0

在 SuiteSparse 的 C++ 接口中，我可以使用

SuiteSparseQR_factorization <double> *QR;
QR = SuiteSparseQR_factorize(A) ;

计算矩阵 A 的 QR 分解，以便我可以重用 QR 进行进一步计算。但我想知道我可以直接从这个 QR 对象中获得真正的 Q、R 吗？

4

1 回答 1

0

SuiteSparse 很棒，但界面可能令人困惑。不幸的是，涉及SuiteSparseQR_factorization结构的方法似乎是最方便的，但在实践中对我来说效果并不好。例如，使用SuiteSparseQR_factorize然后SuiteSparseQR_qmult使用稀疏矩阵输入参数实际上首先将其转换为密集矩阵，这似乎完全没有必要！

相反，使用

template <typename Entry> SuiteSparse_long SuiteSparseQR
(
    // inputs, not modified
    int ordering,           // all, except 3:given treated as 0:fixed
    double tol,             // only accept singletons above tol

    SuiteSparse_long econ,  // number of rows of C and R to return; a value
                            // less than the rank r of A is treated as r, and
                            // a value greater than m is treated as m.

    int getCTX,             // if 0: return Z = C of size econ-by-bncols
                            // if 1: return Z = C' of size bncols-by-econ
                            // if 2: return Z = X of size econ-by-bncols

    cholmod_sparse *A,      // m-by-n sparse matrix

    // B is either sparse or dense.  If Bsparse is non-NULL, B is sparse and
    // Bdense is ignored.  If Bsparse is NULL and Bdense is non-NULL, then B is
    // dense.  B is not present if both are NULL.
    cholmod_sparse *Bsparse,
    cholmod_dense *Bdense,

    // output arrays, neither allocated nor defined on input.

    // Z is the matrix C, C', or X
    cholmod_sparse **Zsparse,
    cholmod_dense  **Zdense,
    cholmod_sparse **R,     // the R factor
    SuiteSparse_long **E,   // size n; fill-reducing ordering of A.
    cholmod_sparse **H,     // the Householder vectors (m-by-nh)
    SuiteSparse_long **HPinv,// size m; row permutation for H
    cholmod_dense **HTau,   // size nh, Householder coefficients

    // workspace and parameters
    cholmod_common *cc
) ;

此方法将执行分解，然后可选地输出（除其他外）R、矩阵乘积 Z = Q^T * B（或其转置 -- B^T * Q）或线性系统的解。要获得 Q，请将 B 定义为单位矩阵。这是获取 Q 和 R 的示例。

cholmod_common Common, * cc;
cc = &Common;
cholmod_l_start(cc);
cholmod_sparse *A;//assume you have already defined this
int ordering = SPQR_ORDERING_BEST;
double tol = 0;
Long econ = A->nrow;
int getCTX = 1;// Z = (Q^T * B)^T = B^T * Q
cholmod_sparse *B = cholmod_l_speye(A->nrow, A->nrow, CHOLMOD_REAL, cc);//the identity matrix
cholmod_sparse *Q, *R;//output pointers to the Q and R sparse matrices

SuiteSparseQR<double>(ordering, tol, econ, getCTX, A, B, NULL, &Q, NULL, &R, NULL, NULL, NULL, NULL, cc);

如果您希望任何其他输出在不使用显式形成的 Q 和/或 R 的情况下执行后续操作，则需要将 NULL 替换为其他指针，然后调用SuiteSparseQR_qmult.

于 2020-06-07T10:14:23.000 回答