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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, Matrix, OMatrix, OVector, Unit};
<span class="kw">use </span><span class="kw">crate</span>::dimension::{Const, Dim, DimDiff, DimMin, DimMinimum, DimSub, U1};
<span class="kw">use </span>simba::scalar::ComplexField;
<span class="kw">use </span><span class="kw">crate</span>::geometry::Reflection;
<span class="kw">use </span><span class="kw">crate</span>::linalg::householder;
<span class="kw">use </span>std::mem::MaybeUninit;
<span class="doccomment">/// The bidiagonalization of a general 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">"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"</span>))
)]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(deserialize = <span class="string">"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>"</span>))
)]
#[derive(Clone, Debug)]
</span><span class="kw">pub struct </span>Bidiagonal<T: ComplexField, R: DimMin<C>, C: Dim>
<span class="kw">where
</span>DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C>
+ Allocator<T, DimMinimum<R, C>>
+ Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
{
<span class="comment">// TODO: perhaps we should pack the axes into different vectors so that axes for `v_t` are
// contiguous. This prevents some useless copies.
</span>uv: OMatrix<T, R, C>,
<span class="doccomment">/// The diagonal elements of the decomposed matrix.
</span>diagonal: OVector<T, DimMinimum<R, C>>,
<span class="doccomment">/// The off-diagonal elements of the decomposed matrix.
</span>off_diagonal: OVector<T, DimDiff<DimMinimum<R, C>, U1>>,
upper_diagonal: bool,
}
<span class="kw">impl</span><T: ComplexField, R: DimMin<C>, C: Dim> Copy <span class="kw">for </span>Bidiagonal<T, R, C>
<span class="kw">where
</span>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,
{
}
<span class="kw">impl</span><T: ComplexField, R: DimMin<C>, C: Dim> Bidiagonal<T, R, C>
<span class="kw">where
</span>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>>,
{
<span class="doccomment">/// Computes the Bidiagonal decomposition using householder reflections.
</span><span class="kw">pub fn </span>new(<span class="kw-2">mut </span>matrix: OMatrix<T, R, C>) -> <span class="self">Self </span>{
<span class="kw">let </span>(nrows, ncols) = matrix.shape_generic();
<span class="kw">let </span>min_nrows_ncols = nrows.min(ncols);
<span class="kw">let </span>dim = min_nrows_ncols.value();
<span class="macro">assert!</span>(
dim != <span class="number">0</span>,
<span class="string">"Cannot compute the bidiagonalization of an empty matrix."
</span>);
<span class="kw">let </span><span class="kw-2">mut </span>diagonal = Matrix::uninit(min_nrows_ncols, Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>off_diagonal = Matrix::uninit(min_nrows_ncols.sub(Const::<<span class="number">1</span>>), Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>axis_packed = Matrix::zeros_generic(ncols, Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>work = Matrix::zeros_generic(nrows, Const::<<span class="number">1</span>>);
<span class="kw">let </span>upper_diagonal = nrows.value() >= ncols.value();
<span class="kw">if </span>upper_diagonal {
<span class="kw">for </span>ite <span class="kw">in </span><span class="number">0</span>..dim - <span class="number">1 </span>{
diagonal[ite] = MaybeUninit::new(householder::clear_column_unchecked(
<span class="kw-2">&mut </span>matrix,
ite,
<span class="number">0</span>,
<span class="prelude-val">None</span>,
));
off_diagonal[ite] = MaybeUninit::new(householder::clear_row_unchecked(
<span class="kw-2">&mut </span>matrix,
<span class="kw-2">&mut </span>axis_packed,
<span class="kw-2">&mut </span>work,
ite,
<span class="number">1</span>,
));
}
diagonal[dim - <span class="number">1</span>] = MaybeUninit::new(householder::clear_column_unchecked(
<span class="kw-2">&mut </span>matrix,
dim - <span class="number">1</span>,
<span class="number">0</span>,
<span class="prelude-val">None</span>,
));
} <span class="kw">else </span>{
<span class="kw">for </span>ite <span class="kw">in </span><span class="number">0</span>..dim - <span class="number">1 </span>{
diagonal[ite] = MaybeUninit::new(householder::clear_row_unchecked(
<span class="kw-2">&mut </span>matrix,
<span class="kw-2">&mut </span>axis_packed,
<span class="kw-2">&mut </span>work,
ite,
<span class="number">0</span>,
));
off_diagonal[ite] = MaybeUninit::new(householder::clear_column_unchecked(
<span class="kw-2">&mut </span>matrix,
ite,
<span class="number">1</span>,
<span class="prelude-val">None</span>,
));
}
diagonal[dim - <span class="number">1</span>] = MaybeUninit::new(householder::clear_row_unchecked(
<span class="kw-2">&mut </span>matrix,
<span class="kw-2">&mut </span>axis_packed,
<span class="kw-2">&mut </span>work,
dim - <span class="number">1</span>,
<span class="number">0</span>,
));
}
<span class="comment">// Safety: diagonal and off_diagonal have been fully initialized.
</span><span class="kw">let </span>(diagonal, off_diagonal) =
<span class="kw">unsafe </span>{ (diagonal.assume_init(), off_diagonal.assume_init()) };
Bidiagonal {
uv: matrix,
diagonal,
off_diagonal,
upper_diagonal,
}
}
<span class="doccomment">/// Indicates whether this decomposition contains an upper-diagonal matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_upper_diagonal(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="self">self</span>.upper_diagonal
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>axis_shift(<span class="kw-2">&</span><span class="self">self</span>) -> (usize, usize) {
<span class="kw">if </span><span class="self">self</span>.upper_diagonal {
(<span class="number">0</span>, <span class="number">1</span>)
} <span class="kw">else </span>{
(<span class="number">1</span>, <span class="number">0</span>)
}
}
<span class="doccomment">/// Unpacks this decomposition into its three matrix factors `(U, D, V^t)`.
///
/// The decomposed matrix `M` is equal to `U * D * V^t`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>unpack(
<span class="self">self</span>,
) -> (
OMatrix<T, R, DimMinimum<R, C>>,
OMatrix<T, DimMinimum<R, C>, DimMinimum<R, C>>,
OMatrix<T, DimMinimum<R, C>, C>,
)
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>>
+ Allocator<T, R, DimMinimum<R, C>>
+ Allocator<T, DimMinimum<R, C>, C>,
{
<span class="comment">// TODO: optimize by calling a reallocator.
</span>(<span class="self">self</span>.u(), <span class="self">self</span>.d(), <span class="self">self</span>.v_t())
}
<span class="doccomment">/// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>d(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, DimMinimum<R, C>, DimMinimum<R, C>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.uv.shape_generic();
<span class="kw">let </span>d = nrows.min(ncols);
<span class="kw">let </span><span class="kw-2">mut </span>res = OMatrix::identity_generic(d, d);
res.set_partial_diagonal(
<span class="self">self</span>.diagonal
.iter()
.map(|e| T::from_real(e.clone().modulus())),
);
<span class="kw">let </span>start = <span class="self">self</span>.axis_shift();
res.view_mut(start, (d.value() - <span class="number">1</span>, d.value() - <span class="number">1</span>))
.set_partial_diagonal(
<span class="self">self</span>.off_diagonal
.iter()
.map(|e| T::from_real(e.clone().modulus())),
);
res
}
<span class="doccomment">/// Computes the orthogonal matrix `U` of this `U * D * V` decomposition.
</span><span class="comment">// TODO: code duplication with householder::assemble_q.
// Except that we are returning a rectangular matrix here.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>u(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, R, DimMinimum<R, C>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.uv.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::identity_generic(nrows, nrows.min(ncols));
<span class="kw">let </span>dim = <span class="self">self</span>.diagonal.len();
<span class="kw">let </span>shift = <span class="self">self</span>.axis_shift().<span class="number">0</span>;
<span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..dim - shift).rev() {
<span class="kw">let </span>axis = <span class="self">self</span>.uv.view_range(i + shift.., i);
<span class="comment">// TODO: sometimes, the axis might have a zero magnitude.
</span><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 + shift.., i..);
<span class="kw">let </span>sign = <span class="kw">if </span><span class="self">self</span>.upper_diagonal {
<span class="self">self</span>.diagonal[i].clone().signum()
} <span class="kw">else </span>{
<span class="self">self</span>.off_diagonal[i].clone().signum()
};
refl.reflect_with_sign(<span class="kw-2">&mut </span>res_rows, sign);
}
res
}
<span class="doccomment">/// Computes the orthogonal matrix `V_t` of this `U * D * V_t` decomposition.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>v_t(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, DimMinimum<R, C>, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.uv.shape_generic();
<span class="kw">let </span>min_nrows_ncols = nrows.min(ncols);
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::identity_generic(min_nrows_ncols, ncols);
<span class="kw">let </span><span class="kw-2">mut </span>work = Matrix::zeros_generic(min_nrows_ncols, Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>axis_packed = Matrix::zeros_generic(ncols, Const::<<span class="number">1</span>>);
<span class="kw">let </span>shift = <span class="self">self</span>.axis_shift().<span class="number">1</span>;
<span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..min_nrows_ncols.value() - shift).rev() {
<span class="kw">let </span>axis = <span class="self">self</span>.uv.view_range(i, i + shift..);
<span class="kw">let </span><span class="kw-2">mut </span>axis_packed = axis_packed.rows_range_mut(i + shift..);
axis_packed.tr_copy_from(<span class="kw-2">&</span>axis);
<span class="comment">// TODO: sometimes, the axis might have a zero magnitude.
</span><span class="kw">let </span>refl = Reflection::new(Unit::new_unchecked(axis_packed), T::zero());
<span class="kw">let </span><span class="kw-2">mut </span>res_rows = res.view_range_mut(i.., i + shift..);
<span class="kw">let </span>sign = <span class="kw">if </span><span class="self">self</span>.upper_diagonal {
<span class="self">self</span>.off_diagonal[i].clone().signum()
} <span class="kw">else </span>{
<span class="self">self</span>.diagonal[i].clone().signum()
};
refl.reflect_rows_with_sign(<span class="kw-2">&mut </span>res_rows, <span class="kw-2">&mut </span>work.rows_range_mut(i..), sign);
}
res
}
<span class="doccomment">/// The diagonal part of this decomposed matrix.
</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, DimMinimum<R, C>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>>,
{
<span class="self">self</span>.diagonal.map(|e| e.modulus())
}
<span class="doccomment">/// The off-diagonal part of this decomposed matrix.
</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<DimMinimum<R, C>, U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,
{
<span class="self">self</span>.off_diagonal.map(|e| e.modulus())
}
<span class="attr">#[doc(hidden)]
</span><span class="kw">pub fn </span>uv_internal(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>OMatrix<T, R, C> {
<span class="kw-2">&</span><span class="self">self</span>.uv
}
}
<span class="comment">// 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()
// // }
// }
</span></code></pre></div>
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