library(tensorPredictors)

setwd("~/Work/tensorPredictors/sim/")
base.name <- format(Sys.time(), "sim_tsir-%Y%m%dT%H%M")

# Source utility function used in most simulations (extracted for convenience)
source("./sim_utils.R")

# Set PRNG seed for reproducability
# Sequence 'T', 'S', 'I', 'R' in ASCII is 84, 83, 73, 82.
set.seed(84837382L, "Mersenne-Twister", "Inversion", "Rejection")

### Simulation configuration
reps <- 100                     # number of simulation replications
sample.sizes <- c(100, 200, 300, 500, 750)  # sample sizes `n`
signal.noise.ratios <- 2^(-3:4) # Signal to Noise Ratios (from 50/50 to very high)
dimX <- c(2, 3, 5)              # predictor `X` dimension
dimF <- rep(2, length(dimX))    # "function" `F(y)` of responce `y` dimension

# setup true model parameters
eta1 <- 0
# rank 1 betas
betas <- Map(function(nr, nc) {
    tcrossprod((-1)^seq_len(nr), (-1)^seq_len(nc))
}, dimX, dimF)
# True (minimal) reduction matrix
B.true <- Reduce(kronecker, rev(betas))[, 1L, drop = FALSE]
# GMLM second moment parameters (mode-wise precition matrices)
Omegas <- Map(function(pj) 0.5^abs(outer(1:pj, 1:pj, `-`)), dimX)   # AR(0.5)
# True (minimal) Gamma (Projection Direction)
Gamma.true <- Reduce(kronecker, rev(Map(solve, Omegas, betas)))[, 1L, drop = FALSE]
# true (full) covariance matrix
covX.true <- Reduce(kronecker, rev(Map(solve, Omegas)))

# define projections onto rank 1 matrices for betas
proj.betas <- Map(.projRank, rep(1L, length(betas)))

# data sampling routine
sample.data <- function(sample.size, eta1, betas, Omegas, snr) {
    # responce is a standard normal variable
    y <- rnorm(sample.size)
    # F(y) is a tensor of monomials
    y.pow <- Reduce(function(a, b) outer(a, b, `+`), Map(seq, 0L, len = dimF))
    F <- t(outer(y, as.vector(y.pow), `^`))
    dim(F) <- c(dimF, sample.size)

    # sample predictors from tensor normal X | Y = y (last axis is sample axis)
    sample.axis <- length(betas) + 1L
    Deltas <- Map(solve, Omegas)                                    # normal covariances
    mu_y <- mlm(mlm(F, betas) + as.vector(eta1), Deltas)            # conditional mean
    noise <- rtensornorm(sample.size, 0, Deltas, sample.axis)       # error term
    # scale noise to given signal to noise ratio
    snr.est <- sd(mu_y) / sd(noise)
    noise <- (snr.est / snr) * noise
    X <- mu_y + noise                                               # responses X

    list(X = X, F = F, y = y, sample.axis = sample.axis)
}

# Create a CSV logger to save simulation results
log.file <- paste(base.name, "csv", sep = ".")
logger <- CSV.logger(
    file.name = log.file,
    header = c(
        "snr", "sample.size", "rep",
        "dist.subspace.gmlm", "dist.subspace.tsir", "dist.subspace.partial", "dist.subspace.gamma"
    )
)

# different Signal to Noise Ratios
for (snr in signal.noise.ratios) {

    # simulation for multiple data set sizes
    for (sample.size in sample.sizes) {

        # simulation replications
        for (rep in seq_len(reps)) {

            # sample a data set
            c(X, F, y, sample.axis) %<-% sample.data(sample.size, eta1, betas, Omegas, snr)

            # call GMLM and TSIR
            fit.gmlm <- gmlm_tensor_normal(X, F, sample.axis = sample.axis, proj.betas = proj.betas)
            fit.tsir <- TSIR(X, y, c(1L, 1L, 1L), sample.axis = sample.axis)

            # GMLM, TSIR reduction estimates and TSIR (internal) projections
            B.gmlm <- Reduce(kronecker, Map(function(beta) qr.Q(qr(beta))[, 1L, drop = FALSE], rev(fit.gmlm$betas)))
            B.tsir <- Reduce(kronecker, rev(fit.tsir))
            Gamma <- Reduce(kronecker, rev(attr(fit.tsir, "Gammas")))

            # Subspace distances to true minimal reduction
            dist.subspace.gmlm    <- dist.subspace(B.true, B.gmlm, normalize = TRUE)
            dist.subspace.tsir    <- dist.subspace(B.true, B.tsir, normalize = TRUE)
            dist.subspace.partial <- dist.subspace(B.true, solve(covX.true, Gamma), normalize = TRUE)
            dist.subspace.gamma   <- dist.subspace(Gamma.true, Gamma, normalize = TRUE)

            # Write to simulation log file (CSV file)
            logger()

            # and print progress
            cat(sprintf("SNR %.2f, sample size %d: rep: %d/%d\n", snr, sample.size, rep, reps))
        }
    }
}


### read simulation results generate plots
if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }

# Read siulation results from log file
sim <- read.csv(log.file)

# reset the correlation configuration parameter
signal.noise.ratios <- sort(unique(sim$snr))

# build plot layout for every `snr` param
ncols <- ceiling(sqrt(length(signal.noise.ratios)))
nrows <- ceiling(length(signal.noise.ratios) / ncols)
par(mfrow = c(nrows, ncols))

# One plot for every Singal to Noise Ratio
for (.snr in signal.noise.ratios) {
    plot.sim(subset(sim, snr == .snr), "dist.subspace",
        main = sprintf("Signal to Noise Ratio: %.3f", .snr), xlab = "Sample Size", ylab = "Subspace Distance",
        cols = c(gmlm = "black", tsir = "#009E73", partial = "orange", gamma = "skyblue")
    )
}