easy_ml/tensors/

mod.rs

/*!
 * Generic N dimensional [named tensors](http://nlp.seas.harvard.edu/NamedTensor).
 *
 * Tensors are generic over some type `T` and some usize `D`. If `T` is [Numeric](super::numeric)
 * then the tensor can be used in a mathematical way. `D` is the number of dimensions in the tensor
 * and a compile time constant. Each tensor also carries `D` dimension name and length pairs.
 */
use crate::linear_algebra;
use crate::numeric::extra::{Real, RealRef};
use crate::numeric::{Numeric, NumericRef};
use crate::tensors::indexing::{
    ShapeIterator, TensorAccess, TensorIterator, TensorOwnedIterator, TensorReferenceIterator,
    TensorReferenceMutIterator, TensorTranspose,
};
use crate::tensors::views::{
    DataLayout, IndexRange, IndexRangeValidationError, TensorExpansion, TensorIndex, TensorMask,
    TensorMut, TensorRange, TensorRef, TensorRename, TensorReshape, TensorReverse, TensorView,
};

use std::error::Error;
use std::fmt;

#[cfg(feature = "serde")]
use serde::Serialize;

pub mod dimensions;
mod display;
pub mod einsum;
pub mod indexing;
pub mod operations;
pub mod views;

#[cfg(feature = "serde")]
pub use serde_impls::{TensorDeserialize, TensorDeserializeOwned};

/**
 * Dimension names are represented as static string references.
 *
 * This allows you to use string literals to refer to named dimensions, for example you might want
 * to construct a tensor with a shape of
 * `[("batch", 1000), ("height", 100), ("width", 100), ("rgba", 4)]`.
 *
 * Alternatively you can define the strings once as constants and refer to your dimension
 * names by the constant identifiers.
 *
 * ```
 * const BATCH: &'static str = "batch";
 * const HEIGHT: &'static str = "height";
 * const WIDTH: &'static str = "width";
 * const RGBA: &'static str = "rgba";
 * ```
 *
 * Although `Dimension` is interchangable with `&'static str` as it is just a type alias, Easy ML
 * uses `Dimension` whenever dimension names are expected to distinguish the types from just
 * strings.
 */
pub type Dimension = &'static str;

/**
 * An error indicating failure to do something with a Tensor because the requested shape
 * is not valid.
 */
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct InvalidShapeError<const D: usize> {
    shape: [(Dimension, usize); D],
}

impl<const D: usize> InvalidShapeError<D> {
    /**
     * Checks if this shape is valid. This is mainly for internal library use but may also be
     * useful for unit testing.
     *
     * Note: in some functions and methods, an InvalidShapeError may be returned which is a valid
     * shape, but not the right size for the quantity of data provided.
     */
    pub fn is_valid(&self) -> bool {
        !crate::tensors::dimensions::has_duplicates(&self.shape)
            && !self.shape.iter().any(|d| d.1 == 0)
    }

    /**
     * Constructs an InvalidShapeError for assistance with unit testing. Note that you can
     * construct an InvalidShapeError that *is* a valid shape in this way.
     */
    pub fn new(shape: [(Dimension, usize); D]) -> InvalidShapeError<D> {
        InvalidShapeError { shape }
    }

    pub fn shape(&self) -> [(Dimension, usize); D] {
        self.shape
    }

    pub fn shape_ref(&self) -> &[(Dimension, usize); D] {
        &self.shape
    }

    // Panics if the shape is invalid for any reason with the appropriate error message.
    #[track_caller]
    #[inline]
    fn validate_dimensions_or_panic(shape: &[(Dimension, usize); D], data_len: usize) {
        let elements = crate::tensors::dimensions::elements(shape);
        if data_len != elements {
            panic!(
                "Product of dimension lengths must match size of data. {} != {}",
                elements, data_len
            );
        }
        if crate::tensors::dimensions::has_duplicates(shape) {
            panic!("Dimension names must all be unique: {:?}", &shape);
        }
        if shape.iter().any(|d| d.1 == 0) {
            panic!("No dimension can have 0 elements: {:?}", &shape);
        }
    }

    // Returns true if the shape is valid and matches the data length
    fn validate_dimensions(shape: &[(Dimension, usize); D], data_len: usize) -> bool {
        let elements = crate::tensors::dimensions::elements(shape);
        data_len == elements
            && !crate::tensors::dimensions::has_duplicates(shape)
            && !shape.iter().any(|d| d.1 == 0)
    }
}

impl<const D: usize> fmt::Display for InvalidShapeError<D> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(
            f,
            "Dimensions must all be at least length 1 with unique names: {:?}",
            self.shape
        )
    }
}

impl<const D: usize> Error for InvalidShapeError<D> {}

/**
 * An error indicating failure to do something with a Tensor because the dimension names that
 * were provided did not match with the dimension names that were valid.
 *
 * Typically this would be due to the same dimension name being provided multiple times, or a
 * dimension name being provided that is not present in the shape of the Tensor in use.
 */
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct InvalidDimensionsError<const D: usize, const P: usize> {
    valid: [Dimension; D],
    provided: [Dimension; P],
}

impl<const D: usize, const P: usize> InvalidDimensionsError<D, P> {
    /**
     * Checks if the provided dimensions have duplicate names. This is mainly for internal library
     * use but may also be useful for unit testing.
     */
    pub fn has_duplicates(&self) -> bool {
        crate::tensors::dimensions::has_duplicates_names(&self.provided)
    }

    // TODO: method to check provided is a subset of valid

    /**
     * Constructs an InvalidDimensions for assistance with unit testing.
     */
    pub fn new(provided: [Dimension; P], valid: [Dimension; D]) -> InvalidDimensionsError<D, P> {
        InvalidDimensionsError { valid, provided }
    }

    pub fn provided_names(&self) -> [Dimension; P] {
        self.provided
    }

    pub fn provided_names_ref(&self) -> &[Dimension; P] {
        &self.provided
    }

    pub fn valid_names(&self) -> [Dimension; D] {
        self.valid
    }

    pub fn valid_names_ref(&self) -> &[Dimension; D] {
        &self.valid
    }
}

impl<const D: usize, const P: usize> fmt::Display for InvalidDimensionsError<D, P> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        if P > 0 {
            write!(
                f,
                "Dimensions names {:?} were incorrect, valid dimensions in this context are: {:?}",
                self.provided, self.valid
            )
        } else {
            write!(f, "Dimensions names {:?} were incorrect", self.provided)
        }
    }
}

impl<const D: usize, const P: usize> Error for InvalidDimensionsError<D, P> {}

#[test]
fn test_sync() {
    fn assert_sync<T: Sync>() {}
    assert_sync::<InvalidShapeError<2>>();
    assert_sync::<InvalidDimensionsError<2, 2>>();
}

#[test]
fn test_send() {
    fn assert_send<T: Send>() {}
    assert_send::<InvalidShapeError<2>>();
    assert_send::<InvalidDimensionsError<2, 2>>();
}

/**
 * A [named tensor](http://nlp.seas.harvard.edu/NamedTensor) of some type `T` and number of
 * dimensions `D`.
 *
 * Tensors are a generalisation of matrices; whereas [Matrix](crate::matrices::Matrix) only
 * supports 2 dimensions, and vectors are represented in Matrix by making either the rows or
 * columns have a length of one, [Tensor] supports an arbitary number of dimensions,
 * with 0 through 6 having full API support. A `Tensor<T, 2>` is very similar to a `Matrix<T>`
 * except that this type associates each dimension with a name, and favors names to refer to
 * dimensions instead of index order.
 *
 * Like Matrix, the type of the data in this Tensor may implement no traits, in which case the
 * tensor will be rather useless. If the type implements Clone most storage and accessor methods
 * are defined and if the type implements Numeric then the tensor can be used in a mathematical
 * way.
 *
 * Like Matrix, a Tensor must always contain at least one element, and it may not not have more
 * elements than `std::isize::MAX`. Concerned readers should note that on a 64 bit computer this
 * maximum value is 9,223,372,036,854,775,807 so running out of memory is likely to occur first.
 *
 * When doing numeric operations with Tensors you should be careful to not consume a tensor by
 * accidentally using it by value. All the operations are also defined on references to tensors
 * so you should favor &x + &y style notation for tensors you intend to continue using.
 *
 * See also:
 * - [indexing]
 */
#[derive(Debug)]
#[cfg_attr(feature = "serde", derive(Serialize))]
pub struct Tensor<T, const D: usize> {
    data: Vec<T>,
    #[cfg_attr(feature = "serde", serde(with = "serde_arrays"))]
    shape: [(Dimension, usize); D],
    #[cfg_attr(feature = "serde", serde(skip))]
    strides: [usize; D],
}

impl<T, const D: usize> Tensor<T, D> {
    /**
     * Creates a Tensor with a particular number of dimensions and lengths in each dimension.
     *
     * The product of the dimension lengths corresponds to the number of elements the Tensor
     * will store. Elements are stored in what would be row major order for a Matrix.
     * Each step in memory through the N dimensions corresponds to incrementing the rightmost
     * index, hence a shape of `[("row", 5), ("column", 5)]` would mean the first 6 elements
     * passed in the Vec would be for (0,0), (0,1), (0,2), (0,3), (0,4), (1,0) and so on to (4,4)
     * for the 25th and final element.
     *
     * # Panics
     *
     * - If the number of provided elements does not match the product of the dimension lengths.
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     *
     * Note that an empty list for dimensions is valid, and constructs a 0 dimensional tensor with
     * a single element (since the product of an empty list is 1).
     */
    #[track_caller]
    pub fn from(shape: [(Dimension, usize); D], data: Vec<T>) -> Self {
        InvalidShapeError::validate_dimensions_or_panic(&shape, data.len());
        let strides = compute_strides(&shape);
        Tensor {
            data,
            shape,
            strides,
        }
    }

    /**
     * Creates a Tensor with a particular shape initialised from a function.
     *
     * The product of the dimension lengths corresponds to the number of elements the Tensor
     * will store. Elements are stored in what would be row major order for a Matrix.
     * Each step in memory through the N dimensions corresponds to incrementing the rightmost
     * index, hence a shape of `[("row", 5), ("column", 5)]` would mean the first 6 elements
     * passed in the Vec would be for (0,0), (0,1), (0,2), (0,3), (0,4), (1,0) and so on to (4,4)
     * for the 25th and final element. These same indexes will be passed to the producer function
     * to initialised the values for the Tensor.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let tensor = Tensor::from_fn([("rows", 4), ("columns", 4)], |[r, c]| r * c);
     * assert_eq!(
     *     tensor,
     *     Tensor::from([("rows", 4), ("columns", 4)], vec![
     *         0, 0, 0, 0,
     *         0, 1, 2, 3,
     *         0, 2, 4, 6,
     *         0, 3, 6, 9,
     *     ])
     * );
     * ```
     *
     * # Panics
     *
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     *
     * Note that an empty list for dimensions is valid, and constructs a 0 dimensional tensor with
     * a single element (since the product of an empty list is 1).
     */
    #[track_caller]
    pub fn from_fn<F>(shape: [(Dimension, usize); D], mut producer: F) -> Self
    where
        F: FnMut([usize; D]) -> T,
    {
        let length = dimensions::elements(&shape);
        let mut data = Vec::with_capacity(length);
        let iterator = ShapeIterator::from(shape);
        for index in iterator {
            data.push(producer(index));
        }
        Tensor::from(shape, data)
    }

    /**
     * The shape of this tensor. Since Tensors are named Tensors, their shape is not just a
     * list of lengths along each dimension, but instead a list of pairs of names and lengths.
     *
     * See also
     * - [dimensions]
     * - [indexing]
     */
    pub fn shape(&self) -> [(Dimension, usize); D] {
        self.shape
    }

    /**
     * Returns the length of the dimension name provided, if one is present in the Tensor.
     *
     * See also
     * - [dimensions]
     * - [indexing]
     */
    pub fn length_of(&self, dimension: Dimension) -> Option<usize> {
        dimensions::length_of(&self.shape, dimension)
    }

    /**
     * Returns the last index of the dimension name provided, if one is present in the Tensor.
     *
     * This is always 1 less than the length, the 'index' in this sense is based on what the
     * Tensor's shape is, not any implementation index.
     *
     * See also
     * - [dimensions]
     * - [indexing]
     */
    pub fn last_index_of(&self, dimension: Dimension) -> Option<usize> {
        dimensions::last_index_of(&self.shape, dimension)
    }

    /**
     * A non panicking version of [from](Tensor::from) which returns `Result::Err` if the input
     * is invalid.
     *
     * Creates a Tensor with a particular number of dimensions and lengths in each dimension.
     *
     * The product of the dimension lengths corresponds to the number of elements the Tensor
     * will store. Elements are stored in what would be row major order for a Matrix.
     * Each step in memory through the N dimensions corresponds to incrementing the rightmost
     * index, hence a shape of `[("row", 5), ("column", 5)]` would mean the first 6 elements
     * passed in the Vec would be for (0,0), (0,1), (0,2), (0,3), (0,4), (1,0) and so on to (4,4)
     * for the 25th and final element.
     *
     * Returns the Err variant if
     * - If the number of provided elements does not match the product of the dimension lengths.
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     *
     * Note that an empty list for dimensions is valid, and constructs a 0 dimensional tensor with
     * a single element (since the product of an empty list is 1).
     */
    pub fn try_from(
        shape: [(Dimension, usize); D],
        data: Vec<T>,
    ) -> Result<Self, InvalidShapeError<D>> {
        let valid = InvalidShapeError::validate_dimensions(&shape, data.len());
        if !valid {
            return Err(InvalidShapeError::new(shape));
        }
        let strides = compute_strides(&shape);
        Ok(Tensor {
            data,
            shape,
            strides,
        })
    }

    /// Unverified constructor for interal use when we know the dimensions/data/strides are
    /// unchanged and don't need reverification
    pub(crate) fn direct_from(
        data: Vec<T>,
        shape: [(Dimension, usize); D],
        strides: [usize; D],
    ) -> Self {
        Tensor {
            data,
            shape,
            strides,
        }
    }

    /// Unverified constructor for interal use when we know the dimensions/data/strides are
    /// the same as the existing instance and don't need reverification
    #[allow(dead_code)] // pretty sure something else will want this in the future
    pub(crate) fn new_with_same_shape(&self, data: Vec<T>) -> Self {
        Tensor {
            data,
            shape: self.shape,
            strides: self.strides,
        }
    }
}

impl<T> Tensor<T, 0> {
    /**
     * Creates a 0 dimensional tensor from some scalar
     */
    pub fn from_scalar(value: T) -> Tensor<T, 0> {
        Tensor {
            data: vec![value],
            shape: [],
            strides: [],
        }
    }

    /**
     * Returns the sole element of the 0 dimensional tensor.
     */
    pub fn into_scalar(self) -> T {
        self.data
            .into_iter()
            .next()
            .expect("Tensors always have at least 1 element")
    }
}

impl<T> Tensor<T, 0>
where
    T: Clone,
{
    /**
     * Returns a copy of the sole element in the 0 dimensional tensor.
     */
    pub fn scalar(&self) -> T {
        self.data
            .first()
            .expect("Tensors always have at least 1 element")
            .clone()
    }
}

impl<T> From<T> for Tensor<T, 0> {
    fn from(scalar: T) -> Tensor<T, 0> {
        Tensor::from_scalar(scalar)
    }
}
// TODO: See if we can find a way to write the reverse Tensor<T, 0> -> T conversion using From or Into (doesn't seem like we can?)

// # Safety
//
// We promise to never implement interior mutability for Tensor.
/**
 * A Tensor implements TensorRef.
 */
unsafe impl<T, const D: usize> TensorRef<T, D> for Tensor<T, D> {
    fn get_reference(&self, indexes: [usize; D]) -> Option<&T> {
        let i = get_index_direct(&indexes, &self.strides, &self.shape)?;
        self.data.get(i)
    }

    fn view_shape(&self) -> [(Dimension, usize); D] {
        Tensor::shape(self)
    }

    unsafe fn get_reference_unchecked(&self, indexes: [usize; D]) -> &T {
        unsafe {
            // The point of get_reference_unchecked is no bounds checking, and therefore
            // it does not make any sense to just use `unwrap` here. The trait documents that
            // it's undefind behaviour to call this method with an out of bounds index, so we
            // can assume the None case will never happen.
            let i = get_index_direct(&indexes, &self.strides, &self.shape).unwrap_unchecked();
            self.data.get_unchecked(i)
        }
    }

    fn data_layout(&self) -> DataLayout<D> {
        // We always have our memory in most significant to least
        DataLayout::Linear(std::array::from_fn(|i| self.shape[i].0))
    }
}

// # Safety
//
// We promise to never implement interior mutability for Tensor.
unsafe impl<T, const D: usize> TensorMut<T, D> for Tensor<T, D> {
    fn get_reference_mut(&mut self, indexes: [usize; D]) -> Option<&mut T> {
        let i = get_index_direct(&indexes, &self.strides, &self.shape)?;
        self.data.get_mut(i)
    }

    unsafe fn get_reference_unchecked_mut(&mut self, indexes: [usize; D]) -> &mut T {
        unsafe {
            // The point of get_reference_unchecked_mut is no bounds checking, and therefore
            // it does not make any sense to just use `unwrap` here. The trait documents that
            // it's undefind behaviour to call this method with an out of bounds index, so we
            // can assume the None case will never happen.
            let i = get_index_direct(&indexes, &self.strides, &self.shape).unwrap_unchecked();
            self.data.get_unchecked_mut(i)
        }
    }
}

/**
 * Any tensor of a Cloneable type implements Clone.
 */
impl<T: Clone, const D: usize> Clone for Tensor<T, D> {
    fn clone(&self) -> Self {
        self.map(|element| element)
    }
}

/**
 * Any tensor of a Displayable type implements Display
 *
 * You can control the precision of the formatting using format arguments, i.e.
 * `format!("{:.3}", tensor)`
 */
impl<T: std::fmt::Display, const D: usize> std::fmt::Display for Tensor<T, D> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        crate::tensors::display::format_view(self, f)
    }
}

/**
 * Any 2 dimensional tensor can be converted to a matrix with rows equal to the length of the
 * first dimension in the tensor, and columns equal to the length of the second.
 */
impl<T> From<Tensor<T, 2>> for crate::matrices::Matrix<T> {
    fn from(tensor: Tensor<T, 2>) -> Self {
        crate::matrices::Matrix::from_flat_row_major(
            (tensor.shape[0].1, tensor.shape[1].1),
            tensor.data,
        )
    }
}

pub(crate) fn compute_strides<const D: usize>(shape: &[(Dimension, usize); D]) -> [usize; D] {
    std::array::from_fn(|d| shape.iter().skip(d + 1).map(|d| d.1).product())
}

/// returns the 1 dimensional index to use to get the requested index into some tensor
#[inline]
pub(crate) fn get_index_direct<const D: usize>(
    // indexes to use
    indexes: &[usize; D],
    // strides for indexing into the tensor
    strides: &[usize; D],
    // shape of the tensor to index into
    shape: &[(Dimension, usize); D],
) -> Option<usize> {
    let mut index = 0;
    for d in 0..D {
        let n = indexes[d];
        if n >= shape[d].1 {
            return None;
        }
        index += n * strides[d];
    }
    Some(index)
}

/// returns the 1 dimensional index to use to get the requested index into some tensor, without
/// checking the indexes are within bounds for the shape.
#[inline]
fn get_index_direct_unchecked<const D: usize>(
    // indexes to use
    indexes: &[usize; D],
    // strides for indexing into the tensor
    strides: &[usize; D],
) -> usize {
    let mut index = 0;
    for d in 0..D {
        let n = indexes[d];
        index += n * strides[d];
    }
    index
}

impl<T, const D: usize> Tensor<T, D> {
    pub fn view(&self) -> TensorView<T, &Tensor<T, D>, D> {
        TensorView::from(self)
    }

    pub fn view_mut(&mut self) -> TensorView<T, &mut Tensor<T, D>, D> {
        TensorView::from(self)
    }

    pub fn view_owned(self) -> TensorView<T, Tensor<T, D>, D> {
        TensorView::from(self)
    }

    /**
     * Returns a TensorAccess which can be indexed in the order of the supplied dimensions
     * to read values from this tensor.
     *
     * # Panics
     *
     * If the set of dimensions supplied do not match the set of dimensions in this tensor's shape.
     */
    #[track_caller]
    pub fn index_by(&self, dimensions: [Dimension; D]) -> TensorAccess<T, &Tensor<T, D>, D> {
        TensorAccess::from(self, dimensions)
    }

    /**
     * Returns a TensorAccess which can be indexed in the order of the supplied dimensions
     * to read or write values from this tensor.
     *
     * # Panics
     *
     * If the set of dimensions supplied do not match the set of dimensions in this tensor's shape.
     */
    #[track_caller]
    pub fn index_by_mut(
        &mut self,
        dimensions: [Dimension; D],
    ) -> TensorAccess<T, &mut Tensor<T, D>, D> {
        TensorAccess::from(self, dimensions)
    }

    /**
     * Returns a TensorAccess which can be indexed in the order of the supplied dimensions
     * to read or write values from this tensor.
     *
     * # Panics
     *
     * If the set of dimensions supplied do not match the set of dimensions in this tensor's shape.
     */
    #[track_caller]
    pub fn index_by_owned(self, dimensions: [Dimension; D]) -> TensorAccess<T, Tensor<T, D>, D> {
        TensorAccess::from(self, dimensions)
    }

    /**
     * Creates a TensorAccess which will index into the dimensions this Tensor was created with
     * in the same order as they were provided. See [TensorAccess::from_source_order].
     */
    pub fn index(&self) -> TensorAccess<T, &Tensor<T, D>, D> {
        TensorAccess::from_source_order(self)
    }

    /**
     * Creates a TensorAccess which will index into the dimensions this Tensor was
     * created with in the same order as they were provided. The TensorAccess mutably borrows
     * the Tensor, and can therefore mutate it. See [TensorAccess::from_source_order].
     */
    pub fn index_mut(&mut self) -> TensorAccess<T, &mut Tensor<T, D>, D> {
        TensorAccess::from_source_order(self)
    }

    /**
     * Creates a TensorAccess which will index into the dimensions this Tensor was
     * created with in the same order as they were provided. The TensorAccess takes ownership
     * of the Tensor, and can therefore mutate it. See [TensorAccess::from_source_order].
     */
    pub fn index_owned(self) -> TensorAccess<T, Tensor<T, D>, D> {
        TensorAccess::from_source_order(self)
    }

    /**
     * Returns an iterator over references to the data in this Tensor.
     */
    pub fn iter_reference(&self) -> TensorReferenceIterator<'_, T, Tensor<T, D>, D> {
        TensorReferenceIterator::from(self)
    }

    /**
     * Returns an iterator over mutable references to the data in this Tensor.
     */
    pub fn iter_reference_mut(&mut self) -> TensorReferenceMutIterator<'_, T, Tensor<T, D>, D> {
        TensorReferenceMutIterator::from(self)
    }

    /**
     * Creates an iterator over the values in this Tensor.
     */
    pub fn iter_owned(self) -> TensorOwnedIterator<T, Tensor<T, D>, D>
    where
        T: Default,
    {
        TensorOwnedIterator::from(self)
    }

    // Non public index order reference iterator since we don't want to expose our implementation
    // details to public API since then we could never change them.
    pub(crate) fn direct_iter_reference(&self) -> std::slice::Iter<'_, T> {
        self.data.iter()
    }

    // Non public index order reference iterator since we don't want to expose our implementation
    // details to public API since then we could never change them.
    pub(crate) fn direct_iter_reference_mut(&mut self) -> std::slice::IterMut<'_, T> {
        self.data.iter_mut()
    }

    /**
     * Renames the dimension names of the tensor without changing the lengths of the dimensions
     * in the tensor or moving any data around.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let mut tensor = Tensor::from([("x", 2), ("y", 3)], vec![1, 2, 3, 4, 5, 6]);
     * tensor.rename(["y", "z"]);
     * assert_eq!([("y", 2), ("z", 3)], tensor.shape());
     * ```
     *
     * # Panics
     *
     * - If a dimension name is not unique
     */
    #[track_caller]
    pub fn rename(&mut self, dimensions: [Dimension; D]) {
        if crate::tensors::dimensions::has_duplicates_names(&dimensions) {
            panic!("Dimension names must all be unique: {:?}", &dimensions);
        }
        #[allow(clippy::needless_range_loop)]
        for d in 0..D {
            self.shape[d].0 = dimensions[d];
        }
    }

    /**
     * Renames the dimension names of the tensor and returns it without changing the lengths
     * of the dimensions in the tensor or moving any data around.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let tensor = Tensor::from([("x", 2), ("y", 3)], vec![1, 2, 3, 4, 5, 6])
     *     .rename_owned(["y", "z"]);
     * assert_eq!([("y", 2), ("z", 3)], tensor.shape());
     * ```
     *
     * # Panics
     *
     * - If a dimension name is not unique
     */
    #[track_caller]
    pub fn rename_owned(mut self, dimensions: [Dimension; D]) -> Tensor<T, D> {
        self.rename(dimensions);
        self
    }

    /**
     * Returns a TensorView with the dimension names of the shape renamed to the provided
     * dimensions. The data of this tensor and the dimension lengths and order remain unchanged.
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * use easy_ml::tensors::views::{TensorView, TensorRename};
     * let abc = Tensor::from([("a", 3), ("b", 3), ("c", 3)], (0..27).collect());
     * let xyz = abc.rename_view(["x", "y", "z"]);
     * let also_xyz = TensorView::from(TensorRename::from(&abc, ["x", "y", "z"]));
     * assert_eq!(xyz, also_xyz);
     * assert_eq!(xyz, Tensor::from([("x", 3), ("y", 3), ("z", 3)], (0..27).collect()));
     * ```
     *
     * # Panics
     *
     * - If a dimension name is not unique
     */
    #[track_caller]
    pub fn rename_view(
        &self,
        dimensions: [Dimension; D],
    ) -> TensorView<T, TensorRename<T, &Tensor<T, D>, D>, D> {
        TensorView::from(TensorRename::from(self, dimensions))
    }

    /**
     * Changes the shape of the tensor without changing the number of dimensions or moving any
     * data around.
     *
     * # Panics
     *
     * - If the number of provided elements in the new shape does not match the product of the
     * dimension lengths in the existing tensor's shape.
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let mut tensor = Tensor::from([("width", 2), ("height", 2)], vec![
     *     1, 2,
     *     3, 4
     * ]);
     * tensor.reshape_mut([("batch", 1), ("image", 4)]);
     * assert_eq!(tensor, Tensor::from([("batch", 1), ("image", 4)], vec![ 1, 2, 3, 4 ]));
     * ```
     */
    #[track_caller]
    pub fn reshape_mut(&mut self, shape: [(Dimension, usize); D]) {
        InvalidShapeError::validate_dimensions_or_panic(&shape, self.data.len());
        let strides = compute_strides(&shape);
        self.shape = shape;
        self.strides = strides;
    }

    /**
     * Consumes the tensor and changes the shape of the tensor without moving any
     * data around. The new Tensor may also have a different number of dimensions.
     *
     * # Panics
     *
     * - If the number of provided elements in the new shape does not match the product of the
     * dimension lengths in the existing tensor's shape.
     * - If a dimension name is not unique
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let tensor = Tensor::from([("width", 2), ("height", 2)], vec![
     *     1, 2,
     *     3, 4
     * ]);
     * let flattened = tensor.reshape_owned([("image", 4)]);
     * assert_eq!(flattened, Tensor::from([("image", 4)], vec![ 1, 2, 3, 4 ]));
     * ```
     *
     * See also [reshape_view_owned](Tensor::reshape_view_owned)
     */
    #[track_caller]
    pub fn reshape_owned<const D2: usize>(self, shape: [(Dimension, usize); D2]) -> Tensor<T, D2> {
        Tensor::from(shape, self.data)
    }

    /**
     * Returns a TensorView with the dimensions changed to the provided shape without moving any
     * data around. The new Tensor may also have a different number of dimensions.
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If the number of provided elements in the new shape does not match the product of the
     * dimension lengths in the existing tensor's shape.
     * - If a dimension name is not unique
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let tensor = Tensor::from([("width", 2), ("height", 2)], vec![
     *     1, 2,
     *     3, 4
     * ]);
     * let flattened = tensor.reshape_view([("image", 4)]);
     * assert_eq!(flattened, Tensor::from([("image", 4)], vec![ 1, 2, 3, 4 ]));
     * ```
     */
    pub fn reshape_view<const D2: usize>(
        &self,
        shape: [(Dimension, usize); D2],
    ) -> TensorView<T, TensorReshape<T, &Tensor<T, D>, D, D2>, D2> {
        TensorView::from(TensorReshape::from(self, shape))
    }

    /**
     * Returns a TensorView with the dimensions changed to the provided shape without moving any
     * data around. The new Tensor may also have a different number of dimensions.
     *
     * This is a shorthand for constructing the TensorView from this Tensor. The TensorReshape
     * mutably borrows this Tensor, and can therefore mutate it
     *
     * # Panics
     *
     * - If the number of provided elements in the new shape does not match the product of the
     * dimension lengths in the existing tensor's shape.
     * - If a dimension name is not unique
     */
    pub fn reshape_view_mut<const D2: usize>(
        &mut self,
        shape: [(Dimension, usize); D2],
    ) -> TensorView<T, TensorReshape<T, &mut Tensor<T, D>, D, D2>, D2> {
        TensorView::from(TensorReshape::from(self, shape))
    }

    /**
     * Returns a TensorView with the dimensions changed to the provided shape without moving any
     * data around. The new Tensor may also have a different number of dimensions.
     *
     * This is a shorthand for constructing the TensorView from this Tensor. The TensorReshape
     * takes ownership of this Tensor, and can therefore mutate it
     *
     * # Panics
     *
     * - If the number of provided elements in the new shape does not match the product of the
     * dimension lengths in the existing tensor's shape.
     * - If a dimension name is not unique
     *
     * See also [reshape_owned](Tensor::reshape_owned)
     */
    pub fn reshape_view_owned<const D2: usize>(
        self,
        shape: [(Dimension, usize); D2],
    ) -> TensorView<T, TensorReshape<T, Tensor<T, D>, D, D2>, D2> {
        TensorView::from(TensorReshape::from(self, shape))
    }

    /**
     * Given the dimension name, returns a view of this tensor reshaped to one dimension
     * with a length equal to the number of elements in this tensor.
     */
    pub fn flatten_view(
        &self,
        dimension: Dimension,
    ) -> TensorView<T, TensorReshape<T, &Tensor<T, D>, D, 1>, 1> {
        self.reshape_view([(dimension, dimensions::elements(&self.shape))])
    }

    /**
     * Given the dimension name, returns a view of this tensor reshaped to one dimension
     * with a length equal to the number of elements in this tensor.
     */
    pub fn flatten_view_mut(
        &mut self,
        dimension: Dimension,
    ) -> TensorView<T, TensorReshape<T, &mut Tensor<T, D>, D, 1>, 1> {
        self.reshape_view_mut([(dimension, dimensions::elements(&self.shape))])
    }

    /**
     * Given the dimension name, returns a view of this tensor reshaped to one dimension
     * with a length equal to the number of elements in this tensor.
     *
     * If you intend to query the tensor a lot after creating the view, consider
     * using [flatten](Tensor::flatten) instead as it will have less overhead to
     * index after creation.
     */
    pub fn flatten_view_owned(
        self,
        dimension: Dimension,
    ) -> TensorView<T, TensorReshape<T, Tensor<T, D>, D, 1>, 1> {
        let length = dimensions::elements(&self.shape);
        self.reshape_view_owned([(dimension, length)])
    }

    /**
     * Given the dimension name, returns a new tensor reshaped to one dimension
     * with a length equal to the number of elements in this tensor.
     */
    pub fn flatten(self, dimension: Dimension) -> Tensor<T, 1> {
        let length = dimensions::elements(&self.shape);
        self.reshape_owned([(dimension, length)])
    }

    /**
     * Returns a TensorView with a range taken in P dimensions, hiding the values **outside** the
     * range from view. Error cases are documented on [TensorRange].
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * use easy_ml::tensors::views::{TensorView, TensorRange, IndexRange};
     * # use easy_ml::tensors::views::IndexRangeValidationError;
     * # fn main() -> Result<(), IndexRangeValidationError<3, 2>> {
     * let samples = Tensor::from([("batch", 5), ("x", 7), ("y", 7)], (0..(5 * 7 * 7)).collect());
     * let cropped = samples.range([("x", IndexRange::new(1, 5)), ("y", IndexRange::new(1, 5))])?;
     * let also_cropped = TensorView::from(
     *     TensorRange::from(&samples, [("x", 1..6), ("y", 1..6)])?
     * );
     * assert_eq!(cropped, also_cropped);
     * assert_eq!(
     *     cropped.select([("batch", 0)]),
     *     Tensor::from([("x", 5), ("y", 5)], vec![
     *          8,  9, 10, 11, 12,
     *         15, 16, 17, 18, 19,
     *         22, 23, 24, 25, 26,
     *         29, 30, 31, 32, 33,
     *         36, 37, 38, 39, 40
     *     ])
     * );
     * # Ok(())
     * # }
     * ```
     */
    pub fn range<R, const P: usize>(
        &self,
        ranges: [(Dimension, R); P],
    ) -> Result<TensorView<T, TensorRange<T, &Tensor<T, D>, D>, D>, IndexRangeValidationError<D, P>>
    where
        R: Into<IndexRange>,
    {
        TensorRange::from(self, ranges).map(|range| TensorView::from(range))
    }

    /**
     * Returns a TensorView with a range taken in P dimensions, hiding the values **outside** the
     * range from view. Error cases are documented on [TensorRange]. The TensorRange
     * mutably borrows this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     */
    pub fn range_mut<R, const P: usize>(
        &mut self,
        ranges: [(Dimension, R); P],
    ) -> Result<
        TensorView<T, TensorRange<T, &mut Tensor<T, D>, D>, D>,
        IndexRangeValidationError<D, P>,
    >
    where
        R: Into<IndexRange>,
    {
        TensorRange::from(self, ranges).map(|range| TensorView::from(range))
    }

    /**
     * Returns a TensorView with a range taken in P dimensions, hiding the values **outside** the
     * range from view. Error cases are documented on [TensorRange]. The TensorRange
     * takes ownership of this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     */
    pub fn range_owned<R, const P: usize>(
        self,
        ranges: [(Dimension, R); P],
    ) -> Result<TensorView<T, TensorRange<T, Tensor<T, D>, D>, D>, IndexRangeValidationError<D, P>>
    where
        R: Into<IndexRange>,
    {
        TensorRange::from(self, ranges).map(|range| TensorView::from(range))
    }

    /**
     * Returns a TensorView with a mask taken in P dimensions, hiding the values **inside** the
     * range from view. Error cases are documented on [TensorMask].
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * use easy_ml::tensors::views::{TensorView, TensorMask, IndexRange};
     * # use easy_ml::tensors::views::IndexRangeValidationError;
     * # fn main() -> Result<(), IndexRangeValidationError<3, 2>> {
     * let samples = Tensor::from([("batch", 5), ("x", 7), ("y", 7)], (0..(5 * 7 * 7)).collect());
     * let corners = samples.mask([("x", IndexRange::new(3, 2)), ("y", IndexRange::new(3, 2))])?;
     * let also_corners = TensorView::from(
     *     TensorMask::from(&samples, [("x", 3..5), ("y", 3..5)])?
     * );
     * assert_eq!(corners, also_corners);
     * assert_eq!(
     *     corners.select([("batch", 0)]),
     *     Tensor::from([("x", 5), ("y", 5)], vec![
     *          0,  1,  2,    5, 6,
     *          7,  8,  9,   12, 13,
     *         14, 15, 16,   19, 20,
     *
     *         35, 36, 37,   40, 41,
     *         42, 43, 44,   47, 48
     *     ])
     * );
     * # Ok(())
     * # }
     * ```
     */
    pub fn mask<R, const P: usize>(
        &self,
        masks: [(Dimension, R); P],
    ) -> Result<TensorView<T, TensorMask<T, &Tensor<T, D>, D>, D>, IndexRangeValidationError<D, P>>
    where
        R: Into<IndexRange>,
    {
        TensorMask::from(self, masks).map(|mask| TensorView::from(mask))
    }

    /**
     * Returns a TensorView with a mask taken in P dimensions, hiding the values **inside** the
     * range from view. Error cases are documented on [TensorMask]. The TensorMask
     * mutably borrows this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     */
    pub fn mask_mut<R, const P: usize>(
        &mut self,
        masks: [(Dimension, R); P],
    ) -> Result<
        TensorView<T, TensorMask<T, &mut Tensor<T, D>, D>, D>,
        IndexRangeValidationError<D, P>,
    >
    where
        R: Into<IndexRange>,
    {
        TensorMask::from(self, masks).map(|mask| TensorView::from(mask))
    }

    /**
     * Returns a TensorView with a mask taken in P dimensions, hiding the values **inside** the
     * range from view. Error cases are documented on [TensorMask]. The TensorMask
     * takes ownership of this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     */
    pub fn mask_owned<R, const P: usize>(
        self,
        masks: [(Dimension, R); P],
    ) -> Result<TensorView<T, TensorMask<T, Tensor<T, D>, D>, D>, IndexRangeValidationError<D, P>>
    where
        R: Into<IndexRange>,
    {
        TensorMask::from(self, masks).map(|mask| TensorView::from(mask))
    }

    /**
     * Returns a TensorView with a mask taken in the provided dimension, hiding
     * all but the start_and_end number of values at the start and end of the
     * dimension from view.
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If the start_and_end value is 0 - this is not a valid mask as it would
     * hide all elements
     * - If the dimension is not in the tensor's shape.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let samples = Tensor::from([("batch", 5), ("x", 2), ("y", 2)], (0..20).collect());
     * let shortlist = samples.start_and_end_of("batch", 1);
     * assert_eq!(
     *     shortlist,
     *     Tensor::from([("batch", 2), ("x", 2), ("y", 2)], vec![
     *         0, 1,
     *         2, 3,
     *
     *         16, 17,
     *         18, 19,
     *     ])
     * )
     * ```
     */
    #[track_caller]
    pub fn start_and_end_of(
        &self,
        dimension: Dimension,
        start_and_end: usize,
    ) -> TensorView<T, TensorMask<T, &Tensor<T, D>, D>, D> {
        TensorMask::panicking_start_and_end_of(self, dimension, start_and_end)
    }

    /**
     * Returns a TensorView with a mask taken in the provided dimension, hiding
     * all but the start_and_end number of values at the start and end of the
     * dimension from view. The TensorMask mutably borrows this Tensor, and can
     * therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If the start_and_end value is 0 - this is not a valid mask as it would
     * hide all elements
     * - If the dimension is not in the tensor's shape.
     */
    #[track_caller]
    pub fn start_and_end_of_mut(
        &mut self,
        dimension: Dimension,
        start_and_end: usize,
    ) -> TensorView<T, TensorMask<T, &mut Tensor<T, D>, D>, D> {
        TensorMask::panicking_start_and_end_of(self, dimension, start_and_end)
    }

    /**
     * Returns a TensorView with a mask taken in the provided dimension, hiding
     * all but the start_and_end number of values at the start and end of the
     * dimension from view. The TensorMask takes ownership of this Tensor, and
     * can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If the start_and_end value is 0 - this is not a valid mask as it would
     * hide all elements
     * - If the dimension is not in the tensor's shape.
     */
    #[track_caller]
    pub fn start_and_end_of_owned(
        self,
        dimension: Dimension,
        start_and_end: usize,
    ) -> TensorView<T, TensorMask<T, Tensor<T, D>, D>, D> {
        TensorMask::panicking_start_and_end_of(self, dimension, start_and_end)
    }

    /**
     * Returns a TensorView with the dimension names provided of the shape reversed in iteration
     * order. The data of this tensor and the dimension lengths remain unchanged.
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * use easy_ml::tensors::views::{TensorView, TensorReverse};
     * let ab = Tensor::from([("a", 2), ("b", 3)], (0..6).collect());
     * let reversed = ab.reverse(&["a"]);
     * let also_reversed = TensorView::from(TensorReverse::from(&ab, &["a"]));
     * assert_eq!(reversed, also_reversed);
     * assert_eq!(
     *     reversed,
     *     Tensor::from(
     *         [("a", 2), ("b", 3)],
     *         vec![
     *             3, 4, 5,
     *             0, 1, 2,
     *         ]
     *     )
     * );
     * ```
     *
     * # Panics
     *
     * - If a dimension name is not in the tensor's shape or is repeated.
     */
    #[track_caller]
    pub fn reverse(
        &self,
        dimensions: &[Dimension],
    ) -> TensorView<T, TensorReverse<T, &Tensor<T, D>, D>, D> {
        TensorView::from(TensorReverse::from(self, dimensions))
    }

    /**
     * Returns a TensorView with the dimension names provided of the shape reversed in iteration
     * order. The data of this tensor and the dimension lengths remain unchanged. The TensorReverse
     * mutably borrows this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If a dimension name is not in the tensor's shape or is repeated.
     */
    #[track_caller]
    pub fn reverse_mut(
        &mut self,
        dimensions: &[Dimension],
    ) -> TensorView<T, TensorReverse<T, &mut Tensor<T, D>, D>, D> {
        TensorView::from(TensorReverse::from(self, dimensions))
    }

    /**
     * Returns a TensorView with the dimension names provided of the shape reversed in iteration
     * order. The data of this tensor and the dimension lengths remain unchanged. The TensorReverse
     * takes ownership of this Tensor, and can therefore mutate it
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * # Panics
     *
     * - If a dimension name is not in the tensor's shape or is repeated.
     */
    #[track_caller]
    pub fn reverse_owned(
        self,
        dimensions: &[Dimension],
    ) -> TensorView<T, TensorReverse<T, Tensor<T, D>, D>, D> {
        TensorView::from(TensorReverse::from(self, dimensions))
    }

    /**
     * Creates and returns a new tensor with all value pairs of two tensors with the same shape
     * mapped by a function. The value pairs are not copied for you, if you're using `Copy` types
     * or need to clone the values anyway, you can use
     * [`Tensor::elementwise`](Tensor::elementwise) instead.
     *
     * # Generics
     *
     * This method can be called with any right hand side that can be converted to a TensorView,
     * which includes `Tensor`, `&Tensor`, `&mut Tensor` as well as references to a `TensorView`.
     *
     * # Panics
     *
     * If the two tensors have different shapes.
     */
    #[track_caller]
    pub fn elementwise_reference<S, I, M>(&self, rhs: I, mapping_function: M) -> Tensor<T, D>
    where
        I: Into<TensorView<T, S, D>>,
        S: TensorRef<T, D>,
        M: Fn(&T, &T) -> T,
    {
        self.elementwise_reference_less_generic(rhs.into(), mapping_function)
    }

    /**
     * Creates and returns a new tensor with all value pairs of two tensors with the same shape
     * mapped by a function. The mapping function also receives each index corresponding to the
     * value pairs. The value pairs are not copied for you, if you're using `Copy` types
     * or need to clone the values anyway, you can use
     * [`Tensor::elementwise_with_index`](Tensor::elementwise_with_index) instead.
     *
     * # Generics
     *
     * This method can be called with any right hand side that can be converted to a TensorView,
     * which includes `Tensor`, `&Tensor`, `&mut Tensor` as well as references to a `TensorView`.
     *
     * # Panics
     *
     * If the two tensors have different shapes.
     */
    #[track_caller]
    pub fn elementwise_reference_with_index<S, I, M>(
        &self,
        rhs: I,
        mapping_function: M,
    ) -> Tensor<T, D>
    where
        I: Into<TensorView<T, S, D>>,
        S: TensorRef<T, D>,
        M: Fn([usize; D], &T, &T) -> T,
    {
        self.elementwise_reference_less_generic_with_index(rhs.into(), mapping_function)
    }

    #[track_caller]
    fn elementwise_reference_less_generic<S, M>(
        &self,
        rhs: TensorView<T, S, D>,
        mapping_function: M,
    ) -> Tensor<T, D>
    where
        S: TensorRef<T, D>,
        M: Fn(&T, &T) -> T,
    {
        let left_shape = self.shape();
        let right_shape = rhs.shape();
        if left_shape != right_shape {
            panic!(
                "Dimensions of left and right tensors are not the same: (left: {:?}, right: {:?})",
                left_shape, right_shape
            );
        }
        let mapped = self
            .direct_iter_reference()
            .zip(rhs.iter_reference())
            .map(|(x, y)| mapping_function(x, y))
            .collect();
        // We're not changing the shape of the Tensor, so don't need to revalidate
        Tensor::direct_from(mapped, self.shape, self.strides)
    }

    #[track_caller]
    fn elementwise_reference_less_generic_with_index<S, M>(
        &self,
        rhs: TensorView<T, S, D>,
        mapping_function: M,
    ) -> Tensor<T, D>
    where
        S: TensorRef<T, D>,
        M: Fn([usize; D], &T, &T) -> T,
    {
        let left_shape = self.shape();
        let right_shape = rhs.shape();
        if left_shape != right_shape {
            panic!(
                "Dimensions of left and right tensors are not the same: (left: {:?}, right: {:?})",
                left_shape, right_shape
            );
        }
        // we just checked both shapes were the same, so we don't need to propagate indexes
        // for both tensors because they'll be identical
        let mapped = self
            .direct_iter_reference()
            .zip(rhs.iter_reference().with_index())
            .map(|(x, (i, y))| mapping_function(i, x, y))
            .collect();
        // We're not changing the shape of the Tensor, so don't need to revalidate
        Tensor::direct_from(mapped, self.shape, self.strides)
    }

    /**
     * Returns a TensorView which makes the order of the data in this tensor appear to be in
     * a different order. The order of the dimension names is unchanged, although their lengths
     * may swap.
     *
     * This is a shorthand for constructing the TensorView from this Tensor.
     *
     * See also: [transpose](Tensor::transpose), [TensorTranspose]
     *
     * # Panics
     *
     * If the set of dimensions in the tensor does not match the set of dimensions provided. The
     * order need not match.
     */
    pub fn transpose_view(
        &self,
        dimensions: [Dimension; D],
    ) -> TensorView<T, TensorTranspose<T, &Tensor<T, D>, D>, D> {
        TensorView::from(TensorTranspose::from(self, dimensions))
    }
}

impl<T, const D: usize> Tensor<T, D>
where
    T: Clone,
{
    /**
     * Creates a tensor with a particular number of dimensions and length in each dimension
     * with all elements initialised to the provided value.
     *
     * # Panics
     *
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     */
    #[track_caller]
    pub fn empty(shape: [(Dimension, usize); D], value: T) -> Self {
        let elements = crate::tensors::dimensions::elements(&shape);
        Tensor::from(shape, vec![value; elements])
    }

    /**
     * Gets a copy of the first value in this tensor.
     * For 0 dimensional tensors this is the only index `[]`, for 1 dimensional tensors this
     * is `[0]`, for 2 dimensional tensors `[0,0]`, etcetera.
     */
    pub fn first(&self) -> T {
        self.data
            .first()
            .expect("Tensors always have at least 1 element")
            .clone()
    }

    /**
     * Returns a new Tensor which has the same data as this tensor, but with the order of data
     * changed. The order of the dimension names is unchanged, although their lengths may swap.
     *
     * For example, with a `[("x", x), ("y", y)]` tensor you could call
     * `transpose(["y", "x"])` which would return a new tensor with a shape of
     * `[("x", y), ("y", x)]` where every (x,y) of its data corresponds to (y,x) in the original.
     *
     * This method need not shift *all* the dimensions though, you could also swap the width
     * and height of images in a tensor with a shape of
     * `[("batch", b), ("h", h), ("w", w), ("c", c)]` via `transpose(["batch", "w", "h", "c"])`
     * which would return a new tensor where all the images have been swapped over the diagonal.
     *
     * See also: [TensorAccess], [reorder](Tensor::reorder)
     *
     * # Panics
     *
     * If the set of dimensions in the tensor does not match the set of dimensions provided. The
     * order need not match (and if the order does match, this function is just an expensive
     * clone).
     */
    #[track_caller]
    pub fn transpose(&self, dimensions: [Dimension; D]) -> Tensor<T, D> {
        let shape = self.shape;
        let mut reordered = self.reorder(dimensions);
        // Transposition is essentially reordering, but we retain the dimension name ordering
        // of the original order, this means we may swap dimension lengths, but the dimensions
        // will not change order.
        #[allow(clippy::needless_range_loop)]
        for d in 0..D {
            reordered.shape[d].0 = shape[d].0;
        }
        reordered
    }

    /**
     * Modifies this tensor to have the same data as before, but with the order of data changed.
     * The order of the dimension names is unchanged, although their lengths may swap.
     *
     * For example, with a `[("x", x), ("y", y)]` tensor you could call
     * `transpose_mut(["y", "x"])` which would edit the tensor, updating its shape to
     * `[("x", y), ("y", x)]`, so every (x,y) of its data corresponds to (y,x) before the
     * transposition.
     *
     * The order swapping will try to be in place, but this is currently only supported for
     * square tensors with 2 dimensions. Other types of tensors will not be transposed in place.
     *
     * # Panics
     *
     * If the set of dimensions in the tensor does not match the set of dimensions provided. The
     * order need not match (and if the order does match, this function is just an expensive
     * clone).
     */
    #[track_caller]
    pub fn transpose_mut(&mut self, dimensions: [Dimension; D]) {
        let shape = self.shape;
        self.reorder_mut(dimensions);
        // Transposition is essentially reordering, but we retain the dimension name ordering
        // we had before, this means we may swap dimension lengths, but the dimensions
        // will not change order.
        #[allow(clippy::needless_range_loop)]
        for d in 0..D {
            self.shape[d].0 = shape[d].0;
        }
    }

    /**
     * Returns a new Tensor which has the same data as this tensor, but with the order of the
     * dimensions and corresponding order of data changed.
     *
     * For example, with a `[("x", x), ("y", y)]` tensor you could call
     * `reorder(["y", "x"])` which would return a new tensor with a shape of
     * `[("y", y), ("x", x)]` where every (y,x) of its data corresponds to (x,y) in the original.
     *
     * This method need not shift *all* the dimensions though, you could also swap the width
     * and height of images in a tensor with a shape of
     * `[("batch", b), ("h", h), ("w", w), ("c", c)]` via `reorder(["batch", "w", "h", "c"])`
     * which would return a new tensor where every (b,w,h,c) of its data corresponds to (b,h,w,c)
     * in the original.
     *
     * See also: [TensorAccess], [transpose](Tensor::transpose)
     *
     * # Panics
     *
     * If the set of dimensions in the tensor does not match the set of dimensions provided. The
     * order need not match (and if the order does match, this function is just an expensive
     * clone).
     */
    #[track_caller]
    pub fn reorder(&self, dimensions: [Dimension; D]) -> Tensor<T, D> {
        let reorderd = match TensorAccess::try_from(&self, dimensions) {
            Ok(reordered) => reordered,
            Err(_error) => panic!(
                "Dimension names provided {:?} must be the same set of dimension names in the tensor: {:?}",
                dimensions, &self.shape,
            ),
        };
        let reorderd_shape = reorderd.shape();
        Tensor::from(reorderd_shape, reorderd.iter().collect())
    }

    /**
     * Modifies this tensor to have the same data as before, but with the order of the
     * dimensions and corresponding order of data changed.
     *
     * For example, with a `[("x", x), ("y", y)]` tensor you could call
     * `reorder_mut(["y", "x"])` which would edit the tensor, updating its shape to
     * `[("y", y), ("x", x)]`, so every (y,x) of its data corresponds to (x,y) before the
     * transposition.
     *
     * The order swapping will try to be in place, but this is currently only supported for
     * square tensors with 2 dimensions. Other types of tensors will not be reordered in place.
     *
     * # Panics
     *
     * If the set of dimensions in the tensor does not match the set of dimensions provided. The
     * order need not match (and if the order does match, this function is just an expensive
     * clone).
     */
    #[track_caller]
    pub fn reorder_mut(&mut self, dimensions: [Dimension; D]) {
        use crate::tensors::dimensions::DimensionMappings;
        if D == 2 && crate::tensors::dimensions::is_square(&self.shape) {
            let dimension_mapping = match DimensionMappings::new(&self.shape, &dimensions) {
                Some(dimension_mapping) => dimension_mapping,
                None => panic!(
                    "Dimension names provided {:?} must be the same set of dimension names in the tensor: {:?}",
                    dimensions, &self.shape,
                ),
            };

            let shape = dimension_mapping.map_shape_to_requested(&self.shape);
            let shape_iterator = ShapeIterator::from(shape);

            for index in shape_iterator {
                let i = index[0];
                let j = index[1];
                if j >= i {
                    let mapped_index = dimension_mapping.map_dimensions_to_source(&index);
                    // Swap elements from the upper triangle (using index order of the actual tensor's
                    // shape)
                    let temp = self.get_reference(index).unwrap().clone();
                    // tensor[i,j] becomes tensor[mapping(i,j)]
                    *self.get_reference_mut(index).unwrap() =
                        self.get_reference(mapped_index).unwrap().clone();
                    // tensor[mapping(i,j)] becomes tensor[i,j]
                    *self.get_reference_mut(mapped_index).unwrap() = temp;
                    // If the mapping is a noop we've assigned i,j to i,j
                    // If the mapping is i,j -> j,i we've assigned i,j to j,i and j,i to i,j
                }
            }

            // now update our shape and strides to match
            self.shape = shape;
            self.strides = compute_strides(&shape);
        } else {
            // fallback to allocating a new reordered tensor
            let reordered = self.reorder(dimensions);
            self.data = reordered.data;
            self.shape = reordered.shape;
            self.strides = reordered.strides;
        }
    }

    /**
     * Returns an iterator over copies of the data in this Tensor.
     */
    pub fn iter(&self) -> TensorIterator<'_, T, Tensor<T, D>, D> {
        TensorIterator::from(self)
    }

    /**
     * Creates and returns a new tensor with all values from the original with the
     * function applied to each. This can be used to change the type of the tensor
     * such as creating a mask:
     * ```
     * use easy_ml::tensors::Tensor;
     * let x = Tensor::from([("a", 2), ("b", 2)], vec![
     *    0.0, 1.2,
     *    5.8, 6.9
     * ]);
     * let y = x.map(|element| element > 2.0);
     * let result = Tensor::from([("a", 2), ("b", 2)], vec![
     *    false, false,
     *    true, true
     * ]);
     * assert_eq!(&y, &result);
     * ```
     */
    pub fn map<U>(&self, mapping_function: impl Fn(T) -> U) -> Tensor<U, D> {
        let mapped = self
            .data
            .iter()
            .map(|x| mapping_function(x.clone()))
            .collect();
        // We're not changing the shape of the Tensor, so don't need to revalidate
        Tensor::direct_from(mapped, self.shape, self.strides)
    }

    /**
     * Creates and returns a new tensor with all values from the original and
     * the index of each value mapped by a function.
     */
    pub fn map_with_index<U>(&self, mapping_function: impl Fn([usize; D], T) -> U) -> Tensor<U, D> {
        let mapped = self
            .iter()
            .with_index()
            .map(|(i, x)| mapping_function(i, x))
            .collect();
        // We're not changing the shape of the Tensor, so don't need to revalidate
        Tensor::direct_from(mapped, self.shape, self.strides)
    }

    /**
     * Applies a function to all values in the tensor, modifying
     * the tensor in place.
     */
    pub fn map_mut(&mut self, mapping_function: impl Fn(T) -> T) {
        for value in self.data.iter_mut() {
            *value = mapping_function(value.clone());
        }
    }

    /**
     * Applies a function to all values and each value's index in the tensor, modifying
     * the tensor in place.
     */
    pub fn map_mut_with_index(&mut self, mapping_function: impl Fn([usize; D], T) -> T) {
        self.iter_reference_mut()
            .with_index()
            .for_each(|(i, x)| *x = mapping_function(i, x.clone()));
    }

    /**
     * Creates and returns a new tensor with all value pairs of two tensors with the same shape
     * mapped by a function.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let lhs = Tensor::from([("a", 4)], vec![1, 2, 3, 4]);
     * let rhs = Tensor::from([("a", 4)], vec![0, 1, 2, 3]);
     * let multiplied = lhs.elementwise(&rhs, |l, r| l * r);
     * assert_eq!(
     *     multiplied,
     *     Tensor::from([("a", 4)], vec![0, 2, 6, 12])
     * );
     * ```
     *
     * # Generics
     *
     * This method can be called with any right hand side that can be converted to a TensorView,
     * which includes `Tensor`, `&Tensor`, `&mut Tensor` as well as references to a `TensorView`.
     *
     * # Panics
     *
     * If the two tensors have different shapes.
     */
    #[track_caller]
    pub fn elementwise<S, I, M>(&self, rhs: I, mapping_function: M) -> Tensor<T, D>
    where
        I: Into<TensorView<T, S, D>>,
        S: TensorRef<T, D>,
        M: Fn(T, T) -> T,
    {
        self.elementwise_reference_less_generic(rhs.into(), |lhs, rhs| {
            mapping_function(lhs.clone(), rhs.clone())
        })
    }

    /**
     * Creates and returns a new tensor with all value pairs of two tensors with the same shape
     * mapped by a function. The mapping function also receives each index corresponding to the
     * value pairs.
     *
     * # Generics
     *
     * This method can be called with any right hand side that can be converted to a TensorView,
     * which includes `Tensor`, `&Tensor`, `&mut Tensor` as well as references to a `TensorView`.
     *
     * # Panics
     *
     * If the two tensors have different shapes.
     */
    #[track_caller]
    pub fn elementwise_with_index<S, I, M>(&self, rhs: I, mapping_function: M) -> Tensor<T, D>
    where
        I: Into<TensorView<T, S, D>>,
        S: TensorRef<T, D>,
        M: Fn([usize; D], T, T) -> T,
    {
        self.elementwise_reference_less_generic_with_index(rhs.into(), |i, lhs, rhs| {
            mapping_function(i, lhs.clone(), rhs.clone())
        })
    }
}

impl<T> Tensor<T, 1>
where
    T: Numeric,
    for<'a> &'a T: NumericRef<T>,
{
    /**
     * Computes the scalar product of two equal length vectors. For two vectors `[a,b,c]` and
     * `[d,e,f]`, returns `a*d + b*e + c*f`. This is also known as the dot product.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let tensor = Tensor::from([("sequence", 5)], vec![3, 4, 5, 6, 7]);
     * assert_eq!(tensor.scalar_product(&tensor), 3*3 + 4*4 + 5*5 + 6*6 + 7*7);
     * ```
     *
     * # Generics
     *
     * This method can be called with any right hand side that can be converted to a TensorView,
     * which includes `Tensor`, `&Tensor`, `&mut Tensor` as well as references to a `TensorView`.
     *
     * # Panics
     *
     * If the two vectors are not of equal length or their dimension names do not match.
     */
    // Would like this impl block to be in operations.rs too but then it would show first in the
    // Tensor docs which isn't ideal
    pub fn scalar_product<S, I>(&self, rhs: I) -> T
    where
        I: Into<TensorView<T, S, 1>>,
        S: TensorRef<T, 1>,
    {
        self.scalar_product_less_generic(rhs.into())
    }
}

impl<T> Tensor<T, 2>
where
    T: Numeric,
    for<'a> &'a T: NumericRef<T>,
{
    /**
     * Returns the determinant of this square matrix, or None if the matrix
     * does not have a determinant. See [`linear_algebra`](super::linear_algebra::determinant_tensor())
     */
    pub fn determinant(&self) -> Option<T> {
        linear_algebra::determinant_tensor::<T, _, _>(self)
    }

    /**
     * Computes the inverse of a matrix provided that it exists. To have an inverse a
     * matrix must be square (same number of rows and columns) and it must also have a
     * non zero determinant. See [`linear_algebra`](super::linear_algebra::inverse_tensor())
     */
    pub fn inverse(&self) -> Option<Tensor<T, 2>> {
        linear_algebra::inverse_tensor::<T, _, _>(self)
    }

    /**
     * Computes the covariance matrix for this feature matrix along the specified feature
     * dimension in this matrix. See [`linear_algebra`](crate::linear_algebra::covariance()).
     */
    pub fn covariance(&self, feature_dimension: Dimension) -> Tensor<T, 2> {
        linear_algebra::covariance::<T, _, _>(self, feature_dimension)
    }
}

// FIXME: want this to be callable in the main numeric impl block
impl<T> Tensor<T, 2>
where
    T: Numeric,
{
    /**
     * Creates a diagonal matrix of the provided size with the diagonal elements
     * set to the provided value and all other elements in the tensor set to 0.
     * A diagonal matrix is always square.
     *
     * The size is still taken as a shape to facilitate creating a diagonal matrix
     * from the dimensionality of an existing one. If the provided value is 1 then
     * this will create an identity matrix.
     *
     * A 3 x 3 identity matrix:
     * ```ignore
     * [
     *   1, 0, 0
     *   0, 1, 0
     *   0, 0, 1
     * ]
     * ```
     *
     * # Panics
     *
     * - If the shape is not square.
     * - If a dimension name is not unique
     * - If any dimension has 0 elements
     */
    #[track_caller]
    pub fn diagonal(shape: [(Dimension, usize); 2], value: T) -> Tensor<T, 2> {
        if !crate::tensors::dimensions::is_square(&shape) {
            panic!("Shape must be square: {:?}", shape);
        }
        let mut tensor = Tensor::empty(shape, T::zero());
        for ([r, c], x) in tensor.iter_reference_mut().with_index() {
            if r == c {
                *x = value.clone();
            }
        }
        tensor
    }
}

impl<T> Tensor<T, 2> {
    /**
     * Converts this 2 dimensional Tensor into a Matrix.
     *
     * This is a wrapper around the `From<Tensor<T, 2>>` implementation.
     *
     * The Matrix will have the data in the same order, with rows equal to the length of
     * the first dimension in the tensor, and columns equal to the length of the second.
     */
    pub fn into_matrix(self) -> crate::matrices::Matrix<T> {
        self.into()
    }
}

/**
 * Methods for tensors with numerical real valued types, such as f32 or f64.
 *
 * This excludes signed and unsigned integers as they do not support decimal
 * precision and hence can't be used for operations like square roots.
 *
 * Third party fixed precision and infinite precision decimal types should
 * be able to implement all of the methods for [Real] and then utilise these functions.
 */
impl<T: Real> Tensor<T, 1>
where
    for<'a> &'a T: RealRef<T>,
{
    /**
     * Computes the [L2 norm](https://en.wikipedia.org/wiki/Euclidean_vector#Length)
     * of this vector, also referred to as the length or magnitude,
     * and written as ||x||, or sometimes |x|.
     *
     * ||**a**|| = sqrt(a<sub>1</sub><sup>2</sup> + a<sub>2</sub><sup>2</sup> + a<sub>3</sub><sup>2</sup>...) = sqrt(**a**<sup>T</sup> * **a**)
     *
     * This is a shorthand for `(x.iter().map(|x| x * x).sum().sqrt()`, ie
     * the square root of the dot product of a vector with itself.
     *
     * The euclidean length can be used to compute a
     * [unit vector](https://en.wikipedia.org/wiki/Unit_vector), that is, a
     * vector with length of 1. This should not be confused with a unit matrix,
     * which is another name for an identity matrix.
     *
     * ```
     * use easy_ml::tensors::Tensor;
     * let a = Tensor::from([("data", 3)], vec![ 1.0, 2.0, 3.0 ]);
     * let length = a.euclidean_length(); // (1^2 + 2^2 + 3^2)^0.5
     * let unit = a.map(|x| x / length);
     * assert_eq!(unit.euclidean_length(), 1.0);
     * ```
     */
    // TODO: Scalar ops for tensors
    pub fn euclidean_length(&self) -> T {
        self.direct_iter_reference()
            .map(|x| x * x)
            .sum::<T>()
            .sqrt()
    }
}

#[cfg(feature = "serde")]
mod serde_impls {
    use crate::tensors::{Dimension, InvalidShapeError, Tensor};
    use serde::Deserialize;
    use std::convert::TryFrom;

    /**
     * Deserialized data for a Tensor. Can be converted into a Tensor by
     * providing `&'static str` dimension names.
     *
     * This struct borrows the string references, so will not be supported
     * by any serde library that doesn't support deserializing to borrowed types.
     * However, if used with a serde library that can deserialize to borrowed
     * types, you could create a TensorDeserialize with a static lifetime by
     * using a static input, and then it will be possible to convert to a
     * Tensor using the [TryFrom](TryFrom) implementation without providing
     * dimension names to use via [into_tensor](TensorDeserialize::into_tensor).
     */
    #[derive(Deserialize, Debug)]
    #[serde(rename = "Tensor")]
    pub struct TensorDeserialize<'a, T, const D: usize> {
        data: Vec<T>,
        #[serde(with = "serde_arrays")]
        #[serde(borrow)]
        shape: [(&'a str, usize); D],
    }

    /**
     * Deserialized data for a Tensor. Can be converted into a Tensor by providing
     * `&'static str` dimension names.
     *
     * This struct owns the string references, so can be parsed by serde
     * libraries that don't support deserializing to borrowed types. However,
     * we can't convert from `String` to `&'static str` without leaking, so
     * there is no TryFrom implementation to convert to a Tensor, and
     * instead new static dimension names must always be provided via
     * [into_tensor](TensorDeserializeOwned::into_tensor).
     */
    #[derive(Deserialize, Debug)]
    #[serde(rename = "Tensor")]
    pub struct TensorDeserializeOwned<T, const D: usize> {
        data: Vec<T>,
        #[serde(with = "serde_arrays")]
        shape: [(String, usize); D],
    }

    impl<'a, T, const D: usize> TensorDeserialize<'a, T, D> {
        /**
         * Converts this deserialised Tensor data to a Tensor, using the provided `&'static str`
         * dimension names in place of what was serialised (which wouldn't necessarily live
         * long enough).
         */
        pub fn into_tensor(
            self,
            dimensions: [Dimension; D],
        ) -> Result<Tensor<T, D>, InvalidShapeError<D>> {
            let shape = std::array::from_fn(|d| (dimensions[d], self.shape[d].1));
            // Safety: Use the normal constructor that performs validation to prevent invalid
            // serialized data being created as a Tensor, which would then break all the
            // code that's relying on these invariants.
            // By never serialising the strides in the first place, we reduce the possibility
            // of creating invalid serialised representations at the slight increase in
            // serialisation work.
            Tensor::try_from(shape, self.data)
        }
    }

    impl<T, const D: usize> TensorDeserializeOwned<T, D> {
        /**
         * Converts this deserialised Tensor data to a Tensor, using the provided `&'static str`
         * dimension names in place of what was serialised (which wouldn't live
         * long enough).
         */
        pub fn into_tensor(
            self,
            dimensions: [Dimension; D],
        ) -> Result<Tensor<T, D>, InvalidShapeError<D>> {
            let shape = std::array::from_fn(|d| (dimensions[d], self.shape[d].1));
            // Safety: Use the normal constructor that performs validation to prevent invalid
            // serialized data being created as a Tensor, which would then break all the
            // code that's relying on these invariants.
            // By never serialising the strides in the first place, we reduce the possibility
            // of creating invalid serialised representations at the slight increase in
            // serialisation work.
            Tensor::try_from(shape, self.data)
        }
    }

    /**
     * Converts this deserialised Tensor data which has a static lifetime for the dimension
     * names to a Tensor, using the serialised data.
     */
    impl<T, const D: usize> TryFrom<TensorDeserialize<'static, T, D>> for Tensor<T, D> {
        type Error = InvalidShapeError<D>;

        fn try_from(value: TensorDeserialize<'static, T, D>) -> Result<Self, Self::Error> {
            Tensor::try_from(value.shape, value.data)
        }
    }
}

#[cfg(feature = "serde")]
#[test]
fn test_serialize() {
    fn assert_serialize<T: Serialize>() {}
    assert_serialize::<Tensor<f64, 3>>();
    assert_serialize::<Tensor<f64, 2>>();
    assert_serialize::<Tensor<f64, 1>>();
    assert_serialize::<Tensor<f64, 0>>();
}

#[cfg(feature = "serde")]
#[test]
fn test_deserialize() {
    use serde::Deserialize;
    fn assert_deserialize<'de, T: Deserialize<'de>>() {}
    assert_deserialize::<TensorDeserialize<f64, 3>>();
    assert_deserialize::<TensorDeserialize<f64, 2>>();
    assert_deserialize::<TensorDeserialize<f64, 1>>();
    assert_deserialize::<TensorDeserialize<f64, 0>>();
}

#[cfg(feature = "serde")]
#[test]
fn test_serialization_deserialization_loop_toml() {
    #[rustfmt::skip]
    let tensor = Tensor::from(
        [("rows", 3), ("columns", 4)],
        vec![
            1,  2,  3,  4,
            5,  6,  7,  8,
            9, 10, 11, 12
        ],
    );
    let encoded = toml::to_string(&tensor).unwrap();
    assert_eq!(
        encoded,
        r#"data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
shape = [["rows", 3], ["columns", 4]]
"#,
    );
    let parsed: Result<TensorDeserializeOwned<i32, 2>, _> = toml::from_str(&encoded);
    assert!(parsed.is_ok());
    let result = parsed.unwrap().into_tensor(["rows", "columns"]);
    assert!(result.is_ok());
    assert_eq!(result.unwrap(), tensor);
}

#[cfg(feature = "serde")]
#[test]
fn test_serialization_deserialization_loop_json() {
    #[rustfmt::skip]
    let tensor = Tensor::from(
        [("rows", 3), ("columns", 4)],
        vec![
            1,  2,  3,  4,
            5,  6,  7,  8,
            9, 10, 11, 12
        ],
    );
    let encoded = serde_json::ser::to_string(&tensor).unwrap();
    assert_eq!(
        encoded,
        r#"{"data":[1,2,3,4,5,6,7,8,9,10,11,12],"shape":[["rows",3],["columns",4]]}"#,
    );
    let parsed: Result<TensorDeserialize<i32, 2>, _> = serde_json::de::from_str(&encoded);
    assert!(parsed.is_ok());
    let result = parsed.unwrap().into_tensor(["rows", "columns"]);
    assert!(result.is_ok());
    assert_eq!(result.unwrap(), tensor);
}

#[cfg(feature = "serde")]
#[test]
fn test_deserialization_validation() {
    let parsed: Result<TensorDeserializeOwned<i32, 2>, _> = toml::from_str(
        r#"data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
shape = [["rows", 4], ["columns", 4]]
"#,
    );
    assert!(parsed.is_ok());
    let result = parsed.unwrap().into_tensor(["rows", "columns"]);
    assert!(result.is_err());
}

#[cfg(feature = "serde")]
#[cfg(test)]
const TENSOR_DATA: &'static str = r#"
{
    "data": [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
    "shape": [["rows", 3], ["columns", 4]]
}
"#;

#[cfg(feature = "serde")]
#[test]
fn test_deserialization_static_data() {
    #[rustfmt::skip]
    let tensor = Tensor::from(
        [("rows", 3), ("columns", 4)],
        vec![
            12, 11, 10, 9,
            8,   7,  6,  5,
            4,   3,  2, 1,
        ],
    );
    // To test TensorDeserialize we can't use toml because later
    // versions don't support parsing borrowed data, so we use
    // serde_json instead
    let parsed: Result<TensorDeserialize<i32, 2>, _> = serde_json::de::from_str(TENSOR_DATA);
    assert!(parsed.is_ok());
    let result: Result<Tensor<i32, 2>, _> = parsed.unwrap().try_into();
    assert!(result.is_ok());
    assert_eq!(result.unwrap(), tensor);
}

macro_rules! tensor_select_impl {
    (impl Tensor $d:literal 1) => {
        impl<T> Tensor<T, $d> {
            /**
             * Selects the provided dimension name and index pairs in this Tensor, returning a
             * TensorView which has fewer dimensions than this Tensor, with the removed dimensions
             * always indexed as the provided values.
             *
             * This is a shorthand for manually constructing the TensorView and
             * [TensorIndex]
             *
             * Note: due to limitations in Rust's const generics support, this method is only
             * implemented for `provided_indexes` of length 1 and `D` from 1 to 6. You can fall
             * back to manual construction to create `TensorIndex`es with multiple provided
             * indexes if you need to reduce dimensionality by more than 1 dimension at a time.
             */
            #[track_caller]
            pub fn select(
                &self,
                provided_indexes: [(Dimension, usize); 1],
            ) -> TensorView<T, TensorIndex<T, &Tensor<T, $d>, $d, 1>, { $d - 1 }> {
                TensorView::from(TensorIndex::from(self, provided_indexes))
            }

            /**
             * Selects the provided dimension name and index pairs in this Tensor, returning a
             * TensorView which has fewer dimensions than this Tensor, with the removed dimensions
             * always indexed as the provided values. The TensorIndex mutably borrows this
             * Tensor, and can therefore mutate it
             *
             * See [select](Tensor::select)
             */
            #[track_caller]
            pub fn select_mut(
                &mut self,
                provided_indexes: [(Dimension, usize); 1],
            ) -> TensorView<T, TensorIndex<T, &mut Tensor<T, $d>, $d, 1>, { $d - 1 }> {
                TensorView::from(TensorIndex::from(self, provided_indexes))
            }

            /**
             * Selects the provided dimension name and index pairs in this Tensor, returning a
             * TensorView which has fewer dimensions than this Tensor, with the removed dimensions
             * always indexed as the provided values. The TensorIndex takes ownership of this
             * Tensor, and can therefore mutate it
             *
             * See [select](Tensor::select)
             */
            #[track_caller]
            pub fn select_owned(
                self,
                provided_indexes: [(Dimension, usize); 1],
            ) -> TensorView<T, TensorIndex<T, Tensor<T, $d>, $d, 1>, { $d - 1 }> {
                TensorView::from(TensorIndex::from(self, provided_indexes))
            }
        }
    };
}

tensor_select_impl!(impl Tensor 6 1);
tensor_select_impl!(impl Tensor 5 1);
tensor_select_impl!(impl Tensor 4 1);
tensor_select_impl!(impl Tensor 3 1);
tensor_select_impl!(impl Tensor 2 1);
tensor_select_impl!(impl Tensor 1 1);

macro_rules! tensor_expand_impl {
    (impl Tensor $d:literal 1) => {
        impl<T> Tensor<T, $d> {
            /**
             * Expands the dimensionality of this tensor by adding dimensions of length 1 at
             * a particular position within the shape, returning a TensorView which has more
             * dimensions than this Tensor.
             *
             * This is a shorthand for manually constructing the TensorView and
             * [TensorExpansion]
             *
             * Note: due to limitations in Rust's const generics support, this method is only
             * implemented for `extra_dimension_names` of length 1 and `D` from 0 to 5. You can
             * fall back to manual construction to create `TensorExpansion`s with multiple provided
             * indexes if you need to increase dimensionality by more than 1 dimension at a time.
             */
            #[track_caller]
            pub fn expand(
                &self,
                extra_dimension_names: [(usize, Dimension); 1],
            ) -> TensorView<T, TensorExpansion<T, &Tensor<T, $d>, $d, 1>, { $d + 1 }> {
                TensorView::from(TensorExpansion::from(self, extra_dimension_names))
            }

            /**
             * Expands the dimensionality of this tensor by adding dimensions of length 1 at
             * a particular position within the shape, returning a TensorView which has more
             * dimensions than this Tensor. The TensorIndex mutably borrows this
             * Tensor, and can therefore mutate it
             *
             * See [expand](Tensor::expand)
             */
            #[track_caller]
            pub fn expand_mut(
                &mut self,
                extra_dimension_names: [(usize, Dimension); 1],
            ) -> TensorView<T, TensorExpansion<T, &mut Tensor<T, $d>, $d, 1>, { $d + 1 }> {
                TensorView::from(TensorExpansion::from(self, extra_dimension_names))
            }

            /**
             * Expands the dimensionality of this tensor by adding dimensions of length 1 at
             * a particular position within the shape, returning a TensorView which has more
             * dimensions than this Tensor. The TensorIndex takes ownership of this
             * Tensor, and can therefore mutate it
             *
             * See [expand](Tensor::expand)
             */
            #[track_caller]
            pub fn expand_owned(
                self,
                extra_dimension_names: [(usize, Dimension); 1],
            ) -> TensorView<T, TensorExpansion<T, Tensor<T, $d>, $d, 1>, { $d + 1 }> {
                TensorView::from(TensorExpansion::from(self, extra_dimension_names))
            }
        }
    };
}

tensor_expand_impl!(impl Tensor 0 1);
tensor_expand_impl!(impl Tensor 1 1);
tensor_expand_impl!(impl Tensor 2 1);
tensor_expand_impl!(impl Tensor 3 1);
tensor_expand_impl!(impl Tensor 4 1);
tensor_expand_impl!(impl Tensor 5 1);