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SuperLU (Supernodal LU) is a mathematical library which implements a direct solver for large systems of linear equations represented with sparse matrices. As implied by its name, solving is done through LU decomposition. This part of the code can also deal with rectangular matrices.

The library is written in C, but may also be called from Fortran. Two parallel variants exist for SuperLU: SuperLU_MT for shared memory systems, and SuperLU_DIST for distributed memory systems. The latter uses MPI for parallelizing.

A user guide is available in PDF on the Lawrence Berkeley National Laboratory website. The library requires a version of BLAS to be installed.


The following file contains an example (in C) to solve a system of complex linear equations with SuperLU:

File : ex_superlu.c
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
#include "slu_zdefs.h"
main(int argc, char *argv[])
    SuperMatrix A;
    NCformat *Astore;
    doublecomplex   *a;
    int      *asub, *xa;
    int      *perm_c; /* column permutation vector */
    int      *perm_r; /* row permutations from partial pivoting */
    SuperMatrix L;      /* factor L */
    SCformat *Lstore;
    SuperMatrix U;      /* factor U */
    NCformat *Ustore;
    SuperMatrix B;
    int      nrhs, ldx, info, m, n, nnz;
    doublecomplex   *xact, *rhs;
    mem_usage_t   mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
    /* Set the default input options:
	options.Fact = DOFACT;
        options.Equil = YES;
    	options.ColPerm = COLAMD;
	options.DiagPivotThresh = 1.0;
    	options.Trans = NOTRANS;
    	options.IterRefine = NOREFINE;
    	options.SymmetricMode = NO;
    	options.PivotGrowth = NO;
    	options.ConditionNumber = NO;
    	options.PrintStat = YES;
    /* Read the matrix in Harwell-Boeing format. */
    zreadhb(&m, &n, &nnz, &a, &asub, &xa);
    zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    nrhs   = 1;
    if ( !(rhs = doublecomplexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
    zCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_Z, SLU_GE);
    xact = doublecomplexMalloc(n * nrhs);
    ldx = n;
    zGenXtrue(n, nrhs, xact, ldx);
    zFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);
    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
    /* Initialize the statistics variables. */
    zgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
    if ( info == 0 ) {
	/* This is how you could access the solution matrix. */
        doublecomplex *sol = (doublecomplex*) ((DNformat*) B.Store)->nzval; 
	 /* Compute the infinity norm of the error. */
	zinf_norm_error(nrhs, &B, xact);
	Lstore = (SCformat *) L.Store;
	Ustore = (NCformat *) U.Store;
    	printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
    	printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
    	printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
	zQuerySpace(&L, &U, &mem_usage);
	printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
	       mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
    } else {
	printf("zgssv() error returns INFO= %d\n", info);
	if ( info <= n ) { /* factorization completes */
	    zQuerySpace(&L, &U, &mem_usage);
	    printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
		   mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
    if ( options.PrintStat ) StatPrint(&stat);
    SUPERLU_FREE (rhs);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");

The example can be compiled with a command line such as the following if a SuperLU module is loaded:

[name@server $] 
icc ex_superlu.c -lsuperlu -lmkl_lapack95_lp64 -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core -liomp5 -lpthread -lm

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