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Contents
ARPACK Users' Guide:
Solution of Large Scale Eigenvalue Problems
with Implicitly Restarted Arnoldi Methods.
R. B. Lehoucq, D. C. Sorensen, C. Yang
8 Oct 97
Contents
List of Figures
List of Tables
Preface
How to use this Guide
Introduction to ARPACK
Important Features
Getting Started
Reverse Communication Interface
Availability
Installation
Documentation
Dependence on LAPACK and BLAS
Expected Performance
P_ARPACK
Contributed Additions
Trouble Shooting and Problems
Research Funding of ARPACK
Getting Started with ARPACK
Directory Structure and Contents
Getting Started
An Example for a Symmetric Eigenvalue Problem
The Reverse Communication Interface
Post Processing for Eigenvalues and Eigenvectors
Setting up the problem
Storage Declarations
Stopping Criterion
Initial Parameter Settings
Setting the Starting Vector
Trace Debugging Capability
General Use of ARPACK
Naming Conventions, Precisions and Types
Shift and Invert Spectral Transformation Mode
is Hermitian Positive Definite
is NOT Hermitian Positive Semi-Definite
Reverse Communication Structure for Shift-Invert
Shift and invert on a Generalized Eigen-problem
Using the Computational Modes
Computational Modes for Real Symmetric Problems
Post-Processing for Eigenvectors Using
dseupd
Computational Modes for Real Non-Symmetric Problems
Post-Processing for Eigenvectors Using
dneupd
Computational Modes for Complex Problems
Post-Processing for Eigenvectors Using
zneupd
The Implicitly Restarted Arnoldi Method
Structure of the Eigenvalue Problem
Krylov Subspaces and Projection Methods
The Arnoldi Factorization
Restarting the Arnoldi Method
Implicit Restarting
Block Methods
The Generalized Eigenvalue Problem
Structure of the Spectral Transformation
Eigenvector/Null-Space Purification
Stopping Criterion
Computational Routines
ARPACK subroutines
XYaupd
XYaup2
XYaitr
Xgetv0
Xneigh
[s,d]seigt
[s,d]Yconv
XYapps
XYeupd
LAPACK routines used by ARPACK
BLAS routines used by ARPACK
Templates and Driver Routines
Symmetric Drivers
Selecting a Symmetric Driver
Standard Mode
Shift-Invert Mode
Generalized Eigenvalue Problem
Regular Inverse Mode
Shift-Invert Mode
Buckling Mode
Cayley Transformation Mode
Identify
OP
and
B
for the Driver
The Reverse Communication Interface
Driver
dsdrv1
Driver
dsdrv2
Driver
dsdrv3
Driver
dsdrv4
Driver
dsdrv5
Driver
dsdrv6
Modify the Problem Dependent Variables
Other Variables
Postprocessing and Accuracy Checking
Real Nonsymmetric Drivers
Selecting a Non-symmetric Driver
Standard Mode
Shift-Invert Mode
Generalized Nonsymmetric Eigenvalue Problem
Regular Inverse Mode
Spectral Transformations for Non-symmetric Eigenvalue Problems
Identify
OP
and
B
for the Driver
The Reverse Communication Interface
Driver
dndrv1
Driver
dndrv2
Driver
dndrv3
Driver
dndrv4
Driver
dndrv5
Driver
dndrv6
Modify the Problem Dependent Variables
Other Variables
Postprocessing and Accuracy Checking
Complex Drivers
Selecting a Complex Arithmetic Driver
Standard Mode
Shift and Invert Spectral Transformation
Generalized Eigenvalue Problems
Regular Inverse Mode
General Shift-Invert Spectral Transformation
Identify
OP
and
B
for the Driver to be Modified
The Reverse Communication Interface
Driver
zndrv1
Driver
zndrv2
Driver
zndrv3
Driver
zndrv4
Modify the Problem Dependent Variables
Other Variables
Post-processing and Accuracy Checking
Band Drivers
Selecting a Band Storage Driver
Store the matrix correctly
Modify problem dependent variables
Modify other variables if necessary
Accuracy checking
The Singular Value Decomposition
The SVD Drivers
Tracking the progress of ARPACK
Obtaining Trace Output
Check Pointing ARPACK
The XYaupd ARPACK Routines
DSAUPD
DNAUPD
ZNAUPD
References
Index
About this document ...
Chao Yang
11/7/1997