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c++matrixlinear-algebraeigen
ThePlowKing
ThePlowKing

Reputation: 341

Solving a Tridiagonal Matrix using Eigen package in C++

At present I have a system Ax = b such that A is a tridiagonal matrix. Using Eigen, I can already solve this system using the line:

x = A.colPivHouseholderQr().solve(b);

However, since A is a tridiagonal matrix this works rather slowly compared to say in MATLAB, since the program is mostly likely computing the solution for all values rather than just on the three diagonals. Can Eigen solve this system faster? This is probably quite a dumb questions but I'm fairly new to C++ and I only started using Eigen a few days ago so there's a lot to take in at the moment! Thanks in advance.

Upvotes: 0

Views: 6123

Answers (1)

Chiel
Chiel

Reputation: 6194

The best you can do is to implement the Thomas algorithm yourself. Nothing can beat the speed of that. The algorithm is so simple, that nor Eigen nor BLAS will beat your hand-written code. In case you have to solve a series of matrices, the procedure is very well vectorizable.

https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

If you want to stick with standard libraries, the BLAS DGTSV (double precision) or SGTSV (single precision) is probably the best solution.

Upvotes: 2

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