Actual source code: ex28.c

slepc-3.18.1 2022-11-02
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "A quadratic eigenproblem defined using shell matrices.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n";

 15: #include <slepcpep.h>

 17: /*
 18:    User-defined routines
 19: */
 20: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
 21: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
 22: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y);
 23: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag);
 24: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y);
 25: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag);

 27: int main(int argc,char **argv)
 28: {
 29:   Mat            M,C,K,A[3];      /* problem matrices */
 30:   PEP            pep;             /* polynomial eigenproblem solver context */
 31:   PEPType        type;
 32:   PetscInt       N,n=10,nev;
 33:   PetscMPIInt    size;
 34:   PetscBool      terse;
 35:   ST             st;

 38:   SlepcInitialize(&argc,&argv,(char*)0,help);
 39:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 42:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 43:   N = n*n;
 44:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n);

 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 47:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 50:   /* K is the 2-D Laplacian */
 51:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K);
 52:   MatShellSetOperation(K,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D);
 53:   MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D);
 54:   MatShellSetOperation(K,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D);

 56:   /* C is the zero matrix */
 57:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&C);
 58:   MatShellSetOperation(C,MATOP_MULT,(void(*)(void))MatMult_Zero);
 59:   MatShellSetOperation(C,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Zero);
 60:   MatShellSetOperation(C,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Zero);

 62:   /* M is the identity matrix */
 63:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&M);
 64:   MatShellSetOperation(M,MATOP_MULT,(void(*)(void))MatMult_Identity);
 65:   MatShellSetOperation(M,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Identity);
 66:   MatShellSetOperation(M,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Identity);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:                 Create the eigensolver and set various options
 70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 72:   /*
 73:      Create eigensolver context
 74:   */
 75:   PEPCreate(PETSC_COMM_WORLD,&pep);

 77:   /*
 78:      Set matrices and problem type
 79:   */
 80:   A[0] = K; A[1] = C; A[2] = M;
 81:   PEPSetOperators(pep,3,A);
 82:   PEPGetST(pep,&st);
 83:   STSetMatMode(st,ST_MATMODE_SHELL);

 85:   /*
 86:      Set solver parameters at runtime
 87:   */
 88:   PEPSetFromOptions(pep);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 91:                       Solve the eigensystem
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 94:   PEPSolve(pep);

 96:   /*
 97:      Optional: Get some information from the solver and display it
 98:   */
 99:   PEPGetType(pep,&type);
100:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
101:   PEPGetDimensions(pep,&nev,NULL,NULL);
102:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105:                     Display solution and clean up
106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   /* show detailed info unless -terse option is given by user */
109:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
110:   if (terse) PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL);
111:   else {
112:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
113:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
114:     PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
115:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
116:   }
117:   PEPDestroy(&pep);
118:   MatDestroy(&M);
119:   MatDestroy(&C);
120:   MatDestroy(&K);
121:   SlepcFinalize();
122:   return 0;
123: }

125: /*
126:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
127:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
128:     DU on the superdiagonal.
129:  */
130: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
131: {
132:   PetscScalar dd,dl,du;
133:   int         j;

135:   dd  = 4.0;
136:   dl  = -1.0;
137:   du  = -1.0;

139:   y[0] =  dd*x[0] + du*x[1];
140:   for (j=1;j<nx-1;j++)
141:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
142:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
143: }

145: /*
146:     Matrix-vector product subroutine for the 2D Laplacian.

148:     The matrix used is the 2 dimensional discrete Laplacian on unit square with
149:     zero Dirichlet boundary condition.

151:     Computes y <-- A*x, where A is the block tridiagonal matrix

153:                  | T -I          |
154:                  |-I  T -I       |
155:              A = |   -I  T       |
156:                  |        ...  -I|
157:                  |           -I T|

159:     The subroutine TV is called to compute y<--T*x.
160:  */
161: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
162: {
163:   void              *ctx;
164:   int               nx,lo,i,j;
165:   const PetscScalar *px;
166:   PetscScalar       *py;

169:   MatShellGetContext(A,&ctx);
170:   nx = *(int*)ctx;
171:   VecGetArrayRead(x,&px);
172:   VecGetArray(y,&py);

174:   tv(nx,&px[0],&py[0]);
175:   for (i=0;i<nx;i++) py[i] -= px[nx+i];

177:   for (j=2;j<nx;j++) {
178:     lo = (j-1)*nx;
179:     tv(nx,&px[lo],&py[lo]);
180:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
181:   }

183:   lo = (nx-1)*nx;
184:   tv(nx,&px[lo],&py[lo]);
185:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

187:   VecRestoreArrayRead(x,&px);
188:   VecRestoreArray(y,&py);
189:   return 0;
190: }

192: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
193: {
195:   VecSet(diag,4.0);
196:   return 0;
197: }

199: /*
200:     Matrix-vector product subroutine for the Null matrix.
201:  */
202: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
203: {
205:   VecSet(y,0.0);
206:   return 0;
207: }

209: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
210: {
212:   VecSet(diag,0.0);
213:   return 0;
214: }

216: /*
217:     Matrix-vector product subroutine for the Identity matrix.
218:  */
219: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
220: {
222:   VecCopy(x,y);
223:   return 0;
224: }

226: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
227: {
229:   VecSet(diag,1.0);
230:   return 0;
231: }

233: /*TEST

235:    test:
236:       suffix: 1
237:       args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
238:       filter: grep -v Solution | sed -e "s/2.7996[1-8]i/2.79964i/g" | sed -e "s/2.7570[5-9]i/2.75708i/g" | sed -e "s/0.00000-2.79964i, 0.00000+2.79964i/0.00000+2.79964i, 0.00000-2.79964i/" | sed -e "s/0.00000-2.75708i, 0.00000+2.75708i/0.00000+2.75708i, 0.00000-2.75708i/"

240: TEST*/