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</pre><pre class="rust"><code><span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">use </span>serde::{Deserialize, Serialize};
<span class="kw">use </span><span class="kw">crate</span>::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::{DefaultAllocator, OMatrix, OVector};
<span class="kw">use </span><span class="kw">crate</span>::dimension::{Const, DimDiff, DimSub, U1};
<span class="kw">use </span>simba::scalar::ComplexField;
<span class="kw">use </span><span class="kw">crate</span>::linalg::householder;
<span class="kw">use </span><span class="kw">crate</span>::Matrix;
<span class="kw">use </span>std::mem::MaybeUninit;
<span class="doccomment">/// Tridiagonalization of a symmetric matrix.
</span><span class="attr">#[cfg_attr(feature = <span class="string">"serde-serialize-no-std"</span>, derive(Serialize, Deserialize))]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(serialize = <span class="string">"DefaultAllocator: Allocator<T, D, D> +
Allocator<T, DimDiff<D, U1>>,
OMatrix<T, D, D>: Serialize,
OVector<T, DimDiff<D, U1>>: Serialize"</span>))
)]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(deserialize = <span class="string">"DefaultAllocator: Allocator<T, D, D> +
Allocator<T, DimDiff<D, U1>>,
OMatrix<T, D, D>: Deserialize<'de>,
OVector<T, DimDiff<D, U1>>: Deserialize<'de>"</span>))
)]
#[derive(Clone, Debug)]
</span><span class="kw">pub struct </span>SymmetricTridiagonal<T: ComplexField, D: DimSub<U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
{
tri: OMatrix<T, D, D>,
off_diagonal: OVector<T, DimDiff<D, U1>>,
}
<span class="kw">impl</span><T: ComplexField, D: DimSub<U1>> Copy <span class="kw">for </span>SymmetricTridiagonal<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
OMatrix<T, D, D>: Copy,
OVector<T, DimDiff<D, U1>>: Copy,
{
}
<span class="kw">impl</span><T: ComplexField, D: DimSub<U1>> SymmetricTridiagonal<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
{
<span class="doccomment">/// Computes the tridiagonalization of the symmetric matrix `m`.
///
/// Only the lower-triangular part (including the diagonal) of `m` is read.
</span><span class="kw">pub fn </span>new(<span class="kw-2">mut </span>m: OMatrix<T, D, D>) -> <span class="self">Self </span>{
<span class="kw">let </span>dim = m.shape_generic().<span class="number">0</span>;
<span class="macro">assert!</span>(
m.is_square(),
<span class="string">"Unable to compute the symmetric tridiagonal decomposition of a non-square matrix."
</span>);
<span class="macro">assert!</span>(
dim.value() != <span class="number">0</span>,
<span class="string">"Unable to compute the symmetric tridiagonal decomposition of an empty matrix."
</span>);
<span class="kw">let </span><span class="kw-2">mut </span>off_diagonal = Matrix::uninit(dim.sub(Const::<<span class="number">1</span>>), Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>p = Matrix::zeros_generic(dim.sub(Const::<<span class="number">1</span>>), Const::<<span class="number">1</span>>);
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim.value() - <span class="number">1 </span>{
<span class="kw">let </span><span class="kw-2">mut </span>m = m.rows_range_mut(i + <span class="number">1</span>..);
<span class="kw">let </span>(<span class="kw-2">mut </span>axis, <span class="kw-2">mut </span>m) = m.columns_range_pair_mut(i, i + <span class="number">1</span>..);
<span class="kw">let </span>(norm, not_zero) = householder::reflection_axis_mut(<span class="kw-2">&mut </span>axis);
off_diagonal[i] = MaybeUninit::new(norm);
<span class="kw">if </span>not_zero {
<span class="kw">let </span><span class="kw-2">mut </span>p = p.rows_range_mut(i..);
p.hegemv(<span class="kw">crate</span>::convert(<span class="number">2.0</span>), <span class="kw-2">&</span>m, <span class="kw-2">&</span>axis, T::zero());
<span class="kw">let </span>dot = axis.dotc(<span class="kw-2">&</span>p);
m.hegerc(-T::one(), <span class="kw-2">&</span>p, <span class="kw-2">&</span>axis, T::one());
m.hegerc(-T::one(), <span class="kw-2">&</span>axis, <span class="kw-2">&</span>p, T::one());
m.hegerc(dot * <span class="kw">crate</span>::convert(<span class="number">2.0</span>), <span class="kw-2">&</span>axis, <span class="kw-2">&</span>axis, T::one());
}
}
<span class="comment">// Safety: off_diagonal has been fully initialized.
</span><span class="kw">let </span>off_diagonal = <span class="kw">unsafe </span>{ off_diagonal.assume_init() };
<span class="self">Self </span>{
tri: m,
off_diagonal,
}
}
<span class="attr">#[doc(hidden)]
</span><span class="comment">// For debugging.
</span><span class="kw">pub fn </span>internal_tri(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>OMatrix<T, D, D> {
<span class="kw-2">&</span><span class="self">self</span>.tri
}
<span class="doccomment">/// Retrieve the orthogonal transformation, diagonal, and off diagonal elements of this
/// decomposition.
</span><span class="kw">pub fn </span>unpack(
<span class="self">self</span>,
) -> (
OMatrix<T, D, D>,
OVector<T::RealField, D>,
OVector<T::RealField, DimDiff<D, U1>>,
)
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, D> + Allocator<T::RealField, DimDiff<D, U1>>,
{
<span class="kw">let </span>diag = <span class="self">self</span>.diagonal();
<span class="kw">let </span>q = <span class="self">self</span>.q();
(q, diag, <span class="self">self</span>.off_diagonal.map(T::modulus))
}
<span class="doccomment">/// Retrieve the diagonal, and off diagonal elements of this decomposition.
</span><span class="kw">pub fn </span>unpack_tridiagonal(
<span class="self">self</span>,
) -> (
OVector<T::RealField, D>,
OVector<T::RealField, DimDiff<D, U1>>,
)
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, D> + Allocator<T::RealField, DimDiff<D, U1>>,
{
(<span class="self">self</span>.diagonal(), <span class="self">self</span>.off_diagonal.map(T::modulus))
}
<span class="doccomment">/// The diagonal components of this decomposition.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>diagonal(<span class="kw-2">&</span><span class="self">self</span>) -> OVector<T::RealField, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, D>,
{
<span class="self">self</span>.tri.map_diagonal(|e| e.real())
}
<span class="doccomment">/// The off-diagonal components of this decomposition.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>off_diagonal(<span class="kw-2">&</span><span class="self">self</span>) -> OVector<T::RealField, DimDiff<D, U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, DimDiff<D, U1>>,
{
<span class="self">self</span>.off_diagonal.map(T::modulus)
}
<span class="doccomment">/// Computes the orthogonal matrix `Q` of this decomposition.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>q(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D> {
householder::assemble_q(<span class="kw-2">&</span><span class="self">self</span>.tri, <span class="self">self</span>.off_diagonal.as_slice())
}
<span class="doccomment">/// Recomputes the original symmetric matrix.
</span><span class="kw">pub fn </span>recompose(<span class="kw-2">mut </span><span class="self">self</span>) -> OMatrix<T, D, D> {
<span class="kw">let </span>q = <span class="self">self</span>.q();
<span class="self">self</span>.tri.fill_lower_triangle(T::zero(), <span class="number">2</span>);
<span class="self">self</span>.tri.fill_upper_triangle(T::zero(), <span class="number">2</span>);
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.off_diagonal.len() {
<span class="kw">let </span>val = T::from_real(<span class="self">self</span>.off_diagonal[i].clone().modulus());
<span class="self">self</span>.tri[(i + <span class="number">1</span>, i)] = val.clone();
<span class="self">self</span>.tri[(i, i + <span class="number">1</span>)] = val;
}
<span class="kw-2">&</span>q * <span class="self">self</span>.tri * q.adjoint()
}
}
</code></pre></div>
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