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