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.claude-plugin/plugin.json Normal file
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"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"
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# Julia
Julia模型编写与数据处理SKILLS

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---
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
```

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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]

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skills/julia-numerical/SKILL.md Normal file
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---
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

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# 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

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# 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!")