test_that("test_alpha", {





  scores_mat <- matrix(c(
    NaN, 1, 0, 0,
    0, 0, 0, 0,
    NaN, 0, 0, 0,
    2, 0, 0, 1,
    NaN, 0, 0, 0,
    0, 0, 0, 0,
    NaN, 0, 0, 0,
    1, 0, 0, 0,
    NaN, 0, 0, 0,
    0, 0, 1, 2,
    NaN, 0, 0, 0,
    0, 0, 0, 0,
    NaN, 1, 0, 0,
    0, 0, 0, 1,
    NaN, 1, 0, 0,
    0, 0, 0, 1,
    NaN, 0, 1, 0,
    0, 0, 1, 0,
    NaN, 1, 0, 1,
    0, 0, 0, 0,
    1, 1, 1, 0,
    0, 1, 0, 0,
    1, 1, 2, 0,
    1, 0, 2, 0,
    0, 0, 2, 1,
    0, 0, 0, 0,
    1, 1, 0, 2,
    0, 1, 0, 0,
    0, 0, 1, 1,
    1, 2, 0, 0,
    0, 0, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 0,
    1, 0, 0, 0,
    1, 2, 2, 1,
    0, 0, 0, 0,
    0, 0, 0, 0,
    1, 0, 0, 1,
    0, 0, 0, 0,
    2, 1, 2, 0,
    1, 1, 0, 1,
    0, 0, 0, 0,
    1, 0, 0, 0,
    0, 0, 1, 0,
    0, 1, 0, 0,
    1, 1, 0, 1,
    0, 1, 1, 0,
    0, 0, 0, 0,
    1, 0, 1, 1,
    1, 0, 1, 1
  ), nrow = 50, ncol = 4, byrow = TRUE)

  unknown_info = unknown_loc(scores_mat)

  unknown_value <- c(3, 3, 4, 4, 1, 4, 2, 0, 1, 0)


  generate_scores_mat_bernoulli(50, 10, 20, 2)



  # Assigning the values to variables in R
  n <- 10
  A <- matrix(c(
    -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004, -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004, -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004, -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004, -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004,  0.0004, -0.0196,  0.0004,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004, -0.0196,  0.0004,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004, -0.0196,  0.0004,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004, -0.0196,  0.0004,
    0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004,  0.0004, -0.0196
  ), nrow = 10, byrow = TRUE)

  b <- c(0.00553469, -0.01528163, -0.01528163, -0.01528163, -0.01528163,
         -0.01528163, 0.00553469, 0.00553469, 0.00553469, 0.02635102)

  c <- -0.2378938775510202
  x_max <- 4
  # Call the qp_solver function in R
  result <- qp_solver(n, A, b, c, x_max)





  # Input Data
  alpha <- 0.5
  n_person <- 50

  # sigma_x_info
  A_mat_x <- matrix(c(
    # First row
    0.04,        -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Second row
    -0.00081633,  0.04,       -0.00081633, -0.00081633, -0.00081633,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Third row
    -0.00081633, -0.00081633,  0.04,       -0.00081633, -0.00081633,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Fourth row
    -0.00081633, -0.00081633, -0.00081633,  0.04,       -0.00081633,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Fifth row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Sixth row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    0.04,       -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    # Seventh row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    -0.00081633,  0.04,       -0.00081633, -0.00081633, -0.00081633,
    # Eighth row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    -0.00081633, -0.00081633,  0.04,       -0.00081633, -0.00081633,
    # Ninth row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    -0.00081633, -0.00081633, -0.00081633,  0.04,       -0.00081633,
    # Tenth row
    -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
    -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04
  ), nrow = 10, byrow = TRUE)

  b_array_x <- rep(-0.01469388, 10)

  c_scaler_x <- 1.3861224489795916

  sigma_x_info <- list(A_mat_x, b_array_x, c_scaler_x)

  # sigma_y_info
  A_mat_y <- A_mat_x  # Same as A_mat_x in this case

  b_array_y <- c(
    -0.01795918, -0.05877551, -0.05877551, -0.05877551, -0.05877551,
    -0.05877551, -0.01795918, -0.01795918, -0.01795918, 0.02285714
  )

  c_scaler_y <- 2.2514285714285713

  sigma_y_info <- list(A_mat_y, b_array_y, c_scaler_y)

  alpha_type <- 'min'
  score_max <- 4
  num_try <- 1

  # Run the examine_alpha_bound function
  result <- examine_alpha_bound(
    alpha = alpha,
    n_person = n_person,
    sigma_x_info = sigma_x_info,
    sigma_y_info = sigma_y_info,
    alpha_type = alpha_type,
    score_max = score_max,
    num_try = num_try
  )




  # Define the parameters
  n_person <- 50

  sigma_x_info <- list(
    matrix(c(
      0.04      , -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633,  0.04      , -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633,  0.04      , -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633,  0.04      , -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04
    ), nrow = 10, byrow = TRUE),
    c(-0.01469388, -0.01469388, -0.01469388, -0.01469388, -0.01469388,
      -0.01469388, -0.01469388, -0.01469388, -0.01469388, -0.01469388),
    1.3861224489795916
  )

  sigma_y_info <- list(
    matrix(c(
      0.04      , -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633,  0.04      , -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633,  0.04      , -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633,  0.04      , -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04      ,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633, -0.00081633,
      -0.00081633, -0.00081633, -0.00081633, -0.00081633,  0.04
    ), nrow = 10, byrow = TRUE),
    c(-0.01795918, -0.05877551, -0.05877551, -0.05877551, -0.05877551,
      -0.05877551, -0.01795918, -0.01795918, -0.01795918,  0.02285714),
    2.2514285714285713
  )

  score_max <- 4
  alpha_lb <- 0.0
  alpha_ub <- 1.0
  tol <- 0.001
  num_try <- 1

  result <- compute_alpha_min(
    n_person,
    sigma_x_info,
    sigma_y_info,
    score_max = score_max,
    alpha_lb = alpha_lb,
    alpha_ub = alpha_ub,
    tol = tol,
    num_try = num_try
  )


  result <- compute_alpha_max(
    n_person,
    sigma_x_info,
    sigma_y_info,
    score_max = score_max,
    alpha_lb = alpha_lb,
    alpha_ub = alpha_ub,
    tol = tol,
    num_try = num_try
  )





  score_max = 2
  scores_mat_bernoulli = generate_scores_mat_bernoulli(
    50, 10, 20, score_max
  )
  result = cronbachs_alpha(
    scores_mat_bernoulli, score_max, enum_all = FALSE
  )
  scores_df <- missalpha::sample
  scores_mat <- as.matrix(scores_df)
  result <- cronbachs_alpha(scores_mat, 4, enum_all = FALSE)
  summary(result)
  print(result$alpha_min_opt)
  print(result$alpha_max_opt)

  all_result = display_all(scores_mat = scores_mat,score_max = 2)
  summary(all_result)
})