Actual source code: ex28.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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;
 36:   ST             st;

 38:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 39:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 40:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

 42:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 43:   N = n*n;
 44:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%D (%Dx%D 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: %D\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) {
111:     PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL);
112:   } else {
113:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
114:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
115:     PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
116:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
117:   }
118:   PEPDestroy(&pep);
119:   MatDestroy(&M);
120:   MatDestroy(&C);
121:   MatDestroy(&K);
122:   SlepcFinalize();
123:   return ierr;
124: }

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

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

140:   y[0] =  dd*x[0] + du*x[1];
141:   for (j=1;j<nx-1;j++)
142:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
143:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
144: }

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

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

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

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

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

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

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

179:   for (j=2;j<nx;j++) {
180:     lo = (j-1)*nx;
181:     tv(nx,&px[lo],&py[lo]);
182:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
183:   }

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

189:   VecRestoreArrayRead(x,&px);
190:   VecRestoreArray(y,&py);
191:   return(0);
192: }

194: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
195: {

199:   VecSet(diag,4.0);
200:   return(0);
201: }

203: /*
204:     Matrix-vector product subroutine for the Null matrix.
205:  */
206: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
207: {

211:   VecSet(y,0.0);
212:   return(0);
213: }

215: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
216: {

220:   VecSet(diag,0.0);
221:   return(0);
222: }

224: /*
225:     Matrix-vector product subroutine for the Identity matrix.
226:  */
227: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
228: {
229:   PetscErrorCode    ierr;

232:   VecCopy(x,y);
233:   return(0);
234: }

236: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
237: {

241:   VecSet(diag,1.0);
242:   return(0);
243: }

245: /*TEST

247:    test:
248:       suffix: 1
249:       args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
250:       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/"

252: TEST*/