如何从SuiteSparseQR_factorization对象中查找(Q，R)？

Question

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。但是我想知道我能不能直接从这个QR对象中得到真正的Q，R？

Answer 1

SuiteSparse很棒，但它的界面可能会让人感到困惑。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是很好。例如，先使用SuiteSparseQR_factorize，然后使用带有稀疏矩阵输入参数的SuiteSparseQR_qmult，实际上会首先将其转换为密集矩阵，这似乎完全没有必要！

相反，您可以使用

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
) ;

此方法将执行因子分解，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。要得到Q，请将B定义为单位矩阵。下面是一个获取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，则需要用NULL替换额外的指针，然后调用SuiteSparseQR_qmult。