QRDecompositionField

feanor_math::algorithms::qr

Trait QRDecompositionField 

Source 
pub trait QRDecompositionField: Field {
    // Required method
    fn scaled_qr_decomposition<V1, V2>(
        &self,
        matrix: SubmatrixMut<'_, V1, Self::Element>,
        q: SubmatrixMut<'_, V2, Self::Element>,
    ) -> Vec<Self::Element>
       where V1: AsPointerToSlice<Self::Element>,
             V2: AsPointerToSlice<Self::Element>;

    // Provided methods
    fn ldl_decomposition<V>(
        &self,
        matrix: SubmatrixMut<'_, V, Self::Element>,
    ) -> Vec<Self::Element>
       where V: AsPointerToSlice<Self::Element> { ... }
    fn qr_decomposition<V1, V2>(
        &self,
        matrix: SubmatrixMut<'_, V1, Self::Element>,
        q: SubmatrixMut<'_, V2, Self::Element>,
    )
       where V1: AsPointerToSlice<Self::Element>,
             V2: AsPointerToSlice<Self::Element>,
             Self: SqrtRing { ... }
}
Available on crate feature unstable-enable only.
Expand description

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

Required Methods§

Source

fn scaled_qr_decomposition<V1, V2>( &self, matrix: SubmatrixMut<'_, V1, Self::Element>, q: SubmatrixMut<'_, V2, Self::Element>, ) -> Vec<Self::Element>
where V1: AsPointerToSlice<Self::Element>, V2: AsPointerToSlice<Self::Element>,

Given a matrix A, computes an orthogonal matrix Q and an upper triangular matrix R with A = Q R. The function writes Q diag(x_1, ..., x_n) to q and diag(1/x_1, ..., 1/x_n) R to matrix, and returns x_1^2, ..., x_n^2, where x_1, ..., x_n are the elements on the diagonal of R.

Returning the values as given above instead of just Q and R is done to avoid the computation of square-roots, which may not be supported by the underlying ring. If it is supported, you can use QRDecompositionField::qr_decomposition() instead. Note that this means that diag(x_1^2, ..., x_n^2) and R are the LDL-decomposition of A^T A.

§Rank-deficient matrices

Do not use this for matrices that do not have full rank. If the underlying ring is exact, this will panic. For approximate rings (in particular floating-point numbers), matrices that don’t have full rank, or are very badly conditioned, will give inaccurate results.

Clearly, rank-deficient matrices cannot be supported, since for those the value diag(1/x_1, ..., 1/x_n) is not defined.

Provided Methods§

Source

fn ldl_decomposition<V>( &self, matrix: SubmatrixMut<'_, V, Self::Element>, ) -> Vec<Self::Element>
where V: AsPointerToSlice<Self::Element>,

Given a square symmetric matrix A, computes a strict lower triangular matrix L and a diagonal matrix D such that A = L D L^T. The function writes L to matrix and returns the diagonal elements of D.

§Singular matrices

Do not use this for matrices that are singular. If the underlying ring is exact, this will panic. For approximate rings (in particular floating-point numbers), matrices that don’t have full rank, or are very badly conditioned, will give inaccurate results. Note however that the matrix is not required to be positive definite, it may have both positive and negative eigenvalues (but no zero eigenvalues).

Why don’t we support singular matrices? Because many singular matrices don’t have an LDL decomposition. For example, the matrix [[ 0, 1 ], [ 1, 1 ]] doesn’t.

Source

fn qr_decomposition<V1, V2>( &self, matrix: SubmatrixMut<'_, V1, Self::Element>, q: SubmatrixMut<'_, V2, Self::Element>, )
where V1: AsPointerToSlice<Self::Element>, V2: AsPointerToSlice<Self::Element>, Self: SqrtRing,

Given a matrix A, computes an orthogonal matrix Q and an upper triangular matrix R with A = Q R. These are returned in matrix and q, respectively.

Note that if the ring is not a SqrtRing, you can still use QRDecompositionField::scaled_qr_decomposition().

This function supports non-full-rank matrices as well.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§