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// Matrix properties checks.
use approx::RelativeEq;
use num::{One, Zero};
use simba::scalar::{ClosedAdd, ClosedMul, ComplexField, RealField};
use crate::base::allocator::Allocator;
use crate::base::dimension::{Dim, DimMin};
use crate::base::storage::Storage;
use crate::base::{DefaultAllocator, Matrix, Scalar, SquareMatrix};
impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// The total number of elements of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.len(), 12);
/// ```
#[inline]
pub fn len(&self) -> usize {
let (nrows, ncols) = self.shape();
nrows * ncols
}
/// Returns true if the matrix contains no elements.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert!(!mat.is_empty());
/// ```
#[inline]
pub fn is_empty(&self) -> bool {
self.len() == 0
}
/// Indicates if this is a square matrix.
#[inline]
pub fn is_square(&self) -> bool {
let (nrows, ncols) = self.shape();
nrows == ncols
}
// TODO: 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
where
N: Zero + One + RelativeEq,
N::Epsilon: Copy,
{
let (nrows, ncols) = self.shape();
let d;
if nrows > ncols {
d = ncols;
for i in d..nrows {
for j in 0..ncols {
if !relative_eq!(self[(i, j)], N::zero(), epsilon = eps) {
return false;
}
}
}
} else {
// nrows <= ncols
d = nrows;
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.
for i in 1..d {
for j in 0..i {
// TODO: use unsafe indexing.
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.
for i in 0..d {
if !relative_eq!(self[(i, i)], N::one(), epsilon = eps) {
return false;
}
}
true
}
}
impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// 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
where
N: Zero + One + ClosedAdd + ClosedMul + RelativeEq,
S: Storage<N, R, C>,
N::Epsilon: Copy,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, C, C>,
{
(self.ad_mul(self)).is_identity(eps)
}
}
impl<N: RealField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
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
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 {
// TODO: improve this?
self.clone_owned().try_inverse().is_some()
}
}