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')