This page contains documentation of our Bachelor's project made in Spring 2012. The aim of the project was to investigate properties of the matrices generated by the No-Core Shell Model for bosons (NCSMb) code, and to study the Lanczos method. The thesis, presentations and the Matlab programs, which were used for testing the Lanczos algorithm, are available for download.
The thesis can be downloaded from Chalmers Publication Library.
There were two presentations for this project; one was about the NCSMb code
and the matrix properties, and the other about the Lanczos and Block Lanczos methods. The presentations
used Prezi, a flash program, and are contained in zip-files.
What follows are descriptions and links to the source code and data that were used in order to test the properties of the Lanczos algorithm and its variations.
Package | Description |
---|---|
Data_MatricesWithMaps |
Some 6-boson matrices, with the corresponding model space mappings. This data is necessary for the Matlab scripts. |
funk_BLKLAN
| A flexible Block Lanczos function where the user can choose between full or partial reorthogonalization, as well as starting block. Additionally, the function also has the possibility to ban undesired vectors from the Krylov space. It returns a specified number of Ritz-pairs along with the number of required number of matrix multiplications. |
FinalExample (.tar.bz2) |
A package including the program ultimateRun.m , along with
required functions and data for an illustrating example. In the example
some eigenvalues of a large matrix are calculated by using Block Lanczos
to systematically work the way up through larger and larger model spaces,
while storing data of the overlapping residual norms, the needed number
of matrix multiplications and the eigenvalues of the successive model
spaces. This is done by using the eigenvalue solver IRBLEIGS. For more
information, read the attached README file. |
Matlab script | Description |
---|---|
BlockSizesEffects.m |
A program that relates the convergence of Block Lanczos to the block sizes. |
MatrixAprx.m |
A program that compares the eigenvectors of smaller model spaces to eigenvectors of larger model spaces. |
StartAprx.m |
Compares the effects of different strategies of starting vectors, by applying two eigenvector approximations. |
SimulatedLanczos.m |
A test program for illustrating how Lanczos converges by looking at the occurrence of the different eigenvectors in the Krylov basis, as it is successively built up. |