千万自由度大规模线性方程组并行求解库PETSc的介绍

typedef const char *KSPType;#define KSPRICHARDSON "richardson"#define KSPCHEBYSHEV  "chebyshev"#define KSPCG         "cg"#define KSPGROPPCG    "groppcg"#define KSPPIPECG     "pipecg"#define KSPPIPECGRR   "pipecgrr"#define KSPPIPELCG    "pipelcg"#define KSPPIPEPRCG   "pipeprcg"#define KSPPIPECG2    "pipecg2"#define KSPCGNE       "cgne"#define KSPNASH       "nash"#define KSPSTCG       "stcg"#define KSPGLTR       "gltr"#define KSPCGNASH     PETSC_DEPRECATED_MACRO("GCC warning \"KSPCGNASH macro is deprecated use KSPNASH (since version 3.11)\"") "nash"#define KSPCGSTCG     PETSC_DEPRECATED_MACRO("GCC warning \"KSPCGSTCG macro is deprecated use KSPSTCG (since version 3.11)\"") "stcg"#define KSPCGGLTR     PETSC_DEPRECATED_MACRO("GCC warning \"KSPCGGLTR macro is deprecated use KSPSGLTR (since version 3.11)\"") "gltr"#define KSPFCG        "fcg"#define KSPPIPEFCG    "pipefcg"#define KSPGMRES      "gmres"#define KSPPIPEFGMRES "pipefgmres"#define KSPFGMRES     "fgmres"#define KSPLGMRES     "lgmres"#define KSPDGMRES     "dgmres"#define KSPPGMRES     "pgmres"#define KSPTCQMR      "tcqmr"#define KSPBCGS       "bcgs"#define KSPIBCGS      "ibcgs"#define KSPQMRCGS     "qmrcgs"#define KSPFBCGS      "fbcgs"#define KSPFBCGSR     "fbcgsr"#define KSPBCGSL      "bcgsl"#define KSPPIPEBCGS   "pipebcgs"#define KSPCGS        "cgs"#define KSPTFQMR      "tfqmr"#define KSPCR         "cr"#define KSPPIPECR     "pipecr"#define KSPLSQR       "lsqr"#define KSPPREONLY    "preonly"#define KSPNONE       "none"#define KSPQCG        "qcg"#define KSPBICG       "bicg"#define KSPMINRES     "minres"#define KSPSYMMLQ     "symmlq"#define KSPLCD        "lcd"#define KSPPYTHON     "python"#define KSPGCR        "gcr"#define KSPPIPEGCR    "pipegcr"#define KSPTSIRM      "tsirm"#define KSPCGLS       "cgls"#define KSPFETIDP     "fetidp"#define KSPHPDDM      "hpddm"

typedef const char *PCType;#define PCNONE               "none"#define PCJACOBI             "jacobi"#define PCSOR                "sor"#define PCLU                 "lu"#define PCQR                 "qr"#define PCSHELL              "shell"#define PCAMGX               "amgx"#define PCBJACOBI            "bjacobi"#define PCMG                 "mg"#define PCEISENSTAT          "eisenstat"#define PCILU                "ilu"#define PCICC                "icc"#define PCASM                "asm"#define PCGASM               "gasm"#define PCKSP                "ksp"#define PCBJKOKKOS           "bjkokkos"#define PCCOMPOSITE          "composite"#define PCREDUNDANT          "redundant"#define PCSPAI               "spai"#define PCNN                 "nn"#define PCCHOLESKY           "cholesky"#define PCPBJACOBI           "pbjacobi"#define PCVPBJACOBI          "vpbjacobi"#define PCMAT                "mat"#define PCHYPRE              "hypre"#define PCPARMS              "parms"#define PCFIELDSPLIT         "fieldsplit"#define PCTFS                "tfs"#define PCML                 "ml"#define PCGALERKIN           "galerkin"#define PCEXOTIC             "exotic"#define PCCP                 "cp"#define PCBFBT               "bfbt"#define PCLSC                "lsc"#define PCPYTHON             "python"#define PCPFMG               "pfmg"#define PCSMG                "smg"#define PCSYSPFMG            "syspfmg"#define PCREDISTRIBUTE       "redistribute"#define PCSVD                "svd"#define PCGAMG               "gamg"#define PCCHOWILUVIENNACL    "chowiluviennacl"#define PCROWSCALINGVIENNACL "rowscalingviennacl"#define PCSAVIENNACL         "saviennacl"#define PCBDDC               "bddc"#define PCKACZMARZ           "kaczmarz"#define PCTELESCOPE          "telescope"#define PCPATCH              "patch"#define PCLMVM               "lmvm"#define PCHMG                "hmg"#define PCDEFLATION          "deflation"#define PCHPDDM              "hpddm"#define PCH2OPUS             "h2opus"#define PCMPI                "mpi"

static char help[]="linear solve";#include <petscmat.h>#include <petscksp.h>#undef __FUNCT__#define __FUNCT__ "main"int main(int argc,char **args){  Mat            A;  Vec            b,u,u_tmp,x;  char           Ain[PETSC_MAX_PATH_LEN],rhs[PETSC_MAX_PATH_LEN];   PetscErrorCode ierr;  int            m,n,nz,dummy;   PetscInt       i,col,row,rstart,rend,rstart1,rend1;;  PetscScalar    val;  FILE           *Afile,*bfile;  PetscViewer    view;  PetscBool      ***_A,***_b,***;  PetscMPIInt    size,rank;    int shift;  KSP ksp;  PC pc;   PetscInitialize(&argc,&args,(char *)0,help);  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);  ierr = PetscOptionsGetString(PETSC_NULL,PETSC_NULL,"-Ain",Ain,PETSC_MAX_PATH_LEN,&***_A);CHKERRQ(ierr);  if (***) shift = 0;  if (***_A){   // ierr = PetscPrintf(PETSC_COMM_WORLD,"\n Read matrix in ascii format ...\n");CHKERRQ(ierr);    Afile=fopen(Ain,"r");    fscanf(Afile,"%d %d %d\n",&m,&n,&nz);    //ierr = PetscPrintf(PETSC_COMM_WORLD,"m: %d, n: %d, nz: %d \n", m,n,nz);CHKERRQ(ierr);    if (m != n) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_SIZ, "Number of rows, cols must be same for this example\n");    ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);    ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,n);CHKERRQ(ierr);    ierr = MatSetFromOptions(A);CHKERRQ(ierr);    PetscCall(MatSetUp(A));    ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);   // printf("\nThis is process %d reading from %d to %d ...\n",rank,rstart,rend-1);     for (i=0; i<nz; i++) {      fscanf(Afile,"%d %d %le\n",&row,&col,(double*)&val);     if (row>=rstart && row<rend)      ierr = MatSetValues(A,1,&row,1,&col,&val,INSERT_VALUES);CHKERRQ(ierr);    }      ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);      ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);      fflush(stdout);      fclose(Afile); }   ierr = PetscOptionsGetString(PETSC_NULL,PETSC_NULL,"-rhs",rhs,PETSC_MAX_PATH_LEN,&***_b);CHKERRQ(ierr); ierr = PetscOptionsGetString(PETSC_NULL,PETSC_NULL,"-rhs",rhs,PETSC_MAX_PATH_LEN,&***_b);CHKERRQ(ierr);if (***_b){    ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);    ierr = VecSetSizes(b,PETSC_DECIDE,n);CHKERRQ(ierr);    ierr = VecSetFromOptions(b);CHKERRQ(ierr);    ierr = VecGetOwnershipRange(b,&rstart1,&rend1);CHKERRQ(ierr);   // printf("\nThis is process %d reading from %d to %d ...\n",rank,rstart1,rend1-1);    bfile = fopen(rhs,"r");    for (i=0; i<n; i++) {          fscanf(bfile,"%d %le\n",&dummy,(double*)&val);        if (dummy>=rstart1 && dummy<rend1)    ierr = VecSetValues(b,1,&i,&val,INSERT_VALUES);CHKERRQ(ierr);}    ierr = VecAssemblyBegin(b);CHKERRQ(ierr);    ierr = VecAssemblyEnd(b);CHKERRQ(ierr);    fflush(stdout);    fclose(bfile);  }  /*ierr = PetsfcPrint(PETSC_COMM_WORLD,"\n Write matrix in binary to 'matrix.dat' ...\n");CHKERRQ(ierr);  ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"matrix.dat",FILE_MODE_WRITE,&view);CHKERRQ(ierr);  ierr = MatView(A,view);CHKERRQ(ierr);   if (***_b){ ierr = PetscPrintf(PETSC_COMM_WORLD,"\n Write rhs in binary to 'matrix.dat' ...\n");CHKERRQ(ierr);    ierr = VecView(b,view);CHKERRQ(ierr);  }  ierr = MatDestroy(&A);CHKERRQ(ierr);  if (***_b) {ierr = VecDestroy(&b);CHKERRQ(ierr);}  ierr = PetscViewerDestroy(&view);CHKERRQ(ierr);*/PetscCall(VecDuplicate(b, &x));PetscLogDouble start_time,end_time,time;PetscTime(&start_time);PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));PetscCall(KSPSetOperators(ksp, A, A));PetscCall(KSPGetPC(ksp, &pc));  PetscCall(PCSetType(pc, PCJACOBI));  PetscCall(KSPSetType(ksp,KSPCG));  PetscCall(KSPSetTolerances(ksp, 1.e-6, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));  PetscCall(KSPSetFromOptions(ksp));  PetscCall(KSPSolve(ksp, b, x));PetscTime(&end_time);time = end_time - start_time;PetscPrintf(PETSC_COMM_WORLD, "\n%-15s%-7.5f seconds\n", "Average time:",time ); PetscCall( VecView(x,PETSC_VIEWER_STDOUT_WORLD));  PetscCall(KSPDestroy(&ksp));  PetscCall(VecDestroy(&x));  PetscCall(MatDestroy(&A));  ierr = PetscFinalize();  return 0;}

mpiexec -n 10 ./solve -Ain mat1.txt -rhs vec1.txt