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skills/julia-hydrotools/SKILL.md

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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
+```

skills/julia-hydrotools/examples.jl

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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]

skills/julia-numerical/SKILL.md

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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

skills/julia-numerical/examples.jl

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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

skills/julia-numerical/test_basic.jl

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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!")