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lines changed Original file line number Diff line number Diff line change @@ -53,6 +53,7 @@ impl_lu!(c32, lapack_sys::cgetrf_);
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impl_lu ! ( f64 , lapack_sys:: dgetrf_) ;
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impl_lu ! ( f32 , lapack_sys:: sgetrf_) ;
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+ #[ cfg_attr( doc, katexit:: katexit) ]
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/// Helper trait to abstract `*getrs` LAPACK routines for implementing [Lapack::solve]
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///
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/// If the array has C layout, then it needs to be handled
@@ -63,13 +64,15 @@ impl_lu!(f32, lapack_sys::sgetrf_);
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/// or "no transpose", respectively. For the "Hermite" case, we
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/// can take advantage of the following:
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///
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- /// ```text
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- /// A^H x = b
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- /// ⟺ conj(A^T) x = b
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- /// ⟺ conj(conj(A^T) x) = conj(b)
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- /// ⟺ conj(conj(A^T)) conj(x) = conj(b)
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- /// ⟺ A^T conj(x) = conj(b)
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- /// ```
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+ /// $$
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+ /// \begin{align*}
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+ /// A^H x &= b \\\\
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+ /// \Leftrightarrow \overline{A^T} x &= b \\\\
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+ /// \Leftrightarrow \overline{\overline{A^T} x} &= \overline{b} \\\\
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+ /// \Leftrightarrow \overline{\overline{A^T}} \overline{x} &= \overline{b} \\\\
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+ /// \Leftrightarrow A^T \overline{x} &= \overline{b}
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+ /// \end{align*}
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+ /// $$
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///
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/// So, we can handle this case by switching to "no transpose"
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/// (which is equivalent to transposing the array since it will
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