📝 docs(tsl): restructure agent-facing reference

Rework TSL syntax, catalog, modules, and routing docs around deterministic agent lookup and generation. Split large catalog pages into focused function fact pages, remove obsolete pending/verified/unavailable paths, and update consistency tests for the new structure.
2026-06-09 17:24:30 +08:00
parent 9c194170a1
commit 540b3c0a1b
192 changed files with 32929 additions and 13533 deletions
@@ -1,661 +1,37 @@
 # 数学函数

-这一页只负责函数定位：先按主题找到模块，再在页内搜索函数名。
+文档类型：函数事实路由页
+是否可直接用于生成代码：是；进入分类详情页后按函数事实条目生成调用
+遇到不确定时：回到 [../index.md](../index.md)、[../../syntax/index.md](../../syntax/index.md)

-## 候选函数索引说明
-
- 本页是候选函数索引，只说明函数名被归入当前模块。
- 候选名没有进入 verified 函数页前不能当成可调用事实。
- 生成代码前必须先查 [../verified/index.md](../verified/index.md)；只从 verified 函数页读取参数类型。
-
-## 使用方式
-
- 返回总目录：[catalog/index.md](index.md)
- 需要基础语法时回到 [../../syntax/index.md](../../syntax/index.md)
- 需要金融任务组织方式时回到 [../../finance/index.md](../../finance/index.md)
+这一页是数学函数的轻量入口，不直接承载全部函数事实。生成函数调用时，先按分类目录进入详情页，再只读取命中的函数条目和参数表。

 ## 模块范围

 - 说明：数值计算、统计分析、矩阵处理与数学算法
- 主题数：40
- 函数数：518
-
-## 主题目录
-
-### 数值计算 / 数值微积分
-
- `ig_Romberg`
- `integral`
- `ig_Trapezoid_1`
- `ig_Trapezoid_2`
- `ig_Simpson_1`
- `ig_Gauss`
- `ig_Chebyshev`
- `ig_Simpson_2`
- `sf_SinX`
- `sf_CosX`
- `sf_eX`
- `sf_EllipseX_1`
- `sf_EllipseX_2`
- `Conv`
- `Hessian`
-
-### 数值计算 / 线性方程组的求解
-
- `se_Gauss`
- `se_Gauss_Jordan`
- `se_Ldl`
- `se_Cholesky`
- `se_Gauss_Seidel`
-
-### 数值计算 / 插值
-
- `interp`
- `interp_unit`
- `ip_Lagrangian_A`
- `ip_Lagrangian_B`
- `ip_Parabola_A`
- `ip_Parabola_B`
- `ip_Hermite_A`
- `ip_Hermite_B`
- `ip_Aitken_A`
- `ip_Aitken_B`
- `ip_Spline_A`
- `ip_Spline_B`
- `ip_Spline_C`
- `ip_SLQ`
- `ip_SLG`
-
-### 数值计算 / 矩阵运算及分解
-
- `mt_Transposition`
- `mt_Multiplication`
- `mt_Addition`
- `mt_iv_Gauss_Jordan`
- `mt_iv_Ldl`
- `mt_Subtraction`
- `Mt_decompose_lu`
- `mt_decompose_qr`
- `mt_decompose_chol`
- `chol`
- `mt_va_Gauss_Jordan`
- `mt_decompose_svd`
- `mt_decompose_ldl`
- `mt_decompose_eig`
- `Standarize_II`
- `ReIndex2`
- `Det`
- `isSymmetry`
- `Orth`
- `roots`
- `Eigen`
- `pinv`
- `norm2`
- `Cond`
- `diag`
- `isDefinite`
-
-### 数值计算 / 数组扩展
-
- `Any`
- `ALL`
-
-### 数值计算 / 其他
-
- `perms`
- `nchoosek`
- `MaxDrawDown`
- `MinRecoveryTime`
- `Betainc`
- `PercentileOfScore`
- `GenerateCombinations`
- `Percentage`
-
-### 常用数学函数
-
- `Pi`
- `Odd`
- `Abs`
- `Sqr`
- `Sqrt`
- `DivMod`
- `Frexp`
- `Ldexp`
- `Poly`
-
-### 三角函数
-
- `Sin`
- `Cos`
- `SinCos`
- `Tan`
- `Cot`
- `CoTan`
- `Sec`
- `Csc`
- `Secant`
- `Cosecant`
- `ArcSin`
- `ArcCos`
- `ArcTan`
- `ArcTan2`
- `ArcCot`
- `ArcSec`
- `ArcCsc`
- `Hypot`
-
-### 角度量转换
-
- `RadToDeg`
- `RadToGrad`
- `RadToCycle`
- `DegToRad`
- `DegToGrad`
- `DegToCycle`
- `GradToRad`
- `GradToDeg`
- `GradToCycle`
- `CycleToRad`
- `CycleToDeg`
- `CycleToGrad`
-
-### 双曲线函数
-
- `Sinh`
- `Cosh`
- `Tanh`
- `CotH`
- `SecH`
- `CscH`
- `ArcCosh`
- `ArcSinh`
- `ArcTanh`
- `ArcCotH`
- `ArcSecH`
- `ArcCscH`
-
-### 指数对数函数
-
- `Ln`
- `LnXP1`
- `Log10`
- `Log2`
- `LogN`
- `Exp`
- `IntPower`
- `Power`
-
-### 精度设置及取整运算
-
- `Int`
- `Ceil`
- `Ceil32`
- `Ceil64`
- `Floor`
- `Floor32`
- `Floor64`
- `Trunc`
- `Trunc32`
- `Trunc64`
- `Frac`
- `Round`
- `Round32`
- `Round64`
- `SimpleRound`
- `SimpleRound32`
- `SimpleRound64`
- `RoundTo`
- `SimpleRoundTo`
-
-### 比较判断函数
-
- `IsNan`
- `IsInfinite`
- `Sign`
- `IsZero`
- `Min`
- `Max`
- `CompareValue`
- `SameValue`
- `RandomRange`
- `InRange`
- `EnsureRange`
-
-### 一般统计量
-
- `MinIntValue`
- `SumOfSquares`
- `StdDev`
- `Mean`
- `Sum`
- `MaxValue`
- `MinValue`
- `Norm`
- `SumsAndSquares`
- `MaxIntValue`
- `SumInt`
- `Harmean`
- `Variance`
- `MeanAndStdDev`
- `AveDev`
- `Skewness`
- `TotalVariance`
- `Product`
- `PopnStdDev`
- `kurtosis2`
- `Median`
- `skewness2`
- `Kurtosis`
- `Mode`
- `RandG`
- `Geomean`
- `PopnVariance`
- `MomentSkewKurtosis`
- `DevSq`
- `randomfrom`
-
-### 次序统计量
-
- `Large`
- `Small`
- `Percentile`
- `Percentrank`
- `Quartile`
- `Rank`
- `Trimmean`
- `Frequency`
-
-### 统计函数
-
- `Cov`
- `Correl`
- `Slope`
- `Intercept`
- `Rsq`
- `Steyx`
- `Slopeandintercept`
- `VariationCoefficient`
- `Skew`
- `SelfStddev`
- `RegressionChannel`
- `Kurt`
- `MeanAndPopnStdDevWithRate`
- `BetaAndAlpha`
- `correlpaired`
- `correlpaired_side`
-
-### 统计函数 / 扩充统计
-
- `Expanding_Unit`
-
-### 统计函数 / 含NAN统计
-
- `NanMean`
- `NanSum`
- `NanStd`
- `NanVariance`
- `NanPopnStd`
- `NanPopnVariance`
- `NanRankArr`
- `NanPercentRankArr`
-
-### 统计分布
-
- `Gammaln`
- `Hist`
- `sf_Error`
- `erfc`
- `sf_Gamma`
- `erf`
- `erfcinv`
- `sf_Beta`
- `sf_IntegerBessel_1`
- `sf_IncompleteGamma`
- `Gamma`
- `erfinv`
- `Randnorm`
- `sf_F`
- `sf_geopdf`
- `sf_RealBessel_1`
- `sf_unidcdf`
- `sf_normpdf`
- `sf_geoinv`
- `sf_unidpdf`
- `sf_IncompleteBeta`
- `sf_normalinv2`
- `sf_norminv`
- `Randunid`
- `sf_Normal`
- `sf_unidinv`
- `sf_X2`
- `sf_IntegerBessel_2`
- `sf_normcdf`
- `sf_t`
- `sf_geocdf`
- `Randgeo`
- `sf_normalinv`
- `Normfit`
- `sf_RealBessel_2`
- `sf_hygeinv`
- `poissfit`
- `sf_binocdf`
- `Randhyge`
- `sf_poissinv`
- `sf_poisscdf`
- `sf_nbininv`
- `binofit`
- `sf_hygepdf`
- `sf_unifcdf`
- `sf_exppdf`
- `sf_binoinv`
- `uniffit`
- `sf_nbinpdf`
- `Randnbin`
- `Randpoiss`
- `sf_hygecdf`
- `sf_poisspdf`
- `Randbino`
- `Randunif`
- `sf_unifinv`
- `sf_binopdf`
- `sf_nbincdf`
- `sf_unifpdf`
- `sf_tcdf`
- `sf_fpdf`
- `sf_tinv`
- `expfit`
- `Randgam`
- `sf_ch2inv`
- `sf_ch2cdf`
- `sf_finv1`
- `Randt`
- `sf_expcdf`
- `sf_finv`
- `sf_gamcdf`
- `sf_tpdf`
- `sf_x2inv`
- `sf_gampdf`
- `sf_gammainv`
- `sf_fcdf`
- `sf_ch2pdf`
- `Randf`
- `Randexp`
- `Randch2`
- `sf_gaminv`
- `sf_expinv`
- `sf_betapdf`
- `sf_tinv1`
- `RandCauchy`
- `sf_Laplacecdf`
- `Randbeta`
- `sf_Cauchypdf`
- `sf_logninv`
- `sf_Laplaceinv`
- `sf_betacdf`
- `sf_raylinv`
- `sf_wblcdf`
- `sf_lognpdf`
- `sf_Cauchycdf`
- `Randlogn`
- `Randrayl`
- `sf_Laplacepdf`
- `sf_raylpdf`
- `sf_wblinv`
- `sf_logncdf`
- `sf_Cauchyinv`
- `sf_raylcdf`
- `Randwbl`
- `sf_betainv`
- `RandLaplace`
- `sf_wblpdf`
- `sf_betainv1`
- `sf_mvtcdf`
- `Mvtcdfqmc`
- `sf_mvncdf`
- `sf_copulacdf`
- `sf_copulafit`
- `RandCopula`
- `sf_exp`
- `Norminv`
-
-### 统计推断
-
- `Estimate_SNU`
- `Estimate_TNU`
- `Estimate_TND`
- `Estimate_SP`
- `Estimate_TP`
- `Hypoth_TailRes`
- `NormPlot`
- `Hypoth_Kstest`
- `Hypoth_lillietest`
- `Hypoth_IndepTest`
- `Hypoth_KruskalWallis`
- `Hypoth_SNUTest`
- `Hypoth_TNUTest`
- `Hypoth_SNDTest`
- `Hypoth_TNDTest`
- `Hypoth_LSUTest`
- `Anova_Single`
- `Anova_Twice`
- `Anova_Bartlett`
- `Anova_Levene`
-
-### 统计推断 / 假设检验
-
- `Hypoth_SignTest`
- `Hypoth_WilcoxonTest`
- `Hypoth_McNemarTest`
-
-### 统计推断 / 配对检验
-
- `Hypoth_PNUTest`
-
-### 多元统计分析
-
- `Corr`
- `CorrelationMatrix`
- `Covariance`
- `Corrcoef`
- `Corr_partial`
- `Distance`
- `Cluster_Kmeans`
- `Cluster_System`
- `Cluster_ward`
- `Discrim`
- `princomp`
- `Factor`
- `corr_canonical`
- `corr_Spearman`
- `Cov2CorrMatrix`
- `CorrMatrixAdjust`
- `corr_Kendall`
- `HISTC`
-
-### 多元统计分析 / 相对重要性
-
- `Regress_domin_formula`
- `Regress_domin_marginal`
-
-### 回归 / 回归检验
-
- `Regress_Ridge`
- `Regress_AdjustedR2`
- `Regress_Logistic`
- `Regression`
- `Regress_DWTest`
- `Regress_Stepwise`
- `Regress_Constraint`
- `Regress_White`
- `Regress_MLS`
- `Regress_CMLS`
- `Regress_JBTest`
- `Regress_pri`
- `Regress_FTest`
- `Regression_WLS`
- `Regress_Binary`
- `Regress_TTest`
- `Regress_NLM`
- `Regress_WLS`
- `Regress_AicAndSbic`
- `Regress_RSquare`
- `Regress_QRlsq`
- `boxcox`
- `Regress_HettestSpearman`
- `Regress_VIF`
- `Regress_TTest_RWLS`
- `Regress_TTest_White`
- `Regress_TTest_NW`
- `Regression_OLS_White`
- `Regression_OLS_NW`
- `NW_Adjustment_Simplification`
- `Robustfit_M`
- `Regress_GRStest`
-
-### 回归 / 回归公用函数
-
- `LeastSquares_CurveFitting`
-
-### 灰色系统
-
- `GM_Initial`
- `GM_Corr`
- `GM_AGO`
- `GM_Icorr`
- `GM_Scorr`
-
-### 主成分分析
-
- `PrincaipalComponentAnalysis`
-
-### 主成分分析 / 中间函数
-
- `Mbbub`
- `ComponentScoreMatrix`
- `FactorScoreMatrix`
- `ComponentMatrix`
- `RotatedComponentMatrix`
- `Eigen_Jacobi`
- `GetEigenValue`
- `FScoreResult`
-
-### 时间序列分析
-
- `Time_Diff`
- `Time_AutoCov`
- `Time_ACF`
- `Time_PACF`
- `Time_RandomTest`
- `Time_DanielTest`
- `AR`
- `ARMA`
- `Time_ARCH`
- `Time_GARCH`
- `Times_ADFTest`
- `Times_Cointergration_test`
- `Times_ECM`
- `Times_Granger`
- `Time_ARp`
- `Time_MAq`
- `Time_ARMA`
- `Time_GreenFun`
- `Time_InvFun`
- `Time_Analyse`
- `Time_ChoseP`
- `Times_Cointergration`
- `GM_Estimate`
- `Time_ARCHTest`
- `GarchFit`
- `Times_johansen`
- `Times_GrangerCausality`
-
-### 时间序列分析 / 因果推断
-
- `Time_VolatilitySpillover`
-
-### 优化
-
- `NonLP_Hooke_Jeeves`
- `Prog_L`
- `NonLP_minPS`
- `NonLP_Fibonacci`
- `NonLP_Range`
- `Fmin`
- `NonLP_BSearch`
- `Prog_M`
- `NonLP_minFactor`
- `NonLP_GP`
- `NonLP_Fminsearch`
- `NonLP_Fmincon`
- `NonLP_minSUMT`
- `Prog_Q`
- `Prog_N`
- `NonLP_Nelder`
- `NonLP_Fminbnd`
- `NonLP_Golden`
- `TSOptimizer`
- `Quadprog`
- `LinearProgramming`
- `NonLP_Rosenbrock`
- `QuadLagR`
- `OZProg`
- `QuadTrackRoute`
- `IntLinProg`
-
-### 优化 / 有约束优化算法
-
- `SUMT_Method`
-
-### 优化 / 无约束优化算法
-
- `Hooke_Jeeves_Method`
-
-### 优化 / 测试
-
- `H_J_Method_Pgm`
- `Sumt_Method_CallBack`
-
-### 小波分析
-
- `Wavedec`
- `wrcoef`
- `wavelet`
-
-### 财务函数
-
- `DoubleDecliningBalance`
- `FutureValue`
- `InterestPayment`
- `InterestRate`
- `InternalRateOfReturn`
- `NumberOfPeriods`
- `NetPresentValue`
- `Payment`
- `PeriodPayment`
- `PresentValue`
- `SLNDepreciation`
- `SYDDepreciation`
-
-### 增长率与比率
-
- `AccumulativeYTMtoYTM`
- `YTMToAccumulativeYTM`
- `RatioValue`
- `OutPutValueByUnit`
- `OutPutLnGrowRatio`
- `OutPutGrowValue`
- `OutPutGrowValue2`
- `OutPutGrowRatio`
- `OutPutGrowRatio2`
- `MultyValue`
- `OutPutGrowValue3`
- `OutPutGrowRatio3`
- `RatioValue_Math`
-
-### 概率分布 / 线性变换
-
- `Norm_LinearTransform`
-
-### 信号处理
-
- `filter_hp`
+- 函数事实数：472
+
+## 智能体检索规则
+
+1. 用户只描述能力时，先按“分类目录”选择候选详情页。
+2. 用户给出函数名时，优先在 `math/` 子目录中搜索三级函数标题。
+3. 只读取命中的函数条目、相邻分类标题和必要参数表；不要把同页其它函数混进当前调用。
+4. 没有命中函数事实条目时，不要发明函数名；回到 [../index.md](../index.md) 或项目实际代码确认。
+
+## 分类目录
+
+| 分类               | 详情页                                                             | 函数事实数 |
+| ------------------ | ------------------------------------------------------------------ | ---------: |
+| 矩阵与数组         | [math/matrix_and_arrays.md](math/matrix_and_arrays.md)             |         14 |
+| 数值方法           | [math/numerical_methods.md](math/numerical_methods.md)             |         39 |
+| 初等数学与判断     | [math/elementary_math.md](math/elementary_math.md)                 |         55 |
+| 三角、角度与双曲线 | [math/trig_angle_hyperbolic.md](math/trig_angle_hyperbolic.md)     |         42 |
+| 描述统计           | [math/statistics_descriptive.md](math/statistics_descriptive.md)   |         67 |
+| 统计分布           | [math/distribution.md](math/distribution.md)                       |        116 |
+| 财务数学           | [math/financial_math.md](math/financial_math.md)                   |         12 |
+| 统计推断           | [math/statistical_inference.md](math/statistical_inference.md)     |         25 |
+| 多元统计分析       | [math/multivariate_statistics.md](math/multivariate_statistics.md) |         26 |
+| 回归分析           | [math/regression.md](math/regression.md)                           |         34 |
+| 灰色系统与小波分析 | [math/gray_and_wavelet.md](math/gray_and_wavelet.md)               |          9 |
+| 时间序列分析       | [math/time_series.md](math/time_series.md)                         |         25 |
+| 优化与规划         | [math/optimization.md](math/optimization.md)                       |          8 |