Relax invertibility test in try_inverse()
The previous implementation of try_inverse() used an approximate check of the determinant against 0 for small matrices to determine if the matrix was invertible. This is not a reliable test, and may fail for perfectly invertible matrices. This change simply makes the test criterion an exact comparison instead.
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@ -45,18 +45,19 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
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match dim {
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0 => true,
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1 => {
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if relative_eq!(self.get_unchecked(0, 0), &N::zero()) {
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let determinant = self.get_unchecked(0, 0).clone();
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if determinant == N::zero() {
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false
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}
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else {
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*self.get_unchecked_mut(0, 0) = N::one() / self.determinant();
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*self.get_unchecked_mut(0, 0) = N::one() / determinant;
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true
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}
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},
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2 => {
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let determinant = self.determinant();
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if relative_eq!(&determinant, &N::zero()) {
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if determinant == N::zero() {
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false
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}
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else {
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@ -94,7 +95,7 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
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m12 * minor_m11_m23 +
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m13 * minor_m11_m22;
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if relative_eq!(&determinant, &N::zero()) {
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if determinant == N::zero() {
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false
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}
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else {
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@ -61,3 +61,61 @@ fn matrix5_try_inverse() {
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assert_relative_eq!(a_inv, expected_inverse, max_relative=1e-4);
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}
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#[test]
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fn matrix1_try_inverse_scaled_identity() {
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// A perfectly invertible matrix with
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// very small coefficients
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let a = Matrix1::new(1.0e-20);
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let expected_inverse = Matrix1::new(1.0e20);
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let a_inv = a.try_inverse().expect("Matrix is invertible");
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assert_relative_eq!(a_inv, expected_inverse);
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}
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#[test]
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fn matrix2_try_inverse_scaled_identity() {
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// A perfectly invertible matrix with
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// very small coefficients
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let a = Matrix2::new(1.0e-20, 0.0,
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0.0, 1.0e-20);
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let expected_inverse = Matrix2::new(1.0e20, 0.0,
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0.0, 1.0e20);
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let a_inv = a.try_inverse().expect("Matrix is invertible");
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assert_relative_eq!(a_inv, expected_inverse);
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}
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#[test]
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fn matrix3_try_inverse_scaled_identity() {
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// A perfectly invertible matrix with
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// very small coefficients
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let a = Matrix3::new(1.0e-20, 0.0, 0.0,
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0.0, 1.0e-20, 0.0,
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0.0, 0.0, 1.0e-20);
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let expected_inverse = Matrix3::new(1.0e20, 0.0, 0.0,
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0.0, 1.0e20, 0.0,
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0.0, 0.0, 1.0e20);
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let a_inv = a.try_inverse().expect("Matrix is invertible");
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assert_relative_eq!(a_inv, expected_inverse);
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}
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#[test]
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fn matrix5_try_inverse_scaled_identity() {
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// A perfectly invertible matrix with
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// very small coefficients
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let a = Matrix5::new(1.0e-20, 0.0, 0.0, 0.0, 0.0,
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0.0, 1.0e-20, 0.0, 0.0, 0.0,
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0.0, 0.0, 1.0e-20, 0.0, 0.0,
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0.0, 0.0, 0.0, 1.0e-20, 0.0,
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0.0, 0.0, 0.0, 0.0, 1.0e-20);
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let expected_inverse = Matrix5::new(1.0e+20, 0.0, 0.0, 0.0, 0.0,
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0.0, 1.0e+20, 0.0, 0.0, 0.0,
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0.0, 0.0, 1.0e+20, 0.0, 0.0,
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0.0, 0.0, 0.0, 1.0e+20, 0.0,
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0.0, 0.0, 0.0, 0.0, 1.0e+20);;
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let a_inv = a.try_inverse().expect("Matrix is invertible");
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assert_relative_eq!(a_inv, expected_inverse);
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}
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