Train a two layer neural network with a recursive prediction error
％ algorithm ("recursive Gauss-Newton"). Also pruned (i.e., not fully
％ connected) networks can be trained.
％
％ The activation functions can either be linear or tanh. The network
％ architecture is defined by the matrix NetDef , which has of two
％ rows. The first row specifies the hidden layer while the second
％ specifies the output layer.
密碼學界牛人Victor Shoup用C++編寫數論類庫。
NTL is a high-performance, portable C++ library providing data structures and algorithms for arbitrary length integers for vectors, matrices, and polynomials over the integers and over finite fields and for arbitrary precision floating point arithmetic.
NTL provides high quality implementations of state-of-the-art algorithms for:
* arbitrary length integer arithmetic and arbitrary precision floating point arithmetic
* polynomial arithmetic over the integers and finite fields including basic arithmetic, polynomial factorization, irreducibility testing, computation of minimal polynomials, traces, norms, and more
* lattice basis reduction, including very robust and fast implementations of Schnorr-Euchner, block Korkin-Zolotarev reduction, and the new Schnorr-Horner pruning heuristic for block Korkin-Zolotarev
* basic linear algebra over the integers, finite fields, and arbitrary precision floating point numbers.
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.
cordic methods describe essentially the same algorithm that with suitably chosen inputs can be used to calculate a whole range of scientific functions including sin, cos, tan, arctan, arcsin, arccos, sinh, cosh, tanh, arctanh, log, exp, square root and even multiply and divide.
the method dates back to volder [1959], and due to its versatility and compactness, it made possible the microcoding of the hp35 pocket scientific calculator in 1972.
here is some code to illustrate the techniques. ive split the methods into three parts linear, circular and hyperbolic. in the hp35 microcode these would be unified into one function (for space reasons). because the linear mode can perform multiply and divide, you only need add/subtract and shift to complete the implementation.
you can select in the code whether to do the multiples and divides also by cordic means. other multiplies and divides are all powers of 2 (these dont count). to eliminate these too, would involve ieee hackery.
In an electromagnetic cloak based on a transformation approach, reduced sets of
material properties are generally favored due to their easier implementation in reality,
although a seemingly inevitable drawback of undesired reflection exists in such cloaks.
Here we suggest using high-order transformations to create smooth moduli at the outer
boundary of the cloak, therefore completely eliminating the detrimental scattering
within the limit of geometric optics. We apply this scheme to a non-magnetic
cylindrical cloak and demonstrate that the scattered field is reduced substantially in a
cloak with optimal quadratic transformation as compared to its linear counterpart.
An introduction to some of the key ideas in computer graphics is given. Modeling, 2D and 3D viewing,
transformations and related ideas from linear algebra are presented.
統計模式識別工具箱（Statistical Pattern Recognition Toolbox）包含：
1，Analysis of linear discriminant function
2，Feature extraction: linear Discriminant Analysis
3，Probability distribution estimation and clustering
4，Support Vector and other Kernel Machines
WSNs being energy constrained systems, one major problem is to employ the sensor nodes in such a manner so as to ensure maximum coverage and connectivity with minimal or optimal number of nodes and furthermore elongate network lifetime with maximum energy utilization.
The problem addressed has been tackled for 1-D linear array and further extended to 2-Dimensions as stated in the next slides.
