# Questions tagged [arpack]

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### How do compute lowest eigenvalue using Arpack in C language

Hi I have a problem to calculate lowest eigenvalue in non-symmetric matrix using Arpack, because my matrix is very complicated and even I have a lot of trouble to made a matrix - vector multiplication....
1 vote
66 views

### Optimal Krylov subspace dimension and iteration limits for eigs

When using the eigs function in MATLAB, which is based off of ARPACK, one can manually modify the maximal dimension of the constructed Krylov subspaces, the maximum iteration counts, and the error ...
49 views

### How to reconcile difference between Arpack manual and example?

The ARPACK manual for znaupd on pp. 128–129 says: Mode 2:[...] OP = inv[M]*A and B = M. [...] IDO = 1: compute Y = OP * Z and Z = B * X where IPNTR(1) is the ...
• 223
839 views

### Accuracy issues with Arpack in Julia for eigenvalues of smallest magnitude

Following the documentation of Julia's Arpack package (Cf. https://julialinearalgebra.github.io/Arpack.jl/stable/eigs/) I have computed some largest and smallest magnitude eigenvalues of sparse ...
740 views

### Python scipy eigh(Arpack) giving wrong eigenvalues for generalized eigenvalue problem

I am trying to solve a generalized eigenvalue problem using Arpack, right now the code is using LAPACK but that's too slow, we only need a few eigenvalues and the matrices are sparse so using Arpack ...
102 views

### Efficient way to find eigenvalues of complex symmetric matrix with real off-diagonal elements

My goal is to find all eigenvalues (and eigenvectors) in a given range of magnitudes of a complex symmetric matrix with real off-diagonal elements (only diagonal elements are complex). Currently I'm ...
• 151
1 vote
37 views

### Can I use the Schur basis returned by ARPACK in a restart capacity?

Reading ARPACK documentation, I see that ARPACK will return an "orthogonal basis for the invariant subspace corresponding to the eigenvalues in D" if eigenvectors are not requested. Can this subspace ...
• 403
1 vote
116 views

### How can I maximise orthonormality between degenerate eigenvectors using ARPACK?

I am using ARPACK's zndrv1 to diagonalise a matrix (the context is quantum chemistry). While all vectors have a norm 1, as expected, vectors corresponding to degenerate eigenstates aren't always ...
• 403
307 views

### Can ARPACK exploit hermiticity when diagonalising a complex matrix?

I have noticed arpack comes with a driver dsdrv1 that exploits symmetry of a real-valued matrix. Is there a way to analogously exploit a Hermitian matrix in some way via z--- drivers? The manual ...
• 403
70 views

### Partial diagonalisation of large symmetric positive-definite band-diagonal matrices

I want to partially diagonalise real sparse symmetric positive-definite matrices, that are of dimension $n = 10^5$ and I need on the order of $k = 500$ of the smallest eigenvalues and eigenvectors. ...
• 141
347 views

### Left eigenvectors using ARPACK

I'm trying to find both the dominant $k$ left and right eigenvectors, that is, $$V_L\mathcal{A} = \Lambda V_L\\ \mathcal{A}V_R = V_R\Lambda\\ V_LV_R = I_{k\times k}$$ $V_L$ being the $k\times N$ ...
• 31
1 vote
63 views

### Solving 2D Schrodinger Equation with ARPACK: Can I ensure all eigenvectors have the same phase?

I use arpack to solve the 2D Schrodinger, and eigenvalue problem of the form $$Hx = \epsilon x$$ on a uniform grid. All eigenvectors are real in my case. Arpack doesn't normalise the eigenvectors, ...
• 403
421 views

### Eigenvalue with largest imaginary part

Iterative eigensolvers such as ARPACK, give the option to find a subset of the eigenvalues which have the largest imaginary part. My question is how do these algorithms work. As I understand it, ...
• 243
482 views

### Computation time of eigenvalues with ARPACK depends on what?

My goal is to compute the k smallest eigenvalues of large symmetric sparse matrices. For this purpose I use python scipy's eigsh method in shift-invert mode which uses ARPACK. The matrices usually ...
• 21
646 views

### Preconditioning ARPACK eigenvalue solver

I am working on a generalized eigenvalue problem of the form $$\boldsymbol{A}\cdot\boldsymbol{x}=\lambda\boldsymbol{B}\cdot\boldsymbol{x}$$ where $\boldsymbol{B}$ is not symmetric positive. ...
• 297
343 views

### Iteratively obtaining m eigenvectors using arpack: If I have a good initial guess, how do I use it?

I am trying out the arpack driver dsdrv1, which is used to iteratively obtain the first m eigenvectors from the eigenvalue problem. $$\hat{A}\mathbf{x} = \lambda\mathbf{x}$$ As it is an iterative ...
• 403
1 vote
194 views

### ARPACK- Reverse Communication Interface [closed]

I am trying to use ARPACK to diagonalize a sparse Hermitian matrix. My program is executing without error but returning incorrect eigenvalues. I have tried to trace the problem back. The work is ...
• 11
481 views

### Arpack and Matlab give different values for eigenvalues

I am solving a generalized eigenvalues problem with inversed complex shift: $$(M-\sigma J)^{-1}J \boldsymbol{x} = \boldsymbol{x} \nu \enspace .$$ My matrices are obtained from a finite element ...
• 173