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# HE illustrated primer

# define some parameters (small as an example)
# N.B. these parameters are not secure, they are completely insecure
d =   4
n =   2^d
t =   (n/2)-1
q = 874

# load library to create polynomials

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library(matrixStats)

# Softmax function
softmax <- function(x) {
  exp_x <- exp(x - max(x))
  exp_x / sum(exp_x)
}

# Scaled dot product attention
scaled_dot_product_attention <- function(Q, K, V, mask = NULL) {

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# rnn.R
# Bastiaan Quast
# [email protected]

# Set the seed to obtain identical random values
set.seed(0)

# compute sigmoid nonlinearity
sigmoid = function(x)
  1 / (1+exp(-x))

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# cnn.R
# Bastiaan Quast
# [email protected]

# Convolution function
conv2d <- function(input, filter, stride = 1) {
  input_height <- dim(input)[1]
  input_width <- dim(input)[2]
  filter_height <- dim(filter)[1]
  filter_width <- dim(filter)[2]

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# NN-1-layer.R
# Bastiaan Quast
# [email protected]

# create data
inputs      = matrix(c(0,1,1,
                       1,0,1,
                       1,0,1,
                       1,1,0 ), nrow=4, byrow=TRUE)

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# DNN2.R
# Bastiaan Quast
# [email protected]

# derivative
der <- function(x){
  x * (1-x)
}

# input data

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# transformer simple.R
# Bastiaan Quast

softmax <- function(x) {
  e_x <- exp(x - max(x))  # subtract max to avoid numerical instability
  return(e_x / sum(e_x))
}

# Initialize input queries, keys, and values
query <- rnorm(5)

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import numpy as np
from numpy.polynomial import Polynomial

# Set the parameters
M = 8
N = M // 2
scale = 64
xi = np.exp(2 * np.pi * 1j / M)

def vandermonde(xi: np.complex128, M: int) -> np.array:

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library(polynom)

M <- 8
N <- M %/% 2
scale <- 64
xi <- complex(real = cos(2 * pi / M), imaginary = sin(2 * pi / M))

vandermonde <- function(xi, M) {
  N <- M %/% 2
  # Initialize an empty matrix with complex data type

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import numpy as np
from numpy.polynomial import Polynomial

def polynomial_modulo(polynomial, mod):
    """
    Perform polynomial modulo operation using divmod.
    """
    q, r = divmod(polynomial, mod)
    return r