【发布时间】：2014-03-25 02:20:09
【问题描述】：
我正在尝试用 C++ 中的QR factorization 分解矩阵，使用 Lapack 的函数来求解线性方程组 (Ax=b)
据我了解，dgeqrf 计算 QR 分解并覆盖输入矩阵。输出清楚地包含 L（上三角）的值，但我如何获得 Q？
我试过dormqr，据说是从dgeqrf的输出中计算Q，但结果和之前调用的矩阵是一样的。
这是我的完整代码：
boost::numeric::ublas::matrix<double> in_A(4, 3);
in_A(0, 0) = 1.0;
in_A(0, 1) = 2.0;
in_A(0, 2) = 3.0;
in_A(1, 1) = -3.0;
in_A(1, 2) = 2.0;
in_A(1, 3) = 1.0;
in_A(2, 1) = 2.0;
in_A(2, 2) = 0.0;
in_A(2, 3) = -1.0;
in_A(3, 1) = 3.0;
in_A(3, 2) = -1.0;
in_A(3, 3) = 2.0;
boost::numeric::ublas::vector<double> in_b(4);
in_b(0) = 2;
in_b(1) = 4;
in_b(2) = 6;
in_b(3) = 8;
int rows = in_A.size1();
int cols = in_A.size2();
double *A = (double *)malloc(rows*cols*sizeof(double));
double *b = (double *)malloc(in_b.size()*sizeof(double));
//Lapack has column-major order
for(size_t col=0; col<in_A.size2(); ++col)
{
for(size_t row = 0; row<in_A.size1(); ++row)
{
int D1_idx = col*in_A.size1() + row;
A[D1_idx] = in_A(row, col);
}
b[col] = in_b(col);
}
integer m = rows;
integer n = cols;
integer info = 0;
integer k = n; /* k = min(m,n); */
integer lda = m; /* lda = max(m,1); */
integer lwork = n; /* lwork = max(n,1); */
int max = lwork; /* max = max(lwork,1); */
double *work;
double *tau;
char *side = "L";
char *TR = "T";
integer one = 1;
int i;
double *vec;
work = (double *) malloc( max * sizeof( double ) );
tau = (double *) malloc( k * sizeof( double ) );
vec = (double *) malloc( m * sizeof( double ) );
memset(work, 0, max * sizeof(double));
memset(tau, 0, k * sizeof(double));
std::cout << std::endl;
for(size_t row = 0; row < rows; ++row)
{
for(size_t col = 0; col < cols; ++col)
{
size_t idx = col*rows + row;
std::cout << A[idx] << " ";
}
std::cout << std::endl;
}
dgeqrf_(&m, &n, A, &lda, tau, work, &lwork, &info);
//printf("tau[0] = %f tau[1] = %f\n",tau[0],tau[1]);
std::cout << std::endl;
for(size_t row = 0; row < rows; ++row)
{
for(size_t col = 0; col < cols; ++col)
{
size_t idx = col*rows + row;
std::cout << A[idx] << " ";
}
std::cout << std::endl;
}
memset(vec, 0, m * sizeof(double));
vec[2] = 1.0;
dormqr_(side, TR, &m, &one, &k, A, &lda, tau, vec, &lda, work, &lwork, &info);
free(vec);
free(tau);
free(work);
我的代码有什么问题？
如何分解矩阵并求解相应的线性方程组？
【问题讨论】：
-
请检查您的 in_A 结构。列索引是 (0,1,2) 还是 (1,2,3)？
标签： c++ math visual-studio-2012 linear-algebra lapack