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</pre><pre class="rust"><code><span class="doccomment">//! Construction of householder elementary reflections.
</span><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, Unit, Vector};
<span class="kw">use </span><span class="kw">crate</span>::dimension::Dim;
<span class="kw">use </span><span class="kw">crate</span>::storage::StorageMut;
<span class="kw">use </span>num::Zero;
<span class="kw">use </span>simba::scalar::ComplexField;
<span class="kw">use </span><span class="kw">crate</span>::geometry::Reflection;
<span class="doccomment">/// Replaces `column` by the axis of the householder reflection that transforms `column` into
/// `(+/-|column|, 0, ..., 0)`.
///
/// The unit-length axis is output to `column`. Returns what would be the first component of
/// `column` after reflection and `false` if no reflection was necessary.
</span><span class="attr">#[doc(hidden)]
#[inline(always)]
</span><span class="kw">pub fn </span>reflection_axis_mut<T: ComplexField, D: Dim, S: StorageMut<T, D>>(
column: <span class="kw-2">&mut </span>Vector<T, D, S>,
) -> (T, bool) {
<span class="kw">let </span>reflection_sq_norm = column.norm_squared();
<span class="kw">let </span>reflection_norm = reflection_sq_norm.clone().sqrt();
<span class="kw">let </span>factor;
<span class="kw">let </span>signed_norm;
<span class="kw">unsafe </span>{
<span class="kw">let </span>(modulus, sign) = column.vget_unchecked(<span class="number">0</span>).clone().to_exp();
signed_norm = sign.scale(reflection_norm.clone());
factor = (reflection_sq_norm + modulus * reflection_norm) * <span class="kw">crate</span>::convert(<span class="number">2.0</span>);
<span class="kw-2">*</span>column.vget_unchecked_mut(<span class="number">0</span>) += signed_norm.clone();
};
<span class="kw">if </span>!factor.is_zero() {
column.unscale_mut(factor.sqrt());
(-signed_norm, <span class="bool-val">true</span>)
} <span class="kw">else </span>{
<span class="comment">// TODO: not sure why we don't have a - sign here.
</span>(signed_norm, <span class="bool-val">false</span>)
}
}
<span class="doccomment">/// Uses an householder reflection to zero out the `icol`-th column, starting with the `shift + 1`-th
/// subdiagonal element.
///
/// Returns the signed norm of the column.
</span><span class="attr">#[doc(hidden)]
#[must_use]
</span><span class="kw">pub fn </span>clear_column_unchecked<T: ComplexField, R: Dim, C: Dim>(
matrix: <span class="kw-2">&mut </span>OMatrix<T, R, C>,
icol: usize,
shift: usize,
bilateral: <span class="prelude-ty">Option</span><<span class="kw-2">&mut </span>OVector<T, R>>,
) -> T
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C> + Allocator<T, R>,
{
<span class="kw">let </span>(<span class="kw-2">mut </span>left, <span class="kw-2">mut </span>right) = matrix.columns_range_pair_mut(icol, icol + <span class="number">1</span>..);
<span class="kw">let </span><span class="kw-2">mut </span>axis = left.rows_range_mut(icol + shift..);
<span class="kw">let </span>(reflection_norm, not_zero) = reflection_axis_mut(<span class="kw-2">&mut </span>axis);
<span class="kw">if </span>not_zero {
<span class="kw">let </span>refl = Reflection::new(Unit::new_unchecked(axis), T::zero());
<span class="kw">let </span>sign = reflection_norm.clone().signum();
<span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">mut </span>work) = bilateral {
refl.reflect_rows_with_sign(<span class="kw-2">&mut </span>right, <span class="kw-2">&mut </span>work, sign.clone());
}
refl.reflect_with_sign(<span class="kw-2">&mut </span>right.rows_range_mut(icol + shift..), sign.conjugate());
}
reflection_norm
}
<span class="doccomment">/// Uses an householder reflection to zero out the `irow`-th row, ending before the `shift + 1`-th
/// superdiagonal element.
///
/// Returns the signed norm of the column.
</span><span class="attr">#[doc(hidden)]
#[must_use]
</span><span class="kw">pub fn </span>clear_row_unchecked<T: ComplexField, R: Dim, C: Dim>(
matrix: <span class="kw-2">&mut </span>OMatrix<T, R, C>,
axis_packed: <span class="kw-2">&mut </span>OVector<T, C>,
work: <span class="kw-2">&mut </span>OVector<T, R>,
irow: usize,
shift: usize,
) -> T
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C> + Allocator<T, R> + Allocator<T, C>,
{
<span class="kw">let </span>(<span class="kw-2">mut </span>top, <span class="kw-2">mut </span>bottom) = matrix.rows_range_pair_mut(irow, irow + <span class="number">1</span>..);
<span class="kw">let </span><span class="kw-2">mut </span>axis = axis_packed.rows_range_mut(irow + shift..);
axis.tr_copy_from(<span class="kw-2">&</span>top.columns_range(irow + shift..));
<span class="kw">let </span>(reflection_norm, not_zero) = reflection_axis_mut(<span class="kw-2">&mut </span>axis);
axis.conjugate_mut(); <span class="comment">// So that reflect_rows actually cancels the first row.
</span><span class="kw">if </span>not_zero {
<span class="kw">let </span>refl = Reflection::new(Unit::new_unchecked(axis), T::zero());
refl.reflect_rows_with_sign(
<span class="kw-2">&mut </span>bottom.columns_range_mut(irow + shift..),
<span class="kw-2">&mut </span>work.rows_range_mut(irow + <span class="number">1</span>..),
reflection_norm.clone().signum().conjugate(),
);
top.columns_range_mut(irow + shift..)
.tr_copy_from(refl.axis());
} <span class="kw">else </span>{
top.columns_range_mut(irow + shift..).tr_copy_from(<span class="kw-2">&</span>axis);
}
reflection_norm
}
<span class="doccomment">/// Computes the orthogonal transformation described by the elementary reflector axii stored on
/// the lower-diagonal element of the given matrix.
/// matrices.
</span><span class="attr">#[doc(hidden)]
</span><span class="kw">pub fn </span>assemble_q<T: ComplexField, D: Dim>(m: <span class="kw-2">&</span>OMatrix<T, D, D>, signs: <span class="kw-2">&</span>[T]) -> OMatrix<T, D, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="macro">assert!</span>(m.is_square());
<span class="kw">let </span>dim = m.shape_generic().<span class="number">0</span>;
<span class="comment">// NOTE: we could build the identity matrix and call p_mult on it.
// Instead we don't so that we take in account the matrix sparseness.
</span><span class="kw">let </span><span class="kw-2">mut </span>res = OMatrix::identity_generic(dim, dim);
<span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..dim.value() - <span class="number">1</span>).rev() {
<span class="kw">let </span>axis = m.view_range(i + <span class="number">1</span>.., i);
<span class="kw">let </span>refl = Reflection::new(Unit::new_unchecked(axis), T::zero());
<span class="kw">let </span><span class="kw-2">mut </span>res_rows = res.view_range_mut(i + <span class="number">1</span>.., i..);
refl.reflect_with_sign(<span class="kw-2">&mut </span>res_rows, signs[i].clone().signum());
}
res
}
</code></pre></div>
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