{"id":89078,"date":"2026-08-02T11:40:32","date_gmt":"2026-08-02T03:40:32","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/89078.html"},"modified":"2026-08-02T11:40:32","modified_gmt":"2026-08-02T03:40:32","slug":"python-numpy-%e9%ab%98%e7%ba%a7%e6%8a%80%e5%b7%a7","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/89078.html","title":{"rendered":"Python-numpy-\u9ad8\u7ea7\u6280\u5de7"},"content":{"rendered":"

NumPy \u9ad8\u7ea7\u6280\u5de7<\/h2>\n

🧠 \u5411\u91cf\u5316\u601d\u7ef4<\/h3>\n

NumPy \u7684\u7cbe\u9ad3\u4e0d\u662f\u7528 ndarray \u5b58\u6570\u636e，\u800c\u662f\u7528\u5411\u91cf\u5316\u64cd\u4f5c\u4ee3\u66ff\u5faa\u73af\u3002<\/p>\n

\u53cd\u6a21\u5f0f vs \u6700\u4f73\u5b9e\u8df5<\/h4>\n

import<\/span> numpy as<\/span> np<\/p>\n

data =<\/span> np.<\/span>random.<\/span>rand(<\/span>1000000<\/span>)<\/span><\/p>\n

# \u274c \u5faa\u73af（Python \u7ea7\u522b，\u6781\u6162）<\/span>
\nresult =<\/span> np.<\/span>empty_like(<\/span>data)<\/span>
\nfor<\/span> i in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>data)<\/span>)<\/span>:<\/span>
\n result[<\/span>i]<\/span> =<\/span> np.<\/span>sin(<\/span>data[<\/span>i]<\/span>)<\/span> if<\/span> data[<\/span>i]<\/span> ><\/span> 0.5<\/span> else<\/span> np.<\/span>cos(<\/span>data[<\/span>i]<\/span>)<\/span><\/p>\n

# \u2705 \u5411\u91cf\u5316（C \u7ea7\u522b）<\/span>
\nmask =<\/span> data ><\/span> 0.5<\/span>
\nresult =<\/span> np.<\/span>where(<\/span>mask,<\/span> np.<\/span>sin(<\/span>data)<\/span>,<\/span> np.<\/span>cos(<\/span>data)<\/span>)<\/span><\/p>\n

# \u901f\u5ea6\u5dee 10~100 \u500d<\/span><\/p>\n

\u66f4\u591a\u4f8b\u5b50<\/h4>\n

# \u274c \u9010\u5143\u7d20\u5904\u7406<\/span>
\nsquared =<\/span> np.<\/span>array(<\/span>[<\/span>x**<\/span>2<\/span> for<\/span> x in<\/span> data]<\/span>)<\/span><\/p>\n

# \u2705<\/span>
\nsquared =<\/span> data **<\/span> 2<\/span><\/p>\n

# \u274c \u624b\u52a8\u8ba1\u7b97\u884c\u5747\u503c<\/span>
\nmeans =<\/span> np.<\/span>zeros(<\/span>len<\/span>(<\/span>mat)<\/span>)<\/span>
\nfor<\/span> i in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>mat)<\/span>)<\/span>:<\/span>
\n means[<\/span>i]<\/span> =<\/span> mat[<\/span>i]<\/span>.<\/span>mean(<\/span>)<\/span><\/p>\n

# \u2705<\/span>
\nmeans =<\/span> mat.<\/span>mean(<\/span>axis=<\/span>1<\/span>)<\/span><\/p>\n

\n

🎯 np.einsum \u2014 \u7231\u56e0\u65af\u5766\u6c42\u548c\u7ea6\u5b9a \u2b50<\/h3>\n

einsum \u662f\u6700\u5f3a\u5927\u5374\u5e38\u88ab\u5ffd\u89c6\u7684\u51fd\u6570\u3002\u5b83\u7528\u7b80\u6d01\u7684\u5b57\u7b26\u4e32\u8868\u8fbe\u5f0f\u63cf\u8ff0\u4efb\u610f\u5f20\u91cf\u8fd0\u7b97\u3002<\/p>\n

\u57fa\u672c\u8bed\u6cd5<\/h4>\n

# np.einsum(subscripts, *operands)<\/span>
\n# subscripts: '\u8f93\u51651\u8f74\u6807\u7b7e, \u8f93\u51652\u8f74\u6807\u7b7e -> \u8f93\u51fa\u8f74\u6807\u7b7e'<\/span><\/p>\n

\u7ecf\u5178\u8fd0\u7b97<\/h4>\n

a =<\/span> np.<\/span>random.<\/span>rand(<\/span>3<\/span>,<\/span> 4<\/span>)<\/span>
\nb =<\/span> np.<\/span>random.<\/span>rand(<\/span>4<\/span>,<\/span> 5<\/span>)<\/span>
\nv =<\/span> np.<\/span>random.<\/span>rand(<\/span>3<\/span>,<\/span> 4<\/span>)<\/span>
\nw =<\/span> np.<\/span>random.<\/span>rand(<\/span>4<\/span>)<\/span><\/p>\n

# \u77e9\u9635\u4e58\u6cd5<\/span>
\nC =<\/span> np.<\/span>einsum(<\/span>'ij,jk->ik'<\/span>,<\/span> a,<\/span> b)<\/span> # = a @ b<\/span><\/p>\n

# \u9010\u5143\u7d20\u4e58\u6cd5<\/span>
\nC =<\/span> np.<\/span>einsum(<\/span>'ij,ij->ij'<\/span>,<\/span> a,<\/span> v)<\/span> # = a * v<\/span><\/p>\n

# \u70b9\u79ef<\/span>
\ns =<\/span> np.<\/span>einsum(<\/span>'i,i->'<\/span>,<\/span> w,<\/span> w)<\/span> # = w @ w<\/span><\/p>\n

# \u5916\u79ef<\/span>
\nC =<\/span> np.<\/span>einsum(<\/span>'i,j->ij'<\/span>,<\/span> w,<\/span> w)<\/span> # = np.outer(w, w)<\/span><\/p>\n

# \u8f6c\u7f6e<\/span>
\nC =<\/span> np.<\/span>einsum(<\/span>'ij->ji'<\/span>,<\/span> a)<\/span> # = a.T<\/span><\/p>\n

# \u5bf9\u89d2\u7ebf<\/span>
\nd =<\/span> np.<\/span>einsum(<\/span>'ii->i'<\/span>,<\/span> a)<\/span> # = np.diag(a)（\u53d6 3\u00d74 \u7684\u4e3b\u5bf9\u89d2\u7ebf）<\/span><\/p>\n

# \u8ff9<\/span>
\nt =<\/span> np.<\/span>einsum(<\/span>'ii->'<\/span>,<\/span> a)<\/span> # = np.trace(a)<\/span><\/p>\n

# \u6309\u884c\u6c42\u548c<\/span>
\nrow_sum =<\/span> np.<\/span>einsum(<\/span>'ij->i'<\/span>,<\/span> a)<\/span> # = a.sum(axis=1)<\/span><\/p>\n

# \u6309\u5217\u6c42\u548c<\/span>
\ncol_sum =<\/span> np.<\/span>einsum(<\/span>'ij->j'<\/span>,<\/span> a)<\/span> # = a.sum(axis=0)<\/span><\/p>\n

# \u6240\u6709\u5143\u7d20\u6c42\u548c<\/span>
\ntotal =<\/span> np.<\/span>einsum(<\/span>'ij->'<\/span>,<\/span> a)<\/span> # = a.sum()<\/span><\/p>\n

\u9ad8\u7ea7 einsum<\/h4>\n

# \u6279\u91cf\u77e9\u9635\u4e58\u6cd5<\/span>
\nA =<\/span> np.<\/span>random.<\/span>rand(<\/span>10<\/span>,<\/span> 3<\/span>,<\/span> 4<\/span>)<\/span> # batch=10<\/span>
\nB =<\/span> np.<\/span>random.<\/span>rand(<\/span>10<\/span>,<\/span> 4<\/span>,<\/span> 5<\/span>)<\/span>
\nC =<\/span> np.<\/span>einsum(<\/span>'bij,bjk->bik'<\/span>,<\/span> A,<\/span> B)<\/span> # (10, 3, 5)<\/span><\/p>\n

# \u6ce8\u610f\u529b\u5206\u6570（QK^T \/ sqrt(d)）<\/span>
\nQ =<\/span> np.<\/span>random.<\/span>rand(<\/span>32<\/span>,<\/span> 100<\/span>,<\/span> 64<\/span>)<\/span> # (batch, seq, d_k)<\/span>
\nK =<\/span> np.<\/span>random.<\/span>rand(<\/span>32<\/span>,<\/span> 100<\/span>,<\/span> 64<\/span>)<\/span>
\nscores =<\/span> np.<\/span>einsum(<\/span>'bqd,bkd->bqk'<\/span>,<\/span> Q,<\/span> K)<\/span> \/<\/span> np.<\/span>sqrt(<\/span>64<\/span>)<\/span><\/p>\n

# \u5f20\u91cf\u6536\u7f29（Tensor Contraction）<\/span>
\nX =<\/span> np.<\/span>random.<\/span>rand(<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 4<\/span>,<\/span> 5<\/span>)<\/span>
\nY =<\/span> np.<\/span>random.<\/span>rand(<\/span>5<\/span>,<\/span> 6<\/span>)<\/span>
\nZ =<\/span> np.<\/span>einsum(<\/span>'abcd,de->abce'<\/span>,<\/span> X,<\/span> Y)<\/span> # (2, 3, 4, 6)<\/span><\/p>\n

\u7701\u7565\u53f7 … \u5728 einsum \u4e2d<\/h4>\n

# \u5904\u7406\u4efb\u610f\u7ef4\u5ea6\u7684\u5f20\u91cf<\/span>
\nX =<\/span> np.<\/span>random.<\/span>rand(<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 4<\/span>,<\/span> 5<\/span>)<\/span><\/p>\n

# \u5bf9\u6700\u540e\u4e24\u7ef4\u505a\u77e9\u9635\u4e58\u6cd5<\/span>
\nZ =<\/span> np.<\/span>einsum(<\/span>'…ij,…jk->…ik'<\/span>,<\/span> X,<\/span> X)<\/span> # (2, 3, 4, 4)<\/span><\/p>\n

\n

🏗\ufe0f \u7ed3\u6784\u5316\u6570\u7ec4（Structured Arrays）<\/h3>\n

\u5b58\u50a8\u5f02\u6784\u6570\u636e（\u7c7b\u4f3c\u6570\u636e\u5e93\u8868\u7684\u884c），\u6bcf\u5217\u53ef\u4e0d\u540c\u7c7b\u578b\u3002<\/p>\n

# \u5b9a\u4e49\u7ed3\u6784\u5316 dtype<\/span>
\ndtype =<\/span> np.<\/span>dtype(<\/span>[<\/span>
\n (<\/span>'name'<\/span>,<\/span> 'U20'<\/span>)<\/span>,<\/span> # Unicode \u5b57\u7b26\u4e32，\u6700\u957f 20 \u5b57\u7b26<\/span>
\n (<\/span>'age'<\/span>,<\/span> 'i4'<\/span>)<\/span>,<\/span> # 32 \u4f4d\u6574\u6570<\/span>
\n (<\/span>'score'<\/span>,<\/span> 'f8'<\/span>)<\/span>,<\/span> # 64 \u4f4d\u6d6e\u70b9\u6570<\/span>
\n (<\/span>'passed'<\/span>,<\/span> '?'<\/span>)<\/span> # \u5e03\u5c14\u503c<\/span>
\n]<\/span>)<\/span><\/p>\n

# \u521b\u5efa\u7ed3\u6784\u5316\u6570\u7ec4<\/span>
\nstudents =<\/span> np.<\/span>array(<\/span>[<\/span>
\n (<\/span>'\u5f20\u4e09'<\/span>,<\/span> 20<\/span>,<\/span> 92.5<\/span>,<\/span> True<\/span>)<\/span>,<\/span>
\n (<\/span>'\u674e\u56db'<\/span>,<\/span> 22<\/span>,<\/span> 78.0<\/span>,<\/span> True<\/span>)<\/span>,<\/span>
\n (<\/span>'\u738b\u4e94'<\/span>,<\/span> 21<\/span>,<\/span> 55.0<\/span>,<\/span> False<\/span>)<\/span>,<\/span>
\n (<\/span>'\u8d75\u516d'<\/span>,<\/span> 23<\/span>,<\/span> 88.5<\/span>,<\/span> True<\/span>)<\/span>,<\/span>
\n]<\/span>,<\/span> dtype=<\/span>dtype)<\/span><\/p>\n

# \u8bbf\u95ee<\/span>
\nprint<\/span>(<\/span>students[<\/span>'name'<\/span>]<\/span>)<\/span> # ['\u5f20\u4e09' '\u674e\u56db' '\u738b\u4e94' '\u8d75\u516d']<\/span>
\nprint<\/span>(<\/span>students[<\/span>'age'<\/span>]<\/span>.<\/span>mean(<\/span>)<\/span>)<\/span> # 21.5<\/span>
\nprint<\/span>(<\/span>students[<\/span>students[<\/span>'passed'<\/span>]<\/span>]<\/span>)<\/span> # \u53ea\u53d6\u901a\u8fc7\u7684\u5b66\u751f<\/span>
\nprint<\/span>(<\/span>students[<\/span>students[<\/span>'score'<\/span>]<\/span> ><\/span> 60<\/span>]<\/span>[<\/span>'name'<\/span>]<\/span>)<\/span> # \u53ca\u683c\u7684\u59d3\u540d<\/span><\/p>\n

# \u6392\u5e8f<\/span>
\nsorted_by_score =<\/span> np.<\/span>sort(<\/span>students,<\/span> order=<\/span>'score'<\/span>)<\/span>[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>
\nprint<\/span>(<\/span>sorted_by_score[<\/span>'name'<\/span>]<\/span>)<\/span> # \u6309\u5206\u6570\u964d\u5e8f<\/span><\/p>\n

\u5d4c\u5957 dtype<\/h4>\n

# \u5d4c\u5957\u7ed3\u6784<\/span>
\ndtype =<\/span> np.<\/span>dtype(<\/span>[<\/span>
\n (<\/span>'id'<\/span>,<\/span> 'i4'<\/span>)<\/span>,<\/span>
\n (<\/span>'position'<\/span>,<\/span> [<\/span>
\n (<\/span>'x'<\/span>,<\/span> 'f8'<\/span>)<\/span>,<\/span>
\n (<\/span>'y'<\/span>,<\/span> 'f8'<\/span>)<\/span>,<\/span>
\n (<\/span>'z'<\/span>,<\/span> 'f8'<\/span>)<\/span>
\n ]<\/span>)<\/span>,<\/span>
\n (<\/span>'color'<\/span>,<\/span> [<\/span>
\n (<\/span>'r'<\/span>,<\/span> 'u1'<\/span>)<\/span>,<\/span>
\n (<\/span>'g'<\/span>,<\/span> 'u1'<\/span>)<\/span>,<\/span>
\n (<\/span>'b'<\/span>,<\/span> 'u1'<\/span>)<\/span>
\n ]<\/span>)<\/span>
\n]<\/span>)<\/span><\/p>\n

points =<\/span> np.<\/span>zeros(<\/span>100<\/span>,<\/span> dtype=<\/span>dtype)<\/span>
\npoints[<\/span>'position'<\/span>]<\/span>[<\/span>'x'<\/span>]<\/span> =<\/span> np.<\/span>random.<\/span>rand(<\/span>100<\/span>)<\/span>
\npoints[<\/span>'position'<\/span>]<\/span>[<\/span>'y'<\/span>]<\/span> =<\/span> np.<\/span>random.<\/span>rand(<\/span>100<\/span>)<\/span><\/p>\n

\n

🎭 \u63a9\u7801\u6570\u7ec4（Masked Arrays）<\/h3>\n

\u5904\u7406\u542b\u7f3a\u5931\u503c \/ \u65e0\u6548\u503c\u7684\u6570\u636e\u3002<\/p>\n

import<\/span> numpy.<\/span>ma as<\/span> ma<\/p>\n

# \u521b\u5efa\u63a9\u7801\u6570\u7ec4<\/span>
\ndata =<\/span> np.<\/span>array(<\/span>[<\/span>1<\/span>,<\/span> 2<\/span>,<\/span> –<\/span>999<\/span>,<\/span> 4<\/span>,<\/span> –<\/span>999<\/span>,<\/span> 6<\/span>]<\/span>)<\/span>
\nmasked =<\/span> ma.<\/span>masked_where(<\/span>data ==<\/span> –<\/span>999<\/span>,<\/span> data)<\/span>
\n# \u6216: masked = ma.masked_values(data, -999)<\/span><\/p>\n

print<\/span>(<\/span>masked)<\/span>
\n# [1 2 — 4 — 6]<\/span><\/p>\n

# \u7edf\u8ba1\u81ea\u52a8\u5ffd\u7565\u63a9\u7801\u503c<\/span>
\nprint<\/span>(<\/span>masked.<\/span>mean(<\/span>)<\/span>)<\/span> # 3.25（\u800c\u975e\u5305\u62ec -999）<\/span>
\nprint<\/span>(<\/span>masked.<\/span>std(<\/span>)<\/span>)<\/span> # \u5ffd\u7565\u63a9\u7801\u7684\u6807\u51c6\u5dee<\/span>
\nprint<\/span>(<\/span>masked.<\/span>sum<\/span>(<\/span>)<\/span>)<\/span><\/p>\n

# \u586b\u5145\u63a9\u7801\u503c<\/span>
\nfilled =<\/span> masked.<\/span>filled(<\/span>0<\/span>)<\/span> # \u63a9\u7801\u66ff\u6362\u4e3a 0<\/span>
\nprint<\/span>(<\/span>filled)<\/span> # [1 2 0 4 0 6]<\/span><\/p>\n

# \u521b\u5efa\u63a9\u7801<\/span>
\nmask =<\/span> np.<\/span>array(<\/span>[<\/span>False<\/span>,<\/span> False<\/span>,<\/span> True<\/span>,<\/span> False<\/span>,<\/span> False<\/span>,<\/span> False<\/span>]<\/span>)<\/span>
\nmasked =<\/span> ma.<\/span>array(<\/span>data,<\/span> mask=<\/span>mask)<\/span><\/p>\n

# \u8986\u76d6\u63a9\u7801<\/span>
\nmasked[<\/span>0<\/span>]<\/span> =<\/span> ma.<\/span>masked # \u624b\u52a8\u6807\u8bb0\u4e3a\u7f3a\u5931<\/span><\/p>\n

\u4e8c\u7ef4\u63a9\u7801\u6570\u7ec4<\/h4>\n

# \u4ee5\u6761\u4ef6\u521b\u5efa\u63a9\u7801<\/span>
\ndata =<\/span> np.<\/span>random.<\/span>randn(<\/span>5<\/span>,<\/span> 5<\/span>)<\/span>
\ndata[<\/span>0<\/span>,<\/span> 0<\/span>]<\/span> =<\/span> np.<\/span>nan
\ndata[<\/span>2<\/span>,<\/span> 3<\/span>]<\/span> =<\/span> np.<\/span>nan<\/p>\n

# \u81ea\u52a8\u5c4f\u853d NaN<\/span>
\nmasked =<\/span> ma.<\/span>masked_invalid(<\/span>data)<\/span><\/p>\n

print<\/span>(<\/span>masked.<\/span>mean(<\/span>)<\/span>)<\/span> # \u5ffd\u7565 NaN<\/span>
\nprint<\/span>(<\/span>masked.<\/span>mean(<\/span>axis=<\/span>0<\/span>)<\/span>)<\/span> # \u6bcf\u5217\u5747\u503c（\u5ffd\u7565 NaN）<\/span><\/p>\n

# \u83b7\u53d6\u63a9\u7801\u77e9\u9635<\/span>
\nprint<\/span>(<\/span>masked.<\/span>mask)<\/span> # True = \u88ab\u5c4f\u853d<\/span><\/p>\n

\n

🔬 Strides \u2014 \u7406\u89e3\u5185\u5b58\u5e03\u5c40<\/h3>\n

arr =<\/span> np.<\/span>arange(<\/span>12<\/span>)<\/span>.<\/span>reshape(<\/span>3<\/span>,<\/span> 4<\/span>)<\/span>.<\/span>astype(<\/span>np.<\/span>int64)<\/span>
\nprint<\/span>(<\/span>arr.<\/span>strides)<\/span> # (32, 8)<\/span>
\n# axis=0: \u8de8 32 \u5b57\u8282 = 4 \u4e2a int64<\/span>
\n# axis=1: \u8de8 8 \u5b57\u8282 = 1 \u4e2a int64<\/span><\/p>\n

# C-order (row-major): \u6700\u540e\u4e00\u7ef4\u6b65\u957f\u6700\u5c0f<\/span>
\n# [[ 0 1 2 3]<\/span>
\n# [ 4 5 6 7]<\/span>
\n# [ 8 9 10 11]]<\/span>
\n# \u5185\u5b58\u4e2d: [0 1 2 3 4 5 6 7 8 9 10 11] \u2190 \u4e00\u884c\u4e00\u884c<\/span><\/p>\n

# Fortran-order (column-major): \u7b2c\u4e00\u7ef4\u6b65\u957f\u6700\u5c0f<\/span>
\narr_f =<\/span> np.<\/span>asfortranarray(<\/span>np.<\/span>arange(<\/span>12<\/span>)<\/span>.<\/span>reshape(<\/span>3<\/span>,<\/span> 4<\/span>)<\/span>.<\/span>astype(<\/span>np.<\/span>int64)<\/span>)<\/span>
\nprint<\/span>(<\/span>arr_f.<\/span>strides)<\/span> # (8, 24)<\/span>
\n# \u5185\u5b58\u4e2d: [0 4 8 1 5 9 2 6 10 3 7 11] \u2190 \u4e00\u5217\u4e00\u5217<\/span><\/p>\n

\u5229\u7528 strides \u505a\u6280\u5de7\u6027\u64cd\u4f5c<\/h4>\n

# \u521b\u5efa\u6b65\u8fdb\u6570\u7ec4（\u65e0\u9700\u590d\u5236）<\/span>
\nfrom<\/span> numpy.<\/span>lib.<\/span>stride_tricks import<\/span> as_strided,<\/span> sliding_window_view<\/p>\n

# \u6ed1\u52a8\u7a97\u53e3（NumPy 1.20+）<\/span>
\narr =<\/span> np.<\/span>arange(<\/span>10<\/span>)<\/span>
\nwindows =<\/span> np.<\/span>lib.<\/span>stride_tricks.<\/span>sliding_window_view(<\/span>arr,<\/span> window_shape=<\/span>3<\/span>)<\/span>
\nprint<\/span>(<\/span>windows.<\/span>shape)<\/span> # (8, 3)<\/span>
\n# [[0 1 2]<\/span>
\n# [1 2 3]<\/span>
\n# …<\/span>
\n# [7 8 9]]<\/span><\/p>\n

# \u5e94\u7528\u4e8e\u4e8c\u7ef4<\/span>
\nmat =<\/span> np.<\/span>arange(<\/span>25<\/span>)<\/span>.<\/span>reshape(<\/span>5<\/span>,<\/span> 5<\/span>)<\/span>
\npatches =<\/span> np.<\/span>lib.<\/span>stride_tricks.<\/span>sliding_window_view(<\/span>mat,<\/span> (<\/span>2<\/span>,<\/span> 2<\/span>)<\/span>)<\/span>
\nprint<\/span>(<\/span>patches.<\/span>shape)<\/span> # (4, 4, 2, 2) \u2014 4\u00d74 \u4e2a 2\u00d72 \u7684\u5757<\/span><\/p>\n

\n

\u26a1 \u6027\u80fd\u4f18\u5316\u6e05\u5355<\/h3>\n

1. \u907f\u514d Python \u5faa\u73af<\/h4>\n

# \u274c<\/span>
\nresult =<\/span> np.<\/span>array(<\/span>[<\/span>np.<\/span>mean(<\/span>mat[<\/span>i,<\/span> :<\/span>]<\/span>)<\/span> for<\/span> i in<\/span> range<\/span>(<\/span>mat.<\/span>shape[<\/span>0<\/span>]<\/span>)<\/span>]<\/span>)<\/span><\/p>\n

# \u2705<\/span>
\nresult =<\/span> mat.<\/span>mean(<\/span>axis=<\/span>1<\/span>)<\/span><\/p>\n

2. \u4f7f\u7528 ufunc \u4ee3\u66ff\u81ea\u5b9a\u4e49\u51fd\u6570<\/h4>\n

# \u274c<\/span>
\nresult =<\/span> np.<\/span>array(<\/span>[<\/span>1<\/span> \/<\/span> x if<\/span> x !=<\/span> 0<\/span> else<\/span> 0<\/span> for<\/span> x in<\/span> data]<\/span>)<\/span><\/p>\n

# \u2705<\/span>
\nresult =<\/span> np.<\/span>divide(<\/span>1<\/span>,<\/span> data,<\/span> where=<\/span>data !=<\/span> 0<\/span>,<\/span> out=<\/span>np.<\/span>zeros_like(<\/span>data)<\/span>)<\/span><\/p>\n

3. \u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u6570\u636e\u590d\u5236<\/h4>\n

# \u274c \u94fe\u5f0f\u64cd\u4f5c\u6bcf\u6b65\u521b\u5efa\u4e34\u65f6\u6570\u7ec4<\/span>
\nresult =<\/span> (<\/span>arr *<\/span> 2<\/span> +<\/span> 1<\/span>)<\/span>.<\/span>mean(<\/span>)<\/span><\/p>\n

# \u2705 numexpr \/ numba \u53ef\u51cf\u5c11\u4e2d\u95f4\u4f53（\u6216\u8005\u76f4\u63a5\u63a5\u53d7，\u5f71\u54cd\u4e0d\u5927）<\/span>
\n# NumPy 2.0+ \u4f18\u5316\u4e86\u8fd9\u4e2a，\u4f46\u4ecd\u9700\u6ce8\u610f<\/span><\/p>\n

4. \u7528 out \u53c2\u6570\u7701\u5185\u5b58<\/h4>\n

result =<\/span> np.<\/span>empty_like(<\/span>a)<\/span>
\nnp.<\/span>multiply(<\/span>a,<\/span> b,<\/span> out=<\/span>result)<\/span> # \u7ed3\u679c\u76f4\u63a5\u5199\u5165 result<\/span><\/p>\n

5. \u6279\u91cf\u64cd\u4f5c\u4ee3\u66ff\u5c0f\u64cd\u4f5c<\/h4>\n

# \u274c \u9010\u884c\u5904\u7406<\/span>
\nfor<\/span> i in<\/span> range<\/span>(<\/span>mat.<\/span>shape[<\/span>0<\/span>]<\/span>)<\/span>:<\/span>
\n mat[<\/span>i]<\/span> =<\/span> mat[<\/span>i]<\/span> \/<\/span> mat[<\/span>i]<\/span>.<\/span>sum<\/span>(<\/span>)<\/span><\/p>\n

# \u2705 \u6279\u91cf\u64cd\u4f5c<\/span>
\nmat =<\/span> mat \/<\/span> mat.<\/span>sum<\/span>(<\/span>axis=<\/span>1<\/span>,<\/span> keepdims=<\/span>True<\/span>)<\/span><\/p>\n

6. \u6570\u636e\u5bf9\u9f50（\u5185\u5b58\u8fde\u7eed\u6027）<\/h4>\n

# \u68c0\u67e5\u5185\u5b58\u662f\u5426\u8fde\u7eed<\/span>
\nprint<\/span>(<\/span>arr.<\/span>flags[<\/span>'C_CONTIGUOUS'<\/span>]<\/span>)<\/span> # C \u8fde\u7eed<\/span>
\nprint<\/span>(<\/span>arr.<\/span>flags[<\/span>'F_CONTIGUOUS'<\/span>]<\/span>)<\/span> # Fortran \u8fde\u7eed<\/span><\/p>\n

# \u5982\u679c\u4e0d\u8fde\u7eed，\u67d0\u4e9b\u64cd\u4f5c\u53ef\u80fd\u53d8\u6162<\/span>
\narr =<\/span> np.<\/span>ascontiguousarray(<\/span>arr)<\/span> # \u5f3a\u5236 C \u8fde\u7eed<\/span>
\narr =<\/span> np.<\/span>asfortranarray(<\/span>arr)<\/span> # \u5f3a\u5236 Fortran \u8fde\u7eed<\/span><\/p>\n

\n

🔧 \u81ea\u5b9a\u4e49 ufunc<\/h3>\n

# \u7528 frompyfunc \u521b\u5efa ufunc（\u6bd4 Python \u5faa\u73af\u5feb，\u4f46\u4ecd\u4e0d\u5982\u5185\u7f6e ufunc）<\/span>
\ndef<\/span> my_func<\/span>(<\/span>x)<\/span>:<\/span>
\n return<\/span> x**<\/span>2<\/span> +<\/span> 3<\/span>*<\/span>x +<\/span> 1<\/span><\/p>\n

my_ufunc =<\/span> np.<\/span>frompyfunc(<\/span>my_func,<\/span> nin=<\/span>1<\/span>,<\/span> nout=<\/span>1<\/span>)<\/span>
\nresult =<\/span> my_ufunc(<\/span>np.<\/span>arange(<\/span>10<\/span>)<\/span>)<\/span>
\nprint<\/span>(<\/span>result.<\/span>dtype)<\/span> # object（frompyfunc \u603b\u662f\u8fd4\u56de object \u7c7b\u578b）<\/span><\/p>\n

# \u5f3a\u8f6c\u7c7b\u578b<\/span>
\nresult =<\/span> result.<\/span>astype(<\/span>np.<\/span>float64)<\/span><\/p>\n

# \u66f4\u597d\u7684\u505a\u6cd5\u662f\u7528 vectorize<\/span>
\n@np.<\/span>vectorize<\/span>
\ndef<\/span> my_vec_func<\/span>(<\/span>x)<\/span>:<\/span>
\n return<\/span> x**<\/span>2<\/span> +<\/span> 3<\/span>*<\/span>x +<\/span> 1<\/span><\/p>\n

result =<\/span> my_vec_func(<\/span>np.<\/span>arange(<\/span>10<\/span>)<\/span>)<\/span>.<\/span>astype(<\/span>np.<\/span>float64)<\/span><\/p>\n

\u26a0\ufe0f frompyfunc \u548c vectorize \u672c\u8d28\u4ecd\u662f Python \u5faa\u73af，\u53ea\u662f\u8bed\u6cd5\u7cd6\u3002\u8ffd\u6c42\u6781\u81f4\u6027\u80fd\u5e94\u76f4\u63a5\u7528 NumPy \u5185\u7f6e ufunc \u6216 Numba\u3002<\/p>\n

\n

💡 \u5b9e\u7528\u5c0f\u6280\u5de7<\/h3>\n

\u627e\u5230\u6ee1\u8db3\u6761\u4ef6\u7684\u7b2c\u4e00\u4e2a\/\u6700\u540e\u4e00\u4e2a\u7d22\u5f15<\/h4>\n

arr =<\/span> np.<\/span>array(<\/span>[<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>,<\/span> 0<\/span>,<\/span> 4<\/span>]<\/span>)<\/span><\/p>\n

# \u7b2c\u4e00\u4e2a >1 \u7684\u7d22\u5f15<\/span>
\nfirst =<\/span> np.<\/span>argmax(<\/span>arr ><\/span> 1<\/span>)<\/span> # 3<\/span>
\n# \u6700\u540e\u4e00\u4e2a \u22600 \u7684\u7d22\u5f15<\/span>
\nlast =<\/span> len<\/span>(<\/span>arr)<\/span> –<\/span> 1<\/span> –<\/span> np.<\/span>argmax(<\/span>(<\/span>arr !=<\/span> 0<\/span>)<\/span>[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>)<\/span> # 6<\/span>
\n# \u6216\u7528 where<\/span>
\nindices =<\/span> np.<\/span>where(<\/span>arr ><\/span> 1<\/span>)<\/span>[<\/span>0<\/span>]<\/span>
\nfirst,<\/span> last =<\/span> indices[<\/span>0<\/span>]<\/span>,<\/span> indices[<\/span>–<\/span>1<\/span>]<\/span><\/p>\n

\u5206\u7bb1\u7edf\u8ba1<\/h4>\n

# bincount: \u6574\u6570\u5206\u7bb1\u8ba1\u6570（\u6bd4 np.histogram \u5feb）<\/span>
\ndata =<\/span> np.<\/span>random.<\/span>randint(<\/span>0<\/span>,<\/span> 10<\/span>,<\/span> 100000<\/span>)<\/span>
\ncounts =<\/span> np.<\/span>bincount(<\/span>data)<\/span> # [0-9 \u7684\u51fa\u73b0\u6b21\u6570]<\/span>
\nprint<\/span>(<\/span>counts)<\/span> # [10001 10023 9945 …]<\/span><\/p>\n

# bincount + weights: \u6309\u7bb1\u6c42\u548c<\/span>
\nvalues =<\/span> np.<\/span>random.<\/span>rand(<\/span>100000<\/span>)<\/span>
\nsums =<\/span> np.<\/span>bincount(<\/span>data,<\/span> weights=<\/span>values)<\/span>
\nmeans =<\/span> sums \/<\/span> counts # \u6bcf\u7c7b\u7684\u5747\u503c<\/span><\/p>\n

\u552f\u4e00\u503c\u6620\u5c04（\u66ff\u4ee3 pandas factorize）<\/h4>\n

labels =<\/span> np.<\/span>array(<\/span>[<\/span>'cat'<\/span>,<\/span> 'dog'<\/span>,<\/span> 'bird'<\/span>,<\/span> 'cat'<\/span>,<\/span> 'dog'<\/span>,<\/span> 'fish'<\/span>]<\/span>)<\/span><\/p>\n

# \u8fd4\u56de\u552f\u4e00\u503c\u548c\u7f16\u7801<\/span>
\nunique,<\/span> inverse =<\/span> np.<\/span>unique(<\/span>labels,<\/span> return_inverse=<\/span>True<\/span>)<\/span>
\nprint<\/span>(<\/span>unique)<\/span> # ['bird' 'cat' 'dog' 'fish']（\u5df2\u6392\u5e8f）<\/span>
\nprint<\/span>(<\/span>inverse)<\/span> # [1 2 0 1 2 3] \u2014 \u6bcf\u4e2a\u5143\u7d20\u5728 unique \u4e2d\u7684\u7d22\u5f15<\/span><\/p>\n

\u591a\u7ef4\u6570\u7ec4\u7684 argpartition（Top-K）<\/h4>\n

arr =<\/span> np.<\/span>array(<\/span>[<\/span>3<\/span>,<\/span> 1<\/span>,<\/span> 4<\/span>,<\/span> 1<\/span>,<\/span> 5<\/span>,<\/span> 9<\/span>,<\/span> 2<\/span>,<\/span> 6<\/span>]<\/span>)<\/span><\/p>\n

# \u627e\u524d 3 \u5927\u7684\u503c（\u4e0d\u4fdd\u8bc1\u6392\u5e8f，\u4f46\u6bd4 argsort \u5feb\u5f97\u591a）<\/span>
\nindices =<\/span> np.<\/span>argpartition(<\/span>arr,<\/span> –<\/span>3<\/span>)<\/span>[<\/span>–<\/span>3<\/span>:<\/span>]<\/span>
\nprint<\/span>(<\/span>arr[<\/span>indices]<\/span>)<\/span> # [5 9 6]（\u4e0d\u4e00\u5b9a\u6709\u5e8f）<\/span><\/p>\n

# \u786e\u4fdd\u6709\u5e8f<\/span>
\ntop_k_indices =<\/span> np.<\/span>argpartition(<\/span>arr,<\/span> –<\/span>3<\/span>)<\/span>[<\/span>–<\/span>3<\/span>:<\/span>]<\/span>
\ntop_k_indices =<\/span> top_k_indices[<\/span>np.<\/span>argsort(<\/span>arr[<\/span>top_k_indices]<\/span>)<\/span>[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>]<\/span>
\nprint<\/span>(<\/span>arr[<\/span>top_k_indices]<\/span>)<\/span> # [9 6 5]（\u5df2\u6392\u5e8f）<\/span><\/p>\n

\u6570\u7ec4\u7684\u5c5e\u6027\u8d4b\u503c<\/h4>\n

arr =<\/span> np.<\/span>array(<\/span>[<\/span>1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>,<\/span> 4<\/span>,<\/span> 5<\/span>]<\/span>)<\/span><\/p>\n

# \u5bf9\u7b5b\u9009\u51fa\u7684\u5143\u7d20\u6279\u91cf\u8d4b\u503c<\/span>
\narr[<\/span>arr %<\/span> 2<\/span> ==<\/span> 0<\/span>]<\/span> =<\/span> –<\/span>1<\/span> # [ 1 -1 3 -1 5]<\/span><\/p>\n

# \u7528\u82b1\u5f0f\u7d22\u5f15\u8d4b\u503c<\/span>
\narr[<\/span>[<\/span>0<\/span>,<\/span> 2<\/span>,<\/span> 4<\/span>]<\/span>]<\/span> =<\/span> [<\/span>10<\/span>,<\/span> 30<\/span>,<\/span> 50<\/span>]<\/span> # [10 -1 30 -1 50]<\/span><\/p>\n

\n

📊 \u4e0e Numba \u7ed3\u5408（\u8d85\u9ad8\u52a0\u901f）<\/h3>\n

# pip install numba<\/span>
\nfrom<\/span> numba import<\/span> jit
\nimport<\/span> numpy as<\/span> np<\/p>\n

# \u5bf9\u65e0\u6cd5\u5b8c\u5168\u5411\u91cf\u5316\u7684\u590d\u6742\u7b97\u6cd5，\u7528 Numba JIT \u7f16\u8bd1<\/span>
\n@jit<\/span>(<\/span>nopython=<\/span>True<\/span>)<\/span>
\ndef<\/span> complex_algorithm<\/span>(<\/span>data)<\/span>:<\/span>
\n result =<\/span> np.<\/span>empty_like(<\/span>data)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>data)<\/span>)<\/span>:<\/span>
\n s =<\/span> 0.0<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>i+<\/span>1<\/span>)<\/span>:<\/span>
\n s +=<\/span> data[<\/span>j]<\/span> *<\/span> np.<\/span>exp(<\/span>–<\/span>(<\/span>i–<\/span>j)<\/span> \/<\/span> 10<\/span>)<\/span> # \u6307\u6570\u8870\u51cf\u52a0\u6743<\/span>
\n result[<\/span>i]<\/span> =<\/span> s
\n return<\/span> result<\/p>\n

# \u901f\u5ea6\u63a5\u8fd1 C \u8bed\u8a00<\/span>
\ndata =<\/span> np.<\/span>random.<\/span>rand(<\/span>100000<\/span>)<\/span>
\nresult =<\/span> complex_algorithm(<\/span>data)<\/span><\/p>\n

\n

📝 \u901f\u67e5\u8868<\/h3>\n\n\u9700\u6c42\u4ee3\u7801<\/tr>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u77e9\u9635\u4e58\u6cd5<\/td>\nnp.einsum('ij,jk->ik', A, B)<\/td>\n<\/tr>\n
\u8f6c\u7f6e<\/td>\nnp.einsum('ij->ji', A)<\/td>\n<\/tr>\n
\u5bf9\u89d2\u7ebf<\/td>\nnp.einsum('ii->i', A)<\/td>\n<\/tr>\n
\u5916\u79ef<\/td>\nnp.einsum('i,j->ij', a, b)<\/td>\n<\/tr>\n
\u6279\u77e9\u9635\u4e58\u6cd5<\/td>\nnp.einsum('bij,bjk->bik', A, B)<\/td>\n<\/tr>\n
\u7ed3\u6784\u5316\u6570\u7ec4<\/td>\nnp.array(data, dtype=[('name','U10'),('age','i4')])<\/td>\n<\/tr>\n
\u63a9\u7801\u6570\u7ec4<\/td>\nma.masked_where(cond, arr)<\/td>\n<\/tr>\n
\u5ffd\u7565 NaN<\/td>\nma.masked_invalid(arr)<\/td>\n<\/tr>\n
\u6ed1\u52a8\u7a97\u53e3<\/td>\nnp.lib.stride_tricks.sliding_window_view(arr, k)<\/td>\n<\/tr>\n
\u8fde\u7eed\u5316<\/td>\nnp.ascontiguousarray(arr)<\/td>\n<\/tr>\n
\u627e\u5230\u975e\u96f6<\/td>\nnp.argmax(cond)<\/td>\n<\/tr>\n
\u6574\u6570\u5206\u7bb1<\/td>\nnp.bincount(data)<\/td>\n<\/tr>\n
\u552f\u4e00\u503c\u7f16\u7801<\/td>\nnp.unique(labels, return_inverse=True)<\/td>\n<\/tr>\n
Top-K<\/td>\nnp.argpartition(arr, -k)[-k:]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

[[numpy-\u603b\u89c8|\u2190 \u8fd4\u56de\u603b\u89c8]]<\/p>\n","protected":false},"excerpt":{"rendered":"

NumPy \u9ad8\u7ea7\u6280\u5de7
\n🧠 \u5411\u91cf\u5316\u601d\u7ef4
\nNumPy \u7684\u7cbe\u9ad3\u4e0d\u662f\u7528 ndarray \u5b58\u6570\u636e，\u800c\u662f\u7528\u5411\u91cf\u5316\u64cd\u4f5c\u4ee3\u66ff\u5faa\u73af\u3002
\n\u53cd\u6a21\u5f0f vs \u6700\u4f73\u5b9e\u8df5
\nimport numpy as npdata np.random.rand(1000000)# \u274c \u5faa\u73af（Python \u7ea7\u522b，\u6781\u6162）
\nresult np.empty_like(data)
\nfor i in range(len(data)):result[i] n<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[1818,81,123,190,305],"topic":[],"class_list":["post-89078","post","type-post","status-publish","format-standard","hentry","category-server","tag-numpy","tag-python","tag-123","tag-190","tag-305"],"yoast_head":"\nPython-numpy-\u9ad8\u7ea7\u6280\u5de7 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/89078.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python-numpy-\u9ad8\u7ea7\u6280\u5de7 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"NumPy \u9ad8\u7ea7\u6280\u5de7 🧠 \u5411\u91cf\u5316\u601d\u7ef4 NumPy \u7684\u7cbe\u9ad3\u4e0d\u662f\u7528 ndarray \u5b58\u6570\u636e，\u800c\u662f\u7528\u5411\u91cf\u5316\u64cd\u4f5c\u4ee3\u66ff\u5faa\u73af\u3002 \u53cd\u6a21\u5f0f vs \u6700\u4f73\u5b9e\u8df5 import numpy as npdata np.random.rand(1000000)# \u274c \u5faa\u73af（Python \u7ea7\u522b，\u6781\u6162） result np.empty_like(data) for i in range(len(data)):result[i] n\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/89078.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-08-02T03:40:32+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/89078.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/89078.html\",\"name\":\"Python-numpy-\u9ad8\u7ea7\u6280\u5de7 - 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