789 lines
22 KiB
Rust
789 lines
22 KiB
Rust
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use num::{Zero, One};
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use alga::general::{AbstractMagma, AbstractGroupAbelian, AbstractGroup, AbstractLoop,
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AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, AbstractModule,
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Module, Field, RingCommutative, Real, Inverse, Additive, Multiplicative,
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MeetSemilattice, JoinSemilattice, Lattice, Identity,
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ClosedAdd, ClosedNeg, ClosedMul};
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use alga::linear::{VectorSpace, NormedSpace, InnerSpace, FiniteDimVectorSpace, FiniteDimInnerSpace};
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use core::{Scalar, Matrix, SquareMatrix};
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use core::dimension::{Dim, DimName};
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use core::storage::OwnedStorage;
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use core::allocator::OwnedAllocator;
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/*
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*
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* Additive structures.
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*
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*/
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impl<N, R: DimName, C: DimName, S> Identity<Additive> for Matrix<N, R, C, S>
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where N: Scalar + Zero,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn identity() -> Self {
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Self::from_element(N::zero())
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}
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}
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impl<N, R: DimName, C: DimName, S> AbstractMagma<Additive> for Matrix<N, R, C, S>
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where N: Scalar + ClosedAdd,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn operate(&self, other: &Self) -> Self {
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self + other
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}
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}
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impl<N, R: DimName, C: DimName, S> Inverse<Additive> for Matrix<N, R, C, S>
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where N: Scalar + ClosedNeg,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn inverse(&self) -> Matrix<N, R, C, S> {
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-self
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}
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#[inline]
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fn inverse_mut(&mut self) {
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*self = -self.clone()
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}
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}
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macro_rules! inherit_additive_structure(
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($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
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impl<N, R: DimName, C: DimName, S> $marker<$operator> for Matrix<N, R, C, S>
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where N: Scalar + $marker<$operator> $(+ $bounds)*,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> { }
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)*}
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);
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inherit_additive_structure!(
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AbstractSemigroup<Additive> + ClosedAdd,
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AbstractMonoid<Additive> + Zero + ClosedAdd,
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AbstractQuasigroup<Additive> + ClosedAdd + ClosedNeg,
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AbstractLoop<Additive> + Zero + ClosedAdd + ClosedNeg,
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AbstractGroup<Additive> + Zero + ClosedAdd + ClosedNeg,
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AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
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);
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impl<N, R: DimName, C: DimName, S> AbstractModule for Matrix<N, R, C, S>
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where N: Scalar + RingCommutative,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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type AbstractRing = N;
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#[inline]
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fn multiply_by(&self, n: N) -> Self {
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self * n
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}
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}
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impl<N, R: DimName, C: DimName, S> Module for Matrix<N, R, C, S>
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where N: Scalar + RingCommutative,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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type Ring = N;
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}
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impl<N, R: DimName, C: DimName, S> VectorSpace for Matrix<N, R, C, S>
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where N: Scalar + Field,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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type Field = N;
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}
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impl<N, R: DimName, C: DimName, S> FiniteDimVectorSpace for Matrix<N, R, C, S>
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where N: Scalar + Field,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn dimension() -> usize {
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R::dim() * C::dim()
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}
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#[inline]
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fn canonical_basis_element(i: usize) -> Self {
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assert!(i < Self::dimension(), "Index out of bound.");
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let mut res = Self::zero();
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unsafe { *res.data.get_unchecked_linear_mut(i) = N::one(); }
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res
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}
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#[inline]
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fn dot(&self, other: &Self) -> N {
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self.dot(other)
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}
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#[inline]
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unsafe fn component_unchecked(&self, i: usize) -> &N {
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self.data.get_unchecked_linear(i)
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}
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#[inline]
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unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
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self.data.get_unchecked_linear_mut(i)
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}
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}
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impl<N, R: DimName, C: DimName, S> NormedSpace for Matrix<N, R, C, S>
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where N: Real,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn norm_squared(&self) -> N {
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self.norm_squared()
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}
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#[inline]
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fn norm(&self) -> N {
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self.norm()
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}
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#[inline]
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fn normalize(&self) -> Self {
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self.normalize()
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}
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#[inline]
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fn normalize_mut(&mut self) -> N {
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self.normalize_mut()
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}
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#[inline]
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fn try_normalize(&self, min_norm: N) -> Option<Self> {
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self.try_normalize(min_norm)
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}
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#[inline]
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fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
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self.try_normalize_mut(min_norm)
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}
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}
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impl<N, R: DimName, C: DimName, S> InnerSpace for Matrix<N, R, C, S>
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where N: Real,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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type Real = N;
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#[inline]
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fn angle(&self, other: &Self) -> N {
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self.angle(other)
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}
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#[inline]
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fn inner_product(&self, other: &Self) -> N {
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self.dot(other)
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}
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}
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// FIXME: specialization will greatly simplify this implementation in the future.
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// In particular:
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// − use `x()` instead of `::canonical_basis_element`
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// − use `::new(x, y, z)` instead of `::from_slice`
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impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
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where N: Real,
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S: OwnedStorage<N, R, C>,
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S::Alloc: OwnedAllocator<N, R, C, S> {
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#[inline]
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fn orthonormalize(vs: &mut [Matrix<N, R, C, S>]) -> usize {
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let mut nbasis_elements = 0;
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for i in 0 .. vs.len() {
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{
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let (elt, basis) = vs[.. i + 1].split_last_mut().unwrap();
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for basis_element in &basis[.. nbasis_elements] {
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*elt -= &*basis_element * elt.dot(basis_element)
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}
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}
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if vs[i].try_normalize_mut(N::zero()).is_some() {
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// FIXME: this will be efficient on dynamically-allocated vectors but for
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// statically-allocated ones, `.clone_from` would be better.
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vs.swap(nbasis_elements, i);
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nbasis_elements += 1;
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// All the other vectors will be dependent.
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if nbasis_elements == Self::dimension() {
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break;
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}
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}
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}
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nbasis_elements
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}
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#[inline]
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fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
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where F: FnMut(&Self) -> bool {
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// FIXME: is this necessary?
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assert!(vs.len() <= Self::dimension(), "The given set of vectors has no chance of being a free family.");
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match Self::dimension() {
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1 => {
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if vs.len() == 0 {
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f(&Self::canonical_basis_element(0));
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}
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},
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2 => {
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if vs.len() == 0 {
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let _ = f(&Self::canonical_basis_element(0)) &&
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f(&Self::canonical_basis_element(1));
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}
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else if vs.len() == 1 {
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let v = &vs[0];
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let res = Self::from_column_slice(&[-v[1], v[0]]);
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f(&res.normalize());
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}
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// Otherwise, nothing.
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},
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3 => {
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if vs.len() == 0 {
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let _ = f(&Self::canonical_basis_element(0)) &&
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f(&Self::canonical_basis_element(1)) &&
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f(&Self::canonical_basis_element(2));
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}
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else if vs.len() == 1 {
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let v = &vs[0];
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let mut a;
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if v[0].abs() > v[1].abs() {
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a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
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}
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else {
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a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);
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};
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a.normalize_mut();
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if f(&a.cross(v)) {
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f(&a);
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}
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}
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else if vs.len() == 2 {
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f(&vs[0].cross(&vs[1]).normalize());
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}
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},
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_ => {
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// XXX: use a GenericArray instead.
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let mut known_basis = Vec::new();
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|
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|||
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for v in vs.iter() {
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known_basis.push(v.normalize())
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}
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|
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|||
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for i in 0 .. Self::dimension() - vs.len() {
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|
let mut elt = Self::canonical_basis_element(i);
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|
|
|
|||
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for v in &known_basis {
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|
elt -= v * elt.dot(v)
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|
};
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|||
|
|
|
|||
|
|
if let Some(subsp_elt) = elt.try_normalize(N::zero()) {
|
|||
|
|
if !f(&subsp_elt) { return };
|
|||
|
|
|
|||
|
|
known_basis.push(subsp_elt);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* Multiplicative structures.
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
*/
|
|||
|
|
impl<N, D: DimName, S> Identity<Multiplicative> for SquareMatrix<N, D, S>
|
|||
|
|
where N: Scalar + Zero + One,
|
|||
|
|
S: OwnedStorage<N, D, D>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, D, D, S> {
|
|||
|
|
#[inline]
|
|||
|
|
fn identity() -> Self {
|
|||
|
|
Self::identity()
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
impl<N, D: DimName, S> AbstractMagma<Multiplicative> for SquareMatrix<N, D, S>
|
|||
|
|
where N: Scalar + Zero + ClosedAdd + ClosedMul,
|
|||
|
|
S: OwnedStorage<N, D, D>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, D, D, S> {
|
|||
|
|
#[inline]
|
|||
|
|
fn operate(&self, other: &Self) -> Self {
|
|||
|
|
self * other
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
macro_rules! impl_multiplicative_structure(
|
|||
|
|
($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
|
|||
|
|
impl<N, D: DimName, S> $marker<$operator> for SquareMatrix<N, D, S>
|
|||
|
|
where N: Scalar + Zero + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
|
|||
|
|
S: OwnedStorage<N, D, D>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, D, D, S> { }
|
|||
|
|
)*}
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
impl_multiplicative_structure!(
|
|||
|
|
AbstractSemigroup<Multiplicative>,
|
|||
|
|
AbstractMonoid<Multiplicative> + One
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
// // FIXME: Field too strong?
|
|||
|
|
// impl<N, S> Matrix for Matrix<N, S>
|
|||
|
|
// where N: Scalar + Field,
|
|||
|
|
// S: Storage<N> {
|
|||
|
|
// type Field = N;
|
|||
|
|
// type Row = OwnedMatrix<N, Static<U1>, S::C, S::Alloc>;
|
|||
|
|
// type Column = OwnedMatrix<N, S::R, Static<U1>, S::Alloc>;
|
|||
|
|
// type Transpose = OwnedMatrix<N, S::C, S::R, S::Alloc>;
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn nrows(&self) -> usize {
|
|||
|
|
// self.shape().0
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn ncolumns(&self) -> usize {
|
|||
|
|
// self.shape().1
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn row(&self, row: usize) -> Self::Row {
|
|||
|
|
// let mut res: Self::Row = ::zero();
|
|||
|
|
|
|||
|
|
// for (column, e) in res.iter_mut().enumerate() {
|
|||
|
|
// *e = self[(row, column)];
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// res
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn column(&self, column: usize) -> Self::Column {
|
|||
|
|
// let mut res: Self::Column = ::zero();
|
|||
|
|
|
|||
|
|
// for (row, e) in res.iter_mut().enumerate() {
|
|||
|
|
// *e = self[(row, column)];
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// res
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
|
|||
|
|
// self.get_unchecked(i, j)
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn transpose(&self) -> Self::Transpose {
|
|||
|
|
// self.transpose()
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// impl<N, S> MatrixMut for Matrix<N, S>
|
|||
|
|
// where N: Scalar + Field,
|
|||
|
|
// S: StorageMut<N> {
|
|||
|
|
// #[inline]
|
|||
|
|
// fn set_row_mut(&mut self, irow: usize, row: &Self::Row) {
|
|||
|
|
// assert!(irow < self.shape().0, "Row index out of bounds.");
|
|||
|
|
|
|||
|
|
// for (icol, e) in row.iter().enumerate() {
|
|||
|
|
// unsafe { self.set_unchecked(irow, icol, *e) }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn set_column_mut(&mut self, icol: usize, col: &Self::Column) {
|
|||
|
|
// assert!(icol < self.shape().1, "Column index out of bounds.");
|
|||
|
|
// for (irow, e) in col.iter().enumerate() {
|
|||
|
|
// unsafe { self.set_unchecked(irow, icol, *e) }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// unsafe fn set_unchecked(&mut self, i: usize, j: usize, val: Self::Field) {
|
|||
|
|
// *self.get_unchecked_mut(i, j) = val
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// // FIXME: Real is needed here only for invertibility...
|
|||
|
|
// impl<N: Real> SquareMatrixMut for $t<N> {
|
|||
|
|
// #[inline]
|
|||
|
|
// fn from_diagonal(diag: &Self::Coordinates) -> Self {
|
|||
|
|
// let mut res: $t<N> = ::zero();
|
|||
|
|
// res.set_diagonal_mut(diag);
|
|||
|
|
// res
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn set_diagonal_mut(&mut self, diag: &Self::Coordinates) {
|
|||
|
|
// for (i, e) in diag.iter().enumerate() {
|
|||
|
|
// unsafe { self.set_unchecked(i, i, *e) }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
// Specializations depending on the dimension.
|
|||
|
|
// matrix_group_approx_impl!(common: $t, 1, $vector, $($compN),+);
|
|||
|
|
|
|||
|
|
// // FIXME: Real is needed here only for invertibility...
|
|||
|
|
// impl<N: Real> SquareMatrix for $t<N> {
|
|||
|
|
// type Vector = $vector<N>;
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn diagonal(&self) -> Self::Coordinates {
|
|||
|
|
// $vector::new(self.m11)
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn determinant(&self) -> Self::Field {
|
|||
|
|
// self.m11
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse(&self) -> Option<Self> {
|
|||
|
|
// let mut res = *self;
|
|||
|
|
// if res.try_inverse_mut() {
|
|||
|
|
// Some(res)
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// None
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse_mut(&mut self) -> bool {
|
|||
|
|
// if relative_eq!(&self.m11, &::zero()) {
|
|||
|
|
// false
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// self.m11 = ::one::<N>() / ::determinant(self);
|
|||
|
|
|
|||
|
|
// true
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn transpose_mut(&mut self) {
|
|||
|
|
// // no-op
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// ident, 2, $vector: ident, $($compN: ident),+) => {
|
|||
|
|
// matrix_group_approx_impl!(common: $t, 2, $vector, $($compN),+);
|
|||
|
|
|
|||
|
|
// // FIXME: Real is needed only for inversion here.
|
|||
|
|
// impl<N: Real> SquareMatrix for $t<N> {
|
|||
|
|
// type Vector = $vector<N>;
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn diagonal(&self) -> Self::Coordinates {
|
|||
|
|
// $vector::new(self.m11, self.m22)
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn determinant(&self) -> Self::Field {
|
|||
|
|
// self.m11 * self.m22 - self.m21 * self.m12
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse(&self) -> Option<Self> {
|
|||
|
|
// let mut res = *self;
|
|||
|
|
// if res.try_inverse_mut() {
|
|||
|
|
// Some(res)
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// None
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse_mut(&mut self) -> bool {
|
|||
|
|
// let determinant = ::determinant(self);
|
|||
|
|
|
|||
|
|
// if relative_eq!(&determinant, &::zero()) {
|
|||
|
|
// false
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// *self = Matrix2::new(
|
|||
|
|
// self.m22 / determinant , -self.m12 / determinant,
|
|||
|
|
// -self.m21 / determinant, self.m11 / determinant);
|
|||
|
|
|
|||
|
|
// true
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn transpose_mut(&mut self) {
|
|||
|
|
// mem::swap(&mut self.m12, &mut self.m21)
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// ident, 3, $vector: ident, $($compN: ident),+) => {
|
|||
|
|
// matrix_group_approx_impl!(common: $t, 3, $vector, $($compN),+);
|
|||
|
|
|
|||
|
|
// // FIXME: Real is needed only for inversion here.
|
|||
|
|
// impl<N: Real> SquareMatrix for $t<N> {
|
|||
|
|
// type Vector = $vector<N>;
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn diagonal(&self) -> Self::Coordinates {
|
|||
|
|
// $vector::new(self.m11, self.m22, self.m33)
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn determinant(&self) -> Self::Field {
|
|||
|
|
// let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
|
|||
|
|
// let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
|
|||
|
|
// let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
|
|||
|
|
|
|||
|
|
// self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse(&self) -> Option<Self> {
|
|||
|
|
// let mut res = *self;
|
|||
|
|
// if res.try_inverse_mut() {
|
|||
|
|
// Some(res)
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// None
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse_mut(&mut self) -> bool {
|
|||
|
|
// let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
|
|||
|
|
// let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
|
|||
|
|
// let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
|
|||
|
|
|
|||
|
|
// let determinant = self.m11 * minor_m12_m23 -
|
|||
|
|
// self.m12 * minor_m11_m23 +
|
|||
|
|
// self.m13 * minor_m11_m22;
|
|||
|
|
|
|||
|
|
// if relative_eq!(&determinant, &::zero()) {
|
|||
|
|
// false
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// *self = Matrix3::new(
|
|||
|
|
// (minor_m12_m23 / determinant),
|
|||
|
|
// ((self.m13 * self.m32 - self.m33 * self.m12) / determinant),
|
|||
|
|
// ((self.m12 * self.m23 - self.m22 * self.m13) / determinant),
|
|||
|
|
|
|||
|
|
// (-minor_m11_m23 / determinant),
|
|||
|
|
// ((self.m11 * self.m33 - self.m31 * self.m13) / determinant),
|
|||
|
|
// ((self.m13 * self.m21 - self.m23 * self.m11) / determinant),
|
|||
|
|
|
|||
|
|
// (minor_m11_m22 / determinant),
|
|||
|
|
// ((self.m12 * self.m31 - self.m32 * self.m11) / determinant),
|
|||
|
|
// ((self.m11 * self.m22 - self.m21 * self.m12) / determinant)
|
|||
|
|
// );
|
|||
|
|
|
|||
|
|
// true
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn transpose_mut(&mut self) {
|
|||
|
|
// mem::swap(&mut self.m12, &mut self.m21);
|
|||
|
|
// mem::swap(&mut self.m13, &mut self.m31);
|
|||
|
|
// mem::swap(&mut self.m23, &mut self.m32);
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// ident, $dimension: expr, $vector: ident, $($compN: ident),+) => {
|
|||
|
|
// matrix_group_approx_impl!(common: $t, $dimension, $vector, $($compN),+);
|
|||
|
|
|
|||
|
|
// // FIXME: Real is needed only for inversion here.
|
|||
|
|
// impl<N: Real> SquareMatrix for $t<N> {
|
|||
|
|
// type Vector = $vector<N>;
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn diagonal(&self) -> Self::Coordinates {
|
|||
|
|
// let mut diagonal: $vector<N> = ::zero();
|
|||
|
|
|
|||
|
|
// for i in 0 .. $dimension {
|
|||
|
|
// unsafe { diagonal.unsafe_set(i, self.get_unchecked(i, i)) }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// diagonal
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn determinant(&self) -> Self::Field {
|
|||
|
|
// // FIXME: extremely naive implementation.
|
|||
|
|
// let mut det = ::zero();
|
|||
|
|
|
|||
|
|
// for icol in 0 .. $dimension {
|
|||
|
|
// let e = unsafe { self.unsafe_at((0, icol)) };
|
|||
|
|
|
|||
|
|
// if e != ::zero() {
|
|||
|
|
// let minor_mat = self.delete_row_column(0, icol);
|
|||
|
|
// let minor = minor_mat.determinant();
|
|||
|
|
|
|||
|
|
// if icol % 2 == 0 {
|
|||
|
|
// det += minor;
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// det -= minor;
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// det
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse(&self) -> Option<Self> {
|
|||
|
|
// let mut res = *self;
|
|||
|
|
// if res.try_inverse_mut() {
|
|||
|
|
// Some(res)
|
|||
|
|
// }
|
|||
|
|
// else {
|
|||
|
|
// None
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn try_inverse_mut(&mut self) -> bool {
|
|||
|
|
// let mut res: $t<N> = ::one();
|
|||
|
|
|
|||
|
|
// // Inversion using Gauss-Jordan elimination
|
|||
|
|
// for k in 0 .. $dimension {
|
|||
|
|
// // search a non-zero value on the k-th column
|
|||
|
|
// // FIXME: would it be worth it to spend some more time searching for the
|
|||
|
|
// // max instead?
|
|||
|
|
|
|||
|
|
// let mut n0 = k; // index of a non-zero entry
|
|||
|
|
|
|||
|
|
// while n0 != $dimension {
|
|||
|
|
// if self[(n0, k)] != ::zero() {
|
|||
|
|
// break;
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// n0 = n0 + 1;
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// if n0 == $dimension {
|
|||
|
|
// return false
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// // swap pivot line
|
|||
|
|
// if n0 != k {
|
|||
|
|
// for j in 0 .. $dimension {
|
|||
|
|
// self.swap((n0, j), (k, j));
|
|||
|
|
// res.swap((n0, j), (k, j));
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// let pivot = self[(k, k)];
|
|||
|
|
|
|||
|
|
// for j in k .. $dimension {
|
|||
|
|
// let selfval = self[(k, j)] / pivot;
|
|||
|
|
// self[(k, j)] = selfval;
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// for j in 0 .. $dimension {
|
|||
|
|
// let resval = res[(k, j)] / pivot;
|
|||
|
|
// res[(k, j)] = resval;
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// for l in 0 .. $dimension {
|
|||
|
|
// if l != k {
|
|||
|
|
// let normalizer = self[(l, k)];
|
|||
|
|
|
|||
|
|
// for j in k .. $dimension {
|
|||
|
|
// let selfval = self[(l, j)] - self[(k, j)] * normalizer;
|
|||
|
|
// self[(l, j)] = selfval;
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// for j in 0 .. $dimension {
|
|||
|
|
// let resval = res[(l, j)] - res[(k, j)] * normalizer;
|
|||
|
|
// res[(l, j)] = resval;
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// *self = res;
|
|||
|
|
|
|||
|
|
// true
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
// #[inline]
|
|||
|
|
// fn transpose_mut(&mut self) {
|
|||
|
|
// for i in 1 .. $dimension {
|
|||
|
|
// for j in 0 .. i {
|
|||
|
|
// self.swap((i, j), (j, i))
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
// }
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
*
|
|||
|
|
* Ordering
|
|||
|
|
*
|
|||
|
|
*/
|
|||
|
|
impl<N, R: Dim, C: Dim, S> MeetSemilattice for Matrix<N, R, C, S>
|
|||
|
|
where N: Scalar + MeetSemilattice,
|
|||
|
|
S: OwnedStorage<N, R, C>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, R, C, S> {
|
|||
|
|
#[inline]
|
|||
|
|
fn meet(&self, other: &Self) -> Self {
|
|||
|
|
self.zip_map(other, |a, b| a.meet(&b))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
impl<N, R: Dim, C: Dim, S> JoinSemilattice for Matrix<N, R, C, S>
|
|||
|
|
where N: Scalar + JoinSemilattice,
|
|||
|
|
S: OwnedStorage<N, R, C>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, R, C, S> {
|
|||
|
|
#[inline]
|
|||
|
|
fn join(&self, other: &Self) -> Self {
|
|||
|
|
self.zip_map(other, |a, b| a.join(&b))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
impl<N, R: Dim, C: Dim, S> Lattice for Matrix<N, R, C, S>
|
|||
|
|
where N: Scalar + Lattice,
|
|||
|
|
S: OwnedStorage<N, R, C>,
|
|||
|
|
S::Alloc: OwnedAllocator<N, R, C, S> {
|
|||
|
|
#[inline]
|
|||
|
|
fn meet_join(&self, other: &Self) -> (Self, Self) {
|
|||
|
|
let shape = self.data.shape();
|
|||
|
|
assert!(shape == other.data.shape(), "Matrix meet/join error: mismatched dimensions.");
|
|||
|
|
|
|||
|
|
let mut mres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
|
|||
|
|
let mut jres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
|
|||
|
|
|
|||
|
|
for i in 0 .. shape.0.value() * shape.1.value() {
|
|||
|
|
unsafe {
|
|||
|
|
let mj = self.data.get_unchecked_linear(i).meet_join(other.data.get_unchecked_linear(i));
|
|||
|
|
*mres.data.get_unchecked_linear_mut(i) = mj.0;
|
|||
|
|
*jres.data.get_unchecked_linear_mut(i) = mj.1;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
(mres, jres)
|
|||
|
|
}
|
|||
|
|
}
|