data-raw/DATASET.R

In MikeJaredS/hermiter: Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric Correlation (Bivariate)

# Matrix \eqn{W_{kl} = \int_{-\infty}^{\infty} h_k(u) \int_{-\infty}^{u} 
# h_l(v)dvdu}
W_matrix <- function(num_r,num_s, hermite_norm){
  integrand <- function(x,r,s, hermite_norm){
    hermite_vec <- hermite_function_N(r,x)
    hermite_integral_vec <- hermite_int_lower(s,x)
    result <- hermite_integral_vec[s+1,]*hermite_vec[r+1,]
    return(result)
  }
  result <- matrix(rep(0,(num_r+1)*(num_s+1)), nrow=(num_r+1),ncol=(num_s+1),
                   byrow = TRUE)
  for (r in c(0:num_r)) {
    for (s in c(0:num_s)) {
      result[r+1,s+1] <- stats::integrate(function(t){integrand(t,r,s)},
                                          lower=-Inf,upper=Inf)$value
    }
  }
  return(result)
}

# Vector \eqn{z_{k} = \int_{-\infty}^{\infty} h_k(u)du}
z_vector <- function(num_r){
  result <- hermite_int_full(num_r)
  return(result)
}

h_norm_serialized <-
  hermite_normalization_N(N=75)
W_serialized <- W_matrix(75,75)
z_serialized <- z_vector(75)

h_k_mat <-
  hermite_function_N(N=75, x=0)
h_int_lower_zero_serialized <-  hermite_int_lower(N=75,x=0,
                                                hermite_function_matrix=h_k_mat)
h_int_upper_zero_serialized <- hermite_int_upper(N=75,x=0,
                                                hermite_function_matrix=h_k_mat)

x_lower_serialized <- seq(-10,-6.05,by=0.05)
x_lower_serialized <- c(x_lower_serialized,seq(-6,-0.01,by=0.01))

x_upper_serialized <- seq(0,6,by=0.01)
x_upper_serialized <- c(x_upper_serialized, seq(6.05,10,by=0.05))

x_full_domain_serialized <- c(x_lower_serialized,x_upper_serialized)
h_int_lower_serialized <- hermite_int_lower(N=75,x_lower_serialized)
h_int_upper_serialized <- hermite_int_upper(N=75,x_upper_serialized)
h_int_full_domain_serialized <- cbind(h_int_lower_serialized, 
                                      h_int_upper_serialized)

shift_pvec <- c(rep(0,680), rep(1,681))
scale_pvec <- c(rep(1,680), rep(-1,681))

root_x_serialized <-  c(
  -13.4064873381449,
  -12.8237997494878,
  -12.3429642228597,
  -11.9150619431142,
  -11.521415400787,
  -11.1524043855851,
  -10.8022607536847,
  -10.4671854213428,
  -10.1445099412928,
  -9.83226980777796,
  -9.52896582339012,
  -9.23342089021917,
  -8.94468921732548,
  -8.66199616813451,
  -8.38469694041626,
  -8.11224731116279,
  -7.84418238446082,
  -7.58010080785749,
  -7.31965282230454,
  -7.06253106024887,
  -6.8084633528588,
  -6.55720703192154,
  -6.30854436111214,
  -6.0622788326143,
  -5.81823213520351,
  -5.57624164932992,
  -5.33615836013836,
  -5.09784510508913,
  -4.86117509179121,
  -4.62603063578716,
  -4.39230207868268,
  -4.15988685513103,
  -3.92868868342767,
  -3.69861685931849,
  -3.46958563641859,
  -3.24151367963101,
  -3.01432358033116,
  -2.78794142398199,
  -2.56229640237261,
  -2.33732046390688,
  -2.11294799637119,
  -1.88911553742701,
  -1.66576150874151,
  -1.44282597021593,
  -1.22025039121895,
  -0.997977436098105,
  -0.775950761540146,
  -0.554114823591617,
  -0.332414692342232,
  -0.11079587242244,
  0.110795872422439,
  0.332414692342232,
  0.554114823591617,
  0.775950761540147,
  0.997977436098105,
  1.22025039121895,
  1.44282597021593,
  1.66576150874151,
  1.88911553742701,
  2.11294799637119,
  2.33732046390688,
  2.56229640237261,
  2.78794142398199,
  3.01432358033115,
  3.24151367963101,
  3.46958563641859,
  3.69861685931849,
  3.92868868342767,
  4.15988685513102,
  4.39230207868269,
  4.62603063578715,
  4.86117509179121,
  5.09784510508914,
  5.33615836013836,
  5.57624164932992,
  5.81823213520351,
  6.06227883261431,
  6.30854436111214,
  6.55720703192154,
  6.8084633528588,
  7.06253106024887,
  7.31965282230454,
  7.58010080785748,
  7.84418238446082,
  8.1122473111628,
  8.38469694041626,
  8.66199616813452,
  8.94468921732548,
  9.23342089021917,
  9.52896582339011,
  9.83226980777798,
  10.1445099412928,
  10.4671854213428,
  10.8022607536847,
  11.1524043855851,
  11.521415400787,
  11.9150619431142,
  12.3429642228597,
  12.8237997494878,
  13.4064873381449)

weight_w_serialized <-
  c(
    5.90806786503136e-79,
    1.97286057487966e-72,
    3.08302899000352e-67,
    9.01922230369306e-63,
    8.5188830817621e-59,
    3.45947793647628e-55,
    7.19152946346327e-52,
    8.5975639548245e-49,
    6.42072520534952e-46,
    3.18521787783607e-43,
    1.10047068271427e-40,
    2.74878488435702e-38,
    5.11623260438513e-36,
    7.27457259688755e-34,
    8.06743427870996e-32,
    7.10181222638551e-30,
    5.03779116621317e-28,
    2.91735007262933e-26,
    1.3948415260688e-24,
    5.56102696165903e-23,
    1.86499767513031e-21,
    5.30231618313183e-20,
    1.28683292112102e-18,
    2.68249216476029e-17,
    4.82983532170321e-16,
    7.54889687791516e-15,
    1.02887493735095e-13,
    1.22787851441014e-12,
    1.2879038257316e-11,
    1.19130063492909e-10,
    9.74792125387198e-10,
    7.07585728388953e-09,
    4.56812750848495e-08,
    2.62909748375378e-07,
    1.35179715911035e-06,
    6.22152481777787e-06,
    2.56761593845493e-05,
    9.51716277855104e-05,
    0.000317291971043298,
    0.000952692188548627,
    0.00257927326005911,
    0.00630300028560803,
    0.0139156652202319,
    0.0277791273859335,
    0.0501758126774286,
    0.0820518273912242,
    0.121537986844104,
    0.163130030502783,
    0.198462850254186,
    0.218892629587438,
    0.21889262958744,
    0.198462850254186,
    0.163130030502783,
    0.121537986844105,
    0.0820518273912245,
    0.0501758126774285,
    0.0277791273859335,
    0.0139156652202319,
    0.00630300028560803,
    0.0025792732600591,
    0.000952692188548612,
    0.000317291971043307,
    9.51716277855083e-05,
    2.56761593845492e-05,
    6.22152481777791e-06,
    1.35179715911039e-06,
    2.62909748375372e-07,
    4.56812750848485e-08,
    7.07585728388976e-09,
    9.74792125387174e-10,
    1.19130063492908e-10,
    1.28790382573152e-11,
    1.22787851441009e-12,
    1.02887493735099e-13,
    7.54889687791549e-15,
    4.82983532170316e-16,
    2.68249216476006e-17,
    1.28683292112115e-18,
    5.30231618313228e-20,
    1.8649976751302e-21,
    5.56102696165923e-23,
    1.3948415260688e-24,
    2.9173500726293e-26,
    5.03779116621325e-28,
    7.10181222638503e-30,
    8.06743427870959e-32,
    7.27457259688751e-34,
    5.11623260438556e-36,
    2.74878488435699e-38,
    1.10047068271428e-40,
    3.18521787783571e-43,
    6.42072520534916e-46,
    8.59756395482604e-49,
    7.19152946346429e-52,
    3.45947793647629e-55,
    8.51888308176195e-59,
    9.0192223036942e-63,
    3.0830289900037e-67,
    1.9728605748794e-72,
    5.90806786503142e-79
  )

save(h_norm_serialized,W_serialized,z_serialized,
     root_x_serialized,weight_w_serialized, 
     h_int_lower_zero_serialized,
     h_int_upper_zero_serialized,
     h_int_lower_serialized, 
     h_int_upper_serialized,
     h_int_full_domain_serialized,
     x_full_domain_serialized,
     shift_pvec,
     scale_pvec,
     file = "sysdata.rda",compress="xz")