+// /home/couturie/work/petsc-3.5.1/arch-linux2-c-debug/bin/mpirun -np 4 ./ex15 -m 400 -n 400
+
+
+
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=15, 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);
+
+ KrylovMinimize(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);
+
+ }
--- /dev/null
+
+
+// /home/couturie/work/petsc-3.5.1/arch-linux2-c-debug/bin/mpirun -np 3 ex29 -da_grid_x 900 -da_grid_y 900
+
+
+
+/*T
+ Concepts: KSP^solving a system of linear equations
+ Concepts: KSP^Laplacian, 2d
+ Processors: n
+T*/
+
+/*
+Added at the request of Marc Garbey.
+
+Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
+
+ -div \rho grad u = f, 0 < x,y < 1,
+
+with forcing function
+
+ f = e^{-x^2/\nu} e^{-y^2/\nu}
+
+with Dirichlet boundary conditions
+
+ u = f(x,y) for x = 0, x = 1, y = 0, y = 1
+
+or pure Neumman boundary conditions
+
+This uses multigrid to solve the linear system
+*/
+
+static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
+
+#include <petscdm.h>
+#include <petscdmda.h>
+#include <petscksp.h>
+
+extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
+extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
+
+typedef enum {DIRICHLET, NEUMANN} BCType;
+
+typedef struct {
+ PetscReal rho;
+ PetscReal nu;
+ BCType bcType;
+} UserContext;
+
+#undef __FUNCT__
+#define __FUNCT__ "main"
+
+
+
+
+
+
+
+
+
+int KrylovMinimize(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar gamma, alpha, oldgamma, beta;
+ PetscReal norm=20, Eprecision=1e-5, cgprec=1e-40;
+ PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=15, 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 Alpha, p, ss, vect, r, q, Ax;
+
+
+ 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 = VecCreate(PETSC_COMM_WORLD, &Alpha); CHKERRQ(ierr);
+ ierr = VecSetSizes(Alpha, PETSC_DECIDE, ColS); CHKERRQ(ierr);
+ ierr = VecSetFromOptions(Alpha); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &vect); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &p); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &ss); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &r); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &q); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &Ax); CHKERRQ(ierr);
+
+ ierr = VecDuplicate(b,&x_old);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&residu);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);
+
+
+
+
+ //Minimization with CGLS
+ MatMult(AS, Alpha, r); VecAYPX(r, -1, b); //r_0 = b-AS*x_0
+
+
+ MatMultTranspose(AS, r, p); //p_0 = AS'*r_0
+
+
+
+
+ ierr = VecCopy(p, ss); CHKERRQ(ierr); //p_0 = s_0
+ VecNorm(ss, NORM_2, &gamma); gamma = gamma * gamma; //gamma = norm2(s)^2
+ while(gamma>cgprec && iter<iterations){
+ MatMult(AS, p, q); //q = AS*p
+ VecNorm(q, NORM_2, &alpha); alpha = alpha * alpha; //alpha = norm2(q)^2
+ alpha = gamma / alpha;
+ VecAXPY(Alpha, alpha, p); //Alpha += alpha*p
+ VecAXPY(r, -alpha, q); //r -= alpha*q
+ MatMultTranspose(AS, r, ss); // ss = AS'*r
+ oldgamma = gamma;
+ VecNorm(ss, NORM_2, &gamma); gamma = gamma * gamma; //gamma = norm2(s)^2
+ beta = gamma / oldgamma;
+ VecAYPX(p, beta, ss); //p = s+beta*p;
+ iter ++;
+ }
+
+ iter = 0; giter ++;
+ //Minimizer
+ MatMult(S, Alpha, x); //x = S*Alpha;
+ }
+
+ }
+ T2 = MPI_Wtime();
+ 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);
+
+ return 0;
+
+}
+
+
+
+
+
+
+
+
+
+int KrylovMinimizeLSQR(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar alpha, beta;
+ PetscReal norm=20, Eprecision=1e-5, tol=1e-40;
+ PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=15, 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 **argv)
+{
+ KSP ksp;
+ DM da;
+ UserContext user;
+ const char *bcTypes[2] = {"dirichlet","neumann"};
+ PetscErrorCode ierr;
+ PetscInt bc;
+ Vec b,x;
+ Mat A;
+ PetscScalar T1,T2,norm;
+ Vec sol;
+ PetscInt total;
+
+ PetscInitialize(&argc,&argv,(char*)0,help);
+
+ ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+ ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-3,-3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr);
+ ierr = DMDASetUniformCoordinates(da,0,1,0,1,0,0);CHKERRQ(ierr);
+ ierr = DMDASetFieldName(da,0,"Pressure");CHKERRQ(ierr);
+
+ ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
+ user.rho = 1.0;
+ ierr = PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);CHKERRQ(ierr);
+ user.nu = 0.1;
+ ierr = PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);CHKERRQ(ierr);
+ bc = (PetscInt)DIRICHLET;
+ ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr);
+ user.bcType = (BCType)bc;
+ ierr = PetscOptionsEnd();
+
+ ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr);
+ ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr);
+ ierr = KSPSetDM(ksp,da);CHKERRQ(ierr);
+ ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
+ ierr = KSPSetUp(ksp);CHKERRQ(ierr);
+
+ ierr = KSPSetTolerances(ksp, 1e-5, 1e-5, PETSC_DEFAULT, 50000000); CHKERRQ(ierr);
+ T1 = MPI_Wtime();
+ ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr);
+ T2 = MPI_Wtime();
+
+
+
+ ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
+ ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
+ KSPGetOperators(ksp,&A,NULL);
+
+ VecDuplicate(x,&sol);
+ MatMult(A,x,sol);
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Error %g\n",norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time : %g (s)\n", T2-T1); CHKERRQ(ierr);
+
+ ierr = KSPGetIterationNumber(ksp, &total); CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations : %D\n", total); CHKERRQ(ierr);
+
+ {
+
+ Vec x;
+ VecDuplicate(b,&x);
+
+ KrylovMinimize(A, b, x);
+
+
+
+ MatMult(A,x,sol);
+
+
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Error2 %g\n",norm);
+
+ }
+
+
+ {
+
+ Vec x;
+ VecDuplicate(b,&x);
+
+ KrylovMinimizeLSQR(A, b, x);
+
+
+
+ MatMult(A,x,sol);
+
+
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Error LSQR %g\n",norm);
+
+ }
+
+
+
+
+ ierr = DMDestroy(&da);CHKERRQ(ierr);
+ ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
+ ierr = PetscFinalize();
+
+ return 0;
+}
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeRHS"
+PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
+{
+ UserContext *user = (UserContext*)ctx;
+ PetscErrorCode ierr;
+ PetscInt i,j,mx,my,xm,ym,xs,ys;
+ PetscScalar Hx,Hy;
+ PetscScalar **array;
+ DM da;
+
+ PetscFunctionBeginUser;
+ ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
+ ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
+ Hx = 1.0 / (PetscReal)(mx-1);
+ Hy = 1.0 / (PetscReal)(my-1);
+ ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
+ ierr = DMDAVecGetArray(da, b, &array);CHKERRQ(ierr);
+ for (j=ys; j<ys+ym; j++) {
+ for (i=xs; i<xs+xm; i++) {
+ array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
+ }
+ }
+ ierr = DMDAVecRestoreArray(da, b, &array);CHKERRQ(ierr);
+ ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
+ ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
+
+ /* force right hand side to be consistent for singular matrix */
+ /* note this is really a hack, normally the model would provide you with a consistent right handside */
+ if (user->bcType == NEUMANN) {
+ MatNullSpace nullspace;
+
+ ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
+ ierr = MatNullSpaceRemove(nullspace,b);CHKERRQ(ierr);
+ ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
+ }
+ PetscFunctionReturn(0);
+}
+
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeRho"
+PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
+{
+ PetscFunctionBeginUser;
+ if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
+ *rho = centerRho;
+ } else {
+ *rho = 1.0;
+ }
+ PetscFunctionReturn(0);
+}
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeMatrix"
+PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
+{
+ UserContext *user = (UserContext*)ctx;
+ PetscReal centerRho;
+ PetscErrorCode ierr;
+ PetscInt i,j,mx,my,xm,ym,xs,ys;
+ PetscScalar v[5];
+ PetscReal Hx,Hy,HydHx,HxdHy,rho;
+ MatStencil row, col[5];
+ DM da;
+
+ PetscFunctionBeginUser;
+ ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
+ centerRho = user->rho;
+ ierr = DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
+ Hx = 1.0 / (PetscReal)(mx-1);
+ Hy = 1.0 / (PetscReal)(my-1);
+ HxdHy = Hx/Hy;
+ HydHx = Hy/Hx;
+ ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
+ for (j=ys; j<ys+ym; j++) {
+ for (i=xs; i<xs+xm; i++) {
+ row.i = i; row.j = j;
+ ierr = ComputeRho(i, j, mx, my, centerRho, &rho);CHKERRQ(ierr);
+ if (i==0 || j==0 || i==mx-1 || j==my-1) {
+ if (user->bcType == DIRICHLET) {
+ v[0] = 2.0*rho*(HxdHy + HydHx);
+ ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
+ } else if (user->bcType == NEUMANN) {
+ PetscInt numx = 0, numy = 0, num = 0;
+ if (j!=0) {
+ v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
+ numy++; num++;
+ }
+ if (i!=0) {
+ v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
+ numx++; num++;
+ }
+ if (i!=mx-1) {
+ v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
+ numx++; num++;
+ }
+ if (j!=my-1) {
+ v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
+ numy++; num++;
+ }
+ v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j;
+ num++;
+ ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
+ }
+ } else {
+ v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
+ v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
+ v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
+ v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
+ v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
+ ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
+ }
+ }
+ }
+ ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+ ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+ if (user->bcType == NEUMANN) {
+ MatNullSpace nullspace;
+
+ ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
+ ierr = MatSetNullSpace(jac,nullspace);CHKERRQ(ierr);
+ ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
+ }
+ PetscFunctionReturn(0);
+}
