Comments more tailored to QZ
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@ -13,7 +13,7 @@ use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
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use lapack;
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/// Eigendecomposition of a real square matrix with complex eigenvalues.
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/// Generalized eigendecomposition of a pair of N*N square matrices.
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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#[cfg_attr(
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feature = "serde-serialize",
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@ -57,14 +57,15 @@ impl<T: QZScalar + RealField, D: Dim> QZ<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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/// Computes the eigenvalues and real Schur form of the matrix `m`.
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/// Attempts to compute the QZ decomposition of input square matrices `a` and `b`.
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///
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/// Panics if the method did not converge.
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pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self {
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Self::try_new(a, b).expect("Schur decomposition: convergence failed.")
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Self::try_new(a, b).expect("QZ decomposition: convergence failed.")
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}
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/// Computes the eigenvalues and real Schur form of the matrix `m`.
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/// Computes the decomposition of input matrices `a` and `b` into a pair of matrices of Schur vectors
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/// , a quasi-upper triangular matrix and an upper-triangular matrix .
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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 a: OMatrix<T, D, D>, mut b: OMatrix<T, D, D>) -> Option<Self> {
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@ -73,14 +74,14 @@ where
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"Unable to compute the qz decomposition of non-square matrices."
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);
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// another assert to compare shape?
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assert!(
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a.shape_generic() == b.shape_generic(),
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"Unable to compute the qz decomposition of two square matrices of different dimensions."
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);
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let (nrows, ncols) = a.shape_generic();
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let n = nrows.value();
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let lda = n as i32;
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let ldb = lda.clone();
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let mut info = 0;
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let mut alphar = Matrix::zeros_generic(nrows, Const::<1>);
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@ -151,8 +152,10 @@ where
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})
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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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/// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
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/// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
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/// decomposed matrix `A` equals `VSL * S * VSL.transpose()` and
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/// decomposed matrix `B` equals `VSL * T * VSL.transpose()`.
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pub fn unpack(
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self,
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) -> (
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