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43   * of sparse matrices. When a column has a norm less than a given tolerance
47 * P is the column permutation which is the product of the fill-reducing and the
57 * \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>
149 /** \returns a const reference to the column permutation P that was applied to A such that A*P = Q*R
150 * It is the combination of the fill-in reducing permutation and numerical column pivoting.
182 // Apply the column permutation
193 * In practice, if during the factorization the norm of the column that has to be eliminated is below
194 * this threshold, then the entire column is treated as zero, and it is moved at the end.
256 PermutationType m_perm_c; // Fill-reducing Column permutation
258 PermutationType m_outputPerm_c; // The final column permutation
262 IndexVector m_etree; // Column elimination tree
277 * and the column elimination tree is computed as well. Only the sparsity pattern of \a mat is exploited.
285 // Copy to a column major matrix if the input is rowmajor
287 // Compute the column fill reducing ordering
300 // Compute the column elimination tree of the permuted matrix
320 * \param mat The sparse column-major matrix
333 IndexVector Ridx(n), Qidx(m); // Store temporarily the row indexes for the current column of R and Q
334 Index nzcolR, nzcolQ; // Number of nonzero for the current column of R and Q
335 ScalarVector tval(m); // The dense vector used to compute the current column
352 // If the input is row major, copy the original column indices,
390 // Left looking rank-revealing QR factorization: compute a column of R and Q at a time
401 // Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,
402 // all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.
411 // Get the nonzeros indexes of the current column of R
451 // Apply the curIdx-th householder vector to the current column (temporarily stored into tval)
464 // Detect fill-in for the current column of Q
477 } // End update current column
484 // Compute the Householder reflection that eliminate the current column
539 // Zero pivot found: move implicitly this column to the end
543 // Recompute the column elimination tree
551 // Finalize the column pointers of the sparse matrices R and Q
566 // Update the column permutation
626 //Compute res = Q' * other column by column
641 // Compute res = Q * other column by column