Actual source code: ex28.c

slepc-3.17.1 2022-04-11
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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;

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

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

 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

 67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 68:                 Create the eigensolver and set various options
 69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 71:   /*
 72:      Create eigensolver context
 73:   */
 74:   PEPCreate(PETSC_COMM_WORLD,&pep);

 76:   /*
 77:      Set matrices and problem type
 78:   */
 79:   A[0] = K; A[1] = C; A[2] = M;
 80:   PEPSetOperators(pep,3,A);
 81:   PEPGetST(pep,&st);
 82:   STSetMatMode(st,ST_MATMODE_SHELL);

 84:   /*
 85:      Set solver parameters at runtime
 86:   */
 87:   PEPSetFromOptions(pep);

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:                       Solve the eigensystem
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 93:   PEPSolve(pep);

 95:   /*
 96:      Optional: Get some information from the solver and display it
 97:   */
 98:   PEPGetType(pep,&type);
 99:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
100:   PEPGetDimensions(pep,&nev,NULL,NULL);
101:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104:                     Display solution and clean up
105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

124: /*
125:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
126:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
127:     DU on the superdiagonal.
128:  */
129: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
130: {
131:   PetscScalar dd,dl,du;
132:   int         j;

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

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

144: /*
145:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

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

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

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

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

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

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

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

191: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
192: {
194:   VecSet(diag,4.0);
195:   PetscFunctionReturn(0);
196: }

198: /*
199:     Matrix-vector product subroutine for the Null matrix.
200:  */
201: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
202: {
204:   VecSet(y,0.0);
205:   PetscFunctionReturn(0);
206: }

208: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
209: {
211:   VecSet(diag,0.0);
212:   PetscFunctionReturn(0);
213: }

215: /*
216:     Matrix-vector product subroutine for the Identity matrix.
217:  */
218: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
219: {
221:   VecCopy(x,y);
222:   PetscFunctionReturn(0);
223: }

225: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
226: {
228:   VecSet(diag,1.0);
229:   PetscFunctionReturn(0);
230: }

232: /*TEST

234:    test:
235:       suffix: 1
236:       args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
237:       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/"

239: TEST*/