boost压缩矩阵基础知识

发布于 2024-09-24 02:14:58 字数 362 浏览 4 评论 0原文

我对 boost::compressed_matrix 的工作原理感到困惑。假设我像这样声明压缩矩阵：

boost::numeric::ublas::compressed_matrix<double> T(1000, 1000, 3*1000);

这为 1000x1000 矩阵中的 3*1000 个元素分配空间。现在我如何给它非零元素的位置？何时以及如何设置非零元素？是否每次我在矩阵中分配一个元素（例如 B(4,4)=4）时，它都会将该元素标记为非零？

如果可能的话，如果您能通过示例帮助我学习这一点，我将非常感激。对内部实施的一些了解会很棒。我想确保我不会编写通过猜测而次优的程序。

谢谢你！

原文

I am confused on how the boost::compressed_matrix works. Suppose I declare the compressed_matrix like this:

boost::numeric::ublas::compressed_matrix<double> T(1000, 1000, 3*1000);

This allocates space for 3*1000 elements in a 1000x1000 matrix. Now how do I give it the locations which are the non-zero elements? When and how are the non-zero elements set? Is it each time I assign an element in the matrix, e.g. B(4,4)=4, it would mark that element as non-zero?

I would really appreciate if you could help me learn this using an example if possible. Some insight into the internal implementation would be great. I want to make sure I don't write programs that are sub-optimal by guess work.

thank you!

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妥活 2024-10-01 02:14:58

压缩矩阵有一个底层线性容器（默认情况下为unbounded_array，但如果需要，您可以将其设为bounded_array或std::vector），其中包含矩阵的所有非零元素，按行优先（默认）顺序。这意味着每当您向压缩矩阵写入新的非零元素时，它都会插入到该基础数组中。如果您不按（行优先）顺序填充矩阵，则每次插入都将是 O(n)。当您更改现有的非零元素时，它只是在底层数组中进行更改。

这是一个简单的测试，看看底层结构是什么样的：

#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/storage.hpp>
namespace ublas = boost::numeric::ublas;
void show_array(const ublas::unbounded_array<double>& a)
{
    for(size_t i=0; i<a.size(); ++i)
            std::cout << a[i] << ' ';
    std::cout << '\n';
}
int main()
{
    ublas::compressed_matrix<double> m (10, 10, 3 * 10);
    m(0, 5) = 1; // underlying array is {1, 0, 0, 0, ...}
    show_array(m.value_data());
    m(0, 6) = 2; // underlying array is {1, 2, 0, 0, ...}
    show_array(m.value_data());
    m(0, 4) = 3;  // underlying array is {3, 1, 2, 0, ...}
    show_array(m.value_data());
    m(0, 4) = 7;  // underlying array is {7, 1, 2, 0, ...}
    show_array(m.value_data());
}

compressed matrix has an underlying linear container (unbounded_array by default, but you can make it bounded_array or std::vector if you want), which contains all non-zero elements of the matrix, in row-major (by default) order. That means that whenever you write a new non-zero element to compressed matrix, it is inserted into that underlying array. If you're not filling the matrix in (row-major) order, every insert will be O(n). When you're changing an existing non-zero element, it is simply changed in the underlying array.

Here's a simple test to see what the underlying structure looks like:

#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/storage.hpp>
namespace ublas = boost::numeric::ublas;
void show_array(const ublas::unbounded_array<double>& a)
{
    for(size_t i=0; i<a.size(); ++i)
            std::cout << a[i] << ' ';
    std::cout << '\n';
}
int main()
{
    ublas::compressed_matrix<double> m (10, 10, 3 * 10);
    m(0, 5) = 1; // underlying array is {1, 0, 0, 0, ...}
    show_array(m.value_data());
    m(0, 6) = 2; // underlying array is {1, 2, 0, 0, ...}
    show_array(m.value_data());
    m(0, 4) = 3;  // underlying array is {3, 1, 2, 0, ...}
    show_array(m.value_data());
    m(0, 4) = 7;  // underlying array is {7, 1, 2, 0, ...}
    show_array(m.value_data());
}

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恍梦境° 2024-10-01 02:14:58

您可以使用 (i,j) 运算符隐式创建非零元素，也可以使用 insert_element 函数显式插入元素。

最好的地方实际上是查看内部实现：

http://www.tena-sda.org/doc/5.2.2/boost/d2/db7/matrix__sparse_8hpp-source.html#l02761

true_reference insert_element (size_type i, size_type j, const_reference t)
将值 t 插入到第 i 行的第 j 个元素处。不允许有重复的元素。
<小时>
void擦除元素（尺寸类型i，尺寸类型j）
删除第 i 行第 j 个元素的值。