105 lines
3.5 KiB
Rust
105 lines
3.5 KiB
Rust
use alga::general::Real;
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use core::{MatrixN, MatrixMN, VectorN, DefaultAllocator};
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use dimension::{DimSub, DimDiff, U1};
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use storage::Storage;
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use allocator::Allocator;
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use linalg::householder;
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/// The tridiagonalization of a symmetric matrix.
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pub struct SymmetricTridiagonal<N: Real, D: DimSub<U1>>
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where DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, DimDiff<D, U1>> {
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tri: MatrixN<N, D>,
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off_diagonal: VectorN<N, DimDiff<D, U1>>
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}
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impl<N: Real, D: DimSub<U1>> SymmetricTridiagonal<N, D>
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where DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, DimDiff<D, U1>> {
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/// Computes the tridiagonalization of the symmetric matrix `m`.
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///
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/// Only the lower-triangular and diagonal parts of `m` are read.
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pub fn new(mut m: MatrixN<N, D>) -> Self {
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let dim = m.data.shape().0;
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assert!(m.is_square(), "Unable to compute the symmetric tridiagonal decomposition of a non-square matrix.");
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assert!(dim.value() != 0, "Unable to compute the symmetric tridiagonal decomposition of an empty matrix.");
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let mut off_diagonal = unsafe { MatrixMN::new_uninitialized_generic(dim.sub(U1), U1) };
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let mut p = unsafe { MatrixMN::new_uninitialized_generic(dim.sub(U1), U1) };
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for i in 0 .. dim.value() - 1 {
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let mut m = m.rows_range_mut(i + 1 ..);
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let (mut axis, mut m) = m.columns_range_pair_mut(i, i + 1 ..);
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let (norm, not_zero) = householder::reflection_axis_mut(&mut axis);
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off_diagonal[i] = norm;
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if not_zero {
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let mut p = p.rows_range_mut(i ..);
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p.gemv_symm(::convert(2.0), &m, &axis, N::zero());
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let dot = axis.dot(&p);
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p.axpy(-dot, &axis, N::one());
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m.ger_symm(-N::one(), &p, &axis, N::one());
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m.ger_symm(-N::one(), &axis, &p, N::one());
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}
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}
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SymmetricTridiagonal {
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tri: m,
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off_diagonal: off_diagonal
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}
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}
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#[doc(hidden)]
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// For debugging.
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pub fn internal_tri(&self) -> &MatrixN<N, D> {
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&self.tri
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}
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/// Retrieve the orthogonal transformation, diagonal, and off diagonal elements of this
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/// decomposition.
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pub fn unpack(self) -> (MatrixN<N, D>, VectorN<N, D>, VectorN<N, DimDiff<D, U1>>)
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where DefaultAllocator: Allocator<N, D> {
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let diag = self.diagonal();
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let q = self.q();
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(q, diag, self.off_diagonal)
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}
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/// The diagonal components of this decomposition.
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pub fn diagonal(&self) -> VectorN<N, D>
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where DefaultAllocator: Allocator<N, D> {
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self.tri.diagonal()
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}
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/// The off-diagonal components of this decomposition.
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pub fn off_diagonal(&self) -> &VectorN<N, DimDiff<D, U1>>
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where DefaultAllocator: Allocator<N, D> {
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&self.off_diagonal
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}
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/// Computes the orthogonal matrix `Q` of this decomposition.
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pub fn q(&self) -> MatrixN<N, D> {
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householder::assemble_q(&self.tri)
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}
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/// Recomputes the original symmetric matrix.
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pub fn recompose(mut self) -> MatrixN<N, D> {
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let q = self.q();
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self.tri.fill_lower_triangle(N::zero(), 2);
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self.tri.fill_upper_triangle(N::zero(), 2);
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for i in 0 .. self.off_diagonal.len() {
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self.tri[(i + 1, i)] = self.off_diagonal[i];
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self.tri[(i, i + 1)] = self.off_diagonal[i];
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}
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&q * self.tri * q.transpose()
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}
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}
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