C++ Eigen 只读稀疏 block 子表达式？怎么写？

Question

我想使用 Eigen 的 block 表达式从四个不同的矩阵创建一个大矩阵。

但是，在左上角添加第一个矩阵会导致错误:

error: static assertion failed: THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY
  451 |       EIGEN_STATIC_ASSERT(sizeof(T)==0, THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY);

我无法找到导致此问题的确切原因。不要将矩阵转换为密集表示，这一点非常重要。这是我的代码:

 Eigen::SparseMatrix<double> top_left = K + Eigen::SparseMatrix<double>(K.transpose());

 Eigen::SparseMatrix<double> block_laplacian_sq;
 block_laplacian_sq.resize(top_left.rows() + C.rows(), top_left.cols() + C.rows());
 block_laplacian_sq.topLeftCorner(top_left.rows(), top_left.cols()) = top_left; 
//                                                       error here^^^

Answer 1

如the tutorial explains :

Regarding read-access, sparse matrices expose the same API than for dense matrices to access to sub-matrices such as blocks, columns, and rows. See Block operations for a detailed introduction. However, for performance reasons, writing to a sub-sparse-matrix is much more limited, and currently only contiguous sets of columns (resp. rows) of a column-major (resp. row-major) SparseMatrix are writable. Moreover, this information has to be known at compile-time, leaving out methods such as block(...) and corner*(...).

对于您想要初始化左上角的特定用例，您可以利用以下事实:调整大小后，未初始化的矩阵条目隐式为零。所以这有效:

top_left.conservativeResize(block_laplacian_sq.rows(), top_left.cols());
block_laplacian_sq.leftCols(top_left.cols()) = top_left;

但是当您想要初始化底部行时，这对您没有帮助。假设您想用子矩阵初始化所有 4 个角，我建议构建一个大的三元组 vector (请参阅 Convert an Eigen matrix to Triplet form C++ )，然后一次性初始化最终矩阵。

一种可能的替代方案是用完整的列子矩阵的条目填充行主矩阵。我不知道这会如何更快，但也许它对于您的用例来说更优雅。

Eigen::SparseMatrix<double, Eigen::RowMajor> left(
      block_laplacian_sq.rows(), top_left.cols());
left.topRows(top_left.rows()) = top_left;
left.bottomRows(bottom_left.rows()) = bottom_left;
block_laplacian_sq.leftCols(left.cols()) = left;

(显然，您会尝试重新排列表达式以避免可能的行主要 <-> 列主要更改)