# library(CVEpureR)
# path <- '~/Projects/CVE/tmp/logger.R.pdf'

library(CVE)
path <- '~/Projects/CVE/tmp/seeded_test.pdf'

epochs <- 100
attempts <- 25

# 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
}

pdf(path)
par(mfrow = c(2, 2))

for (name in paste0("M", seq(5))) {
    # Seed random number generator
    set.seed(42)

    # Create a dataset
    ds <- dataset(name)
    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)

    # Setup histories.
    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)

    dr <- cve(Y ~ X, k = k, logger = logger, epochs = epochs, attempts = attempts)

    # Plot history's
    matplot(loss.history,       type = 'l', log = 'y', xlab = 'i (iteration)',
        main = paste('loss', name),
        ylab = expression(L(V[i])))
    matplot(true.error.history, type = 'l', log = 'y', xlab = 'i (iteration)',
        main = paste('true error', name),
        ylab = expression(group('|', B * B^T - B[i] * B[i]^T, '|')[F] / sqrt(2 * k)))
    matplot(error.history,      type = 'l', log = 'y', xlab = 'i (iteration)',
        main = paste('error', name),
        ylab = expression(group('|', V[i-1] * V[i-1]^T - V[i] * V[i]^T, '|')[F]))
    matplot(tau.history,        type = 'l', log = 'y', xlab = 'i (iteration)',
        main = paste('learning rate', name),
        ylab = expression(tau[i]))
}