如何扩展Boost Interval实现标量乘法及Eigen矩阵向量运算？

Hey there! No worries at all—every question starts somewhere, especially when mixing powerful libraries like Eigen and Boost Interval. Let's walk through your concerns with efficient, idiomatic C++ solutions tailored to your use case.

First off, while Boost Interval doesn't ship with a built-in operator* for Interval and double, you can implement this in a way that plays nicely with Eigen's expression template system—this is key for avoiding manual loops and keeping performance on par with Eigen's native operations.

Instead of writing per-element loops, define global overloads for the multiplication operators. Eigen will automatically pick these up and apply them across vector/matrix elements using its optimized expression pipeline:

// Global overloads to enable Interval <-> double multiplication
Interval operator*(const Interval& iv, double d) {
    // Directly compute the new interval bounds—no extra overhead
    return Interval(iv.lower() * d, iv.upper() * d);
}

Interval operator*(double d, const Interval& iv) {
    // Reuse the above implementation to avoid code duplication
    return iv * d;
}

This lets you write natural Eigen-style code like:

Vector iv_vec = ...;
double scalar = 2.5;
Vector scaled_vec = iv_vec * scalar; // Eigen handles element-wise multiplication efficiently

As shown above, leveraging Eigen's expression templates is the most idiomatic and efficient approach. Manual loops skip Eigen's built-in optimizations (like loop unrolling, vectorization, and avoiding temporary objects), so sticking to Eigen's native syntax is always better.

If you ever need more control (e.g., custom transformations), you can use Eigen's cwise methods, but the operator overloads are cleaner for standard multiplication:

// Equivalent to the operator* approach, but more explicit if needed
Vector scaled_vec = iv_vec.cwiseProduct(Eigen::Vector3d::Constant(scalar));

To use std::inner_product, you just need two things:

• A way to multiply an Interval and a double (which we already have from the operator overloads)
• A way to add two Interval values (which Boost Interval provides by default—its operator+ is already implemented for Interval)

You can use it directly like this:

#include <numeric>

Vector iv_vec = ...;
Eigen::Vector3d d_vec = ...;

// Initialize with the additive identity for Interval: [0, 0]
Interval inner_result = std::inner_product(
    iv_vec.begin(), iv_vec.end(),
    d_vec.begin(),
    Interval(0.0)
);

No extra operator overloads are needed here—Boost Interval's default arithmetic covers the addition step, and our custom multiplication handles the element-wise product.

• Enable compiler optimizations: Compile with -O2 or -O3—both Eigen and Boost Interval rely heavily on compiler optimizations to eliminate overhead from expression templates and interval arithmetic.
• Adjust Boost Interval policies: Your current policy uses bi::checking_base<double>, which adds runtime checks for invalid intervals (like empty ranges). If you're confident your operations won't produce invalid intervals, switch to bi::no_checking to save some overhead:

  using Interval = bn::interval<
      double,
      bi::policies<
          bi::save_state<bi::rounded_transc_std<double>>,
          bi::no_checking // Skip validity checks for better performance
      >
  >;
  

• Minimize copies: Use Eigen's const references and expression templates to avoid unnecessary copies of vectors/matrices. For example, pass vectors by const Vector& instead of value when possible.

Hope this helps you write clean, efficient code! Don't hesitate to ask follow-up questions if you run into edge cases.

内容的提问来源于stack exchange，提问作者bernhard_e