| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 6 | This file is part of SLEPc. | ||
| 7 | SLEPc is distributed under a 2-clause BSD license (see LICENSE). | ||
| 8 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 9 | */ | ||
| 10 | |||
| 11 | static char help[] = "Test the NEPProjectOperator() function.\n\n" | ||
| 12 | "This is based on ex22.\n" | ||
| 13 | "The command line options are:\n" | ||
| 14 | " -n <n>, where <n> = number of grid subdivisions.\n" | ||
| 15 | " -tau <tau>, where <tau> is the delay parameter.\n"; | ||
| 16 | |||
| 17 | /* | ||
| 18 | Solve parabolic partial differential equation with time delay tau | ||
| 19 | |||
| 20 | u_t = u_xx + a*u(t) + b*u(t-tau) | ||
| 21 | u(0,t) = u(pi,t) = 0 | ||
| 22 | |||
| 23 | with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)). | ||
| 24 | |||
| 25 | Discretization leads to a DDE of dimension n | ||
| 26 | |||
| 27 | -u' = A*u(t) + B*u(t-tau) | ||
| 28 | |||
| 29 | which results in the nonlinear eigenproblem | ||
| 30 | |||
| 31 | (-lambda*I + A + exp(-tau*lambda)*B)*u = 0 | ||
| 32 | */ | ||
| 33 | |||
| 34 | #include <slepcnep.h> | ||
| 35 | |||
| 36 | 10 | int main(int argc,char **argv) | |
| 37 | { | ||
| 38 | 10 | NEP nep; | |
| 39 | 10 | Mat Id,A,B,mats[3]; | |
| 40 | 10 | FN f1,f2,f3,funs[3]; | |
| 41 | 10 | BV V; | |
| 42 | 10 | DS ds; | |
| 43 | 10 | Vec v; | |
| 44 | 10 | PetscScalar coeffs[2],b,*M; | |
| 45 | 10 | PetscInt n=32,Istart,Iend,i,j,k,nc; | |
| 46 | 10 | PetscReal tau=0.001,h,a=20,xi; | |
| 47 | |||
| 48 |
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10 | PetscFunctionBeginUser; |
| 49 |
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10 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 50 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
| 51 |
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10 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL)); |
| 52 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n",n,(double)tau)); |
| 53 | 10 | h = PETSC_PI/(PetscReal)(n+1); | |
| 54 | |||
| 55 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 56 | Create nonlinear eigensolver context | ||
| 57 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 58 | |||
| 59 |
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10 | PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep)); |
| 60 | |||
| 61 | /* Identity matrix */ | ||
| 62 |
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10 | PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id)); |
| 63 |
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10 | PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE)); |
| 64 | |||
| 65 | /* A = 1/h^2*tridiag(1,-2,1) + a*I */ | ||
| 66 |
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10 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); |
| 67 |
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10 | PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n)); |
| 68 |
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10 | PetscCall(MatSetFromOptions(A)); |
| 69 |
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10 | PetscCall(MatGetOwnershipRange(A,&Istart,&Iend)); |
| 70 |
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330 | for (i=Istart;i<Iend;i++) { |
| 71 |
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320 | if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES)); |
| 72 |
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320 | if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES)); |
| 73 |
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320 | PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES)); |
| 74 | } | ||
| 75 |
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10 | PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); |
| 76 |
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10 | PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); |
| 77 |
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10 | PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE)); |
| 78 | |||
| 79 | /* B = diag(b(xi)) */ | ||
| 80 |
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10 | PetscCall(MatCreate(PETSC_COMM_WORLD,&B)); |
| 81 |
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10 | PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n)); |
| 82 |
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10 | PetscCall(MatSetFromOptions(B)); |
| 83 |
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10 | PetscCall(MatGetOwnershipRange(B,&Istart,&Iend)); |
| 84 |
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330 | for (i=Istart;i<Iend;i++) { |
| 85 | 320 | xi = (i+1)*h; | |
| 86 | 320 | b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI)); | |
| 87 |
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320 | PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES)); |
| 88 | } | ||
| 89 |
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10 | PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); |
| 90 |
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10 | PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); |
| 91 |
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10 | PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE)); |
| 92 | |||
| 93 | /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */ | ||
| 94 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f1)); |
| 95 |
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10 | PetscCall(FNSetType(f1,FNRATIONAL)); |
| 96 | 10 | coeffs[0] = -1.0; coeffs[1] = 0.0; | |
| 97 |
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10 | PetscCall(FNRationalSetNumerator(f1,2,coeffs)); |
| 98 | |||
| 99 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f2)); |
| 100 |
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10 | PetscCall(FNSetType(f2,FNRATIONAL)); |
| 101 | 10 | coeffs[0] = 1.0; | |
| 102 |
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10 | PetscCall(FNRationalSetNumerator(f2,1,coeffs)); |
| 103 | |||
| 104 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f3)); |
| 105 |
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10 | PetscCall(FNSetType(f3,FNEXP)); |
| 106 |
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10 | PetscCall(FNSetScale(f3,-tau,1.0)); |
| 107 | |||
| 108 | /* Set the split operator */ | ||
| 109 | 10 | mats[0] = A; funs[0] = f2; | |
| 110 | 10 | mats[1] = Id; funs[1] = f1; | |
| 111 | 10 | mats[2] = B; funs[2] = f3; | |
| 112 |
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10 | PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN)); |
| 113 |
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10 | PetscCall(NEPSetType(nep,NEPNARNOLDI)); |
| 114 |
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10 | PetscCall(NEPSetFromOptions(nep)); |
| 115 | |||
| 116 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 117 | Project the NEP | ||
| 118 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 119 | |||
| 120 |
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10 | PetscCall(NEPSetUp(nep)); |
| 121 |
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10 | PetscCall(NEPGetBV(nep,&V)); |
| 122 |
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10 | PetscCall(BVGetSizes(V,NULL,NULL,&nc)); |
| 123 |
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60 | for (i=0;i<nc;i++) { |
| 124 |
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50 | PetscCall(BVGetColumn(V,i,&v)); |
| 125 |
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50 | PetscCall(VecSetValue(v,i,1.0,INSERT_VALUES)); |
| 126 |
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50 | PetscCall(VecAssemblyBegin(v)); |
| 127 |
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50 | PetscCall(VecAssemblyEnd(v)); |
| 128 |
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50 | PetscCall(BVRestoreColumn(V,i,&v)); |
| 129 | } | ||
| 130 |
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10 | PetscCall(NEPGetDS(nep,&ds)); |
| 131 |
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10 | PetscCall(DSSetType(ds,DSNEP)); |
| 132 |
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10 | PetscCall(DSNEPSetFN(ds,3,funs)); |
| 133 |
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10 | PetscCall(DSAllocate(ds,nc)); |
| 134 |
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10 | PetscCall(DSSetDimensions(ds,nc,0,0)); |
| 135 |
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10 | PetscCall(NEPProjectOperator(nep,0,nc)); |
| 136 | |||
| 137 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 138 | Display projected matrices and clean up | ||
| 139 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 140 | |||
| 141 |
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40 | for (k=0;k<3;k++) { |
| 142 |
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30 | PetscCall(DSGetArray(ds,DSMatExtra[k],&M)); |
| 143 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k)); |
| 144 |
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180 | for (i=0;i<nc;i++) { |
| 145 |
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900 | for (j=0;j<nc;j++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %.5g",(double)PetscRealPart(M[i+j*nc]))); |
| 146 |
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150 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n")); |
| 147 | } | ||
| 148 |
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30 | PetscCall(DSRestoreArray(ds,DSMatExtra[k],&M)); |
| 149 | } | ||
| 150 | |||
| 151 |
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10 | PetscCall(NEPDestroy(&nep)); |
| 152 |
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10 | PetscCall(MatDestroy(&Id)); |
| 153 |
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10 | PetscCall(MatDestroy(&A)); |
| 154 |
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10 | PetscCall(MatDestroy(&B)); |
| 155 |
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10 | PetscCall(FNDestroy(&f1)); |
| 156 |
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10 | PetscCall(FNDestroy(&f2)); |
| 157 |
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10 | PetscCall(FNDestroy(&f3)); |
| 158 |
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10 | PetscCall(SlepcFinalize()); |
| 159 | return 0; | ||
| 160 | } | ||
| 161 | |||
| 162 | /*TEST | ||
| 163 | |||
| 164 | test: | ||
| 165 | suffix: 1 | ||
| 166 | args: -nep_ncv 5 | ||
| 167 | |||
| 168 | TEST*/ | ||
| 169 |