Questions tagged [arpack]
The arpack tag has no usage guidance.
22
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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
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0
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66
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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 ...
- 43
2
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49
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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
9
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3
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839
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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 ...
2
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2
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740
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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 ...
5
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102
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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
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37
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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
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116
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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
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2
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307
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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
2
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1
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70
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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
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347
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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
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63
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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
8
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0
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421
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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
2
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1
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482
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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
2
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1
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646
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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
3
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343
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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
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194
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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
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481
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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
5
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519
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Iteratively finding both left and right eigenvectors for non-symmetric complex matrix
I have a complex, non-Hermitian matrix $\mathbf{A}$, for which I need to find a few eigenvalues and eigenvectors in the generalised eigenvalue problem:
$$\mathbf{A}\cdot \mathbf{x} = \lambda \mathbf{...
- 161
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225
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Compute eigenvalues with Arpack
I am using Arpack to compute the eigenvalues of the problem $\lambda Mx = Ax$ with reverse shift method with complex shift. $A$ and $M$ are real, $M$ is symmetric. Then, I use znaupd e zneupd. I use ...
- 173
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344
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ARPACK gives different answers from Matlab and NAG
I'm playing with ARPACK. I looked into the examples they provide, zndrv4.f illustrating the usage of the routine znaupd, in the directory of ARPACK/EXAMPLES/COMPLEX/. I also came cross NAG Fortran ...
- 51
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Time-stepper approach to eigenvalue problem
For a linear system
$$
M \dot{u} = Au \qquad \textrm{or} \qquad \dot{u} = L u
$$
The generalized eigenvalue problem is
$$
A e = \lambda M e
$$
We can use the time-stepper approach which essentially ...
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