From 4a5dec7a76f0f85f1cc4b8f0c5392f672d51e3ae Mon Sep 17 00:00:00 2001 From: Zhongwei Li Date: Sun, 30 Nov 2025 08:35:33 +0800 Subject: [PATCH] Initial commit --- .claude-plugin/plugin.json | 13 +++ README.md | 3 + plugin.lock.json | 60 +++++++++++ skills/julia-hydrotools/SKILL.md | 32 ++++++ skills/julia-hydrotools/examples.jl | 22 ++++ skills/julia-numerical/SKILL.md | 120 +++++++++++++++++++++ skills/julia-numerical/examples.jl | 155 +++++++++++++++++++++++++++ skills/julia-numerical/test_basic.jl | 34 ++++++ 8 files changed, 439 insertions(+) create mode 100644 .claude-plugin/plugin.json create mode 100644 README.md create mode 100644 plugin.lock.json create mode 100644 skills/julia-hydrotools/SKILL.md create mode 100644 skills/julia-hydrotools/examples.jl create mode 100644 skills/julia-numerical/SKILL.md create mode 100644 skills/julia-numerical/examples.jl create mode 100644 skills/julia-numerical/test_basic.jl diff --git a/.claude-plugin/plugin.json b/.claude-plugin/plugin.json new file mode 100644 index 0000000..1cb4fd7 --- /dev/null +++ b/.claude-plugin/plugin.json @@ -0,0 +1,13 @@ +{ + "name": "Julia", + "description": "Julia模型编写与数据处理SKILLS", + "version": "0.0.0-2025.11.28", + "author": { + "name": "Dongdong Kong", + "email": "kongdd.sysu@gmail.com" + }, + "skills": [ + "./skills/julia-hydrotools", + "./skills/julia-numerical" + ] +} \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..8eb2b70 --- /dev/null +++ b/README.md @@ -0,0 +1,3 @@ +# Julia + +Julia模型编写与数据处理SKILLS diff --git a/plugin.lock.json b/plugin.lock.json new file mode 100644 index 0000000..aaba231 --- /dev/null +++ b/plugin.lock.json @@ -0,0 +1,60 @@ +{ + "$schema": "internal://schemas/plugin.lock.v1.json", + "pluginId": "gh:kongdd/Skills_for_Your_AI_Student:julia", + "normalized": { + "repo": null, + "ref": "refs/tags/v20251128.0", + "commit": "002282baeb41e5c33ccc00e03f278105edea206b", + "treeHash": "c09443e36bc20692f3d629162d704619d5d6477890c4cd4fd42421c39801397d", + "generatedAt": "2025-11-28T10:19:55.831931Z", + "toolVersion": "publish_plugins.py@0.2.0" + }, + "origin": { + "remote": "git@github.com:zhongweili/42plugin-data.git", + "branch": "master", + "commit": "aa1497ed0949fd50e99e70d6324a29c5b34f9390", + "repoRoot": "/Users/zhongweili/projects/openmind/42plugin-data" + }, + "manifest": { + "name": "Julia", + "description": "Julia模型编写与数据处理SKILLS" + }, + "content": { + "files": [ + { + "path": "README.md", + "sha256": "37b58e2c2120cdfab5b993f6c22e9e96632cf225e753a7f97bfefae7c4185bda" + }, + { + "path": ".claude-plugin/plugin.json", + "sha256": "582230d774c71dd2b1575ac516f13e7a5612e2f0f386754ae97089f540b60296" + }, + { + "path": "skills/julia-numerical/examples.jl", + "sha256": "918c3df7fc48fde70bd5bb75f7c6636ff68f5331a61cbe8c1eea666a69662c8d" + }, + { + "path": "skills/julia-numerical/SKILL.md", + "sha256": "381dd118c82ee8631e462c3ab1e137e2cd286d4f0102435036a5265daa88cc11" + }, + { + "path": "skills/julia-numerical/test_basic.jl", + "sha256": "1a47c402edbd91a12024411967d2a427331e6cc9e4cad81e38d10118caf86a85" + }, + { + "path": "skills/julia-hydrotools/examples.jl", + "sha256": "2962c429ca92208da63123ab7234245e19b7710d58fca256f364a741b19fac05" + }, + { + "path": "skills/julia-hydrotools/SKILL.md", + "sha256": "1615b3e2fb09ba38cee4304f3f4f8d2a8da51e1411fe4ceb219002177e71350d" + } + ], + "dirSha256": "c09443e36bc20692f3d629162d704619d5d6477890c4cd4fd42421c39801397d" + }, + "security": { + "scannedAt": null, + "scannerVersion": null, + "flags": [] + } +} \ No newline at end of file diff --git a/skills/julia-hydrotools/SKILL.md b/skills/julia-hydrotools/SKILL.md new file mode 100644 index 0000000..8f2adb4 --- /dev/null +++ b/skills/julia-hydrotools/SKILL.md @@ -0,0 +1,32 @@ +--- +name: julia-hydrotools +description: 计算短波辐射、长波辐射、潜在蒸散发、日出日落时间、湿度的基本变量处理。 +--- + +# 1 运行环境说明 + +- 在Julia中运行 + +- 在julia中首先加载包，`using HydroTools` + +- 若没有包加载出错，则安装之，`using Pkg; Pkg.add("HydroTools")` + + +## 1.1 函数说明 + +- `cal_Rsi_toa(lat, J)`: daily extraterrestrial radiation in MJ m-2 day-1 + + `lat`: latitude in deg + + `J`: doy of year + > 注意lat和J是scalar + > 如果是vector，按照Julia的语法，采用`cal_Rsi_toa.(lat, J)`调用 + + 默认返回单位是`MJ d-1`，若想转为`W m-2`，需要调用[MJ2W]函数，告诉用户返回的数字单位 + + +## 1.2 文件保存 + +文件保存采用Julia包`DataFrames`，`RTableTools` + +```julia +using RTableTools +fwrite(df, "out.csv") # df is a DataFrame +``` diff --git a/skills/julia-hydrotools/examples.jl b/skills/julia-hydrotools/examples.jl new file mode 100644 index 0000000..38f4c1e --- /dev/null +++ b/skills/julia-hydrotools/examples.jl @@ -0,0 +1,22 @@ +using HydroTools +using Dates + +lat = 20.0 +doy = 120 + +ws = HourAngleSunSet(lat, doy) +# doy +cal_Rsi_toa(lat, doy) + +# date +date = Date(2010, 6, 12) +doy = dayofyear(date) +cal_Rsi_toa(lat, doy) + +# datetime +time = DateTime(2010, 6, 12) +doy = dayofyear(date) +Rsi = cal_Rsi_toa(lat, doy) # [MJ d-1 m-2] + + +MJ2W(Rsi) # [MJ d-1 m-2] to [W m-2] diff --git a/skills/julia-numerical/SKILL.md b/skills/julia-numerical/SKILL.md new file mode 100644 index 0000000..03189a7 --- /dev/null +++ b/skills/julia-numerical/SKILL.md @@ -0,0 +1,120 @@ +--- +name: julia-numerical +description: Execute numerical calculations and mathematical computations using Julia. Use this skill for matrix operations, linear algebra, numerical integration, optimization, statistics, and scientific computing tasks. +--- + +# Julia Numerical Calculation Skill + +This skill enables you to execute numerical calculations using Julia, a high-performance programming language designed for numerical and scientific computing. + +## When to Use + +Use this skill when you need to: +- Perform matrix operations and linear algebra +- Solve differential equations +- Execute numerical integration or optimization +- Calculate statistical measures +- Handle large-scale numerical computations +- Work with complex mathematical operations + +## Setup + +Before using this skill, ensure Julia is installed on your system: + +```bash +# On macOS (using Homebrew) +brew install julia + +# On Linux (Ubuntu/Debian) +sudo apt-get install julia + +# On Windows (using Chocolatey) +choco install julia + +# Or download from https://julialang.org/downloads/ +``` + +## Basic Examples + +### Linear Algebra + +```julia +using LinearAlgebra + +# Create matrices +A = [1 2; 3 4] +B = [5 6; 7 8] + +# Matrix multiplication +C = A * B + +# Eigenvalues and eigenvectors +eigenvals, eigenvecs = eigen(A) + +# Matrix inverse +A_inv = inv(A) +``` + +### Numerical Integration + +```julia +using QuadGK + +# Define a function +f(x) = sin(x) * exp(-x) + +# Integrate from 0 to ∞ +result, error = quadgk(f, 0, Inf) +``` + +### Optimization + +```julia +using Optim + +# Define objective function +f(x) = (x[1] - 2)^2 + (x[2] - 3)^2 + +# Minimize +result = optimize(f, [0.0, 0.0]) +``` + +### Statistics + +```julia +using Statistics + +data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] + +# Statistical measures +mean_val = mean(data) +std_val = std(data) +var_val = var(data) +median_val = median(data) +``` + +## How to Use This Skill + +When you ask me to perform a numerical calculation: +1. I'll identify the appropriate Julia packages needed +2. Write Julia code to solve the problem +3. Execute the code +4. Return results and explanations + +## Common Julia Packages + +- **LinearAlgebra**: Matrix operations and linear algebra +- **Statistics**: Statistical functions +- **QuadGK**: Numerical integration +- **Optim**: Optimization algorithms +- **DifferentialEquations**: Solving differential equations +- **Plots**: Visualization +- **Distributions**: Probability distributions +- **Random**: Random number generation + +## Notes + +- Julia is JIT-compiled, so first runs may include compilation time +- Use `.jl` files for organizing longer scripts +- Install packages with `using Pkg; Pkg.add("PackageName")` +- Results are returned as Julia objects that are converted to readable format diff --git a/skills/julia-numerical/examples.jl b/skills/julia-numerical/examples.jl new file mode 100644 index 0000000..2c527b4 --- /dev/null +++ b/skills/julia-numerical/examples.jl @@ -0,0 +1,155 @@ +# Julia Numerical Calculation Examples +# This file contains common numerical computation patterns + +# ============================================================================ +# Linear Algebra Examples +# ============================================================================ + +function linear_algebra_examples() + using LinearAlgebra + + println("=== Linear Algebra Examples ===") + + # Matrix creation and basic operations + A = [1 2 3; 4 5 6; 7 8 10] + b = [1, 2, 3] + + println("Matrix A:") + println(A) + + # Solve linear system Ax = b + x = A \ b + println("\nSolution to Ax = b:") + println(x) + + # Eigenvalues + eigenvals, eigenvecs = eigen(A) + println("\nEigenvalues:") + println(eigenvals) + + # Singular value decomposition + U, S, V = svd(A) + println("\nSingular values:") + println(S) + + # Determinant and norm + println("\nDeterminant: ", det(A)) + println("Frobenius norm: ", norm(A)) +end + + +# ============================================================================ +# Numerical Integration Examples +# ============================================================================ + +function integration_examples() + using QuadGK + + println("\n=== Numerical Integration Examples ===") + + # Integrate sin(x) from 0 to π + f1(x) = sin(x) + result1, error1 = quadgk(f1, 0, π) + println("∫sin(x)dx from 0 to π = ", result1) + println("Estimated error: ", error1) + + # Integrate exp(-x^2) from -∞ to ∞ (Gaussian) + f2(x) = exp(-x^2) + result2, error2 = quadgk(f2, -Inf, Inf) + println("\n∫exp(-x²)dx from -∞ to ∞ = ", result2) + println("Theoretical value: ", sqrt(π)) + + # Integrate 1/(1+x^2) from 0 to 1 + f3(x) = 1/(1 + x^2) + result3, error3 = quadgk(f3, 0, 1) + println("\n∫1/(1+x²)dx from 0 to 1 = ", result3) + println("Theoretical value (π/4): ", π/4) +end + +# ============================================================================ +# Optimization Examples +# ============================================================================ + +function optimization_examples() + using Optim + + println("\n=== Optimization Examples ===") + + # Simple quadratic function + f(x) = (x[1] - 2)^2 + (x[2] - 3)^2 + + result = optimize(f, [0.0, 0.0]) + println("Minimize f(x,y) = (x-2)² + (y-3)²") + println("Minimum found at: ", Optim.minimizer(result)) + println("Minimum value: ", Optim.minimum(result)) + + # Rosenbrock function (more challenging) + rosenbrock(x) = (1 - x[1])^2 + 100(x[2] - x[1]^2)^2 + + result2 = optimize(rosenbrock, [0.0, 0.0]) + println("\nMinimize Rosenbrock function") + println("Minimum found at: ", Optim.minimizer(result2)) + println("Minimum value: ", Optim.minimum(result2)) +end + +# ============================================================================ +# Statistics Examples +# ============================================================================ + +function statistics_examples() + using Statistics + + println("\n=== Statistics Examples ===") + + data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20] + + println("Data: ", data) + println("\nStatistical measures:") + println("Mean: ", mean(data)) + println("Median: ", median(data)) + println("Standard deviation: ", std(data)) + println("Variance: ", var(data)) + println("Minimum: ", minimum(data)) + println("Maximum: ", maximum(data)) + println("Range: ", maximum(data) - minimum(data)) + + # Quantiles + println("\nQuantiles:") + println("25th percentile: ", quantile(data, 0.25)) + println("50th percentile: ", quantile(data, 0.50)) + println("75th percentile: ", quantile(data, 0.75)) +end + +# ============================================================================ +# Root Finding Examples +# ============================================================================ + +function root_finding_examples() + using Roots + + println("\n=== Root Finding Examples ===") + + # Find root of f(x) = x^3 - 2 + f(x) = x^3 - 2 + root = find_zero(f, 1.0) + println("Root of x³ - 2 = 0: ", root) + println("Verification: f(root) = ", f(root)) + + # Find root of f(x) = sin(x) - 0.5 + f2(x) = sin(x) - 0.5 + root2 = find_zero(f2, 0.5) + println("\nRoot of sin(x) - 0.5 = 0: ", root2) + println("Verification: f(root) = ", f2(root2)) +end + +# ============================================================================ +# Main execution +# ============================================================================ + +if abspath(PROGRAM_FILE) == @__FILE__ + linear_algebra_examples() + integration_examples() + optimization_examples() + statistics_examples() + root_finding_examples() +end diff --git a/skills/julia-numerical/test_basic.jl b/skills/julia-numerical/test_basic.jl new file mode 100644 index 0000000..ca74eb3 --- /dev/null +++ b/skills/julia-numerical/test_basic.jl @@ -0,0 +1,34 @@ +# Basic Julia numerical test +using LinearAlgebra +using Statistics + +println("Testing Julia Numerical Calculation Skill") +println("==========================================\n") + +# Test 1: Basic arithmetic +println("Test 1: Basic Arithmetic") +result = 2 + 2 * 3 +println("2 + 2 * 3 = ", result) + +# Test 2: Vector operations +println("\nTest 2: Vector Operations") +v1 = [1, 2, 3] +v2 = [4, 5, 6] +dot_product = dot(v1, v2) +println("dot([1,2,3], [4,5,6]) = ", dot_product) + +# Test 3: Matrix operations +println("\nTest 3: Matrix Operations") +A = [1 2; 3 4] +println("Matrix A:") +println(A) +println("det(A) = ", det(A)) + +# Test 4: Statistics +println("\nTest 4: Statistics") +data = [10, 20, 30, 40, 50] +println("Data: ", data) +println("mean = ", mean(data)) +println("std = ", std(data)) + +println("\n✓ All basic tests passed!")