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</pre><pre class="rust"><code><span class="comment">// Matrix properties checks.
</span><span class="kw">use </span>approx::RelativeEq;
<span class="kw">use </span>num::{One, Zero};
<span class="kw">use </span>simba::scalar::{ClosedAdd, ClosedMul, ComplexField, RealField};
<span class="kw">use </span><span class="kw">crate</span>::base::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::{Dim, DimMin};
<span class="kw">use </span><span class="kw">crate</span>::base::storage::Storage;
<span class="kw">use </span><span class="kw">crate</span>::base::{DefaultAllocator, Matrix, SquareMatrix};
<span class="kw">use </span><span class="kw">crate</span>::RawStorage;
<span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// The total number of elements of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.len(), 12);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>len(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
nrows * ncols
}
<span class="doccomment">/// Returns true if the matrix contains no elements.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert!(!mat.is_empty());
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_empty(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="self">self</span>.len() == <span class="number">0
</span>}
<span class="doccomment">/// Indicates if this is a square matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_square(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
nrows == ncols
}
<span class="comment">// TODO: RelativeEq prevents us from using those methods on integer matrices…
</span><span class="doccomment">/// Indicated if this is the identity matrix within a relative error of `eps`.
///
/// If the matrix is diagonal, this checks that diagonal elements (i.e. at coordinates `(i, i)`
/// for i from `0` to `min(R, C)`) are equal one; and that all other elements are zero.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_identity(<span class="kw-2">&</span><span class="self">self</span>, eps: T::Epsilon) -> bool
<span class="kw">where
</span>T: Zero + One + RelativeEq,
T::Epsilon: Clone,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">let </span>el = <span class="kw">unsafe </span>{ <span class="self">self</span>.get_unchecked((i, j)) };
<span class="kw">if </span>(i == j && !<span class="macro">relative_eq!</span>(<span class="kw-2">*</span>el, T::one(), epsilon = eps.clone()))
|| (i != j && !<span class="macro">relative_eq!</span>(<span class="kw-2">*</span>el, T::zero(), epsilon = eps.clone()))
{
<span class="kw">return </span><span class="bool-val">false</span>;
}
}
}
<span class="bool-val">true
</span>}
}
<span class="kw">impl</span><T: ComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Checks that `Mᵀ × M = Id`.
///
/// In this definition `Id` is approximately equal to the identity matrix with a relative error
/// equal to `eps`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_orthogonal(<span class="kw-2">&</span><span class="self">self</span>, eps: T::Epsilon) -> bool
<span class="kw">where
</span>T: Zero + One + ClosedAdd + ClosedMul + RelativeEq,
S: Storage<T, R, C>,
T::Epsilon: Clone,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, C>,
{
(<span class="self">self</span>.ad_mul(<span class="self">self</span>)).is_identity(eps)
}
}
<span class="kw">impl</span><T: RealField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="doccomment">/// Checks that this matrix is orthogonal and has a determinant equal to 1.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_special_orthogonal(<span class="kw-2">&</span><span class="self">self</span>, eps: T) -> bool
<span class="kw">where
</span>D: DimMin<D, Output = D>,
DefaultAllocator: Allocator<(usize, usize), D>,
{
<span class="self">self</span>.is_square() && <span class="self">self</span>.is_orthogonal(eps) && <span class="self">self</span>.determinant() > T::zero()
}
<span class="doccomment">/// Returns `true` if this matrix is invertible.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>is_invertible(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="comment">// TODO: improve this?
</span><span class="self">self</span>.clone_owned().try_inverse().is_some()
}
}
</code></pre></div>
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