A TRUST REGION METHOD FOR PARABOLIC BOUNDARY CONTROL PROBLEMS
A TRUST REGION METHOD FOR PARABOLIC BOUNDARY CONTROL PROBLEMS
C.T.KELLEY AND E.W.SACHS
Abstract.In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. The method is a projected form of the Steihaug trust-region-CG method with a smoothing step added at each iteration to improve performance in the global phase and provide mesh-independent sup-norm convergence in the terminal phase.
Key words.Trust region methods,inexact Newton methods,optimal control
AMS subject classi?cations.49K20,65F10,49M15,65J15,65K10
1.Introduction.In this paper we show how methods that combine CG iteration and trust re-gion globalization for optimization problems subject to simple bounds can be applied in a in?nite dimensional setting to parabolic optimal control problems.This paper addresses the global conver-gence questions left open by our previous work[11],[13],[14],on fast multilevel algorithms for local convergence by showing how trust region-CG algorithms can solve the coarse mesh problems needed to initialize the multilevel method in an ef?cient and mesh-independent way.The algorithm uses the postsmoothing step from[14]and[11]to improve the performance of the iteration.
For unconstrained problems,our approach differs from[18]only in that after a step and trust region radius have been accepted,a smoothing iteration like those in[11]and[14]is attempted. Unlike our previous work,however,an Armijo[1]line search is added to the smoothing step to ensure decrease in the objective function.This new form of the smoothing step is a scaled steepest descent algorithm.The local theory from[11]and[14]implies that full smoothing steps are taken near the solution.
The effect of this in the in?nite dimensional case is to allow one to make sup-norm error estimates in the terminal phase of the iteration[11],[14].In the constrained case,we differ from the algorithm in[8]in more ways.We use trust region and solve unconstrained trust region problems,using the reduced Hessian at the current point to build the quadratic model.The reason for this is to make the trust region problem as easy to solve as possible and to eliminate the need to explicitly compute a generalized Cauchy point.We update the active set after the trust region step has been computed with a scaled projected gradient step(similar to[8]).The scaling serves the purpose of becoming an inexact implementation of the algorithm in[11]and[14]when full steps are taken.We then obtain fast local convergence in the norm.Our local convergence theory does not depend on identi?cation of the active set in?nitely many iterations but rather applies the measure-theoretic ideas in[14].Hence,our trust region algorithm becomes an inexact projected Newton method in the terminal phase of the iteration with local convergence properties covered by
Kelley@https://www.wendangku.net/doc/5212471633.html,).The research of this author was supported by National Science Foundation grant#DMS-9321938and North Atlantic Treaty Organization grant#CRG920067. Computing was partially supported by an allocation of time from the North Carolina Supercomputing Center.
Universit¨a t Trier,FB IV–Mathematik and Graduiertenkolleg Mathematische Optimierung,54296Trier,Germany (sachs@uni-trier.de).The research of this author was supported by North Atlantic Treaty Organization grant #CRG920067.
1
2
the theory developed in[3],[11],and[14].
We consider the problem of minimizing
(1.1)
where is given and is the solution to the nonlinear parabolic problem (1.2)
In(1.1)–(1.2)is constrained to be in the set
(1.3)
for a.e.
for?xed and the nonlinear function is assumed to satisfy
(1.4)
See[21]for examples of applications.
The gradient of in is
(1.5)
where is the solution of the adjoint problem
(1.6)
The map is completely continuous as a map on and as a map from, ,to,[17].We will make use of these compactness properties in this paper.
We base our methods on the work in[7],[8],and[18](where and
for unconstrained problems).These methods solve the trust region problem and by searching along the piecewise linear path having the CG iterates as nodes,terminating either on the trust region boundary,with an inexact Newton step,or a direction of negative curvature.The compact-ness of the map insures that the performance of the CG iteration is independent of the discretization.This is consistent with results on linear equations and CG(see[9]and[20]). Another bene?t of the compactness is that the reduced Hessian of is a compact perturbation of a constant multiple of the identity and hence no preconditioning is needed for fast convergence.
We close this section with some notation and de?nitions.
Let denote the inner product in or the Euclidean inner product in any?nite dimensional space.We denote the-norm by and the-norm by.
We let be the projection onto de?ned for any measurable on and almost every as
if,
if,
(1.7)
if.
TRUST REGION METHODS FOR CONTROL3 We de?ne
(1.8)
The nonsmooth nonlinear equation is a necessary condition for stationarity[2].
The map,given by
(1.9)
is a completely continuous map from for any[11],[14].
For,we de?ne the active set for as
(1.10)
and the inactive set as.It is clear that for any
(1.11)
for all.
2.Algorithms.The algorithms are all based on the trust region-CG method in[18]and the general convergence analysis in[19].The trust region problem is solved approximately by using a piecewise linear path whose nodes are the CG iterates.This approximate solution of the trust region problem is used in a standard way[10],[18],[16],to test for suf?cient decrease and adjust the trust region radius.We incorporate the CG-TR method into the inexact projected Newton approach of[11]to give a superlinearly convergent algorithm.
2.1.Inexact Projected Newton Algorithm.To specify the algorithm we must de?ne projec-tions that correspond to the active and inactive set.For any measurable we de?ne the multiplication operator by
(2.1)
where is the characteristic function of.In particular,if and and are approximations to and,we will use
and
(2.2)
We follow[14]and[11]and approximate the active set by
(2.3)
and let
The parameter may be adjusted as the iteration progresses to give local superlinear conver-gence[11],[14].
Note that for all we have
4
and hence
(2.4)
for all and.
In the constrained case,the necessary conditions for optimality can be expressed as a nondif-ferentiable compact?xed point problem
(2.5)
where
Recall from1that the map(and hence)is a compact map from to for any.In that sense is a smoother.We will use that property to(1)improve the global convergence properties of our proposed algorithm and(2)provide a uniform norm local convergence theory as in[14]and[11].
We de?ne the reduced Hessian at by
(2.6)
with.
The inexact projected Newton algorithms from[11]and[14]have several stages.We describe the one from[11]here in terms of the transition from a current approximation to a new one. The understanding here is that the parameter in the approximation to the active set and the forcing term in the inexact Newton process change as the iteration progresses.
A LGORITHM2.1.pnstep
1.Identi?cation:Given and set.
2.Error Reduction:Find Im which satis?es
(2.7)
Set
to reduce the error in.
3.Postsmoothing:Set to recover convergence.
In the context of this paper,in which global convergence is the issue,Algorithm pnstep presents two problems.Firstly,the smoothing step is a scaled gradient projection step and may lead to dramatic increases in the objective function when is far from the solution.We remedy this by adding an Armijo line search to this phase of the algorithm but do not demand, which may never be possible,but only that by a certain small amount.The results in[11]and[14]insure that if is suf?ciently near the solution,then the full smoothing step will be accepted and hence the fast local convergence(the precise speed of convergence depends on the choice of forcing term)will not be effected by the line search.Secondly,there is no guarantee that the reduced Hessian will be positive de?nite.We address this problem with an inexact trust region algorithm that will exploit any negative curvature direction that it?nds.
As is standard we use the measure of nonstationarity
(2.8)
For example,a locally convergent algorithm using Algorithm pnstep is
A LGORITHM2.2.pnlocal
TRUST REGION METHODS FOR CONTROL5
1.If,terminate the iteration.
2.,
3.Take an inexact step pnstep.
4..Go to step1.
The values of and in step2will ensure superlinear convergence with q-order,[11], [14].
Under standard assumptions,[14],[11],Algorithm pnlocal will produce iterates that con-verge locally q-superlinearly(in the norm)to a minimizer.Q-linear convergence can be ob-tained if the formula for in step2is replaced by and is suf?ciently small.The purpose of this paper is to develop a trust region globalization for this algorithm that preserves the norm local convergence in the terminal phase while converging globally in.
2.2.Solution of the Trust Region Problem.We use a standard solver form[18]for our unconstrained trust region subproblems.The inputs to Algorithm trcg,which approximately solves the trust region problem,are the current point,the objective,a preconditioner,the forcing term,the current trust region radius,and a limit on the number of iterations. The output is the approximate solution of the trust region problem.We formulate the algorithm using the preconditioned CG framework from[12].
We will assume for the present that gradients are computed exactly and that Hessian-vector product is approximated by the difference quotient
(2.9)
We present the algorithm of[18]for approximate solution of the trust region problem
In practice the action of on a vector may be inaccurate and even nonlinear,as would be the case with.However,the effects of such inaccuracy are simply that the method is equivalent to one in which the Hessian is a difference approximation based on the basis for the Krylov subspace.
A LGORITHM2.3.trcg
1.,,,
2.Do While
6
(d)
If then
Find such that
;return
(e)
(f)
(g)
(h)
(i)If then
Find such that
;return
(j);
Trust region algorithms for bound constrained problems have been analyzed in considerable generality in[7].A concrete algorithm,proposed in[8],follows a piecewise linear path in a search for a generalized Cauchy point,freezes the active set at that point,and then solves the trust region problem approximately on the current active set.This process is important for the theory in[7]not only because it guarantees Cauchy decrease but also for the proof of superlinear convergence after the active set has been identi?ed.
In the problems considered here,where there is a continuum of constraints,it is not clear how to use the method of[8]because the active set,being uncountable,will never be fully identi?ed, and the construction of a path on which to search for a Cauchy point would lead to in?nitely many knots to test.Instead we solve an unconstrained trust region problem for a reduced quadratic model and project the solution of that problem onto the active set.
Our approach to minimization of the reduced quadratic model also differs from that in[8].In that paper,and in the convergence analysis in[7],the fact that all norms in?nite dimension are equivalent was used to justify trust region bounds.We use the standard trust region and therefore do not include the constraints explicitly in the trust region.We then use a smoothing step to deal with the nonequivalence of norms and recover fast uniform convergence in the terminal phase of the iteration.
Given and we consider the reduced quadratic model
(2.10)
In(2.10),the reduced Hessian is given by(2.6).Note that the action of on a function can easily be computed by differences.This is a somewhat nonstandard model in that is used in the?rst order part of(2.10)rather than and
instead of.The reasons for this are that this model performed better in our numerical experiments and also makes a smoother transition to a fast local algorithm that can be analyzed with the ideas from[11]and[14].The nonstandard quadratic term presents no problems,however the linear term must be accounted for in the analysis,but,as we shall show next,this is easy to do because our algorithm is a dog-leg.
TRUST REGION METHODS FOR CONTROL7 The analysis of the global convergence is not affected by the linear term because,in view of (2.4),the model we use and the more standard quadratic model
(2.11)
agree if
(2.12)
for some.To see this note that since,we must have if(2.12)holds.
Algorithm boxtr returns a trial point by using Algorithm trcg for a the reduced quadratic model.
A LGORITHM2.4.boxtr
https://www.wendangku.net/doc/5212471633.html,pute
2.Find the direction by calling
trcg
3.
Having computed the trial point,one must decide whether to accept the new point or change the trust region radius.Both decisions are based on a comparison of the actual reduction
(2.13)
to a predicted reduction based on the reduced quadratic model.Here
(2.14)
In a typical trust region algorithm,the step is accepted if
(2.16)
and increased()if
(2.19)
8
2.3.Termination.No algorithm that depends upon a measurement of decrease like is reliable if the decreases in the function are smaller than the accuracy with which the function is computed.Once we have resolved a local minimum to that point,our view is that the iteration has succeeded.
Hence we terminate the algorithm if either,or
(2.20)
Here and are small tolerances.We test for(2.20)every time the trust region radius is changed and if(2.20)holds at any point during an iteration,we terminate and accept the previous iteration. This stopping criterion is used only in the implementation.
2.4.The Complete Algorithm.In the interest of clarity,we do not make the trust region algorithmic parameters,,,,,,,,,the preconditioner,and the initial trust region radius,formal arguments to the algorithm.The trust region radius is limited to a maximum value.
The notation is that is the current iteration.Upon exit from the trust region phase of the algorithm,we obtain and pass that intermediate iterate to the smoother to produce.Choose a constant.
The inputs are,the bounds,and the function.
A LGORITHM2.5.trmin
1.Initialize,.
2.Test for termination
if or
if and terminate successfully
3.Fix and for this iterate.Set,.
4.Find a new trial point using Algorithm boxtr.
Terminate with failure if more than iterations are taken.
5.Set.
(a)if or(2.18)does not hold,then;,go to step4.
(b)if,,
(c)if and,
(d)if,or and,
(e)if and,,go to step4
6.(a)Find the smallest integer such that
then postsmooth,i.e.set
(b);;go to step2
The?ag is used to avoid an in?nite loop of increasing and decreasing the trust region radius.
In the context of a globally convergent algorithm,attention must be paid to the postsmooth-ing step(6a).The line search prevents divergence in the early phase of the iteration when the approximate solutions are not accurate.
TRUST REGION METHODS FOR CONTROL9
3.Convergence Results.In this section we derive global convergence results for Algorithm trmin.Recall that our notation is that(resp.)is the current(resp th)iteration.Upon exit from the trust region phase of the algorithm,we obtain(resp)and pass that intermediate iterate to the smoother to produce(resp).
3.1.Global Convergence.Given and a the quadratic model function from(2.10) we must?rst show that the trust region radius can be bounded from below.
Our assumptions are
A SSUMPTION3.1.
1.is twice continuously differentiable in.
2.There is such that for all and
and.
The second assumption is sort of a second order suf?ciency condition as it is common in the convergence analysis of higher order methods.The?nite difference approximation(2.9)satis?es this assumption for suf?ciently small,if the assumption holds for the original Hessian.
In this section we will use some notation from[2].For de?ne
(3.1)
We begin with the lower bound for the gradient projection step from[2].
T HEOREM3.1.Let Assumption3.1hold and let.Then there is such that for any and,
10
Proof.Since Algorithm trmin will,in the worst case of small trust region radius,take steps of the form
the algorithm will therefore behave like the gradient projection algorithm[2],since by(1.11) .In view of this,we can use known properties of the gradient projection algorithm to bound the trust region radius from below.
Algorithm boxtr,with no preconditioner,will return a trial point of the form
(3.9)
Since,by(3.7)and(2.19)
we obtain from Lemma3.2,
Therefore,since,from(3.9)we obtain
which is(2.18).
We summarize the analysis so far.We have shown that if(3.8)holds then for some and(2.18)holds.
We now describe how the right side of(3.8)must be augmented to imply that. Assume that(3.8)holds.By Lemma3.2we have
TRUST REGION METHODS FOR CONTROL11 and hence by the de?nition of(2.14)
(3.10)
Note that
and
Since we have
So,if the trust region radius ever satis?es
then all acceptance tests will be passed and a further increase will be attempted.Hence,on exit from step5(3.4)will hold with
which completes the proof.
Our main global convergence result is.
T HEOREM3.4.Let Assumption3.1hold and let be the sequence produced by Algorithm trmin Then
Proof.Step6of Algorithm trmin,(2.13)and(2.18)yield
12
with de?ned by(2.19).The boundedness from below of on implies Since by(2.19),Lemma3.2yields
Theorem3.3implies that either or
TRUST REGION METHODS FOR CONTROL13 where the norm in(3.12)is any of,or.
The other assumption is related to a nondegeneracy assumption on the optimal control and a generalization of the fact that for?nite dimensional problems the active set is identi?ed in?nitely many steps.We refer the reader to[14]for motivation and discussion.
We de?ne sets
(3.13)
and
Clearly.
A SSUMPTION3.3.There is such for all.Let be given by(2.3)and let be given.Then there are such that for all and all such that
(3.14)
(3.15)
and
(3.16)
In Assumption3.3,denotes Lebesgue measure.
On these assumptions we have the following local convergence result.The proof is,on the assumptions made above,a variation of those in[11]and[14].
T HEOREM3.5.Let Assumptions3.1,3.2,and3.3hold.Let and be given. Then if is suf?ciently near in,,
(3.17)
and and are given by Algoritm trmin then satis?es(2.7)(i.e.a full inexact Newton step is taken),
and
4.Numerical Example.All the results reported in this section were obtained on a SUN SPARC-20running SUN fortran f77version SC3.0.1and SUN-OS4.1.3.
Our numerical results are based on the problem posed by(1.1),(1.2),(1.3),(1.5),and(1.6). We set
and
We report results for both the constrained and unconstrained problems.Our constraints are given by
and
14
We used the trust region parameters
and
The radius of the trust region was initialized to.In the test for postsmoothing we used .
The approximate active set was computed with
Here where is the number of nodes.The forcing term was
For a mesh of size we use the tolerances
and set the relative and absolute local truncation errors in DASPK to be
Following[14]we limited the time step in DASPK to the spatial mesh width.Our difference increment in(2.9)for the numerical reduced Hessian was
The initial iterate was
for both the constrained and unconstrained problems.
The solutions for the unconstrained(left)and constrained(right)problems,both with
are plotted in Figure4.1.From the plot of the constrained minimizer on the right one can see that both the upper and lower bound constraints are attained on different parts of.
For all computations we tabulate the iteration counter,the value of the objective, the actual reduction(for),the norm of the projected gradient,,the number of CG iterations required(for),and the radius of the trust region.For the constrained problem we also tabulate,the fraction of points that are in the approximate active set.means that the steepest descent or gradient projection step either went beyond the trust region boundary or satis?ed the inexact Newton condition.
The iterations for the both the constrained and unconstrained problem,reported in Tables4.1 and4.2terminated when.For the unconstrained problem,full smoothing steps were taken at each iteration.For the constrained problem,a full smoothing step was taken at the?nal iteration only.
T ABLE4.1
Unconstrained Problem,h=1/639.
09.77e+00 4.33e+00 5.00
1 2.81e-01-9.11e+00 2.45e-010 5.00
2 2.21e-01-5.99e-02 3.30e-022 5.00
3 2.20e-01-1.41e-03 1.32e-021 5.00
4 2.19e-01-6.98e-04 2.83e-022 5.00
5 2.19e-01-3.88e-04 1.00e-020 5.00
6 2.19e-01-3.85e-048.75e-041 5.00
7 2.19e-01-2.15e-06 5.93e-054 5.00
8 2.19e-01-4.44e-08 1.34e-053 5.00
16
T ABLE4.2
Constrained Problem,h=1/639.
09.77e+00 4.33e+00 5.00
1 2.60e+00-9.11e+00 1.91e+000 5.000.209
2 1.53e+00-2.30e+00 1.49e+000 5.000.025
37.90e-01-1.23e+009.81e-011 5.000.000
4 2.81e-01-4.90e-01 2.63e-021 5.000.141
5 2.78e-01-1.88e-037.24e-0310.610.223
6 2.78e-01-4.32e-05 2.64e-0310.030.322
7 2.78e-01-1.06e-048.88e-0310.260.350
8 2.78e-01-6.04e-05 5.87e-0300.260.331
9 2.78e-01-2.16e-059.12e-0410.020.375
10 2.78e-01-6.21e-07 6.70e-0410.020.380
11 2.78e-01-3.19e-07 1.28e-0500.020.380
TRUST REGION METHODS FOR CONTROL17
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LZ77压缩算法实验报告
LZ77压缩算法实验报告 一、实验内容 使用C++编程实现LZ77压缩算法的实现。 二、实验目的 用LZ77实现文件的压缩。 三、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 四、实验原理 LZ77 算法在某种意义上又可以称为“滑动窗口压缩”，这是由于该算法将一个虚拟的，可以跟随压缩进程滑动的窗口作为术语字典，要压缩的字符串如果在该窗口中出现，则输出其出现位置和长度。使用固定大小窗口进行术语匹配，而不是在所有已经编码的信息中匹配，是因为匹配算法的时间消耗往往很多，必须限制字典的大小才能保证算法的效率；随着压缩的进程滑动字典窗口，使其中总包含最近编码过的信息，是因为对大多数信息而言，要编码的字符串往往在最近的上下文中更容易找到匹配串。 五、LZ77算法的基本流程 1、从当前压缩位置开始，考察未编码的数据，并试图在滑动窗口中找出最长的匹 配字符串，如果找到，则进行步骤2，否则进行步骤3。 2、输出三元符号组( off, len, c )。其中off 为窗口中匹
配字符串相对窗口边 界的偏移，len 为可匹配的长度，c 为下一个字符。然后将窗口向后滑动len + 1 个字符，继续步骤1。 3、输出三元符号组( 0, 0, c )。其中c 为下一个字符。然后将窗口向后滑动 len + 1 个字符，继续步骤1。 六、源程序 /********************************************************************* * * Project description: * Lz77 compression/decompression algorithm. * *********************************************************************/ #include LTE现阶段常用参数详解 1、功率相关参数 1.1、Pb（天线端口信号功率比） 功能含义：Element）和TypeA PDSCH EPRE的比值。该参数提供PDSCH EPRE（TypeA）和PDSCH EPRE（TypeB）的功率偏置信息（线性值）。用于确定PDSCH（TypeB） 的发射功率。若进行RS功率boosting时，为了保持Type A 和Type B PDSCH 中的OFDM符号的功率平衡，需要根据天线配置情况和RS功率boosting值根 据下表确定该参数。1，2，4天线端口下的小区级参数ρB/ρA取值： PB 1个天线端口2个和4个天线端口 0 1 5/4 1 4/5 1 2 3/5 3/4 3 2/5 1/2 对网络质量的影响：PB取值越大，RS功率在原来的基础上抬升得越高，能获得更好的 信道估计性能，增强PDSCH的解调性能，但同时减少了PDSCH （Type B）的发射功率，合适的PB取值可以改善边缘用户速率， 提高小区覆盖性能。 取值建议：1 1.2、Pa（不含CRS的符号上PDSCH的RE功率与CRS 的RE功率比） 功能含义：不含CRS的符号上PDSCH的RE功率与CRS的RE功率比 对网络质量的影响：在CRS功率一定的情况下，增大该参数会增大数据RE功率 取值建议：-3 1.3、PreambleInitialReceivedTargetPower（初始接收目标功率(dBm)） 功能含义：表示当PRACH前导格式为格式0时，eNB期望的目标信号功率水平，由广播消息下发。 对网络质量的影响：该参数的设置和调整需要结合实际系统中的测量来进行。该参数设 置的偏高，会增加本小区的吞吐量，但是会降低整网的吞吐量；设 置偏低，降低对邻区的干扰，导致本小区的吞吐量的降低，提高整 网吞吐量。 取值建议：-100dBm~-104dBm 1.4、PreambleTransMax（前导码最大传输次数） 功能含义：该参数表示前导传送最大次数。 对网络质量的影响：最大传输次数设置的越大，随机接入的成功率越高，但是会增加对 邻区的干扰；最大传输次数设置的越小，存在上行干扰的场景随机 接入的成功率会降低，但是会减小对邻区的干扰 取值建议：n8，n10 实验名称：LZSS压缩算法实验报告 一、实验内容 使用Visual 6..0 C++编程实现LZ77压缩算法。 二、实验目的 用LZSS实现文件的压缩。 三、实验原理 LZSS压缩算法是词典编码无损压缩技术的一种。LZSS压缩算法的字典模型使用了自适应的方式，也就是说，将已经编码过的信息作为字典， 四、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 五、实验代码 #include -- need byte-swap function for big endian CPU */ #define READ_LE32(X) *(uint32_t *)(X) #define WRITE_LE32(X,Y) *(uint32_t *)(X) = (Y) /* this assumes sizeof(long)==4 */ typedef unsigned long uint32_t; /* text (input) size counter, code (output) size counter, and counter for reporting progress every 1K bytes */ static unsigned long g_text_size, g_code_size, g_print_count; /* ring buffer of size N, with extra F-1 bytes to facilitate string comparison */ static unsigned char g_ring_buffer[N + F - 1]; /* position and length of longest match; set by insert_node() */ static unsigned g_match_pos, g_match_len; /* left & right children & parent -- these constitute binary search tree */ static unsigned g_left_child[N + 1], g_right_child[N + 257], g_parent[N + 1]; /* input & output files */ static FILE *g_infile, *g_outfile; /***************************************************************************** initialize trees *****************************************************************************/ static void init_tree(void) { unsigned i; /* For i = 0 to N - 1, g_right_child[i] and g_left_child[i] will be the right and left children of node i. These nodes need not be initialized. Also, g_parent[i] is the parent of node i. These are initialized to NIL (= N), which stands for 'not used.' For i = 0 to 255, g_right_child[N + i + 1] is the root of the tree for strings that begin with character i. These are initialized to NIL. Note there are 256 trees. */ for(i = N + 1; i <= N + 256; i++) g_right_child[i] = NIL; for(i = 0; i < N; i++) g_parent[i] = NIL; } /***************************************************************************** Inserts string of length F, g_ring_buffer[r..r+F-1], into one of the trees (g_ring_buffer[r]'th tree) and returns the longest-match position and length via the global variables g_match_pos and g_match_len. If g_match_len = F, then removes the old node in favor of the new one, because the old one will be deleted sooner. DATAGUARD配置参数详细解释 DB_NAME 只需注意DataGuard的主备各节点instance使用相同的db_name即可。推荐与service_name一致。 DB_UNIQUE_NAME Primary与Standby端数据库的唯一名字，设定后不可再更改。 注意: 如果主备db_unique_name不一样，需要与LOG_ARCHIVE_CONFIG配合使用 db_unique_name并未规定需要与数据库service_name一致，可以自定义任意名称。 LOG_ARCHIVE_CONFIG 列出主备库上的DB_UNIQUE_NAME 参数。默认情况下，定义该参数能确保主备库数据库能够互相识别对方Primary与Standby端的db_unique_name不一致时 如在主备库db_unique_name不一致的情况下未配置LOG_ARCHIVE_CONFIG则会出现如下报错 ORA-16057: DGID from server not in Data Guard configuration 原因:主库没有设置参数log_archive_config 解决方法*.log_archive_config='dg_config=( Primary, Standby)' alter system set log_archive_config='dg_config=( Primary, Standby)' scope=both; Primary与Standby端的db_unique_name一致时 LOG_ARCHIVE_DEST_1 本地归档路径。Primary与Standby需要定义各自的online redo log的归档地址，以系统实际的存放路径为准。格式如下： Primary Site: *.LOG_ARCHIVE_DEST_1='LOCATION=/arch/ VALID_FOR=(ALL_LOGFILES,ALL_ROLES) ' Standby Site: *.LOG_ARCHIVE_DEST_1='LOCATION=/stdby/ VALID_FOR=(ALL_LOGFILES,ALL_ROLES) ' 注意： 在LOG_ARCHIVE_DEST_n设置DB_UNIQUE_NAME表示该参数在DB_UNIQUE_NAME指定的数据库上生效，设置为本地的db_unique_name。以priamry端为例，格式如下： *.LOG_ARCHIVE_DEST_1='LOCATION=/archivelog/ VALID_FOR=(ALL_LOGFILES, ALL_ROLES) DB_UNIQUE_NAME=Primary' 这样配置的意义为：在数据库Primary上log_archive_dest_1对主备库上的联机日志都有效，这里的 db_unique_name可以省略 LOG_ARCHIVE_DEST_2 该参数仅当数据库角色为primary时生效，指定primary归档redo log到该参数定义的standby database上。 log_archive_dest_2可以说是dataguard上最重要的参数之一，它定义了redo log的传输方式(sync or async)以及传输目标(即standby apply node)，直接决定了dataguard的数据保护级别。 格式如下： Primary Site: *.LOG_ARCHIVE_DEST_2='SERVICE=DR2 lgwr async VALID_FOR=(ONLINE_LOGFILES, PRIMARY_ROLE) ' Standby Site: (switch over后生效) *.LOG_ARCHIVE_DEST_2='SERVICE=DR1 lgwr async VALID_FOR=(ONLINE_LOGFILES, PRIMARY_ROLE) ' 注意： LOG_ARCHIVE_DEST_2参数里定义的service值，比如DR1，是tnsnames.ora文件里定义的Oracle Net名称。 多媒体数据压缩实验报告 篇一：多媒体实验报告_文件压缩 课程设计报告 实验题目：文件压缩程序 姓名：指导教师：学院：计算机学院专业：计算机科学与技术学号： 提交报告时间：20年月日 四川大学 一，需求分析： 有两种形式的重复存在于计算机数据中，文件压缩程序就是对这两种重复进行了压 缩。 一种是短语形式的重复，即三个字节以上的重复，对于这种重复，压缩程序用两个数字：1.重复位置距当前压缩位置的距离；2.重复的长度，来表示这个重复，假设这两个数字各占一个字节，于是数据便得到了压缩。 第二种重复为单字节的重复，一个字节只有256种可能的取值，所以这种重复是必然的。给 256 种字节取值重新编码，使出现较多的字节使用较短的编码，出现较少的字节使用较长的编码，这样一来，变短的字节相对于变长的字节更多，文件的总长度就会减少，并且，字节使用比例越不均 匀，压缩比例就越大。 编码式压缩必须在短语式压缩之后进行，因为编码式压缩后，原先八位二进制值的字节就被破坏了，这样文件中短语式重复的倾向也会被破坏（除非先进行解码）。另外，短语式压缩后的结果：那些剩下的未被匹配的单、双字节和得到匹配的距离、长度值仍然具有取值分布不均匀性，因此，两种压缩方式的顺序不能变。 本程序设计只做了编码式压缩，采用Huffman编码进行压缩和解压缩。Huffman编码是一种可变长编码方式，是二叉树的一种特殊转化形式。编码的原理是：将使用次数多的代码转换成长度较短的代码，而使用次数少的可以使用较长的编码，并且保持编码的唯一可解性。根据 ascii 码文件中各 ascii 字符出现的频率情况创建 Huffman 树，再将各字符对应的哈夫曼编码写入文件中。同时，亦可根据对应的哈夫曼树，将哈夫曼编码文件解压成字符文件. 一、概要设计： 压缩过程的实现: 压缩过程的流程是清晰而简单的: 1. 创建 Huffman 树 2. 打开需压缩文件 3. 将需压缩文件中的每个 ascii 码对应的 huffman 编码按 bit 单位输出生成压缩文件压缩结束。 CPU Intel Pentium E5300/盒装450 主板：捷波蓝光X-BLUE P43 399元 内存宇瞻2GB DDR3 1333 300 显卡:昂达9600GSO 384M 400元 电源航嘉冷静王钻石2.3版本1 ￥200 硬盘希捷500GB 7200.12 ￥350 光驱三星TS-H352 115 显示器:AOC 919SW 760元 处理器(CPU) AMD Athlon(速龙) II X2 245 430(原装） 主板映泰A770 A2G+ 420 内存金士顿2GB DDR2 800 245 显卡铭瑄极光9500GT高清版-TC512M 375 电源航嘉冷静王钻石2.3版本1 ￥200 硬盘希捷250GB 7200.12 16M（串口/散）1234 ￥280光驱东芝-三星DVD-ROM TS-H352D DVD光驱120 LCD 三星943NW ￥870 硬盘希捷160 300 CPU Intel 奔腾双核E5200(盒) 1 ￥420 主板捷波XBLUE-P43 1 ￥399 内存三星2GB DDR2 800(金条) 1234 ￥156 硬盘希捷250GB 7200.12 16M（串口/散）1234 ￥280 显卡双敏无极2 9600GT金牛版1234 ￥599 LCD HKC S988A 1 ￥690 机箱大水牛A0707（空箱）1 ￥105 电源航嘉冷静王钻石2.3版本1 ￥228 键鼠装灵标经济套装1 ￥35 合计金额：2967 元 处理器(CPU) AMD Athlon(速龙) II X2 245 430(原装） 主板华擎M3A785GMH/128M 500 内存宇瞻2GB DDR3 1333 300 硬盘希捷ST3500418AS ( 500 GB ) 340 显示器LG GSM4B6F W1942 ( 19.1 英寸) 785（包点）光驱东芝-三星DVD-ROM TS-H352D DVD光驱120 机箱绝尘侠X5 115 电源航嘉冷钻王2.30版本185 价值工程 置，是一项十分有意义的工作。另外恶意代码的检测和分析是一个长期的过程，应对其新的特征和发展趋势作进一步研究，建立完善的分析库。 参考文献： [1]CNCERT/CC.https://www.wendangku.net/doc/5212471633.html,/publish/main/46/index.html. [2]LO R,LEVITTK,OL SSONN R.MFC:a malicious code filter [J].Computer and Security,1995,14(6):541-566. [3]KA SP ER SKY L.The evolution of technologies used to detect malicious code [M].Moscow:Kaspersky Lap,2007. [4]LC Briand,J Feng,Y Labiche.Experimenting with Genetic Algorithms and Coupling Measures to devise optimal integration test orders.Software Engineering with Computational Intelligence,Kluwer,2003. [5]Steven A.Hofmeyr,Stephanie Forrest,Anil Somayaji.Intrusion Detection using Sequences of System calls.Journal of Computer Security Vol,Jun.1998. [6]李华,刘智,覃征,张小松.基于行为分析和特征码的恶意代码检测技术[J].计算机应用研究，2011，28（3）：1127-1129. [7]刘威，刘鑫，杜振华.2010年我国恶意代码新特点的研究.第26次全国计算机安全学术交流会论文集，2011，（09）. [8]IDIKA N,MATHUR A P.A Survey of Malware Detection Techniques [R].Tehnical Report,Department of Computer Science,Purdue University,2007. 0引言 现有的压缩算法有很多种，但是都存在一定的局限性，比如：LZw [1]。主要是针对数据量较大的图像之类的进行压缩，不适合对简单报文的压缩。比如说，传输中有长度限制的数据，而实际传输的数据大于限制传输的数据长度，总体数据长度在100字节左右，此时使用一些流行算法反而达不到压缩的目的，甚至增大数据的长度。本文假设该批数据为纯数字数据，实现压缩并解压缩算法。 1数据压缩概念 数据压缩是指在不丢失信息的前提下，缩减数据量以减少存储空间，提高其传输、存储和处理效率的一种技术方法。或按照一定的算法对数据进行重新组织，减少数据的冗余和存储的空间。常用的压缩方式[2,3]有统计编码、预测编码、变换编码和混合编码等。统计编码包含哈夫曼编码、算术编码、游程编码、字典编码等。 2常见几种压缩算法的比较2.1霍夫曼编码压缩[4]：也是一种常用的压缩方法。其基本原理是频繁使用的数据用较短的代码代替，很少使用 的数据用较长的代码代替，每个数据的代码各不相同。这些代码都是二进制码，且码的长度是可变的。 2.2LZW 压缩方法[5,6]：LZW 压缩技术比其它大多数压缩技术都复杂，压缩效率也较高。其基本原理是把每一个第一次出现的字符串用一个数值来编码，在还原程序中再将这个数值还成原来的字符串，如用数值0x100代替字符串ccddeee"这样每当出现该字符串时，都用0x100代替，起到了压缩的作用。 3简单报文数据压缩算法及实现 3.1算法的基本思想数字0-9在内存中占用的位最 大为4bit ， 而一个字节有8个bit ，显然一个字节至少可以保存两个数字，而一个字符型的数字在内存中是占用一个字节的，那么就可以实现2:1的压缩，压缩算法有几种，比如，一个自己的高四位保存一个数字，低四位保存另外一个数字，或者，一组数字字符可以转换为一个n 字节的数值。N 为C 语言某种数值类型的所占的字节长度，本文讨论后一种算法的实现。 3.2算法步骤 ①确定一种C 语言的数值类型。 —————————————————————— —作者简介：安建梅（1981-），女，山西忻州人，助理实验室，研究方 向为软件开发与软交换技术；季松华（1978-），男，江苏 南通人，高级软件工程师，研究方向为软件开发。 数据快速压缩算法的研究以及C 语言实现 The Study of Data Compression and Encryption Algorithm and Realization with C Language 安建梅①AN Jian-mei ；季松华②JI Song-hua （①重庆文理学院软件工程学院，永川402160；②中信网络科技股份有限公司，重庆400000）（①The Software Engineering Institute of Chongqing University of Arts and Sciences ，Chongqing 402160，China ； ②CITIC Application Service Provider Co.，Ltd.，Chongqing 400000，China ） 摘要：压缩算法有很多种，但是对需要压缩到一定长度的简单的报文进行处理时，现有的算法不仅达不到目的，并且变得复杂， 本文针对目前一些企业的需要，实现了对简单报文的压缩加密，此算法不仅可以快速对几十上百位的数据进行压缩，而且通过不断 的优化，解决了由于各种情况引发的解密错误，在解密的过程中不会出现任何差错。 Abstract:Although,there are many kinds of compression algorithm,the need for encryption and compression of a length of a simple message processing,the existing algorithm is not only counterproductive,but also complicated.To some enterprises need,this paper realizes the simple message of compression and encryption.This algorithm can not only fast for tens of hundreds of data compression,but also,solve the various conditions triggered by decryption errors through continuous optimization;therefore,the decryption process does not appear in any error. 关键词：压缩；解压缩；数字字符；简单报文Key words:compression ；decompression ；encryption ；message 中图分类号：TP39文献标识码：A 文章编号：1006-4311（2012）35-0192-02 ·192· 八年级下学期全部长篇课文 Unit 1 3a P6 In ten years , I think I'll be a reporter . I'll live in Shanghai, because I went to Shanfhai last year and fell in love with it. I think it's really a beautiful city . As a reporter, I think I will meet lots of interesting people. I think I'll live in an apartment with my best friends, because I don' like living alone. I'll have pets. I can't have an pets now because my mother hates them, and our apartment is too small . So in ten yers I'll have mny different pets. I might even keep a pet parrot!I'll probably go skating and swimming every day. During the week I'll look smart, and probably will wear a suit. On the weekend , I'll be able to dress more casully. I think I'll go to Hong Kong vacation , and one day I might even visit Australia. P8 Do you think you will have your own robot In some science fiction movies, people in the future have their own robots. These robots are just like humans. They help with the housework and do most unpleasant jobs. Some scientists believe that there will be such robots in the future. However, they agree it may take hundreds of years. Scientist ae now trying to make robots look like people and do the same things as us. Janpanese companies have already made robts walk and dance. This kond of roots will also be fun to watch. But robot scientist James White disagrees. He thinks that it will be difficult fo a robot to do the same rhings as a person. For example, it's easy for a child to wake up and know where he or she is. Mr White thinks that robots won't be able to do this. But other scientists disagree. They think thast robots will be able t walk to people in 25 to 50tars. Robots scientists are not just trying to make robots look like people . For example, there are already robots working in factories . These robots look more like huge arms. They do simple jobs over and over again. People would not like to do such as jobs and would get bored. But robots will never bored. In the futhre, there will be more robots everwhere, and humans will have less work to do. New robots will have different shapes. Some will look like humans, and others might look like snakes. After an earthquake, a snake robot could help look for people under buildings. That may not seem possibe now, but computers, space rockets and even electric toothbrushes seemed 压缩编码算法设计与实现实验报告 一、实验目的：用C语言或C++编写一个实现Huffman编码的程序，理解对数据进行无损压缩的原理。 二、实验内容：设计一个有n个叶节点的huffman树，从终端读入n个叶节 点的权值。设计出huffman编码的压缩算法，完成对n个节点的编码，并写出程序予以实现。 三、实验步骤及原理： 1、原理：Huffman算法的描述 (1)初始化，根据符号权重的大小按由大到小顺序对符号进行排序。 (2)把权重最小的两个符号组成一个节点， (3)重复步骤2，得到节点P2，P3，P4……，形成一棵树。 (4)从根节点开始顺着树枝到每个叶子分别写出每个符号的代码 2、实验步骤： 根据算法原理，设计程序流程，完成代码设计。 首先，用户先输入一个数n，以实现n个叶节点的Huffman 树； 之后，输入n个权值w[1]~w[n]，注意是unsigned int型数值； 然后，建立Huffman 树； 最后，完成Huffman编码。 四、实验代码：#include int min(HuffmanTree t,int i) { int j,flag; unsigned int k = MAX; for(j=1;j<=i;j++) if(t[j].parent==0&&t[j].weight 计算机配置参数解释 主频为地频率（如地主频为倍频为外频缓存（）缓存*) 主频外频倍频.也就是倍频是指和系统总线之间相差地倍数，当外频不变时，提高倍频，主频也就越高 主频，就是地时钟频率，简单说是运算时地工作频率（秒内发生地同步脉冲数）地简称.单位是.它决定计算机地运行速度，随着计算机地发展，主频由过去发展到了现在地（）.通常来讲，在同系列微处理器，主频越高就代表计算机地速度也越快，但对与不同类型地处理器，它就只能作为一个参数来作参考.另外地运算速度还要看地流水线地各方面地性能指标.由于主频并不直接代表运算速度，所以在一定情况下，很可能会出现主频较高地实际运算速度较低地现象.因此主频仅仅是性能表现地一个方面，而不代表地整体性能. 说到处理器主频，就要提到与之密切相关地两个概念：倍频与外频，外频是地基准频率，单位也是.外频是与主板之间同步运行地速度，而且目前地绝大部分电脑系统中外频也是内存与主板之间地同步运行地速度，在这种方式下，可以理解为地外频直接与内存相连通，实现两者间地同步运行状态；倍频即主频与外频之比地倍数.主频、外频、倍频，其关系式：主频＝外频×倍频.早期地并没有“倍频”这个概念，那时主频和系统总线地速度是一样地.随着技术地发展，速度越来越快，内存、硬盘等配件逐渐跟不上地速度了，而倍频地出现解决了这个问题，它可使内存等部件仍然工作在相对较低地系统总线频率下，而地主频可以通过倍频来无限提升（理论上）.我们可以把外频看作是机器内地一条生产线，而倍频则是生产线地条数，一台机器生产速度地快慢（主频）自然就是生产线地速度（外频）乘以生产线地条数（倍频）了.现在地厂商基本上都已经把倍频锁死，要超频只有从外频下手，通过倍频与外频地搭配来对主板地跳线或在中设置软超频，从而达到计算机总体性能地部分提升.所以在购买地时候要尽量注意地外频. 处理器外频 外频是乃至整个计算机系统地基准频率，单位是（兆赫兹）.在早期地电脑中，内存与主板之间地同步运行地速度等于外频，在这种方式下，可以理解为外频直接与内存相连通，实现两者间地同步运行状态.对于目前地计算机系统来说，两者完全可以不相同，但是外频地意义仍然存在，计算机系统中大多数地频率都是在外频地基础上，乘以一定地倍数来实现，这个倍数可以是大于地，也可以是小于地. 说到处理器外频，就要提到与之密切相关地两个概念：倍频与主频，主频就是地时钟频率；倍频即主频与外频之比地倍数.主频、外频、倍频，其关系式：主频＝外频×倍频. 在之前，地主频还处于一个较低地阶段，地主频一般都等于外频.而在出现以后，由于工作频率不断提高，而机地一些其他设备（如插卡、硬盘等）却受到工艺地限制，不能承受更高地频率，因此限制了频率地进一步提高.因此出现了倍频技术，该技术能够使内部工作频率变为外部频率地倍数，从而通过提升倍频而达到提升主频地目地.倍频技术就是使外部设备可以工作在一个较低外频上，而主频是外频地倍数. 在时代，地外频一般是，从Ⅱ开始，外频提高到，目前外频已经达到了.由于正常情况下外频和内存总线频率相同，所以当外频提高后，与内存之间地交换速度也相应得到了提高，对提高电脑整体运行速度影响较大.LTE常用参数详解
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