Actual source code: test37.c

slepc-3.16.3 2022-04-11
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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[] = "Tests solving an eigenproblem defined with MatNest. "
 12:   "Based on ex9.\n"
 13:   "The command line options are:\n"
 14:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
 15:   "  -L <L>, where <L> = bifurcation parameter.\n"
 16:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
 17:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

 19: #include <slepceps.h>

 21: /*
 22:    This example computes the eigenvalues with largest real part of the
 23:    following matrix

 25:         A = [ tau1*T+(beta-1)*I     alpha^2*I
 26:                   -beta*I        tau2*T-alpha^2*I ],

 28:    where

 30:         T = tridiag{1,-2,1}
 31:         h = 1/(n+1)
 32:         tau1 = delta1/(h*L)^2
 33:         tau2 = delta2/(h*L)^2
 34:  */

 36: int main(int argc,char **argv)
 37: {
 38:   EPS            eps;
 39:   Mat            A,T1,T2,D1,D2,mats[4];
 40:   PetscScalar    alpha,beta,tau1,tau2,delta1,delta2,L,h;
 41:   PetscInt       N=30,i,Istart,Iend;

 44:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 45:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
 46:   PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%D\n\n",N);

 48:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 49:         Generate the matrix
 50:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 52:   alpha  = 2.0;
 53:   beta   = 5.45;
 54:   delta1 = 0.008;
 55:   delta2 = 0.004;
 56:   L      = 0.51302;

 58:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
 59:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&alpha,NULL);
 60:   PetscOptionsGetScalar(NULL,NULL,"-beta",&beta,NULL);
 61:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
 62:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

 64:   h    = 1.0 / (PetscReal)(N+1);
 65:   tau1 = delta1 / ((h*L)*(h*L));
 66:   tau2 = delta2 / ((h*L)*(h*L));

 68:   /* Create matrices T1, T2 */
 69:   MatCreate(PETSC_COMM_WORLD,&T1);
 70:   MatSetSizes(T1,PETSC_DECIDE,PETSC_DECIDE,N,N);
 71:   MatSetFromOptions(T1);
 72:   MatSetUp(T1);
 73:   MatGetOwnershipRange(T1,&Istart,&Iend);
 74:   for (i=Istart;i<Iend;i++) {
 75:     if (i>0) { MatSetValue(T1,i,i-1,1.0,INSERT_VALUES); }
 76:     if (i<N-1) { MatSetValue(T1,i,i+1,1.0,INSERT_VALUES); }
 77:     MatSetValue(T1,i,i,-2.0,INSERT_VALUES);
 78:   }
 79:   MatAssemblyBegin(T1,MAT_FINAL_ASSEMBLY);
 80:   MatAssemblyEnd(T1,MAT_FINAL_ASSEMBLY);

 82:   MatDuplicate(T1,MAT_COPY_VALUES,&T2);
 83:   MatScale(T1,tau1);
 84:   MatShift(T1,beta-1.0);
 85:   MatScale(T2,tau2);
 86:   MatShift(T2,-alpha*alpha);

 88:   /* Create matrices D1, D2 */
 89:   MatCreate(PETSC_COMM_WORLD,&D1);
 90:   MatSetSizes(D1,PETSC_DECIDE,PETSC_DECIDE,N,N);
 91:   MatSetFromOptions(D1);
 92:   MatSetUp(D1);
 93:   MatAssemblyBegin(D1,MAT_FINAL_ASSEMBLY);
 94:   MatAssemblyEnd(D1,MAT_FINAL_ASSEMBLY);
 95:   MatDuplicate(D1,MAT_COPY_VALUES,&D2);
 96:   MatShift(D1,alpha*alpha);
 97:   MatShift(D2,-beta);

 99:   /* Create the nest matrix */
100:   mats[0] = T1;
101:   mats[1] = D1;
102:   mats[2] = D2;
103:   mats[3] = T2;
104:   MatCreateNest(PETSC_COMM_WORLD,2,NULL,2,NULL,mats,&A);

106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107:                 Create the eigensolver and solve the problem
108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

110:   EPSCreate(PETSC_COMM_WORLD,&eps);
111:   EPSSetOperators(eps,A,NULL);
112:   EPSSetProblemType(eps,EPS_NHEP);
113:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
114:   EPSSetTrueResidual(eps,PETSC_FALSE);
115:   EPSSetFromOptions(eps);
116:   EPSSolve(eps);

118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119:                     Display solution and clean up
120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

122:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
123:   EPSDestroy(&eps);
124:   MatDestroy(&A);
125:   MatDestroy(&T1);
126:   MatDestroy(&T2);
127:   MatDestroy(&D1);
128:   MatDestroy(&D2);
129:   SlepcFinalize();
130:   return ierr;
131: }

133: /*TEST

135:    test:
136:       suffix: 1
137:       args: -eps_nev 4
138:       requires: !single
139:       filter: sed -e "s/0.00019-2.13938i, 0.00019+2.13938i/0.00019+2.13938i, 0.00019-2.13938i/" | sed -e "s/-0.67192-2.52712i, -0.67192+2.52712i/-0.67192+2.52712i, -0.67192-2.52712i/"

141: TEST*/