Bessel function J1

The Bessel function J1

German 1

wir haben uns kennengelernt

Da begrüßte er mich, wir hatten uns persönlich nie kennengelernt, aber er legte Wert darauf, mich am 4. November kennenzulernen.

He greeted me, we had never met in person, but it was important to him that he meet me on the 4th of November.

独处也是一种能力

独处也是一种能力
周国平

                                       1
    人们往往把交往看作一种能力，却忽略了独处也是一种能力，并且在一定意义上是比交往更为重要的一种能力。反过来说，不擅交际固然是一种遗憾，不耐孤独也未尝不是一种很严重的缺陷。

                                       2
    独处也是一种能力，并非任何人任何时候都可具备的。具备这种能力并不意味着不再感到寂寞，而在于安于寂寞并使之具有生产力。人在寂寞中有三种状态。一是惶惶不安，茫无头绪，百事无心，一心逃出寂寞。二是渐渐习惯于寂寞，安下心来，建立起生活的条理，用读书、写作或别的事务来驱逐寂寞。三是寂寞本身成为一片诗意的土壤，一种创造的契机，诱发出关于存在、生命、自我的深邃思考和体验。

                                       3
    独处是人生中的美好时刻和美好体验，虽则有些寂寞，寂寞中却又有一种充实。独处是灵魂生长的必要空间，在独处时，我们从别人和事务中抽身出来，回到了自己。这时候，我们独自面对自己和上帝，开始了与自己的心灵以及与宇宙中的神秘力量的对话。一切严格意义上的灵魂生活都是在独处时展开的。和别人一起谈古说今，引经据典，那是闲聊和讨论；唯有自己沉浸于古往今来大师们的杰作之时，才会有真正的心灵感悟。和别人一起游山玩水，那只是旅游；唯有自己独自面对苍茫的群山和大海之时，才会真正感受到与大自然的沟通。

                                       4
    从心理学的观点看，人之需要独处，是为了进行内在的整合。所谓整合，就是把新的经验放到内在记忆中的某个恰当位置上。唯有经过这一整合的过程，外来的印象才能被自我所消化，自我也才能成为一个既独立又生长着的系统。所以，有无独处的能力，关系到一个人能否真正形成一个相对自足的内心世界，而这又会进而影响到他与外部世界的关系。

                                       5
    怎么判断一个人究竟有没有他的“自我”呢?有一个可靠的检验方法，就是看他能不能独处。当你自己一个人呆着时，你是感到百无聊赖，难以忍受呢，还是感到一种宁静、充实和满足?

                                       6
    对于独处的爱好与一个人的性格完全无关，爱好独处的人同样可能是一个性格活泼、喜欢朋友的人，只是无论他怎么乐于与别人交往，独处始终是他生活中的必需。在他看来，一种缺乏交往的生活当然是一种缺陷，一种缺乏独处的生活则简直是一种灾难了。

                                       7
    世上没有一个人能够忍受绝对的孤独。但是，绝对不能忍受孤独的人却是一个灵魂空虚的人。世上正有这样的一些人，他们最怕的就是独处，让他们和自己呆一会儿，对于他们简直是一种酷刑。只要闲了下来，他们就必须找个地方去消遣。他们的日子表面上过得十分热闹，实际上他们的内心极其空虚。他们所做的一切都是为了想方设法避免面对面看见自己。对此我只能有一个解释，就是连他们自己也感觉到了自己的贫乏，和这样贫乏的自己呆在一起是顶没有意思的，再无聊的消遣也比这有趣得多。这样做的结果是他们变得越来越贫乏，越来越没有了自己，形成了一个恶性循环。

【助您成才的15个建议】1.学会换位思考；2.学会适应环境；3.学会大方；4.学会低调；5.嘴要甜；6.有礼貌；7.言多必失；8.学会感恩；9.遵守时间；10.信守诺言；11.学会忍耐；12.有一颗平常心；13.学会赞扬别人；14.待上以敬，待下以宽；15.经常检讨自己。

【励志语录】1.好多人做不好自己，是因为总想着做别人！2.从不奢求生活能给予我最好的，只是执着于寻求最适合我的！3.宁愿跑起来被拌倒无数次，也不愿规规矩矩走一辈子，就算跌倒也要豪迈的笑 。4.不要生气要争气，不要看破要突破，不要嫉妒要欣赏，不要托延要积极，不要心动要行动。

Convex Optimization

Reference in Convex optimization

• Stephen Boyd and Lieven Vandenberghe, Convex optimization (book in pdf)
• EE364a: Convex Optimization I and EE364b: Convex Optimization II, Stanford course homepages
• 6.253: Convex Analysis and Optimization, an MIT OCW course homepage
• Brian Borchers, An overview of software for convex optimization

Examples

The following problems are all convex minimization problems, or can be transformed into convex minimizations problems via a change of variables:

• Least squares
• Linear programming
• Convex quadratic minimization with linear constraints
• Quadratically constrained Convex-quadratic minimization with convex quadratic constraints
• Conic optimization
• Geometric programming
• Second order cone programming
• Semidefinite programming
• Entropy maximization with appropriate constraints

Methods

Convex minimization problems can be solved by the following contemporary methods:^[4]

• "Bundle methods" (Wolfe, Lemaréchal, Kiwiel), and
• Subgradient projection methods (Polyak),
• Interior-point methods (Nemirovskii and Nesterov).

Other methods of interest:

• Cutting-plane methods
• Ellipsoid method
• Subgradient method
• Dual subgradients and the drift-plus-penalty method

Subgradient methods can be implemented simply and so are widely used.^[5] Dual subgradient methods are subgradient methods applied to a dual problem. The drift-plus-penalty method is similar to the dual subgradient method, but takes a time average of the primal variables.

OpenOF Framework for Sparse Non-linear Least Squares Optimization on a GPU

2013-3-2
OpenOF Framework for Sparse Non-linear Least Squares Optimization on a GPU
With OpenOF, a framework is presented, which enables developers to design sparse optimizations regarding parameters and measurements and utilize the parallel power of a GPU


This code is written in Python with three major libraries: Thrust, CUSP and SymPy. Code framework is written in Python but can also generate C++ code.


Code website
https://github.com/OpenOF/OpenOF

Process of Nonlinear least squares optimization: 
1. Iterative method
2. Linearize the cost function in each iteration
3. Levenberg-Marquardt(LM) algorithm is standard, combing the Gauss-Newton algorithm with the gradient descent approach. LM guarantees convergence.
4. In each interation , solving linear Ax = b is most intensive.
5. Sparse matrix representation is used: sparseLM (Lourakis, 2010) and g2o (Kummerle et al., 2011), but on CPU
6. Solving Ax =b, many algorithms can achieve, Cholesky docomposition A = LDL'
7. this paper use Conjugate gradient (CG) approach on GPU.

Nonlinear least squares optimization is widely used in SLAM and BA. 
The authors' some comments about three BA libraries:
   1.The SBA library (Lourakis and Argyros,2009) takes advantage of the special structure of the Hessian matrix to apply the Schur complement for solving the linear system. Nevertheless it has several drawbacks. Integrating additional parameters which remain identical for all measurements (e.g. camera calibration) is not possible, as the structure would change such that the Schur complement could not be applied anymore.

2. sparseLM (Lourakis, 2010) is slow.
3. g2o: the Jacobian is evaluated by numerical differentiation which is time consuming and also degrades the convergence rate.
4. ISAM: (Kaess et al., 2011),which address only a subset of problems, have been presented previously for least squares optimization

Overall Comment: this paper is claims to present an open source framework for sparse nonlinear opitmization. The cost functions is described in high level scripting language. It can not be used without GPU yet. It seems for me g2o or iSam would be more useful on CPU.