This example computes the cholesky decomposition `L`
of a symmetric positive matrix `A`: `LL ^{T} = A`

The example shows the use of dense, triangular and banded matrices and corresponding adapters.

cholesky.hpp | header file: defines templates doing the decomposition. |

cholesky_test.cpp | main file: containes test methods and helper functions. |

This example computes the solution `x` of the system `Ax=b` of linear equations using the iterative method of conjugate gradients. The influence of different preconditioners can be seen. The numer of iterations of the original CG, a diagonal preconditioner, a cholesky preconditioner and an incomplete cholesky preconditioner can be compared.

*Note:*The structure of the matrix is chosen such that the incomplete cholesky is equivalent to the comlete cholesky decomposition.

This example shows the usage of sparse matrices and demonstrates some template programming techniques.

cholesky.hpp | header file: defines templates doing the decomposition. |

precond.hpp | header file: defines template classes defining the preconditioners. |

pcg.hpp | header file: defines template functions of the conjugate gradient iteration. |

pcg_test.cpp | main file: defines templates doing the decomposition. |

This example implements a (minimal) read only array adaptor which can be used to create ublas data structures using a prepared chunk of memory as underlying storage.

storage_adaptors.hpp | template header file: contains class readonly_array_adaptor. |

point.h | template header for a small fixed size vector class using storage adaptors |

ex_ro_adapt.cpp | example file that shows the usage of these adaptors |

This example implements a method to read and write sparse matrices as triplets.

sparse_io.cpp | example for sparse matrix i/o. |

sparse_matrices.zip | some sparse matrices in triplet form. (see README inside) |

This example provides simple scatter/gather and AXPY operations for sparse vectors. The code needs some clean up and it should be optimized much more.

scatter-gather.hpp | Scatter/gather operations and working_row class. |

scatter_main.cpp | Sample application an benchmark using scatter/gather operations. |

This example computes the solution `x` of the system `Ax=b` of linear equations using the iterative method of generalized minimal residuals.

This example shows the usage of sparse matrices and demonstrates some template programming techniques.

orthogonal.hpp | header file: GMRES implementation, orthogonalization of vectors. |

lin_op.hpp | header file: linear operator wrapper for ublas matrices. |

precond.hpp | header file: defines template classes defining the preconditioners. |

cholesky.hpp | header file: defines templates doing the decomposition. (not used, but included from precond.hpp) |

main_gmres.cpp | main file: example of calling GMRES. |

All files here are provided under the Boost Software License, Version 1.0, unless the file itself contains other license information.

Purpose: compute exp(A) for a real or complex matrix.

Author: Tsai, Dung-Bang

expm.hpp | header file: EXPGM_PAD computes the matrix exponential exp(H) for general matrixs. |

expm_sample.cpp | main file: example of using expm_pad() to compute rotation matrix around z axis. |