🔍📊 Summary of the Code with Emojis for FindRoot.C in SWMM5

 🔍📊 Summary of the Code with Emojis

This code snippet focuses on finding the roots of a function, i.e., solving for func(x) = 0, using two distinct methods: Newton-Raphson method and Ridder's Method. Authored by L. Rossman on 11/19/13, it's a part of a larger numerical analysis routine.

1. Newton-Raphson Method 📐🔢

• Purpose: Used to find the root of a function bracketed between x1 and x2.
• Process: Combines Newton-Raphson and bisection methods.
• Root Refinement: Refines the root rts within an accuracy of +/-xacc.
• Function Evaluations: Returns the number of evaluations used or 0 if maximum iterations are exceeded.
• Constraints: Requires that func(x1) and func(x2) have opposite signs.
• Adjustments: May need to recalibrate subcatchment's properties like Percent Impervious and Width after LID placement.
• Special Conditions: Handles cases where Green Roofs and Roof Disconnection only treat direct precipitation.

2. Ridder's Method 🧮📉

• Functionality: Finds the root of func between x1 and x2 within an accuracy of xacc.
• Return Values: Returns the root if found, or a large negative number if not.
• Methodology: Uses an algorithmic approach to refine the root estimate.
• Conditions: Effective when func(x1) and func(x2) have opposite signs.
• Iterations: Executes up to a maximum of MAXIT iterations.
• Result: If the method converges, it returns the estimated root value.

Common Aspects of Both Methods 🔍🔄

• Max Iterations: Both methods limit the number of iterations to MAXIT (60).
• Accuracy: Aim to refine the root estimate to within a specified accuracy (xacc).
• Error Checking: Includes checks for function values and bisection requirements.

Implementation Details 🖥️💡

• Header File: Utilizes a custom header file findroot.h.
• Mathematical Functions: Employs standard math functions from math.h.
• Constants: Defines a SIGN function and sets MAXIT as 60.

Application Scenario 🌍📚

This code is typically used in scenarios like hydrological modeling or environmental simulations where root-finding algorithms are crucial for analyzing and predicting natural processes.

🔎 In summary, the code effectively implements two root-finding algorithms with careful considerations for accuracy, iteration limits, and method-specific conditions, making it a valuable tool for numerical computations in various scientific and engineering applications.