<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/linalg/cholesky.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>cholesky.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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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>num::{One, Zero};
<span class="kw">use </span>simba::scalar::ComplexField;
<span class="kw">use </span>simba::simd::SimdComplexField;
<span class="kw">use </span><span class="kw">crate</span>::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::{Const, DefaultAllocator, Matrix, OMatrix, Vector};
<span class="kw">use </span><span class="kw">crate</span>::constraint::{SameNumberOfRows, ShapeConstraint};
<span class="kw">use </span><span class="kw">crate</span>::dimension::{Dim, DimAdd, DimDiff, DimSub, DimSum, U1};
<span class="kw">use </span><span class="kw">crate</span>::storage::{Storage, StorageMut};
<span class="doccomment">/// The Cholesky decomposition of a symmetric-definite-positive 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>,
OMatrix<T, D, D>: Serialize"</span>))
)]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(deserialize = <span class="string">"DefaultAllocator: Allocator<T, D>,
OMatrix<T, D, D>: Deserialize<'de>"</span>))
)]
#[derive(Clone, Debug)]
</span><span class="kw">pub struct </span>Cholesky<T: SimdComplexField, D: Dim>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
chol: OMatrix<T, D, D>,
}
<span class="kw">impl</span><T: SimdComplexField, D: Dim> Copy <span class="kw">for </span>Cholesky<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Copy,
{
}
<span class="kw">impl</span><T: SimdComplexField, D: Dim> Cholesky<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="doccomment">/// Computes the Cholesky decomposition of `matrix` without checking that the matrix is definite-positive.
///
/// If the input matrix is not definite-positive, the decomposition may contain trash values (Inf, NaN, etc.)
</span><span class="kw">pub fn </span>new_unchecked(<span class="kw-2">mut </span>matrix: OMatrix<T, D, D>) -> <span class="self">Self </span>{
<span class="macro">assert!</span>(matrix.is_square(), <span class="string">"The input matrix must be square."</span>);
<span class="kw">let </span>n = matrix.nrows();
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..n {
<span class="kw">for </span>k <span class="kw">in </span><span class="number">0</span>..j {
<span class="kw">let </span>factor = <span class="kw">unsafe </span>{ -matrix.get_unchecked((j, k)).clone() };
<span class="kw">let </span>(<span class="kw-2">mut </span>col_j, col_k) = matrix.columns_range_pair_mut(j, k);
<span class="kw">let </span><span class="kw-2">mut </span>col_j = col_j.rows_range_mut(j..);
<span class="kw">let </span>col_k = col_k.rows_range(j..);
col_j.axpy(factor.simd_conjugate(), <span class="kw-2">&</span>col_k, T::one());
}
<span class="kw">let </span>diag = <span class="kw">unsafe </span>{ matrix.get_unchecked((j, j)).clone() };
<span class="kw">let </span>denom = diag.simd_sqrt();
<span class="kw">unsafe </span>{
<span class="kw-2">*</span>matrix.get_unchecked_mut((j, j)) = denom.clone();
}
<span class="kw">let </span><span class="kw-2">mut </span>col = matrix.view_range_mut(j + <span class="number">1</span>.., j);
col /= denom;
}
Cholesky { chol: matrix }
}
<span class="doccomment">/// Uses the given matrix as-is without any checks or modifications as the
/// Cholesky decomposition.
///
/// It is up to the user to ensure all invariants hold.
</span><span class="kw">pub fn </span>pack_dirty(matrix: OMatrix<T, D, D>) -> <span class="self">Self </span>{
Cholesky { chol: matrix }
}
<span class="doccomment">/// Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly
/// upper-triangular part filled with zeros.
</span><span class="kw">pub fn </span>unpack(<span class="kw-2">mut </span><span class="self">self</span>) -> OMatrix<T, D, D> {
<span class="self">self</span>.chol.fill_upper_triangle(T::zero(), <span class="number">1</span>);
<span class="self">self</span>.chol
}
<span class="doccomment">/// Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out
/// its strict upper-triangular part.
///
/// The values of the strict upper-triangular part are garbage and should be ignored by further
/// computations.
</span><span class="kw">pub fn </span>unpack_dirty(<span class="self">self</span>) -> OMatrix<T, D, D> {
<span class="self">self</span>.chol
}
<span class="doccomment">/// Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly
/// uppen-triangular part filled with zeros.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>l(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D> {
<span class="self">self</span>.chol.lower_triangle()
}
<span class="doccomment">/// Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out
/// its strict upper-triangular part.
///
/// This is an allocation-less version of `self.l()`. The values of the strict upper-triangular
/// part are garbage and should be ignored by further computations.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>l_dirty(<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>.chol
}
<span class="doccomment">/// Solves the system `self * x = b` where `self` is the decomposed matrix and `x` the unknown.
///
/// The result is stored on `b`.
</span><span class="kw">pub fn </span>solve_mut<R2: Dim, C2: Dim, S2>(<span class="kw-2">&</span><span class="self">self</span>, b: <span class="kw-2">&mut </span>Matrix<T, R2, C2, S2>)
<span class="kw">where
</span>S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
<span class="self">self</span>.chol.solve_lower_triangular_unchecked_mut(b);
<span class="self">self</span>.chol.ad_solve_lower_triangular_unchecked_mut(b);
}
<span class="doccomment">/// Returns the solution of the system `self * x = b` where `self` is the decomposed matrix and
/// `x` the unknown.
</span><span class="attr">#[must_use = <span class="string">"Did you mean to use solve_mut()?"</span>]
</span><span class="kw">pub fn </span>solve<R2: Dim, C2: Dim, S2>(<span class="kw-2">&</span><span class="self">self</span>, b: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>) -> OMatrix<T, R2, C2>
<span class="kw">where
</span>S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
<span class="kw">let </span><span class="kw-2">mut </span>res = b.clone_owned();
<span class="self">self</span>.solve_mut(<span class="kw-2">&mut </span>res);
res
}
<span class="doccomment">/// Computes the inverse of the decomposed matrix.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>inverse(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D> {
<span class="kw">let </span>shape = <span class="self">self</span>.chol.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = OMatrix::identity_generic(shape.<span class="number">0</span>, shape.<span class="number">1</span>);
<span class="self">self</span>.solve_mut(<span class="kw-2">&mut </span>res);
res
}
<span class="doccomment">/// Computes the determinant of the decomposed matrix.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>determinant(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField {
<span class="kw">let </span>dim = <span class="self">self</span>.chol.nrows();
<span class="kw">let </span><span class="kw-2">mut </span>prod_diag = T::one();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim {
prod_diag <span class="kw-2">*</span>= <span class="kw">unsafe </span>{ <span class="self">self</span>.chol.get_unchecked((i, i)).clone() };
}
prod_diag.simd_modulus_squared()
}
<span class="doccomment">/// Computes the natural logarithm of determinant of the decomposed matrix.
///
/// This method is more robust than `.determinant()` to very small or very
/// large determinants since it returns the natural logarithm of the
/// determinant rather than the determinant itself.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>ln_determinant(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField {
<span class="kw">let </span>dim = <span class="self">self</span>.chol.nrows();
<span class="kw">let </span><span class="kw-2">mut </span>sum_diag = T::SimdRealField::zero();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim {
sum_diag += <span class="kw">unsafe </span>{
<span class="self">self</span>.chol
.get_unchecked((i, i))
.clone()
.simd_modulus_squared()
.simd_ln()
};
}
sum_diag
}
}
<span class="kw">impl</span><T: ComplexField, D: Dim> Cholesky<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="doccomment">/// Attempts to compute the Cholesky decomposition of `matrix`.
///
/// Returns `None` if the input matrix is not definite-positive. The input matrix is assumed
/// to be symmetric and only the lower-triangular part is read.
</span><span class="kw">pub fn </span>new(matrix: OMatrix<T, D, D>) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="self">Self</span>::new_internal(matrix, <span class="prelude-val">None</span>)
}
<span class="doccomment">/// Attempts to approximate the Cholesky decomposition of `matrix` by
/// replacing non-positive values on the diagonals during the decomposition
/// with the given `substitute`.
///
/// [`try_sqrt`](ComplexField::try_sqrt) will be applied to the `substitute`
/// when it has to be used.
///
/// If your input matrix results only in positive values on the diagonals
/// during the decomposition, `substitute` is unused and the result is just
/// the same as if you used [`new`](Cholesky::new).
///
/// This method allows to compensate for matrices with very small or even
/// negative values due to numerical errors but necessarily results in only
/// an approximation: it is basically a hack. If you don't specifically need
/// Cholesky, it may be better to consider alternatives like the
/// [`LU`](crate::linalg::LU) decomposition/factorization.
</span><span class="kw">pub fn </span>new_with_substitute(matrix: OMatrix<T, D, D>, substitute: T) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="self">Self</span>::new_internal(matrix, <span class="prelude-val">Some</span>(substitute))
}
<span class="doccomment">/// Common implementation for `new` and `new_with_substitute`.
</span><span class="kw">fn </span>new_internal(<span class="kw-2">mut </span>matrix: OMatrix<T, D, D>, substitute: <span class="prelude-ty">Option</span><T>) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="macro">assert!</span>(matrix.is_square(), <span class="string">"The input matrix must be square."</span>);
<span class="kw">let </span>n = matrix.nrows();
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..n {
<span class="kw">for </span>k <span class="kw">in </span><span class="number">0</span>..j {
<span class="kw">let </span>factor = <span class="kw">unsafe </span>{ -matrix.get_unchecked((j, k)).clone() };
<span class="kw">let </span>(<span class="kw-2">mut </span>col_j, col_k) = matrix.columns_range_pair_mut(j, k);
<span class="kw">let </span><span class="kw-2">mut </span>col_j = col_j.rows_range_mut(j..);
<span class="kw">let </span>col_k = col_k.rows_range(j..);
col_j.axpy(factor.conjugate(), <span class="kw-2">&</span>col_k, T::one());
}
<span class="kw">let </span>sqrt_denom = |v: T| {
<span class="kw">if </span>v.is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
v.try_sqrt()
};
<span class="kw">let </span>diag = <span class="kw">unsafe </span>{ matrix.get_unchecked((j, j)).clone() };
<span class="kw">if let </span><span class="prelude-val">Some</span>(denom) =
sqrt_denom(diag).or_else(|| substitute.clone().and_then(sqrt_denom))
{
<span class="kw">unsafe </span>{
<span class="kw-2">*</span>matrix.get_unchecked_mut((j, j)) = denom.clone();
}
<span class="kw">let </span><span class="kw-2">mut </span>col = matrix.view_range_mut(j + <span class="number">1</span>.., j);
col /= denom;
<span class="kw">continue</span>;
}
<span class="comment">// The diagonal element is either zero or its square root could not
// be taken (e.g. for negative real numbers).
</span><span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="prelude-val">Some</span>(Cholesky { chol: matrix })
}
<span class="doccomment">/// Given the Cholesky decomposition of a matrix `M`, a scalar `sigma` and a vector `v`,
/// performs a rank one update such that we end up with the decomposition of `M + sigma * (v * v.adjoint())`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>rank_one_update<R2: Dim, S2>(<span class="kw-2">&mut </span><span class="self">self</span>, x: <span class="kw-2">&</span>Vector<T, R2, S2>, sigma: T::RealField)
<span class="kw">where
</span>S2: Storage<T, R2, U1>,
DefaultAllocator: Allocator<T, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
<span class="self">Self</span>::xx_rank_one_update(<span class="kw-2">&mut </span><span class="self">self</span>.chol, <span class="kw-2">&mut </span>x.clone_owned(), sigma)
}
<span class="doccomment">/// Updates the decomposition such that we get the decomposition of a matrix with the given column `col` in the `j`th position.
/// Since the matrix is square, an identical row will be added in the `j`th row.
</span><span class="kw">pub fn </span>insert_column<R2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
j: usize,
col: Vector<T, R2, S2>,
) -> Cholesky<T, DimSum<D, U1>>
<span class="kw">where
</span>D: DimAdd<U1>,
R2: Dim,
S2: Storage<T, R2, U1>,
DefaultAllocator: Allocator<T, DimSum<D, U1>, DimSum<D, U1>> + Allocator<T, R2>,
ShapeConstraint: SameNumberOfRows<R2, DimSum<D, U1>>,
{
<span class="kw">let </span><span class="kw-2">mut </span>col = col.into_owned();
<span class="comment">// for an explanation of the formulas, see https://en.wikipedia.org/wiki/Cholesky_decomposition#Updating_the_decomposition
</span><span class="kw">let </span>n = col.nrows();
<span class="macro">assert_eq!</span>(
n,
<span class="self">self</span>.chol.nrows() + <span class="number">1</span>,
<span class="string">"The new column must have the size of the factored matrix plus one."
</span>);
<span class="macro">assert!</span>(j < n, <span class="string">"j needs to be within the bound of the new matrix."</span>);
<span class="comment">// loads the data into a new matrix with an additional jth row/column
// TODO: would it be worth it to avoid the zero-initialization?
</span><span class="kw">let </span><span class="kw-2">mut </span>chol = Matrix::zeros_generic(
<span class="self">self</span>.chol.shape_generic().<span class="number">0</span>.add(Const::<<span class="number">1</span>>),
<span class="self">self</span>.chol.shape_generic().<span class="number">1</span>.add(Const::<<span class="number">1</span>>),
);
chol.view_range_mut(..j, ..j)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(..j, ..j));
chol.view_range_mut(..j, j + <span class="number">1</span>..)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(..j, j..));
chol.view_range_mut(j + <span class="number">1</span>.., ..j)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(j.., ..j));
chol.view_range_mut(j + <span class="number">1</span>.., j + <span class="number">1</span>..)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(j.., j..));
<span class="comment">// update the jth row
</span><span class="kw">let </span>top_left_corner = <span class="self">self</span>.chol.view_range(..j, ..j);
<span class="kw">let </span>col_j = col[j].clone();
<span class="kw">let </span>(<span class="kw-2">mut </span>new_rowj_adjoint, <span class="kw-2">mut </span>new_colj) = col.rows_range_pair_mut(..j, j + <span class="number">1</span>..);
<span class="macro">assert!</span>(
top_left_corner.solve_lower_triangular_mut(<span class="kw-2">&mut </span>new_rowj_adjoint),
<span class="string">"Cholesky::insert_column : Unable to solve lower triangular system!"
</span>);
new_rowj_adjoint.adjoint_to(<span class="kw-2">&mut </span>chol.view_range_mut(j, ..j));
<span class="comment">// update the center element
</span><span class="kw">let </span>center_element = T::sqrt(col_j - T::from_real(new_rowj_adjoint.norm_squared()));
chol[(j, j)] = center_element.clone();
<span class="comment">// update the jth column
</span><span class="kw">let </span>bottom_left_corner = <span class="self">self</span>.chol.view_range(j.., ..j);
<span class="comment">// new_colj = (col_jplus - bottom_left_corner * new_rowj.adjoint()) / center_element;
</span>new_colj.gemm(
-T::one() / center_element.clone(),
<span class="kw-2">&</span>bottom_left_corner,
<span class="kw-2">&</span>new_rowj_adjoint,
T::one() / center_element,
);
chol.view_range_mut(j + <span class="number">1</span>.., j).copy_from(<span class="kw-2">&</span>new_colj);
<span class="comment">// update the bottom right corner
</span><span class="kw">let </span><span class="kw-2">mut </span>bottom_right_corner = chol.view_range_mut(j + <span class="number">1</span>.., j + <span class="number">1</span>..);
<span class="self">Self</span>::xx_rank_one_update(
<span class="kw-2">&mut </span>bottom_right_corner,
<span class="kw-2">&mut </span>new_colj,
-T::RealField::one(),
);
Cholesky { chol }
}
<span class="doccomment">/// Updates the decomposition such that we get the decomposition of the factored matrix with its `j`th column removed.
/// Since the matrix is square, the `j`th row will also be removed.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>remove_column(<span class="kw-2">&</span><span class="self">self</span>, j: usize) -> Cholesky<T, DimDiff<D, U1>>
<span class="kw">where
</span>D: DimSub<U1>,
DefaultAllocator: Allocator<T, DimDiff<D, U1>, DimDiff<D, U1>> + Allocator<T, D>,
{
<span class="kw">let </span>n = <span class="self">self</span>.chol.nrows();
<span class="macro">assert!</span>(n > <span class="number">0</span>, <span class="string">"The matrix needs at least one column."</span>);
<span class="macro">assert!</span>(j < n, <span class="string">"j needs to be within the bound of the matrix."</span>);
<span class="comment">// loads the data into a new matrix except for the jth row/column
// TODO: would it be worth it to avoid this zero initialization?
</span><span class="kw">let </span><span class="kw-2">mut </span>chol = Matrix::zeros_generic(
<span class="self">self</span>.chol.shape_generic().<span class="number">0</span>.sub(Const::<<span class="number">1</span>>),
<span class="self">self</span>.chol.shape_generic().<span class="number">1</span>.sub(Const::<<span class="number">1</span>>),
);
chol.view_range_mut(..j, ..j)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(..j, ..j));
chol.view_range_mut(..j, j..)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(..j, j + <span class="number">1</span>..));
chol.view_range_mut(j.., ..j)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(j + <span class="number">1</span>.., ..j));
chol.view_range_mut(j.., j..)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.chol.view_range(j + <span class="number">1</span>.., j + <span class="number">1</span>..));
<span class="comment">// updates the bottom right corner
</span><span class="kw">let </span><span class="kw-2">mut </span>bottom_right_corner = chol.view_range_mut(j.., j..);
<span class="kw">let </span><span class="kw-2">mut </span>workspace = <span class="self">self</span>.chol.column(j).clone_owned();
<span class="kw">let </span><span class="kw-2">mut </span>old_colj = workspace.rows_range_mut(j + <span class="number">1</span>..);
<span class="self">Self</span>::xx_rank_one_update(<span class="kw-2">&mut </span>bottom_right_corner, <span class="kw-2">&mut </span>old_colj, T::RealField::one());
Cholesky { chol }
}
<span class="doccomment">/// Given the Cholesky decomposition of a matrix `M`, a scalar `sigma` and a vector `x`,
/// performs a rank one update such that we end up with the decomposition of `M + sigma * (x * x.adjoint())`.
///
/// This helper method is called by `rank_one_update` but also `insert_column` and `remove_column`
/// where it is used on a square view of the decomposition
</span><span class="kw">fn </span>xx_rank_one_update<Dm, Sm, Rx, Sx>(
chol: <span class="kw-2">&mut </span>Matrix<T, Dm, Dm, Sm>,
x: <span class="kw-2">&mut </span>Vector<T, Rx, Sx>,
sigma: T::RealField,
) <span class="kw">where
</span><span class="comment">//T: ComplexField,
</span>Dm: Dim,
Rx: Dim,
Sm: StorageMut<T, Dm, Dm>,
Sx: StorageMut<T, Rx, U1>,
{
<span class="comment">// heavily inspired by Eigen's `llt_rank_update_lower` implementation https://eigen.tuxfamily.org/dox/LLT_8h_source.html
</span><span class="kw">let </span>n = x.nrows();
<span class="macro">assert_eq!</span>(
n,
chol.nrows(),
<span class="string">"The input vector must be of the same size as the factorized matrix."
</span>);
<span class="kw">let </span><span class="kw-2">mut </span>beta = <span class="kw">crate</span>::one::<T::RealField>();
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..n {
<span class="comment">// updates the diagonal
</span><span class="kw">let </span>diag = T::real(<span class="kw">unsafe </span>{ chol.get_unchecked((j, j)).clone() });
<span class="kw">let </span>diag2 = diag.clone() * diag.clone();
<span class="kw">let </span>xj = <span class="kw">unsafe </span>{ x.get_unchecked(j).clone() };
<span class="kw">let </span>sigma_xj2 = sigma.clone() * T::modulus_squared(xj.clone());
<span class="kw">let </span>gamma = diag2.clone() * beta.clone() + sigma_xj2.clone();
<span class="kw">let </span>new_diag = (diag2.clone() + sigma_xj2.clone() / beta.clone()).sqrt();
<span class="kw">unsafe </span>{ <span class="kw-2">*</span>chol.get_unchecked_mut((j, j)) = T::from_real(new_diag.clone()) };
beta += sigma_xj2 / diag2;
<span class="comment">// updates the terms of L
</span><span class="kw">let </span><span class="kw-2">mut </span>xjplus = x.rows_range_mut(j + <span class="number">1</span>..);
<span class="kw">let </span><span class="kw-2">mut </span>col_j = chol.view_range_mut(j + <span class="number">1</span>.., j);
<span class="comment">// temp_jplus -= (wj / T::from_real(diag)) * col_j;
</span>xjplus.axpy(-xj.clone() / T::from_real(diag.clone()), <span class="kw-2">&</span>col_j, T::one());
<span class="kw">if </span>gamma != <span class="kw">crate</span>::zero::<T::RealField>() {
<span class="comment">// col_j = T::from_real(nljj / diag) * col_j + (T::from_real(nljj * sigma / gamma) * T::conjugate(wj)) * temp_jplus;
</span>col_j.axpy(
T::from_real(new_diag.clone() * sigma.clone() / gamma) * T::conjugate(xj),
<span class="kw-2">&</span>xjplus,
T::from_real(new_diag / diag),
);
}
}
}
}
</code></pre></div>
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