int main(int argc,char **argv)
{
DM da;
SNES snes; /* nonlinear solver */
AppCtx *user; /* user-defined work context */
PetscBag bag;
PetscInt its; /* iterations for convergence */
PetscMPIInt size;
SNESConvergedReason reason;
PetscErrorCode ierr;
PetscReal lambda_max = 6.81, lambda_min = 0.0, error;
Vec x;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Example only works for one process.");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize problem parameters
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(AppCtx), &bag);CHKERRQ(ierr);
ierr = PetscBagGetData(bag, (void**) &user);CHKERRQ(ierr);
ierr = PetscBagSetName(bag, "params", "Parameters for SNES example 4");CHKERRQ(ierr);
ierr = PetscBagRegisterReal(bag, &user->alpha, 1.0, "alpha", "Linear coefficient");CHKERRQ(ierr);
ierr = PetscBagRegisterReal(bag, &user->lambda, 6.0, "lambda", "Nonlinear coefficient");CHKERRQ(ierr);
ierr = PetscBagSetFromOptions(bag);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-alpha",&user->alpha,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-lambda",&user->lambda,NULL);CHKERRQ(ierr);
if (user->lambda > lambda_max || user->lambda < lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda %g is out of range [%g, %g]", (double)user->lambda, (double)lambda_min, (double)lambda_max);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create multilevel DM data structure (SNES) to manage hierarchical solvers
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,-3,-3,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da, 0, "ooblek");CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,user);CHKERRQ(ierr);
ierr = SNESSetDM(snes, (DM) da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set the discretization functions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,user);CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(da,(PetscErrorCode (*)(DMDALocalInfo*,void*,Mat,Mat,void*))FormJacobianLocal,user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = SNESSetComputeInitialGuess(snes, FormInitialGuess,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESSolve(snes,NULL,NULL);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(snes, &reason);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D, %s\n",its,SNESConvergedReasons[reason]);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = SNESGetDM(snes,&da);CHKERRQ(ierr);
ierr = SNESGetSolution(snes,&x);CHKERRQ(ierr);
ierr = L_2Error(da, x, &error, user);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"L_2 error in the solution: %g\n", (double)error);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = PetscBagDestroy(&bag);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
void Delta::BuildDensityGridSmooth(double smooth, Particle& pp, Vec& delta)
{
BuildDensityGrid(pp, delta);
if (rmasksmooth > 1.e-5) PetscPrintf(PETSC_COMM_WORLD, "WARNING!!! POSSIBLE MULTIPLE SMOOTHING DETECTED\n");
dg1.GaussSmooth(delta, smooth);
}
int main(int argc,char **argv)
{
Mat A[NMAT]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt n=128,nlocal,k,Istart,Iend,i,j,start_ct,end_ct;
PetscReal w=9.92918,a=0.0,b=2.0,h,deltasq;
PetscReal nref[NL],K2[NL],q[NL],*md,*supd,*subd;
PetscScalar v,alpha;
PetscBool terse;
PetscErrorCode ierr;
PetscLogDouble time1,time2;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
n = (n/4)*4;
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nPlanar waveguide, n=%D\n\n",n+1);CHKERRQ(ierr);
h = (b-a)/n;
nlocal = (n/4)-1;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set waveguide parameters used in construction of matrices
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* refractive indices in each layer */
nref[0] = 1.5;
nref[1] = 1.66;
nref[2] = 1.6;
nref[3] = 1.53;
nref[4] = 1.66;
nref[5] = 1.0;
for (i=0;i<NL;i++) K2[i] = w*w*nref[i]*nref[i];
deltasq = K2[0] - K2[NL-1];
for (i=0;i<NL;i++) q[i] = K2[i] - (K2[0] + K2[NL-1])/2;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the polynomial matrices
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* initialize matrices */
for (i=0;i<NMAT;i++) {
ierr = MatCreate(PETSC_COMM_WORLD,&A[i]);CHKERRQ(ierr);
ierr = MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n+1,n+1);CHKERRQ(ierr);
ierr = MatSetFromOptions(A[i]);CHKERRQ(ierr);
ierr = MatSetUp(A[i]);CHKERRQ(ierr);
}
ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);
/* A0 */
alpha = (h/6)*(deltasq*deltasq/16);
for (i=Istart;i<Iend;i++) {
v = 4.0;
if (i==0 || i==n) v = 2.0;
ierr = MatSetValue(A[0],i,i,v*alpha,INSERT_VALUES);CHKERRQ(ierr);
if (i>0) { ierr = MatSetValue(A[0],i,i-1,alpha,INSERT_VALUES);CHKERRQ(ierr); }
if (i<n) { ierr = MatSetValue(A[0],i,i+1,alpha,INSERT_VALUES);CHKERRQ(ierr); }
}
/* A1 */
if (Istart==0) { ierr = MatSetValue(A[1],0,0,-deltasq/4,INSERT_VALUES);CHKERRQ(ierr); }
if (Iend==n+1) { ierr = MatSetValue(A[1],n,n,deltasq/4,INSERT_VALUES);CHKERRQ(ierr); }
/* A2 */
alpha = 1.0/h;
for (i=Istart;i<Iend;i++) {
v = 2.0;
if (i==0 || i==n) v = 1.0;
ierr = MatSetValue(A[2],i,i,v*alpha,ADD_VALUES);CHKERRQ(ierr);
if (i>0) { ierr = MatSetValue(A[2],i,i-1,-alpha,ADD_VALUES);CHKERRQ(ierr); }
if (i<n) { ierr = MatSetValue(A[2],i,i+1,-alpha,ADD_VALUES);CHKERRQ(ierr); }
}
ierr = PetscMalloc3(n+1,&md,n+1,&supd,n+1,&subd);CHKERRQ(ierr);
md[0] = 2.0*q[1];
supd[1] = q[1];
subd[0] = q[1];
for (k=1;k<=NL-2;k++) {
end_ct = k*(nlocal+1);
start_ct = end_ct-nlocal;
for (j=start_ct;j<end_ct;j++) {
md[j] = 4*q[k];
supd[j+1] = q[k];
subd[j] = q[k];
}
if (k < 4) { /* interface points */
md[end_ct] = 4*(q[k] + q[k+1])/2.0;
supd[end_ct+1] = q[k+1];
subd[end_ct] = q[k+1];
}
}
md[n] = 2*q[NL-2];
supd[n] = q[NL-2];
subd[n] = q[NL-2];
alpha = -h/6.0;
for (i=Istart;i<Iend;i++) {
ierr = MatSetValue(A[2],i,i,md[i]*alpha,ADD_VALUES);CHKERRQ(ierr);
if (i>0) { ierr = MatSetValue(A[2],i,i-1,subd[i-1]*alpha,ADD_VALUES);CHKERRQ(ierr); }
if (i<n) { ierr = MatSetValue(A[2],i,i+1,supd[i+1]*alpha,ADD_VALUES);CHKERRQ(ierr); }
}
ierr = PetscFree3(md,supd,subd);CHKERRQ(ierr);
/* A3 */
if (Istart==0) { ierr = MatSetValue(A[3],0,0,1.0,INSERT_VALUES);CHKERRQ(ierr); }
if (Iend==n+1) { ierr = MatSetValue(A[3],n,n,1.0,INSERT_VALUES);CHKERRQ(ierr); }
/* A4 */
alpha = (h/6);
for (i=Istart;i<Iend;i++) {
v = 4.0;
if (i==0 || i==n) v = 2.0;
ierr = MatSetValue(A[4],i,i,v*alpha,INSERT_VALUES);CHKERRQ(ierr);
if (i>0) { ierr = MatSetValue(A[4],i,i-1,alpha,INSERT_VALUES);CHKERRQ(ierr); }
if (i<n) { ierr = MatSetValue(A[4],i,i+1,alpha,INSERT_VALUES);CHKERRQ(ierr); }
}
/* assemble matrices */
for (i=0;i<NMAT;i++) {
ierr = MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
for (i=0;i<NMAT;i++) {
ierr = MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
ierr = PEPSetOperators(pep,NMAT,A);CHKERRQ(ierr);
ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);
ierr = PetscTime(&time1); CHKERRQ(ierr);
ierr = PEPSolve(pep);CHKERRQ(ierr);
ierr = PetscTime(&time2); CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* show detailed info unless -terse option is given by user */
ierr = PetscOptionsHasName(NULL,"-terse",&terse);CHKERRQ(ierr);
if (terse) {
ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);CHKERRQ(ierr);
} else {
ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
ierr = PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = PetscPrintf(PETSC_COMM_WORLD,"Time: %g\n\n\n",time2-time1);CHKERRQ(ierr);
ierr = PEPDestroy(&pep);CHKERRQ(ierr);
for (i=0;i<NMAT;i++) {
ierr = MatDestroy(&A[i]);CHKERRQ(ierr);
}
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
Matrix C is copied from ~petsc/src/ksp/ksp/examples/tutorials/ex5.c\n\n";
/*
Example: ./ex132 -mat_view_info
*/
#include <petscmat.h>
#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **args)
{
Mat C,C1,C2; /* matrix */
PetscScalar v;
PetscInt Ii,J,Istart,Iend;
PetscErrorCode ierr;
PetscInt i,j,m = 3,n = 2;
PetscMPIInt size,rank;
PetscBool mat_nonsymmetric = PETSC_FALSE;
MatInfo info;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
n = 2*size;
/* Set flag if we are doing a nonsymmetric problem; the default is symmetric. */
ierr = PetscOptionsGetBool(PETSC_NULL,"-mat_nonsym",&mat_nonsymmetric,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(C,5,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {J = Ii - n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
}
/* Make the matrix nonsymmetric if desired */
if (mat_nonsymmetric) {
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.5; i = Ii/n;
if (i>1) {J = Ii-n-1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
}
} else {
ierr = MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* First, create C1 = 2.0*C1 + C, C1 has less non-zeros than C */
ierr = PetscPrintf(PETSC_COMM_WORLD, "\ncreate C1 = 2.0*C1 + C, C1 has less non-zeros than C \n");
ierr = MatCreate(PETSC_COMM_WORLD,&C1);CHKERRQ(ierr);
ierr = MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C1);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(C1,1,PETSC_NULL);CHKERRQ(ierr);
for (Ii=Istart; Ii<Iend; Ii++) {
ierr = MatSetValues(C1,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," MatAXPY(C1,2.0,C,DIFFERENT_NONZERO_PATTERN)...\n");
ierr = MatAXPY(C1,2.0,C,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatGetInfo(C1,MAT_GLOBAL_SUM,&info);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," C1: nz_allocated = %g; nz_used = %g; nz_unneeded = %g\n",info.nz_allocated,info.nz_used, info.nz_unneeded);
/* Secondly, create C2 = 2.0*C2 + C, C2 has non-zero pattern of C2 + C */
ierr = PetscPrintf(PETSC_COMM_WORLD, "\ncreate C2 = 2.0*C2 + C, C2 has non-zero pattern of C2 + C \n");
ierr = MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&C2);CHKERRQ(ierr);
/*
ierr = MatCreate(PETSC_COMM_WORLD,&C2);CHKERRQ(ierr);
ierr = MatSetSizes(C2,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C2);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(C2,5,PETSC_NULL);CHKERRQ(ierr);
*/
for (Ii=Istart; Ii<Iend; Ii++) {
v = 1.0;
ierr = MatSetValues(C2,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
printf(" MatAXPY(C2,2.0,C,SUBSET_NONZERO_PATTERN)...\n");
ierr = MatAXPY(C2,2.0,C,SUBSET_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatGetInfo(C2,MAT_GLOBAL_SUM,&info);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," C2: nz_allocated = %g; nz_used = %g; nz_unneeded = %g\n",info.nz_allocated,info.nz_used, info.nz_unneeded);
ierr = MatDestroy(&C1);CHKERRQ(ierr);
ierr = MatDestroy(&C2);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
KSP ksp;
DM da;
UserContext user;
PetscReal norm;
const char *bcTypes[2] = {"dirichlet","neumann"};
PetscErrorCode ierr;
PetscInt bc;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
PetscScalar Hx,Hy,Hz;
PetscScalar ***array;
Vec x,b,r;
Mat J;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = DMDACreate3d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,12,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);CHKERRQ(ierr);
ierr = DMDASetInterpolationType(da, DMDA_Q0);CHKERRQ(ierr);
ierr = KSPSetDM(ksp,da);CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
bc = (PetscInt)NEUMANN;
ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex34.c",bcTypes,2,bcTypes[0],&bc,PETSC_NULL);CHKERRQ(ierr);
user.bcType = (BCType)bc;
ierr = PetscOptionsEnd();
ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr);
ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
ierr = KSPGetOperators(ksp,PETSC_NULL,&J,PETSC_NULL);CHKERRQ(ierr);
ierr = VecDuplicate(b,&r);CHKERRQ(ierr);
ierr = MatMult(J,x,r);CHKERRQ(ierr);
ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
Hx = 1.0 / (PetscReal)(mx);
Hy = 1.0 / (PetscReal)(my);
Hz = 1.0 / (PetscReal)(mz);
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da, x, &array);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++){
for (j=ys; j<ys+ym; j++){
for(i=xs; i<xs+xm; i++){
array[k][j][i] -=
PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
}
}
}
ierr = DMDAVecRestoreArray(da, x, &array);CHKERRQ(ierr);
ierr = VecAssemblyBegin(x);CHKERRQ(ierr);
ierr = VecAssemblyEnd(x);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",norm);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_1,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz)));CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz)));CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat A,Atrans,sA,*submatA,*submatsA;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt bs=1,mbs=10,ov=1,i,j,k,*rows,*cols,nd=2,*idx,rstart,rend,sz,M,N,Mbs;
PetscScalar *vals,rval,one=1.0;
IS *is1,*is2;
PetscRandom rand;
PetscBool flg,TestOverlap,TestSubMat,TestAllcols;
PetscLogStage stages[2];
PetscInt vid = -1;
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 = PetscOptionsGetInt(PETSC_NULL,"-mat_block_size",&bs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_mbs",&mbs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-ov",&ov,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-nd",&nd,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-view_id",&vid,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-test_overlap", &TestOverlap);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-test_submat", &TestSubMat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-test_allcols", &TestAllcols);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,mbs*bs,mbs*bs,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(A,MATBAIJ);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,PETSC_DEFAULT,PETSC_NULL);
ierr = MatMPIBAIJSetPreallocation(A,bs,PETSC_DEFAULT,PETSC_NULL,PETSC_DEFAULT,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
ierr = MatGetSize(A,&M,&N);
Mbs = M/bs;
ierr = PetscMalloc(bs*sizeof(PetscInt),&rows);CHKERRQ(ierr);
ierr = PetscMalloc(bs*sizeof(PetscInt),&cols);CHKERRQ(ierr);
ierr = PetscMalloc(bs*bs*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
ierr = PetscMalloc(M*sizeof(PetscScalar),&idx);CHKERRQ(ierr);
/* Now set blocks of values */
for (j=0; j<bs*bs; j++) vals[j] = 0.0;
for (i=0; i<Mbs; i++){
cols[0] = i*bs; rows[0] = i*bs;
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
/* second, add random blocks */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
cols[0] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
rows[0] = rstart + bs*(PetscInt)(PetscRealPart(rval)*mbs);
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
for (j=0; j<bs*bs; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
vals[j] = rval;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* make A a symmetric matrix: A <- A^T + A */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,one,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);
ierr = MatEqual(A, Atrans, &flg);
if (flg) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
} else {
SETERRQ(PETSC_COMM_SELF,1,"A+A^T is non-symmetric");
}
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
/* create a SeqSBAIJ matrix sA (= A) */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
if (vid >= 0 && vid < size){
if (!rank) printf("A: \n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
if (!rank) printf("sA: \n");
ierr = MatView(sA,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test sA==A through MatMult() */
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG ,"Error in MatConvert(): A != sA");
/* Test MatIncreaseOverlap() */
ierr = PetscMalloc(nd*sizeof(IS **),&is1);CHKERRQ(ierr);
ierr = PetscMalloc(nd*sizeof(IS **),&is2);CHKERRQ(ierr);
for (i=0; i<nd; i++) {
if (!TestAllcols){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
sz = (PetscInt)((0.5+0.2*PetscRealPart(rval))*mbs); /* 0.5*mbs < sz < 0.7*mbs */
for (j=0; j<sz; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
idx[j*bs] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
for (k=1; k<bs; k++) idx[j*bs+k] = idx[j*bs]+k;
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is1+i);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is2+i);CHKERRQ(ierr);
if (rank == vid){
ierr = PetscPrintf(PETSC_COMM_SELF," [%d] IS sz[%d]: %d\n",rank,i,sz);CHKERRQ(ierr);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
} else { /* Test all rows and colums */
sz = M;
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is1+i);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is2+i);CHKERRQ(ierr);
if (rank == vid){
PetscBool colflag;
ierr = ISIdentity(is2[i],&colflag);CHKERRQ(ierr);
printf("[%d] is2[%d], colflag %d\n",rank,i,colflag);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
}
}
ierr = PetscLogStageRegister("MatOv_SBAIJ",&stages[0]);
ierr = PetscLogStageRegister("MatOv_BAIJ",&stages[1]);
/* Test MatIncreaseOverlap */
if (TestOverlap){
ierr = PetscLogStagePush(stages[0]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(sA,nd,is2,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
ierr = PetscLogStagePush(stages[1]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(A,nd,is1,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
if (rank == vid){
printf("\n[%d] IS from BAIJ:\n",rank);
ierr = ISView(is1[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
printf("\n[%d] IS from SBAIJ:\n",rank);
ierr = ISView(is2[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
for (i=0; i<nd; ++i) {
ierr = ISEqual(is1[i],is2[i],&flg);CHKERRQ(ierr);
if (!flg ){
if (rank == 0){
ierr = ISSort(is1[i]);CHKERRQ(ierr);
/* ISView(is1[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
ierr = ISSort(is2[i]);CHKERRQ(ierr);
/* ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
}
SETERRQ1(PETSC_COMM_SELF,1,"i=%D, is1 != is2",i);
}
}
}
/* Test MatGetSubmatrices */
if (TestSubMat){
for(i = 0; i < nd; ++i) {
ierr = ISSort(is1[i]); CHKERRQ(ierr);
ierr = ISSort(is2[i]); CHKERRQ(ierr);
}
ierr = MatGetSubMatrices(A,nd,is1,is1,MAT_INITIAL_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatGetSubMatrices(sA,nd,is2,is2,MAT_INITIAL_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A != sA");
/* Now test MatGetSubmatrices with MAT_REUSE_MATRIX option */
ierr = MatGetSubMatrices(A,nd,is1,is1,MAT_REUSE_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatGetSubMatrices(sA,nd,is2,is2,MAT_REUSE_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetSubmatrices(): A != sA");
for (i=0; i<nd; ++i) {
ierr = MatDestroy(&submatA[i]);CHKERRQ(ierr);
ierr = MatDestroy(&submatsA[i]);CHKERRQ(ierr);
}
ierr = PetscFree(submatA);CHKERRQ(ierr);
ierr = PetscFree(submatsA);CHKERRQ(ierr);
}
/* Free allocated memory */
for (i=0; i<nd; ++i) {
ierr = ISDestroy(&is1[i]);CHKERRQ(ierr);
ierr = ISDestroy(&is2[i]);CHKERRQ(ierr);
}
ierr = PetscFree(is1);CHKERRQ(ierr);
ierr = PetscFree(is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = PetscFree(cols);CHKERRQ(ierr);
ierr = PetscFree(vals);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
void petsc_lobpcg_solve_c(
Vec* u, /* prototype of a vector, not used */
int* my_own_eq, /* equations owned by this processor */
int* num_eval, /* number of eigenvalues to compute */
int* maxit, /* maximum number of iterations */
double* atol, /* absolute error tolerance */
double* rtol, /* relative error tolerance */
double* eigenvalues, /* computed eigenvalues */
void *matmult_opA, /* Fortran routine for operator A */
void *matmult_opB, /* Fortran routine for operator B */
void *matmult_opT, /* Fortran routine for operator T */
void *petsc_lobpcg_return_evec, /* Fortran routine gets eigenvectors */
void *petsc_lobpcg_initial_guess, /* Fortran routine for initial guess */
int* info) /* error code */
{
PetscErrorCode ierr; /* for PETSc return code */
mv_MultiVectorPtr eigenvectors; /* the eigenvectors */
double * eigs; /* the eigenvalues */
double * eigs_hist; /* history of eigenvalues */
double * resid; /* the residuals */
double * resid_hist; /* history of residuals */
int iterations; /* number of iterations */
int n_eigs; /* number of eigenvalues */
int i,j;
PetscTruth outpt=PETSC_FALSE; /* print evals and resids */
lobpcg_Tolerance lobpcg_tol; /* residual tolerance */
mv_InterfaceInterpreter ii; /* Interface Interpreter */
lobpcg_BLASLAPACKFunctions blap_fn; /* BLAS functions */
aux_data_struct aux_data; /* auxillary data */
/* set the number of eigenvalues to compute */
n_eigs = *num_eval;
/* set pointers to the Fortran callback functions */
hold_matmult_opA = matmult_opA;
hold_matmult_opB = matmult_opB;
hold_matmult_opT = matmult_opT;
hold_petsc_lobpcg_initial_guess = petsc_lobpcg_initial_guess;
hold_petsc_lobpcg_return_evec = petsc_lobpcg_return_evec;
/* allocate memory for the eigenvalues, residuals and histories */
ierr = PetscMalloc(sizeof(double)*n_eigs,&eigs);
ierr = PetscMalloc(sizeof(double)*n_eigs*(*maxit+1),&eigs_hist);
ierr = PetscMalloc(sizeof(double)*n_eigs,&resid);
ierr = PetscMalloc(sizeof(double)*n_eigs*(*maxit+1),&resid_hist);
/* create the Interface Interpreter and put it in auxillary data */
PETSCSetupInterpreter( &ii );
aux_data.ii = ii;
/* set tolerances and BLAS routines */
lobpcg_tol.absolute = *atol;
lobpcg_tol.relative = *rtol;
blap_fn.dpotrf = PETSC_dpotrf_interface;
blap_fn.dsygv = PETSC_dsygv_interface;
/* create the multivector for eigenvectors */
eigenvectors = mv_MultiVectorCreateFromSampleVector(&ii, n_eigs,*u);
/* set the initial guess. The second instance of eigenvectors in this
call isn't actually used, but something has to be passed in */
petsc_lobpcg_initial_guess_MultiVector(&aux_data,
mv_MultiVectorGetData(eigenvectors),
mv_MultiVectorGetData(eigenvectors));
/* call the lobpcg solver from BLOPEX */
ierr = lobpcg_solve( eigenvectors,
&aux_data,
OperatorAMultiVector,
&aux_data,
OperatorBMultiVector,
&aux_data,
OperatorTMultiVector,
NULL,
blap_fn,
lobpcg_tol,
*maxit,
0, /* verbosity, use 2 for debugging */
&iterations,
eigs,
eigs_hist,
n_eigs,
resid,
resid_hist,
n_eigs
);
/* set the return error code to lobpcg's error code */
*info = ierr;
/* copy the eigenvalues to the return variable */
for (i=0;i<n_eigs;i++) eigenvalues[i] = eigs[i];
/* return the eigenvectors. The second instance of eigenvectors isn't used
here either */
petsc_lobpcg_return_evec_MultiVector(&aux_data,
mv_MultiVectorGetData(eigenvectors),
mv_MultiVectorGetData(eigenvectors));
/* printed output, for debugging */
if (outpt)
{
PetscPrintf(PETSC_COMM_WORLD,"Output from LOBPCG driver\n");
PetscPrintf(PETSC_COMM_WORLD," iterations: %d\n",iterations);
PetscPrintf(PETSC_COMM_WORLD," eigenvalues and residuals:\n");
for (i=0;i<n_eigs;i++)
{
ierr = PetscPrintf(PETSC_COMM_WORLD,"%e %e\n",eigs[i],resid[i]);
}
/*
PetscPrintf(PETSC_COMM_WORLD,"Output from LOBPCG, eigenvalues history:\n");
for (j=0; j<iterations+1; j++)
for (i=0;i<n_eigs;i++)
{
ierr = PetscPrintf(PETSC_COMM_WORLD,"%e\n",*(eigs_hist+j*n_eigs+i));
}
PetscPrintf(PETSC_COMM_WORLD,"Output from LOBPCG, residual norms:\n");
for (i=0;i<n_eigs;i++)
{
ierr = PetscPrintf(PETSC_COMM_WORLD,"%e\n",resid[i]);
}
PetscPrintf(PETSC_COMM_WORLD,"Output from LOBPCG, residual norms history:\n");
for (j=0; j<iterations+1; j++)
for (i=0;i<n_eigs;i++)
{
ierr = PetscPrintf(PETSC_COMM_WORLD,"%e\n",*(resid_hist+j*n_eigs+i));
}
*/
}
/* free work space */
mv_MultiVectorDestroy(eigenvectors);
ierr = PetscFree(eigs);
ierr = PetscFree(eigs_hist);
ierr = PetscFree(resid);
ierr = PetscFree(resid_hist);
}
void Delta::HoffmanRibak(Vec& c, vector<double>& kprior, vector<double>& pkprior,
int seed, int dorandom, double tol ) {
// Set up preconditioner
vector<double> precondpk(pkprior);
for (int ii=0; ii<pkprior.size(); ++ii) precondpk[ii] = 1./pkprior[ii];
// Allocate space for a random Gaussian field
Vec f; f = dg1.Allocate();
// Define the RHS vector
// Start by generating a Gaussian density field
// We only do this if we are generating a random Gaussian field
if (dorandom > 0) {
dg1.FakeGauss(seed, f, kprior, pkprior);
VecAXPY(c, -1.0, f);
}
VecPointwiseMult(c, W, c);
// Now set up for CG solution
Vec rk, pk, Axk, zk;
double bnorm, rnorm, rnorm1, rz, rz1;
VecDuplicate(c, &pk); VecDuplicate(c, &rk); VecDuplicate(c, &Axk); VecDuplicate(c, &zk);
// Compute initial residual and norms
VecNorm(c, NORM_2, &bnorm);
VecCopy(c, rk); rnorm = bnorm;
VecCopy(rk, zk); dg1.kConvolve(zk, kprior, precondpk); VecPointwiseMult(zk, W, zk);
VecCopy(zk, pk);
VecSet(c, 0.0);
int iter = 0;
double alphak, betak, tmp1, relnorm;
relnorm = sqrt(rnorm/bnorm);
while(relnorm > tol) {
// CG iteration
PetscPrintf(PETSC_COMM_WORLD, "Starting iteration %4d .... rnorm = %10.5e, frac = %10.5e\n",iter,rnorm, relnorm);
// Compute alpha_k
VecCopy(pk, Axk); dg1.kConvolve(Axk, kprior, pkprior); VecPointwiseMult(Axk, W, Axk);
rz = VecDot(rk, zk);
tmp1 = VecDot(pk, Axk);
alphak = rz/tmp1;
// Update x and r
rnorm1 = rnorm; rz1 = rz;
VecAXPY(c, alphak, pk);
VecAXPY(rk, -alphak, Axk);
VecNorm(rk, NORM_2, &rnorm);
VecCopy(rk, zk); dg1.kConvolve(zk, kprior, precondpk); VecPointwiseMult(zk, W, zk);
rz = VecDot(rk, zk);
// Compute beta_k
betak = rz/rz1;
VecAYPX(pk, betak, zk);
// Update iteration count
iter+=1;
relnorm = sqrt(rnorm/bnorm);
}
PetscPrintf(PETSC_COMM_WORLD, "Converged after %4d iterations .... rnorm = %10.5e, frac = %10.5e\n",iter,rnorm, relnorm);
// Finish up generating the realization
dg1.kConvolve(c, kprior, pkprior);
// If we are generating a random field, instead of the simple WF
if (dorandom > 0)
VecAXPY(c, 1.0, f);
// Clean up the CG vectors
VecDestroy(rk); VecDestroy(f); VecDestroy(pk); VecDestroy(Axk); VecDestroy(zk);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
PetscBool flg,disp_mat=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
KSP ksp;
PC pc;
Mat F;
PetscInt nneg, nzero, npos;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(&Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test MatGetInertia() */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,As,As,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
ierr = PCSetUp(pc);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc,&F);CHKERRQ(ierr);
ierr = MatGetInertia(F,&nneg,&nzero,&npos);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF," MatInertia: nneg: %D, nzero: %D, npos: %D\n",nneg,nzero,npos);CHKERRQ(ierr);
}
/* Free spaces */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&As);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
DM da; /* distributed array */
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscRandom rctx; /* random number generator context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,its;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE;
PetscLogStage stage;
DMDALocalInfo info;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/*
Create distributed array to handle parallel distribution.
The problem size will default to 8 by 7, but this can be
changed using -da_grid_x M -da_grid_y N
*/
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix preallocated according to the DMDA, format AIJ by default.
To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
*/
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Rows and columns are specified by the stencil
- Entries are normalized for a domain [0,1]x[0,1]
*/
ierr = PetscLogStageRegister("Assembly", &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscReal hx = 1./info.mx,hy = 1./info.my;
MatStencil row = {0},col[5] = {{0}};
PetscScalar v[5];
PetscInt ncols = 0;
row.j = j; row.i = i;
col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
/* boundaries */
if (i>0) {col[ncols].j = j; col[ncols].i = i-1; v[ncols++] = -hy/hx;}
if (i<info.mx-1) {col[ncols].j = j; col[ncols].i = i+1; v[ncols++] = -hy/hx;}
if (j>0) {col[ncols].j = j-1; col[ncols].i = i; v[ncols++] = -hx/hy;}
if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i; v[ncols++] = -hx/hy;}
ierr = MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
/*
Create parallel vectors compatible with the DMDA.
*/
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
By default we use an exact solution of a vector with all
elements of 1.0; Alternatively, using the runtime option
-random_sol forms a solution vector with random components.
*/
ierr = PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,1.);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
These options will override those specified above as long as
KSPSetFromOptions() is called _after_ any other customization
routines.
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecAXPY(x,-1.,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single
print statement from all processes that share a communicator.
An alternative is PetscFPrintf(), which prints to a file.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_summary).
*/
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
Vec x,y,w; /* vectors */
Vec *z; /* array of vectors */
PetscReal norm,v,v1,v2,maxval;
PetscInt n = 20,maxind;
PetscErrorCode ierr;
PetscScalar one = 1.0,two = 2.0,three = 3.0,dots[3],dot;
PetscInitialize(&argc,&argv,(char*)0,help);
PetscFunctionBegin;
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
/*
Create a vector, specifying only its global dimension.
When using VecCreate(), VecSetSizes() and VecSetFromOptions(), the vector format
(currently parallel, shared, or sequential) is determined at runtime. Also, the
parallel partitioning of the vector is determined by PETSc at runtime.
Routines for creating particular vector types directly are:
VecCreateSeq() - uniprocessor vector
VecCreateMPI() - distributed vector, where the user can
determine the parallel partitioning
VecCreateShared() - parallel vector that uses shared memory
(available only on the SGI); otherwise,
is the same as VecCreateMPI()
With VecCreate(), VecSetSizes() and VecSetFromOptions() the option -vec_type mpi or
-vec_type shared causes the particular type of vector to be formed.
y
*/
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
/*
Duplicate some work vectors (of the same format and
partitioning as the initial vector).
*/
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&w);CHKERRQ(ierr);
/*
Duplicate more work vectors (of the same format and
partitioning as the initial vector). Here we duplicate
an array of vectors, which is often more convenient than
duplicating individual ones.
*/
ierr = VecDuplicateVecs(x,3,&z);CHKERRQ(ierr);
/*
Set the vectors to entries to a constant value.
*/
ierr = VecSet(x,one);CHKERRQ(ierr);
ierr = VecSet(y,two);CHKERRQ(ierr);
ierr = VecSet(z[0],one);CHKERRQ(ierr);
ierr = VecSet(z[1],two);CHKERRQ(ierr);
ierr = VecSet(z[2],three);CHKERRQ(ierr);
/*
Demonstrate various basic vector routines.
*/
MPI_Barrier(PETSC_COMM_WORLD);
ierr = VecDot(x,y,&dot);CHKERRQ(ierr);
ierr = VecMDot(x,3,z,dots);CHKERRQ(ierr);
/*
Note: If using a complex numbers version of PETSc, then
PETSC_USE_COMPLEX is defined in the makefiles; otherwise,
(when using real numbers) it is undefined.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Vector length %D\n",n);CHKERRQ(ierr);
ierr = VecMax(x,&maxind,&maxval);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecMax %g, VecInd %D\n",(double)maxval,maxind);CHKERRQ(ierr);
ierr = VecMin(x,&maxind,&maxval);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecMin %g, VecInd %D\n",(double)maxval,maxind);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"All other values should be near zero\n");CHKERRQ(ierr);
ierr = VecScale(x,two);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
v = norm-2.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecScale %g\n",(double)v);CHKERRQ(ierr);
ierr = VecCopy(x,w);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
v = norm-2.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecCopy %g\n",(double)v);CHKERRQ(ierr);
ierr = VecAXPY(y,three,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
v = norm-8.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecAXPY %g\n",(double)v);CHKERRQ(ierr);
ierr = VecAYPX(y,two,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
v = norm-18.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecAYPX %g\n",(double)v);CHKERRQ(ierr);
ierr = VecSwap(x,y);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
v = norm-2.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecSwap %g\n",(double)v);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
v = norm-18.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecSwap %g\n",(double)v);CHKERRQ(ierr);
ierr = VecWAXPY(w,two,x,y);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
v = norm-38.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecWAXPY %g\n",(double)v);CHKERRQ(ierr);
ierr = VecPointwiseMult(w,y,x);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
v = norm-36.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecPointwiseMult %g\n",(double)v);CHKERRQ(ierr);
ierr = VecPointwiseDivide(w,x,y);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
v = norm-9.0*PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecPointwiseDivide %g\n",(double)v);CHKERRQ(ierr);
dots[0] = one;
dots[1] = three;
dots[2] = two;
ierr = VecSet(x,one);CHKERRQ(ierr);
ierr = VecMAXPY(x,3,dots,z);CHKERRQ(ierr);
ierr = VecNorm(z[0],NORM_2,&norm);CHKERRQ(ierr);
v = norm-PetscSqrtReal((PetscReal)n); if (v > -PETSC_SMALL && v < PETSC_SMALL) v = 0.0;
ierr = VecNorm(z[1],NORM_2,&norm);CHKERRQ(ierr);
v1 = norm-2.0*PetscSqrtReal((PetscReal)n); if (v1 > -PETSC_SMALL && v1 < PETSC_SMALL) v1 = 0.0;
ierr = VecNorm(z[2],NORM_2,&norm);CHKERRQ(ierr);
v2 = norm-3.0*PetscSqrtReal((PetscReal)n); if (v2 > -PETSC_SMALL && v2 < PETSC_SMALL) v2 = 0.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"VecMAXPY %g %g %g \n",(double)v,(double)v1,(double)v2);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&w);CHKERRQ(ierr);
ierr = VecDestroyVecs(3,&z);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
/*
FormFunctionLocal - Form the local residual F from the local input X
Input Parameters:
+ dm - The mesh
. X - Local input vector
- user - The user context
Output Parameter:
. F - Local output vector
Note:
We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
like a GPU, or vectorize on a multicore machine.
.seealso: FormJacobianLocal()
*/
PetscErrorCode FormFunctionLocal(DM dm, Vec X, Vec F, AppCtx *user)
{
const PetscInt debug = user->debug;
const PetscInt dim = user->dim;
PetscReal *coords, *v0, *J, *invJ, *detJ;
PetscScalar *elemVec, *u;
PetscInt cellDof = 0;
PetscInt maxQuad = 0;
PetscInt jacSize = dim*dim;
PetscInt numCells, cStart, cEnd, c, field, d;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscLogEventBegin(user->residualEvent,0,0,0,0);CHKERRQ(ierr);
ierr = VecSet(F, 0.0);CHKERRQ(ierr);
ierr = DMDAGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
numCells = cEnd - cStart;
for (field = 0; field < numFields; ++field) {
cellDof += user->q[field].numBasisFuncs*user->q[field].numComponents;
maxQuad = PetscMax(maxQuad, user->q[field].numQuadPoints);
}
for (d = 0; d < dim; ++d) jacSize *= maxQuad;
ierr = PetscMalloc3(dim,&coords,dim,&v0,jacSize,&J);CHKERRQ(ierr);
ierr = PetscMalloc4(numCells*cellDof,&u,numCells*jacSize,&invJ,numCells*maxQuad,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
for (c = cStart; c < cEnd; ++c) {
PetscScalar *x = NULL;
PetscInt i;
ierr = DMDAComputeCellGeometry(dm, c, &user->q[0], v0, J, &invJ[c*jacSize], &detJ[c]);CHKERRQ(ierr);
if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
ierr = DMDAVecGetClosure(dm, NULL, X, c, &x);CHKERRQ(ierr);
for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
}
for (field = 0; field < numFields; ++field) {
const PetscInt numQuadPoints = user->q[field].numQuadPoints;
const PetscInt numBasisFuncs = user->q[field].numBasisFuncs;
void (*f0)(PetscScalar u[], const PetscScalar gradU[], PetscScalar f0[]) = user->f0Funcs[field];
void (*f1)(PetscScalar u[], const PetscScalar gradU[], PetscScalar f1[]) = user->f1Funcs[field];
/* Conforming batches */
PetscInt blockSize = numBasisFuncs*numQuadPoints;
PetscInt numBlocks = 1;
PetscInt batchSize = numBlocks * blockSize;
PetscInt numBatches = user->numBatches;
PetscInt numChunks = numCells / (numBatches*batchSize);
ierr = IntegrateResidualBatchCPU(numChunks*numBatches*batchSize, numFields, field, u, invJ, detJ, user->q, f0, f1, elemVec, user);CHKERRQ(ierr);
/* Remainder */
PetscInt numRemainder = numCells % (numBatches * batchSize);
PetscInt offset = numCells - numRemainder;
ierr = IntegrateResidualBatchCPU(numRemainder, numFields, field, &u[offset*cellDof], &invJ[offset*dim*dim], &detJ[offset],
user->q, f0, f1, &elemVec[offset*cellDof], user);CHKERRQ(ierr);
}
for (c = cStart; c < cEnd; ++c) {
if (debug) {ierr = DMPrintCellVector(c, "Residual", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
ierr = DMDAVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
}
ierr = PetscFree4(u,invJ,detJ,elemVec);CHKERRQ(ierr);
ierr = PetscFree3(coords,v0,J);CHKERRQ(ierr);
if (user->showResidual) {
PetscInt p;
ierr = PetscPrintf(PETSC_COMM_WORLD, "Residual:\n");CHKERRQ(ierr);
for (p = 0; p < user->numProcs; ++p) {
if (p == user->rank) {
Vec f;
ierr = VecDuplicate(F, &f);CHKERRQ(ierr);
ierr = VecCopy(F, f);CHKERRQ(ierr);
ierr = VecChop(f, 1.0e-10);CHKERRQ(ierr);
ierr = VecView(f, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecDestroy(&f);CHKERRQ(ierr);
}
ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
}
}
ierr = PetscLogEventEnd(user->residualEvent,0,0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode IntegrateResidualBatchCPU(PetscInt Ne, PetscInt numFields, PetscInt field, const PetscScalar coefficients[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscQuadrature quad[], void (*f0_func)(PetscScalar u[], const PetscScalar gradU[], PetscScalar f0[]), void (*f1_func)(PetscScalar u[], const PetscScalar gradU[], PetscScalar f1[]), PetscScalar elemVec[], AppCtx *user)
{
const PetscInt debug = user->debug;
const PetscInt dim = SPATIAL_DIM_0;
PetscInt cOffset = 0;
PetscInt eOffset = 0, e;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscLogEventBegin(user->integrateResCPUEvent,0,0,0,0);CHKERRQ(ierr);
for (e = 0; e < Ne; ++e) {
const PetscReal detJ = jacobianDeterminants[e];
const PetscReal *invJ = &jacobianInverses[e*dim*dim];
const PetscInt Nq = quad[field].numQuadPoints;
PetscScalar f0[NUM_QUADRATURE_POINTS_0*dim];
PetscScalar f1[NUM_QUADRATURE_POINTS_0*dim*dim];
PetscInt q, f;
if (Nq > NUM_QUADRATURE_POINTS_0) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_LIB, "Number of quadrature points %d should be <= %d", Nq, NUM_QUADRATURE_POINTS_0);
if (debug > 1) {
ierr = PetscPrintf(PETSC_COMM_SELF, " detJ: %g\n", detJ);CHKERRQ(ierr);
ierr = DMPrintCellMatrix(e, "invJ", dim, dim, invJ);CHKERRQ(ierr);
}
for (q = 0; q < Nq; ++q) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, " quad point %d\n", q);CHKERRQ(ierr);}
PetscScalar u[dim+1];
PetscScalar gradU[dim*(dim+1)];
PetscInt fOffset = 0;
PetscInt dOffset = cOffset;
const PetscInt Ncomp = quad[field].numComponents;
const PetscReal *quadWeights = quad[field].quadWeights;
PetscInt d, f, i;
for (d = 0; d <= dim; ++d) u[d] = 0.0;
for (d = 0; d < dim*(dim+1); ++d) gradU[d] = 0.0;
for (f = 0; f < numFields; ++f) {
const PetscInt Nb = quad[f].numBasisFuncs;
const PetscInt Ncomp = quad[f].numComponents;
const PetscReal *basis = quad[f].basis;
const PetscReal *basisDer = quad[f].basisDer;
PetscInt b, comp;
for (b = 0; b < Nb; ++b) {
for (comp = 0; comp < Ncomp; ++comp) {
const PetscInt cidx = b*Ncomp+comp;
PetscScalar realSpaceDer[dim];
PetscInt d, g;
u[fOffset+comp] += coefficients[dOffset+cidx]*basis[q*Nb*Ncomp+cidx];
for (d = 0; d < dim; ++d) {
realSpaceDer[d] = 0.0;
for (g = 0; g < dim; ++g) {
realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+cidx)*dim+g];
}
gradU[(fOffset+comp)*dim+d] += coefficients[dOffset+cidx]*realSpaceDer[d];
}
}
}
if (debug > 1) {
PetscInt d;
for (comp = 0; comp < Ncomp; ++comp) {
ierr = PetscPrintf(PETSC_COMM_SELF, " u[%d,%d]: %g\n", f, comp, u[fOffset+comp]);CHKERRQ(ierr);
for (d = 0; d < dim; ++d) {
ierr = PetscPrintf(PETSC_COMM_SELF, " gradU[%d,%d]_%c: %g\n", f, comp, 'x'+d, gradU[(fOffset+comp)*dim+d]);CHKERRQ(ierr);
}
}
}
fOffset += Ncomp;
dOffset += Nb*Ncomp;
}
f0_func(u, gradU, &f0[q*Ncomp]);
for (i = 0; i < Ncomp; ++i) {
f0[q*Ncomp+i] *= detJ*quadWeights[q];
}
f1_func(u, gradU, &f1[q*Ncomp*dim]);
for (i = 0; i < Ncomp*dim; ++i) {
f1[q*Ncomp*dim+i] *= detJ*quadWeights[q];
}
if (debug > 1) {
PetscInt c,d;
for (c = 0; c < Ncomp; ++c) {
ierr = PetscPrintf(PETSC_COMM_SELF, " f0[%d]: %g\n", c, f0[q*Ncomp+c]);CHKERRQ(ierr);
for (d = 0; d < dim; ++d) {
ierr = PetscPrintf(PETSC_COMM_SELF, " f1[%d]_%c: %g\n", c, 'x'+d, f1[(q*Ncomp + c)*dim+d]);CHKERRQ(ierr);
}
}
}
if (q == Nq-1) cOffset = dOffset;
}
for (f = 0; f < numFields; ++f) {
const PetscInt Nq = quad[f].numQuadPoints;
const PetscInt Nb = quad[f].numBasisFuncs;
const PetscInt Ncomp = quad[f].numComponents;
const PetscReal *basis = quad[f].basis;
const PetscReal *basisDer = quad[f].basisDer;
PetscInt b, comp;
if (f == field) {
for (b = 0; b < Nb; ++b) {
for (comp = 0; comp < Ncomp; ++comp) {
const PetscInt cidx = b*Ncomp+comp;
PetscInt q;
elemVec[eOffset+cidx] = 0.0;
for (q = 0; q < Nq; ++q) {
PetscScalar realSpaceDer[dim];
PetscInt d, g;
elemVec[eOffset+cidx] += basis[q*Nb*Ncomp+cidx]*f0[q*Ncomp+comp];
for (d = 0; d < dim; ++d) {
realSpaceDer[d] = 0.0;
for (g = 0; g < dim; ++g) {
realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+cidx)*dim+g];
}
elemVec[eOffset+cidx] += realSpaceDer[d]*f1[(q*Ncomp+comp)*dim+d];
}
}
}
}
if (debug > 1) {
PetscInt b, comp;
for (b = 0; b < Nb; ++b) {
for (comp = 0; comp < Ncomp; ++comp) {
ierr = PetscPrintf(PETSC_COMM_SELF, " elemVec[%d,%d]: %g\n", b, comp, elemVec[eOffset+b*Ncomp+comp]);CHKERRQ(ierr);
}
}
}
}
eOffset += Nb*Ncomp;
}
}
/* ierr = PetscLogFlops((((2+(2+2*dim)*dim)*Ncomp*Nb+(2+2)*dim*Ncomp)*Nq + (2+2*dim)*dim*Nq*Ncomp*Nb)*Ne);CHKERRQ(ierr); */
ierr = PetscLogEventEnd(user->integrateResCPUEvent,0,0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
};
void BuildDensityGrid(int N, double L, Mask3D& mask, Particle& pp, int nover, double thresh, Vec& delta, Vec& W, double smooth) {
/* Parameters :
* INPUT ---
* N : grid size
* L : box size
* mask : A 3D positive mask (assumed to be 1 or 0)
* nover : Oversampling rate for defining the mean density (we use the GridInitialize routine)
* This determines the displacement.
* For a periodic box, nover means there will be nover**3 particles per grid.
* thresh: Fractional threshold below which to remove grid point from survey
* smooth: This is an optional parameter -- if set to > 0, it will smooth the density and mask
* fields before computing the overdensity.
* OUTPUT ---
* delta : What do think this is???
* W : Window function, 1 in survey, 0 elsewhere.
* Note that the output vectors are not cleared, so you had better make sure you don't leak memory.
*/
// Allocate two density grids
DensityGrid dg1(N,L), dg2(N,L);
delta = dg1.Allocate();
W = dg2.Allocate();
// First the particles
pp.TrimMask(mask);
pp.SlabDecompose(dg1);
dg2.CIC(delta,pp, false);
PetscPrintf(PETSC_COMM_WORLD, "Particles assigned to the grid.....\n");
// Now do the randoms
double nrand=0.0, nexp, nthresh;
nexp = pow((double) nover, 3);
nthresh = nexp*thresh;
{
double tmp = 1./nover, dx, dy, dz;
VecSet(W, 0.0); // Manually set to zero
Vec W1; VecDuplicate(W, &W1);
for (int ix = 0; ix < nover; ++ix) {
PetscPrintf(PETSC_COMM_WORLD,"Starting random loop %i of %i....\n",ix,nover-1);
dx = ix*tmp + tmp/2.0;
for (int iy = 0; iy < nover; ++iy) {
dy = iy*tmp + tmp/2.0;
for (int iz = 0; iz < nover; ++iz) {
dz = iz*tmp + tmp/2.0;
Particle rr; // Definition here is important, since it ensures destruction, before recreating
rr.GridInitialize(N, dx, dy, dz, L);
rr.TrimMask(mask); nrand += rr.npart;
// rr.SlabDecompose(dg2); We don't need to slab decompose because nproc divides N by construction
dg2.CIC(W1, rr, false); // No overdensity
VecAXPY(W, 1.0, W1);
}
}
}
}
PetscPrintf(PETSC_COMM_WORLD, "%f grid particles accumulated....\n", nrand);
PetscPrintf(PETSC_COMM_WORLD, "Expected number of particles=%f, threshold=%f\n", nexp, nthresh);
// Smooth if desired
if (smooth > 1.e-5) {
dg1.GaussSmooth(delta, smooth);
dg2.GaussSmooth(W, smooth);
}
// Now build up delta
int lo, hi;
nrand /= pp.npart;
dg1.slab(lo, hi);
dg1.Pull(delta); dg2.Pull(W);
for (int ix=lo; ix < hi; ++ix)
for (int iy=0; iy < N; ++iy)
for (int iz=0; iz < N; ++iz) {
if (dg2(ix, iy,iz) > nthresh) {
dg1(ix, iy,iz) = (dg1(ix,iy,iz)/dg2(ix, iy, iz)) * nrand - 1.0;
dg2(ix, iy,iz) = 1.0;
} else {
dg1(ix, iy, iz) = 0.0;
dg2(ix, iy, iz) = 0.0;
}
}
dg1.Push(delta, INSERT_VALUES, false);
dg2.Push(W, INSERT_VALUES, false);
VecSum(W, &nrand);
PetscPrintf(PETSC_COMM_WORLD,"Nonzero grid points in W : %f\n",nrand);
}
int main(int argc,char **args)
{
Mat A,F;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscErrorCode ierr;
PetscBool flg;
Vec x,y,w;
MatFactorInfo iluinfo;
IS perm;
PetscInt m;
PetscReal norm;
PetscInitialize(&argc,&args,(char *)0,help);
/*
Determine file from which we read the matrix
*/
ierr = PetscOptionsGetString(PETSC_NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/*
Open binary file. Note that we use FILE_MODE_READ to indicate
reading from this file.
*/
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
/*
Load the matrix; then destroy the viewer.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecLoad(x,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&w);CHKERRQ(ierr);
ierr = MatGetFactor(A,"petsc",MAT_FACTOR_ILU,&F);CHKERRQ(ierr);
iluinfo.fill = 1.0;
ierr = MatGetSize(A,&m,0);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_WORLD,m,0,1,&perm);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(F,A,perm,perm,&iluinfo);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(F,A,&iluinfo);CHKERRQ(ierr);
ierr = MatSolveTranspose(F,x,y);CHKERRQ(ierr);
F->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;
ierr = MatSolveTranspose(F,x,w);CHKERRQ(ierr);
// VecView(w,0);VecView(y,0);
ierr = VecAXPY(w,-1.0,y);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
if (norm) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Norm of difference is nonzero %g\n",norm);CHKERRQ(ierr);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&w);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
Delta::Delta(int _N, double _L, int _nover, double thresh, Mask3D& _mask)
// RS 2010/07/06: Comments!
{
// Cache values
N=_N; L=_L; nover=_nover; maskptr=&_mask; rmasksmooth = 0.0;
// Set up the density
// RS: dg2 is some kind of local variable; dg1 is a class member.
// W and _W are contents of a grid of the same size and dimensions
// as dg1 and dg2.
DensityGrid dg2(N, L);
dg1.Init(N, L);
_W = dg1.Allocate();
W = dg1.Allocate(); VecSet(W, 0.0);
// Now do the randoms
// RS: "Doing" the randoms in this context means "oversampling" each grid
// cell into subcells, where the main cell is nover times as large as each
// subcell and hence there are nover^3 subcells to a cell.
nrand=0.0;
double nexp, nthresh;
nexp = pow((double) nover, 3);
// RS: thresh is the *fraction* of the main cell's volume to be included
// inside the mask for it to be counted as not masked, so nthresh is the
// corresponding number of subcells.
nthresh = nexp*thresh;
{
double tmp = 1./nover, dx, dy, dz;
VecSet(_W, 0.0); // Manually set to zero
Vec W1; VecDuplicate(_W, &W1);
// RS: Loop over all subcell *offsets*. The loop over actual grid cells
// is implicit in the calls to methods like GridInitialize below.
for (int ix = 0; ix < nover; ++ix) {
PetscPrintf(PETSC_COMM_WORLD,"Starting random loop %i of %i....\n",ix,nover-1);
dx = ix*tmp + tmp/2.0;
for (int iy = 0; iy < nover; ++iy) {
dy = iy*tmp + tmp/2.0;
for (int iz = 0; iz < nover; ++iz) {
dz = iz*tmp + tmp/2.0;
Particle rr; // Definition here is important, since it ensures destruction, before recreating
// RS: Generate a bunch of particles uniformly spaced, and offset
// from the low-(x,y,z) corner of each grid cell by (dx,dy,dz).
rr.GridInitialize(N, dx, dy, dz, L);
// RS: Remove from the list any particles which were not allowed
// by the mask. Add to the total.
rr.TrimMask(*maskptr); nrand += rr.npart;
// rr.SlabDecompose(dg2); We don't need to slab decompose because nproc divides N by construction
// RS: CIC assign remaining particles to temporary grid vector W1.
dg1.CIC(W1, rr, false); // No overdensity
// RS: Now add to _W the CIC contents of W1.
VecAXPY(_W, 1.0, W1);
}
}
}
}
// RS: At this point, nrand equals the total number of oversampled subcells
// found to be allowed by the masked region. _W contains the number of
// particles allowed by an oversampled mask at each grid location.
PetscPrintf(PETSC_COMM_WORLD, "%f grid particles accumulated....\n", nrand);
// Now set the mask
// RS: For each cell, if the contents of _W exceed nthresh, set W = 1.
// Use dg1 and dg2 as wrappers to index the copies of _W and W.
int lo, hi;
dg1.slab(lo, hi);
dg1.Pull(_W); dg2.Pull(W);
for (int ix=lo; ix < hi; ++ix)
for (int iy=0; iy < N; ++iy)
for (int iz=0; iz < N; ++iz)
if (dg1(ix, iy,iz) > nthresh) {
dg2(ix, iy,iz) = 1.0;
} else {
dg1(ix, iy, iz) = 0.0; // Good to explicitly set this to zero as well
}
dg1.Push(_W, INSERT_VALUES, false);
dg2.Push(W, INSERT_VALUES, false);
double tmp;
VecSum(W, &tmp);
PetscPrintf(PETSC_COMM_WORLD,"Nonzero grid points in W : %f\n",tmp);
VecSum(_W, &nrand);
PetscPrintf(PETSC_COMM_WORLD,"Sum of background density vector : %f\n",nrand);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
/*
Every PETSc program should begin with the PetscInitialize() routine.
argc, argv - These command line arguments are taken to extract the options
supplied to PETSc and options supplied to MPI.
help - When PETSc executable is invoked with the option -help,
it prints the various options that can be applied at
runtime. The user can use the "help" variable place
additional help messages in this printout.
*/
ierr = PetscInitialize(&argc,&argv,NULL,help);CHKERRQ(ierr);
/*
The following MPI calls return the number of processes
being used and the rank of this process in the group.
*/
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/*
Here we would like to print only one message that represents
all the processes in the group. We use PetscPrintf() with the
communicator PETSC_COMM_WORLD. Thus, only one message is
printed representing PETSC_COMM_WORLD, i.e., all the processors.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of processors = %d, rank = %d\n",size,rank);CHKERRQ(ierr);
/*
Here we would like to print info from each process, such that
output from process "n" appears after output from process "n-1".
To do this we use a combination of PetscSynchronizedPrintf() and
PetscSynchronizedFlush() with the communicator PETSC_COMM_WORLD.
All the processes print the message, one after another.
PetscSynchronizedFlush() indicates that the current process in the
given communicator has concluded printing, so that the next process
in the communicator can begin printing to the screen.
*/
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d] Synchronized Hello World.\n",rank);CHKERRQ(ierr);
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d] Synchronized Hello World - Part II.\n",rank);CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);CHKERRQ(ierr);
/*
Here a barrier is used to separate the two states.
*/
ierr = MPI_Barrier(PETSC_COMM_WORLD);CHKERRQ(ierr);
/*
Here we simply use PetscPrintf() with the communicator PETSC_COMM_SELF
(where each process is considered separately). Thus, this time the
output from different processes does not appear in any particular order.
*/
ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] Jumbled Hello World\n",rank);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_view).
See the PetscFinalize() manpage for more information.
*/
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Vec x, b, u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PC pc; /* preconditioner context */
PetscReal norm; /* norm of solution error */
PetscErrorCode ierr;
PetscInt i,n = 10,col[3],its,rstart,rend,nlocal;
PetscScalar neg_one = -1.0,one = 1.0,value[3];
PetscBool TEST_PROCEDURAL=PETSC_FALSE;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-procedural",&TEST_PROCEDURAL,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create vectors. Note that we form 1 vector from scratch and
then duplicate as needed. For this simple case let PETSc decide how
many elements of the vector are stored on each processor. The second
argument to VecSetSizes() below causes PETSc to decide.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr);
/* Identify the starting and ending mesh points on each
processor for the interior part of the mesh. We let PETSc decide
above. */
ierr = VecGetOwnershipRange(x,&rstart,&rend);CHKERRQ(ierr);
ierr = VecGetLocalSize(x,&nlocal);CHKERRQ(ierr);
/* Create a tridiagonal matrix. See ../tutorials/ex23.c */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,nlocal,nlocal,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/* Assemble matrix */
if (!rstart) {
rstart = 1;
i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (rend == n) {
rend = n-1;
i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* Set entries corresponding to the mesh interior */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=rstart; i<rend; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Set exact solution; then compute right-hand-side vector. */
ierr = VecSet(u,one);CHKERRQ(ierr);
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
/*
Set linear solver defaults for this problem (optional).
- By extracting the KSP and PC contexts from the KSP context,
we can then directly call any KSP and PC routines to set
various options.
- The following statements are optional; all of these
parameters could alternatively be specified at runtime via
KSPSetFromOptions();
*/
if (TEST_PROCEDURAL) {
/* Example of runtime options: '-pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type bjacobi' */
PetscMPIInt size,rank,subsize;
Mat A_redundant;
KSP innerksp;
PC innerpc;
MPI_Comm subcomm;
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCREDUNDANT);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (size < 3) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "Num of processes %d must greater than 2",size);
ierr = PCRedundantSetNumber(pc,size-2);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* Get subcommunicator and redundant matrix */
ierr = KSPSetUp(ksp);CHKERRQ(ierr);
ierr = PCRedundantGetKSP(pc,&innerksp);CHKERRQ(ierr);
ierr = KSPGetPC(innerksp,&innerpc);CHKERRQ(ierr);
ierr = PCGetOperators(innerpc,NULL,&A_redundant,NULL);CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)A_redundant,&subcomm);CHKERRQ(ierr);
ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
if (subsize==1 && !rank) {
printf("A_redundant:\n");
ierr = MatView(A_redundant,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
} else {
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
}
/* Solve linear system */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(x,neg_one,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > 1.e-14) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G, Iterations %D\n",norm,its);CHKERRQ(ierr);
}
/* Free work space. */
ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
TS ts,quadts; /* ODE integrator */
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
Mat Jacp; /* Jacobian matrix */
Mat DRDU,DRDP;
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 2;
AppCtx ctx;
PetscScalar *u;
PetscReal du[2] = {0.0,0.0};
PetscBool ensemble = PETSC_FALSE,flg1,flg2;
PetscReal ftime;
PetscInt steps;
PetscScalar *x_ptr,*y_ptr;
Vec lambda[1],q,mu[1];
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Jacp);CHKERRQ(ierr);
ierr = MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
ierr = MatSetFromOptions(Jacp);CHKERRQ(ierr);
ierr = MatSetUp(Jacp);CHKERRQ(ierr);
ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDP);CHKERRQ(ierr);
ierr = MatSetUp(DRDP);CHKERRQ(ierr);
ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDU);CHKERRQ(ierr);
ierr = MatSetUp(DRDU);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr);
{
ctx.beta = 2;
ctx.c = 10000.0;
ctx.u_s = 1.0;
ctx.omega_s = 1.0;
ctx.omega_b = 120.0*PETSC_PI;
ctx.H = 5.0;
ierr = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
ctx.D = 5.0;
ierr = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr);
ctx.E = 1.1378;
ctx.V = 1.0;
ctx.X = 0.545;
ctx.Pmax = ctx.E*ctx.V/ctx.X;;
ierr = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr);
ctx.Pm = 1.1;
ierr = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr);
ctx.tf = 0.1;
ctx.tcl = 0.2;
ierr = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);CHKERRQ(ierr);
if (ensemble) {
ctx.tf = -1;
ctx.tcl = -1;
}
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
u[1] = 1.0;
ierr = PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);CHKERRQ(ierr);
n = 2;
ierr = PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);CHKERRQ(ierr);
u[0] += du[0];
u[1] += du[1];
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
if (flg1 || flg2) {
ctx.tf = -1;
ctx.tcl = -1;
}
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSRK);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);CHKERRQ(ierr);
ierr = TSCreateQuadratureTS(ts,PETSC_TRUE,&quadts);CHKERRQ(ierr);
ierr = TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(quadts,DRDU,DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);CHKERRQ(ierr);
ierr = TSSetRHSJacobianP(quadts,DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Save trajectory of solution so that TSAdjointSolve() may be used
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr);
/* Set initial conditions for the adjoint integration */
ierr = VecGetArray(lambda[0],&y_ptr);CHKERRQ(ierr);
y_ptr[0] = 0.0; y_ptr[1] = 0.0;
ierr = VecRestoreArray(lambda[0],&y_ptr);CHKERRQ(ierr);
ierr = MatCreateVecs(Jacp,&mu[0],NULL);CHKERRQ(ierr);
ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = -1.0;
ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
ierr = TSSetCostGradients(ts,1,lambda,mu);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetMaxTime(ts,10.0);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
if (ensemble) {
for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
u[1] = ctx.omega_s;
u[0] += du[0];
u[1] += du[1];
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr);
ierr = TSSolve(ts,U);CHKERRQ(ierr);
}
} else {
ierr = TSSolve(ts,U);CHKERRQ(ierr);
}
ierr = VecView(U,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Adjoint model starts here
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Set initial conditions for the adjoint integration */
ierr = VecGetArray(lambda[0],&y_ptr);CHKERRQ(ierr);
y_ptr[0] = 0.0; y_ptr[1] = 0.0;
ierr = VecRestoreArray(lambda[0],&y_ptr);CHKERRQ(ierr);
ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = -1.0;
ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
/* Set RHS JacobianP */
ierr = TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&ctx);CHKERRQ(ierr);
ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n");CHKERRQ(ierr);
ierr = VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
ierr = VecView(q,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecGetArray(q,&x_ptr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n cost function=%g\n",(double)(x_ptr[0]-ctx.Pm));CHKERRQ(ierr);
ierr = VecRestoreArray(q,&x_ptr);CHKERRQ(ierr);
ierr = ComputeSensiP(lambda[0],mu[0],&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&Jacp);CHKERRQ(ierr);
ierr = MatDestroy(&DRDU);CHKERRQ(ierr);
ierr = MatDestroy(&DRDP);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
ierr = VecDestroy(&mu[0]);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}