# Returns whether the given matrix is diagonal
is_diagonal <- function(mat) {
  if (!is.matrix(mat)) {
    stop("Not a matrix")
  }
  
  for (i in 1:nrow(mat)) {
    for (j in 1:ncol(mat)) {
      if (i != j && mat[i,j] != 0)
        return(FALSE)
    }
  }
  
  return(TRUE)
}

is_diagonal2 <- function(mat) {
  if (!is.matrix(mat)) {
    stop("Not a matrix")
  }
  
  all(mat * diag(nrow(mat)) == mat)
}

is_diagonal3 <- function(mat) {
  if (!is.matrix(mat)) {
    stop("Not a matrix")
  }
  all(mat[!diag(nrow(mat))] == 0)
}

# Matrix summary
# Inputs: matrix mat
# Outputs: Basic properties od the matrix
# E.g. Square? Diagonal? Symmetric? Rank, dimensions,
# eigenvalues, inverse, Singular?, determinant
matrix_summary <- function(mat) {
  output <- list()
  
  output$matrix <- mat
  
  output$dimensions <- dim(mat)
  
  library(Matrix)
  output$rank <- rankMatrix(mat)
  
  output$is_square <- diff(dim(mat)) == 0
  
  if (output$is_square) {
    output$is_singular <- !(output$rank == dim(mat)[1])
    
    if (!output$is_singular) {
      output$inverse <- solve(mat)
    }
    
    output$determinant <- det(mat)
    
    output$eigenvalues <- eigen(mat)$values
    
    output$is_symmetric <- all(mat == t(mat))
    
    output$is_diagonal <- is_diagonal2(mat)
  }
  
  class(output) <- "matrixSummary"
  
  return(output)
}

summary.matrix <- matrix_summary

# Prints out matrix description
# E.g. "m by n matrix of rank r"
#      "n by n square, symmetric, nonsingular matrix of rank n"
#      "n by n square, singular matrix of rank 7"
print_matrix_summary <- function(mat) {
  library(glue)
  mat_summary <- matrix_summary(mat)
  
  if (!mat_summary$is_square) {
    print(
      glue("{dim(mat)[1]} by {dim(mat)[2]} matrix of rank {mat_summary$rank}")
    )
  } else {
    properties <- ""
    if (mat_summary$is_symmetric)
      properties <- glue(properties, ", symmetric")
    if (mat_summary$is_diagonal) 
      properties <- glue(properties, ", diagonal")
    
    properties <- glue(properties, 
                       ifelse(mat_summary$is_singular,
                              ", singular",
                              ", nonsingular"))
    print(
      glue(
        "{dim(mat)[1]} by {dim(mat)[2]} square{properties}",
        " matrix of rank {mat_summary$rank}"
      )
    )
  }
}

print.matrixSummary <- function(mat_summary) {
  print_matrix_summary(mat_summary$matrix)
}