用 LAPACKE 求解线性方程

Question

我正在尝试求解一些线性方程（对称的、三对角的和正的）。我必须使用 LAPACKE。我的代码如下：

#include <lapacke.h>
#include <stdio.h>



void print_mtrx(double * mtrx, int n, int m)
{
    int i, j;

    for(i = 0; i < n; i++)
    {
        for(j = 0; j < m; j++)
        {
            printf("%f ", mtrx[i*m+j]);
        }
        printf("\n");
    }
    printf("\n");
}

int main()
{
    double matrix[5*5] = {
        2,  0,  0,  0,  0,
        0,  2,  0,  0,  0,
        0,  0,  2,  0,  0,
        0,  0,  0,  2,  0,
        0,  0,  0,  0,  2
    };

    double rozw[5] = {1,2,3,4,5};

    double matrix2[5*5] = {
        7,  0,  0,  0,  0,
        0,  7,  0,  0,  0,
        0,  0,  7,  0,  0,
        0,  0,  0,  7,  0,
        0,  0,  0,  0,  7
    };



    LAPACKE_dptsv(LAPACK_COL_MAJOR, 5, 5, matrix, matrix2, rozw, 5);

    print_mtrx(matrix, 5, 5);
    print_mtrx(matrix2, 5, 5);
    print_mtrx(rozw, 5, 1);

}

LAPACKE的函数好像什么都不做，没有任何错误。主要问题是，我不知道函数参数代表什么。我搜索了很长时间，但没有真正的文档。这是我设法找到或猜测的内容：

int matrix_order -- LAPACK_COL_MAJOR或LAPACK_ROW_MAJOR，矩阵在内存中是如何表示的
lapack_int n -- 矩阵的大小（即列数）
lapack_int nrhs -- 不确定，可能是矢量 b
double* d -- 方程矩阵
double* e -- 不知道。
double* b -- 来自 d
lapack_int ldb -- b 的引导方向（为什么？它与 nrhs 不相同，而 nrhs 本身与 n 相同？）

我怎样才能找到这些论点的真正含义？我怎样才能让我的代码工作？

Answer 1

因此必须查看纯 LAPACK (http://www.netlib.org/lapack/explore-html/d0/dea/dptsv_8f.html#af1bd4c731915bd8755a4da8086fd79a8) 的文档，并忽略不正确的（在 LAPACKE 的情况下）关于 LDB 大于或等于 max(1,N) 的注释。

正确的程序如下：

#include <lapacke.h>
#include <stdio.h>



void print_mtrx(double * mtrx, int n, int m)
{
    int i, j;

    for(i = 0; i < n; i++)
    {
        for(j = 0; j < m; j++)
        {
            printf("%f ", mtrx[i*m+j]);
        }
        printf("\n");
    }
    printf("\n");
}

int main()
{
    double diagonal[5] = {5,1,5,1,5};
    double subdiagonal[4] = {0,0,0,0};

    double solution[5] = {1,2,3,4,5};


    LAPACKE_dptsv(LAPACK_ROW_MAJOR, 5 /*size of matrix*/, 1 /*number of columns in solution*/,
                  diagonal, subdiagonal, solution, 1 /*leading dimension of solution vector*/);

    print_mtrx(solution, 5, 1);
}

Answer 2

当谈到 BLAS and/or LAPACK 的文档时，Intel is probably the most comprehensive out there. You can look up the docs for ?ptsv 解释了每个参数的用途。

（提示：在 Google 中搜索 BLAS 或 LAPACK 时，请务必删除 s/d/c/z前缀。)

这是相关的片段：

The routine solves for X the real or complex system of linear equations A*X = B, where A is an n-by-n symmetric/Hermitian positive-definite tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

A is factored as A = L*D*LT (real flavors) or A = L*D*LH (complex flavors), and the factored form of A is then used to solve the system of equations A*X = B.

Input Parameters

n: The order of matrix A; n ≥ 0.

nrhs: The number of right-hand sides, the number of columns in B; nrhs ≥ 0.

d: Array, dimension at least max(1, n). Contains the diagonal elements of the tridiagonal matrix A.

e, b: Arrays: e(n - 1), b(ldb,*). The array e contains the (n - 1) subdiagonal elements of A. The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs).

ldb: The leading dimension of b; ldb ≥ max(1, n).

Output Parameters

d: Overwritten by the n diagonal elements of the diagonal matrix D from the L*D*LT (real) / L*D*LH (complex) factorization of A.

e: Overwritten by the (n - 1) subdiagonal elements of the unit bidiagonal factor L from the factorization of A.

b: Overwritten by the solution matrix X.

info: If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value. If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the solution has not been computed. The factorization has not been completed unless i = n.

用 LAPACKE 求解线性方程

Solving linear equation with LAPACKE

c

linear-algebra

lapack

lapacke

Input Parameters

Output Parameters