Add calculation for tridiagonal matrices (solve, factorize, det, rcond) #196
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I removed a 1-norm field |
termoshtt
reviewed
Jun 28, 2020
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| /// An interface for making a Tridiagonal struct. | ||
| pub trait ToTridiagonal<A: Scalar> { |
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| pub trait ToTridiagonal<A: Scalar> { | |
| pub trait ExtractTridiagonal<A: Scalar> { |
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| pub trait TridiagIndex { | ||
| fn to_tuple(&self) -> (i32, i32); | ||
| } | ||
| impl TridiagIndex for [Ix; 2] { | ||
| fn to_tuple(&self) -> (i32, i32) { | ||
| (self[0] as i32, self[1] as i32) | ||
| } | ||
| } |
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I think ndarray::NdIndex<Ix2> could be better for it, but it does not enough iterface for implementing this PR, e.g. Into<Ix2>. I keep this code as it is.
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Thank a lot :) |
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I added the calculation for tridiagonal matrices, which might be important for solving differential equations.
First, I made a struct of
TriDiagonalfor LU factorization and solving equation using LAPACK. It represents a tridiagonal matrix as 3 one-dimensionalArray(diagonal, sub-diagonal and super-diagonal elements).And this struct also holds the layout and 1-norm of the raw matrix. They are used in some methods (
solve_tridiagonal,rcond_tridiagonal, etc.)Second,
LUFactorizedTriDiagonalstruct contains additional 1DArrayof the second super-diagonal of matrix U andipiv, just likeLUFactorized.These structs and
ArrayBase<S, Ix2>havelu (*gttrf),rcond (*gtcon),solve (*gttrs)like methods using LAPACK and adetlike method using a recurrent relation implemented in Rust.I also added an example and some test functions. Please confirm that you can use them just like any other methods implemented for general or triangular matrices.