## LAPACK dgetrs vs dgesv

Open discussion regarding features, bugs, issues, vendors, etc.

### LAPACK dgetrs vs dgesv

In LAPACK documentation,

dgesv Solves a general system of linear equations AX=B.

dgetrs Solves a general system of linear equations AX=B, AT X=B or AH X=B, using the LU factorization computed by DGETRF.

What is the difference ? Also, I made following C/C++ program and both give different result. Why is it so ?

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`#include <iostream>#include <iomanip>#include <vector>#include <math.h>#include <time.h>#include "stdafx.h"using namespace std;extern "C" {   // LU decomoposition of a general matrix   void dgetrf_(int* M, int *N, double* A, int* lda, int* IPIV, int* INFO);   //// generate inverse of a matrix given its LU decomposition   //void dgetri_(int* N, double* A, int* lda, int* IPIV, double* WORK, int* lwork, int* INFO);   void dgetrs_(char* C, int* N, int* NRHS, double* A, int* LDA, int* IPIV, double* B, int* LDB, int* INFO);   void dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);}void solvelineq(double* A, double* B, int N){   int *IPIV = new int[N + 1];   int LWORK = N*N;   double *WORK = new double[LWORK];   int INFO;   char C = 'N';   int NRHS = 1;   dgetrf_(&N, &N, A, &N, IPIV, &INFO);   dgetrs_(&C, &N, &NRHS, A, &N, IPIV, B, &N, &INFO);   //dgetri_(&N, A, &N, IPIV, WORK, &LWORK, &INFO);   delete IPIV;   delete WORK;}double comparematrices(double* A, double* B, int N){   double sum = 0.;   for (int i = 0; i < N; ++i)      sum += fabs(A[i] - B[i]);   return sum;}int main() {   int dim;   std::cout << "Enter Dimensions of Matrix : \n";   std::cin >> dim;   clock_t c1, c2;   c1 = clock();   vector<double> a(dim*dim);   vector<double> b(dim);   vector<double> c(dim);   vector<int> ipiv(dim);   srand(1);              // seed the random # generator with a known value   double maxr = (double)RAND_MAX;   for (int r = 0; r < dim; r++) {  // set a to a random matrix, i to the identity      for (int c = 0; c < dim; c++) {         a[r + c*dim] = rand() / maxr;      }      b[r] = rand() / maxr;      c[r] = b[r];   }   c2 = clock();   cout << endl << dim << " x " << dim << " matrix generated in : " << double(c2 - c1) / CLK_TCK << " seconds " << endl;   // C is identical matrix to B because we are solving by two methods.   c1 = clock();   solvelineq(&*a.begin(), &*c.begin(), dim);   c2 = clock();   cout << endl << " dgetrf_ and dgetrs_ completed in : " << double(c2 - c1) / CLK_TCK << " seconds " << endl;   vector<double> a1(a);   vector<double> b1(b);   int info;   int one = 1;   c1 = clock();   dgesv_(&dim, &one, &*a.begin(), &dim, &*ipiv.begin(), &*b.begin(), &dim, &info);   c2 = clock();   cout << endl << " dgesv_ completed in : " << double(c2 - c1) / CLK_TCK << " seconds " << endl;   cout << "info is " << info << endl;   double eps = 0.;   c1 = clock();   for (int i = 0; i < dim; ++i)   {      double sum = 0.;      for (int j = 0; j < dim; ++j)         sum += a1[i + j*dim] * b[j];      eps += fabs(b1[i] - sum);   }   c2 = clock();   cout << endl << " dgesv_ check completed in : " << double(c2 - c1) / CLK_TCK << " seconds " << endl;   cout << "check is " << eps << endl;   cout << "\nFinal Matrix 1 : " << endl;   for (int i = 0; i < dim; ++i)      cout << b[i] << endl;   cout << "\nFinal Matrix 2 : " << endl;   for (int i = 0; i < dim; ++i)      cout << c[i] << endl;   double diff;   c1 = clock();   diff = comparematrices(&*b.begin(), &*c.begin(), dim);   c2 = clock();   cout << endl << " Both functions compared in : " << double(c2 - c1) / CLK_TCK << " seconds " << endl;   cout << "Sum of difference is : " << diff << endl;   return 0;}`

My Result :
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`My Result : Enter Dimensions of Matrix : 55 x 5 matrix generated in : 0 secondsdgetrf_ and dgetrs_ completed in : 0.001 secondsdgesv_ completed in : 0 seconds info is 0dgesv_ check completed in : 0 seconds check is 2.02009e-15Final Matrix 1 : -2.97629 4.83948 2.00769 -1.98887 -5.15561Final Matrix 2 : -1.40622 2.29029 0.480829 -1.63597 0.71962Both functions compared in : 0 secondsSum of difference is : 11.8743`
mailmaverick

Posts: 2
Joined: Thu Mar 17, 2016 11:37 am

### Re: LAPACK dgetrs vs dgesv

If you look at the code for DGESV, it does nothing more than call DGETRF and then DGETRS:

http://www.netlib.org/lapack/explore-3.1.1-html/dgesv.f.html

The reason you get different results is because DGETRF replaces the matrix with the LU factorization in-place, so if you call DGESV afterwards, it will think the LU factorization is your original matrix, and give you something completely different. You need to save the original matrix before calling
Code: Select all
`solvelineq`
in order to do a comparison. Also, pet peeve: you need to use "delete []" instead of just "delete" on arrays.
CyLith

Posts: 41
Joined: Sun Feb 08, 2009 7:23 am
Location: Stanford, CA