forked from M-Labs/nalgebra
nalgebra-lapack: add schur decomposition.
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@ -21,16 +21,18 @@ mod cholesky;
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mod lu;
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mod lu;
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mod qr;
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mod qr;
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mod hessenberg;
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mod hessenberg;
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mod schur;
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use num_complex::Complex;
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use num_complex::Complex;
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pub use self::svd::SVD;
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pub use self::svd::SVD;
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pub use self::cholesky::{Cholesky, CholeskyScalar};
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pub use self::cholesky::{Cholesky, CholeskyScalar};
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pub use self::lu::{LU, LUScalar};
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pub use self::lu::{LU, LUScalar};
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pub use self::eigen::RealEigensystem;
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pub use self::eigen::Eigen;
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pub use self::symmetric_eigen::SymmetricEigen;
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pub use self::symmetric_eigen::SymmetricEigen;
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pub use self::qr::QR;
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pub use self::qr::QR;
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pub use self::hessenberg::Hessenberg;
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pub use self::hessenberg::Hessenberg;
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pub use self::schur::RealSchur;
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trait ComplexHelper {
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trait ComplexHelper {
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191
nalgebra-lapack/src/schur.rs
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191
nalgebra-lapack/src/schur.rs
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@ -0,0 +1,191 @@
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use num::Zero;
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use num_complex::Complex;
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use alga::general::Real;
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use ::ComplexHelper;
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use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixN};
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use na::dimension::{Dim, U1};
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use na::storage::Storage;
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use na::allocator::Allocator;
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use lapack::fortran as interface;
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/// Eigendecomposition of a real square matrix with real eigenvalues.
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pub struct RealSchur<N: Scalar, D: Dim>
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where DefaultAllocator: Allocator<N, D> +
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Allocator<N, D, D> {
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re: VectorN<N, D>,
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im: VectorN<N, D>,
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t: MatrixN<N, D>,
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q: MatrixN<N, D>
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}
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impl<N: EigenScalar + Real, D: Dim> RealSchur<N, D>
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where DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, D> {
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/// Computes the eigenvalues and real Schur foorm of the matrix `m`.
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///
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/// Panics if the method did not converge.
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pub fn new(m: MatrixN<N, D>) -> Self {
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Self::try_new(m).expect("RealSchur decomposition: convergence failed.")
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}
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/// Computes the eigenvalues and real Schur foorm of the matrix `m`.
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///
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/// Returns `None` if the method did not converge.
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pub fn try_new(mut m: MatrixN<N, D>) -> Option<Self> {
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assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
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let (nrows, ncols) = m.data.shape();
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let n = nrows.value();
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let lda = n as i32;
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let mut info = 0;
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let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut q = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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// Placeholders:
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let mut bwork = [ 0i32 ];
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let mut unused = 0;
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let lwork = N::xgees_work_size(b'V', b'N', n as i32, m.as_mut_slice(), lda, &mut unused,
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wr.as_mut_slice(), wi.as_mut_slice(), q.as_mut_slice(), n as i32,
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&mut bwork, &mut info);
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lapack_check!(info);
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let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
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N::xgees(b'V', b'N', n as i32, m.as_mut_slice(), lda, &mut unused,
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wr.as_mut_slice(), wi.as_mut_slice(), q.as_mut_slice(),
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n as i32, &mut work, lwork, &mut bwork, &mut info);
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lapack_check!(info);
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Some(RealSchur { re: wr, im: wi, t: m, q: q })
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}
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/// Retrieves the unitary matrix `Q` and the upper-quasitriangular matrix `T` such that the
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/// decomposed matrix equals `Q * T * Q.transpose()`.
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pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
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(self.q, self.t)
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}
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/// Computes the real eigenvalues of the decomposed matrix.
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///
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/// Return `None` if some eigenvalues are complex.
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pub fn eigenvalues(&self) -> Option<VectorN<N, D>> {
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if self.im.iter().all(|e| e.is_zero()) {
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Some(self.re.clone())
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}
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else {
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None
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}
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}
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/// Computes the complex eigenvalues of the decomposed matrix.
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pub fn complex_eigenvalues(&self) -> VectorN<Complex<N>, D>
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where DefaultAllocator: Allocator<Complex<N>, D> {
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let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
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for i in 0 .. out.len() {
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out[i] = Complex::new(self.re[i], self.im[i])
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}
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out
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}
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}
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/*
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*
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* Lapack functions dispatch.
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*
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*/
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pub trait EigenScalar: Scalar {
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fn xgees(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [Self],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vs: &mut [Self],
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ldvs: i32,
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work: &mut [Self],
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lwork: i32,
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bwork: &mut [i32],
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info: &mut i32);
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fn xgees_work_size(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [Self],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vs: &mut [Self],
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ldvs: i32,
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bwork: &mut [i32],
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info: &mut i32)
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-> i32;
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}
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macro_rules! real_eigensystem_scalar_impl (
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($N: ty, $xgees: path) => (
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impl EigenScalar for $N {
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#[inline]
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fn xgees(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [$N],
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wi: &mut [$N],
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vs: &mut [$N],
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ldvs: i32,
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work: &mut [$N],
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lwork: i32,
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bwork: &mut [i32],
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info: &mut i32) {
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$xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, work, lwork, bwork, info);
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}
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#[inline]
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fn xgees_work_size(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [$N],
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wi: &mut [$N],
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vs: &mut [$N],
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ldvs: i32,
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bwork: &mut [i32],
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info: &mut i32)
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-> i32 {
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let mut work = [ Zero::zero() ];
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let lwork = -1 as i32;
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$xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, &mut work, lwork, bwork, info);
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ComplexHelper::real_part(work[0]) as i32
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}
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}
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)
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);
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real_eigensystem_scalar_impl!(f32, interface::sgees);
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real_eigensystem_scalar_impl!(f64, interface::dgees);
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@ -4,3 +4,4 @@ mod cholesky;
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mod lu;
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mod lu;
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mod qr;
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mod qr;
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mod svd;
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mod svd;
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mod real_schur;
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21
nalgebra-lapack/tests/linalg/real_schur.rs
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21
nalgebra-lapack/tests/linalg/real_schur.rs
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use std::cmp;
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use nl::RealSchur;
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use na::{DMatrix, Matrix4};
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quickcheck! {
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fn schur(n: usize) -> bool {
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let n = cmp::max(1, cmp::min(n, 10));
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let m = DMatrix::<f64>::new_random(n, n);
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let (vecs, vals) = RealSchur::new(m.clone()).unpack();
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relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7)
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}
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fn schur_static(m: Matrix4<f64>) -> bool {
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let (vecs, vals) = RealSchur::new(m.clone()).unpack();
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relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7)
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}
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}
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