Actual source code: ex28.c

slepc-3.20.1 2023-11-27
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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:   PetscFunctionBeginUser;
 38:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
 39:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
 40:   PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

 42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 43:   N = n*n;
 44:   PetscCall(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:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K));
 52:   PetscCall(MatShellSetOperation(K,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D));
 53:   PetscCall(MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D));
 54:   PetscCall(MatShellSetOperation(K,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D));

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

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

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

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

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

 94:   PetscCall(PEPSolve(pep));

 96:   /*
 97:      Optional: Get some information from the solver and display it
 98:   */
 99:   PetscCall(PEPGetType(pep,&type));
100:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
101:   PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
102:   PetscCall(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:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
110:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL));
111:   else {
112:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
113:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
114:     PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
115:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
116:   }
117:   PetscCall(PEPDestroy(&pep));
118:   PetscCall(MatDestroy(&M));
119:   PetscCall(MatDestroy(&C));
120:   PetscCall(MatDestroy(&K));
121:   PetscCall(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;

168:   PetscFunctionBeginUser;
169:   PetscCall(MatShellGetContext(A,&ctx));
170:   nx = *(int*)ctx;
171:   PetscCall(VecGetArrayRead(x,&px));
172:   PetscCall(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:   PetscCall(VecRestoreArrayRead(x,&px));
188:   PetscCall(VecRestoreArray(y,&py));
189:   PetscFunctionReturn(PETSC_SUCCESS);
190: }

192: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
193: {
194:   PetscFunctionBeginUser;
195:   PetscCall(VecSet(diag,4.0));
196:   PetscFunctionReturn(PETSC_SUCCESS);
197: }

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

209: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
210: {
211:   PetscFunctionBeginUser;
212:   PetscCall(VecSet(diag,0.0));
213:   PetscFunctionReturn(PETSC_SUCCESS);
214: }

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

226: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
227: {
228:   PetscFunctionBeginUser;
229:   PetscCall(VecSet(diag,1.0));
230:   PetscFunctionReturn(PETSC_SUCCESS);
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*/