construction.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/base/construction.rs`.
Keywords: rust, rustlang, rust-lang

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    #[cfg(all(feature = "alloc", not(feature = "std")))]
    use alloc::vec::Vec;

    #[cfg(feature = "arbitrary")]
    use crate::base::storage::Owned;
    #[cfg(feature = "arbitrary")]
    use quickcheck::{Arbitrary, Gen};

    use num::{Bounded, One, Zero};
    #[cfg(feature = "rand-no-std")]
    use rand::{
        distributions::{Distribution, Standard},
        Rng,
    };

    use std::iter;
    use typenum::{self, Cmp, Greater};

    use simba::scalar::{ClosedAdd, ClosedMul};

    use crate::base::allocator::Allocator;
    use crate::base::dimension::{Dim, DimName, Dyn, ToTypenum};
    use crate::base::storage::RawStorage;
    use crate::base::{
        ArrayStorage, Const, DefaultAllocator, Matrix, OMatrix, OVector, Scalar, Unit, Vector,
    };
    use crate::UninitMatrix;
    use std::mem::MaybeUninit;

    impl<T: Scalar, R: Dim, C: Dim> UninitMatrix<T, R, C>
    where
        DefaultAllocator: Allocator<T, R, C>,
    {
        /// Builds a matrix with uninitialized elements of type `MaybeUninit<T>`.
        #[inline(always)]
        pub fn uninit(nrows: R, ncols: C) -> Self {
            // SAFETY: this is OK because the dimension automatically match the storage
            //         because we are building an owned storage.
            unsafe {
                Self::from_data_statically_unchecked(DefaultAllocator::allocate_uninit(nrows, ncols))
            }
        }
    }

    /// # Generic constructors
    /// This set of matrix and vector construction functions are all generic
    /// with-regard to the matrix dimensions. They all expect to be given
    /// the dimension as inputs.
    ///
    /// These functions should only be used when working on dimension-generic code.
    impl<T: Scalar, R: Dim, C: Dim> OMatrix<T, R, C>
    where
        DefaultAllocator: Allocator<T, R, C>,
    {
        /// Creates a matrix with all its elements set to `elem`.
        #[inline]
        pub fn from_element_generic(nrows: R, ncols: C, elem: T) -> Self {
            let len = nrows.value() * ncols.value();
            Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
        }

        /// Creates a matrix with all its elements set to `elem`.
        ///
        /// Same as `from_element_generic`.
        #[inline]
        pub fn repeat_generic(nrows: R, ncols: C, elem: T) -> Self {
            let len = nrows.value() * ncols.value();
            Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
        }

        /// Creates a matrix with all its elements set to 0.
        #[inline]
        pub fn zeros_generic(nrows: R, ncols: C) -> Self
        where
            T: Zero,
        {
            Self::from_element_generic(nrows, ncols, T::zero())
        }

        /// Creates a matrix with all its elements filled by an iterator.
        #[inline]
        pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
        where
            I: IntoIterator<Item = T>,
        {
            Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
        }

        /// Creates a matrix with all its elements filled by an row-major order iterator.
        #[inline]
        pub fn from_row_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
        where
            I: IntoIterator<Item = T>,
        {
            Self::from_data(DefaultAllocator::allocate_from_row_iterator(
                nrows, ncols, iter,
            ))
        }

        /// Creates a matrix with its elements filled with the components provided by a slice in
        /// row-major order.
        ///
        /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
        /// row-by-row.
        #[inline]
        pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self {
            assert!(
                slice.len() == nrows.value() * ncols.value(),
                "Matrix init. error: the slice did not contain the right number of elements."
            );

            let mut res = Matrix::uninit(nrows, ncols);
            let mut iter = slice.iter();

            unsafe {
                for i in 0..nrows.value() {
                    for j in 0..ncols.value() {
                        *res.get_unchecked_mut((i, j)) = MaybeUninit::new(iter.next().unwrap().clone())
                    }
                }

                // SAFETY: the result has been fully initialized above.
                res.assume_init()
            }
        }

        /// Creates a matrix with its elements filled with the components provided by a slice. The
        /// components must have the same layout as the matrix data storage (i.e. column-major).
        #[inline]
        pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self {
            Self::from_iterator_generic(nrows, ncols, slice.iter().cloned())
        }

        /// Creates a matrix filled with the results of a function applied to each of its component
        /// coordinates.
        #[inline]
        pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
        where
            F: FnMut(usize, usize) -> T,
        {
            let mut res = Matrix::uninit(nrows, ncols);

            unsafe {
                for j in 0..ncols.value() {
                    for i in 0..nrows.value() {
                        *res.get_unchecked_mut((i, j)) = MaybeUninit::new(f(i, j));
                    }
                }

                // SAFETY: the result has been fully initialized above.
                res.assume_init()
            }
        }

        /// Creates a new identity matrix.
        ///
        /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
        /// to the identity matrix. All other entries are set to zero.
        #[inline]
        pub fn identity_generic(nrows: R, ncols: C) -> Self
        where
            T: Zero + One,
        {
            Self::from_diagonal_element_generic(nrows, ncols, T::one())
        }

        /// Creates a new matrix with its diagonal filled with copies of `elt`.
        ///
        /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
        /// to the identity matrix. All other entries are set to zero.
        #[inline]
        pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: T) -> Self
        where
            T: Zero + One,
        {
            let mut res = Self::zeros_generic(nrows, ncols);

            for i in 0..crate::min(nrows.value(), ncols.value()) {
                unsafe { *res.get_unchecked_mut((i, i)) = elt.clone() }
            }

            res
        }

        /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal elements are
        /// filled with the content of `elts`. Others are set to 0.
        ///
        /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
        #[inline]
        pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[T]) -> Self
        where
            T: Zero,
        {
            let mut res = Self::zeros_generic(nrows, ncols);
            assert!(
                elts.len() <= crate::min(nrows.value(), ncols.value()),
                "Too many diagonal elements provided."
            );

            for (i, elt) in elts.iter().enumerate() {
                unsafe { *res.get_unchecked_mut((i, i)) = elt.clone() }
            }

            res
        }

        /// Builds a new matrix from its rows.
        ///
        /// Panics if not enough rows are provided (for statically-sized matrices), or if all rows do
        /// not have the same dimensions.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::{RowVector3, Matrix3};
        /// # use std::iter;
        ///
        /// let m = Matrix3::from_rows(&[ RowVector3::new(1.0, 2.0, 3.0),  RowVector3::new(4.0, 5.0, 6.0),  RowVector3::new(7.0, 8.0, 9.0) ]);
        ///
        /// assert!(m.m11 == 1.0 && m.m12 == 2.0 && m.m13 == 3.0 &&
        ///         m.m21 == 4.0 && m.m22 == 5.0 && m.m23 == 6.0 &&
        ///         m.m31 == 7.0 && m.m32 == 8.0 && m.m33 == 9.0);
        /// ```
        #[inline]
        pub fn from_rows<SB>(rows: &[Matrix<T, Const<1>, C, SB>]) -> Self
        where
            SB: RawStorage<T, Const<1>, C>,
        {
            assert!(!rows.is_empty(), "At least one row must be given.");
            let nrows = R::try_to_usize().unwrap_or_else(|| rows.len());
            let ncols = rows[0].len();
            assert!(
                rows.len() == nrows,
                "Invalid number of rows provided to build this matrix."
            );

            if C::try_to_usize().is_none() {
                assert!(
                    rows.iter().all(|r| r.len() == ncols),
                    "The provided rows must all have the same dimension."
                );
            }

            // TODO: optimize that.
            Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
                rows[i][(0, j)].clone()
            })
        }

        /// Builds a new matrix from its columns.
        ///
        /// Panics if not enough columns are provided (for statically-sized matrices), or if all
        /// columns do not have the same dimensions.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::{Vector3, Matrix3};
        /// # use std::iter;
        ///
        /// let m = Matrix3::from_columns(&[ Vector3::new(1.0, 2.0, 3.0),  Vector3::new(4.0, 5.0, 6.0),  Vector3::new(7.0, 8.0, 9.0) ]);
        ///
        /// assert!(m.m11 == 1.0 && m.m12 == 4.0 && m.m13 == 7.0 &&
        ///         m.m21 == 2.0 && m.m22 == 5.0 && m.m23 == 8.0 &&
        ///         m.m31 == 3.0 && m.m32 == 6.0 && m.m33 == 9.0);
        /// ```
        #[inline]
        pub fn from_columns<SB>(columns: &[Vector<T, R, SB>]) -> Self
        where
            SB: RawStorage<T, R>,
        {
            assert!(!columns.is_empty(), "At least one column must be given.");
            let ncols = C::try_to_usize().unwrap_or_else(|| columns.len());
            let nrows = columns[0].len();
            assert!(
                columns.len() == ncols,
                "Invalid number of columns provided to build this matrix."
            );

            if R::try_to_usize().is_none() {
                assert!(
                    columns.iter().all(|r| r.len() == nrows),
                    "The columns provided must all have the same dimension."
                );
            }

            // TODO: optimize that.
            Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
                columns[j][i].clone()
            })
        }

        /// Creates a matrix filled with random values.
        #[inline]
        #[cfg(feature = "rand")]
        pub fn new_random_generic(nrows: R, ncols: C) -> Self
        where
            Standard: Distribution<T>,
        {
            let mut rng = rand::thread_rng();
            Self::from_fn_generic(nrows, ncols, |_, _| rng.gen())
        }

        /// Creates a matrix filled with random values from the given distribution.
        #[inline]
        #[cfg(feature = "rand-no-std")]
        pub fn from_distribution_generic<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>(
            nrows: R,
            ncols: C,
            distribution: &Distr,
            rng: &mut G,
        ) -> Self {
            Self::from_fn_generic(nrows, ncols, |_, _| distribution.sample(rng))
        }

        /// Creates a matrix backed by a given `Vec`.
        ///
        /// The output matrix is filled column-by-column.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::{Dyn, DMatrix, Matrix, Const};
        ///
        /// let vec = vec![0, 1, 2, 3, 4, 5];
        /// let vec_ptr = vec.as_ptr();
        ///
        /// let matrix = Matrix::from_vec_generic(Dyn(vec.len()), Const::<1>, vec);
        /// let matrix_storage_ptr = matrix.data.as_vec().as_ptr();
        ///
        /// // `matrix` is backed by exactly the same `Vec` as it was constructed from.
        /// assert_eq!(matrix_storage_ptr, vec_ptr);
        /// ```
        #[inline]
        #[cfg(any(feature = "std", feature = "alloc"))]
        pub fn from_vec_generic(nrows: R, ncols: C, data: Vec<T>) -> Self {
            Self::from_iterator_generic(nrows, ncols, data)
        }
    }

    impl<T, D: Dim> OMatrix<T, D, D>
    where
        T: Scalar,
        DefaultAllocator: Allocator<T, D, D>,
    {
        /// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::{Vector3, DVector, Matrix3, DMatrix};
        /// # use std::iter;
        ///
        /// let m = Matrix3::from_diagonal(&Vector3::new(1.0, 2.0, 3.0));
        /// // The two additional arguments represent the matrix dimensions.
        /// let dm = DMatrix::from_diagonal(&DVector::from_row_slice(&[1.0, 2.0, 3.0]));
        ///
        /// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        ///         m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
        ///         m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 3.0);
        /// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        ///         dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
        ///         dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 3.0);
        /// ```
        #[inline]
        pub fn from_diagonal<SB: RawStorage<T, D>>(diag: &Vector<T, D, SB>) -> Self
        where
            T: Zero,
        {
            let (dim, _) = diag.shape_generic();
            let mut res = Self::zeros_generic(dim, dim);

            for i in 0..diag.len() {
                unsafe {
                    *res.get_unchecked_mut((i, i)) = diag.vget_unchecked(i).clone();
                }
            }

            res
        }
    }

    /*
     *
     * Generate constructors with varying number of arguments, depending on the object type.
     *
     */
    macro_rules! impl_constructors(
        ($($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
            /// Creates a matrix or vector with all its elements set to `elem`.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            ///
            /// let v = Vector3::from_element(2.0);
            /// // The additional argument represents the vector dimension.
            /// let dv = DVector::from_element(3, 2.0);
            /// let m = Matrix2x3::from_element(2.0);
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_element(2, 3, 2.0);
            ///
            /// assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
            /// assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
            /// assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
            ///         m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
            /// assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
            ///         dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);
            /// ```
            #[inline]
            pub fn from_element($($args: usize,)* elem: T) -> Self {
                Self::from_element_generic($($gargs, )* elem)
            }

            /// Creates a matrix or vector with all its elements set to `elem`.
            ///
            /// Same as `.from_element`.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            ///
            /// let v = Vector3::repeat(2.0);
            /// // The additional argument represents the vector dimension.
            /// let dv = DVector::repeat(3, 2.0);
            /// let m = Matrix2x3::repeat(2.0);
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::repeat(2, 3, 2.0);
            ///
            /// assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
            /// assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
            /// assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
            ///         m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
            /// assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
            ///         dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);
            /// ```
            #[inline]
            pub fn repeat($($args: usize,)* elem: T) -> Self {
                Self::repeat_generic($($gargs, )* elem)
            }

            /// Creates a matrix or vector with all its elements set to `0`.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            ///
            /// let v = Vector3::<f32>::zeros();
            /// // The argument represents the vector dimension.
            /// let dv = DVector::<f32>::zeros(3);
            /// let m = Matrix2x3::<f32>::zeros();
            /// // The two arguments represent the matrix dimensions.
            /// let dm = DMatrix::<f32>::zeros(2, 3);
            ///
            /// assert!(v.x == 0.0 && v.y == 0.0 && v.z == 0.0);
            /// assert!(dv[0] == 0.0 && dv[1] == 0.0 && dv[2] == 0.0);
            /// assert!(m.m11 == 0.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
            ///         m.m21 == 0.0 && m.m22 == 0.0 && m.m23 == 0.0);
            /// assert!(dm[(0, 0)] == 0.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
            ///         dm[(1, 0)] == 0.0 && dm[(1, 1)] == 0.0 && dm[(1, 2)] == 0.0);
            /// ```
            #[inline]
            pub fn zeros($($args: usize),*) -> Self
                where T: Zero {
                Self::zeros_generic($($gargs),*)
            }

            /// Creates a matrix or vector with all its elements filled by an iterator.
            ///
            /// The output matrix is filled column-by-column.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            /// # use std::iter;
            ///
            /// let v = Vector3::from_iterator((0..3).into_iter());
            /// // The additional argument represents the vector dimension.
            /// let dv = DVector::from_iterator(3, (0..3).into_iter());
            /// let m = Matrix2x3::from_iterator((0..6).into_iter());
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_iterator(2, 3, (0..6).into_iter());
            ///
            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
            /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
            ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
            ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
            /// ```
            #[inline]
            pub fn from_iterator<I>($($args: usize,)* iter: I) -> Self
                where I: IntoIterator<Item = T> {
                Self::from_iterator_generic($($gargs, )* iter)
            }

            /// Creates a matrix or vector with all its elements filled by a row-major iterator.
            ///
            /// The output matrix is filled row-by-row.
            ///
            /// ## Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            /// # use std::iter;
            ///
            /// let v = Vector3::from_row_iterator((0..3).into_iter());
            /// // The additional argument represents the vector dimension.
            /// let dv = DVector::from_row_iterator(3, (0..3).into_iter());
            /// let m = Matrix2x3::from_row_iterator((0..6).into_iter());
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_row_iterator(2, 3, (0..6).into_iter());
            ///
            /// // For Vectors from_row_iterator is identical to from_iterator
            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
            /// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
            ///         m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
            ///         dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
            /// ```
            #[inline]
            pub fn from_row_iterator<I>($($args: usize,)* iter: I) -> Self
                where I: IntoIterator<Item = T> {
                Self::from_row_iterator_generic($($gargs, )* iter)
            }

            /// Creates a matrix or vector filled with the results of a function applied to each of its
            /// component coordinates.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
            /// # use std::iter;
            ///
            /// let v = Vector3::from_fn(|i, _| i);
            /// // The additional argument represents the vector dimension.
            /// let dv = DVector::from_fn(3, |i, _| i);
            /// let m = Matrix2x3::from_fn(|i, j| i * 3 + j);
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_fn(2, 3, |i, j| i * 3 + j);
            ///
            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
            /// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
            ///         m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
            ///         dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
            /// ```
            #[inline]
            pub fn from_fn<F>($($args: usize,)* f: F) -> Self
                where F: FnMut(usize, usize) -> T {
                Self::from_fn_generic($($gargs, )* f)
            }

            /// Creates an identity matrix. If the matrix is not square, the largest square
            /// submatrix (starting at the first row and column) is set to the identity while all
            /// other entries are set to zero.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, DMatrix};
            /// # use std::iter;
            ///
            /// let m = Matrix2x3::<f32>::identity();
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::<f32>::identity(2, 3);
            ///
            /// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
            ///         m.m21 == 0.0 && m.m22 == 1.0 && m.m23 == 0.0);
            /// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
            ///         dm[(1, 0)] == 0.0 && dm[(1, 1)] == 1.0 && dm[(1, 2)] == 0.0);
            /// ```
            #[inline]
            pub fn identity($($args: usize,)*) -> Self
                where T: Zero + One {
                Self::identity_generic($($gargs),* )
            }

            /// Creates a matrix filled with its diagonal filled with `elt` and all other
            /// components set to zero.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix2x3, DMatrix};
            /// # use std::iter;
            ///
            /// let m = Matrix2x3::from_diagonal_element(5.0);
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_diagonal_element(2, 3, 5.0);
            ///
            /// assert!(m.m11 == 5.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
            ///         m.m21 == 0.0 && m.m22 == 5.0 && m.m23 == 0.0);
            /// assert!(dm[(0, 0)] == 5.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
            ///         dm[(1, 0)] == 0.0 && dm[(1, 1)] == 5.0 && dm[(1, 2)] == 0.0);
            /// ```
            #[inline]
            pub fn from_diagonal_element($($args: usize,)* elt: T) -> Self
                where T: Zero + One {
                Self::from_diagonal_element_generic($($gargs, )* elt)
            }

            /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal
            /// elements are filled with the content of `elts`. Others are set to 0.
            ///
            /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
            ///
            /// # Example
            /// ```
            /// # use nalgebra::{Matrix3, DMatrix};
            /// # use std::iter;
            ///
            /// let m = Matrix3::from_partial_diagonal(&[1.0, 2.0]);
            /// // The two additional arguments represent the matrix dimensions.
            /// let dm = DMatrix::from_partial_diagonal(3, 3, &[1.0, 2.0]);
            ///
            /// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
            ///         m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
            ///         m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 0.0);
            /// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
            ///         dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
            ///         dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 0.0);
            /// ```
            #[inline]
            pub fn from_partial_diagonal($($args: usize,)* elts: &[T]) -> Self
                where T: Zero {
                Self::from_partial_diagonal_generic($($gargs, )* elts)
            }

            /// Creates a matrix or vector filled with random values from the given distribution.
            #[inline]
            #[cfg(feature = "rand-no-std")]
            pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>(
                $($args: usize,)*
                distribution: &Distr,
                rng: &mut G,
            ) -> Self {
                Self::from_distribution_generic($($gargs, )* distribution, rng)
            }

            /// Creates a matrix filled with random values.
            #[inline]
            #[cfg(feature = "rand")]
            pub fn new_random($($args: usize),*) -> Self
                where Standard: Distribution<T> {
                Self::new_random_generic($($gargs),*)
            }
        }
    );

    /// # Constructors of statically-sized vectors or statically-sized matrices
    impl<T: Scalar, R: DimName, C: DimName> OMatrix<T, R, C>
    where
        DefaultAllocator: Allocator<T, R, C>,
    {
        // TODO: this is not very pretty. We could find a better call syntax.
        impl_constructors!(R, C;                         // Arguments for Matrix<T, ..., S>
        => R: DimName, => C: DimName; // Type parameters for impl<T, ..., S>
        R::name(), C::name();         // Arguments for `_generic` constructors.
        ); // Arguments for non-generic constructors.
    }

    /// # Constructors of matrices with a dynamic number of columns
    impl<T: Scalar, R: DimName> OMatrix<T, R, Dyn>
    where
        DefaultAllocator: Allocator<T, R, Dyn>,
    {
        impl_constructors!(R, Dyn;
                       => R: DimName;
                       R::name(), Dyn(ncols);
                       ncols);
    }

    /// # Constructors of dynamic vectors and matrices with a dynamic number of rows
    impl<T: Scalar, C: DimName> OMatrix<T, Dyn, C>
    where
        DefaultAllocator: Allocator<T, Dyn, C>,
    {
        impl_constructors!(Dyn, C;
                       => C: DimName;
                       Dyn(nrows), C::name();
                       nrows);
    }

    /// # Constructors of fully dynamic matrices
    impl<T: Scalar> OMatrix<T, Dyn, Dyn>
    where
        DefaultAllocator: Allocator<T, Dyn, Dyn>,
    {
        impl_constructors!(Dyn, Dyn;
                       ;
                       Dyn(nrows), Dyn(ncols);
                       nrows, ncols);
    }

    /*
     *
     * Constructors that don't necessarily require all dimensions
     * to be specified when one dimension is already known.
     *
     */
    macro_rules! impl_constructors_from_data(
        ($data: ident; $($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
            impl<T: Scalar, $($DimIdent: $DimBound, )*> OMatrix<T $(, $Dims)*>
            where DefaultAllocator: Allocator<T $(, $Dims)*> {
                /// Creates a matrix with its elements filled with the components provided by a slice
                /// in row-major order.
                ///
                /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
                /// row-by-row.
                ///
                /// # Example
                /// ```
                /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
                /// # use std::iter;
                ///
                /// let v = Vector3::from_row_slice(&[0, 1, 2]);
                /// // The additional argument represents the vector dimension.
                /// let dv = DVector::from_row_slice(&[0, 1, 2]);
                /// let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
                /// // The two additional arguments represent the matrix dimensions.
                /// let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
                ///
                /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
                /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
                /// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
                ///         m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
                /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
                ///         dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
                /// ```
                #[inline]
                pub fn from_row_slice($($args: usize,)* $data: &[T]) -> Self {
                    Self::from_row_slice_generic($($gargs, )* $data)
                }

                /// Creates a matrix with its elements filled with the components provided by a slice
                /// in column-major order.
                ///
                /// # Example
                /// ```
                /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
                /// # use std::iter;
                ///
                /// let v = Vector3::from_column_slice(&[0, 1, 2]);
                /// // The additional argument represents the vector dimension.
                /// let dv = DVector::from_column_slice(&[0, 1, 2]);
                /// let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
                /// // The two additional arguments represent the matrix dimensions.
                /// let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
                ///
                /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
                /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
                /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
                ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
                /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
                ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
                /// ```
                #[inline]
                pub fn from_column_slice($($args: usize,)* $data: &[T]) -> Self {
                    Self::from_column_slice_generic($($gargs, )* $data)
                }

                /// Creates a matrix backed by a given `Vec`.
                ///
                /// The output matrix is filled column-by-column.
                ///
                /// # Example
                /// ```
                /// # use nalgebra::{DMatrix, Matrix2x3};
                ///
                /// let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);
                ///
                /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
                ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
                ///
                ///
                /// // The two additional arguments represent the matrix dimensions.
                /// let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);
                ///
                /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
                ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
                /// ```
                #[inline]
                #[cfg(any(feature = "std", feature = "alloc"))]
                pub fn from_vec($($args: usize,)* $data: Vec<T>) -> Self {
                    Self::from_vec_generic($($gargs, )* $data)
                }
            }
        }
    );

    // TODO: this is not very pretty. We could find a better call syntax.
    impl_constructors_from_data!(data; R, C;                  // Arguments for Matrix<T, ..., S>
    => R: DimName, => C: DimName; // Type parameters for impl<T, ..., S>
    R::name(), C::name();         // Arguments for `_generic` constructors.
    ); // Arguments for non-generic constructors.

    impl_constructors_from_data!(data; R, Dyn;
    => R: DimName;
    R::name(), Dyn(data.len() / R::dim());
    );

    impl_constructors_from_data!(data; Dyn, C;
    => C: DimName;
    Dyn(data.len() / C::dim()), C::name();
    );

    impl_constructors_from_data!(data; Dyn, Dyn;
                                ;
                                Dyn(nrows), Dyn(ncols);
                                nrows, ncols);

    /*
     *
     * Zero, One, Rand traits.
     *
     */
    impl<T, R: DimName, C: DimName> Zero for OMatrix<T, R, C>
    where
        T: Scalar + Zero + ClosedAdd,
        DefaultAllocator: Allocator<T, R, C>,
    {
        #[inline]
        fn zero() -> Self {
            Self::from_element(T::zero())
        }

        #[inline]
        fn is_zero(&self) -> bool {
            self.iter().all(|e| e.is_zero())
        }
    }

    impl<T, D: DimName> One for OMatrix<T, D, D>
    where
        T: Scalar + Zero + One + ClosedMul + ClosedAdd,
        DefaultAllocator: Allocator<T, D, D>,
    {
        #[inline]
        fn one() -> Self {
            Self::identity()
        }
    }

    impl<T, R: DimName, C: DimName> Bounded for OMatrix<T, R, C>
    where
        T: Scalar + Bounded,
        DefaultAllocator: Allocator<T, R, C>,
    {
        #[inline]
        fn max_value() -> Self {
            Self::from_element(T::max_value())
        }

        #[inline]
        fn min_value() -> Self {
            Self::from_element(T::min_value())
        }
    }

    #[cfg(feature = "rand-no-std")]
    impl<T: Scalar, R: Dim, C: Dim> Distribution<OMatrix<T, R, C>> for Standard
    where
        DefaultAllocator: Allocator<T, R, C>,
        Standard: Distribution<T>,
    {
        #[inline]
        fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> OMatrix<T, R, C> {
            let nrows = R::try_to_usize().unwrap_or_else(|| rng.gen_range(0..10));
            let ncols = C::try_to_usize().unwrap_or_else(|| rng.gen_range(0..10));

            OMatrix::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| rng.gen())
        }
    }

    #[cfg(feature = "arbitrary")]
    impl<T, R, C> Arbitrary for OMatrix<T, R, C>
    where
        R: Dim,
        C: Dim,
        T: Scalar + Arbitrary + Send,
        DefaultAllocator: Allocator<T, R, C>,
        Owned<T, R, C>: Clone + Send,
    {
        #[inline]
        fn arbitrary(g: &mut Gen) -> Self {
            let nrows = R::try_to_usize().unwrap_or(usize::arbitrary(g) % 10);
            let ncols = C::try_to_usize().unwrap_or(usize::arbitrary(g) % 10);

            Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| {
                T::arbitrary(g)
            })
        }
    }

    // TODO(specialization): faster impls possible for D≤4 (see rand_distr::{UnitCircle, UnitSphere})
    #[cfg(feature = "rand")]
    impl<T: crate::RealField, D: DimName> Distribution<Unit<OVector<T, D>>> for Standard
    where
        DefaultAllocator: Allocator<T, D>,
        rand_distr::StandardNormal: Distribution<T>,
    {
        /// Generate a uniformly distributed random unit vector.
        #[inline]
        fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> Unit<OVector<T, D>> {
            Unit::new_normalize(OVector::from_distribution_generic(
                D::name(),
                Const::<1>,
                &rand_distr::StandardNormal,
                rng,
            ))
        }
    }

    /*
     *
     * Constructors for small matrices and vectors.
     *
     */

    macro_rules! transpose_array(
        [$($a: ident),*;] => {
            [$([$a]),*]
        };
        [$($a: ident),*; $($b: ident),*;] => {
            [$([$a, $b]),*]
        };
        [$($a: ident),*; $($b: ident),*; $($c: ident),*;] => {
            [$([$a, $b, $c]),*]
        };
        [$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*;] => {
            [$([$a, $b, $c, $d]),*]
        };
        [$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*; $($e: ident),*;] => {
            [$([$a, $b, $c, $d, $e]),*]
        };
        [$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*; $($e: ident),*; $($f: ident),*;] => {
            [$([$a, $b, $c, $d, $e, $f]),*]
        };
    );

    macro_rules! componentwise_constructors_impl(
        ($($R: expr, $C: expr, [$($($args: ident),*);*] $(;)*)*) => {$(
            impl<T> Matrix<T, Const<$R>, Const<$C>, ArrayStorage<T, $R, $C>> {
                /// Initializes this matrix from its components.
                #[inline]
                #[allow(clippy::too_many_arguments)]
                pub const fn new($($($args: T),*),*) -> Self {
                    unsafe {
                        Self::from_data_statically_unchecked(
                            ArrayStorage(
                                transpose_array![
                                    $(
                                        $($args),*
                                    ;)*
                                ]
                            )
                        )
                    }
                }
            }
        )*}
    );

    componentwise_constructors_impl!(
        /*
         * Square matrices 1 .. 6.
         */
        2, 2, [m11, m12;
               m21, m22];
        3, 3, [m11, m12, m13;
              m21, m22, m23;
              m31, m32, m33];
        4, 4, [m11, m12, m13, m14;
              m21, m22, m23, m24;
              m31, m32, m33, m34;
              m41, m42, m43, m44];
        5, 5, [m11, m12, m13, m14, m15;
              m21, m22, m23, m24, m25;
              m31, m32, m33, m34, m35;
              m41, m42, m43, m44, m45;
              m51, m52, m53, m54, m55];
        6, 6, [m11, m12, m13, m14, m15, m16;
              m21, m22, m23, m24, m25, m26;
              m31, m32, m33, m34, m35, m36;
              m41, m42, m43, m44, m45, m46;
              m51, m52, m53, m54, m55, m56;
              m61, m62, m63, m64, m65, m66];

        /*
         * Rectangular matrices with 2 rows.
         */
        2, 3, [m11, m12, m13;
              m21, m22, m23];
        2, 4, [m11, m12, m13, m14;
              m21, m22, m23, m24];
        2, 5, [m11, m12, m13, m14, m15;
              m21, m22, m23, m24, m25];
        2, 6, [m11, m12, m13, m14, m15, m16;
              m21, m22, m23, m24, m25, m26];

        /*
         * Rectangular matrices with 3 rows.
         */
        3, 2, [m11, m12;
              m21, m22;
              m31, m32];
        3, 4, [m11, m12, m13, m14;
              m21, m22, m23, m24;
              m31, m32, m33, m34];
        3, 5, [m11, m12, m13, m14, m15;
              m21, m22, m23, m24, m25;
              m31, m32, m33, m34, m35];
        3, 6, [m11, m12, m13, m14, m15, m16;
              m21, m22, m23, m24, m25, m26;
              m31, m32, m33, m34, m35, m36];

        /*
         * Rectangular matrices with 4 rows.
         */
        4, 2, [m11, m12;
              m21, m22;
              m31, m32;
              m41, m42];
        4, 3, [m11, m12, m13;
              m21, m22, m23;
              m31, m32, m33;
              m41, m42, m43];
        4, 5, [m11, m12, m13, m14, m15;
              m21, m22, m23, m24, m25;
              m31, m32, m33, m34, m35;
              m41, m42, m43, m44, m45];
        4, 6, [m11, m12, m13, m14, m15, m16;
              m21, m22, m23, m24, m25, m26;
              m31, m32, m33, m34, m35, m36;
              m41, m42, m43, m44, m45, m46];

        /*
         * Rectangular matrices with 5 rows.
         */
        5, 2, [m11, m12;
              m21, m22;
              m31, m32;
              m41, m42;
              m51, m52];
        5, 3, [m11, m12, m13;
              m21, m22, m23;
              m31, m32, m33;
              m41, m42, m43;
              m51, m52, m53];
        5, 4, [m11, m12, m13, m14;
              m21, m22, m23, m24;
              m31, m32, m33, m34;
              m41, m42, m43, m44;
              m51, m52, m53, m54];
        5, 6, [m11, m12, m13, m14, m15, m16;
              m21, m22, m23, m24, m25, m26;
              m31, m32, m33, m34, m35, m36;
              m41, m42, m43, m44, m45, m46;
              m51, m52, m53, m54, m55, m56];

        /*
         * Rectangular matrices with 6 rows.
         */
        6, 2, [m11, m12;
              m21, m22;
              m31, m32;
              m41, m42;
              m51, m52;
              m61, m62];
        6, 3, [m11, m12, m13;
              m21, m22, m23;
              m31, m32, m33;
              m41, m42, m43;
              m51, m52, m53;
              m61, m62, m63];
        6, 4, [m11, m12, m13, m14;
              m21, m22, m23, m24;
              m31, m32, m33, m34;
              m41, m42, m43, m44;
              m51, m52, m53, m54;
              m61, m62, m63, m64];
        6, 5, [m11, m12, m13, m14, m15;
              m21, m22, m23, m24, m25;
              m31, m32, m33, m34, m35;
              m41, m42, m43, m44, m45;
              m51, m52, m53, m54, m55;
              m61, m62, m63, m64, m65];

        /*
         * Row vectors 1 .. 6.
         */
        1, 1, [x];
        1, 2, [x, y];
        1, 3, [x, y, z];
        1, 4, [x, y, z, w];
        1, 5, [x, y, z, w, a];
        1, 6, [x, y, z, w, a, b];

        /*
         * Column vectors 1 .. 6.
         */
        2, 1, [x; y];
        3, 1, [x; y; z];
        4, 1, [x; y; z; w];
        5, 1, [x; y; z; w; a];
        6, 1, [x; y; z; w; a; b];
    );

    /*
     *
     * Axis constructors.
     *
     */
    impl<T, R: DimName> OVector<T, R>
    where
        R: ToTypenum,
        T: Scalar + Zero + One,
        DefaultAllocator: Allocator<T, R>,
    {
        /// The column vector with `val` as its i-th component.
        #[inline]
        pub fn ith(i: usize, val: T) -> Self {
            let mut res = Self::zeros();
            res[i] = val;
            res
        }

        /// The column unit vector with `T::one()` as its i-th component.
        #[inline]
        pub fn ith_axis(i: usize) -> Unit<Self> {
            Unit::new_unchecked(Self::ith(i, T::one()))
        }

        /// The column vector with a 1 as its first component, and zero elsewhere.
        #[inline]
        pub fn x() -> Self
        where
            R::Typenum: Cmp<typenum::U0, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(0) = T::one();
            }

            res
        }

        /// The column vector with a 1 as its second component, and zero elsewhere.
        #[inline]
        pub fn y() -> Self
        where
            R::Typenum: Cmp<typenum::U1, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(1) = T::one();
            }

            res
        }

        /// The column vector with a 1 as its third component, and zero elsewhere.
        #[inline]
        pub fn z() -> Self
        where
            R::Typenum: Cmp<typenum::U2, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(2) = T::one();
            }

            res
        }

        /// The column vector with a 1 as its fourth component, and zero elsewhere.
        #[inline]
        pub fn w() -> Self
        where
            R::Typenum: Cmp<typenum::U3, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(3) = T::one();
            }

            res
        }

        /// The column vector with a 1 as its fifth component, and zero elsewhere.
        #[inline]
        pub fn a() -> Self
        where
            R::Typenum: Cmp<typenum::U4, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(4) = T::one();
            }

            res
        }

        /// The column vector with a 1 as its sixth component, and zero elsewhere.
        #[inline]
        pub fn b() -> Self
        where
            R::Typenum: Cmp<typenum::U5, Output = Greater>,
        {
            let mut res = Self::zeros();
            unsafe {
                *res.vget_unchecked_mut(5) = T::one();
            }

            res
        }

        /// The unit column vector with a 1 as its first component, and zero elsewhere.
        #[inline]
        pub fn x_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U0, Output = Greater>,
        {
            Unit::new_unchecked(Self::x())
        }

        /// The unit column vector with a 1 as its second component, and zero elsewhere.
        #[inline]
        pub fn y_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U1, Output = Greater>,
        {
            Unit::new_unchecked(Self::y())
        }

        /// The unit column vector with a 1 as its third component, and zero elsewhere.
        #[inline]
        pub fn z_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U2, Output = Greater>,
        {
            Unit::new_unchecked(Self::z())
        }

        /// The unit column vector with a 1 as its fourth component, and zero elsewhere.
        #[inline]
        pub fn w_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U3, Output = Greater>,
        {
            Unit::new_unchecked(Self::w())
        }

        /// The unit column vector with a 1 as its fifth component, and zero elsewhere.
        #[inline]
        pub fn a_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U4, Output = Greater>,
        {
            Unit::new_unchecked(Self::a())
        }

        /// The unit column vector with a 1 as its sixth component, and zero elsewhere.
        #[inline]
        pub fn b_axis() -> Unit<Self>
        where
            R::Typenum: Cmp<typenum::U5, Output = Greater>,
        {
            Unit::new_unchecked(Self::b())
        }
    }