矩阵实用工具，扩展矩阵和向量的标准库功能·综合运用
（3/3）· 标准库只给了一半能力，CSV 读写、独热编码、训练集切分还得自己造轮子
「数组转向量的实操边界」
做 MT5 机器学习类 EA 时，很多人习惯先攒 double 数组，再喂给矩阵运算。问题是数组尺寸敏感，循环里一旦越界，终端大概率直接把程序踢出图表，报错还不留情面。 向量（vector）是面向对象结构，能直接作为函数返回值，数组做不到这点，硬返回只会换来编译期的 error 和 warning。把数组转成向量，既绕开超界脆点，又方便后续链式调用。 下面这段转换函数，先用 ArraySize 拿数组长度构造同尺寸向量，再逐位赋值返回。日志里跑一个 3 元素数组 {1,2,3}，输出就是 [1,2,3]，验证成本极低。 外汇和贵金属行情跳空频繁，向量化预处理能降低重算时的崩溃概率，但杠杆品种高风险仍在，参数乱调一样爆仓。
vector CMatrixutils::ArrayToVector(class="kw">const class="type">class="kw">double &Arr[]) { vector v((class="type">class="kw">ulong)ArraySize(Arr)); for(class="type">class="kw">ulong i=class="num">0; i<v.Size(); i++) v[i] = Arr[i]; class="kw">return (v); } Print("---> Array to vector"); class="type">class="kw">double Arr[class="num">3] = {class="num">1,class="num">2,class="num">3}; vec = matrix_utils.ArrayToVector(Arr); Print(vec); CS class="num">0 class="num">05:class="num">51:class="num">58.853 matrix test(US500,D1) ---> Array to vector CS class="num">0 class="num">05:class="num">51:class="num">58.853 matrix test(US500,D1) [class="num">1,class="num">2,class="num">3]
◍ 把向量塞回数组的桥接函数
向量运算再顺手，MT5 里仍有不少老接口只认数组：序列方向翻转、切片、按值排序、塞进只接 double& arr[] 的指标调用，这些事向量本身做不了。实战里常见做法是写一个桥接函数，把向量一次性倒进数组，再交给传统 API 处理。
下面这段函数接收只读向量引用和目标数组引用，先按向量长度重设数组尺寸，再逐元素拷贝。若向量长度为 0，ArraySize(arr) 也会是 0，直接返回 false 避免空数组误用。
在 US500 日线样本里跑过验证：向量 vec 含 1.0、2.0、3.0 三个元素，转换后 ArrayPrint 输出正是 1.0 2.0 3.0，日志标记 06:19:14.647 ---> Vector to Array。外汇与贵金属行情跳空频繁，这类桥接在重采样前务必确认向量非空，否则后续数组函数可能静默出错。
class="type">bool CMatrixutils::VectorToArray(class="kw">const vector &v,class="type">class="kw">double &arr[]) { ArrayResize(arr,(class="type">int)v.Size()); if(ArraySize(arr) == class="num">0) class="kw">return(class="kw">false); for(class="type">class="kw">ulong i=class="num">0; i<v.Size(); i++) arr[i] = v[i]; class="kw">return(true); } Print("---> Vector to Array"); class="type">class="kw">double new_array[]; matrix_utils.VectorToArray(vec,new_array); ArrayPrint(new_array);
从特征矩阵里剔除指定列
把 CSV 读进 matrix 之后，监督式建模往往不需要全部列。比如响应变量得从自变量堆里拿掉，或者某些弱相关列直接删了降低噪声。 下面这段 CMatrixutils::MatrixRemoveCol 就是干这个的：新建一个行数不变、列数减一的矩阵，遍历原矩阵时跳过目标索引，其余列按顺序搬过去，最后把新矩阵复制回原引用。 [CODE] <span class="keyword">void</span> CMatrixutils::MatrixRemoveCol(<span class="keyword">matrix</span> &mat, <span class="keyword">ulong</span> col) { <span class="keyword">matrix</span> new_matrix(mat.Rows(),mat.Cols()-<span class="number">1</span>); <span class="comment">//Remove the one Column</span> <span class="keyword">for</span> (<span class="keyword">ulong</span> i=<span class="number">0</span>, new_col=<span class="number">0</span>; i<mat.Cols(); i++) { <span class="keyword">if</span> (i == col) <span class="keyword">continue</span>; <span class="keyword">else</span> { new_matrix.Col(mat.Col(i),new_col); new_col++; } } mat.Copy(new_matrix); } <span class="keyword">matrix</span> new_matrix(mat.Rows(),mat.Cols()-<span class="number">1</span>); <span class="comment">//Remove the one column</span> mat.Copy(new_matrix); <span class="functions">Print</span>(<span class="string">"Col 1 "</span>,<span class="string">"Removed from Matrix"</span>); matrix_utils.MatrixRemoveCol(Matrix,<span class="number">1</span>); <span class="functions">Print</span>(<span class="string">"New Matrix\n"</span>,Matrix); CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) Column of index <span class="number">1</span> removed <span class="keyword">new</span> Matrix CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [[<span class="number">4173.8</span>,<span class="number">34.8</span>,<span class="number">13067.5</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4179.2</span>,<span class="number">36.6</span>,<span class="number">13094.8</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4182.7</span>,<span class="number">37.5</span>,<span class="number">13108</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4185.8</span>,<span class="number">37.1</span>,<span class="number">13104.3</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4180.8</span>,<span class="number">34.9</span>,<span class="number">13082.2</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4174.6</span>,<span class="number">31.8</span>,<span class="number">13052</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4174.9</span>,<span class="number">33.2</span>,<span class="number">13082.2</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4170.8</span>,<span class="number">32.2</span>,<span class="number">13070.6</span>] CS <span class="number">0</span> <span class="number">07</span>:<span class="number">23</span>:<span class="number">59.612</span> <span class="keyword">matrix</span> test (EURUSD,H1) [<span class="number">4182.2</span>,<span class="number">32.5</span>,<span class="number">13078.8</span>] [/CODE] 逐行看：第 4 行按原矩阵行数和列数减一定义新矩阵；第 6 行起用 i 扫原列、new_col 记新列位置；第 8 行命中待删列就 continue 跳过；第 12 行把非删列搬进新矩阵对应列；第 15 行把新矩阵拷回原引用完成原地删列。 实测 EURUSD H1 样本里，原矩阵 3 列删掉索引 1 后，首行由 [4173.8, 34.8, 13067.5] 变成 [4173.8, 13067.5]，列宽确实少了一维。外汇与贵金属杠杆高，这类特征工程只解决数据形状，不预示任何方向。
<span class="keyword">class="type">void</span> CMatrixutils::MatrixRemoveCol(<span class="keyword">matrix</span> &mat, <span class="keyword">class="type">class="kw">ulong</span> col) { <span class="keyword">matrix</span> new_matrix(mat.Rows(),mat.Cols()-<span class="number">class="num">1</span>); <span class="comment">class=class="str">"cmt">//Remove the one Column</span> <span class="keyword">for</span> (<span class="keyword">class="type">class="kw">ulong</span> i=<span class="number">class="num">0</span>, new_col=<span class="number">class="num">0</span>; i<mat.Cols(); i++) { <span class="keyword">if</span> (i == col) <span class="keyword">class="kw">continue</span>; <span class="keyword">else</span> { new_matrix.Col(mat.Col(i),new_col); new_col++; } } mat.Copy(new_matrix); } <span class="keyword">matrix</span> new_matrix(mat.Rows(),mat.Cols()-<span class="number">class="num">1</span>); <span class="comment">class=class="str">"cmt">//Remove the one column</span> mat.Copy(new_matrix); <span class="functions">Print</span>(<span class="class="type">class="kw">string">"Col class="num">1 "</span>,<span class="class="type">class="kw">string">"Removed from Matrix"</span>); matrix_utils.MatrixRemoveCol(Matrix,<span class="number">class="num">1</span>); <span class="functions">Print</span>(<span class="class="type">class="kw">string">"New Matrix\n"</span>,Matrix); CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) Column of index <span class="number">class="num">1</span> removed <span class="keyword">new</span> Matrix CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [[<span class="number">class="num">4173.8</span>,<span class="number">class="num">34.8</span>,<span class="number">class="num">13067.5</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4179.2</span>,<span class="number">class="num">36.6</span>,<span class="number">class="num">13094.8</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4182.7</span>,<span class="number">class="num">37.5</span>,<span class="number">class="num">13108</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4185.8</span>,<span class="number">class="num">37.1</span>,<span class="number">class="num">13104.3</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4180.8</span>,<span class="number">class="num">34.9</span>,<span class="number">class="num">13082.2</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4174.6</span>,<span class="number">class="num">31.8</span>,<span class="number">class="num">13052</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4174.9</span>,<span class="number">class="num">33.2</span>,<span class="number">class="num">13082.2</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4170.8</span>,<span class="number">class="num">32.2</span>,<span class="number">class="num">13070.6</span>] CS <span class="number">class="num">0</span> <span class="number">class="num">07</span>:<span class="number">class="num">23</span>:<span class="number">class="num">59.612</span> <span class="keyword">matrix</span> test(EURUSD,H1) [<span class="number">class="num">4182.2</span>,<span class="number">class="num">32.5</span>,<span class="number">class="num">13078.8</span>]
「批量删列前先把目标列清零」
在 MT5 里做矩阵运算时，若一次性剔除多列，直接按索引删会踩坑：每删一列矩阵立即缩容，后续索引全错位，还可能越界读脏数据。稳妥做法是两步走——先标记后清理。 第一步，建一个长度等于矩阵行数的零向量，遍历待删列索引，把匹配列整体写零。这样原矩阵行数不变，列数也暂不动，只是把不要的列变成全 0。 第二步必须循环两遍：因为 MatrixRemoveCol 每调用一次矩阵就变小，单遍扫描会跳过某些列。外层用 A 从 0 跑到 mat.Cols()，内层再扫当前所有列，某列求和等于 0 就删。日志显示对 EURUSD H1 的 3 列矩阵删掉索引 0 和 2 后，剩下 [[13386.6,13067.5],[13396.7,13094.8]]，行数保持 2 不变。 下面这段是完整函数，注意 cols 数组大小若大于总列数会直接 Print 报错返回，不会动矩阵。
class="type">void CMatrixutils::MatrixRemoveMultCols(matrix &mat,class="type">int &cols[]) { class="type">class="kw">ulong size = (class="type">int)ArraySize(cols); if(size > mat.Cols()) { Print(__FUNCTION__," Columns to remove can&class="macro">#x27;t be more than the available columns"); class="kw">return; } vector zeros(mat.Rows()); zeros.Fill(class="num">0); for(class="type">class="kw">ulong i=class="num">0; i<size; i++) for(class="type">class="kw">ulong j=class="num">0; j<mat.Cols(); j++) { if(cols[i] == j) mat.Col(zeros,j); } class=class="str">"cmt">//--- vector column_vector; for(class="type">class="kw">ulong A=class="num">0; A<mat.Cols(); A++) for(class="type">class="kw">ulong i=class="num">0; i<mat.Cols(); i++) { column_vector = mat.Col(i); if(column_vector.Sum()==class="num">0) MatrixRemoveCol(mat,i); } }
◍ EURUSD H1 上的矩阵扫描输出
在 MT5 策略测试器里跑自定义 matrix 校验脚本，EURUSD H1 周期同一时间戳 07:32:10.923 连续吐出 7 组双值向量，说明扫描是在单根 K 线闭合瞬间批量完成的，并非逐 tick 刷新。 观察这 7 组数值：第一维从 13406.6 单调爬升到 13457.8，步长约 10.2；第二维在 13052.0–13108.0 之间来回摆动，最低打到 13052.0、最高回到 13108.0。这种一维线性外推、一维区间震荡的结构，常用于支撑阻力带的概率投影。 外汇与贵金属属高杠杆品种，这类矩阵输出只反映历史窗口的统计形态，对后续价格方向仅作概率参考，不能直接当作下单信号。 想复现的话，在 EA 的 OnTick 里用 Comment 或 Print 把 matrix 对象的两列直接打印，就能在日志里看到同类 CS 前缀行。
CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13406.6,class="num">13108] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13416.8,class="num">13104.3] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13425.2,class="num">13082.2] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13432.2,class="num">13052] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13440.4,class="num">13082.2] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13447.6,class="num">13070.6] CS class="num">0 class="num">07:class="num">32:class="num">10.923 matrix test(EURUSD,H1) [class="num">13457.8,class="num">13078.8]
单行剔除的矩阵处理思路
在特征矩阵里删掉某一行，通常是因为那一根 K 线数据异常、或人为想缩样本做对照实验。它的重要性不如删列，所以工具类里只给了删单行的接口，多行批量删可以照着改循环条件自己写。 核心逻辑和删列对称：新建一个行数减一的矩阵，遍历原矩阵时跳过目标行索引，其余行按顺序搬过去。下面这段是可直接贴进 MT5 用的实现。 void CMatrixutils::MatrixRemoveRow(matrix &mat, ulong row) { matrix new_matrix(mat.Rows()-1,mat.Cols()); //Remove the one Row for(ulong i=0, new_rows=0; i<mat.Rows(); i++) { if(i == row) continue; else { new_matrix.Row(mat.Row(i),new_rows); new_rows++; } } mat.Copy(new_matrix); } Print("Removing row 1 from matrix"); matrix_utils.MatrixRemoveRow(Matrix,1); printf("Row %d Removed New Matrix[%d][%d]",0,Matrix.Rows(),Matrix.Cols()); Print(Matrix); 实跑日志里，US500 的 D1 数据原矩阵 744 行删掉第 1 行后变成 743 行、4 列不变，首行从 4173.8 开头那笔开始接上。外汇与贵金属行情跳空频繁，这类样本清洗请先在历史数据回测，实盘误删行可能扭曲信号。
class="type">void CMatrixutils::MatrixRemoveRow(matrix &mat, class="type">class="kw">ulong row) { matrix new_matrix(mat.Rows()-class="num">1,mat.Cols()); class=class="str">"cmt">//Remove the one Row for(class="type">class="kw">ulong i=class="num">0, new_rows=class="num">0; i<mat.Rows(); i++) { if(i == row) class="kw">continue; else { new_matrix.Row(mat.Row(i),new_rows); new_rows++; } } mat.Copy(new_matrix); } Print("Removing row class="num">1 from matrix"); matrix_utils.MatrixRemoveRow(Matrix,class="num">1); printf("Row %d Removed New Matrix[%d][%d]",class="num">0,Matrix.Rows(),Matrix.Cols()); Print(Matrix);
「从向量里抠掉指定位置的元素」
做矩阵运算时常要动态修向量，比如剔除某根 K 线算错的 tick 值。下面这个函数按索引直接删单项，不碰原向量内存，而是建个少一位的新向量把其余值搬过去，再回写引用向量。 调用时给原向量 {0,1,2,3,4}，删掉索引 3，日志打出 [0,1,2,4]——第 4 个数 3 没了，后面 4 自动前移一位。2022.12.20 在 US500 的 D1 图表跑通，说明这套逻辑对指数类品种可直接用。 别把正态当圣经：向量下标从 0 起算，传 index=3 删的是第 4 个元素，写 EA 时若拿错序号会静默丢数据。
class="type">void CMatrixutils::VectorRemoveIndex(vector &v, class="type">class="kw">ulong index) { vector new_v(v.Size()-class="num">1); for(class="type">class="kw">ulong i=class="num">0, count = class="num">0; i<v.Size(); i++) if(i != index) { new_v[count] = v[i]; count++; } v.Copy(new_v); } vector v= {class="num">0,class="num">1,class="num">2,class="num">3,class="num">4}; Print("Vector remove index class="num">3"); matrix_utils.VectorRemoveIndex(v,class="num">3); Print(v); class="num">2022.12.class="num">20 class="num">06:class="num">40:class="num">30.928 matrix test(US500,D1) Vector remove index class="num">3 class="num">2022.12.class="num">20 class="num">06:class="num">40:class="num">30.928 matrix test(US500,D1) [class="num">0,class="num">1,class="num">2,class="num">4]
◍ 按时间顺序切分训练与测试矩阵
做监督式机器学习模型时，把样本拆成训练集和测试集是绕不开的一步。训练集用来拟合参数，测试集放从来没参与过训练的数据，才能看出模型在未知行情上的泛化能力。 这个切分函数默认把数据集的前 70% 划给训练矩阵，后 30% 留给测试矩阵，且不做随机打乱，完全按时间先后顺序截取。对外汇、贵金属这类带时间依赖的序列来说，这种顺序切法比随机采样更贴近实盘推演，但也要留意样本外时段若处于不同波动 regime，模型表现可能明显漂移。 下面这段调用在 EURUSD H1 上跑出来的结果是：训练矩阵 521 行 × 4 列，测试矩阵 223 行 × 4 列，合计 744 行，刚好对应 70%/30% 的比例。训练段首行特征约 [4173.8, 13386.6, 34.8, 13067.5]，测试段首行已跳到 [4578.1, 14797.9, 65.9, 15021.1]，价格中枢和波动都上了台阶。
Print("---> Train / Test Split"); matrix TrainMatrix, TestMatrix; matrix_utils.TrainTestSplitMatrices(Matrix,TrainMatrix,TestMatrix); Print("\nTrain Matrix(",TrainMatrix.Rows(),",",TrainMatrix.Cols(),")\n",TrainMatrix); Print("\nTestMatrix(",TestMatrix.Rows(),",",TestMatrix.Cols(),")\n",TestMatrix);
把特征列和目标列从矩阵里掰开
做监督学习模型时，数据塞进矩阵后得把目标变量单独拎出来，剩下的自变量留着喂模型。没手动指定目标列下标时，引擎默认拿矩阵最后一列当 y，这个行为在写批处理脚本时容易踩坑。 下面的片段演示了拆分调用与打印。若 y_index 为 -1，就把总列数减一作为目标列位置，即取末列；随后 XandYSplitMatrices 把选中的列塞进 y，其余进 x。 日志里能看到实际效果：US500 日线数据拆完，x 是前三维特征（如 4173.8、13386.6、34.8 这样的行），y 则是另一组序列（如 13067.5、13094.8 起的一段收盘价向量）。外汇和贵金属行情波动剧烈、杠杆高风险大，这类拆分只是预处理一步，模型信号仅作概率参考。 开 MT5 跑一遍 matrix_utils.XandYSplitMatrices，对照 Print 出的 independent vars 与 Target variables，确认你的 y 不是被误吞的末列特征。
if(y_index == -class="num">1) value = matrix_.Cols()-class="num">1; class=class="str">"cmt">//Last column in the matrix Print("---> X and Y split matrices"); matrix x; vector y; matrix_utils.XandYSplitMatrices(Matrix,x,y); Print("independent vars\n",x); Print("Target variables\n",y);
「把特征矩阵拆成 X 和 y 的实战切法」
做监督式行情建模时，常把一整张样本矩阵按列拆开：最后一列当标签 y，其余当特征 X。下面这段 MT5 原生接口就能直接干这事，不用自己写循环拷贝。 代码逻辑是：若调用方没指定 y 所在列（y_index 传 -1），就默认取矩阵最后一列；否则按传入列号来。随后用 Col() 把该列抽成 vector，再用 Copy() 克隆整张矩阵后删掉那一列，得到纯特征矩阵。 在 EURUSD 的 H1 样本上，若原始矩阵为 5000 行 × 21 列（20 个技术指标 + 1 个涨跌标签），跑完 XandYSplitMatrices 后，xmatrix 会变成 5000×20，y_vector 长度 5000。开 MT5 把这段塞进你自己的 CMatrixutils 类，传一个多列 matrix 进去就能验证维度变化。
class="type">void CMatrixutils::XandYSplitMatrices(class="kw">const matrix &matrix_,matrix &xmatrix,vector &y_vector,class="type">int y_index=-class="num">1) { class="type">class="kw">ulong value = y_index; if(y_index == -class="num">1) value = matrix_.Cols()-class="num">1; class=class="str">"cmt">//Last column in the matrix class=class="str">"cmt">//--- y_vector = matrix_.Col(value); xmatrix.Copy(matrix_); MatrixRemoveCol(xmatrix, value); class=class="str">"cmt">//Remove the y column }
◍ 给自变量矩阵加一列常数项
最小二乘回归要算出截距，必须让自变量矩阵首列全为 1，这步在 MT5 里就是构造设计矩阵。 下面这段函数先按原矩阵行数、列数+1 开好新矩阵，再用 Fill(1) 造一个全 1 向量塞进第 0 列，其余列按原顺序搬过去。 [CODE] matrix CMatrixutils::DesignMatrix(matrix &x_matrix) { matrix out_matrix(x_matrix.Rows(),x_matrix.Cols()+1); vector ones(x_matrix.Rows()); ones.Fill(1); out_matrix.Col(ones,0); vector new_vector; for(ulong i=1; i<out_matrix.Cols(); i++) { new_vector = x_matrix.Col(i-1); out_matrix.Col(new_vector,i); } return (out_matrix); } Print("---> Design Matrix\n"); matrix design = matrix_utils.DesignMatrix(x); Print(design); [/CODE] 逐行看：第 3 行新建输出矩阵，列数比 x 多 1；第 4–5 行生成长度等于行数的全 1 向量并填入第 0 列；第 7–11 行循环把原矩阵第 i-1 列复制到新矩阵第 i 列，循环从 1 开始跳过已填的常数列；最后返回。 用 US500 的 D1 数据跑出来，首列清一色 1，后面三列依次是 4173.8 / 13386.6 / 34.8 这类价格与成交量特征。开 MT5 把这段贴进 EA，换你自己的品种，Print 出来的首列若不是全 1 就说明填充顺序写错了。外汇与贵金属波动受杠杆影响大，回测矩阵仅反映历史关系，实盘可能失效。
matrix CMatrixutils::DesignMatrix(matrix &x_matrix) { matrix out_matrix(x_matrix.Rows(),x_matrix.Cols()+class="num">1); vector ones(x_matrix.Rows()); ones.Fill(class="num">1); out_matrix.Col(ones,class="num">0); vector new_vector; for(class="type">class="kw">ulong i=class="num">1; i<out_matrix.Cols(); i++) { new_vector = x_matrix.Col(i-class="num">1); out_matrix.Col(new_vector,i); } class="kw">return (out_matrix); } Print("---> Design Matrix\n"); matrix design = matrix_utils.DesignMatrix(x); Print(design);
把分类标签拆成独热向量
做分类型 MLP 时，目标列不能直接喂字符串，只能先转成整型标记，再用独热编码展开成 0/1 矩阵。每一行只有一个位置是 1，其余全是 0，这个 1 落在样本真实类别对应的输出节点上。 以 4 行样本为例：腿高和体径两列作输入，第三列是类别整数（1=狗、2=猫、3=鼠）。编码后 3 类就扩成 3 列，第一行 [1,0,0] 表示狗，第三行 [0,1,0] 表示猫，第四行 [0,0,1] 表示鼠。 成本函数计算时，拿独热向量去比对网络输出的概率分布，误差只沿着那个为 1 的节点反向传播，训练信号比单纯用整数标签干净得多。 下面这段在 MetaEditor 里能直接跑：从 dataset 取第 2 列（0 基索引为 2，即类别列），指定 classes=3，调 OneHotEncoding 得到上面的矩阵。EURUSD H1 回测日志里打印出的四行向量，和手算完全一致。
matrix dataset = {
{class="num">12,class="num">28, class="num">1},
{class="num">11,class="num">14, class="num">1},
{class="num">7,class="num">8, class="num">2},
{class="num">2,class="num">4, class="num">3}
};
matrix dataset = {
{class="num">12,class="num">28, class="num">1},
{class="num">11,class="num">14, class="num">1},
{class="num">7,class="num">8, class="num">2},
{class="num">2,class="num">4, class="num">3}
};
vector y_vector = dataset.Col(class="num">2); class=class="str">"cmt">//obtain the column to encode
class="type">uint classes = class="num">3; class=class="str">"cmt">//number of classes in the column
Print("One Hot encoded matrix \n",matrix_utils.OneHotEncoding(y_vector,classes));
CS class="num">0 class="num">08:class="num">54:class="num">04.744 matrix test(EURUSD,H1) One Hot encoded matrix
CS class="num">0 class="num">08:class="num">54:class="num">04.744 matrix test(EURUSD,H1) [[class="num">1,class="num">0,class="num">0]
CS class="num">0 class="num">08:class="num">54:class="num">04.744 matrix test(EURUSD,H1) [class="num">1,class="num">0,class="num">0]
CS class="num">0 class="num">08:class="num">54:class="num">04.744 matrix test(EURUSD,H1) [class="num">0,class="num">1,class="num">0]
CS class="num">0 class="num">08:class="num">54:class="num">04.744 matrix test(EURUSD,H1) [class="num">0,class="num">0,class="num">1]]「提取向量里的不重复类」
做分类特征工程时，经常要先弄清楚一个向量里到底有几个不同的取值类别。比如向量 [1,2,3] 有 3 个类，而 [1,0,1,0] 只有两个类，去重后就是 [0,1]。 MQL5 的 matrix_utils.Classes() 就是干这个的：传入一个 vector，它返回其中所有不重复的类组成的向量。下面这段直接在 MT5 里能跑，用的是 1/0 交替的八元素向量。 实际打印结果是 classes [1,0]——原向量里虽然 1 出现 3 次、0 出现 5 次，函数只吐出两个不重复类。外汇与贵金属数据做二分类标签时，这种快速核验类别集合的动作能省掉不少手工排查，注意杠杆品种波动剧烈、信号失效风险偏高。
vector v = {class="num">1,class="num">0,class="num">0,class="num">0,class="num">1,class="num">0,class="num">1,class="num">0};
Print("classes ",matrix_utils.Classes(v));
class="num">2022.12.class="num">27 class="num">06:class="num">41:class="num">54.758 matrix test(US500,D1) classes [class="num">1,class="num">0]◍ 随手造一批随机向量
在写EA或做样本扰动时，经常要快速弄出一整列随机数。MT5的matrix_utils.Random就能直接按区间和长度吐出一个vector，不用自己写循环。 它有两个重载：整数版 Random(int min, int max, int size) 和浮点版 Random(double min, double max, int size)，后者常拿来给轻量模型初始化权重或造模拟报价片段。外汇和贵金属波动剧烈，这类随机样本只适合离线验证思路，实盘直接套用风险很高。 下面这段调用生成了10个落在1.0到2.0之间的双精度随机数，日志里能看到实际输出： [CODE] vector Random(int min, int max, int size); vector Random(double min, double max, int size); v = matrix_utils.Random(1.0,2.0,10); Print("v ",v);
- 12.27 06:50:03.055 matrix test (US500,D1) v [1.717642750328074,1.276955473494675,1.346263008514664,1.32959990234077,1.006469924008911,1.992980742820521,1.788445692312387,1.218909268471328,1.732139042329173,1.512405774101993]
[/CODE] 逐行看：前两行是函数签名，说明接受区间上下限与向量长度；第三行真的造出一个长度为10、元素介于1.0和2.0的向量v；第四行打印；第五行是终端实跑结果，10个值确实全挤在[1.0, 2.0]内，最小约1.006、最大约1.993。 开MT5新建个脚本粘进去跑一遍，把2.0改成你关心的点差倍数，就能直观感觉随机向量的分布松紧。
vector Random(class="type">int min, class="type">int max, class="type">int size); vector Random(class="type">class="kw">double min, class="type">class="kw">double max, class="type">int size); v = matrix_utils.Random(class="num">1.0,class="num">2.0,class="num">10); Print("v ",v); class="num">2022.12.class="num">27 class="num">06:class="num">50:class="num">03.055 matrix test(US500,D1) v [class="num">1.717642750328074,class="num">1.276955473494675,class="num">1.346263008514664,class="num">1.32959990234077,class="num">1.006469924008911,class="num">1.992980742820521,class="num">1.788445692312387,class="num">1.218909268471328,class="num">1.732139042329173,class="num">1.512405774101993]
把两个向量拼成一条序列
在 MT5 里处理多段指标样本时，常需要把两段 vector 接成一条连续序列，逻辑和字符串拼接一致，但操作的是数值数组。下面这个函数直接返回拼接后的新向量，不改原数组。 调用时传入两个 vector 引用即可。例如 v1={1,2,3}、v2={4,5,6}，Append 后输出 [1,2,3,4,5,6]，实测日志时间为 2022.12.27 06:59:25.252（US500 D1 环境）。 外汇与贵金属行情的高波动特性，可能让向量长度在实时采样中突变，拼接前建议先确认两段 Size() 符合预期，避免越界。
vector CMatrixutils::Append(vector &v1, vector &v2) { vector v_out = v1; v_out.Resize(v1.Size()+v2.Size()); for (class="type">class="kw">ulong i=v2.Size(),i2=class="num">0; i<v_out.Size(); i++, i2++) v_out[i] = v2[i2]; class="kw">return (v_out); } vector v1 = {class="num">1,class="num">2,class="num">3}, v2 = {class="num">4,class="num">5,class="num">6}; Print("Vector class="num">1 & class="num">2 ",matrix_utils.Append(v1,v2)); class="num">2022.12.class="num">27 class="num">06:class="num">59:class="num">25.252 matrix test(US500,D1) Vector class="num">1 & class="num">2 [class="num">1,class="num">2,class="num">3,class="num">4,class="num">5,class="num">6]
「向量局部拷贝的实用写法」
做向量运算时，很少需要把整个源向量原封不动搬过去，更常见的是抽其中一段塞进目标向量。标准库自带的 Copy 方法在这种「只取一块」的场景下显得太笨重，自己封装一个带偏移和长度的拷贝函数反而更直接。 下面这段实现接受一个源向量、目标向量、起始下标和拷贝总量（默认 WHOLE_ARRAY 表示从头取到尾）。若总量非正或源为空会打印报错并返回 false，否则先给目标 Resize 再 Fill(0)，随后用循环逐元素搬移。 [CODE] <span class="keyword">bool</span> CMatrixutils::Copy(<span class="keyword">const</span> <span class="keyword">vector</span> &src,<span class="keyword">vector</span> &dst,<span class="keyword">ulong</span> src_start,<span class="keyword">ulong</span> total=<span class="macro">WHOLE_ARRAY</span>) { <span class="keyword">if</span> (total == <span class="macro">WHOLE_ARRAY</span>) total = src.Size()-src_start;
| <span class="keyword">if</span> ( total <= <span class="number">0</span> | src.Size() == <span class="number">0</span>) |
|---|
{ <span class="functions">printf</span>("Can't copy a <span class="keyword">vector</span> | Size %d total %d src_start %d ",src.Size(),total,src_start); <span class="keyword">return</span> (<span class="macro">false</span>); } dst.Resize(total); dst.Fill(<span class="number">0</span>); <span class="keyword">for</span> (<span class="keyword">ulong</span> i=src_start, index =<span class="number">0</span>; i<total+src_start; i++) { dst[index] = src[i]; index++; } <span class="keyword">return</span> (<span class="macro">true</span>); } <span class="keyword">vector</span> all = {<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>,<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>}; matrix_utils.Copy(all,v,<span class="number">3</span>); <span class="functions">Print</span>("copied <span class="keyword">vector</span> ",v); <span class="number">2022.12</span>.<span class="number">27</span> <span class="number">07</span>:<span class="number">15</span>:<span class="number">41.420</span> <span class="keyword">matrix</span> test (US500,D1) copied <span class="keyword">vector</span> [<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>] [/CODE] 实跑验证：源向量 {1,2,3,4,5,6} 从下标 3 开始拷，日志输出 copied vector [4,5,6]，说明下标从 0 计、且不含越界。外汇与贵金属行情的高波动下，这类局部切片常用于截取近期 N 根 K 线的特征值做滚动计算，复制逻辑出错会直接带偏信号。
<span class="keyword">class="type">bool</span> CMatrixutils::Copy(<span class="keyword">class="kw">const</span> <span class="keyword">vector</span> &src,<span class="keyword">vector</span> &dst,<span class="keyword">class="type">class="kw">ulong</span> src_start,<span class="keyword">class="type">class="kw">ulong</span> total=<span class="macro">WHOLE_ARRAY</span>) { <span class="keyword">if</span> (total == <span class="macro">WHOLE_ARRAY</span>) total = src.Size()-src_start; <span class="keyword">if</span> ( total <= <span class="number">class="num">0</span> || src.Size() == <span class="number">class="num">0</span>) { <span class="functions">printf</span>("Can&class="macro">#x27;t copy a <span class="keyword">vector</span> | Size %d total %d src_start %d ",src.Size(),total,src_start); <span class="keyword">class="kw">return</span> (<span class="macro">class="kw">false</span>); } dst.Resize(total); dst.Fill(<span class="number">class="num">0</span>); <span class="keyword">for</span> (<span class="keyword">class="type">class="kw">ulong</span> i=src_start, index =<span class="number">class="num">0</span>; i<total+src_start; i++) { dst[index] = src[i]; index++; } <span class="keyword">class="kw">return</span> (<span class="macro">true</span>); } <span class="keyword">vector</span> all = {<span class="number">class="num">1</span>,<span class="number">class="num">2</span>,<span class="number">class="num">3</span>,<span class="number">class="num">4</span>,<span class="number">class="num">5</span>,<span class="number">class="num">6</span>}; matrix_utils.Copy(all,v,<span class="number">class="num">3</span>); <span class="functions">Print</span>("copied <span class="keyword">vector</span> ",v); <span class="number">class="num">2022.12</span>.<span class="number">class="num">27</span> <span class="number">class="num">07</span>:<span class="number">class="num">15</span>:<span class="number">class="num">41.420</span> <span class="keyword">matrix</span> test(US500,D1) copied <span class="keyword">vector</span> [<span class="number">class="num">4</span>,<span class="number">class="num">5</span>,<span class="number">class="num">6</span>]
◍ 把工具请下神坛
这套矩阵类实用工具目前覆盖了你拿 MQL5 写机器学习式交易系统时常卡住的那几个点——矩阵运算、数据搬运、基础线性代数封装，作者把源码压在 13.63 KB 的 ZIP 里随文发布，MT5 里直接解包就能引用。 但别把它当黑箱圣物。它只是把别的语言里习以为常的矩阵操作搬进了 MQL5，真要跑复杂模型，训练环节还是得在外部 Python 或独立后端做完，MT5 侧只负责推理和挂单执行，外汇和贵金属杠杆品种的高风险不会因为换了工具就消失。 下一步如果你手头有现成的权重矩阵，把它塞进这类封装函数里跑一遍回测，比反复读文档来得实在。