| 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[] = "Solves the same problem as in ex5, but with a user-defined sorting criterion.\n\n" | ||
| 12 | "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n" | ||
| 13 | "This example illustrates how the user can set a custom spectrum selection.\n\n" | ||
| 14 | "The command line options are:\n" | ||
| 15 | " -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n"; | ||
| 16 | |||
| 17 | #include <slepceps.h> | ||
| 18 | |||
| 19 | /* | ||
| 20 | User-defined routines | ||
| 21 | */ | ||
| 22 | |||
| 23 | PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx); | ||
| 24 | PetscErrorCode MatMarkovModel(PetscInt m,Mat A); | ||
| 25 | |||
| 26 | 50 | int main(int argc,char **argv) | |
| 27 | { | ||
| 28 | 50 | Vec v0; /* initial vector */ | |
| 29 | 50 | Mat A; /* operator matrix */ | |
| 30 | 50 | EPS eps; /* eigenproblem solver context */ | |
| 31 | 50 | ST st; /* spectral transformation associated */ | |
| 32 | 50 | PetscReal tol=PETSC_SMALL; | |
| 33 | 50 | PetscScalar target=0.5; | |
| 34 | 50 | PetscInt N,m=15,nev; | |
| 35 | 50 | char str[50]; | |
| 36 | |||
| 37 |
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50 | PetscFunctionBeginUser; |
| 38 |
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50 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 39 | |||
| 40 |
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50 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL)); |
| 41 | 50 | N = m*(m+1)/2; | |
| 42 |
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50 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m)); |
| 43 |
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50 | PetscCall(PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL)); |
| 44 |
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50 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE)); |
| 45 |
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50 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str)); |
| 46 | |||
| 47 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 48 | Compute the operator matrix that defines the eigensystem, Ax=kx | ||
| 49 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 50 | |||
| 51 |
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50 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); |
| 52 |
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50 | PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N)); |
| 53 |
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50 | PetscCall(MatSetFromOptions(A)); |
| 54 |
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50 | PetscCall(MatMarkovModel(m,A)); |
| 55 | |||
| 56 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 57 | Create the eigensolver and set various options | ||
| 58 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 59 | |||
| 60 | /* | ||
| 61 | Create eigensolver context | ||
| 62 | */ | ||
| 63 |
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50 | PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps)); |
| 64 | |||
| 65 | /* | ||
| 66 | Set operators. In this case, it is a standard eigenvalue problem | ||
| 67 | */ | ||
| 68 |
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50 | PetscCall(EPSSetOperators(eps,A,NULL)); |
| 69 |
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50 | PetscCall(EPSSetProblemType(eps,EPS_NHEP)); |
| 70 |
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50 | PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT)); |
| 71 | |||
| 72 | /* | ||
| 73 | Set the custom comparing routine in order to obtain the eigenvalues | ||
| 74 | closest to the target on the right only | ||
| 75 | */ | ||
| 76 |
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50 | PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&target)); |
| 77 | |||
| 78 | /* | ||
| 79 | Set solver parameters at runtime | ||
| 80 | */ | ||
| 81 |
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50 | PetscCall(EPSSetFromOptions(eps)); |
| 82 | |||
| 83 | /* | ||
| 84 | Set the preconditioner based on A - target * I | ||
| 85 | */ | ||
| 86 |
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50 | PetscCall(EPSGetST(eps,&st)); |
| 87 |
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50 | PetscCall(STSetShift(st,target)); |
| 88 | |||
| 89 | /* | ||
| 90 | Set the initial vector. This is optional, if not done the initial | ||
| 91 | vector is set to random values | ||
| 92 | */ | ||
| 93 |
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50 | PetscCall(MatCreateVecs(A,&v0,NULL)); |
| 94 |
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50 | PetscCall(VecSet(v0,1.0)); |
| 95 |
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50 | PetscCall(EPSSetInitialSpace(eps,1,&v0)); |
| 96 | |||
| 97 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 98 | Solve the eigensystem | ||
| 99 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 100 | |||
| 101 |
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50 | PetscCall(EPSSolve(eps)); |
| 102 |
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50 | PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL)); |
| 103 |
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50 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev)); |
| 104 | |||
| 105 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 106 | Display solution and clean up | ||
| 107 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 108 | |||
| 109 |
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50 | PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL)); |
| 110 |
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50 | PetscCall(EPSDestroy(&eps)); |
| 111 |
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50 | PetscCall(MatDestroy(&A)); |
| 112 |
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50 | PetscCall(VecDestroy(&v0)); |
| 113 |
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50 | PetscCall(SlepcFinalize()); |
| 114 | return 0; | ||
| 115 | } | ||
| 116 | |||
| 117 | 50 | PetscErrorCode MatMarkovModel(PetscInt m,Mat A) | |
| 118 | { | ||
| 119 | 50 | const PetscReal cst = 0.5/(PetscReal)(m-1); | |
| 120 | 50 | PetscReal pd,pu; | |
| 121 | 50 | PetscInt Istart,Iend,i,j,jmax,ix=0; | |
| 122 | |||
| 123 |
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50 | PetscFunctionBeginUser; |
| 124 |
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50 | PetscCall(MatGetOwnershipRange(A,&Istart,&Iend)); |
| 125 |
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800 | for (i=1;i<=m;i++) { |
| 126 | 750 | jmax = m-i+1; | |
| 127 |
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6750 | for (j=1;j<=jmax;j++) { |
| 128 | 6000 | ix = ix + 1; | |
| 129 |
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6000 | if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */ |
| 130 |
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6000 | if (j!=jmax) { |
| 131 | 5250 | pd = cst*(PetscReal)(i+j-1); | |
| 132 | /* north */ | ||
| 133 |
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5250 | if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES)); |
| 134 |
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4550 | else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES)); |
| 135 | /* east */ | ||
| 136 |
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5250 | if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES)); |
| 137 |
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4550 | else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES)); |
| 138 | } | ||
| 139 | /* south */ | ||
| 140 | 6000 | pu = 0.5 - cst*(PetscReal)(i+j-3); | |
| 141 |
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6000 | if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES)); |
| 142 | /* west */ | ||
| 143 |
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6000 | if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES)); |
| 144 | } | ||
| 145 | } | ||
| 146 |
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50 | PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); |
| 147 |
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50 | PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); |
| 148 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 149 | } | ||
| 150 | |||
| 151 | /* | ||
| 152 | Function for user-defined eigenvalue ordering criterion. | ||
| 153 | |||
| 154 | Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose | ||
| 155 | one of them as the preferred one according to the criterion. | ||
| 156 | In this example, the preferred value is the one closest to the target, | ||
| 157 | but on the right side. | ||
| 158 | */ | ||
| 159 | 204175 | PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx) | |
| 160 | { | ||
| 161 | 204175 | PetscScalar target = *(PetscScalar*)ctx; | |
| 162 | 204175 | PetscReal da,db; | |
| 163 | 204175 | PetscBool aisright,bisright; | |
| 164 | |||
| 165 |
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204175 | PetscFunctionBeginUser; |
| 166 |
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204175 | if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE; |
| 167 | 121736 | else aisright = PETSC_FALSE; | |
| 168 |
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204175 | if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE; |
| 169 | 176033 | else bisright = PETSC_FALSE; | |
| 170 |
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204175 | if (aisright == bisright) { |
| 171 | /* both are on the same side of the target */ | ||
| 172 | 140998 | da = SlepcAbsEigenvalue(ar-target,ai); | |
| 173 | 140998 | db = SlepcAbsEigenvalue(br-target,bi); | |
| 174 |
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140998 | if (da < db) *r = -1; |
| 175 |
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38629 | else if (da > db) *r = 1; |
| 176 | 23 | else *r = 0; | |
| 177 |
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63177 | } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */ |
| 178 | 4440 | else *r = 1; /* 'b' is on the right */ | |
| 179 |
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204175 | PetscFunctionReturn(PETSC_SUCCESS); |
| 180 | } | ||
| 181 | |||
| 182 | /*TEST | ||
| 183 | |||
| 184 | testset: | ||
| 185 | args: -eps_nev 4 | ||
| 186 | requires: !single | ||
| 187 | output_file: output/test11_1.out | ||
| 188 | test: | ||
| 189 | suffix: 1 | ||
| 190 | args: -eps_type {{krylovschur arnoldi lapack}} -st_type sinvert | ||
| 191 | test: | ||
| 192 | suffix: 1_ks_cayley | ||
| 193 | args: -st_type cayley -st_cayley_antishift 1 | ||
| 194 | |||
| 195 | test: | ||
| 196 | suffix: 2 | ||
| 197 | args: -target 0.77 -eps_type gd -eps_nev 4 -eps_tol 1e-7 -eps_gd_krylov_start -eps_gd_blocksize 3 | ||
| 198 | requires: double | ||
| 199 | filter: sed -e "s/[+-]0\.0*i//g" | ||
| 200 | |||
| 201 | TEST*/ | ||
| 202 |