Added test for QR factorization and fixed unpack issue
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1316133625
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@ -11,10 +11,7 @@ use crate::storage::{Storage, StorageMut};
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use crate::geometry::Reflection;
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use crate::linalg::householder;
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//=============================================================================
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use crate::linalg::PermutationSequence;
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//=============================================================================
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/// The QRP decomposition of a general matrix.
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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@ -65,7 +62,9 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
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let (nrows, ncols) = matrix.data.shape();
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let min_nrows_ncols = nrows.min(ncols);
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let mut p = PermutationSequence::identity_generic(min_nrows_ncols);
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let mut diag = unsafe { MatrixMN::new_uninitialized_generic(min_nrows_ncols, U1) };
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println!("diag: {:?}", &diag);
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if min_nrows_ncols.value() == 0 {
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return QRP {
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@ -76,12 +75,18 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
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}
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for ite in 0..min_nrows_ncols.value() {
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let mut col_norm = Vec::new();
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for column in matrix.column_iter() {
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col_norm.push(column.norm_squared());
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}
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let piv = matrix.slice_range(ite.., ite..).icamax_full();
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let col_piv = piv.1 + ite;
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matrix.swap_columns(ite, col_piv);
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p.append_permutation(ite, col_piv);
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householder::clear_column_unchecked(&mut matrix, &mut diag[ite], ite, 0, None);
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println!("matrix: {:?}", &matrix.data);
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}
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QRP {
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@ -139,7 +144,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
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res
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}
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/// The column permutations of this decomposition.
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/// Retrieves the column permutation of this decomposition.
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#[inline]
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pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>> {
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&self.p
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@ -151,13 +156,14 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
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) -> (
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MatrixMN<N, R, DimMinimum<R, C>>,
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MatrixMN<N, DimMinimum<R, C>, C>,
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PermutationSequence<DimMinimum<R, C>>,
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)
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where
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DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
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DefaultAllocator:
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Allocator<N, R, DimMinimum<R, C>> + Reallocator<N, R, C, DimMinimum<R, C>, C>,
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Allocator<N, R, DimMinimum<R, C>> + Reallocator<N, R, C, DimMinimum<R, C>, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
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{
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(self.q(), self.unpack_r())
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(self.q(), self.r(), self.p)
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}
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#[doc(hidden)]
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@ -300,18 +306,18 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> +
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true
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}
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// /// Computes the determinant of the decomposed matrix.
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// pub fn determinant(&self) -> N {
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// let dim = self.qrp.nrows();
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// assert!(self.qrp.is_square(), "QRP determinant: unable to compute the determinant of a non-square matrix.");
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/// Computes the determinant of the decomposed matrix.
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pub fn determinant(&self) -> N {
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let dim = self.qrp.nrows();
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assert!(self.qrp.is_square(), "QRP determinant: unable to compute the determinant of a non-square matrix.");
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// let mut res = N::one();
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// for i in 0 .. dim {
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// res *= unsafe { *self.diag.vget_unchecked(i) };
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// }
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let mut res = N::one();
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for i in 0 .. dim {
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res *= unsafe { *self.diag.vget_unchecked(i) };
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}
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// res self.q_determinant()
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// }
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res * self.p.determinant()
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}
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}
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impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
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@ -0,0 +1,156 @@
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#[cfg_attr(rustfmt, rustfmt_skip)]
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use na::Matrix4;
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#[test]
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fn qrp() {
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let m = Matrix4::new (
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1.0, -1.0, 2.0, 1.0,
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-1.0, 3.0, -1.0, -1.0,
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3.0, -5.0, 5.0, 3.0,
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1.0, 2.0, 1.0, -2.0);
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let qrp = m.qrp();
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assert!(relative_eq!(qrp.determinant(), 0.0, epsilon = 1.0e-7));
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let (q, r, p) = qrp.unpack();
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let mut qr = q * r;
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p.inv_permute_columns(& mut qr);
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assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
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}
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#[cfg(feature = "arbitrary")]
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mod quickcheck_tests {
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macro_rules! gen_tests(
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($module: ident, $scalar: ty) => {
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mod $module {
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use na::{DMatrix, DVector, Matrix3x5, Matrix4, Matrix4x3, Matrix5x3, Vector4};
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use std::cmp;
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#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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quickcheck! {
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fn qrp(m: DMatrix<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.clone().qrp();
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let q = qrp.q();
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let r = qrp.r();
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println!("m: {}", m);
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println!("qrp: {}", &q * &r);
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relative_eq!(m, &q * r, epsilon = 1.0e-7) &&
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q.is_orthogonal(1.0e-7)
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}
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fn qrp_static_5_3(m: Matrix5x3<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.qrp();
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let q = qrp.q();
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let r = qrp.r();
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relative_eq!(m, q * r, epsilon = 1.0e-7) &&
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q.is_orthogonal(1.0e-7)
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}
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fn qrp_static_3_5(m: Matrix3x5<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.qrp();
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let q = qrp.q();
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let r = qrp.r();
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relative_eq!(m, q * r, epsilon = 1.0e-7) &&
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q.is_orthogonal(1.0e-7)
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}
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fn qrp_static_square(m: Matrix4<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.qrp();
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let q = qrp.q();
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let r = qrp.r();
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println!("{}{}{}{}", q, r, q * r, m);
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relative_eq!(m, q * r, epsilon = 1.0e-7) &&
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q.is_orthogonal(1.0e-7)
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}
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fn qrp_solve(n: usize, nb: usize) -> bool {
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if n != 0 && nb != 0 {
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let n = cmp::min(n, 50); // To avoid slowing down the test too much.
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let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
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let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
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let qrp = m.clone().qrp();
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let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
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let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
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if qrp.is_invertible() {
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let sol1 = qrp.solve(&b1).unwrap();
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let sol2 = qrp.solve(&b2).unwrap();
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return relative_eq!(&m * sol1, b1, epsilon = 1.0e-6) &&
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relative_eq!(&m * sol2, b2, epsilon = 1.0e-6)
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}
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}
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return true;
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}
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fn qrp_solve_static(m: Matrix4<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.qrp();
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let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
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let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
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if qrp.is_invertible() {
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let sol1 = qrp.solve(&b1).unwrap();
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let sol2 = qrp.solve(&b2).unwrap();
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relative_eq!(m * sol1, b1, epsilon = 1.0e-6) &&
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relative_eq!(m * sol2, b2, epsilon = 1.0e-6)
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}
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else {
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false
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}
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}
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fn qrp_inverse(n: usize) -> bool {
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let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
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let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
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if let Some(m1) = m.clone().qrp().try_inverse() {
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let id1 = &m * &m1;
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let id2 = &m1 * &m;
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id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
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}
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else {
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true
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}
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}
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fn qrp_inverse_static(m: Matrix4<$scalar>) -> bool {
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let m = m.map(|e| e.0);
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let qrp = m.qrp();
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if let Some(m1) = qrp.try_inverse() {
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let id1 = &m * &m1;
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let id2 = &m1 * &m;
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id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
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}
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else {
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true
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}
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}
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}
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}
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}
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);
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gen_tests!(complex, RandComplex<f64>);
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gen_tests!(f64, RandScalar<f64>);
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}
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