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Comments more tailored to QZ

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metric-space 2022-01-19 02:42:22 -05:00
parent 6f7ef387e5
commit 769f20ce6f
1 changed files with 13 additions and 10 deletions
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23
nalgebra-lapack/src/qz.rs
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@ -13,7 +13,7 @@ use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
use lapack; use lapack;
/// Eigendecomposition of a real square matrix with complex eigenvalues. /// Generalized eigendecomposition of a pair of N*N square matrices.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))] #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr( #[cfg_attr(
feature = "serde-serialize", feature = "serde-serialize",
@ -57,14 +57,15 @@ impl<T: QZScalar + RealField, D: Dim> QZ<T, D>
where where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{ {
/// Computes the eigenvalues and real Schur form of the matrix `m`. /// Attempts to compute the QZ decomposition of input square matrices `a` and `b`.
/// ///
/// Panics if the method did not converge. /// Panics if the method did not converge.
pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self { pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self {
Self::try_new(a, b).expect("Schur decomposition: convergence failed.") Self::try_new(a, b).expect("QZ decomposition: convergence failed.")
} }
/// Computes the eigenvalues and real Schur form of the matrix `m`. /// Computes the decomposition of input matrices `a` and `b` into a pair of matrices of Schur vectors
/// , a quasi-upper triangular matrix and an upper-triangular matrix .
/// ///
/// Returns `None` if the method did not converge. /// Returns `None` if the method did not converge.
pub fn try_new(mut a: OMatrix<T, D, D>, mut b: OMatrix<T, D, D>) -> Option<Self> { pub fn try_new(mut a: OMatrix<T, D, D>, mut b: OMatrix<T, D, D>) -> Option<Self> {
@ -73,14 +74,14 @@ where
"Unable to compute the qz decomposition of non-square matrices." "Unable to compute the qz decomposition of non-square matrices."
); );
// another assert to compare shape? assert!(
a.shape_generic() == b.shape_generic(),
"Unable to compute the qz decomposition of two square matrices of different dimensions."
);
let (nrows, ncols) = a.shape_generic(); let (nrows, ncols) = a.shape_generic();
let n = nrows.value(); let n = nrows.value();
let lda = n as i32;
let ldb = lda.clone();
let mut info = 0; let mut info = 0;
let mut alphar = Matrix::zeros_generic(nrows, Const::<1>); let mut alphar = Matrix::zeros_generic(nrows, Const::<1>);
@ -151,8 +152,10 @@ where
}) })
} }
/// Retrieves the unitary matrix `Q` and the upper-quasitriangular matrix `T` such that the /// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
/// decomposed matrix equals `Q * T * Q.transpose()`. /// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
/// decomposed matrix `A` equals `VSL * S * VSL.transpose()` and
/// decomposed matrix `B` equals `VSL * T * VSL.transpose()`.
pub fn unpack( pub fn unpack(
self, self,
) -> ( ) -> (