use std::num::{Zero, One, Algebraic};
use std::vec::{VecIterator, VecMutIterator};
use std::vec::from_elem;
use std::cmp::ApproxEq;
use std::iterator::{FromIterator, IteratorUtil};
use traits::iterable::{Iterable, IterableMut};
use traits::ring::Ring;
use traits::division_ring::DivisionRing;
use traits::dot::Dot;
use traits::sub_dot::SubDot;
use traits::norm::Norm;
use traits::translation::{Translation, Translatable};
use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};

/// Vector with a dimension unknown at compile-time.
#[deriving(Eq, Ord, ToStr, Clone)]
pub struct DVec<N>
{
  /// Components of the vector. Contains as much elements as the vector dimension.
  at: ~[N]
}

/// Builds a vector filled with zeros.
/// 
/// # Arguments
///   * `dim` - The dimension of the vector.
#[inline]
pub fn zero_vec_with_dim<N: Zero + Clone>(dim: uint) -> DVec<N>
{ DVec { at: from_elem(dim, Zero::zero::<N>()) } }

/// Tests if all components of the vector are zeroes.
#[inline]
pub fn is_zero_vec<N: Zero>(vec: &DVec<N>) -> bool
{ vec.at.iter().all(|e| e.is_zero()) }

impl<N> Iterable<N> for DVec<N>
{
  fn iter<'l>(&'l self) -> VecIterator<'l, N>
  { self.at.iter() }
}

impl<N> IterableMut<N> for DVec<N>
{
  fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
  { self.at.mut_iter() }
}

impl<N, Iter: Iterator<N>> FromIterator<N, Iter> for DVec<N>
{
  fn from_iterator(mut param: &mut Iter) -> DVec<N>
  {
    let mut res = DVec { at: ~[] };

    for e in param
    { res.at.push(e) }

    res
  }
}

impl<N: Clone + DivisionRing + Algebraic + ApproxEq<N>> DVec<N>
{
  /// Computes the canonical basis for the given dimension. A canonical basis is a set of
  /// vectors, mutually orthogonal, with all its component equal to 0.0 exept one which is equal to
  /// 1.0.
  pub fn canonical_basis_with_dim(dim: uint) -> ~[DVec<N>]
  {
    let mut res : ~[DVec<N>] = ~[];

    for i in range(0u, dim)
    {
      let mut basis_element : DVec<N> = zero_vec_with_dim(dim);

      basis_element.at[i] = One::one();

      res.push(basis_element);
    }

    res
  }

  /// Computes a basis of the space orthogonal to the vector. If the input vector is of dimension
  /// `n`, this will return `n - 1` vectors.
  pub fn orthogonal_subspace_basis(&self) -> ~[DVec<N>]
  {
    // compute the basis of the orthogonal subspace using Gram-Schmidt
    // orthogonalization algorithm
    let     dim              = self.at.len();
    let mut res : ~[DVec<N>] = ~[];

    for i in range(0u, dim)
    {
      let mut basis_element : DVec<N> = zero_vec_with_dim(self.at.len());

      basis_element.at[i] = One::one();

      if res.len() == dim - 1
      { break; }

      let mut elt = basis_element.clone();

      elt = elt - self.scalar_mul(&basis_element.dot(self));

      for v in res.iter()
      { elt = elt - v.scalar_mul(&elt.dot(v)) };

      if !elt.sqnorm().approx_eq(&Zero::zero())
      { res.push(elt.normalized()); }
    }

    assert!(res.len() == dim - 1);

    res
  }
}

impl<N: Add<N,N>> Add<DVec<N>, DVec<N>> for DVec<N>
{
  #[inline]
  fn add(&self, other: &DVec<N>) -> DVec<N>
  {
    assert!(self.at.len() == other.at.len());
    DVec {
      at: self.at.iter().zip(other.at.iter()).transform(|(a, b)| *a + *b).collect()
    }
  }
}

impl<N: Sub<N,N>> Sub<DVec<N>, DVec<N>> for DVec<N>
{
  #[inline]
  fn sub(&self, other: &DVec<N>) -> DVec<N>
  {
    assert!(self.at.len() == other.at.len());
    DVec {
      at: self.at.iter().zip(other.at.iter()).transform(|(a, b)| *a - *b).collect()
    }
  }
}

impl<N: Neg<N>> Neg<DVec<N>> for DVec<N>
{
  #[inline]
  fn neg(&self) -> DVec<N>
  { DVec { at: self.at.iter().transform(|a| -a).collect() } }
}

impl<N: Ring>
Dot<N> for DVec<N>
{
  #[inline]
  fn dot(&self, other: &DVec<N>) -> N
  {
    assert!(self.at.len() == other.at.len());

    let mut res = Zero::zero::<N>();

    for i in range(0u, self.at.len())
    { res = res + self.at[i] * other.at[i]; }

    res
  } 
}

impl<N: Ring> SubDot<N> for DVec<N>
{
  #[inline]
  fn sub_dot(&self, a: &DVec<N>, b: &DVec<N>) -> N
  {
    let mut res = Zero::zero::<N>();

    for i in range(0u, self.at.len())
    { res = res + (self.at[i] - a.at[i]) * b.at[i]; }

    res
  } 
}

impl<N: Mul<N, N>>
ScalarMul<N> for DVec<N>
{
  #[inline]
  fn scalar_mul(&self, s: &N) -> DVec<N>
  { DVec { at: self.at.iter().transform(|a| a * *s).collect() } }

  #[inline]
  fn scalar_mul_inplace(&mut self, s: &N)
  {
    for i in range(0u, self.at.len())
    { self.at[i] = self.at[i] * *s; }
  }
}


impl<N: Div<N, N>>
ScalarDiv<N> for DVec<N>
{
  #[inline]
  fn scalar_div(&self, s: &N) -> DVec<N>
  { DVec { at: self.at.iter().transform(|a| a / *s).collect() } }

  #[inline]
  fn scalar_div_inplace(&mut self, s: &N)
  {
    for i in range(0u, self.at.len())
    { self.at[i] = self.at[i] / *s; }
  }
}

impl<N: Add<N, N>>
ScalarAdd<N> for DVec<N>
{
  #[inline]
  fn scalar_add(&self, s: &N) -> DVec<N>
  { DVec { at: self.at.iter().transform(|a| a + *s).collect() } }

  #[inline]
  fn scalar_add_inplace(&mut self, s: &N)
  {
    for i in range(0u, self.at.len())
    { self.at[i] = self.at[i] + *s; }
  }
}

impl<N: Sub<N, N>>
ScalarSub<N> for DVec<N>
{
  #[inline]
  fn scalar_sub(&self, s: &N) -> DVec<N>
  { DVec { at: self.at.iter().transform(|a| a - *s).collect() } }

  #[inline]
  fn scalar_sub_inplace(&mut self, s: &N)
  {
    for i in range(0u, self.at.len())
    { self.at[i] = self.at[i] - *s; }
  }
}

impl<N: Add<N, N> + Neg<N> + Clone> Translation<DVec<N>> for DVec<N>
{
  #[inline]
  fn translation(&self) -> DVec<N>
  { self.clone() }

  #[inline]
  fn inv_translation(&self) -> DVec<N>
  { -self }

  #[inline]
  fn translate_by(&mut self, t: &DVec<N>)
  { *self = *self + *t; }
}

impl<N: Add<N, N> + Neg<N> + Clone> Translatable<DVec<N>, DVec<N>> for DVec<N>
{
  #[inline]
  fn translated(&self, t: &DVec<N>) -> DVec<N>
  { self + *t }
}

impl<N: DivisionRing + Algebraic + Clone>
Norm<N> for DVec<N>
{
  #[inline]
  fn sqnorm(&self) -> N
  { self.dot(self) }

  #[inline]
  fn norm(&self) -> N
  { self.sqnorm().sqrt() }

  #[inline]
  fn normalized(&self) -> DVec<N>
  {
    let mut res : DVec<N> = self.clone();

    res.normalize();

    res
  }

  #[inline]
  fn normalize(&mut self) -> N
  {
    let l = self.norm();

    for i in range(0u, self.at.len())
    { self.at[i] = self.at[i] / l; }

    l
  }
}

impl<N: ApproxEq<N>> ApproxEq<N> for DVec<N>
{
  #[inline]
  fn approx_epsilon() -> N
  { ApproxEq::approx_epsilon::<N, N>() }

  #[inline]
  fn approx_eq(&self, other: &DVec<N>) -> bool
  {
    let mut zip = self.at.iter().zip(other.at.iter());

    do zip.all |(a, b)| { a.approx_eq(b) }
  }

  #[inline]
  fn approx_eq_eps(&self, other: &DVec<N>, epsilon: &N) -> bool
  {
    let mut zip = self.at.iter().zip(other.at.iter());

    do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
  }
}