Project: s41467-024-49296-9 | Function: generate_single_transition_matrix (r)

system: You are an expert R programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow R best practices and maintain consistent code style.
Return **only** the complete R function code.

user: Complete this R function:

**DESCRIPTION:** Generates age-specific transition matrices using smoothed coefficients and individual covariates. Implements the core prediction equations by computing logistic regression probabilities and ensuring matrix constraints sum to 1.

**KEY TERMS:** {
  "coeff_array": "age-state-specific smoothed coefficients β_jka",
  "covariates": "individual covariate profile X_ia",
  "absorbing_states": "CAD and death states"
}

**CONTEXT CODE:** 
modelfitfun = function(ages, transit_mat, covariates, df, statusarray, mode = "binomial") {
  stop("Function implementation has been masked")
}
```

Note: This implementation is a simplified version and may need adjustments based on specific data structures and requirements. Proper handling of dimensions and error checking is crucial.




## input transition matrix and
coef_array_func=function(ages,transit_mat,modelfit){
  ncovariates=dim(modelfit$model_list[[1]][[1]][[1]])[1]
  covariates=rownames(modelfit$model_list[[1]][[1]][[1]])
  transit_coef=array(NA,dim=c(length(ages),dim(transit_mat)[1],dim(transit_mat)[2],ncovariates))
  dimnames(transit_coef)=list(ages,rownames(transit_mat),colnames(transit_mat),covariates)

  states=rownames(transit_mat)
  for (start_state in states[-c(5,6)]) {

    # Create a list for this starting state
    start_state_list <- list()

    # Loop through each possible ending state
    for (end_state in states) {

      if(transit_mat[start_state,end_state] == 1){
        # start state age < current age & next_state age < current age + 1


        a = coefplotsmooth2(
          ages = ages,
          start = start_state,
          stop = end_state,
          modelfit = modelfit,
          window_width = 20,
          span = 0.75,
          degree = 2
        )
        transit_coef[,start_state,end_state,]=a$custom_smooth
      }}}
  return(transit_coef)}


generate_single_transition_matrix <- function(age, coeff_array, covariates, absorbing_states = NULL) {
  stop("Function implementation has been masked")
}



mat.test = function(coefficients, covariates, age_start, age_end, absorbing_states) {
  # Pre-allocate the list with the required size
  matlist = vector("list", length = age_end - age_start + 1)
  names(matlist) = age_start:age_end

  for(age in age_start:age_end) {
    current_matrix <- generate_single_transition_matrix(age = age,
                                                        coeff_array = coefficients,
                                                        covariates = covariates,
                                                        absorbing_states = absorbing_states)
    matlist[[as.character(age)]] = current_matrix
  }

  return(matlist)
}




# # Usage of the function:
# age_specific_matrix <- generate_single_transition_matrix(age = 50, coeff_array, covariates, absorbing_states = c(5, 6))
# print(age_specific_matrix)

calculate_matrix_product_over_interval <- function(coefficients, covariates, age_start, age_end,absorbing_states) {
  # 'age_start' and 'age_end' define the interval of ages.

  # Generate the first transition matrix.
  product_matrix <- generate_single_transition_matrix(age = age_start,coeff_array = coefficients,covariates = covariates,absorbing_states = absorbing_states)

  # Multiply the transition matrices for each subsequent year in the interval.
  for (age in (age_start + 1):(age_end-1)) {
    current_matrix <- generate_single_transition_matrix(age = as.character(age),coeff_array = coefficients,covariates = covariates,absorbing_states = absorbing_states)
    product_matrix <- product_matrix %*% current_matrix  # Matrix multiplication.
  }

  return(product_matrix)
}



Complete the function implementation replacing "stop("Not implemented")".