First compiling commit for take-2 of polar-decomposition:
Code inspired by this thread: https://github.com/dimforge/nalgebra/pull/656 Main person behind this is LucasCampos
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@ -643,6 +643,35 @@ where
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}
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}
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}
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}
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impl<T: ComplexField, R: DimMin<C>, C: Dim> SVD<T, R, C>
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where
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DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>
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+ Allocator<T, R, DimMinimum<R, C>>
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+ Allocator<T::RealField, DimMinimum<R, C>>,
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{
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/// converts SVD results to a polar form
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pub fn to_polar(&self) -> Result<(OMatrix<T, R, R>, OMatrix<T, R, C>), &'static str>
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where DefaultAllocator: Allocator<T, R, C> //result
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+ Allocator<T, DimMinimum<R, C>, R> // adjoint
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+ Allocator<T, DimMinimum<R, C>> // mapped vals
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+ Allocator<T, R, R> // square matrix & result
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+ Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>> // ?
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,
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{
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match (&self.u, &self.v_t) {
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(Some(u), Some(v_t)) => Ok((
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u * OMatrix::from_diagonal(&self.singular_values.map(|e| T::from_real(e)))
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* u.adjoint(),
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u * v_t,
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)),
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(None, None) => Err("SVD solve: U and V^t have not been computed."),
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(None, _) => Err("SVD solve: U has not been computed."),
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(_, None) => Err("SVD solve: V^t has not been computed."),
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}
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}
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}
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impl<T: ComplexField, R: DimMin<C>, C: Dim> SVD<T, R, C>
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impl<T: ComplexField, R: DimMin<C>, C: Dim> SVD<T, R, C>
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where
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where
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DimMinimum<R, C>: DimSub<U1>, // for Bidiagonal.
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DimMinimum<R, C>: DimSub<U1>, // for Bidiagonal.
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@ -441,3 +441,14 @@ fn svd_sorted() {
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epsilon = 1.0e-5
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epsilon = 1.0e-5
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);
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);
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}
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}
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#[test]
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fn svd_polar_decomposition() {
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let m = DMatrix::<f64>::new_random(4, 4);
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let svd = m.clone().svd(true, true);
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let (p,u) = svd.to_polar().unwrap();
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assert_relative_eq!(m, p*u, epsilon = 1.0e-5);
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}
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