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Nestor Demeure
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@ -8,7 +8,6 @@ use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, SquareMatrix, Vec
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use crate::constraint::{SameNumberOfRows, ShapeConstraint};
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use crate::dimension::{Dim, DimAdd, DimSum, DimDiff, DimSub, Dynamic, U1};
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use crate::storage::{Storage, StorageMut};
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use crate::base::allocator::Reallocator;
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/// The Cholesky decomposition of a symmetric-definite-positive matrix.
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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@ -156,7 +155,7 @@ where
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DefaultAllocator: Allocator<N, R2, U1>,
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ShapeConstraint: SameNumberOfRows<R2, D>,
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{
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rank_one_update(&mut self.chol, x, sigma)
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Self::xx_rank_one_update(&mut self.chol, x, sigma)
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}
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/// Updates the decomposition such that we get the decomposition of a matrix with the given column `col` in the `j`th position.
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@ -170,7 +169,7 @@ where
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D: DimAdd<U1>,
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R2: Dim,
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S2: Storage<N, R2, U1>,
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DefaultAllocator: Reallocator<N, D, D, D, DimSum<D, U1>> + Reallocator<N, D, DimSum<D, U1>, DimSum<D, U1>, DimSum<D, U1>>,
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DefaultAllocator: Allocator<N, DimSum<D, U1>, DimSum<D, U1>>,
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ShapeConstraint: SameNumberOfRows<R2, DimSum<D, U1>>,
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{
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// for an explanation of the formulas, see https://en.wikipedia.org/wiki/Cholesky_decomposition#Updating_the_decomposition
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@ -178,8 +177,12 @@ where
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assert_eq!(n, self.chol.nrows() + 1, "The new column must have the size of the factored matrix plus one.");
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assert!(j < n, "j needs to be within the bound of the new matrix.");
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// TODO what is the fastest way to produce the new matrix ?
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let mut chol= self.chol.clone().insert_column(j, N::zero()).insert_row(j, N::zero());
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// loads the data into a new matrix with an additional jth row/column
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let mut chol = unsafe { Matrix::new_uninitialized_generic(self.chol.data.shape().0.add(U1), self.chol.data.shape().1.add(U1)) };
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chol.slice_range_mut(..j, ..j).copy_from(&self.chol.slice_range(..j, ..j));
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chol.slice_range_mut(..j, j+1..).copy_from(&self.chol.slice_range(..j, j..));
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chol.slice_range_mut(j+1.., ..j).copy_from(&self.chol.slice_range(j.., ..j));
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chol.slice_range_mut(j+1.., j+1..).copy_from(&self.chol.slice_range(j.., j..));
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// update the jth row
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let top_left_corner = self.chol.slice_range(..j, ..j);
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@ -200,7 +203,7 @@ where
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// update the bottom right corner
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let mut bottom_right_corner = chol.slice_range_mut(j+1.., j+1..);
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rank_one_update(&mut bottom_right_corner, &new_colj, -N::real(N::one()));
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Self::xx_rank_one_update(&mut bottom_right_corner, &new_colj, -N::real(N::one()));
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Cholesky { chol }
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}
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@ -208,27 +211,80 @@ where
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/// Updates the decomposition such that we get the decomposition of the factored matrix with its `j`th column removed.
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/// Since the matrix is square, the `j`th row will also be removed.
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pub fn remove_column(
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self,
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&self,
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j: usize,
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) -> Cholesky<N, DimDiff<D, U1>>
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where
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D: DimSub<U1>,
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DefaultAllocator: Reallocator<N, D, D, D, DimDiff<D, U1>> + Reallocator<N, D, DimDiff<D, U1>, DimDiff<D, U1>, DimDiff<D, U1>>,
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DefaultAllocator: Allocator<N, DimDiff<D, U1>, DimDiff<D, U1>>
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{
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let n = self.chol.nrows();
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assert!(n > 0, "The matrix needs at least one column.");
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assert!(j < n, "j needs to be within the bound of the matrix.");
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// TODO what is the fastest way to produce the new matrix ?
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let mut chol= self.chol.clone().remove_column(j).remove_row(j);
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// loads the data into a new matrix except for the jth row/column
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let mut chol = unsafe { Matrix::new_uninitialized_generic(self.chol.data.shape().0.sub(U1), self.chol.data.shape().1.sub(U1)) };
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chol.slice_range_mut(..j, ..j).copy_from(&self.chol.slice_range(..j, ..j));
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chol.slice_range_mut(..j, j..).copy_from(&self.chol.slice_range(..j, j+1..));
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chol.slice_range_mut(j.., ..j).copy_from(&self.chol.slice_range(j+1.., ..j));
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chol.slice_range_mut(j.., j..).copy_from(&self.chol.slice_range(j+1.., j+1..));
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// updates the bottom right corner
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let mut bottom_right_corner = chol.slice_range_mut(j.., j..);
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let old_colj = self.chol.slice_range(j+1.., j);
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rank_one_update(&mut bottom_right_corner, &old_colj, N::real(N::one()));
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Self::xx_rank_one_update(&mut bottom_right_corner, &old_colj, N::real(N::one()));
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Cholesky { chol }
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}
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/// Given the Cholesky decomposition of a matrix `M`, a scalar `sigma` and a vector `v`,
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/// performs a rank one update such that we end up with the decomposition of `M + sigma * v*v.adjoint()`.
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///
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/// This helper method is calling for by `rank_one_update` but also `insert_column` and `remove_column`
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/// where it is used on a square slice of the decomposition
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fn xx_rank_one_update<Dm, Sm, Rx, Sx>(chol : &mut Matrix<N, Dm, Dm, Sm>, x: &Vector<N, Rx, Sx>, sigma: N::RealField)
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where
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//N: ComplexField,
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Dm: Dim,
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Rx: Dim,
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Sm: StorageMut<N, Dm, Dm>,
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Sx: Storage<N, Rx, U1>,
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DefaultAllocator: Allocator<N, Rx, U1>,
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{
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// heavily inspired by Eigen's `llt_rank_update_lower` implementation https://eigen.tuxfamily.org/dox/LLT_8h_source.html
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let n = x.nrows();
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assert_eq!(
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n,
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chol.nrows(),
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"The input vector must be of the same size as the factorized matrix."
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);
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let mut x = x.clone_owned();
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let mut beta = crate::one::<N::RealField>();
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for j in 0..n {
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// updates the diagonal
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let diag = N::real(unsafe { *chol.get_unchecked((j, j)) });
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let diag2 = diag * diag;
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let xj = unsafe { *x.get_unchecked(j) };
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let sigma_xj2 = sigma * N::modulus_squared(xj);
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let gamma = diag2 * beta + sigma_xj2;
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let new_diag = (diag2 + sigma_xj2 / beta).sqrt();
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unsafe { *chol.get_unchecked_mut((j, j)) = N::from_real(new_diag) };
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beta += sigma_xj2 / diag2;
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// updates the terms of L
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let mut xjplus = x.rows_range_mut(j + 1..);
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let mut col_j = chol.slice_range_mut(j + 1.., j);
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// temp_jplus -= (wj / N::from_real(diag)) * col_j;
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xjplus.axpy(-xj / N::from_real(diag), &col_j, N::one());
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if gamma != crate::zero::<N::RealField>() {
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// col_j = N::from_real(nljj / diag) * col_j + (N::from_real(nljj * sigma / gamma) * N::conjugate(wj)) * temp_jplus;
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col_j.axpy(
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N::from_real(new_diag * sigma / gamma) * N::conjugate(xj),
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&xjplus,
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N::from_real(new_diag / diag),
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);
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}
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}
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}
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}
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impl<N: ComplexField, D: DimSub<Dynamic>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
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@ -243,52 +299,3 @@ where
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Cholesky::new(self.into_owned())
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}
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}
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/// Given the Cholesky decomposition of a matrix `M`, a scalar `sigma` and a vector `v`,
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/// performs a rank one update such that we end up with the decomposition of `M + sigma * v*v.adjoint()`.
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///
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/// This helper method is calling for by `rank_one_update` but also `insert_column` and `remove_column`
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/// where it is used on a square slice of the decomposition
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fn rank_one_update<N, D, S, Rx, Sx>(chol : &mut Matrix<N, D, D, S>, x: &Vector<N, Rx, Sx>, sigma: N::RealField)
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where
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N: ComplexField,
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D: Dim,
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Rx: Dim,
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S: StorageMut<N, D, D>,
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Sx: Storage<N, Rx, U1>,
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DefaultAllocator: Allocator<N, Rx, U1>,
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{
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// heavily inspired by Eigen's `llt_rank_update_lower` implementation https://eigen.tuxfamily.org/dox/LLT_8h_source.html
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let n = x.nrows();
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assert_eq!(
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n,
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chol.nrows(),
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"The input vector must be of the same size as the factorized matrix."
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);
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let mut x = x.clone_owned();
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let mut beta = crate::one::<N::RealField>();
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for j in 0..n {
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// updates the diagonal
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let diag = N::real(unsafe { *chol.get_unchecked((j, j)) });
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let diag2 = diag * diag;
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let xj = unsafe { *x.get_unchecked(j) };
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let sigma_xj2 = sigma * N::modulus_squared(xj);
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let gamma = diag2 * beta + sigma_xj2;
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let new_diag = (diag2 + sigma_xj2 / beta).sqrt();
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unsafe { *chol.get_unchecked_mut((j, j)) = N::from_real(new_diag) };
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beta += sigma_xj2 / diag2;
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// updates the terms of L
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let mut xjplus = x.rows_range_mut(j + 1..);
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let mut col_j = chol.slice_range_mut(j + 1.., j);
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// temp_jplus -= (wj / N::from_real(diag)) * col_j;
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xjplus.axpy(-xj / N::from_real(diag), &col_j, N::one());
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if gamma != crate::zero::<N::RealField>() {
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// col_j = N::from_real(nljj / diag) * col_j + (N::from_real(nljj * sigma / gamma) * N::conjugate(wj)) * temp_jplus;
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col_j.axpy(
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N::from_real(new_diag * sigma / gamma) * N::conjugate(xj),
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&xjplus,
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N::from_real(new_diag / diag),
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);
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}
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}
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}
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@ -100,7 +100,7 @@ macro_rules! gen_tests(
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}
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fn cholesky_insert_column(n: usize) -> bool {
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let n = n.max(1).min(50);
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let n = n.max(1).min(10);
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let j = random::<usize>() % n;
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let m_updated = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
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@ -112,15 +112,11 @@ macro_rules! gen_tests(
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let chol = m.clone().cholesky().unwrap().insert_column(j, &col);
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let m_chol_updated = chol.l() * chol.l().adjoint();
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println!("n={} j={}", n, j);
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println!("chol updated:{}", m_chol_updated);
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println!("m updated:{}", m_updated);
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relative_eq!(m_updated, m_chol_updated, epsilon = 1.0e-7)
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}
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fn cholesky_remove_column(n: usize) -> bool {
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let n = n.max(1).min(5);
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let n = n.max(1).min(10);
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let j = random::<usize>() % n;
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let m = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
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