圆和椭圆的绘制 - MATLAB实现

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圆和椭圆的绘制 - MATLAB实现

在MATLAB中,我们可以使用简单的代码来绘制圆和椭圆。下面将介绍如何使用MATLAB实现这两种图形的绘制,并提供相应的源代码。

绘制圆:

要绘制一个圆,我们需要指定圆心的坐标和半径。以下是一个简单的MATLAB代码示例,用于绘制一个圆:

% 圆心坐标
center = [0, 0];
% 圆的半径
radius = 5;

% 生成一组角度值,用于定义圆上的点
theta = linspace(0, 2 * pi, 100);

% 计算圆上的点的坐标
x = center(1) + radius * cos(theta);
y = center(2) + radius * sin(theta);

% 绘制圆
plot(x, y);
axis equal;

在这个例子中,我们使用center变量指定圆心的坐标,radius变量指定圆的半径。然后,我们生成一组角度值theta,用于定义圆上的点。通过使用三角函数计算出每个点的坐标,然后使用plot函数绘制这些点。最后,使用axis equal函数使得坐标轴的比例相等,以便正确显示圆形。

绘制椭圆:

要绘制一个椭圆,我们需要指定椭圆的中心坐标、长轴和短轴的长度。以下是一个简单的MATLAB代码示例,用于绘制一个椭圆:

% 椭圆中心坐标
center = [0,
椭圆拟合理论推导和Matlab实现 椭圆拟合理论推导和Matlab实现 1 理论推导 前面一篇文章,解决了最小二乘圆拟合的问题。这篇文章将以类似的方法解决椭圆拟合的问题。 首先搞清楚问题,最小二乘拟合椭圆,即输入为散点集{(xi,yi)∣xi∈R,yi∈R}\{(x_i,y_i)|x_i\in \R,y_i\in \R\}{(xi​,yi​)∣xi​∈R,yi​∈R},定义新的向量{X∣X=[x1 x2...xn]T∈Rn}\{X|X=[x_1\ x_2...x_n]^T\in \R^n\}{X∣X=[x1​ x2​... 阅读详情

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plot(cnn.rL);assert(er<0.12, 'Too big error');```Example: Neural Networks---------------------```matlabfunction test_example_NNload mnist_uint8;train_x = double(train_x) / 255;test_x = double(test_x) / 255;train_y = double(train_y);test_y = double(test_y);% normalize[train_x, mu, sigma] = zscore(train_x);test_x = normalize(test_x, mu, sigma);%% ex1 vanilla neural netrand('state',0)nn = nnsetup([784 100 10]);opts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samples[nn, L] = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.08, 'Too big error');%% ex2 neural net with L2 weight decayrand('state',0)nn = nnsetup([784 100 10]);nn.weightPenaltyL2 = 1e-4; % L2 weight decayopts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samplesnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');%% ex3 neural net with dropoutrand('state',0)nn = nnsetup([784 100 10]);nn.dropoutFraction = 0.5; % Dropout fraction opts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samplesnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');%% ex4 neural net with sigmoid activation functionrand('state',0)nn = nnsetup([784 100 10]);nn.activation_function = 'sigm'; % Sigmoid activation functionnn.learningRate = 1; % Sigm require a lower learning rateopts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samplesnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');%% ex5 plotting functionalityrand('state',0)nn = nnsetup([784 20 10]);opts.numepochs = 5; % Number of full sweeps through datann.output = 'softmax'; % use softmax outputopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');%% ex6 neural net with sigmoid activation and plotting of validation and training error% split training data into training and validation datavx = train_x(1:10000,:);tx = train_x(10001:end,:);vy = train_y(1:10000,:);ty = train_y(10001:end,:);rand('state',0)nn = nnsetup([784 20 10]); nn.output = 'softmax'; % use softmax outputopts.numepochs = 5; % Number of full sweeps through dataopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, tx, ty, opts, vx, vy); % nntrain takes validation set as last two arguments (optionally)[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');```[![Bitdeli Badge](https://d2weczhvl823v0.cloudfront.net/rasmusbergpalm/deeplearntoolbox/trend.png)](https://bitdeli.com/free "Bitdeli Badge")

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