conspire 0.6.0

#[cfg(test)]
mod test;

#[cfg(test)]
use super::test::ErrorTensor;

use std::{
    array::from_fn,
    fmt::{self, Display, Formatter},
    iter::Sum,
    ops::{Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Sub, SubAssign},
};

use super::{
    Tensor, TensorArray,
    rank_0::TensorRank0,
    rank_2::{
        TensorRank2, get_identity_1010_parts_1, get_identity_1010_parts_2,
        get_identity_1010_parts_3, get_levi_civita_parts,
    },
};

/// Returns the rank-3 Levi-Civita symbol.
pub fn levi_civita<const I: usize, const J: usize, const K: usize>() -> TensorRank3<3, I, J, K> {
    TensorRank3::from([
        [[0.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, -1.0, 0.0]],
        [[0.0, 0.0, -1.0], [0.0, 0.0, 0.0], [1.0, 0.0, 0.0]],
        [[0.0, 1.0, 0.0], [-1.0, 0.0, 0.0], [0.0, 0.0, 0.0]],
    ])
}

/// A *d*-dimensional tensor of rank 3.
///
/// `D` is the dimension, `I`, `J`, `K` are the configurations.
#[repr(transparent)]
#[derive(Clone, Debug, PartialEq)]
pub struct TensorRank3<const D: usize, const I: usize, const J: usize, const K: usize>(
    [TensorRank2<D, J, K>; D],
);

impl<const D: usize, const I: usize, const J: usize, const K: usize> Default
    for TensorRank3<D, I, J, K>
{
    fn default() -> Self {
        Self::zero()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize>
    From<[[[TensorRank0; D]; D]; D]> for TensorRank3<D, I, J, K>
{
    fn from(array: [[[TensorRank0; D]; D]; D]) -> Self {
        array.into_iter().map(|entry| entry.into()).collect()
    }
}

pub const LEVI_CIVITA: TensorRank3<3, 1, 1, 1> = TensorRank3(get_levi_civita_parts());

pub const fn get_identity_1010_parts<const I: usize, const J: usize, const K: usize>()
-> [TensorRank3<3, I, J, K>; 3] {
    [
        TensorRank3(get_identity_1010_parts_1()),
        TensorRank3(get_identity_1010_parts_2()),
        TensorRank3(get_identity_1010_parts_3()),
    ]
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Display
    for TensorRank3<D, I, J, K>
{
    fn fmt(&self, f: &mut Formatter) -> fmt::Result {
        write!(f, "[")?;
        self.iter()
            .enumerate()
            .try_for_each(|(i, entry)| write!(f, "{entry},\n\x1B[u\x1B[{}B\x1B[1D", i + 1))?;
        write!(f, "\x1B[u\x1B[1A\x1B[{}C]", 16 * D + 1)
    }
}

#[cfg(test)]
impl<const D: usize, const I: usize, const J: usize, const K: usize> ErrorTensor
    for TensorRank3<D, I, J, K>
{
    fn error_fd(&self, comparator: &Self, epsilon: TensorRank0) -> Option<(bool, usize)> {
        let error_count = self
            .iter()
            .zip(comparator.iter())
            .map(|(self_i, comparator_i)| {
                self_i
                    .iter()
                    .zip(comparator_i.iter())
                    .map(|(self_ij, comparator_ij)| {
                        self_ij
                            .iter()
                            .zip(comparator_ij.iter())
                            .filter(|&(&self_ijk, &comparator_ijk)| {
                                (self_ijk / comparator_ijk - 1.0).abs() >= epsilon
                                    && (self_ijk.abs() >= epsilon
                                        || comparator_ijk.abs() >= epsilon)
                            })
                            .count()
                    })
                    .sum::<usize>()
            })
            .sum();
        if error_count > 0 {
            Some((true, error_count))
        } else {
            None
        }
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Tensor
    for TensorRank3<D, I, J, K>
{
    type Item = TensorRank2<D, J, K>;
    fn iter(&self) -> impl Iterator<Item = &Self::Item> {
        self.0.iter()
    }
    fn iter_mut(&mut self) -> impl Iterator<Item = &mut Self::Item> {
        self.0.iter_mut()
    }
    fn len(&self) -> usize {
        D
    }
    fn size(&self) -> usize {
        D * D * D
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> IntoIterator
    for TensorRank3<D, I, J, K>
{
    type Item = TensorRank2<D, J, K>;
    type IntoIter = std::array::IntoIter<Self::Item, D>;
    fn into_iter(self) -> Self::IntoIter {
        self.0.into_iter()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> TensorArray
    for TensorRank3<D, I, J, K>
{
    type Array = [[[TensorRank0; D]; D]; D];
    type Item = TensorRank2<D, J, K>;
    fn as_array(&self) -> Self::Array {
        let mut array = [[[0.0; D]; D]; D];
        array
            .iter_mut()
            .zip(self.iter())
            .for_each(|(entry_rank_2, tensor_rank_2)| *entry_rank_2 = tensor_rank_2.as_array());
        array
    }
    fn identity() -> Self {
        panic!()
    }
    fn zero() -> Self {
        Self(from_fn(|_| Self::Item::zero()))
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize>
    FromIterator<TensorRank2<D, J, K>> for TensorRank3<D, I, J, K>
{
    fn from_iter<Ii: IntoIterator<Item = TensorRank2<D, J, K>>>(into_iterator: Ii) -> Self {
        let mut tensor_rank_3 = Self::zero();
        tensor_rank_3
            .iter_mut()
            .zip(into_iterator)
            .for_each(|(tensor_rank_3_i, value_i)| *tensor_rank_3_i = value_i);
        tensor_rank_3
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Index<usize>
    for TensorRank3<D, I, J, K>
{
    type Output = TensorRank2<D, J, K>;
    fn index(&self, index: usize) -> &Self::Output {
        &self.0[index]
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> IndexMut<usize>
    for TensorRank3<D, I, J, K>
{
    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
        &mut self.0[index]
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Sum
    for TensorRank3<D, I, J, K>
{
    fn sum<Ii>(iter: Ii) -> Self
    where
        Ii: Iterator<Item = Self>,
    {
        iter.reduce(|mut acc, item| {
            acc += item;
            acc
        })
        .unwrap_or_else(Self::default)
    }
}

impl<'a, const D: usize, const I: usize, const J: usize, const K: usize> Sum<&'a Self>
    for TensorRank3<D, I, J, K>
{
    fn sum<Ii>(iter: Ii) -> Self
    where
        Ii: Iterator<Item = &'a Self>,
    {
        iter.fold(Self::default(), |mut acc, item| {
            acc += item;
            acc
        })
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Div<TensorRank0>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn div(mut self, tensor_rank_0: TensorRank0) -> Self::Output {
        self /= &tensor_rank_0;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Div<TensorRank0>
    for &TensorRank3<D, I, J, K>
{
    type Output = TensorRank3<D, I, J, K>;
    fn div(self, tensor_rank_0: TensorRank0) -> Self::Output {
        self.iter().map(|self_i| self_i / tensor_rank_0).collect()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Div<&TensorRank0>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn div(mut self, tensor_rank_0: &TensorRank0) -> Self::Output {
        self /= tensor_rank_0;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> DivAssign<TensorRank0>
    for TensorRank3<D, I, J, K>
{
    fn div_assign(&mut self, tensor_rank_0: TensorRank0) {
        self.iter_mut().for_each(|self_i| *self_i /= &tensor_rank_0);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> DivAssign<&TensorRank0>
    for TensorRank3<D, I, J, K>
{
    fn div_assign(&mut self, tensor_rank_0: &TensorRank0) {
        self.iter_mut().for_each(|self_i| *self_i /= tensor_rank_0);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Mul<TensorRank0>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn mul(mut self, tensor_rank_0: TensorRank0) -> Self::Output {
        self *= &tensor_rank_0;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Mul<&TensorRank0>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn mul(mut self, tensor_rank_0: &TensorRank0) -> Self::Output {
        self *= tensor_rank_0;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Mul<TensorRank0>
    for &TensorRank3<D, I, J, K>
{
    type Output = TensorRank3<D, I, J, K>;
    fn mul(self, tensor_rank_0: TensorRank0) -> Self::Output {
        self.iter().map(|self_i| self_i * tensor_rank_0).collect()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Mul<&TensorRank0>
    for &TensorRank3<D, I, J, K>
{
    type Output = TensorRank3<D, I, J, K>;
    fn mul(self, tensor_rank_0: &TensorRank0) -> Self::Output {
        self.iter().map(|self_i| self_i * tensor_rank_0).collect()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> MulAssign<TensorRank0>
    for TensorRank3<D, I, J, K>
{
    fn mul_assign(&mut self, tensor_rank_0: TensorRank0) {
        self.iter_mut().for_each(|self_i| *self_i *= &tensor_rank_0);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> MulAssign<&TensorRank0>
    for TensorRank3<D, I, J, K>
{
    fn mul_assign(&mut self, tensor_rank_0: &TensorRank0) {
        self.iter_mut().for_each(|self_i| *self_i *= tensor_rank_0);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Add
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn add(mut self, tensor_rank_3: Self) -> Self::Output {
        self += tensor_rank_3;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Add<&Self>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn add(mut self, tensor_rank_3: &Self) -> Self::Output {
        self += tensor_rank_3;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Add<TensorRank3<D, I, J, K>>
    for &TensorRank3<D, I, J, K>
{
    type Output = TensorRank3<D, I, J, K>;
    fn add(self, mut tensor_rank_3: TensorRank3<D, I, J, K>) -> Self::Output {
        tensor_rank_3 += self;
        tensor_rank_3
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> AddAssign
    for TensorRank3<D, I, J, K>
{
    fn add_assign(&mut self, tensor_rank_3: Self) {
        self.iter_mut()
            .zip(tensor_rank_3)
            .for_each(|(self_i, tensor_rank_3_i)| *self_i += tensor_rank_3_i);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> AddAssign<&Self>
    for TensorRank3<D, I, J, K>
{
    fn add_assign(&mut self, tensor_rank_3: &Self) {
        self.iter_mut()
            .zip(tensor_rank_3.iter())
            .for_each(|(self_i, tensor_rank_3_i)| *self_i += tensor_rank_3_i);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Sub
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn sub(mut self, tensor_rank_3: Self) -> Self::Output {
        self -= tensor_rank_3;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Sub<&Self>
    for TensorRank3<D, I, J, K>
{
    type Output = Self;
    fn sub(mut self, tensor_rank_3: &Self) -> Self::Output {
        self -= tensor_rank_3;
        self
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> Sub
    for &TensorRank3<D, I, J, K>
{
    type Output = TensorRank3<D, I, J, K>;
    fn sub(self, tensor_rank_3: Self) -> Self::Output {
        tensor_rank_3
            .iter()
            .zip(self.iter())
            .map(|(tensor_rank_3_i, self_i)| self_i - tensor_rank_3_i)
            .collect()
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> SubAssign
    for TensorRank3<D, I, J, K>
{
    fn sub_assign(&mut self, tensor_rank_3: Self) {
        self.iter_mut()
            .zip(tensor_rank_3)
            .for_each(|(self_i, tensor_rank_3_i)| *self_i -= tensor_rank_3_i);
    }
}

impl<const D: usize, const I: usize, const J: usize, const K: usize> SubAssign<&Self>
    for TensorRank3<D, I, J, K>
{
    fn sub_assign(&mut self, tensor_rank_3: &Self) {
        self.iter_mut()
            .zip(tensor_rank_3.iter())
            .for_each(|(self_i, tensor_rank_3_i)| *self_i -= tensor_rank_3_i);
    }
}