Mapack可用來做矩陣運算
Mapack is a .NET class library for basic linear algebra computations. It supports the following MATRIX operations and properties: Multiplication, Addition, Subtraction, Determinant, Norm1, Norm2, Frobenius Norm, Infinity Norm, Rank, Condition, Trace, Cholesky, LU, QR, Single Value decomposition, Least Squares solver, Eigenproblem solver, Equation System solver. The algorithms were adapted from Mapack for COM, Lapack and the Java MATRIX Package.
The software is capable to simulate space time code [1] for QPSK modulation using different number of state. Examples of generator MATRIX up to 256 stetes are provided. Variable signal to noise ratio (SNR) might be applied to produce bit error rate (BER) or frame error rate (FER) curves.
SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The MATRIX columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions.
IML package provides efficient routines to solve nonsingular systems of
linear equations, certified solve any shape systems of linear equations,
and perform mod p MATRIX operations, such as computing row-echelon form,
determinant, rank profile, inverse of a mod p MATRIX.
c pgm to find redundant paths in a graph.Many fault-tolerant network algorithms rely on an underlying assumption that there are possibly distinct network paths between a source-destination pair. Given a directed graph as input, write a program that uses depth-first search to determine all such paths. Note that, these paths are not vertex-disjoint i.e., the vertices may repeat but they are all edge-disjoint i.e., no two paths have the same edges. The input is the adjacency MATRIX of a directed acyclic graph and a pair(s) of source and destination vertices and the output should be the number of such disjoint paths and the paths themselves on separate lines. In case of multiple paths the output should be in order of paths with minimum vertices first. In case of tie the vertex number should be taken in consideration for ordering.
Shortest Paths with Multiplicative Cost. In a given undirected graph, the path cost is measured as a product of all the edges in the path. The weights are rational numbers (e.g., 0.25, 0.75, 3.75 etc) or integers (2, 3). There are no negative edges. Given such a graph as input, you are to output the shortest path between any two given vertices. Input is the adjacency MATRIX and the two vertices. You must output the path.
In some graphs, the shortest path is given by optimizing two different metrics: the sum of weights of the edges and the number of edges. For example: if two paths with equal cost exist then, the path with the least number of edges is chosen as the shortest path. Given this metric, you have find out the shortest path between a given pair of vertices in the input graph. The output should be the number of edges on the path, the cost of the shortest path, and the path itself. Input is the adjacency MATRIX and the two vertices.
Edge Disjoint Cycles. You are given an input graph that is either directed or undirected. Write a program that reads in a vertex number and lists the number of edge disjoint cycles that start and end at this vertex. The output should also list the edges in each of the cycle discovered. Input will be the adjacency MATRIX preceded by a 0 or 1 representing Directed or Undirected graphs respectively.
