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

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

    use crate::allocator::{Allocator, Reallocator};
    use crate::base::{Const, DefaultAllocator, Matrix, OMatrix, OVector, Unit};
    use crate::constraint::{SameNumberOfRows, ShapeConstraint};
    use crate::dimension::{Dim, DimMin, DimMinimum};
    use crate::storage::StorageMut;
    use crate::ComplexField;

    use crate::geometry::Reflection;
    use crate::linalg::{householder, PermutationSequence};
    use std::mem::MaybeUninit;

    /// The QR decomposition (with column pivoting) of a general matrix.
    #[cfg_attr(feature = "serde-serialize-no-std", derive(Serialize, Deserialize))]
    #[cfg_attr(
        feature = "serde-serialize-no-std",
        serde(bound(serialize = "DefaultAllocator: Allocator<T, R, C> +
                               Allocator<T, DimMinimum<R, C>>,
             OMatrix<T, R, C>: Serialize,
             PermutationSequence<DimMinimum<R, C>>: Serialize,
             OVector<T, DimMinimum<R, C>>: Serialize"))
    )]
    #[cfg_attr(
        feature = "serde-serialize-no-std",
        serde(bound(deserialize = "DefaultAllocator: Allocator<T, R, C> +
                               Allocator<T, DimMinimum<R, C>>,
             OMatrix<T, R, C>: Deserialize<'de>,
             PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>,
             OVector<T, DimMinimum<R, C>>: Deserialize<'de>"))
    )]
    #[derive(Clone, Debug)]
    pub struct ColPivQR<T: ComplexField, R: DimMin<C>, C: Dim>
    where
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<(usize, usize), DimMinimum<R, C>>,
    {
        col_piv_qr: OMatrix<T, R, C>,
        p: PermutationSequence<DimMinimum<R, C>>,
        diag: OVector<T, DimMinimum<R, C>>,
    }

    impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for ColPivQR<T, R, C>
    where
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<(usize, usize), DimMinimum<R, C>>,
        OMatrix<T, R, C>: Copy,
        PermutationSequence<DimMinimum<R, C>>: Copy,
        OVector<T, DimMinimum<R, C>>: Copy,
    {
    }

    impl<T: ComplexField, R: DimMin<C>, C: Dim> ColPivQR<T, R, C>
    where
        DefaultAllocator: Allocator<T, R, C>
            + Allocator<T, R>
            + Allocator<T, DimMinimum<R, C>>
            + Allocator<(usize, usize), DimMinimum<R, C>>,
    {
        /// Computes the `ColPivQR` 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 mut p = PermutationSequence::identity_generic(min_nrows_ncols);

            if min_nrows_ncols.value() == 0 {
                return ColPivQR {
                    col_piv_qr: matrix,
                    p,
                    diag: Matrix::zeros_generic(min_nrows_ncols, Const::<1>),
                };
            }

            let mut diag = Matrix::uninit(min_nrows_ncols, Const::<1>);

            for i in 0..min_nrows_ncols.value() {
                let piv = matrix.view_range(i.., i..).icamax_full();
                let col_piv = piv.1 + i;
                matrix.swap_columns(i, col_piv);
                p.append_permutation(i, col_piv);

                diag[i] =
                    MaybeUninit::new(householder::clear_column_unchecked(&mut matrix, i, 0, None));
            }

            // Safety: diag is now fully initialized.
            let diag = unsafe { diag.assume_init() };

            ColPivQR {
                col_piv_qr: matrix,
                p,
                diag,
            }
        }

        /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
        #[inline]
        #[must_use]
        pub fn r(&self) -> OMatrix<T, DimMinimum<R, C>, C>
        where
            DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,
        {
            let (nrows, ncols) = self.col_piv_qr.shape_generic();
            let mut res = self
                .col_piv_qr
                .rows_generic(0, nrows.min(ncols))
                .upper_triangle();
            res.set_partial_diagonal(self.diag.iter().map(|e| T::from_real(e.clone().modulus())));
            res
        }

        /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
        ///
        /// This is usually faster than `r` but consumes `self`.
        #[inline]
        pub fn unpack_r(self) -> OMatrix<T, DimMinimum<R, C>, C>
        where
            DefaultAllocator: Reallocator<T, R, C, DimMinimum<R, C>, C>,
        {
            let (nrows, ncols) = self.col_piv_qr.shape_generic();
            let mut res = self
                .col_piv_qr
                .resize_generic(nrows.min(ncols), ncols, T::zero());
            res.fill_lower_triangle(T::zero(), 1);
            res.set_partial_diagonal(self.diag.iter().map(|e| T::from_real(e.clone().modulus())));
            res
        }

        /// Computes the orthogonal matrix `Q` of this decomposition.
        #[must_use]
        pub fn q(&self) -> OMatrix<T, R, DimMinimum<R, C>>
        where
            DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,
        {
            let (nrows, ncols) = self.col_piv_qr.shape_generic();

            // NOTE: we could build the identity matrix and call q_mul on it.
            // Instead we don't so that we take in account the matrix sparseness.
            let mut res = Matrix::identity_generic(nrows, nrows.min(ncols));
            let dim = self.diag.len();

            for i in (0..dim).rev() {
                let axis = self.col_piv_qr.view_range(i.., 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.., i..);
                refl.reflect_with_sign(&mut res_rows, self.diag[i].clone().signum());
            }

            res
        }
        /// Retrieves the column permutation of this decomposition.
        #[inline]
        #[must_use]
        pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>> {
            &self.p
        }

        /// Unpacks this decomposition into its two matrix factors.
        pub fn unpack(
            self,
        ) -> (
            OMatrix<T, R, DimMinimum<R, C>>,
            OMatrix<T, DimMinimum<R, C>, C>,
            PermutationSequence<DimMinimum<R, C>>,
        )
        where
            DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
            DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>
                + Reallocator<T, R, C, DimMinimum<R, C>, C>
                + Allocator<(usize, usize), DimMinimum<R, C>>,
        {
            (self.q(), self.r(), self.p)
        }

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

        /// Multiplies the provided matrix by the transpose of the `Q` matrix of this decomposition.
        pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)
        where
            S2: StorageMut<T, R2, C2>,
        {
            let dim = self.diag.len();

            for i in 0..dim {
                let axis = self.col_piv_qr.view_range(i.., i);
                let refl = Reflection::new(Unit::new_unchecked(axis), T::zero());

                let mut rhs_rows = rhs.rows_range_mut(i..);
                refl.reflect_with_sign(&mut rhs_rows, self.diag[i].clone().signum().conjugate());
            }
        }
    }

    impl<T: ComplexField, D: DimMin<D, Output = D>> ColPivQR<T, D, D>
    where
        DefaultAllocator:
            Allocator<T, D, D> + Allocator<T, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
    {
        /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
        ///
        /// Returns `None` if `self` is not invertible.
        #[must_use = "Did you mean to use solve_mut()?"]
        pub fn solve<R2: Dim, C2: Dim, S2>(
            &self,
            b: &Matrix<T, R2, C2, S2>,
        ) -> Option<OMatrix<T, R2, C2>>
        where
            S2: StorageMut<T, R2, C2>,
            ShapeConstraint: SameNumberOfRows<R2, D>,
            DefaultAllocator: Allocator<T, R2, C2>,
        {
            let mut res = b.clone_owned();

            if self.solve_mut(&mut res) {
                Some(res)
            } else {
                None
            }
        }

        /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
        ///
        /// If the decomposed matrix is not invertible, this returns `false` and its input `b` is
        /// overwritten with garbage.
        pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) -> bool
        where
            S2: StorageMut<T, R2, C2>,
            ShapeConstraint: SameNumberOfRows<R2, D>,
        {
            assert_eq!(
                self.col_piv_qr.nrows(),
                b.nrows(),
                "ColPivQR solve matrix dimension mismatch."
            );
            assert!(
                self.col_piv_qr.is_square(),
                "ColPivQR solve: unable to solve a non-square system."
            );

            self.q_tr_mul(b);
            let solved = self.solve_upper_triangular_mut(b);
            self.p.inv_permute_rows(b);

            solved
        }

        // 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>,
        ) -> bool
        where
            S2: StorageMut<T, R2, C2>,
            ShapeConstraint: SameNumberOfRows<R2, D>,
        {
            let dim = self.col_piv_qr.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).clone().modulus();

                        if diag.is_zero() {
                            return false;
                        }

                        coeff = b.vget_unchecked(i).clone().unscale(diag);
                        *b.vget_unchecked_mut(i) = coeff.clone();
                    }

                    b.rows_range_mut(..i)
                        .axpy(-coeff, &self.col_piv_qr.view_range(..i, i), T::one());
                }
            }

            true
        }

        /// Computes the inverse of the decomposed matrix.
        ///
        /// Returns `None` if the decomposed matrix is not invertible.
        #[must_use]
        pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>> {
            assert!(
                self.col_piv_qr.is_square(),
                "ColPivQR inverse: unable to compute the inverse of a non-square matrix."
            );

            // TODO: is there a less naive method ?
            let (nrows, ncols) = self.col_piv_qr.shape_generic();
            let mut res = OMatrix::identity_generic(nrows, ncols);

            if self.solve_mut(&mut res) {
                Some(res)
            } else {
                None
            }
        }

        /// Indicates if the decomposed matrix is invertible.
        #[must_use]
        pub fn is_invertible(&self) -> bool {
            assert!(
                self.col_piv_qr.is_square(),
                "ColPivQR: unable to test the invertibility of a non-square matrix."
            );

            for i in 0..self.diag.len() {
                if self.diag[i].is_zero() {
                    return false;
                }
            }

            true
        }

        /// Computes the determinant of the decomposed matrix.
        #[must_use]
        pub fn determinant(&self) -> T {
            let dim = self.col_piv_qr.nrows();
            assert!(
                self.col_piv_qr.is_square(),
                "ColPivQR 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).clone() };
            }

            res * self.p.determinant()
        }
    }