Actual source code: pdde_stability.c

slepc-3.6.3 2016-03-29
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */
 21: /*
 22:    This example implements one of the problems found at
 23:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
 24:        The University of Manchester.
 25:    The details of the collection can be found at:
 26:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
 27:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

 29:    The pdde_stability problem is a complex-symmetric QEP from the stability
 30:    analysis of a discretized partial delay-differential equation. It requires
 31:    complex scalars.
 32: */

 34: static char help[] = "NLEVP problem: pdde_stability.\n\n"
 35:   "The command line options are:\n"
 36:   "  -m <m>, grid size, the matrices have dimension n=m*m.\n"
 37:   "  -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";

 39: #include <slepcpep.h>

 41: #define NMAT 3

 45: /*
 46:     Function for user-defined eigenvalue ordering criterion.

 48:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
 49:     one of them as the preferred one according to the criterion.
 50:     In this example, the preferred value is the one with absolute value closest to 1.
 51: */
 52: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
 53: {
 54:   PetscReal aa,ab;

 57:   aa = PetscAbsReal(SlepcAbsEigenvalue(ar,ai)-1.0);
 58:   ab = PetscAbsReal(SlepcAbsEigenvalue(br,bi)-1.0);
 59:   *r = aa > ab ? 1 : (aa < ab ? -1 : 0);
 60:   return(0);
 61: }

 65: int main(int argc,char **argv)
 66: {
 67:   Mat            A[NMAT];         /* problem matrices */
 68:   PEP            pep;             /* polynomial eigenproblem solver context */
 69:   PetscInt       m=15,n,II,Istart,Iend,i,j,k;
 70:   PetscReal      h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
 71:   PetscScalar    alpha,beta,gamma;
 72:   PetscBool      flg,terse;

 75:   SlepcInitialize(&argc,&argv,(char*)0,help);
 76: #if !defined(PETSC_USE_COMPLEX)
 77:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex scalars");
 78: #endif

 80:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 81:   n = m*m;
 82:   h = PETSC_PI/(m+1);
 83:   gamma = PetscExpScalar(PETSC_i*c[6]);
 84:   gamma = gamma/PetscAbsScalar(gamma);
 85:   k = 7;
 86:   PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);
 87:   if (flg && k!=7) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 7, you provided %D",k); 
 88:   PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%D (m=%D)\n\n",n,m);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 91:                      Compute the polynomial matrices 
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 94:   /* initialize matrices */
 95:   for (i=0;i<NMAT;i++) {
 96:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 97:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
 98:     MatSetFromOptions(A[i]);
 99:     MatSetUp(A[i]);
100:   }
101:   MatGetOwnershipRange(A[0],&Istart,&Iend);

103:   /* A[1] has a pattern similar to the 2D Laplacian */
104:   for (II=Istart;II<Iend;II++) {
105:     i = II/m; j = II-i*m;
106:     xi = (i+1)*h; xj = (j+1)*h;
107:     alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
108:     beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
109:     MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES);
110:     if (j>0) { MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES); }
111:     if (j<m-1) { MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES); }
112:     if (i>0) { MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES); }
113:     if (i<m-1) { MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES); }
114:   }

116:   /* A[0] and A[2] are diagonal */
117:   for (II=Istart;II<Iend;II++) {
118:     i = II/m; j = II-i*m;
119:     xi = (i+1)*h; xj = (j+1)*h;
120:     alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
121:     beta = c[4]+c[5]*xj*(PETSC_PI-xj);
122:     MatSetValue(A[0],II,II,alpha,INSERT_VALUES);
123:     MatSetValue(A[2],II,II,beta,INSERT_VALUES);
124:   }
125:   
126:   /* assemble matrices */
127:   for (i=0;i<NMAT;i++) {
128:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
129:   }
130:   for (i=0;i<NMAT;i++) {
131:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
132:   }

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
135:                 Create the eigensolver and solve the problem
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   PEPCreate(PETSC_COMM_WORLD,&pep);
139:   PEPSetOperators(pep,NMAT,A);
140:   PEPSetEigenvalueComparison(pep,MyEigenSort,NULL);
141:   PEPSetDimensions(pep,4,PETSC_DEFAULT,PETSC_DEFAULT);
142:   PEPSetFromOptions(pep);
143:   PEPSolve(pep);

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:                     Display solution and clean up
147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148:   
149:   /* show detailed info unless -terse option is given by user */
150:   PetscOptionsHasName(NULL,"-terse",&terse);
151:   if (terse) {
152:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
153:   } else {
154:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
155:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
156:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
157:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
158:   }
159:   PEPDestroy(&pep);
160:   for (i=0;i<NMAT;i++) {
161:     MatDestroy(&A[i]);
162:   }
163:   SlepcFinalize();
164:   return 0;
165: }