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

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    #[cfg(feature = "serde-serialize-no-std")]
    use serde::{Deserialize, Serialize};

    use crate::allocator::Allocator;
    use crate::base::{DefaultAllocator, Matrix, OMatrix, OVector, Unit};
    use crate::dimension::{Const, Dim, DimDiff, DimMin, DimMinimum, DimSub, U1};
    use simba::scalar::ComplexField;

    use crate::geometry::Reflection;
    use crate::linalg::householder;
    use std::mem::MaybeUninit;

    /// The bidiagonalization of a general matrix.
    #[cfg_attr(feature = "serde-serialize-no-std", derive(Serialize, Deserialize))]
    #[cfg_attr(
        feature = "serde-serialize-no-std",
        serde(bound(serialize = "DimMinimum<R, C>: DimSub<U1>,
             DefaultAllocator: Allocator<T, R, C>             +
                               Allocator<T, DimMinimum<R, C>> +
                               Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
             OMatrix<T, R, C>: Serialize,
             OVector<T, DimMinimum<R, C>>: Serialize,
             OVector<T, DimDiff<DimMinimum<R, C>, U1>>: Serialize"))
    )]
    #[cfg_attr(
        feature = "serde-serialize-no-std",
        serde(bound(deserialize = "DimMinimum<R, C>: DimSub<U1>,
             DefaultAllocator: Allocator<T, R, C>             +
                               Allocator<T, DimMinimum<R, C>> +
                               Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
             OMatrix<T, R, C>: Deserialize<'de>,
             OVector<T, DimMinimum<R, C>>: Deserialize<'de>,
             OVector<T, DimDiff<DimMinimum<R, C>, U1>>: Deserialize<'de>"))
    )]
    #[derive(Clone, Debug)]
    pub struct Bidiagonal<T: ComplexField, R: DimMin<C>, C: Dim>
    where
        DimMinimum<R, C>: DimSub<U1>,
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
    {
        // TODO: perhaps we should pack the axes into different vectors so that axes for `v_t` are
        // contiguous. This prevents some useless copies.
        uv: OMatrix<T, R, C>,
        /// The diagonal elements of the decomposed matrix.
        diagonal: OVector<T, DimMinimum<R, C>>,
        /// The off-diagonal elements of the decomposed matrix.
        off_diagonal: OVector<T, DimDiff<DimMinimum<R, C>, U1>>,
        upper_diagonal: bool,
    }

    impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for Bidiagonal<T, R, C>
    where
        DimMinimum<R, C>: DimSub<U1>,
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
        OMatrix<T, R, C>: Copy,
        OVector<T, DimMinimum<R, C>>: Copy,
        OVector<T, DimDiff<DimMinimum<R, C>, U1>>: Copy,
    {
    }

    impl<T: ComplexField, R: DimMin<C>, C: Dim> Bidiagonal<T, R, C>
    where
        DimMinimum<R, C>: DimSub<U1>,
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, C>
            + Allocator<T, R>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
    {
        /// Computes the Bidiagonal decomposition using householder reflections.
        pub fn new(mut matrix: OMatrix<T, R, C>) -> Self {
            let (nrows, ncols) = matrix.shape_generic();
            let min_nrows_ncols = nrows.min(ncols);
            let dim = min_nrows_ncols.value();
            assert!(
                dim != 0,
                "Cannot compute the bidiagonalization of an empty matrix."
            );

            let mut diagonal = Matrix::uninit(min_nrows_ncols, Const::<1>);
            let mut off_diagonal = Matrix::uninit(min_nrows_ncols.sub(Const::<1>), Const::<1>);
            let mut axis_packed = Matrix::zeros_generic(ncols, Const::<1>);
            let mut work = Matrix::zeros_generic(nrows, Const::<1>);

            let upper_diagonal = nrows.value() >= ncols.value();
            if upper_diagonal {
                for ite in 0..dim - 1 {
                    diagonal[ite] = MaybeUninit::new(householder::clear_column_unchecked(
                        &mut matrix,
                        ite,
                        0,
                        None,
                    ));
                    off_diagonal[ite] = MaybeUninit::new(householder::clear_row_unchecked(
                        &mut matrix,
                        &mut axis_packed,
                        &mut work,
                        ite,
                        1,
                    ));
                }

                diagonal[dim - 1] = MaybeUninit::new(householder::clear_column_unchecked(
                    &mut matrix,
                    dim - 1,
                    0,
                    None,
                ));
            } else {
                for ite in 0..dim - 1 {
                    diagonal[ite] = MaybeUninit::new(householder::clear_row_unchecked(
                        &mut matrix,
                        &mut axis_packed,
                        &mut work,
                        ite,
                        0,
                    ));
                    off_diagonal[ite] = MaybeUninit::new(householder::clear_column_unchecked(
                        &mut matrix,
                        ite,
                        1,
                        None,
                    ));
                }

                diagonal[dim - 1] = MaybeUninit::new(householder::clear_row_unchecked(
                    &mut matrix,
                    &mut axis_packed,
                    &mut work,
                    dim - 1,
                    0,
                ));
            }

            // Safety: diagonal and off_diagonal have been fully initialized.
            let (diagonal, off_diagonal) =
                unsafe { (diagonal.assume_init(), off_diagonal.assume_init()) };

            Bidiagonal {
                uv: matrix,
                diagonal,
                off_diagonal,
                upper_diagonal,
            }
        }

        /// Indicates whether this decomposition contains an upper-diagonal matrix.
        #[inline]
        #[must_use]
        pub fn is_upper_diagonal(&self) -> bool {
            self.upper_diagonal
        }

        #[inline]
        fn axis_shift(&self) -> (usize, usize) {
            if self.upper_diagonal {
                (0, 1)
            } else {
                (1, 0)
            }
        }

        /// Unpacks this decomposition into its three matrix factors `(U, D, V^t)`.
        ///
        /// The decomposed matrix `M` is equal to `U * D * V^t`.
        #[inline]
        pub fn unpack(
            self,
        ) -> (
            OMatrix<T, R, DimMinimum<R, C>>,
            OMatrix<T, DimMinimum<R, C>, DimMinimum<R, C>>,
            OMatrix<T, DimMinimum<R, C>, C>,
        )
        where
            DefaultAllocator: Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>>
                + Allocator<T, R, DimMinimum<R, C>>
                + Allocator<T, DimMinimum<R, C>, C>,
        {
            // TODO: optimize by calling a reallocator.
            (self.u(), self.d(), self.v_t())
        }

        /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
        #[inline]
        #[must_use]
        pub fn d(&self) -> OMatrix<T, DimMinimum<R, C>, DimMinimum<R, C>>
        where
            DefaultAllocator: Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>>,
        {
            let (nrows, ncols) = self.uv.shape_generic();

            let d = nrows.min(ncols);
            let mut res = OMatrix::identity_generic(d, d);
            res.set_partial_diagonal(
                self.diagonal
                    .iter()
                    .map(|e| T::from_real(e.clone().modulus())),
            );

            let start = self.axis_shift();
            res.view_mut(start, (d.value() - 1, d.value() - 1))
                .set_partial_diagonal(
                    self.off_diagonal
                        .iter()
                        .map(|e| T::from_real(e.clone().modulus())),
                );
            res
        }

        /// Computes the orthogonal matrix `U` of this `U * D * V` decomposition.
        // TODO: code duplication with householder::assemble_q.
        // Except that we are returning a rectangular matrix here.
        #[must_use]
        pub fn u(&self) -> OMatrix<T, R, DimMinimum<R, C>>
        where
            DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,
        {
            let (nrows, ncols) = self.uv.shape_generic();

            let mut res = Matrix::identity_generic(nrows, nrows.min(ncols));
            let dim = self.diagonal.len();
            let shift = self.axis_shift().0;

            for i in (0..dim - shift).rev() {
                let axis = self.uv.view_range(i + shift.., i);
                // TODO: sometimes, the axis might have a zero magnitude.
                let refl = Reflection::new(Unit::new_unchecked(axis), T::zero());

                let mut res_rows = res.view_range_mut(i + shift.., i..);

                let sign = if self.upper_diagonal {
                    self.diagonal[i].clone().signum()
                } else {
                    self.off_diagonal[i].clone().signum()
                };

                refl.reflect_with_sign(&mut res_rows, sign);
            }

            res
        }

        /// Computes the orthogonal matrix `V_t` of this `U * D * V_t` decomposition.
        #[must_use]
        pub fn v_t(&self) -> OMatrix<T, DimMinimum<R, C>, C>
        where
            DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,
        {
            let (nrows, ncols) = self.uv.shape_generic();
            let min_nrows_ncols = nrows.min(ncols);

            let mut res = Matrix::identity_generic(min_nrows_ncols, ncols);
            let mut work = Matrix::zeros_generic(min_nrows_ncols, Const::<1>);
            let mut axis_packed = Matrix::zeros_generic(ncols, Const::<1>);

            let shift = self.axis_shift().1;

            for i in (0..min_nrows_ncols.value() - shift).rev() {
                let axis = self.uv.view_range(i, i + shift..);
                let mut axis_packed = axis_packed.rows_range_mut(i + shift..);
                axis_packed.tr_copy_from(&axis);
                // TODO: sometimes, the axis might have a zero magnitude.
                let refl = Reflection::new(Unit::new_unchecked(axis_packed), T::zero());

                let mut res_rows = res.view_range_mut(i.., i + shift..);

                let sign = if self.upper_diagonal {
                    self.off_diagonal[i].clone().signum()
                } else {
                    self.diagonal[i].clone().signum()
                };

                refl.reflect_rows_with_sign(&mut res_rows, &mut work.rows_range_mut(i..), sign);
            }

            res
        }

        /// The diagonal part of this decomposed matrix.
        #[must_use]
        pub fn diagonal(&self) -> OVector<T::RealField, DimMinimum<R, C>>
        where
            DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>>,
        {
            self.diagonal.map(|e| e.modulus())
        }

        /// The off-diagonal part of this decomposed matrix.
        #[must_use]
        pub fn off_diagonal(&self) -> OVector<T::RealField, DimDiff<DimMinimum<R, C>, U1>>
        where
            DefaultAllocator: Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,
        {
            self.off_diagonal.map(|e| e.modulus())
        }

        #[doc(hidden)]
        pub fn uv_internal(&self) -> &OMatrix<T, R, C> {
            &self.uv
        }
    }

    // impl<T: ComplexField, D: DimMin<D, Output = D> + DimSub<Dyn>> Bidiagonal<T, D, D>
    //     where DefaultAllocator: Allocator<T, D, D> +
    //                             Allocator<T, D> {
    //     /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
    //     pub fn solve<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<T, R2, C2, S2>) -> OMatrix<T, R2, C2>
    //         where S2: StorageMut<T, R2, C2>,
    //               ShapeConstraint: SameNumberOfRows<R2, D> {
    //         let mut res = b.clone_owned();
    //         self.solve_mut(&mut res);
    //         res
    //     }
    //
    //     /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
    //     pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>)
    //         where S2: StorageMut<T, R2, C2>,
    //               ShapeConstraint: SameNumberOfRows<R2, D> {
    //
    //         assert_eq!(self.uv.nrows(), b.nrows(), "Bidiagonal solve matrix dimension mismatch.");
    //         assert!(self.uv.is_square(), "Bidiagonal solve: unable to solve a non-square system.");
    //
    //         self.q_tr_mul(b);
    //         self.solve_upper_triangular_mut(b);
    //     }
    //
    //     // TODO: duplicate code from the `solve` module.
    //     fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>)
    //         where S2: StorageMut<T, R2, C2>,
    //               ShapeConstraint: SameNumberOfRows<R2, D> {
    //
    //         let dim  = self.uv.nrows();
    //
    //         for k in 0 .. b.ncols() {
    //             let mut b = b.column_mut(k);
    //             for i in (0 .. dim).rev() {
    //                 let coeff;
    //
    //                 unsafe {
    //                     let diag = *self.diag.vget_unchecked(i);
    //                     coeff = *b.vget_unchecked(i) / diag;
    //                     *b.vget_unchecked_mut(i) = coeff;
    //                 }
    //
    //                 b.rows_range_mut(.. i).axpy(-coeff, &self.uv.view_range(.. i, i), T::one());
    //             }
    //         }
    //     }
    //
    //     /// Computes the inverse of the decomposed matrix.
    //     pub fn inverse(&self) -> OMatrix<T, D, D> {
    //         assert!(self.uv.is_square(), "Bidiagonal inverse: unable to compute the inverse of a non-square matrix.");
    //
    //         // TODO: is there a less naive method ?
    //         let (nrows, ncols) = self.uv.shape_generic();
    //         let mut res = OMatrix::identity_generic(nrows, ncols);
    //         self.solve_mut(&mut res);
    //         res
    //     }
    //
    //     // /// Computes the determinant of the decomposed matrix.
    //     // pub fn determinant(&self) -> T {
    //     //     let dim = self.uv.nrows();
    //     //     assert!(self.uv.is_square(), "Bidiagonal determinant: unable to compute the determinant of a non-square matrix.");
    //
    //     //     let mut res = T::one();
    //     //     for i in 0 .. dim {
    //     //         res *= unsafe { *self.diag.vget_unchecked(i) };
    //     //     }
    //
    //     //     res self.q_determinant()
    //     // }
    // }