--- /dev/null
+
+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\
+Input parameters include:\n\
+ -user_defined_pc : Activate a user-defined preconditioner\n\n";
+
+/*T
+ Concepts: KSP^basic parallel example
+ Concepts: PC^setting a user-defined shell preconditioner
+ Concepts: error handling^Using the macro __FUNCT__ to define routine names;
+ Processors: n
+T*/
+
+/*
+ Include "petscksp.h" so that we can use KSP solvers. Note that this file
+ automatically includes:
+ petscsys.h - base PETSc routines petscvec.h - vectors
+ petscmat.h - matrices
+ petscis.h - index sets petscksp.h - Krylov subspace methods
+ petscviewer.h - viewers petscpc.h - preconditioners
+*/
+#include <petscksp.h>
+
+/* Define context for user-provided preconditioner */
+typedef struct {
+ Vec diag;
+} SampleShellPC;
+
+
+
+/*
+ User-defined routines. Note that immediately before each routine below,
+ we define the macro __FUNCT__ to be a string containing the routine name.
+ If defined, this macro is used in the PETSc error handlers to provide a
+ complete traceback of routine names. All PETSc library routines use this
+ macro, and users can optionally employ it as well in their application
+ codes. Note that users can get a traceback of PETSc errors regardless of
+ whether they define __FUNCT__ in application codes; this macro merely
+ provides the added traceback detail of the application routine names.
+*/
+#undef __FUNCT__
+#define __FUNCT__ "main"
+
+
+
+
+
+int KrylovMinimize(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar gamma, alpha, oldgamma, beta, t2;
+ 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;
+ 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;
+ PetscScalar norm_ksp;
+
+
+ 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();
+ 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);
+
+ return 0;
+
+}
+
+
+
+
+
+
+
+
+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 */
+ SampleShellPC *shell; /* user-defined preconditioner context */
+ PetscScalar v,one = 1.0,none = -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);
+ ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
+
+ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+ Compute the matrix and right-hand-side vector that define
+ the linear system, Ax = b.
+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
+ /*
+ Create parallel matrix, specifying only its global dimensions.
+ When using MatCreate(), the matrix format can be specified at
+ runtime. Also, the parallel partioning of the matrix is
+ determined by PETSc at runtime.
+ */
+ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
+ ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
+ ierr = MatSetFromOptions(A);CHKERRQ(ierr);
+ ierr = MatSetUp(A);CHKERRQ(ierr);
+
+ /*
+ Currently, all PETSc parallel matrix formats are partitioned by
+ contiguous chunks of rows across the processors. Determine which
+ rows of the matrix are locally owned.
+ */
+ ierr = MatGetOwnershipRange(A,&Istart,&Iend);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).
+ - Always specify global rows and columns of matrix entries.
+ */
+ for (Ii=Istart; Ii<Iend; 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,INSERT_VALUES);CHKERRQ(ierr);}
+ if (i<m-1) {J = Ii + n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
+ if (j>0) {J = Ii - 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
+ if (j<n-1) {J = Ii + 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
+ v = 4.0; ierr = MatSetValues(A,1,&Ii,1,&Ii,&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);
+
+ /*
+ Create parallel vectors.
+ - When using VecCreate() VecSetSizes() and VecSetFromOptions(),
+ we specify only the vector's global
+ dimension; the parallel partitioning is determined at runtime.
+ - Note: We form 1 vector from scratch and then duplicate as needed.
+ */
+ ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
+ ierr = VecSetSizes(u,PETSC_DECIDE,m*n);CHKERRQ(ierr);
+ ierr = VecSetFromOptions(u);CHKERRQ(ierr);
+ ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&x);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
+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
+
+ /*
+ 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 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.
+ */
+ ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
+ ierr = KSPSetTolerances(ksp,1e-9,1e-9,PETSC_DEFAULT,5000000);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
+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
+ PetscScalar T1,T2;
+ T1 = MPI_Wtime();
+ ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
+ T2 = MPI_Wtime();
+ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+ Check solution and clean up
+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
+
+ /*
+ Check the error
+ */
+ Vec sol;
+ VecDuplicate(b,&sol);
+ MatMult(A,x,sol);
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time : %g (s)\n\n\n", T2-T1); 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 %g\n",norm);
+
+ }
+
+
+
+
+
+ /*
+ 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 = PetscFinalize();
+ return 0;
+
+}
+
