| 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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid.\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 the initial vector.\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 | PetscErrorCode MatMarkovModel(PetscInt m,Mat A); | ||
| 23 | PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx); | ||
| 24 | |||
| 25 | /* | ||
| 26 | Check if computed eigenvectors have unit norm | ||
| 27 | */ | ||
| 28 | 279 | PetscErrorCode CheckNormalizedVectors(EPS eps) | |
| 29 | { | ||
| 30 | 279 | PetscInt i,nconv; | |
| 31 | 279 | Mat A; | |
| 32 | 279 | Vec xr,xi; | |
| 33 | 279 | PetscReal error=0.0,normr; | |
| 34 | #if !PetscDefined(USE_COMPLEX) | ||
| 35 | 140 | PetscReal normi; | |
| 36 | #endif | ||
| 37 | |||
| 38 |
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279 | PetscFunctionBeginUser; |
| 39 |
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279 | PetscCall(EPSGetConverged(eps,&nconv)); |
| 40 |
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279 | if (nconv>0) { |
| 41 |
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279 | PetscCall(EPSGetOperators(eps,&A,NULL)); |
| 42 |
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279 | PetscCall(MatCreateVecs(A,&xr,&xi)); |
| 43 |
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2656 | for (i=0;i<nconv;i++) { |
| 44 |
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2377 | PetscCall(EPSGetEigenvector(eps,i,xr,xi)); |
| 45 | #if PetscDefined(USE_COMPLEX) | ||
| 46 |
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1187 | PetscCall(VecNorm(xr,NORM_2,&normr)); |
| 47 |
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1366 | error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0))); |
| 48 | #else | ||
| 49 |
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1190 | PetscCall(VecNormBegin(xr,NORM_2,&normr)); |
| 50 |
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1190 | PetscCall(VecNormBegin(xi,NORM_2,&normi)); |
| 51 |
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1190 | PetscCall(VecNormEnd(xr,NORM_2,&normr)); |
| 52 |
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1190 | PetscCall(VecNormEnd(xi,NORM_2,&normi)); |
| 53 |
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1190 | error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0))); |
| 54 | #endif | ||
| 55 | } | ||
| 56 |
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279 | PetscCall(VecDestroy(&xr)); |
| 57 |
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279 | PetscCall(VecDestroy(&xi)); |
| 58 |
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279 | if (error>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error)); |
| 59 | } | ||
| 60 |
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60 | PetscFunctionReturn(PETSC_SUCCESS); |
| 61 | } | ||
| 62 | |||
| 63 | 319 | int main(int argc,char **argv) | |
| 64 | { | ||
| 65 | 319 | Vec v0; /* initial vector */ | |
| 66 | 319 | Mat A; /* operator matrix */ | |
| 67 | 319 | EPS eps; /* eigenproblem solver context */ | |
| 68 | 319 | PetscReal tol=0.5*PETSC_SMALL; | |
| 69 | 319 | PetscInt N,m=15,nev; | |
| 70 | 319 | PetscScalar origin=0.0; | |
| 71 | 319 | PetscBool flg,delay,skipnorm=PETSC_FALSE; | |
| 72 | |||
| 73 |
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319 | PetscFunctionBeginUser; |
| 74 |
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319 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 75 | |||
| 76 |
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319 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL)); |
| 77 | 319 | N = m*(m+1)/2; | |
| 78 |
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319 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m)); |
| 79 |
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319 | PetscCall(PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL)); |
| 80 | |||
| 81 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 82 | Compute the operator matrix that defines the eigensystem, Ax=kx | ||
| 83 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 84 | |||
| 85 |
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319 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); |
| 86 |
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319 | PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N)); |
| 87 |
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319 | PetscCall(MatSetFromOptions(A)); |
| 88 |
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319 | PetscCall(MatMarkovModel(m,A)); |
| 89 | |||
| 90 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 91 | Create the eigensolver and set various options | ||
| 92 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 93 | |||
| 94 | /* | ||
| 95 | Create eigensolver context | ||
| 96 | */ | ||
| 97 |
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319 | PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps)); |
| 98 | |||
| 99 | /* | ||
| 100 | Set operators. In this case, it is a standard eigenvalue problem | ||
| 101 | */ | ||
| 102 |
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319 | PetscCall(EPSSetOperators(eps,A,NULL)); |
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319 | PetscCall(EPSSetProblemType(eps,EPS_NHEP)); |
| 104 |
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319 | PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT)); |
| 105 | |||
| 106 | /* | ||
| 107 | Set the custom comparing routine in order to obtain the eigenvalues | ||
| 108 | closest to the target on the right only | ||
| 109 | */ | ||
| 110 |
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319 | PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&origin)); |
| 111 | |||
| 112 | /* | ||
| 113 | Set solver parameters at runtime | ||
| 114 | */ | ||
| 115 |
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319 | PetscCall(EPSSetFromOptions(eps)); |
| 116 |
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319 | PetscCall(PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg)); |
| 117 |
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319 | if (flg) { |
| 118 |
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50 | PetscCall(EPSArnoldiGetDelayed(eps,&delay)); |
| 119 |
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50 | if (delay) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n")); |
| 120 | } | ||
| 121 | |||
| 122 | /* | ||
| 123 | Set the initial vector. This is optional, if not done the initial | ||
| 124 | vector is set to random values | ||
| 125 | */ | ||
| 126 |
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319 | PetscCall(MatCreateVecs(A,&v0,NULL)); |
| 127 |
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319 | PetscCall(VecSetValue(v0,0,-1.5,INSERT_VALUES)); |
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319 | PetscCall(VecSetValue(v0,1,2.1,INSERT_VALUES)); |
| 129 |
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319 | PetscCall(VecAssemblyBegin(v0)); |
| 130 |
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319 | PetscCall(VecAssemblyEnd(v0)); |
| 131 |
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319 | PetscCall(EPSSetInitialSpace(eps,1,&v0)); |
| 132 | |||
| 133 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 134 | Solve the eigensystem | ||
| 135 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 136 | |||
| 137 |
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319 | PetscCall(EPSSolve(eps)); |
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319 | PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL)); |
| 139 |
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319 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev)); |
| 140 | |||
| 141 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 142 | Display solution and clean up | ||
| 143 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 144 | |||
| 145 |
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319 | PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL)); |
| 146 |
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319 | if (!skipnorm) PetscCall(CheckNormalizedVectors(eps)); |
| 147 |
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319 | PetscCall(EPSDestroy(&eps)); |
| 148 |
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319 | PetscCall(MatDestroy(&A)); |
| 149 |
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319 | PetscCall(VecDestroy(&v0)); |
| 150 |
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319 | PetscCall(SlepcFinalize()); |
| 151 | return 0; | ||
| 152 | } | ||
| 153 | |||
| 154 | 319 | PetscErrorCode MatMarkovModel(PetscInt m,Mat A) | |
| 155 | { | ||
| 156 | 319 | const PetscReal cst = 0.5/(PetscReal)(m-1); | |
| 157 | 319 | PetscReal pd,pu; | |
| 158 | 319 | PetscInt Istart,Iend,i,j,jmax,ix=0; | |
| 159 | |||
| 160 |
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319 | PetscFunctionBeginUser; |
| 161 |
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319 | PetscCall(MatGetOwnershipRange(A,&Istart,&Iend)); |
| 162 |
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5104 | for (i=1;i<=m;i++) { |
| 163 | 4785 | jmax = m-i+1; | |
| 164 |
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43065 | for (j=1;j<=jmax;j++) { |
| 165 | 38280 | ix = ix + 1; | |
| 166 |
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38280 | if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */ |
| 167 |
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35880 | if (j!=jmax) { |
| 168 | 31395 | pd = cst*(PetscReal)(i+j-1); | |
| 169 | /* north */ | ||
| 170 |
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31395 | if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES)); |
| 171 |
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27209 | else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES)); |
| 172 | /* east */ | ||
| 173 |
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31395 | if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES)); |
| 174 |
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27209 | else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES)); |
| 175 | } | ||
| 176 | /* south */ | ||
| 177 | 35880 | pu = 0.5 - cst*(PetscReal)(i+j-3); | |
| 178 |
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35880 | if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES)); |
| 179 | /* west */ | ||
| 180 |
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38280 | if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES)); |
| 181 | } | ||
| 182 | } | ||
| 183 |
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319 | PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); |
| 184 |
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319 | PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); |
| 185 |
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68 | PetscFunctionReturn(PETSC_SUCCESS); |
| 186 | } | ||
| 187 | |||
| 188 | /* | ||
| 189 | Function for user-defined eigenvalue ordering criterion. | ||
| 190 | |||
| 191 | Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose | ||
| 192 | one of them as the preferred one according to the criterion. | ||
| 193 | In this example, the preferred value is the one furthest away from the origin. | ||
| 194 | */ | ||
| 195 | 772882 | PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx) | |
| 196 | { | ||
| 197 | 772882 | PetscScalar origin = *(PetscScalar*)ctx; | |
| 198 | 772882 | PetscReal d; | |
| 199 | |||
| 200 |
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772882 | PetscFunctionBeginUser; |
| 201 |
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772882 | d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi)); |
| 202 |
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772882 | *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br))); |
| 203 |
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772882 | PetscFunctionReturn(PETSC_SUCCESS); |
| 204 | } | ||
| 205 | |||
| 206 | /*TEST | ||
| 207 | |||
| 208 | testset: | ||
| 209 | args: -eps_nev 4 | ||
| 210 | output_file: output/test9_1.out | ||
| 211 | filter: sed -e "s/97136/97137/g" | ||
| 212 | test: | ||
| 213 | suffix: 1 | ||
| 214 | args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 8 -eps_max_it 300 | ||
| 215 | test: | ||
| 216 | suffix: 1_gd | ||
| 217 | args: -eps_type gd -st_pc_type none | ||
| 218 | test: | ||
| 219 | suffix: 1_gd2 | ||
| 220 | args: -eps_type gd -eps_gd_double_expansion -st_pc_type none | ||
| 221 | |||
| 222 | test: | ||
| 223 | suffix: 2 | ||
| 224 | args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_max_it 1500 | ||
| 225 | requires: double | ||
| 226 | output_file: output/test9_1.out | ||
| 227 | |||
| 228 | test: | ||
| 229 | suffix: 3 | ||
| 230 | nsize: 2 | ||
| 231 | args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm | ||
| 232 | requires: !single | ||
| 233 | output_file: output/test9_3.out | ||
| 234 | |||
| 235 | test: | ||
| 236 | suffix: 4 | ||
| 237 | args: -eps_nev 4 -eps_true_residual | ||
| 238 | requires: !single | ||
| 239 | output_file: output/test9_1.out | ||
| 240 | |||
| 241 | test: | ||
| 242 | suffix: 5 | ||
| 243 | args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2 | ||
| 244 | filter: sed -e "s/[+-]0\.0*i//g" | ||
| 245 | requires: !single | ||
| 246 | |||
| 247 | test: | ||
| 248 | suffix: 5_arpack | ||
| 249 | args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10 | ||
| 250 | requires: arpack !single | ||
| 251 | output_file: output/test9_5.out | ||
| 252 | |||
| 253 | testset: | ||
| 254 | args: -eps_type ciss -eps_tol 1e-9 -rg_type ellipse -rg_ellipse_center 0.55 -rg_ellipse_radius 0.05 -rg_ellipse_vscale 0.1 -eps_ciss_strategy {{split multishift}} -eps_all | ||
| 255 | requires: !single | ||
| 256 | filter: sed -e "s/[+-]0\.0*i//g" | ||
| 257 | output_file: output/test9_6.out | ||
| 258 | test: | ||
| 259 | suffix: 6 | ||
| 260 | test: | ||
| 261 | suffix: 6_hankel | ||
| 262 | args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 12 | ||
| 263 | test: | ||
| 264 | suffix: 6_cheby | ||
| 265 | args: -eps_ciss_quadrule chebyshev | ||
| 266 | test: | ||
| 267 | suffix: 6_hankel_cheby | ||
| 268 | args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 12 | ||
| 269 | test: | ||
| 270 | suffix: 6_refine | ||
| 271 | args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2 | ||
| 272 | |||
| 273 | test: | ||
| 274 | suffix: 6_bcgs | ||
| 275 | args: -eps_type ciss -eps_tol 1e-9 -rg_type ellipse -rg_ellipse_center 0.55 -rg_ellipse_radius 0.05 -rg_ellipse_vscale 0.1 -eps_ciss_strategy split -eps_all -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type ilu -eps_ciss_integration_points 8 | ||
| 276 | requires: !single | ||
| 277 | output_file: output/test9_6.out | ||
| 278 | |||
| 279 | test: | ||
| 280 | suffix: 6_cheby_interval | ||
| 281 | args: -eps_type ciss -eps_tol 1e-9 -rg_type interval -rg_interval_endpoints 0.5,0.6 -eps_ciss_quadrule chebyshev -eps_ciss_strategy split -eps_all | ||
| 282 | requires: !single | ||
| 283 | output_file: output/test9_6.out | ||
| 284 | |||
| 285 | testset: | ||
| 286 | args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values | ||
| 287 | filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/" -e "s/_[0-9a-fA-F]\{8,\}_/_objectid_/" | ||
| 288 | test: | ||
| 289 | suffix: 7_real | ||
| 290 | requires: !single !complex | ||
| 291 | test: | ||
| 292 | suffix: 7 | ||
| 293 | requires: !single complex | ||
| 294 | |||
| 295 | test: | ||
| 296 | suffix: 8 | ||
| 297 | args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg | ||
| 298 | requires: x | ||
| 299 | output_file: output/test9_1.out | ||
| 300 | |||
| 301 | test: | ||
| 302 | suffix: 5_ksphpddm | ||
| 303 | args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10 | ||
| 304 | requires: hpddm | ||
| 305 | output_file: output/test9_5.out | ||
| 306 | |||
| 307 | test: | ||
| 308 | suffix: 5_pchpddm | ||
| 309 | args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10 | ||
| 310 | requires: hpddm | ||
| 311 | output_file: output/test9_5.out | ||
| 312 | |||
| 313 | TEST*/ | ||
| 314 |