## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 4
)

## ----setup--------------------------------------------------------------------
library(rLifting)

if (!requireNamespace("ggplot2", quietly = TRUE)) {
  knitr::opts_chunk$set(eval = FALSE)
  message("'ggplot2' is required to render plots. Vignette code will not run.")
} else {
  library(ggplot2)
}

data("benchmark_rlifting_irregular", package = "rLifting")
set.seed(20260605)

## ----api, eval = FALSE--------------------------------------------------------
# # Offline and causal accept t as a vector parallel to the signal.
# denoise_signal_offline(x, scheme, t = t_phys)
# denoise_signal_causal(x, scheme, t = t_phys, window_size = 255)
# 
# # Stream creates the processor with irregular = TRUE,
# # then accepts t_val per sample.
# stream = new_wavelet_stream(scheme, irregular = TRUE, window_size = 255)
# for (i in seq_along(x)) y[i] = stream(x[i], t_val = t_phys[i])
# 
# # Step-by-step lwt() also accepts t; the returned `lwt` object
# # carries it forward to ilwt() automatically.
# lwt_obj = lwt(x, scheme, t = t_phys)
# x_back  = ilwt(lwt_obj)

## ----eval = FALSE-------------------------------------------------------------
# denoise_signal_offline(
#   x, lifting_scheme("cdf53"), t = t_phys,
#   extension = "local_linear",
#   threshold_method = "sure",
#   shrinkage = "scad"
# )

## ----eval = FALSE-------------------------------------------------------------
# tuned = tune_alpha_beta(x_slice, lifting_scheme("haar"), levels = 4)
# 
# denoise_signal_causal(
#   x, lifting_scheme("haar"), t = t_phys,
#   window_size = 255,
#   extension = "zero",
#   threshold_method = "universal",
#   shrinkage = "scad",
#   alpha = tuned$alpha,
#   beta = tuned$beta
# )

## ----off-penalty--------------------------------------------------------------
df = benchmark_rlifting_irregular
off = df[df$Mode == "offline" & !is.na(df$MSEpos_median), ]

robust_off = off[
  off$Wavelet == "cdf53" & 
    off$Boundary == "local_linear" &
    off$Method == "sure_scad",
  c("Signal", "MSEpos_median")
]
names(robust_off)[2] = "robust_MSE"

best_off = do.call(
  rbind, 
  by(
    off, off$Signal, function(s) {
      i = which.min(s$MSEpos_median)
      data.frame(
        Signal = s$Signal[i],
        best_MSE = s$MSEpos_median[i],
        best_config = paste(
          s$Wavelet[i], s$Boundary[i],
          s$Method[i], sep = "/"
        )
      )
    }
  )
)

cmp_off = merge(robust_off, best_off, by = "Signal")
cmp_off$penalty = round(cmp_off$robust_MSE / cmp_off$best_MSE, 2)
cmp_off$robust_MSE = round(cmp_off$robust_MSE, 4)
cmp_off$best_MSE = round(cmp_off$best_MSE, 4)
knitr::kable(
  cmp_off[
    , 
    c(
      "Signal", "robust_MSE", "best_MSE",
      "penalty", "best_config"
    )
  ],
  row.names = FALSE,
  caption = "Offline robust default (cdf53 / local_linear / sure_scad) vs per-signal best."
)

## ----cs-penalty---------------------------------------------------------------
cs = df[df$Mode == "causal" & !is.na(df$MSEpos_median), ]
robust_cs = cs[
  cs$Wavelet == "haar" & cs$Boundary == "zero" &
    cs$Method == "universal_tuned_scad",
  c("Signal", "MSEpos_median")
]

names(robust_cs)[2] = "robust_MSE"

best_cs = do.call(
  rbind, 
  by(
    cs, cs$Signal, function(s) {
      i = which.min(s$MSEpos_median)
      data.frame(
        Signal = s$Signal[i],
        best_MSE = s$MSEpos_median[i],
        best_config = paste(s$Wavelet[i], s$Boundary[i], s$Method[i], sep = "/")
      )
    }
  )
)

cmp_cs = merge(robust_cs, best_cs, by = "Signal")
cmp_cs$penalty = round(cmp_cs$robust_MSE / cmp_cs$best_MSE, 2)
cmp_cs$robust_MSE = round(cmp_cs$robust_MSE, 4)
cmp_cs$best_MSE = round(cmp_cs$best_MSE, 4)
knitr::kable(
  cmp_cs[
    , 
    c(
      "Signal", "robust_MSE", "best_MSE",
      "penalty", "best_config"
    )
  ],
  row.names = FALSE,
  caption = "Causal robust default (haar / zero / universal_tuned_scad) vs per-signal best."
)

## ----pos-fix------------------------------------------------------------------
robust_off_pf = off[
  off$Wavelet == "cdf53" & 
    off$Boundary == "local_linear" &
    off$Method == "sure_scad",
  c("Signal", "MSEpos_median", "MSEfix_median")
]

robust_off_pf$ratio = round(
  robust_off_pf$MSEpos_median / robust_off_pf$MSEfix_median, 2
)

robust_off_pf$MSEpos = round(robust_off_pf$MSEpos_median, 4)
robust_off_pf$MSEfix = round(robust_off_pf$MSEfix_median, 4)

knitr::kable(
  robust_off_pf[, c("Signal", "MSEpos", "MSEfix", "ratio")],
  row.names = FALSE,
  caption = "Robust default: position-aware vs uniform-grid baseline, offline mode."
)

## ----worked-example, fig.cap = "Top: noisy Doppler signal on a log-normal-spaced grid (CV approx 0.3). Bottom: offline denoising with the §5 robust default versus the uniform-grid baseline (t ignored).", fig.height = 6----
n = 512
dt = exp(rnorm(n, sd = 0.3))
dt = dt / mean(dt)
t_phys = cumsum(dt)
t_phys = t_phys / max(t_phys)

doppler = function(t) sqrt(t * (1 - t)) * sin(2 * pi * 1.05 / (t + 0.05))
clean = doppler(t_phys)
noisy = clean + rnorm(n, sd = 0.15)

scheme = lifting_scheme("cdf53")

# Baseline: ignore t.
y_fix = denoise_signal_offline(
  noisy, scheme, levels = 4,
  threshold_method = "sure", shrinkage = "scad",
  extension = "local_linear"
)

# Robust default: pass t = t_phys.
y_pos = denoise_signal_offline(
  noisy, scheme, t = t_phys, levels = 4,
  threshold_method = "sure", shrinkage = "scad",
  extension = "local_linear"
)

dat = data.frame(
  t = rep(t_phys, 3),
  y = c(noisy, y_fix, y_pos),
  series = factor(
    rep(
      c(
        "noisy", "uniform-grid baseline (t ignored)",
        "robust default with t = t_phys"
      ), 
      each = n
    ),
    levels = c(
      "noisy", "uniform-grid baseline (t ignored)",
      "robust default with t = t_phys"
    )
  )
)

ggplot(dat, aes(x = t, y = y)) +
  geom_line(linewidth = 0.4) +
  facet_wrap(~ series, ncol = 1, scales = "free_y") +
  labs(x = "physical time t", y = NULL) +
  theme_minimal(base_size = 10)

mse = function(a, b) mean((a - b) ^ 2)
mses = data.frame(
  strategy = c(
    "uniform-grid baseline (t ignored)",
    "robust default with t = t_phys"
  ),
  MSE = round(c(mse(clean, y_fix), mse(clean, y_pos)), 4)
)

knitr::kable(
  mses, row.names = FALSE,
  caption = "MSE against the clean signal on this realisation."
)