nalgebra/src/base/properties.rs

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// Matrix properties checks.
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use approx::RelativeEq;
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use num::{One, Zero};
use alga::general::{ClosedAdd, ClosedMul, Real};
use base::allocator::Allocator;
use base::dimension::{Dim, DimMin};
use base::storage::Storage;
use base::{DefaultAllocator, Matrix, Scalar, SquareMatrix};
impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// Indicates if this is a square matrix.
#[inline]
pub fn is_empty(&self) -> bool {
let (nrows, ncols) = self.shape();
nrows == 0 || ncols == 0
}
/// Indicates if this is a square matrix.
#[inline]
pub fn is_square(&self) -> bool {
let (nrows, ncols) = self.shape();
nrows == ncols
}
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// FIXME: RelativeEq prevents us from using those methods on integer matrices…
/// 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.
#[inline]
pub fn is_identity(&self, eps: N::Epsilon) -> bool
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where
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N: Zero + One + RelativeEq,
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N::Epsilon: Copy,
{
let (nrows, ncols) = self.shape();
let d;
if nrows > ncols {
d = ncols;
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for i in d..nrows {
for j in 0..ncols {
if !relative_eq!(self[(i, j)], N::zero(), epsilon = eps) {
return false;
}
}
}
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} else {
// nrows <= ncols
d = nrows;
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for i in 0..nrows {
for j in d..ncols {
if !relative_eq!(self[(i, j)], N::zero(), epsilon = eps) {
return false;
}
}
}
}
// Off-diagonal elements of the sub-square matrix.
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for i in 1..d {
for j in 0..i {
// FIXME: use unsafe indexing.
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if !relative_eq!(self[(i, j)], N::zero(), epsilon = eps)
|| !relative_eq!(self[(j, i)], N::zero(), epsilon = eps)
{
return false;
}
}
}
// Diagonal elements of the sub-square matrix.
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for i in 0..d {
if !relative_eq!(self[(i, i)], N::one(), epsilon = eps) {
return false;
}
}
true
}
/// Checks that `Mᵀ × M = Id`.
///
/// In this definition `Id` is approximately equal to the identity matrix with a relative error
/// equal to `eps`.
#[inline]
pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool
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where
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N: Zero + One + ClosedAdd + ClosedMul + RelativeEq,
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S: Storage<N, R, C>,
N::Epsilon: Copy,
DefaultAllocator: Allocator<N, C, C>,
{
(self.tr_mul(self)).is_identity(eps)
}
}
impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
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where
DefaultAllocator: Allocator<N, D, D>,
{
/// Checks that this matrix is orthogonal and has a determinant equal to 1.
#[inline]
pub fn is_special_orthogonal(&self, eps: N) -> bool
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where
D: DimMin<D, Output = D>,
DefaultAllocator: Allocator<(usize, usize), D>,
{
self.is_square() && self.is_orthogonal(eps) && self.determinant() > N::zero()
}
/// Returns `true` if this matrix is invertible.
#[inline]
pub fn is_invertible(&self) -> bool {
// FIXME: improve this?
self.clone_owned().try_inverse().is_some()
}
}