三峡大学数学建模matlab题目.doc

1. 在44的棋盘上安置4个皇后，要求任意两个皇后不在同一行、不在同一列、不在同一对角线上，输出所有的方案。for i1=1:4 %i1.。表示皇后的位置 for i2=1:4 for i3=1:4 for i4=1:4 hh=zeros(4,4);%用于模拟棋盘 hh(1,i1)=1; % 1表示此处有皇后 由于分列，所以不再同一列 hh(2,i2)=1; hh(3,i3)=1; hh(4,i4)=1; if i1=i2 | i1=i3 | i1=i4 | i2=i3 | i2=i4 | i3=i4 % 判断是否在同一行 continue; end if abs(i1-i2)=1 | abs(i1-i3)=2 | abs(i1-i4)=3 | abs(i2-i3)=1 | abs(i2-i4)=2 . | abs(i3-i4)=1 % 判断是否在一条对角线上 continue; end disp(hh);%打印棋盘，1为皇后 end end endend2. 问题描述：有形如下图所示的数塔，从顶部出发，在每一结点可以选择向左走或是向右走，一直走到底层，要求找出一条路径，使路径上的数值的和最接近零。n=input(输入数塔的层数n(正整数n=20) );st=zeros(n);for i1=1:n for j1=1:i1 fprintf(输入第%d行第%d个数据(且数字的绝对值不超过1000000) ,i1,j1); st(i1,j1)=input( ); endendsz=inf;ls=zeros(1,n(1)-1);lj=zeros(1,n(1)-1);for i1=0:2n-1 ss=st(1,1); for j1=1:n(1)-1 ls(j1)=mod(i1,2); i1=floor(i1/2); end k=1; for j1=1:n(1)-1 k=k+ls(j1); ss=ss+st(j1+1,k); end if ss=1 & a=4 fprintf(computer take %d awaynthere is %d leftn,5-a,21-5*i); endenddisp(computer win !);麦克斯韦方程组的积分形式：(in matter)这是1873年前后，麦克斯韦提出的表述电磁场普遍规律的四个方程。其中：（1）描述了电场的性质。在一般情况下，电场可以是库仑电场也可以是变化磁场激发的感应电场，而感应电场是涡旋场，它的电位移线是闭合的，对封闭曲面的通量无贡献。（2）描述了磁场的性质。磁场可以由传导电流激发，也可以由变化电场的位移电流所激发，它们的磁场都是涡旋场，磁感应线都是闭合线，对封闭曲面的通量无贡献。（3）描述了变化的磁场激发电场的规律。（4）描述了变化的电场激发磁场的规律。变化场与稳恒场的关系：当时，方程组就还原为静电场和稳恒磁场的方程：(in matter)在没有场源的自由空间，即q=0, I=0，方程组就成为如下形式：(in matter)麦克斯韦方程组的积分形式反映了空间某区域的电磁场量(D、E、B、H)和场源(电荷q、电流I)之间的关系。4.2微分形式麦克斯韦方程组微分形式：在电磁场的实际应用中，经常要知道空间逐点的电磁场量和电荷、电流之间的关系。从数学形式上，就是将麦克斯韦方程组的积分形式化为微分形式。利用矢量分析方法，可得：(in matter)注意：(1)在不同的惯性参照系中，麦克斯韦方程有同样的形式。(2) 应用麦克斯韦方程组解决实际问题，还要考虑介质对电磁场的影响。例如在各向同性介质中，电磁场量与介质特性量有下列关系：在非均匀介质中，还要考虑电磁场量在界面上的边值关系。在利用t=0时场量的初值条件，原则上可以求出任一时刻空间任一点的电磁场，即E(x,y,z,t)和B(x,y,z,t)。麦克斯韦方程组微分形式（高斯单位制）还是试下通俗讲吧：电场分两种，一种是有源，也就是沿着电场线某一段总有终点，如电子产生的电场；一种无源（或称为有旋？），换而言之就是无论沿着线往哪边走都没有尽头，如均匀变化的均匀磁场，电场线是一个个圆，无始无终。Maxwell方程组其一：有源电场由且仅由电荷产生Maxwell方程组其二：无源电场由且仅由变化的磁场产生同样磁场也分这么两种，类比就好Maxwell方程组其三：没有有源磁场，哈哈，意思就是没有磁荷了（与电荷相对应）Maxwell方程组其四：无源磁场由且仅由电流和变化的电场产生Maxwell方程组也诠释了具体的产生方式，但你要通俗的化也没必要说了。其实对电场磁场的描述几乎一模一样，差就差在有电荷却没磁荷这一点，导致了方程一跟方程三的不同。而二四呢，因为电荷可以形成电流，所以方程四多了一个由电流产生。如果有磁荷的话，方程二也会改成由磁流跟变化的磁场产生，方程三也为改成由磁荷产生。如此两者形式便一模一样了。弦论里预言的磁单极子便有此般意味在里面。function features, valid_points = extractFeatures(I, points, varargin)%extractFeatures Extract interest point descriptors% extractFeatures extracts feature vectors, also known as descriptors,% from a binary or intensity image. Descriptors are derived from pixels% surrounding an interest point. They are needed to describe and match % features specified by a single point location.% FEATURES, VALID_POINTS = extractFeatures(I, POINTS) returns FEATURES,% an M-by-N matrix of M feature vectors, also known as descriptors. Each% descriptor is of length N. The function also returns M number of % VALID_POINTS corresponding to each descriptor. The method used for % descriptor extraction depends on class of POINTS:% Class of POINTS Descriptor extraction method% - -% - SURFPoints object - Speeded-Up Robust Features (SURF)% - MSERRegions object - Speeded-Up Robust Features (SURF)% - M-by-2 matrix of x y - Simple square neighborhood around x y% coordinates point location% FEATURES, VALID_POINTS = extractFeatures(I, POINTS, PARAM1, VAL1,% PARAM2, VAL2) can be used to specify additional parameters:% Method - One of the strings: Block, SURF or Auto. % Method Feature vector (descriptor)% - -% Block Simple square neighborhood% SURF Speeded-Up Robust Features (SURF)% Auto Selects the method based on the class of % input points: SURF when POINTS is a SURFPoints % object or MSERRegions object and Block when POINTS% is an M-by-2 matrix of x y coordinates% Default: Auto% BlockSize - An odd integer scalar defining the local square % neighborhood (BlockSize-by-BlockSize) centered at% each interest point. This option is only% applicable to Block method.% Default: 11% SURFSize - Integer scalar set to 64 or 128. Length of the SURF% feature vector (descriptor). This option is only% applicable to SURF method.% Default: 64% Notes% -% - When Block method is used, the function extracts only the % neighborhoods fully contained within the image boundary, therefore % VALID_POINTS may contain fewer points than input POINTS.% - When SURF is used to extract descriptors, the Orientation property% of returned VALID_POINTS SURFPoints object is set to the orientation % of extracted features, in radians. This is useful for visualizing % the SURF descriptor orientation.% - When MSERRegions object is used with SURF, the Centroid property of % the object is used to extract SURF descriptors. The Axes property is % used to select the scale of the SURF descriptors such that the circle% representing the feature has an area proportional to MSER ellipse % area. The Orientation property is not used.% - You can increase SURFSize from the default 64 to 128 to increase% descriptor matching accuracy at the expense of matching speed.% Class Support% -% The input image I can be logical, uint8, uint16, int16, single, or % double, and it must be real and nonsparse. POINTS can be int16, uint16,% int32, uint32, single or double, and it must be real and nonsparse.% Example 1% -% % Extract corner features from an image.% I = imread(pout.tif);% % hcornerdet = vision.CornerDetector;% points = step(hcornerdet, I);% % features, valid_points = extractFeatures(I, points);% % figure; imshow(I); hold on % % Plot interest points% plot(points(:,1), points(:,2), b.)% % Overlay valid interest points% plot(valid_points(:,1), valid_points(:,2), y.)% Example 2% -% % Extract SURF features% I = imread(cameraman.tif);% points = detectSURFFeatures(I);% features, valid_points = extractFeatures(I, points);% % Visualize 10 strongest SURF features, including their scale, and % % orientation which was determined during the descriptor extraction% % process.% figure; imshow(I); hold on;% plot(valid_points.selectStrongest(10),showOrientation,true);% Example 3% -% % Extract MSER features% I = imread(cameraman.tif);% regions = detectMSERFeatures(I);% % Use MSER with SURF feature descriptor% features, valid_points = extractFeatures(I, regions);% % Visualize SURF features corresponding to the MSER ellipse centers % % along with scale and orientation.% figure; imshow(I); hold on;% plot(valid_points,showOrientation,true);% % See also vision.CornerDetector, detectSURFFeatures, detectMSERFeatures,% matchFeatures.% Copyright 2010 The MathWorks, Inc.% $Revision: 1.1.6.8 $ $Date: 2011/09/03 23:36:02 $% Parse and check inputsisXY = cvstGetCoordsChoice(fcnExtractFeatures);method, blockSize, SURFSize = parseInputs(I, points, isXY, varargin:);% Extract features from image Iif strcmp(method, Block) if isa(points,SURFPoints) points = points.Location; elseif isa(points,MSERRegions) points = points.Centroid; elseif isXY % Convert points from R/C, 0-based coordinates to X/Y, 1-based % coordinates. points = fliplr(points + 1); end features, valid_points = cvalgExtractFeatures(I, points, blockSize); if isXY features = features; valid_points = flipud(valid_points - 1); endelse % SURF if isa(points,MSERRegions) centroid = points.Centroid; majorAxes = points.Axes(:,1); minorAxes = points.Axes(:,2); scale = 1/4*sqrt(majorAxes/2).*(minorAxes/2); % Saturate scale to 1.6 as required by SURFPoints scale(scale 1.6) = 1.6; points = SURFPoints(centroid,Scale,scale); end Iu8,ptsStruct = parseSURFInputs(I,points); % we are using cvExtractSurf with point inputs, therefore only % the extended parameter matters; the other can remain unset params.extended = SURFSize = 128; vPts, features = ocvExtractSurf(Iu8, ptsStruct, params); valid_points = SURFPoints(vPts.Location, vPts); end%=% Parse and check inputs%=function method, blockSize,SURFSize = . parseInputs(I, points, isXY, varargin)% Check imagecheckImage(I);% Setup parserparser = inputParser;parser.CaseSensitive = true;parser.FunctionName = mfilename;parser.addParamValue(Method, Auto, checkMethod);parser.addParamValue(BlockSize, 11, checkBlockSize);parser.addParamValue(SURFSize, 64, checkSURFSize);% Parse inputparser.parse(varargin:);% Assign outputsr = parser.Results;method blockSize SURFSize = deal(r.Method, r.BlockSize, r.SURFSize);% Handle Auto choiceif strcmp(method,Auto) if isa(points,SURFPoints) | isa(points,MSERRegions) method = SURF; else method = Block; endend% Check pointsif isa(points, SURFPoints) & isa(points, MSERRegions) checkPoints(points, method, isXY);end;%=% Parse SURF inputs%=function Iu8, ptsStruct = parseSURFInputs(I, points)if isa(I,uint8) Iu8 = I;else Iu8 = im2uint8(I);end% If needed, convert raw X,Y coordinates to SURFPointsif isa(points, SURFPoints) ptsObj = SURFPoints(points);else ptsObj = points;end% convert SURFPoints object back to structure required by% the ocvExtractSurf built-in functionptsStruct.Location = ptsObj.Location;ptsStruct.Scale = ptsObj.Scale;ptsStruct.Metric = ptsObj.Metric;ptsStruct.SignOfLaplacian = ptsObj.SignOfLapl