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diff --git a/shapes/matrix/Matrix.ml b/shapes/matrix/Matrix.ml
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-open Order
-
-module Order = Order
-
-(*************** Exceptions ***************)
-
-exception NonSquare
-exception ImproperDimensions
-
-(* Functor so we can Abstract away! *)
-module MakeMatrix (C: EltsI.ORDERED_AND_OPERATIONAL) :
-  (MatrixI.MATRIX with type elt = C.t) =
-struct
-
-
-  (*************** End Exceptions ***************)
-
-  (*************** Types ***************)
-
-  type elt = C.t
-
-  (* A matrix is a pair of dimension (n x p) and a array of arrays
-   * the first array is the row (n) and the second the column (p) *)
-  type matrix = (int * int) * (elt array array)
-
-  (*************** End Types ***************)
-
-  (*************** Base Functions ***************)
-
-  (* catching negative dimensions AND 0 dimensions and too large
-   * of a dimension so we don't have to worry about it later *)
-  let empty (rows: int) (columns: int) : matrix =
-    if rows > 0 && columns > 0 then
-      try
-        let m = Array.make_matrix rows columns C.zero in ((rows,columns),m)
-      with _ ->
-        raise ImproperDimensions
-    else (* dimension is negative or 0 *)
-      raise ImproperDimensions
-
-  (*************** End Base Functions ***************)
-
-  (*************** Helper Functions ***************)
-
-  (* get's the nth row of a matrix and returns (r, row) where r is the length
-   * of the row and row is a COPY of the original row. For example, calling
-   * calling get_row m 1 will return (3, |1 3 4 |)
-   *         ________
-   *    m = | 1 3 4 |
-   *        |*2 5 6 |
-  *)
-  (* aside: we don't check whether n < 1 because of our matrix invariant *)
-  let get_row (((n,p),m): matrix) (row: int) : int * elt array =
-    if row <= n then
-      let row' = Array.map (fun x -> x) m.(row - 1) in
-      (p, row')
-    else
-      raise (Failure "Row out of bounds.")
-
-  (* similar to get_row. For m, get_column m 1 will return (2, |1 2|) *)
-  let get_column (((n,p),m): matrix) (column: int) : int * elt array =
-    if column <= p then
-      begin
-        let column' = Array.make n C.zero in
-        for i = 0 to n - 1 do
-          column'.(i) <- m.(i).(column - 1)
-        done;
-        (n, column')
-      end
-    else
-      raise (Failure "Column out of bounds.")
-
-  (* sets the nth row of the matrix m to the specified array a.
-   * This is done IN-PLACE. Therefore the function returns unit.  You should
-   * nonetheless enfore immutability whenever possible.  For a clarification on
-   * what nth row means, look at comment for get_row above. *)
-  let set_row (((n, p), m): matrix) (row: int) (a: elt array) : unit =
-    if row <= n then
-      begin
-        assert(Array.length a = p);
-        for i = 0 to p - 1 do
-          m.(row - 1).(i) <- a.(i)
-        done;
-      end
-    else
-      raise (Failure "Row out of bounds.")
-
-  (* Similar to set_row but sets the nth column instead *)
-  let set_column (((n,p),m): matrix) (column: int) (a: elt array) : unit =
-    if column <= p then
-      begin
-        assert(Array.length a = n);
-        for i = 0 to n - 1 do
-          m.(i).(column - 1) <- a.(i)
-        done;
-      end
-    else
-      raise (Failure "Column out of bounds.")
-
-  (* returns the ij-th element of a matrix (not-zero indexed) *)
-  let get_elt (((n,p),m): matrix) ((i,j): int*int) : elt =
-    if i <= n && j <= p then
-      m.(i - 1).(j - 1)
-    else
-      raise ImproperDimensions
-
-  (* Changes the i,j-th element of a matrix to e. Is not zero-indexed, and
-   * changes the matrix in place *)
-  let set_elt (((n,p),m): matrix) ((i,j): int*int) (e: elt) : unit =
-    if i <= n && j <= p then
-      m.(i - 1).(j - 1) <- e
-    else
-      raise ImproperDimensions
-
-  (* similar to map, but applies to function to the entire matrix
-   * Returns a new matrix *)
-  let map (f: elt -> elt) (mat: matrix) : matrix =
-    let (dim,m) = mat in
-    (dim, Array.map (Array.map f) m)
-
-  (* Just some wrapping of Array.iter made for Matrices! *)
-  let iter (f: elt -> unit) (mat: matrix) : unit =
-    let _, m = mat in
-    Array.iter (Array.iter f) m
-
-  (* Just some wrapping of Array.iteri. Useful for pretty
-   * printing matrix. The index is (i,j). NOT zero-indexed *)
-  let iteri (f: int -> int -> elt -> unit) (mat: matrix) : unit =
-    let _, m = mat in
-    Array.iteri (fun i row -> Array.iteri (fun j e -> f i j e) row) m
-
-  (* folds over each row using base case u and function f *)
-  (* could be a bit more efficient? *)
-  let reduce (f: 'a -> elt -> 'a) (u: 'a) (((p,q),m): matrix) : 'a =
-    let total = ref u in
-    for i = 0 to p - 1 do
-      for j = 0 to q - 1 do
-        total := f (!total) m.(i).(j)
-      done;
-    done;
-    !total
-
-  let fold_row ~(f: elt array -> 'b) ((_,m): matrix) : 'b list =
-
-    let call_row acc v = (f v)::acc in
-    Array.fold_left call_row [] m
-    |> List.rev
-
-
-
-
-  (* given two arrays, this will calculate their dot product *)
-  (* It seems a little funky, but this is done for efficiency's sake.
-   * In short, it tries to multiply each element by it's respective
-   * element until the one array is indexed out of bounds. If the
-   * other array is also out of bounds, then it returns their value.
-   * Otherwise, the arrays were the wrong size and raises ImproperDimension
-
-     THE ABOVE COMMENT HAS NOT BEEN IMPLEMENTED
-
-     Instead we calculate the length before starting
-  *)
-  let dot (v1: elt array) (v2: elt array) : elt =
-    let rec dotting (i: int) (total: elt) : elt =
-      if i = 0 then total
-      else
-        let curr = C.multiply v1.(i-1) v2.(i-1) in
-        dotting (i - 1) (C.add curr total) in
-    let len1, len2 = Array.length v1, Array.length v2 in
-    if len1 = len2 then dotting len1 C.zero
-    else raise ImproperDimensions
-
-  (* function to expose the dimensions of a matrix *)
-  let get_dimensions (m: matrix) : (int * int) =
-    let ((x,y), _) = m in (x,y)
-
-  (*************** End Helper Functions ***************)
-
-
-  (*************** Primary Matrix Functions ***************)
-
-  (* scales a matrix by the appropriate factor *)
-  let scale (m: matrix) (sc: elt) : matrix = map (C.multiply sc) m
-
-  (* Generates a matrix from a list of lists. The inners lists are the rows *)
-  let from_list (lsts : elt list list) : matrix =
-    let check_length (length: int) (lst: elt list) : int =
-      if List.length lst = length then length
-      else raise ImproperDimensions in
-    let p = List.length lsts in
-    match lsts with
-    | [] -> raise ImproperDimensions
-    | hd::tl ->
-      let len = List.length hd in
-      if List.fold_left check_length len tl = len then
-        ((p,len),Array.map Array.of_list (Array.of_list lsts))
-      else
-        raise ImproperDimensions
-
-  (* Generates a matrix from a list of lists. The inners lists are the rows *)
-  let from_array (arrs : elt array array) : matrix =
-    let check_length (length: int) (arr: elt array) : unit =
-      if Array.length arr = length then ()
-      else raise ImproperDimensions in
-    let p = Array.length arrs in
-    match Array.length arrs with
-    | 0 -> raise ImproperDimensions
-    | _ ->
-      let len = Array.length (Array.get arrs 0) in
-      Array.iter (check_length len) arrs;
-      ((p, len), arrs)
-
-  (* Adds two matrices. They must have the same dimensions *)
-  let add ((dim1,m1): matrix) ((dim2,m2): matrix) : matrix =
-    if dim1 = dim2 then
-      let n, p = dim1 in
-      let (dim', sum_m) = empty n p in
-      for i = 0 to n - 1 do
-        for j = 0 to p - 1 do
-          sum_m.(i).(j) <- C.add m1.(i).(j) m2.(i).(j)
-        done;
-      done;
-      (dim',sum_m)
-    else
-      raise ImproperDimensions
-
-
-  (* Multiplies two matrices. If the matrices have dimensions m x n and p x q, n
-   * and p must be equal, and the resulting matrix will have dimension n x q *)
-  let mult (matrix1: matrix) (matrix2: matrix) : matrix =
-    let ((m,n), _), ((p,q), _) = matrix1, matrix2 in
-    if n = p then
-      let (dim, result) = empty m q in
-      for i = 0 to m - 1 do
-        for j = 0 to q - 1 do
-          let (_,row), (_,column) = get_row matrix1 (i + 1),
-                                    get_column matrix2 (j + 1) in
-          result.(i).(j) <- dot row column
-        done;
-      done;
-      (dim,result)
-    else
-      raise ImproperDimensions
-
-  (*************** Helper Functions for Row Reduce ***************)
-
-  (*
-  (* returns the index of the first non-zero elt in an array*)
-  let zero (arr: elt array) : int option =
-    let index = ref 1 in
-    let empty (i: int option) (e: elt) : int option =
-      match i, C.compare e C.zero with
-      | None, Equal -> (index := !index + 1; None)
-      | None, _ -> Some (!index)
-      | _, _ -> i in
-    Array.fold_left empty None arr
-
-  (* returns the the location of the nth non-zero
-   * element in the matrix. Scans column wise.  So the nth non-zero element is
-   * the FIRST non-zero element in the nth non-zero column *)
-  let nth_nz_location (m: matrix) (_: int): (int*int) option =
-    let ((n,p), _) = m in
-    let rec check_col (to_skip: int) (j: int) =
-      if j <= p then
-        let (_,col) = get_column m j in
-        match zero col with
-        | None -> check_col to_skip (j + 1)
-        | Some i ->
-          if to_skip = 0 then
-            Some (i,j)
-          else (* we want a later column *)
-            check_col (to_skip - 1) (j + 1)
-      else None in
-    check_col (n - 1) 1
-
-  (* returns the the location of the first
-   * non-zero and non-one elt. Scans column wise, from
-   * left to right. Basically, it ignores columns
-   * that are all zero or that *)
-  let fst_nz_no_loc (m: matrix): (int*int) option =
-    let ((_, p), _) = m in
-    let rec check_col (j: int) =
-      if j <= p then
-        let (_,col) = get_column m j in
-        match zero col with
-        | None -> check_col (j + 1)
-        | Some i ->
-          match C.compare col.(i-1) C.one with
-          | Equal -> check_col (j + 1)
-          | _ -> Some (i,j)
-      else None in
-    check_col 1
-    *)
-
-  (* Compares two elements in an elt array and returns the greater and its
-   * index. Is a helper function for find_max_col_index *)
-  let compare_helper (e1: elt) (e2: elt) (ind1: int) (ind2: int) : (elt*int) =
-    match C.compare e1 e2 with
-    | Equal -> (e2, ind2)
-    | Greater -> (e1, ind1)
-    | Less -> (e2, ind2)
-
-  (* Finds the element with the greatest absolute value in a column. Is not
-   * 0-indexed. If two elements are both the maximum value, returns the one with
-   * the lowest index. Returns None if this element is zero (if column is all 0)
-  *)
-  let find_max_col_index (array1: elt array) (start_index: int) : int option =
-    let rec find_index (max_index: int) (curr_max: elt) (curr_index: int)
-        (arr: elt array) =
-      if curr_index = Array.length arr then
-        (if curr_max = C.zero then None
-         else Some (max_index+1)) (* Arrays are 0-indexed but matrices aren't *)
-      else
-        (match C.compare arr.(curr_index) C.zero with
-         | Equal -> find_index max_index curr_max (curr_index+1) arr
-         | Greater ->
-           (let (el, index) = compare_helper (arr.(curr_index))
-                curr_max curr_index max_index in
-            find_index index el (curr_index+1) arr)
-         | Less ->
-           (let abs_curr_elt = C.subtract C.zero arr.(curr_index) in
-            let (el, index) = compare_helper abs_curr_elt curr_max curr_index
-                max_index in
-            find_index index el (curr_index+1) arr))
-    in
-    find_index 0 C.zero (start_index -1) array1
-
-  (* Basic row operations *)
-  (* Scales a row by sc *)
-  let scale_row (m: matrix) (num: int) (sc: elt) : unit =
-    let (_, row) = get_row m num in
-    let new_row = Array.map (C.multiply sc) row in
-    set_row m num new_row
-
-  (* Swaps two rows of a matrix *)
-  let swap_row (m: matrix) (r1: int) (r2: int) : unit =
-    let (len1, row1) = get_row m r1 in
-    let (len2, row2) = get_row m r2 in
-    let _ = assert (len1 = len2) in
-    let _ = set_row m r1 row2 in
-    let _ = set_row m r2 row1 in
-    ()
-
-  (* Subtracts a multiple of r2 from r1 *)
-  let sub_mult (m: matrix) (r1: int) (r2: int) (sc: elt) : unit =
-    let (len1, row1) = get_row m r1 in
-    let (len2, row2) = get_row m r2 in
-    let _ = assert (len1 = len2) in
-    for i = 0 to len1 - 1 do (* Arrays are 0-indexed *)
-      row1.(i) <- C.subtract row1.(i) (C.multiply sc row2.(i))
-    done;
-    set_row m r1 row1
-
-  (*************** End Helper Functions for Row Reduce ***************)
-
-  (* Returns the row reduced form of a matrix. Is not done in place, but creates
-   * a new matrix *)
-  let row_reduce (mat: matrix) : matrix =
-    let[@tailcall] rec row_reduce_h (n_row: int) (n_col: int) (mat2: matrix) : unit =
-      let ((num_row, _), _) = mat2 in
-      if (n_col = num_row + 1) then ()
-      else
-        let (_,col) = get_column mat2 n_col in
-        match find_max_col_index col n_row with
-        | None (* Column all 0s *) -> row_reduce_h n_row (n_col+1) mat2
-        | Some index ->
-          begin
-            swap_row mat2 index n_row;
-            let pivot = get_elt mat2 (n_row, n_col) in
-            scale_row mat2 (n_row) (C.divide C.one pivot);
-            for i = 1 to num_row do
-              if i <> n_row then sub_mult mat2 i n_row (get_elt mat2 (i,n_col))
-            done;
-            row_reduce_h (n_row+1) (n_col+1) mat2
-          end
-    in
-    (* Copies the matrix *)
-    let ((n,p),m) = mat in
-    let (dim,mat_cp) = empty n p in
-    for i = 0 to n - 1 do
-      for j = 0 to p - 1 do
-        mat_cp.(i).(j) <- m.(i).(j)
-      done;
-    done;
-    let _ = row_reduce_h 1 1 (dim,mat_cp) in (dim,mat_cp)
-
-  (*************** End Main Functions ***************)
-
-  (*************** Optional module functions ***************)
-
-  (* calculates the trace of a matrix *)
-  let trace (((n,p),m): matrix) : elt =
-    let rec build (elt: elt) (i: int) =
-      if i > -1 then
-        build (C.add m.(i).(i) elt) (i - 1)
-      else
-        elt in
-    if n = p then build C.zero (n - 1)
-    else raise ImproperDimensions
-
-  (* calculates the transpose of a matrix and retuns a new one *)
-  let transpose (((n,p),m): matrix) =
-    let (dim,m') = empty p n in
-    for i = 0 to n - 1 do
-      for j = 0 to p - 1 do
-        m'.(j).(i) <- m.(i).(j)
-      done;
-    done;
-    assert(dim = (p,n));
-    ((p,n),m')
-
-  (* Returns the inverse of a matrix. Uses a pretty simple algorithm *)
-  let inverse (mat: matrix) : matrix =
-    let ((n, p), _) = mat in
-    if n = p then
-      (* create augmented matrix *)
-      let augmented = empty n (2*n) in
-      for i = 1 to n do
-        let (dim,col) = get_column mat i in
-        let arr = Array.make n C.zero in
-        begin
-          assert(dim = n);
-          arr.(i-1) <- C.one;
-          set_column augmented i col;
-          set_column augmented (n + i) arr
-        end
-      done;
-      let augmented' = row_reduce augmented in
-      (* create the inverted matrix and fill in with appropriate values *)
-      let inverse = empty n n in
-      for i = 1 to n do
-        let (dim, col) = get_column augmented' (n + i) in
-        let _ = assert(dim = n) in
-        let _ = set_column inverse i col in
-        ()
-      done;
-      inverse
-    else
-      raise NonSquare
-
-  (***************** HELPER FUNCTIONS FOR DETERMINANT *****************)
-  (* creates an identity matrix of size n*)
-  let create_identity (n:int) : matrix =
-    let (dim,m) = empty n n in
-    for i = 0 to n - 1 do
-      m.(i).(i) <- C.one
-    done;
-    (dim,m)
-
-  (* Finds the index of the maximum value of an array *)
-  let find_max_index (arr: elt array) (start_index : int) : int =
-    let rec find_index (max_index: int) (curr_index: int) =
-      if curr_index = Array.length arr then max_index+1
-      else
-        match C.compare arr.(curr_index) arr.(max_index) with
-        | Equal | Less -> find_index max_index (curr_index + 1)
-        | Greater -> find_index curr_index (curr_index + 1) in
-    find_index (start_index - 1) start_index
-
-  (* Creates the pivoting matrix for A. Returns swqps. Adapted from
-   * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *)
-  let pivotize (((n,p),m): matrix) : matrix * int =
-    if n = p then
-      let swaps = ref 0 in
-      let pivot_mat = create_identity n in
-      for j = 1 to n do
-        let (_,col) = get_column ((n,p),m) j in
-        let max_index = find_max_index col j in
-        if max_index <> j then
-          (swaps := !swaps + 1; swap_row pivot_mat max_index j)
-        else ()
-      done;
-      (pivot_mat,!swaps)
-    else raise ImproperDimensions
-
-  (* decomposes a matrix into a lower triangualar, upper triangualar
-   * and a pivot matrix. It returns (L,U,P). Adapted from
-   * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *)
-  let lu_decomposition (((n,p),m): matrix) : (matrix*matrix*matrix)*int =
-    if n = p then
-      let mat = ((n,p),m) in
-      let lower, upper, (pivot,s) = empty n n, empty n n, pivotize mat in
-      let (_ ,l),(_ ,u), _ = lower,upper,pivot in
-      let ((_, _),mat') = mult pivot mat in
-      for j = 0 to n - 1 do
-        l.(j).(j) <- C.one;
-        for i = 0 to j do
-          let sum = ref C.zero in
-          for k = 0 to i - 1 do
-            sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k))
-          done;
-          u.(i).(j) <- C.subtract mat'.(i).(j) (!sum)
-        done;
-        for i = j to n - 1 do
-          let sum = ref C.zero in
-          for k = 0 to j - 1 do
-            sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k))
-          done;
-          let sub = C.subtract mat'.(i).(j) (!sum) in
-          l.(i).(j) <- C.divide sub u.(j).(j)
-        done;
-      done;
-      (lower,upper,pivot),s
-    else raise ImproperDimensions
-
-  (* Computes the determinant of a matrix *)
-  let determinant (m: matrix) : elt =
-    try
-      let ((n,p), _) = m in
-      if n = p then
-        let rec triangualar_det (a,mat) curr_index acc =
-          if curr_index < n then
-            let acc' = C.multiply mat.(curr_index).(curr_index) acc in
-            triangualar_det (a,mat) (curr_index + 1) acc'
-          else acc in
-        let ((dim1,l),(dim2,u), _),s = lu_decomposition m in
-        let det1, det2 = triangualar_det (dim1,l) 0 C.one,
-                         triangualar_det (dim2,u) 0 C.one in
-        if s mod 2 = 0 then C.multiply det1 det2
-        else C.subtract C.zero (C.multiply det1 det2)
-      else raise ImproperDimensions
-    with
-    | _ -> C.zero
-
-
-  (*************** Optional module functions ***************)
-
-
-end