Explain l1 and l2 norms.
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@ -14,24 +14,67 @@ pub fn distance2<N: Real, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
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/// The l1-norm of `x - y`.
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/// The l1-norm of `x - y`.
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///
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/// # See also:
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///
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/// * [`l1_norm`](fn.l1_norm.html)
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/// * [`l2_distance`](fn.l2_distance.html)
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/// * [`l2_norm`](fn.l2_norm.html)
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pub fn l1_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
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pub fn l1_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
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where DefaultAllocator: Alloc<N, D> {
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where DefaultAllocator: Alloc<N, D> {
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l1_norm(&(y - x))
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l1_norm(&(y - x))
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}
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}
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/// The l1-norm of `v`.
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/// The l1-norm of `v`.
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///
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/// This is also known as the "Manhattan distance" or "taxicab distance" and
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/// corresponds to the sum of the absolute values of the components of `v`.
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///
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/// # See also:
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///
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/// * [`l1_distance`](fn.l1_distance.html)
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/// * [`l2_distance`](fn.l2_distance.html)
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/// * [`l2_norm`](fn.l2_norm.html)
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pub fn l1_norm<N: Real, D: Dimension>(v: &TVec<N, D>) -> N
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pub fn l1_norm<N: Real, D: Dimension>(v: &TVec<N, D>) -> N
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where DefaultAllocator: Alloc<N, D> {
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where DefaultAllocator: Alloc<N, D> {
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::comp_add(&v.abs())
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::comp_add(&v.abs())
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}
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}
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/// The l2-norm of `x - y`.
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/// The l2-norm of `x - y`.
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///
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/// This is the same value as returned by [`length2`](fn.length2.html) and
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/// [`magnitude2`](fn.magnitude2.html).
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///
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/// # See also:
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///
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/// * [`l1_distance`](fn.l1_distance.html)
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/// * [`l1_norm`](fn.l1_norm.html)
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/// * [`l2_norm`](fn.l2_norm.html)
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/// * [`length`](fn.length.html)
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/// * [`length2`](fn.length2.html)
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/// * [`magnitude`](fn.magnitude.html)
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/// * [`magnitude2`](fn.magnitude2.html)
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pub fn l2_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
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pub fn l2_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
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where DefaultAllocator: Alloc<N, D> {
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where DefaultAllocator: Alloc<N, D> {
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l2_norm(&(y - x))
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l2_norm(&(y - x))
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}
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}
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/// The l2-norm of `v`.
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/// The l2-norm of `v`.
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///
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/// This is also known as the Euclidean norm.
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///
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/// This is the same value as returned by [`length`](fn.length.html) and
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/// [`magnitude`](fn.magnitude.html).
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///
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/// # See also:
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///
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/// * [`l1_distance`](fn.l1_distance.html)
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/// * [`l1_norm`](fn.l1_norm.html)
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/// * [`l2_distance`](fn.l2_distance.html)
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/// * [`length`](fn.length.html)
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/// * [`length2`](fn.length2.html)
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/// * [`magnitude`](fn.magnitude.html)
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/// * [`magnitude2`](fn.magnitude2.html)
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pub fn l2_norm<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
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pub fn l2_norm<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
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where DefaultAllocator: Alloc<N, D> {
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where DefaultAllocator: Alloc<N, D> {
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x.norm()
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x.norm()
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