MATLAB小技巧整理：你必须知道的30个高效技巧

众所周知Matlab功能全面而强大，那么多知识点要记下来是有亿点点难的哈，那么是时候整理一波了，温故而知新嘛~

系统：windows

MATLAB版本：2016b

1. 随机数、随机噪声

close allclear clc  %% 产生 m 个属于 [1, n] 的随机整数m = 2;n = 3;randperm(n, m); %% 产生指定数值（默认 -1 和 1）分布的随机数，可指定元素分布概率randsrc(10, 10, [-3 -1 1 3; 0.1 0.4 0.4 0.1]); %% 产生指定范围的随机数unifrnd(0, 1:5); %% 产生均值为 0.1 方差为 0.1 的随机数x = 0.1 + sqrt(0.1)*randn(10000, 1); %% 产生 3 个和为 1 的随机数r = rand(3, 1);r = r / sum(r); %% 生成相同的随机数s = rng;x = rand(1,5);rng(s);y = rand(1,5); % 每次运行得到相同的结果% 在使用随机数之前设置rng('default'); %% 添加噪声y = x + rand(length(x), 1);y = x + randn(length(x), 1)

2. 字符串分割

close allclear clc %% 直接分割regexp('Numbers = 2500', '=', 'split') %% 分割得到 cell，需要二次处理textscan('Numbers = 2500', '%s %d', 'Delimiter', '=')

3. 数据标准化

y = (x - mean(x)) ./ std(x);[y, mu, sigma] = zscore(x);

4. R2 计算

x = 1:10;y1 = x + rand(1, 10);p = polyfit(x, y1, 1);y2 = polyval(p, x);R2 = sumsqr(y2 - mean(y1)) / sumsqr(y1 - mean(y1))

5. 鼠标位置、按键

% 相对 Figure 位置% Button down function: UIFigurefunction UIFigureButtonDown(app, event)    pos = get(app.UIFigure, 'CurrentPoint')    pos app.UIFigure.CurrentPointend % 相对 Axes 位置% Button down function: UIAxesfunction UIAxesButtonDown(app, event)    pt = app.UIAxes.CurrentPoint;    x = pt(1, 1)    y = pt(1, 2)end % 鼠标按键% normal：左键；alt：右键；extend：中键；open：双击，会触发两次单击% Button down function: UIFigurefunction UIFigureButtonDown(app, event)    button = get(app.UIFigure, 'SelectionType')end

6. 剪切板操作

clear; clc;x = linspace(0, 2*pi, 20);y = sin(x);plot(x, y);% 把 y 值复制到剪切板clipboard('copy', y);% 获取剪切板内容str = clipboard('paste')% 把当前 figure 复制到剪切板hgexport(gcf, '-clipboard')

7.打开网址

web('https://www.zhihu.com/people/1105936347')

8. 选择颜色

% 单颜色c = uisetcolor([0.6 0.8 1])% 色条cmap = uisetcolormap

9. 符号方程、符号转数值

syms uf = sym('3');Eq = sin(f)*u^2 + u + f;sol = solve(Eq, u)sol_num = double(sol)sol_num = vpa(sol)% 符号替换数字sol = subs(sol, f, 3)

10. 公式格式化输出到公式编辑器

% 动态脚本输出，直接复制到公式编辑器

syms xf = taylor(x*exp(x), x, 'order', 9)% 复制输出字符串到公式编辑器latex(f)

11. 文件读写函数汇总

load、savedlmread、dlmwritecsvread、csvwriteimportdatatextscanfprintfreadtable、writetable

12. 函数可视化

fplotfimplicitfimplicit3fsurfisosurface

13. 绘图字体、坐标轴属性设置

close allclear; clc; %% t = 6*pi*(0 : 100) / 100;y = 1 - exp(- 0.3*t) .* cos(0.7*t);plot(t, y, 'r-', 'LineWidth', 3) %%hold ontt = t(abs(y - 1) > 0.05);ts = max(tt);plot(ts, 0.95, 'bo', 'MarkerSize', 10) %%hold offaxis([-inf, 6*pi, 0.6, inf])set(gca, 'Xtick', [2*pi, 4*pi, 6*pi], 'Ytick', [0.95, 1, 1.05, max(y)])set(gca, 'XtickLabel', {'2*pi'; '4*pi'; '6*pi'})set(gca, 'YtickLabel', {'0.95'; '1'; '1.05'; 'max(y)'})grid ontext(13.5, 1.2, '\fontsize{12}{\alpha} = 0.3')text(13.5, 1.1, '\fontsize{12}{\omega} = 0.7')cell_string{1} = '\fontsize{12}\uparrow';cell_string{2} = '\fontsize{16} \fontname{隶书}镇定时间';cell_string{3} = '\fontsize{6} ';cell_string{4} = ['\fontsize{14}\rmt_{s} = ' num2str(ts)];text(ts, 0.85, cell_string, 'Color', 'b', 'HorizontalAlignment', 'Center')title('\fontsize{14}\it y = 1 - e^{ -\alpha t}cos{\omegat}')xlabel('\fontsize{14} \bft \rightarrow')ylabel('\fontsize{14} \bfy \rightarrow')

14. 三维曲面属性设置

 close allclear; clc; %% 光照[X, Y, Z] = sphere(40);colormap(jet)subplot(1, 2, 1)surf(X, Y, Z)axis equal offshading interplight ('position', [0 -10 1.5], 'style', 'infinite')lighting phongmaterial shinysubplot(1, 2, 2)surf(X, Y, Z, -Z)axis equal offshading flatlightlighting flatlight('position', [-1, -1, -2], 'color', 'y')light('position', [-1, 0.5, 1], 'style', 'local', 'color', 'w')set(gcf, 'Color', 'w') %% 镂空clear; clc;                  [X0, Y0, Z0] = sphere(30);X = 2*X0;Y = 2*Y0;Z = 2*Z0;surf(X0, Y0, Z0);shading interphold onmesh(X,Y,Z)colormap(hot)hold offhidden offaxis equalaxis off
 
 
 

15. 获取坐标轴范围

limit = axisxlim = get(gca, 'xLim')ylim = get(gca, 'YLim')

16. 查找绘图对象

% 查找 figureclear; clc; close all;x = linspace(0, 2*pi, 20);y = sin(x);figure(1)plot(x, y);figure(2)plot(x, y, x, y + 1, '--');figs = findobj('Type', 'figure') % 查找线型为 '--' 的线lines = findobj('Type', 'line', 'LineStyle', '--')

17. 格式化显示

fprintf('%07.4f\n', 2.334)% 02.3340fprintf('%07d\n', 2)% 0000002num2str(5.5, '%07.4f')% ans = '05.5000'num2str(5.5, '%06.4f')% ans = '5.5000'num2str(2, '%06d')% ans = '000002'

18. 刻度显示为 10^4 形式

set(gca, 'xlim', [0 10e4]);set(gca, 'xlim', [0 10e5]);

19. colorbar 设置指数上标

clear;clc;[x, y, z] = peaks(30);z = z / 1000;surf(x, y, z);cb = colorbar;cb.Ruler.Exponent = -3;

20. 坐标轴铺满 figure

clear;clc;close all;x = 0 : 0.1 : 5;y1 = sin(2*x);y2 = cos(3*x);figureplot(x, y1, 'o:', 'LineWidth', 2)xlabel('x');ylabel('y');set(gca, 'looseInset', [0 0 0 0]);figureplot(x, y2, 'o:', 'LineWidth', 2)xlabel('x');ylabel('y');set(gca, 'Position', [0.1 0.1 0.85 0.85]);

21. 设置多种 colormap

close allclear; clc; %%[x, y, z] = peaks(30);figure; %%plot1 = subplot(1,2,1);surf(x, y, z); % 设置第一幅图颜色显示为 springcolormap(plot1,spring); %% plot2 = subplot(1,2,2);surf(x, y, z);% 下面设置的是第二幅图的颜色colormap(plot2,winter);

22. 制作 GIF 动图

close allclear; clc; x = 0:0.01:1;n = 1:9;len = length(n);im = cell(1, len);% 单独显示每个图figure;for idx = 1:len    subplot(3, 3, idx)    plot(x, x.^idx, 'LineWidth',3)    title(['y = x^', num2str(idx)])end% 获取绘制对象fig = figure;for idx = 1:len    y = x.^idx;    plot(x, y, 'LineWidth', 3)    title(['y = x^', num2str(n(idx))])    % drawnow    % pause(0.1);    frame = getframe(fig);    im{idx} = frame2im(frame);end% 输出文件名filename = 'testAnimated.gif';for idx = 1:len    % 制作gif文件，图像必须是index索引图像    [A, map] = rgb2ind(im{idx}, 256);    if idx == 1        imwrite(A, map, filename, 'gif', 'LoopCount', Inf, 'DelayTime', 0.3);    else        imwrite(A, map, filename, 'gif', 'WriteMode', 'append', 'DelayTime', 0.3);    endend

% 读取图像clear;clc;% 保存文件名filename = 'Model.gif';% 4张图for i = 1:4    % 图片路径    fileName = [num2str(i), '.jpg'];    img = imread(fileName);    % 重定义尺寸    img = imresize(img, [256, 256]);    imshow(img);    % 不显示窗口    set(gcf, 'visible', 'off');    % 获取位置    q = get(gca, 'position');    % 设置左边距离值为零    q(1) = 0;    % 设置右边距离值为零    q(2) = 0;    % 重新设置位置    set(gca, 'position', q);    frame = getframe(gcf, [0, 0, 200, 200]);    im = frame2im(frame);    imshow(im);    [I, map] = rgb2ind(im, 256);    if i == 1        imwrite(I, map, filename, 'gif', 'Loopcount', inf, 'DelayTime', 0.3);    else        imwrite(I, map, filename, 'gif', 'WriteMode', 'append', 'DelayTime', 0.3);    endend

23. 绘制带有误差线的柱状图

clear;clc;close all;% 获取到颜色[all_themes, all_colors] = GetColors();% 生成示例数据m = 5;n = 3;x = 1:m;y = rand(m, n) + 2;% 误差限neg = rand(m, n);pos = rand(m, n);% 单系列带有误差线的柱状图figure;bar(x, y(:, 1));hold onerrorbar(x, y(:, 1), neg(:, 1), pos(:, 1), 'LineStyle', 'none', 'Color', 'k', 'LineWidth', 2);hold off% 多系列带有误差线的柱状图figure;% 绘制柱状图h = bar(x, y);% 设置每个系列颜色for i = 1:length(h)    h(1, i).FaceColor = all_colors(i, :);end% 单独设置第二个系列第二个柱子颜色% 这行代码少不了h(1, 2).FaceColor = 'flat';h(1, 2).CData(2,:) = all_colors(6, :); % 获取误差线 x 值 % 也就是 XEndPoints 的值xx = zeros(m, n);for i = 1 : n    xx(:, i) = h(1, i).XEndPoints'; end% 绘制误差线hold onerrorbar(xx, y, neg, pos, 'LineStyle', 'none', 'Color', 'k', 'LineWidth', 2);hold off% 绘制图例legend({'A1', 'A2', 'A3'});% 设置 x 轴标签set(gca, 'XTickLabel', {'label1', 'label2', 'label3', 'label4', 'label5'});% 试试 barwebfigure;barweb(y, neg, 1, {'label1', 'label2', 'label3', 'label4', 'label5'});

24. OLE 方式写入 Excel

clear;clc;% 设置文件保存路径filepath = [pwd, '\test.xlsx'];   % 检查 Excel 是否已经打开try    % 若 Excel 服务器已经打开，返回其句柄    excel = actxGetRunningServer('Excel.Application');catch    % 创建一个Microsoft Excel 服务器     excel = actxserver('Excel.Application'); end% 设置 excel 属性为可见，0表示不可见% set(excel, 'Visible', 1);excel.Visible = 0; % 取消保存提示excel.DisplayAlerts = false;   % 检查文件是否存在if exist(filepath, 'file')    workbook = excel.Workbooks.Open(filepath);    % workbook = invoke(excel.Workbooks, 'Open', filepath);else    workbook = excel.Workbooks.Add;    % workbook = invoke(excel.Workbooks, 'Add');    workbook.SaveAs(filepath);end% 当前工作表句柄sheets = excel.ActiveWorkbook.Sheets;    % sheets = workbook.Sheets;% 返回第1个Sheet句柄sheet1 = sheets.Item(1);% 激活第1个表格sheet1.Activate;   % 修改第1个Sheet的名字sheet1.Name = 'test sheet1';  % 页面设置% 上边距5磅sheet1.PageSetup.TopMargin = 5;      % 下边距10磅sheet1.PageSetup.BottomMargin = 10;  % 左边距15磅sheet1.PageSetup.LeftMargin = 15;   % 右边距20磅sheet1.PageSetup.RightMargin = 20;       % 设置行高和列宽% 定义行高向量RowHeightsheet1.Range('A1:A4').RowHeight = [40, 20, 40, 20];sheet1.Range('A1:C1').ColumnWidth = [30, 10, 40, 20];% 合并单元格sheet1.Range('A1:C1').MergeCells = 1;sheet1.Range('A3:C3').MergeCells = 1;% 设置单元格的边框sheet1.Range('A1:B1').Borders.Weight = 3;sheet1.Range('A4:C4').Borders.Item(3).Linestyle = 0;sheet1.Range('A4:C4').Borders.Item(4).Linestyle = 0;% 设置单元格对齐方式sheet1.Range('A1:B3').HorizontalAlignment = 3;sheet1.Range('C1:C3').VerticalAlignment = 1;% 写入单元格内容sheet1.Range('A1').Value = '写入内容1';sheet1.Range('A3').Value = '写入内容2';% 设置字号sheet1.Range('A1:B3').Font.size = 11; sheet1.Range('A1').Font.size = 16;        sheet1.Range('A1').Font.bold = 2;         % 如果当前工作文档中有图形存在，通过循环将图形全部删除shape = sheet1.Shapes;   % 返回文档中Shape对象的个数shapeCount = shape.Count;   % while shapeCount > 0% shape.Item(1).Delete; % endif shapeCount ~= 0    for i = 1 : shapeCount        shape.Item(1).Delete;      endend% 插入图形% 生成一个Figurefig = figure;% 设置 fig 尺寸且不可见set(fig, 'Position', [400, 400, 300, 300], 'visible', 'off')% z = peaks(40); % 这么写图片空白peaks(40);     % 图形复制hgexport(fig, '-clipboard');% 图形粘贴% 选中 sheet1 的 D3 单元格，插入直方图sheet1.Range('D3').Select;sheet1.Paste;    % sheet1.PasteSpecial;% 删除图形句柄delete(fig);   % 保存文档workbook.Save;   workbook.Close;excel.Quit;

25. OLE 方式写入 Word

clear;clc;% Matlab 操作 Word 文档% 设置文件保存路径filepath = [pwd, '\test.docx'];  % 检查 Word 是否已经打开try    % 若 Word 服务器已经打开，返回其句柄    word = actxGetRunningServer('Word.Application');catch    % 创建一个Microsoft Word服务器    word = actxserver('Word.Application'); end% 设置 word 属性为可见，0表示不可见% set(word, 'Visible', 1);word.Visible = 1;    % 检查文件是否存在if exist(filepath, 'file')    document = word.Documents.Open(filepath);     else    document = word.Documents.Add;         document.SaveAs2(filepath);end% 句柄获取content = document.Content;selection = word.Selection;    paragraphFormat = selection.ParagraphFormat;  % 页面设置% 上边距60磅document.PageSetup.TopMargin = 60;  % 下边距45磅document.PageSetup.BottomMargin = 45;   % 左边距45磅document.PageSetup.LeftMargin = 45;     % 右边距45磅document.PageSetup.RightMargin = 45;       % 标题content.Text = 'test word';% 设置文档内容的起始位置content.Start = 0;     % 设置字号为16content.Font.Size = 16 ;   % 字体加粗content.Font.Bold = 4 ;    % 居中对齐content.Paragraphs.Alignment = 'wdAlignParagraphCenter';    % 设置下面内容的起始位置selection.Start = content.end;   % 回车，另起一段selection.TypeParagraph;    % 在当前位置输入文字内容selection.Text = '文字内容1';  % 设置字号为12selection.Font.Size = 12;   % 字体不加粗selection.Font.Bold = 0;    % 光标下移（取消选中）selection.MoveDown;         % 居中对齐paragraphFormat.Alignment = 'wdAlignParagraphCenter';    selection.TypeParagraph;    selection.TypeParagraph;    selection.Font.Size = 11; % 在光标所在位置插入一个 4 行 3 列的表格tables = document.Tables.Add(selection.Range, 4, 3);    % 返回第1个表格的句柄table = tables;% table = document.Tables.Item(1); % 设置表格边框table.Borders.OutsideLineStyle = 'wdLineStyleSingle';table.Borders.OutsideLineWidth = 'wdLineWidth150pt';table.Borders.InsideLineStyle = 'wdLineStyleSingle';table.Borders.InsideLineWidth = 'wdLineWidth150pt';table.Rows.Alignment = 'wdAlignRowCenter';table.Rows.Item(2).Borders.Item(1).LineStyle = 'wdLineStyleNone';% 设置表格列宽和行高columnWidth = [50, 50, 200];    rowHeight = [20, 25, 20, 200];    for i = 1 : 3    table.Columns.Item(i).Width = columnWidth(i);end% 设置表格的行高for i = 1 : 4    table.Rows.Item(i).Height = rowHeight(i);end% 设置每个单元格的垂直对齐方式for i = 1 : 4    for j = 1 : 3        table.Cell(i,j).VerticalAlignment = 'wdCellAlignVerticalCenter';    endend% 合并单元格table.Cell(1, 2).Merge(table.Cell(1, 3));table.Cell(2, 2).Merge(table.Cell(3, 3));table.Cell(4, 1).Merge(table.Cell(4, 3));selection.Start = content.end;    selection.TypeParagraph;         selection.Text = '文字内容2';    % 右对齐paragraphFormat.Alignment = 'wdAlignParagraphRight';    selection.MoveDown;   % 写入表格内容table.Cell(1, 1).Range.Text = '内容1';table.Cell(3, 1).Range.Text = '内容2';table.Cell(1, 1).Range.ParagraphFormat.Alignment = 'wdAlignParagraphLeft';table.Cell(3, 1).VerticalAlignment = 'wdCellAlignVerticalTop';table.Cell(1, 1).Borders.Item(2).LineStyle = 'wdLineStyleNone';table.Cell(1, 1).Borders.Item(4).LineStyle = 'wdLineStyleNone';% 如果当前工作文档中有图形存在，通过循环将图形全部删除shape = document.Shapes;  % 返回文档中Shape对象的个数shapeCount = shape.Count;   if shapeCount ~= 0    for i = 1 : shapeCount        shape.Item(1).Delete;      endendfig = figure;% 设置 fig 尺寸且不可见set(fig, 'Position', [400, 400, 300, 300], 'visible', 'off')% z = peaks(40); % 这么写图片空白peaks(40);      % 图形复制hgexport(fig, '-clipboard');% 图形粘贴% Selection.Range.PasteSpecial;table.Cell(8,1).Range.Paragraphs.Item(1).Range.Paste;% 删除图形句柄delete(fig);    % 设置视图方式为页面document.ActiveWindow.ActivePane.View.Type = 'wdPrintView'; % 保存文档document.Save;     document.Close;word.Quit;

26. SVD 解病态线性方程组

clear;clc;% 创建一个典型的病态矩阵：Hilbert矩阵N = 15;a = repmat(1:N, N, 1);A = 1 ./ (a + a' - 1);cd = cond(A);% 输出条件数disp(cd);rng('default');% 随机生成一组解x = rand(N,1);% 生成常数项y = A*x;% 左除x0 = A\y;y0 = A*x0;% SVD分解[u,s,v] = svd(A);% 方法一：去掉极小奇异值lemt = 1e-7;s1 = diag(1 ./ s(s > lemt));s1(N,N) = 0;x1 = v*s1*u'*y;y1 = A*x1;% 方法二：添加正则项s2 = diag(1./(diag(s)+lemt*ones(N,1)));x2 = v*s2*u'*y;y2 = A*x2;% 结果比较：disp([x, x0, x1, x2]);disp([y, y0, y1, y2]);

27. 绘制旋转多边形

clear;clc;close all;m = 3;n = 41;d_angle = 2.25;rotate = 45;shift = [0, 0];figureSpiralPolygon(m, n, d_angle, rotate, shift); m = 4;figureSpiralPolygon(m, n, d_angle, rotate, shift); figure;V = SpiralPolygon(m, n, -d_angle, rotate, shift);hold ondx = max(V(1, :)) - min(V(1, :));dy = max(V(2, :)) - min(V(2, :));shift = [dx, 0];SpiralPolygon(m, n, d_angle, rotate, shift);shift = [dx, dy];SpiralPolygon(m, n, -d_angle, rotate, shift);shift = [0, dy];SpiralPolygon(m, n, d_angle, rotate, shift);hold off function V = SpiralPolygon(m, n, d_angle, rotate, shift)th = linspace(0, 360, m + 1) + rotate;V = [cosd(th); sind(th)];C = colormap(hsv(n));scale = sind(150 - abs(d_angle))/sind(30);R = Rot2(d_angle);% hold offfor i = 1:nif i > 1V = scale * R * V;endplot(V(1,:) + shift(1), V(2,:) + shift(2), 'Color', C(i,:));hold onendset(gcf, 'Color', 'w');axis equalaxis offend function R = Rot2(theta)theta = theta*pi/180;R = [cos(theta), -sin(theta); sin(theta), cos(theta)];end

28. 梯度下降法

clear;clc;%% 一元函数梯度下降法% 示例：f(x) = min{(x - 1)^2}% 梯度：g(x) = 2 * (x - 1)yita = 0.25;   % 学习率，一般设置小一点，否则容易在最小值附近震荡或者不收敛x1 = -5 : 0.1 : 5;y1 = (x1 - 1).^2;iteMax = 1000;xInit = 4;yInit = (xInit - 1)^2;err = 1e-6;figure('Position', [50, 50, 900, 400]);subplot(1, 2, 1)plot(x1, y1, 'b', 'LineWidth', 2)xlim([-5, 5])ylim([-1, 25])hold onplot(xInit, yInit, 'or', 'MarkerFaceColor', 'r')for i = 1 : iteMax    % x = x + yita * grad;    xNew = xInit - yita * 2 * (xInit - 1);    yNew = (xNew - 1)^2;    % 退出条件    if abs(xNew - xInit) < err        break;    else        PlotLineArrow(gca, [xInit, xNew], [yInit, yNew], 'r', 'k')        xInit = xNew;        yInit = yNew;        disp(['第', num2str(i), '次迭代结果：', num2str(xInit)]);        plot(xNew, yNew, 'or', 'MarkerFaceColor', 'r')            endendhold offtitle('梯度下降'); %% 多元函数梯度下降法% 示例：f(x) = min{x1^2 + x2^2}% 梯度：g(x) = [2 * x1; 2 * x2][x, y] = meshgrid(-5:0.5:5, -5:0.5:5);z = x.^2 + y.^2;initX = 4;initY = 3;initZ = initX^2 + initY^2;initValue = [initX; initY];subplot(1, 2, 2)contourf(x, y, z, 20);shading interphold ongrad = zeros(1, 2);e = 0.1;yita = 5;   % Adagrad 更快收敛for i = 1 : iteMax    % 标准的梯度法 x = x + yita * grad;% newValue = initValue - yita * [2 * initX; 2 * initY];    % Adagrad 法 x = x + yita * inv(G) * grad;    grad = grad + [(2 * initX)^2, (2 * initY)^2];    newValue = initValue - yita * diag(1 ./ sqrt(grad + e)) * [2 * initX; 2 * initY];    % 退出条件    if norm(newValue - initValue) < err        break;    else        newX = newValue(1);        newY = newValue(2);        newZ = newX^2 + newY^2;% plot([initX, newX], [initY, newY], '-ok', 'MarkerFaceColor', 'r')        PlotLineArrow(gca, [initX, newX], [initY, newY], 'r', 'k')        initValue = newValue;        initX = newX;        initY = newY;        initZ = newZ;        disp(['第', num2str(i), '次迭代结果：', num2str(newValue')]);        endendhold offtitle('梯度下降'); function PlotLineArrow(obj, x, y, markerColor, lineColor)% 绘制带箭头的曲线% 绘制散点图plot(x, y, 'o', 'Color', markerColor', 'MarkerFaceColor', markerColor);% 获取 Axes 位置posAxes = get(obj, 'Position');posX = posAxes(1);posY = posAxes(2);width = posAxes(3);height = posAxes(4);% 获取 Axes 范围limX = get(obj, 'Xlim');limY = get(obj, 'Ylim');minX = limX(1);maxX = limX(2);minY = limY(1);maxY = limY(2);% 转换坐标xNew = posX + (x - minX) / (maxX - minX) * width;yNew = posY + (y - minY) / (maxY - minY) * height;% 画箭头annotation('arrow', xNew, yNew, 'color', lineColor);end

29. Adagrad 多元非线性回归模型

clear; clc;% z = w1 * exp(-x / w2) + w3 * y + w4% z = 900 * exp(-x / 2) + 50 * y + 10len = 40;rng('default');x = randi(len + 1, len, 1) / 5;y = randi(len + 1, len, 1) / 5;z = 900 * exp(-x / 2) + 50 * y + 10;maxi = max(z);z = z / maxi;ratio = 0.0;z = z + ratio * max(z) * rand(len, 1);X = [x, y];fun = @(var, X)var(1) * exp(-X(:, 1) / var(2)) + var(3) * X(:, 2) + var(4);w = lsqcurvefit(fun, [1, 1, 1, 1], X, z);w([1, 3, 4]) = maxi * w([1, 3, 4]);disp(['lsqcurvefit 计算结果：', num2str(w)]);% 梯度下降法学习% obj = 1 / (2 * len) * (w1 * exp(-x / w2) + w3 * y + w4 - z)' * (w1 * exp(-x / w2) + w3 * y + w4 - z)alpha = 1;   % 学习率大收敛快，可能有震荡iteMax = 10000;w1 = 1;w2 = 1;w3 = 1;w4 = 1;initW = [w1; w2; w3; w4];err = 1e-6;J = zeros(iteMax, 1);G = zeros(size(initW));e = 0.1;for i = 1 : iteMax% gradW1 = 1 / len * (exp(-x / w2))' * (w1 * exp(-x / w2) + w3 * y - z);% gradW2 = 1 / len * (w1 * x .* exp(-x / w2) / w2^2)' * (w1 * exp(-x / w2) + w3 * y - z);% gradW3 = 1 / len * y' * (w1 * exp(-x / w2) + w3 * y - z);% grad = [gradW1; gradW2; gradW3];        gradW1 = exp(-x / w2);        gradW2 = w1 * x .* exp(-x / w2) / w2^2;        gradW3 = y;        gradW4 = ones(len, 1);        grad = 1 / len * [gradW1, gradW2, gradW3, gradW4]' * (w1 * exp(-x / w2) + w3 * y + w4 - z);    % Adagrad 法 x = x + yita * inv(G) * grad;    G = G + grad.^2;    newW = initW - alpha * diag(1 ./ sqrt(G + e)) * grad;    if norm(newW - initW) < err        J(i + 1 : end) = [];        disp(['梯度下降法迭代次数：', num2str(i)]);        newW([1, 3, 4]) = maxi * newW([1, 3, 4]);        disp(['梯度下降法迭代结果：', num2str(newW')]);        break;    else        initW = newW;        w1 = newW(1);        w2 = newW(2);        w3 = newW(3);        w4 = newW(4);        J(i) = 1 / (2 * len) * (w1 * exp(-x / w2) + w3 * y + w4 - z)' * (w1 * exp(-x / w2) + w3 * y + w4 - z);    endend% 绘图figure('Position', [50, 50, 900, 400]);subplot(1, 2, 1)loglog(J, 'LineWidth', 2)legend(['alpha = ', num2str(alpha)]);xFit1 = linspace(min(x), max(x), 30);yFit1 = linspace(min(y), max(y), 30);[xFit2, yFit2] = meshgrid(xFit1, yFit1);zFit = w1 * exp(-xFit2 / w2) + w3 * yFit2 + w4;zFit = maxi * zFit;z = maxi * z;subplot(1, 2, 2)scatter3(x, y, z, 'r', 'filled');hold onsurf(xFit2, yFit2, zFit);hold offtitle('Adagrad 多元非线性回归模型');

30. 积分问题

close allclear; clc;format long;%% 数值积分% sample 1fun1 = @(x) sin(x);result = integral(fun1, 0, pi);fprintf('result=%s\n',result);% result = 2.000000000000000 % sample 2fun2 = @(x) sin(x) ./ x;result = integral(fun2, 0, 1);fprintf('result=%s\n',result);% result = 0.946083070367183 %% 解析解syms x t% sample 3y1 = sin(x);f1 = int(y1, x, 0, t);fprintf('f1=%s\n',f1);  % sample 4y2 = sin(x) / x;f2 = int(y2, x, 0, t);fprintf('f2=%s\n',f2);  f2_val = double(subs(f2, t, 1));% f2_val = 0.946083070367183;f3 = MyIntegral1(fun2, 0, 1, 10000);fprintf('f3=%s\n',f3);% f3 = 0.946083070492669 function result = MyIntegral1(fun, minX, maxX, intervalCount)% fun: 函数句柄% minX: 积分下限% maxX: 积分上限% intervalCount: 积分区间份数% 利用积分的定义来求面积result = 0;h = (maxX - minX) / intervalCount; % 步长for i = 1 : intervalCount    result = result + h * fun(minX + (i - 0.5) * h); % 采用简单矩形公式：面积 = 底 × 高endend

31. 批量导入文件

clear;clc;% 获取路径下所有 png 文件信息all_images = dir('https://www.gofarlic.com\MyPrograms\DataSet\halcon\*.png')% 图片数量image_num = size(all_images, 1)% 遍历图像for i = 1 : image_num    folder = all_images(i).folder    name = all_images(i).name    fullname = fullfile(folder, name)end

32. 浮点数判断相等

   编程过程中经常遇到判断两个浮点数是否相等的情况，此时如果直接用 a == b 来做判断，会导致意想不到的错误，肉眼可见判断为 true，但是程序给你判断为 false，原因在于浮点数在计算机里存储会有一定的精度误差，可采用简单方法：
 

% 判定为相等if abs(a - b) < eps end

33. 标题、标签、注释换行

% 用 cell 类型ylabel({'Normalized'; 'optical intensity'});

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