Understanding LAPACK calls in C++ with a simple example

Question

I am a beginner with LAPACK and C++/Fortran interfacing. I need to solve linear equations and eigenvalues problems using LAPACK/BLAS on Mac OS-X Lion. OS-X Lion provides optimized BLAS and LAPACK libraries (in /usr/lib) and I am linking these libraries instead of downloading them from netlib.

My program (reproduced below) is compiling and running fine, but it is giving me wrong answers. I have researched in the web and Stackoverflow and the issue may have to deal with how C++ and Fortran store arrays in differing formats (row major vs Column major). However, as you will see in my example, the simple array for my example should look identical in C++ and fortran. Anyway here goes.

Lets say we want to solve the following linear system:

x + y = 2

x - y = 0

The solution is (x,y) = (1,1). Now I tried to solve this using Lapack as follows

// LAPACK test code

#include<iostream>
#include<vector>

using namespace std;
extern "C" void dgetrs(char *TRANS, int *N, int *NRHS, double *A, 
                      int *LDA, int *IPIV, double *B, int *LDB, int *INFO );

int main()
{
    char trans = 'N';
    int dim = 2;    
    int nrhs = 1;
    int LDA = dim;
    int LDB = dim;
    int info;

    vector<double> a, b;

    a.push_back(1);
    a.push_back(1);
    a.push_back(1);
    a.push_back(-1);

    b.push_back(2);
    b.push_back(0);

    int ipiv[3];


    dgetrs(&trans, &dim, &nrhs, & *a.begin(), &LDA, ipiv, & *b.begin(), &LDB, &info);


    std::cout << "solution is:";    
    std::cout << "[" << b[0] << ", " << b[1] << ", " << "]" << std::endl;
    std::cout << "Info = " << info << std::endl; 

    return(0);
}

This code was compiled as follows:

g++ -Wall -llapack -lblas lapacktest.cpp

On running this, however, I get the solution as (-2,2) which is obviously wrong. I have tried all combination of row/column re-arrangement of my matrix a. Also observe the matrix representation of a should be identical in row and column formats. I think getting this simple example to work will get me started with LAPACK and any help will be appreciated.

Answer 1

You need to factor the matrix (by calling dgetrf) before you can solve the system using dgetrs. Alternatively, you can use the dgesv routine, which does both steps for you.

By the way, you don't need to declare the interfaces yourself, they are in the Accelerate headers:

// LAPACK test code

#include <iostream>
#include <vector>
#include <Accelerate/Accelerate.h>

using namespace std;

int main()
{
    char trans = 'N';
    int dim = 2;    
    int nrhs = 1;
    int LDA = dim;
    int LDB = dim;
    int info;

    vector<double> a, b;

    a.push_back(1);
    a.push_back(1);
    a.push_back(1);
    a.push_back(-1);

    b.push_back(2);
    b.push_back(0);

    int ipiv[3];

    dgetrf_(&dim, &dim, &*a.begin(), &LDA, ipiv, &info);
    dgetrs_(&trans, &dim, &nrhs, & *a.begin(), &LDA, ipiv, & *b.begin(), &LDB, &info);


    std::cout << "solution is:";    
    std::cout << "[" << b[0] << ", " << b[1] << ", " << "]" << std::endl;
    std::cout << "Info = " << info << std::endl; 

    return(0);
}