PetscErrorCode NEPSolve_Interpol(NEP nep)
{
PetscErrorCode ierr;
NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
Mat *A; /*T=nep->function,Tp=nep->jacobian;*/
PetscScalar *x,*fx,t;
PetscReal *cs,a,b,s;
PetscInt i,j,k,deg=ctx->deg;
PetscFunctionBegin;
ierr = PetscMalloc4(deg+1,&A,(deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx);CHKERRQ(ierr);
ierr = RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);CHKERRQ(ierr);
ierr = ChebyshevNodes(deg,a,b,x,cs);CHKERRQ(ierr);
for (j=0;j<nep->nt;j++) {
for (i=0;i<=deg;i++) {
ierr = FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);CHKERRQ(ierr);
}
}
/* Polynomial coefficients */
for (k=0;k<=deg;k++) {
ierr = MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);CHKERRQ(ierr);
t = 0.0;
for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
t *= 2.0/(deg+1);
if (k==0) t /= 2.0;
ierr = MatScale(A[k],t);CHKERRQ(ierr);
for (j=1;j<nep->nt;j++) {
t = 0.0;
for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
t *= 2.0/(deg+1);
if (k==0) t /= 2.0;
ierr = MatAXPY(A[k],t,nep->A[j],SUBSET_NONZERO_PATTERN);CHKERRQ(ierr);
}
}
ierr = PEPSetOperators(ctx->pep,deg+1,A);CHKERRQ(ierr);
for (k=0;k<=deg;k++) {
ierr = MatDestroy(&A[k]);CHKERRQ(ierr);
}
ierr = PetscFree4(A,cs,x,fx);CHKERRQ(ierr);
/* Solve polynomial eigenproblem */
ierr = PEPSolve(ctx->pep);CHKERRQ(ierr);
ierr = PEPGetConverged(ctx->pep,&nep->nconv);CHKERRQ(ierr);
ierr = PEPGetIterationNumber(ctx->pep,&nep->its);CHKERRQ(ierr);
ierr = PEPGetConvergedReason(ctx->pep,(PEPConvergedReason*)&nep->reason);CHKERRQ(ierr);
s = 2.0/(b-a);
for (i=0;i<nep->nconv;i++) {
ierr = PEPGetEigenpair(ctx->pep,i,&nep->eigr[i],&nep->eigi[i],NULL,NULL);CHKERRQ(ierr);
nep->eigr[i] /= s;
nep->eigr[i] += (a+b)/2.0;
nep->eigi[i] /= s;
}
nep->state = NEP_STATE_EIGENVECTORS;
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
Mat A[NMAT]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt m=15,n,II,Istart,Iend,i,j,k;
PetscReal h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
PetscScalar alpha,beta,gamma;
PetscBool flg;
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex scalars");
#endif
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
n = m*m;
h = PETSC_PI/(m+1);
gamma = PetscExpScalar(PETSC_i*c[6]);
gamma = gamma/PetscAbsScalar(gamma);
k = 7;
ierr = PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);CHKERRQ(ierr);
if (flg && k!=7) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 7, you provided %D",k);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%D (m=%D)\n\n",n,m);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A[i]);CHKERRQ(ierr);
ierr = MatSetUp(A[i]);CHKERRQ(ierr);
}
ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);
/* A[1] has a pattern similar to the 2D Laplacian */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
xi = (i+1)*h; xj = (j+1)*h;
alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
ierr = MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES);CHKERRQ(ierr);
if (j>0) { ierr = MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
}
/* A[0] and A[2] are diagonal */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
xi = (i+1)*h; xj = (j+1)*h;
alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
beta = c[4]+c[5]*xj*(PETSC_PI-xj);
ierr = MatSetValue(A[0],II,II,alpha,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValue(A[2],II,II,beta,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 = PEPSolve(pep);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPPrintSolution(pep,NULL);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;
}
int main(int argc,char **argv)
{
Mat M,C,K,A[3]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt m=6,n,II,Istart,Iend,i,j;
PetscScalar z=1.0;
PetscReal h;
char str[50];
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
if (m<2) SETERRQ(PETSC_COMM_SELF,1,"m must be at least 2");
ierr = PetscOptionsGetScalar(NULL,"-z",&z,NULL);CHKERRQ(ierr);
h = 1.0/m;
n = m*(m-1);
ierr = SlepcSNPrintfScalar(str,50,z,PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nAcoustic wave 2-D, n=%D (m=%D), z=%s\n\n",n,m,str);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* K has a pattern similar to the 2D Laplacian */
ierr = MatCreate(PETSC_COMM_WORLD,&K);CHKERRQ(ierr);
ierr = MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(K);CHKERRQ(ierr);
ierr = MatSetUp(K);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(K,&Istart,&Iend);CHKERRQ(ierr);
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
if (i>0) { ierr = MatSetValue(K,II,II-m,(j==m-1)?-0.5:-1.0,INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-2) { ierr = MatSetValue(K,II,II+m,(j==m-1)?-0.5:-1.0,INSERT_VALUES);CHKERRQ(ierr); }
if (j>0) { ierr = MatSetValue(K,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(K,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
ierr = MatSetValue(K,II,II,(j==m-1)?2.0:4.0,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* C is the zero matrix except for a few nonzero elements on the diagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i%m==m-1) {
ierr = MatSetValue(C,i,i,-2*PETSC_PI*h/z,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* M is a diagonal matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&M);CHKERRQ(ierr);
ierr = MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(M);CHKERRQ(ierr);
ierr = MatSetUp(M);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(M,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i%m==m-1) {
ierr = MatSetValue(M,i,i,2*PETSC_PI*PETSC_PI*h*h,INSERT_VALUES);CHKERRQ(ierr);
} else {
ierr = MatSetValue(M,i,i,4*PETSC_PI*PETSC_PI*h*h,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
A[0] = K; A[1] = C; A[2] = M;
ierr = PEPSetOperators(pep,3,A);CHKERRQ(ierr);
ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);
ierr = PEPSolve(pep);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPPrintSolution(pep,NULL);CHKERRQ(ierr);
ierr = PEPDestroy(&pep);CHKERRQ(ierr);
ierr = MatDestroy(&M);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
Mat A[NMAT]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt n,m=8,k,II,Istart,Iend,i,j;
PetscReal c[10] = { 0.6, 1.3, 1.3, 0.1, 0.1, 1.2, 1.0, 1.0, 1.2, 1.0 };
PetscBool flg;
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
n = m*m;
k = 10;
ierr = PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);CHKERRQ(ierr);
if (flg && k!=10) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 10, you provided %D",k);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nButterfly problem, n=%D (m=%D)\n\n",n,m);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A[i]);CHKERRQ(ierr);
ierr = MatSetUp(A[i]);CHKERRQ(ierr);
}
ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);
/* A0 */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
ierr = MatSetValue(A[0],II,II,4.0*c[0]/6.0+4.0*c[1]/6.0,INSERT_VALUES);CHKERRQ(ierr);
if (j>0) { ierr = MatSetValue(A[0],II,II-1,c[0]/6.0,INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[0],II,II+1,c[0]/6.0,INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[0],II,II-m,c[1]/6.0,INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[0],II,II+m,c[1]/6.0,INSERT_VALUES);CHKERRQ(ierr); }
}
/* A1 */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
if (j>0) { ierr = MatSetValue(A[1],II,II-1,c[2],INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[1],II,II+1,-c[2],INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[1],II,II-m,c[3],INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[1],II,II+m,-c[3],INSERT_VALUES);CHKERRQ(ierr); }
}
/* A2 */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
ierr = MatSetValue(A[2],II,II,-2.0*c[4]-2.0*c[5],INSERT_VALUES);CHKERRQ(ierr);
if (j>0) { ierr = MatSetValue(A[2],II,II-1,c[4],INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[2],II,II+1,c[4],INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[2],II,II-m,c[5],INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[2],II,II+m,c[5],INSERT_VALUES);CHKERRQ(ierr); }
}
/* A3 */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
if (j>0) { ierr = MatSetValue(A[3],II,II-1,c[6],INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[3],II,II+1,-c[6],INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[3],II,II-m,c[7],INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[3],II,II+m,-c[7],INSERT_VALUES);CHKERRQ(ierr); }
}
/* A4 */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
ierr = MatSetValue(A[4],II,II,2.0*c[8]+2.0*c[9],INSERT_VALUES);CHKERRQ(ierr);
if (j>0) { ierr = MatSetValue(A[4],II,II-1,-c[8],INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[4],II,II+1,-c[8],INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[4],II,II-m,-c[9],INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[4],II,II+m,-c[9],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 = PEPSolve(pep);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPPrintSolution(pep,NULL);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;
}
int main(int argc,char **argv)
{
Mat M,C,K,A[3]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt n=5,Istart,Iend,i;
PetscReal mu=1,tau=10,kappa=5;
PetscBool terse;
PetscErrorCode ierr;
PetscLogDouble time1,time2;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-mu",&mu,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-tau",&tau,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-kappa",&kappa,NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nDamped mass-spring system, n=%D mu=%g tau=%g kappa=%g\n\n",n,(double)mu,(double)tau,(double)kappa);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* K is a tridiagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&K);CHKERRQ(ierr);
ierr = MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(K);CHKERRQ(ierr);
ierr = MatSetUp(K);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(K,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i>0) {
ierr = MatSetValue(K,i,i-1,-kappa,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES);CHKERRQ(ierr);
if (i<n-1) {
ierr = MatSetValue(K,i,i+1,-kappa,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* C is a tridiagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i>0) {
ierr = MatSetValue(C,i,i-1,-tau,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValue(C,i,i,tau*3.0,INSERT_VALUES);CHKERRQ(ierr);
if (i<n-1) {
ierr = MatSetValue(C,i,i+1,-tau,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* M is a diagonal matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&M);CHKERRQ(ierr);
ierr = MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(M);CHKERRQ(ierr);
ierr = MatSetUp(M);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(M,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
ierr = MatSetValue(M,i,i,mu,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
A[0] = K; A[1] = C; A[2] = M;
ierr = PEPSetOperators(pep,3,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);
ierr = MatDestroy(&M);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
PETSC_EXTERN void PETSC_STDCALL pepsetoperators_(PEP *pep,PetscInt *nmat,Mat A[], int *__ierr ){
*__ierr = PEPSetOperators(*pep,*nmat,A);
}
int main(int argc,char **argv)
{
Mat M,Mo,C,K,Ko,A[3]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
IS isf,isbc,is;
PetscInt n=200,nele,Istart,Iend,i,j,mloc,nloc,bc[2];
PetscReal width=0.05,height=0.005,glength=1.0,dlen,EI,area,rho;
PetscScalar K1[4],K2[4],K2t[4],K3[4],M1[4],M2[4],M2t[4],M3[4],damp=5.0;
PetscBool terse;
PetscErrorCode ierr;
PetscLogDouble time1,time2;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
nele = n/2;
n = 2*nele;
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nSimply supported beam damped in the middle, n=%D (nele=%D)\n\n",n,nele);CHKERRQ(ierr);
dlen = glength/nele;
EI = 7e10*width*height*height*height/12.0;
area = width*height;
rho = 0.674/(area*glength);
K1[0] = 12; K1[1] = 6*dlen; K1[2] = 6*dlen; K1[3] = 4*dlen*dlen;
K2[0] = -12; K2[1] = 6*dlen; K2[2] = -6*dlen; K2[3] = 2*dlen*dlen;
K2t[0] = -12; K2t[1] = -6*dlen; K2t[2] = 6*dlen; K2t[3] = 2*dlen*dlen;
K3[0] = 12; K3[1] = -6*dlen; K3[2] = -6*dlen; K3[3] = 4*dlen*dlen;
M1[0] = 156; M1[1] = 22*dlen; M1[2] = 22*dlen; M1[3] = 4*dlen*dlen;
M2[0] = 54; M2[1] = -13*dlen; M2[2] = 13*dlen; M2[3] = -3*dlen*dlen;
M2t[0] = 54; M2t[1] = 13*dlen; M2t[2] = -13*dlen; M2t[3] = -3*dlen*dlen;
M3[0] = 156; M3[1] = -22*dlen; M3[2] = -22*dlen; M3[3] = 4*dlen*dlen;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* K is block-tridiagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&Ko);CHKERRQ(ierr);
ierr = MatSetSizes(Ko,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);CHKERRQ(ierr);
ierr = MatSetBlockSize(Ko,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(Ko);CHKERRQ(ierr);
ierr = MatSetUp(Ko);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(Ko,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart/2;i<Iend/2;i++) {
if (i>0) {
j = i-1;
ierr = MatSetValuesBlocked(Ko,1,&i,1,&j,K2t,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesBlocked(Ko,1,&i,1,&i,K3,ADD_VALUES);CHKERRQ(ierr);
}
if (i<nele) {
j = i+1;
ierr = MatSetValuesBlocked(Ko,1,&i,1,&j,K2,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesBlocked(Ko,1,&i,1,&i,K1,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Ko,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Ko,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatScale(Ko,EI/(dlen*dlen*dlen));CHKERRQ(ierr);
/* M is block-tridiagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&Mo);CHKERRQ(ierr);
ierr = MatSetSizes(Mo,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);CHKERRQ(ierr);
ierr = MatSetBlockSize(Mo,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(Mo);CHKERRQ(ierr);
ierr = MatSetUp(Mo);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(Mo,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart/2;i<Iend/2;i++) {
if (i>0) {
j = i-1;
ierr = MatSetValuesBlocked(Mo,1,&i,1,&j,M2t,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesBlocked(Mo,1,&i,1,&i,M3,ADD_VALUES);CHKERRQ(ierr);
}
if (i<nele) {
j = i+1;
ierr = MatSetValuesBlocked(Mo,1,&i,1,&j,M2,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesBlocked(Mo,1,&i,1,&i,M1,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Mo,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Mo,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatScale(Mo,rho*area*dlen/420);CHKERRQ(ierr);
/* remove rows/columns from K and M corresponding to boundary conditions */
ierr = ISCreateStride(PETSC_COMM_WORLD,Iend-Istart,Istart,1,&isf);CHKERRQ(ierr);
bc[0] = 0; bc[1] = n;
ierr = ISCreateGeneral(PETSC_COMM_SELF,2,bc,PETSC_USE_POINTER,&isbc);CHKERRQ(ierr);
ierr = ISDifference(isf,isbc,&is);CHKERRQ(ierr);
ierr = MatGetSubMatrix(Ko,is,is,MAT_INITIAL_MATRIX,&K);CHKERRQ(ierr);
ierr = MatGetSubMatrix(Mo,is,is,MAT_INITIAL_MATRIX,&M);CHKERRQ(ierr);
ierr = MatGetLocalSize(M,&mloc,&nloc);CHKERRQ(ierr);
/* C is zero except for the (nele,nele)-entry */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,mloc,nloc,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
if (nele-1>=Istart && nele-1<Iend) {
ierr = MatSetValue(C,nele-1,nele-1,damp,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
A[0] = K; A[1] = C; A[2] = M;
ierr = PEPSetOperators(pep,3,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);
ierr = ISDestroy(&isf);CHKERRQ(ierr);
ierr = ISDestroy(&isbc);CHKERRQ(ierr);
ierr = ISDestroy(&is);CHKERRQ(ierr);
ierr = MatDestroy(&M);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = MatDestroy(&Ko);CHKERRQ(ierr);
ierr = MatDestroy(&Mo);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
Mat M,C,K,A[3]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt n=10,Istart,Iend,i;
PetscScalar z=1.0;
char str[50];
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,"-z",&z,NULL);CHKERRQ(ierr);
ierr = SlepcSNPrintfScalar(str,50,z,PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nAcoustic wave 1-D, n=%D z=%s\n\n",n,str);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* K is a tridiagonal */
ierr = MatCreate(PETSC_COMM_WORLD,&K);CHKERRQ(ierr);
ierr = MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(K);CHKERRQ(ierr);
ierr = MatSetUp(K);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(K,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i>0) {
ierr = MatSetValue(K,i,i-1,-1.0*n,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
ierr = MatSetValue(K,i,i,2.0*n,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValue(K,i,i+1,-1.0*n,INSERT_VALUES);CHKERRQ(ierr);
} else {
ierr = MatSetValue(K,i,i,1.0*n,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* C is the zero matrix but one element*/
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
if (n-1>=Istart && n-1<Iend) {
ierr = MatSetValue(C,n-1,n-1,-2*PETSC_PI/z,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* M is a diagonal matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&M);CHKERRQ(ierr);
ierr = MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(M);CHKERRQ(ierr);
ierr = MatSetUp(M);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(M,&Istart,&Iend);CHKERRQ(ierr);
for (i=Istart;i<Iend;i++) {
if (i<n-1) {
ierr = MatSetValue(M,i,i,4*PETSC_PI*PETSC_PI/n,INSERT_VALUES);CHKERRQ(ierr);
} else {
ierr = MatSetValue(M,i,i,2*PETSC_PI*PETSC_PI/n,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
A[0] = K; A[1] = C; A[2] = M;
ierr = PEPSetOperators(pep,3,A);CHKERRQ(ierr);
ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);
ierr = PEPSolve(pep);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPPrintSolution(pep,NULL);CHKERRQ(ierr);
ierr = PEPDestroy(&pep);CHKERRQ(ierr);
ierr = MatDestroy(&M);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
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;
}