments
# local variabels, needed to enable the manipulation of this local variables # local variabels, needed to enable the manipulation of this local variables
# from within `grad`. # from within `grad`.
environment(grad) <- environment() environment(grad) <- environment()
# Setup histories.
loss.history <- matrix(NA, epochs, attempts)
error.history <- matrix(NA, epochs, attempts)
# Get dimensions. # Get dimensions.
n <- nrow(X) n <- nrow(X) # Number of samples.
p <- ncol(X) p <- ncol(X) # Data dimensions
q <- p - k q <- p - k # Complement dimension of the SDR space.
# Save initial learning rate `tau`. # Save initial learning rate `tau`.
tau.init <- tau tau.init <- tau
@ -32,7 +29,7 @@ cve_simple <- function(X, Y, k,
tol <- sqrt(2 * q) * tol tol <- sqrt(2 * q) * tol
# Estaimate bandwidth if not given. # Estaimate bandwidth if not given.
if (missing(h) | !is.numeric(h)) { if (missing(h) || !is.numeric(h)) {
h <- estimate.bandwidth(X, k, nObs) h <- estimate.bandwidth(X, k, nObs)
} }
@ -40,12 +37,11 @@ cve_simple <- function(X, Y, k,
# Compute lookup indexes for symmetrie, lower/upper # Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization. # triangular parts and vectorization.
pair.index <- elem.pairs(seq(n)) pair.index <- elem.pairs(seq(n))
i <- pair.index[, 1] # `i` indices of `(i, j)` pairs i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[, 2] # `j` indices of `(i, j)` pairs j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Matrix of vectorized indices. (vec(index) -> seq) # Index of vectorized matrix, for lower and upper triangular part.
index <- matrix(seq(n * n), n, n) lower <- ((i - 1) * n) + j
lower <- index[lower.tri(index)] upper <- ((j - 1) * n) + i
upper <- t(index)[lower]
# Create all pairewise differences of rows of `X`. # Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F] X_diff <- X[i, , drop = F] - X[j, , drop = F]
@ -58,8 +54,7 @@ cve_simple <- function(X, Y, k,
# Start loop for multiple attempts. # Start loop for multiple attempts.
for (attempt in 1:attempts) { for (attempt in 1:attempts) {
# Reset learning rate `tau`.
# reset step width `tau`
tau <- tau.init tau <- tau.init
# Sample a `(p, q)` dimensional matrix from the stiefel manifold as # Sample a `(p, q)` dimensional matrix from the stiefel manifold as
@ -75,6 +70,13 @@ cve_simple <- function(X, Y, k,
# Cayley transform matrix `A` # Cayley transform matrix `A`
A <- (G %*% t(V)) - (V %*% t(G)) A <- (G %*% t(V)) - (V %*% t(G))
# Call logger with initial values before starting optimization.
if (is.function(logger)) {
epoch <- 0 # Set epoch count to 0 (only relevant for logging).
error <- NA
logger(environment())
}
## Start optimization loop. ## Start optimization loop.
for (epoch in 1:epochs) { for (epoch in 1:epochs) {
# Apply learning rate `tau`. # Apply learning rate `tau`.
@ -85,7 +87,7 @@ cve_simple <- function(X, Y, k,
# Loss at position after a step. # Loss at position after a step.
loss <- grad(X, Y, V.tau, h, loss.only = TRUE, persistent = TRUE) loss <- grad(X, Y, V.tau, h, loss.only = TRUE, persistent = TRUE)
# Check if step is appropriate # Check if step is appropriate, iff not reduce learning rate.
if ((loss - loss.last) > slack * loss.last) { if ((loss - loss.last) > slack * loss.last) {
tau <- tau / 2 tau <- tau / 2
next() # Keep position and try with smaller `tau`. next() # Keep position and try with smaller `tau`.
@ -94,15 +96,15 @@ cve_simple <- function(X, Y, k,
# Compute error. # Compute error.
error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F") error <- norm(V %*% t(V) - V.tau %*% t(V.tau), type = "F")
# Write history.
loss.history[epoch, attempt] <- loss
error.history[epoch, attempt] <- error
# Check break condition (epoch check to skip ignored gradient calc). # Check break condition (epoch check to skip ignored gradient calc).
# Note: the devision by `sqrt(2 * k)` is included in `tol`. # Note: the devision by `sqrt(2 * k)` is included in `tol`.
if (error < tol | epoch >= epochs) { if (error < tol || epoch >= epochs) {
# take last step and stop optimization. # take last step and stop optimization.
V <- V.tau V <- V.tau
# Call logger last time befor stoping.
if (is.function(logger)) {
logger(environment())
}
break() break()
} }
@ -110,6 +112,11 @@ cve_simple <- function(X, Y, k,
V <- V.tau V <- V.tau
loss.last <- loss loss.last <- loss
# Call logger after taking a step.
if (is.function(logger)) {
logger(environment())
}
# Compute gradient at new position. # Compute gradient at new position.
G <- grad(X, Y, V, h, persistent = TRUE) G <- grad(X, Y, V, h, persistent = TRUE)
@ -126,8 +133,6 @@ cve_simple <- function(X, Y, k,
} }
return(list( return(list(
loss.history = loss.history,
error.history = error.history,
loss = loss.best, loss = loss.best,
V = V.best, V = V.best,
B = null(V.best), B = null(V.best),

13
CVE_R/R/gradient.R
View File

@ -24,12 +24,11 @@ grad <- function(X, Y, V, h,
# Compute lookup indexes for symmetrie, lower/upper # Compute lookup indexes for symmetrie, lower/upper
# triangular parts and vectorization. # triangular parts and vectorization.
pair.index <- elem.pairs(seq(n)) pair.index <- elem.pairs(seq(n))
i <- pair.index[, 1] # `i` indices of `(i, j)` pairs i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
j <- pair.index[, 2] # `j` indices of `(i, j)` pairs j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
# Matrix of vectorized indices. (vec(index) -> seq) # Index of vectorized matrix, for lower and upper triangular part.
index <- matrix(seq(n * n), n, n) lower <- ((i - 1) * n) + j
lower <- index[lower.tri(index)] upper <- ((j - 1) * n) + i
upper <- t.default(index)[lower]
# Create all pairewise differences of rows of `X`. # Create all pairewise differences of rows of `X`.
X_diff <- X[i, , drop = F] - X[j, , drop = F] X_diff <- X[i, , drop = F] - X[j, , drop = F]
@ -39,7 +38,7 @@ grad <- function(X, Y, V, h,
Q <- diag(1, p) - tcrossprod(V, V) Q <- diag(1, p) - tcrossprod(V, V)
# Vectorized distance matrix `D`. # Vectorized distance matrix `D`.
vecD <- rowSums((X_diff %*% Q)^2) vecD <- colSums(tcrossprod(Q, X_diff)^2)
# Weight matrix `W` (dnorm ... gaussean density function) # Weight matrix `W` (dnorm ... gaussean density function)
W <- matrix(1, n, n) # `exp(0) == 1` W <- matrix(1, n, n) # `exp(0) == 1`

35
CVE_R/R/util.R
View File

@ -22,42 +22,19 @@ null <- function(V) {
return(qr.Q(tmp, complete=TRUE)[, set, drop=FALSE]) return(qr.Q(tmp, complete=TRUE)[, set, drop=FALSE])
} }
#' Creates a (numeric) matrix where each row contains #' Creates a (numeric) matrix where each column contains
#' an element to element matching. #' an element to element matching.
#' @param elements numeric vector of elements to match #' @param elements numeric vector of elements to match
#' @return matrix of size `(n * (n - 1) / 2, 2)` for a argument of lenght `n`. #' @return matrix of size `(2, n * (n - 1) / 2)` for a argument of lenght `n`.
#' @keywords internal #' @keywords internal
#' @examples
#' elem.pairs(seq.int(2, 5))
#' @export #' @export
elem.pairs <- function(elements) { elem.pairs <- function(elements) {
# Number of elements to match. # Number of elements to match.
n <- length(elements) n <- length(elements)
# Create all combinations. # Create all combinations.
pairs <- cbind(rep(elements, each=n), rep(elements, n)) pairs <- rbind(rep(elements, each=n), rep(elements, n))
# Select unique combinations without self interaction. # Select unique combinations without self interaction.
return(pairs[pairs[, 1] < pairs[, 2], ]) return(pairs[, pairs[1, ] < pairs[2, ]])
}
#' Apply function to pairs of matrix rows or columns.
#'
#' \code{row.pair.apply} applies \code{FUN} to each unique row pair without self
#' interaction while \code{col.pair.apply} does the same for columns.
#' @param X Matrix.
#' @param FUN Function to apply to each pair.
#' @examples
#' X <- matrix(seq(12), 4, 3)
#' # matrix containing all row to row differences.
#' row.pair.apply(X, `-`)
#' @aliases row.pair.apply, col.pair.apply
#' @keywords internal
#' @export
row.pair.apply <- function(X, FUN) {
pairs <- elem.pairs(seq(nrow(X)))
return(FUN(X[pairs[, 1], ], X[pairs[, 2], ]))
}
#' @rdname row.pair.apply
#' @keywords internal
#' @export
col.pair.apply <- function(X, FUN) {
pairs <- elem.pairs(seq(ncol(X)))
return(FUN(X[, pairs[, 1]], X[, pairs[, 2]]))
} }

2
CVE_R/demo/00Index Normal file
View File

@ -0,0 +1,2 @@
runtime_test Runtime comparison of CVE against MAVE for M1 - M5 datasets.
logging Example of a logger function for cve algorithm analysis.

43
CVE_R/demo/logging.R Normal file
View File

@ -0,0 +1,43 @@
library(CVEpureR)
# 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
}
# Performe SDR for ONE `k`.
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')

89
CVE_R/demo/runtime_test.R Normal file
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@ -0,0 +1,89 @@
# Usage:
# ~$ Rscript runtime_test.R
library(CVEpureR) # load CVE
#' Writes progress to console.
tell.user <- function(name, start.time, i, length) {
cat("\rRunning Test (", name, "):",
i, "/", length,
" - elapsed:", format(Sys.time() - start.time), "\033[K")
}
subspace.dist <- function(B1, B2){
P1 <- B1 %*% solve(t(B1) %*% B1) %*% t(B1)
P2 <- B2 %*% solve(t(B2) %*% B2) %*% t(B2)
return(norm(P1 - P2, type = 'F'))
}
# Number of simulations
SIM.NR <- 50
# maximal number of iterations in curvilinear search algorithm
MAXIT <- 50
# number of arbitrary starting values for curvilinear optimization
ATTEMPTS <- 10
# set names of datasets
dataset.names <- c("M1", "M2", "M3", "M4", "M5")
# Set used CVE method
methods <- c("simple") # c("legacy", "simple", "sgd", "linesearch")
# Setup error and time tracking variables
error <- matrix(NA, SIM.NR, length(methods) * length(dataset.names))
time <- matrix(NA, SIM.NR, ncol(error))
colnames(error) <- kronecker(paste0(dataset.names, '-'), methods, paste0)
colnames(time) <- colnames(error)
# only for telling user (to stdout)
count <- 0
start.time <- Sys.time()
# Start simulation loop.
for (sim in 1:SIM.NR) {
# Repeat for each dataset.
for (name in dataset.names) {
count <- count + 1
tell.user(name, start.time, count, SIM.NR * length(dataset.names))
# Create a new dataset
ds <- dataset(name)
# Prepare X, Y and combine to data matrix
Y <- ds$Y
X <- ds$X
data <- cbind(Y, X)
# get dimensions
dim <- ncol(X)
truedim <- ncol(ds$B)
for (method in methods) {
dr.time <- system.time(
dr <- cve.call(X, Y,
method = method,
k = truedim,
attempts = ATTEMPTS
)
)
dr <- dr[[truedim]]
key <- paste0(name, '-', method)
error[sim, key] <- subspace.dist(dr$B, ds$B) / sqrt(2 * truedim)
time[sim, key] <- dr.time["elapsed"]
}
}
}
cat("\n\n## Time [sec] Means:\n")
print(colMeans(time))
cat("\n## Error Means:\n")
print(colMeans(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
)
boxplot(time,
main = paste0("Time (Nr of simulations ", SIM.NR, ")"),
ylab = "Time [sec]",
las = 2,
at = at
)

20
CVE_R/man/CVEpureR-package.Rd Normal file
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@ -0,0 +1,20 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\docType{package}
\name{CVEpureR-package}
\alias{CVEpureR}
\alias{CVEpureR-package}
\title{Conditional Variance Estimator (CVE)}
\description{
Conditional Variance Estimator for Sufficient Dimension
Reduction
}
\details{
TODO: And some details
}
\references{
Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
}
\author{
Loki
}

5
CVE_R/man/cve.Rd
View File

@ -5,9 +5,10 @@
\alias{cve.call} \alias{cve.call}
\title{Implementation of the CVE method.} \title{Implementation of the CVE method.}
\usage{ \usage{
cve(formula, data, method = "simple", ...) cve(formula, data, method = "simple", max.dim = 10, ...)
cve.call(X, Y, method = "simple", nObs = nrow(X)^0.5, k, ...) cve.call(X, Y, method = "simple", nObs = nrow(X)^0.5, min.dim = 1,
max.dim = 10, k, ...)
} }
\arguments{ \arguments{
\item{formula}{Formel for the regression model defining `X`, `Y`. \item{formula}{Formel for the regression model defining `X`, `Y`.

2
CVE_R/man/cve_linesearch.Rd
View File

@ -7,7 +7,7 @@ conditions.}
\usage{ \usage{
cve_linesearch(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1, cve_linesearch(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1,
tol = 0.001, rho1 = 0.1, rho2 = 0.9, slack = 0, epochs = 50L, tol = 0.001, rho1 = 0.1, rho2 = 0.9, slack = 0, epochs = 50L,
attempts = 10L, max.linesearch.iter = 10L) attempts = 10L, max.linesearch.iter = 10L, logger = NULL)
} }
\description{ \description{
Implementation of the CVE method using curvilinear linesearch with Armijo-Wolfe Implementation of the CVE method using curvilinear linesearch with Armijo-Wolfe

3
CVE_R/man/cve_sgd.Rd
View File

@ -6,7 +6,8 @@
a classic GD method unsing no further tricks.} a classic GD method unsing no further tricks.}
\usage{ \usage{
cve_sgd(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 0.01, cve_sgd(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 0.01,
tol = 0.001, epochs = 50L, batch.size = 16L, attempts = 10L) tol = 0.001, epochs = 50L, batch.size = 16L, attempts = 10L,
logger = NULL)
} }
\description{ \description{
Simple implementation of the CVE method. 'Simple' means that this method is Simple implementation of the CVE method. 'Simple' means that this method is

3
CVE_R/man/cve_simple.Rd
View File

@ -6,7 +6,8 @@
a classic GD method unsing no further tricks.} a classic GD method unsing no further tricks.}
\usage{ \usage{
cve_simple(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1, cve_simple(X, Y, k, nObs = sqrt(nrow(X)), h = NULL, tau = 1,
tol = 0.001, slack = 0, epochs = 50L, attempts = 10L) tol = 0.001, slack = 0, epochs = 50L, attempts = 10L,
logger = NULL)
} }
\description{ \description{
Simple implementation of the CVE method. 'Simple' means that this method is Simple implementation of the CVE method. 'Simple' means that this method is

9
CVE_R/man/elem.pairs.Rd
View File

@ -2,7 +2,7 @@
% Please edit documentation in R/util.R % Please edit documentation in R/util.R
\name{elem.pairs} \name{elem.pairs}
\alias{elem.pairs} \alias{elem.pairs}
\title{Creates a (numeric) matrix where each row contains \title{Creates a (numeric) matrix where each column contains
an element to element matching.} an element to element matching.}
\usage{ \usage{
elem.pairs(elements) elem.pairs(elements)
@ -11,10 +11,13 @@ elem.pairs(elements)
\item{elements}{numeric vector of elements to match} \item{elements}{numeric vector of elements to match}
} }
\value{ \value{
matrix of size `(n * (n - 1) / 2, 2)` for a argument of lenght `n`. matrix of size `(2, n * (n - 1) / 2)` for a argument of lenght `n`.
} }
\description{ \description{
Creates a (numeric) matrix where each row contains Creates a (numeric) matrix where each column contains
an element to element matching. an element to element matching.
} }
\examples{
elem.pairs(seq.int(2, 5))
}
\keyword{internal} \keyword{internal}

27
CVE_R/man/row.pair.apply.Rd
View File

@ -1,27 +0,0 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/util.R
\name{row.pair.apply}
\alias{row.pair.apply}
\alias{row.pair.apply,}
\alias{col.pair.apply}
\title{Apply function to pairs of matrix rows or columns.}
\usage{
row.pair.apply(X, FUN)
col.pair.apply(X, FUN)
}
\arguments{
\item{X}{Matrix.}
\item{FUN}{Function to apply to each pair.}
}
\description{
\code{row.pair.apply} applies \code{FUN} to each unique row pair without self
interaction while \code{col.pair.apply} does the same for columns.
}
\examples{
X <- matrix(seq(12), 4, 3)
# matrix containing all row to row differences.
row.pair.apply(X, `-`)
}
\keyword{internal}

109
notes.md
View File

@ -1,3 +1,12 @@
# 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_.
# Development
## Build and install. ## Build and install.
To build the package the `devtools` package is used. This also provides `roxygen2` which is used for documentation and authomatic creaton of the `NAMESPACE` file. To build the package the `devtools` package is used. This also provides `roxygen2` which is used for documentation and authomatic creaton of the `NAMESPACE` file.
```R ```R
@ -29,6 +38,55 @@ install.packages(path, repos = NULL, type = "source")
``` ```
**Note: I only recommend this approach during development.** **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. ## 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. 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 ```R
@ -66,7 +124,9 @@ jedi.seeks <- function() {
} }
trooper.seeks() trooper.seeks()
# [1] "These aren't the droids you're looking for."
jedi.seeks() jedi.seeks()
# [1] "R2-D2", "C-3PO"
``` ```
The next example ilustrates how to write (without local copies) to variables outside the functions local environment. The next example ilustrates how to write (without local copies) to variables outside the functions local environment.
@ -127,27 +187,25 @@ library(microbenchmark)
A <- matrix(runif(120), 12, 10) A <- matrix(runif(120), 12, 10)
# Matrix trace.
tr <- function(M) sum(diag(M))
# Check correctnes and benckmark performance. # Check correctnes and benckmark performance.
stopifnot( stopifnot(
all.equal( all.equal(
tr(t(A) %*% A), sum(diag(t(A) %*% A)), sum(diag(crossprod(A, A)))
sum(diag(t(A) %*% A)), ),
sum(A * A) all.equal(
sum(diag(t(A) %*% A)), sum(A * A)
) )
) )
microbenchmark( microbenchmark(
tr(t(A) %*% A), MM = sum(diag(t(A) %*% A)),
sum(diag(t(A) %*% A)), cross = sum(diag(crossprod(A, A))),
sum(A * A) elem = sum(A * A)
) )
# Unit: nanoseconds # Unit: nanoseconds
# expr min lq mean median uq max neval # expr min lq mean median uq max neval
# tr(t(A) %*% A) 4335 4713 5076.36 4949.5 5402.5 7928 100 # MM 4232 4570.0 5138.81 4737 4956.0 40308 100
# sum(diag(t(A) %*% A)) 4106 4429 5233.89 4733.5 5057.5 49308 100 # cross 2523 2774.5 2974.93 2946 3114.5 5078 100
# sum(A * A) 540 681 777.07 740.0 818.5 3572 100 # elem 582 762.5 973.02 834 964.0 12945 100
``` ```
```R ```R
@ -243,6 +301,31 @@ microbenchmark(
# outer 1141.479 1216.929 1404.702 1317.7315 1582.800 2531.766 100 # 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. ## Using `Rprof()` for performance.
The standart method for profiling where an algorithm is spending its time is with `Rprof()`. The standart method for profiling where an algorithm is spending its time is with `Rprof()`.

5
runtime_test.R
View File

@ -14,7 +14,7 @@ subspace.dist <- function(B1, B2){
} }
# Number of simulations # Number of simulations
SIM.NR <- 50 SIM.NR <- 20
# maximal number of iterations in curvilinear search algorithm # maximal number of iterations in curvilinear search algorithm
MAXIT <- 50 MAXIT <- 50
# number of arbitrary starting values for curvilinear optimization # number of arbitrary starting values for curvilinear optimization
@ -22,7 +22,7 @@ ATTEMPTS <- 10
# set names of datasets # set names of datasets
dataset.names <- c("M1", "M2", "M3", "M4", "M5") dataset.names <- c("M1", "M2", "M3", "M4", "M5")
# Set used CVE method # Set used CVE method
methods <- c("simple") #, "sgd") # "legacy" methods <- c("simple") # c("legacy", "simple", "sgd", "linesearch")
library(CVE) # load CVE library(CVE) # load CVE
if ("legacy" %in% methods) { if ("legacy" %in% methods) {
@ -83,6 +83,7 @@ for (sim in 1:SIM.NR) {
attempts = ATTEMPTS attempts = ATTEMPTS
) )
) )
dr <- dr[[truedim]]
} }
key <- paste0(name, '-', method) key <- paste0(name, '-', method)

329
wip.R Normal file
View File

@ -0,0 +1,329 @@
library(microbenchmark)
dyn.load("wip.so")
## rowSum* .call --------------------------------------------------------------
rowSums.c <- function(M) {
stopifnot(
is.matrix(M),
is.numeric(M)
)
if (!is.double(M)) {
M <- matrix(as.double(M), nrow = nrow(M))
}
.Call('R_rowSums', PACKAGE = 'wip', M)
}
colSums.c <- function(M) {
stopifnot(
is.matrix(M),
is.numeric(M)
)
if (!is.double(M)) {
M <- matrix(as.double(M), nrow = nrow(M))
}
.Call('R_colSums', PACKAGE = 'wip', M)
}
rowSquareSums.c <- function(M) {
stopifnot(
is.matrix(M),
is.numeric(M)
)
if (!is.double(M)) {
M <- matrix(as.double(M), nrow = nrow(M))
}
.Call('R_rowSquareSums', PACKAGE = 'wip', M)
}
rowSumsSymVec.c <- function(vecA, nrow, diag = 0.0) {
stopifnot(
is.vector(vecA),
is.numeric(vecA),
is.numeric(diag),
nrow * (nrow - 1) == length(vecA) * 2
)
if (!is.double(vecA)) {
vecA <- as.double(vecA)
}
.Call('R_rowSumsSymVec', PACKAGE = 'wip',
vecA, as.integer(nrow), as.double(diag))
}
rowSweep.c <- function(A, v, op = '-') {
stopifnot(
is.matrix(A),
is.numeric(v)
)
if (!is.double(A)) {
A <- matrix(as.double(A), nrow = nrow(A))
}
if (!is.vector(v) || !is.double(v)) {
v <- as.double(v)
}
stopifnot(
nrow(A) == length(v),
op %in% c('+', '-', '*', '/')
)
.Call('R_rowSweep', PACKAGE = 'wip', A, v, op)
}
## row*, col* tests ------------------------------------------------------------
n <- 3000
M <- matrix(runif(n * 12), n, 12)
stopifnot(
all.equal(rowSums(M^2), rowSums.c(M^2)),
all.equal(colSums(M), colSums.c(M))
)
microbenchmark(
rowSums = rowSums(M^2),
rowSums.c = rowSums.c(M^2),
rowSqSums.c = rowSquareSums.c(M)
)
microbenchmark(
colSums = colSums(M),
colSums.c = colSums.c(M)
)
sum = rowSums(M)
stopifnot(all.equal(
sweep(M, 1, sum, FUN = `/`),
rowSweep.c(M, sum, '/') # Col-Normalize)
), all.equal(
sweep(M, 1, sum, FUN = `/`),
M / sum
))
microbenchmark(
sweep = sweep(M, 1, sum, FUN = `/`),
M / sum,
rowSweep.c = rowSweep.c(M, sum, '/') # Col-Normalize)
)
# Create symmetric matrix with constant diagonal entries.
nrow <- 200
diag <- 1.0
Sym <- tcrossprod(runif(nrow))
diag(Sym) <- diag
# Get vectorized lower triangular part of `Sym` matrix.
SymVec <- Sym[lower.tri(Sym)]
stopifnot(all.equal(
rowSums(Sym),
rowSumsSymVec.c(SymVec, nrow, diag)
))
microbenchmark(
rowSums = rowSums(Sym),
rowSums.c = rowSums.c(Sym),
rowSumsSymVec.c = rowSumsSymVec.c(SymVec, nrow, diag)
)
## Matrix-Matrix opperation .call ---------------------------------------------
matrixprod.c <- function(A, B) {
stopifnot(
is.matrix(A), is.numeric(A),
is.matrix(B), is.numeric(B),
ncol(A) == nrow(B)
)
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_matrixprod', PACKAGE = 'wip', A, B)
}
crossprod.c <- function(A, B) {
stopifnot(
is.matrix(A), is.numeric(A),
is.matrix(B), is.numeric(B),
nrow(A) == nrow(B)
)
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_crossprod', PACKAGE = 'wip', A, B)
}
skewSymRank2k.c <- function(A, B, alpha = 1, beta = 0) {
stopifnot(
is.matrix(A), is.numeric(A),
is.matrix(B), is.numeric(B),
all(dim(A) == dim(B)),
is.numeric(alpha), length(alpha) == 1L,
is.numeric(beta), length(beta) == 1L
)
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_skewSymRank2k', PACKAGE = 'wip', A, B,
as.double(alpha), as.double(beta))
}
## Matrix-Matrix opperation tests ---------------------------------------------
n <- 200
k <- 100
m <- 300
A <- matrix(runif(n * k), n, k)
B <- matrix(runif(k * m), k, m)
stopifnot(
all.equal(A %*% B, matrixprod.c(A, B))
)
microbenchmark(
"%*%" = A %*% B,
matrixprod.c = matrixprod.c(A, B)
)
A <- matrix(runif(k * n), k, n)
B <- matrix(runif(k * m), k, m)
stopifnot(
all.equal(crossprod(A, B), crossprod.c(A, B))
)
microbenchmark(
crossprod = crossprod(A, B),
crossprod.c = crossprod.c(A, B)
)
n <- 12
k <- 11
A <- matrix(runif(n * k), n, k)
B <- matrix(runif(n * k), n, k)
stopifnot(all.equal(
A %*% t(B) - B %*% t(A), skewSymRank2k.c(A, B)
))
microbenchmark(
A %*% t(B) - B %*% t(A),
skewSymRank2k.c(A, B)
)
## Orthogonal projection onto null space .Call --------------------------------
nullProj.c <- function(B) {
stopifnot(
is.matrix(B), is.numeric(B)
)
if (!is.double(B)) {
B <- matrix(as.double(B), nrow = nrow(B))
}
.Call('R_nullProj', PACKAGE = 'wip', B)
}
## Orthogonal projection onto null space tests --------------------------------
p <- 12
q <- 10
V <- qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q)))
# Projection matrix onto `span(V)`
Q <- diag(1, p) - tcrossprod(V, V)
stopifnot(
all.equal(Q, nullProj.c(V))
)
microbenchmark(
nullProj = diag(1, p) - tcrossprod(V, V),
nullProj.c = nullProj.c(V)
)
# ## WIP for gradient. ----------------------------------------------------------
gradient.c <- function(X, X_diff, Y, V, h) {
stopifnot(
is.matrix(X), is.double(X),
is.matrix(X_diff), is.double(X_diff),
ncol(X_diff) == ncol(X), nrow(X_diff) == nrow(X) * (nrow(X) - 1) / 2,
is.vector(Y) || (is.matrix(Y) && pmin(dim(Y)) == 1L), is.double(Y),
length(Y) == nrow(X),
is.matrix(V), is.double(V),
nrow(V) == ncol(X),
is.vector(h), is.numeric(h), length(h) == 1
)
.Call('R_gradient', PACKAGE = 'wip',
X, X_diff, as.double(Y), V, as.double(h));
}
elem.pairs <- function(elements) {
# Number of elements to match.
n <- length(elements)
# Create all combinations.
pairs <- rbind(rep(elements, each=n), rep(elements, n))
# Select unique combinations without self interaction.
return(pairs[, pairs[1, ] < pairs[2, ]])
}
grad <- function(X, Y, V, h, persistent = TRUE) {
n <- nrow(X)
p <- ncol(X)
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)
# Weight matrix `W` (dnorm ... gaussean density function)
W <- matrix(1, n, n) # `exp(0) == 1`
W[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part
W[upper] <- t.default(W)[upper] # Mirror lower tri. to upper
W <- sweep(W, 2, colSums(W), FUN = `/`) # Col-Normalize
# Weighted `Y` momentums
y1 <- Y %*% W # Result is 1D -> transposition irrelevant
y2 <- Y^2 %*% W
# Per example loss `L(V, X_i)`
L <- y2 - y1^2
# Vectorized Weights with forced symmetry
vecS <- (L[i] - (Y[j] - y1[i])^2) * W[lower]
vecS <- vecS + ((L[j] - (Y[i] - y1[j])^2) * W[upper])
# Compute scaling of `X` row differences
vecS <- vecS * vecD
G <- crossprod(X_diff, X_diff * vecS) %*% V
G <- (-2 / (n * h^2)) * G
return(G)
}
rStiefl <- function(p, q) {
return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
}
n <- 200
p <- 12
q <- 10
X <- matrix(runif(n * p), n, p)
Y <- runif(n)
V <- rStiefl(p, q)
h <- 0.1
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]
stopifnot(all.equal(
grad(X, Y, V, h),
gradient.c(X, X_diff, Y, V, h)
))
microbenchmark(
grad = grad(X, Y, V, h),
gradient.c = gradient.c(X, X_diff, Y, V, h)
)

421
wip.c Normal file
View File

@ -0,0 +1,421 @@
#include <stdlib.h>
#include <R_ext/BLAS.h>
#include <R_ext/Lapack.h>
#include <R_ext/Error.h>
// #include <Rmath.h>
#include "wip.h"
static inline void rowSums(const double *A,
const int nrow, const int ncol,
double *sum) {
int i, j, block_size, block_size_i;
const double *A_block = A;
const double *A_end = A + nrow * ncol;
if (nrow > CVE_MEM_CHUNK_SIZE) {
block_size = CVE_MEM_CHUNK_SIZE;
} else {
block_size = nrow;
}
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Reset `A` to new block beginning.
A = A_block;
// Take block size of eveything left and reduce to max size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Compute first blocks column,
for (j = 0; j < block_size_i; ++j) {
sum[j] = A[j];
}
// and sum the following columns to the first one.
for (A += nrow; A < A_end; A += nrow) {
for (j = 0; j < block_size_i; ++j) {
sum[j] += A[j];
}
}
// Step one block forth.
A_block += block_size_i;
sum += block_size_i;
}
}
static inline void colSums(const double *A,
const int nrow, const int ncol,
double *sum) {
int j;
double *sum_end = sum + ncol;
memset(sum, 0, sizeof(double) * ncol);
for (; sum < sum_end; ++sum) {
for (j = 0; j < nrow; ++j) {
*sum += A[j];
}
A += nrow;
}
}
static inline void rowSquareSums(const double *A,
const int nrow, const int ncol,
double *sum) {
int i, j, block_size, block_size_i;
const double *A_block = A;
const double *A_end = A + nrow * ncol;
if (nrow < CVE_MEM_CHUNK_SIZE) {
block_size = nrow;
} else {
block_size = CVE_MEM_CHUNK_SIZE;
}
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Reset `A` to new block beginning.
A = A_block;
// Take block size of eveything left and reduce to max size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Compute first blocks column,
for (j = 0; j < block_size_i; ++j) {
sum[j] = A[j] * A[j];
}
// and sum the following columns to the first one.
for (A += nrow; A < A_end; A += nrow) {
for (j = 0; j < block_size_i; ++j) {
sum[j] += A[j] * A[j];
}
}
// Step one block forth.
A_block += block_size_i;
sum += block_size_i;
}
}
static inline void rowSumsSymVec(const double *Avec, const int nrow,
const double *diag,
double *sum) {
int i, j;
if (*diag == 0.0) {
memset(sum, 0, nrow * sizeof(double));
} else {
for (i = 0; i < nrow; ++i) {
sum[i] = *diag;
}
}
for (j = 0; j < nrow; ++j) {
for (i = j + 1; i < nrow; ++i, ++Avec) {
sum[j] += *Avec;
sum[i] += *Avec;
}
}
}
/* C[, j] = A[, j] * v for each j = 1 to ncol */
static void rowSweep(const double *A, const int nrow, const int ncol,
const char* op,
const double *v, // vector of length nrow
double *C) {
int i, j, block_size, block_size_i;
const double *A_block = A;
double *C_block = C;
const double *A_end = A + nrow * ncol;
if (nrow > CVE_MEM_CHUNK_SMALL) { // small because 3 vectors in cache
block_size = CVE_MEM_CHUNK_SMALL;
} else {
block_size = nrow;
}
if (*op == '+') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] + v[j]; // FUN = '+'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '-') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] - v[j]; // FUN = '-'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '*') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] * v[j]; // FUN = '*'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else if (*op == '/') {
// Iterate `(block_size_i, ncol)` submatrix blocks.
for (i = 0; i < nrow; i += block_size_i) {
// Set `A` and `C` to block beginning.
A = A_block;
C = C_block;
// Get current block's row size.
block_size_i = nrow - i;
if (block_size_i > block_size) {
block_size_i = block_size;
}
// Perform element wise operation for block.
for (; A < A_end; A += nrow, C += nrow) {
for (j = 0; j < block_size_i; ++j) {
C[j] = A[j] / v[j]; // FUN = '/'
}
}
// Step one block forth.
A_block += block_size_i;
C_block += block_size_i;
v += block_size_i;
}
} else {
error("Got unknown 'op' (opperation) argument.");
}
}
static inline void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C) {
const double one = 1.0;
const double zero = 0.0;
// DGEMM with parameterization:
// C <- A %*% B
F77_NAME(dgemm)("N", "N", &nrowA, &ncolB, &ncolA,
&one, A, &nrowA, B, &nrowB,
&zero, C, &nrowA);
}
static inline void crossprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C) {
const double one = 1.0;
const double zero = 0.0;
// DGEMM with parameterization:
// C <- t(A) %*% B
F77_NAME(dgemm)("T", "N", &ncolA, &ncolB, &nrowA,
&one, A, &nrowA, B, &nrowB,
&zero, C, &ncolA);
}
static inline void nullProj(const double *B, const int nrowB, const int ncolB,
double *Q) {
const double minusOne = -1.0;
const double one = 1.0;
// Initialize as identity matrix.
memset(Q, 0, sizeof(double) * nrowB * nrowB);
double *Q_diag, *Q_end = Q + nrowB * nrowB;
for (Q_diag = Q; Q_diag < Q_end; Q_diag += nrowB + 1) {
*Q_diag = 1.0;
}
// DGEMM with parameterization:
// C <- (-1.0 * B %*% t(B)) + C
F77_NAME(dgemm)("N", "T", &nrowB, &nrowB, &ncolB,
&minusOne, B, &nrowB, B, &nrowB,
&one, Q, &nrowB);
}
static inline void rangePairs(const int from, const int to, int *pairs) {
int i, j;
for (i = from; i < to; ++i) {
for (j = i + 1; j < to; ++j) {
pairs[0] = i;
pairs[1] = j;
pairs += 2;
}
}
}
// A dence skwe-symmetric rank 2 update.
// Perform the update
// C := alpha (A * B^T - B * A^T) + beta C
static void skewSymRank2k(const int nrow, const int ncol,
double alpha, const double *A, const double *B,
double beta,
double *C) {
F77_NAME(dgemm)("N", "T",
&nrow, &nrow, &ncol,
&alpha, A, &nrow, B, &nrow,
&beta, C, &nrow);
alpha *= -1.0;
beta = 1.0;
F77_NAME(dgemm)("N", "T",
&nrow, &nrow, &ncol,
&alpha, B, &nrow, A, &nrow,
&beta, C, &nrow);
}
// TODO: mutch potential for optimization!!!
static inline void weightedYandLoss(const int n,
const double *Y,
const double *vecD,
const double *vecW,
const double *colSums,
double *y1, double *L, double *vecS,
double *const loss) {
int i, j, k, N = n * (n - 1) / 2;
double l;
for (i = 0; i < n; ++i) {
y1[i] = Y[i] / colSums[i];
L[i] = Y[i] * Y[i] / colSums[i];
}
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
y1[i] += Y[j] * vecW[k] / colSums[i];
y1[j] += Y[i] * vecW[k] / colSums[j];
L[i] += Y[j] * Y[j] * vecW[k] / colSums[i];
L[j] += Y[i] * Y[i] * vecW[k] / colSums[j];
}
}
l = 0.0;
for (i = 0; i < n; ++i) {
l += (L[i] -= y1[i] * y1[i]);
}
*loss = l / (double)n;
for (k = j = 0; j < n; ++j) {
for (i = j + 1; i < n; ++i, ++k) {
l = Y[j] - y1[i];
vecS[k] = (L[i] - (l * l)) / colSums[i];
l = Y[i] - y1[j];
vecS[k] += (L[j] - (l * l)) / colSums[j];
}
}
for (k = 0; k < N; ++k) {
vecS[k] *= vecW[k] * vecD[k];
}
}
inline double gaussKernel(const double x, const double scale) {
return exp(scale * x * x);
}
static void gradient(const int n, const int p, const int q,
const double *X,
const double *X_diff,
const double *Y,
const double *V,
const double h,
double *G, double *const loss) {
// Number of X_i to X_j not trivial pairs.
int i, N = (n * (n - 1)) / 2;
double scale = -0.5 / h;
const double one = 1.0;
if (X_diff == (void*)0) {
// TODO: ...
}
// Allocate and compute projection matrix `Q = I_p - V * V^T`
double *Q = (double*)malloc(p * p * sizeof(double));
nullProj(V, p, q, Q);
// allocate and compute vectorized distance matrix with a temporary
// projection of `X_diff`.
double *vecD = (double*)malloc(N * sizeof(double));
double *X_proj;
if (p < 5) { // TODO: refine that!
X_proj = (double*)malloc(N * 5 * sizeof(double));
} else {
X_proj = (double*)malloc(N * p * sizeof(double));
}
matrixprod(X_diff, N, p, Q, p, p, X_proj);
rowSquareSums(X_proj, N, p, vecD);
// Apply kernel to distence vector for weights computation.
double *vecW = X_proj; // reuse memory area, no longer needed.
for (i = 0; i < N; ++i) {
vecW[i] = gaussKernel(vecD[i], scale);
}
double *colSums = X_proj + N; // still allocated!
rowSumsSymVec(vecW, n, &one, colSums); // rowSums = colSums cause Sym
// compute weighted responces of first end second momontum, aka y1, y2.
double *y1 = X_proj + N + n;
double *L = X_proj + N + (2 * n);
// Allocate X_diff scaling vector `vecS`, not in `X_proj` mem area because
// used symultanious to X_proj in final gradient computation.
double *vecS = (double*)malloc(N * sizeof(double));
weightedYandLoss(n, Y, vecD, vecW, colSums, y1, L, vecS, loss);
// compute the gradient using X_proj for intermidiate scaled X_diff.
rowSweep(X_diff, N, p, "*", vecS, X_proj);
// reuse Q which has the required dim (p, p).
crossprod(X_diff, N, p, X_proj, N, p, Q);
// Product with V
matrixprod(Q, p, p, V, p, q, G);
// And final scaling (TODO: move into matrixprod!)
scale = -2.0 / (((double)n) * h * h);
N = p * q;
for (i = 0; i < N; ++i) {
G[i] *= scale;
}
free(vecS);
free(X_proj);
free(vecD);
free(Q);
}

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#ifndef _CVE_INCLUDE_GUARD_
#define _CVE_INCLUDE_GUARD_
#include <Rinternals.h>
#define CVE_MEM_CHUNK_SMALL 1016
#define CVE_MEM_CHUNK_SIZE 2032
static inline void rowSums(const double *A,
const int nrow, const int ncol,
double *sum);
SEXP R_rowSums(SEXP A) {
SEXP sums = PROTECT(allocVector(REALSXP, nrows(A)));
rowSums(REAL(A), nrows(A), ncols(A), REAL(sums));
UNPROTECT(1);
return sums;
}
static inline void colSums(const double *A,
const int nrow, const int ncol,
double *sum);
SEXP R_colSums(SEXP A) {
SEXP sums = PROTECT(allocVector(REALSXP, ncols(A)));
colSums(REAL(A), nrows(A), ncols(A), REAL(sums));
UNPROTECT(1);
return sums;
}
static inline void rowSquareSums(const double*, const int, const int, double*);
SEXP R_rowSquareSums(SEXP A) {
SEXP result = PROTECT(allocVector(REALSXP, nrows(A)));
rowSquareSums(REAL(A), nrows(A), ncols(A), REAL(result));
UNPROTECT(1);
return result;
}
static inline void rowSumsSymVec(const double *Avec, const int nrow,
const double *diag,
double *sum);
SEXP R_rowSumsSymVec(SEXP Avec, SEXP nrow, SEXP diag) {
SEXP sum = PROTECT(allocVector(REALSXP, *INTEGER(nrow)));
rowSumsSymVec(REAL(Avec), *INTEGER(nrow), REAL(diag), REAL(sum));
UNPROTECT(1);
return sum;
}
static void rowSweep(const double *A, const int nrow, const int ncol,
const char* op,
const double *v, // vector of length nrow
double *C);
SEXP R_rowSweep(SEXP A, SEXP v, SEXP op) {
SEXP C = PROTECT(allocMatrix(REALSXP, nrows(A), ncols(A)));
rowSweep(REAL(A), nrows(A), ncols(A),
CHAR(STRING_ELT(op, 0)),
REAL(v), REAL(C));
UNPROTECT(1);
return C;
}
static inline void matrixprod(const double *A, const int nrowA, const int ncolA,
const double *B, const int nrowB, const int ncolB,
double *C);
SEXP R_matrixprod(SEXP A, SEXP B) {
SEXP C = PROTECT(allocMatrix(REALSXP, nrows(A), ncols(B)));
matrixprod(REAL(A), nrows(A), ncols(A),
REAL(B), nrows(B), ncols(B),
REAL(C));
UNPROTECT(1);
return C;
}
static inline void crossprod(const double* A, const int nrowA, const int ncolA,
const double* B, const int ncolB, const int nrowB,
double* C);
SEXP R_crossprod(SEXP A, SEXP B) {
SEXP C = PROTECT(allocMatrix(REALSXP, ncols(A), ncols(B)));
crossprod(REAL(A), nrows(A), ncols(A),
REAL(B), nrows(B), ncols(B),
REAL(C));
UNPROTECT(1);
return C;
}
static void skewSymRank2k(const int n, const int k,
double alpha, const double *A, const double *B,
double beta,
double *C);
SEXP R_skewSymRank2k(SEXP A, SEXP B, SEXP alpha, SEXP beta) {
SEXP C = PROTECT(allocMatrix(REALSXP, nrows(A), nrows(A)));
memset(REAL(C), 0, nrows(A) * nrows(A) * sizeof(double));
skewSymRank2k(nrows(A), ncols(A),
*REAL(alpha), REAL(A), REAL(B),
*REAL(beta), REAL(C));
UNPROTECT(1);
return C;
}
static inline void nullProj(const double* B, const int nrowB, const int ncolB,
double* Q);
SEXP R_nullProj(SEXP B) {
SEXP Q = PROTECT(allocMatrix(REALSXP, nrows(B), nrows(B)));
nullProj(REAL(B), nrows(B), ncols(B), REAL(Q));
UNPROTECT(1);
return Q;
}
static inline void rangePairs(const int from, const int to, int *pairs);
SEXP R_rangePairs(SEXP from, SEXP to) {
int start = asInteger(from);
int end = asInteger(to) + 1;
int n = end - start;
SEXP out = PROTECT(allocMatrix(INTSXP, 2, n * (n - 1) / 2));
rangePairs(start, end, INTEGER(out));
UNPROTECT(1);
return out;
}
static void gradient(const int n, const int p, const int q,
const double *X,
const double *X_diff,
const double *Y,
const double *V,
const double h,
double *G, double *const loss);
SEXP R_gradient(SEXP X, SEXP X_diff, SEXP Y, SEXP V, SEXP h) {
int N = (nrows(X) * (nrows(X) - 1)) / 2;
SEXP G = PROTECT(allocMatrix(REALSXP, nrows(V), ncols(V)));
SEXP loss = PROTECT(allocVector(REALSXP, 1));
gradient(nrows(X), ncols(X), ncols(V),
REAL(X), REAL(X_diff), REAL(Y), REAL(V), *REAL(h),
REAL(G), REAL(loss));
UNPROTECT(2);
return G;
}
#endif /* _CVE_INCLUDE_GUARD_ */