+// /home/couturie/work/petsc-3.5.1/arch-linux2-c-debug/bin/mpirun -np 4 ./ex15 -m 400 -n 400 -ksp_type fgmres
+
+
+
static char help[] = "Solves a linear system in parallel with KSP. Also\n\
illustrates setting a user-defined shell preconditioner and using the\n\
macro __FUNCT__ to define routine names for use in error handling.\n\
//Variables
- PetscScalar gamma, alpha, oldgamma, beta, t2;
+ PetscScalar gamma, alpha, oldgamma, beta;
PetscReal norm=20, Eprecision=1e-8, cgprec=1e-40;
PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=15, Iiter=0;
PetscErrorCode ierr;
- PetscScalar T1, T2, t1;
+ PetscScalar T1, T2;
KSP ksp;
PetscInt total=0;
PetscInt size;
PetscScalar *array;
PetscInt *ind_row;
Vec Alpha, p, ss, vect, r, q, Ax;
- PetscScalar norm_ksp;
PetscInt first=1;
}
T2 = MPI_Wtime();
- t1 = T2 - T1;
ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time : %g (s)\n", T2-T1); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations : %D\n", total); CHKERRQ(ierr);
+
+int KrylovMinimizeLSQR(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar alpha, beta;
+ PetscReal norm=20, Eprecision=1e-8, tol=1e-40;
+ PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=20, Iiter=0;
+ PetscErrorCode ierr;
+ PetscScalar T1, T2;
+ KSP ksp;
+ PetscInt total=0;
+ PetscInt size;
+ PetscInt Istart,Iend;
+ PetscInt i,its;
+ Vec x_old, residu;
+ Mat S, AS;
+ PetscScalar *array;
+ PetscInt *ind_row;
+ Vec Ax;
+ PetscScalar norm_ksp;
+ Vec u,v,d,uu,vt,zero_long,zero_short,x_lsqr;
+
+ PetscInt first=1;
+
+ ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+ ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
+ ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
+
+
+
+
+ VecGetSize(b,&size);
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Size of vector %D\n", size); CHKERRQ(ierr);
+
+ PetscInt aa,bb;
+ MatGetOwnershipRange(A,&aa,&bb);
+
+ // ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD, "%D %D\n", aa,bb); CHKERRQ(ierr);
+ //PetscSynchronizedFlush(PETSC_COMM_WORLD);
+
+
+ ierr = MatCreate(PETSC_COMM_WORLD, &S);CHKERRQ(ierr);
+ ierr = MatSetSizes(S, bb-aa, PETSC_DECIDE, size, ColS); CHKERRQ(ierr);
+ ierr = MatSetType(S, MATMPIDENSE); CHKERRQ(ierr);
+ ierr = MatSetUp(S); CHKERRQ(ierr);
+
+ ierr = MatGetOwnershipRange(S, &Istart, &Iend); CHKERRQ(ierr);
+
+
+
+ ierr = VecDuplicate(b, &Ax); CHKERRQ(ierr);
+
+ ierr = VecDuplicate(b,&x_old);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&residu);CHKERRQ(ierr);
+
+
+ //long vector
+ ierr = VecDuplicate(b,&u);CHKERRQ(ierr);
+
+
+ ierr = VecDuplicate(b,&uu);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&zero_long);CHKERRQ(ierr);
+ ierr = VecSet(zero_long,0);CHKERRQ(ierr);
+
+ //small vector
+ ierr = VecCreate(PETSC_COMM_WORLD, &v); CHKERRQ(ierr);
+ ierr = VecSetSizes(v, PETSC_DECIDE, ColS); CHKERRQ(ierr);
+ ierr = VecSetFromOptions(v); CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&zero_short);CHKERRQ(ierr);
+ ierr = VecSet(zero_short,0);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&d);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&vt);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&x_lsqr);CHKERRQ(ierr);
+
+
+ //indexes of row (these indexes are global)
+ ind_row = (PetscInt*)malloc(sizeof(PetscInt)*(Iend-Istart));
+ for(i=0; i<Iend-Istart; i++) ind_row[i] = i + Istart;
+
+ //Initializations
+ // ierr = KSPGMRESSetRestart(ksp, 16); CHKERRQ(ierr);
+ ierr = KSPSetTolerances(ksp, 1e-10, 1e-10, PETSC_DEFAULT, 16); CHKERRQ(ierr);
+ ierr = KSPSetInitialGuessNonzero(ksp, PETSC_TRUE); CHKERRQ(ierr);
+
+
+
+
+ //GMRES WITH MINIMIZATION
+ T1 = MPI_Wtime();
+ while(giter<Emaxiter && norm>Eprecision ){
+ for(col=0; col<ColS && norm>Eprecision; col++){
+
+
+ //Solve
+ ierr = KSPSolve(ksp, b, x); CHKERRQ(ierr);
+
+ ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
+ total += its; Iiter ++;
+
+
+
+ //Build S'
+ ierr = VecGetArray(x, &array);
+ ierr = MatSetValues(S, Iend-Istart, ind_row, 1, &col, array, INSERT_VALUES);
+ VecRestoreArray(x, &array);
+
+
+
+ //Error
+ ierr = VecCopy(x, residu); CHKERRQ(ierr);
+ ierr = VecAXPY(residu, -1, x_old); CHKERRQ(ierr);
+ ierr = VecNorm(residu, NORM_INFINITY, &norm); CHKERRQ(ierr);
+
+
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, outer iteration %D\n", norm, giter); CHKERRQ(ierr);
+ ierr = VecCopy(x, x_old); CHKERRQ(ierr);
+
+
+ }
+
+
+ //minimization step
+ if( norm>Eprecision) {
+
+ MatAssemblyBegin(S, MAT_FINAL_ASSEMBLY);
+ MatAssemblyEnd(S, MAT_FINAL_ASSEMBLY);
+
+
+
+
+ //Build AS
+ if(first) {
+ MatMatMult(A,S, MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AS);
+
+ first=0;
+ }
+ else
+ MatMatMult(A,S, MAT_REUSE_MATRIX,PETSC_DEFAULT,&AS);
+
+
+
+
+
+ //LSQR
+ //LSQR
+ //LSQR
+
+
+
+ PetscScalar n2b,tolb,normr,c,s,phibar,normar,norma,thet,rhot,rho,phi;
+ PetscInt stag;
+ tolb = tol * n2b;
+ VecNorm(b, NORM_2, &n2b); //n2b = norm(b);
+ ierr = VecCopy(b, u); CHKERRQ(ierr); //u=b
+ VecNorm(u, NORM_2, &beta); // beta=norm(u)
+ normr=beta;
+ if (beta != 0) {
+ VecAYPX(u,1/beta,zero_long); // u = u / beta;
+ }
+ c=1;
+ s=0;
+ phibar=beta;
+ MatMultTranspose(AS, u, v); //v=A'*u
+ ierr = VecSet(x_lsqr,0);CHKERRQ(ierr);
+ VecNorm(v, NORM_2, &alpha); // alpha=norm(v)
+ if (alpha != 0) {
+ VecAYPX(v,1/alpha,zero_short); // v = v / alpha;
+ }
+ ierr = VecSet(d,0);CHKERRQ(ierr);
+ normar = alpha * beta;
+ norma=0;
+ //stag=0;
+ for(i=0;i<iterations;i++) {
+ MatMult(AS, v, uu); //uu=A*v
+ VecAYPX(u, -alpha, uu); //u = uu-alpha*u;
+ VecNorm(u, NORM_2, &beta); // beta=norm(u)
+ VecAYPX(u,1/beta,zero_long); // u = u / beta;
+ norma=sqrt(norma*norma+alpha*alpha+beta*beta); // norma = norm([norma alpha beta]);
+ thet = - s * alpha;
+ rhot = c * alpha;
+ rho = sqrt(rhot*rhot + beta*beta);
+ c = rhot / rho;
+ s = - beta / rho;
+ phi = c * phibar;
+ if (phi == 0) { // stagnation of the method
+ stag = 1;
+ }
+ phibar = s * phibar;
+ VecAYPX(d,-thet,v); //d = (v - thet * d);
+ VecAYPX(d,1/rho,zero_short); //d=d/ rho;
+
+ /*
+ if (normar/(norma*normr) <= tol) { // check for convergence in min{|b-A*x|}
+ break;
+ }
+ if (normr <= tolb) { // check for convergence in A*x=b
+ break;
+ }
+ */
+
+ VecAXPY(x_lsqr,phi,d); // x_lsqr=x_lsqr+phi*d
+ normr = abs(s) * normr;
+ MatMultTranspose(AS, u, vt); //vt=A'*u;
+ VecAYPX(v,-beta,vt); // v = vt - beta * v;
+ VecNorm(v, NORM_2, &alpha); // alpha=norm(v)
+ VecAYPX(v,1/alpha,zero_short); // v = v / alpha;
+ normar = alpha * abs( s * phi);
+ }
+
+
+
+ iter = 0; giter ++;
+ //Minimizer
+ MatMult(S, x_lsqr, x); //x = S*x_small;
+ }
+
+ }
+ T2 = MPI_Wtime();
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time LSQR : %g (s)\n", T2-T1); CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations LSQR : %D\n", total); CHKERRQ(ierr);
+
+ return 0;
+
+}
+
+
+
+
+
+
+
+
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
KSP ksp; /* linear solver context */
PC pc; /* preconditioner context */
PetscReal norm; /* norm of solution error */
- SampleShellPC *shell; /* user-defined preconditioner context */
- PetscScalar v,one = 1.0,none = -1.0;
+ PetscScalar v,one = 1.0;
PetscInt i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
PetscErrorCode ierr;
- PetscBool user_defined_pc = PETSC_FALSE;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
}
+ {
+
+ Vec x2;
+ Vec sol;
+ VecDuplicate(b,&x2);
+ VecDuplicate(b,&sol);
+
+ KrylovMinimizeLSQR(A, b, x2);
+
+
+
+ MatMult(A,x2,sol);
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Error Krylov Minimization LSQR %g\n",norm);
+
+ }
