| 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 with Bethe-Salpeter structure using shell matrices.\n\n" | ||
| 12 | "The command line options are:\n" | ||
| 13 | " -n <n>, where <n> = dimension of the blocks.\n\n"; | ||
| 14 | |||
| 15 | #include <slepceps.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | This example computes eigenvalues of a matrix | ||
| 19 | |||
| 20 | H = [ R C | ||
| 21 | -C^H -R^T ], | ||
| 22 | |||
| 23 | where R is Hermitian and C is complex symmetric. In particular, R and C have the | ||
| 24 | following Toeplitz structure: | ||
| 25 | |||
| 26 | R = pentadiag{a,b,c,conj(b),conj(a)} | ||
| 27 | C = tridiag{b,d,b} | ||
| 28 | |||
| 29 | where a,b,d are complex scalars, and c is real. | ||
| 30 | */ | ||
| 31 | |||
| 32 | /* | ||
| 33 | User-defined routines | ||
| 34 | */ | ||
| 35 | PetscErrorCode MatMult_R(Mat R,Vec x,Vec y); | ||
| 36 | PetscErrorCode MatMultTranspose_R(Mat R,Vec x,Vec y); | ||
| 37 | PetscErrorCode MatMult_C(Mat C,Vec x,Vec y); | ||
| 38 | PetscErrorCode MatMultHermitianTranspose_C(Mat C,Vec x,Vec y); | ||
| 39 | |||
| 40 | /* | ||
| 41 | User context for shell matrices | ||
| 42 | */ | ||
| 43 | typedef struct { | ||
| 44 | PetscScalar a,b,c,d; | ||
| 45 | } CTX_SHELL; | ||
| 46 | |||
| 47 | 20 | int main(int argc,char **argv) | |
| 48 | { | ||
| 49 | 20 | Mat H,R,C; /* problem matrices */ | |
| 50 | 20 | EPS eps; /* eigenproblem solver context */ | |
| 51 | 20 | PetscReal lev; | |
| 52 | 20 | PetscInt n=24,i,nconv; | |
| 53 | 20 | PetscMPIInt size; | |
| 54 | 20 | PetscBool terse,checkorthog; | |
| 55 | 20 | Vec t,*x,*y; | |
| 56 | 20 | CTX_SHELL *ctx; | |
| 57 | |||
| 58 |
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20 | PetscFunctionBeginUser; |
| 59 |
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20 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 60 |
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20 | PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); |
| 61 |
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20 | PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only"); |
| 62 | |||
| 63 |
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20 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
| 64 |
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20 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nShell Bethe-Salpeter eigenproblem, n=%" PetscInt_FMT "\n\n",n)); |
| 65 | |||
| 66 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 67 | Generate the shell problem matrices R and C | ||
| 68 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 69 | |||
| 70 |
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20 | PetscCall(PetscNew(&ctx)); |
| 71 | #if defined(PETSC_USE_COMPLEX) | ||
| 72 |
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10 | ctx->a = PetscCMPLX(-0.1,0.2); |
| 73 | 10 | ctx->b = PetscCMPLX(1.0,0.5); | |
| 74 | 10 | ctx->d = PetscCMPLX(2.0,0.2); | |
| 75 | #else | ||
| 76 | 10 | ctx->a = -0.1; | |
| 77 | 10 | ctx->b = 1.0; | |
| 78 | 10 | ctx->d = 2.0; | |
| 79 | #endif | ||
| 80 | 20 | ctx->c = 4.5; | |
| 81 | |||
| 82 |
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20 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,(void*)ctx,&R)); |
| 83 |
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20 | PetscCall(MatShellSetOperation(R,MATOP_MULT,(void(*)(void))MatMult_R)); |
| 84 |
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20 | PetscCall(MatShellSetOperation(R,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_R)); |
| 85 |
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20 | PetscCall(MatSetOption(R,MAT_HERMITIAN,PETSC_TRUE)); |
| 86 |
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20 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,(void*)ctx,&C)); |
| 87 |
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20 | PetscCall(MatShellSetOperation(C,MATOP_MULT,(void(*)(void))MatMult_C)); |
| 88 |
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20 | PetscCall(MatShellSetOperation(C,MATOP_MULT_HERMITIAN_TRANSPOSE,(void(*)(void))MatMultHermitianTranspose_C)); |
| 89 |
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20 | PetscCall(MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE)); |
| 90 | |||
| 91 |
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20 | PetscCall(MatCreateBSE(R,C,&H)); |
| 92 |
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20 | PetscCall(MatDestroy(&R)); |
| 93 |
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20 | PetscCall(MatDestroy(&C)); |
| 94 | |||
| 95 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 96 | Create the eigensolver and set various options | ||
| 97 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 98 | |||
| 99 |
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20 | PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps)); |
| 100 |
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20 | PetscCall(EPSSetOperators(eps,H,NULL)); |
| 101 |
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20 | PetscCall(EPSSetProblemType(eps,EPS_BSE)); |
| 102 |
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20 | PetscCall(EPSSetWhichEigenpairs(eps,EPS_SMALLEST_MAGNITUDE)); |
| 103 |
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20 | PetscCall(EPSSetFromOptions(eps)); |
| 104 | |||
| 105 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 106 | Solve the eigensystem and display solution | ||
| 107 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 108 | |||
| 109 |
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20 | PetscCall(EPSSolve(eps)); |
| 110 | |||
| 111 | /* show detailed info unless -terse option is given by user */ | ||
| 112 |
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20 | PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse)); |
| 113 |
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20 | if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL)); |
| 114 | else { | ||
| 115 | ✗ | PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL)); | |
| 116 | ✗ | PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD)); | |
| 117 | ✗ | PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD)); | |
| 118 | ✗ | PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD)); | |
| 119 | } | ||
| 120 | |||
| 121 | /* check bi-orthogonality */ | ||
| 122 |
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20 | PetscCall(PetscOptionsHasName(NULL,NULL,"-checkorthog",&checkorthog)); |
| 123 |
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20 | PetscCall(EPSGetConverged(eps,&nconv)); |
| 124 |
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20 | if (checkorthog && nconv>0) { |
| 125 |
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20 | PetscCall(MatCreateVecs(H,&t,NULL)); |
| 126 |
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20 | PetscCall(VecDuplicateVecs(t,nconv,&x)); |
| 127 |
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20 | PetscCall(VecDuplicateVecs(t,nconv,&y)); |
| 128 |
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240 | for (i=0;i<nconv;i++) { |
| 129 |
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220 | PetscCall(EPSGetEigenvector(eps,i,x[i],NULL)); |
| 130 |
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220 | PetscCall(EPSGetLeftEigenvector(eps,i,y[i],NULL)); |
| 131 | } | ||
| 132 |
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20 | PetscCall(VecCheckOrthogonality(x,nconv,y,nconv,NULL,NULL,&lev)); |
| 133 |
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20 | if (lev<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Level of bi-orthogonality of eigenvectors < 100*eps\n\n")); |
| 134 | ✗ | else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Level of bi-orthogonality of eigenvectors: %g\n\n",(double)lev)); | |
| 135 |
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20 | PetscCall(VecDestroy(&t)); |
| 136 |
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20 | PetscCall(VecDestroyVecs(nconv,&x)); |
| 137 |
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20 | PetscCall(VecDestroyVecs(nconv,&y)); |
| 138 | } | ||
| 139 | |||
| 140 |
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20 | PetscCall(EPSDestroy(&eps)); |
| 141 |
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20 | PetscCall(MatDestroy(&H)); |
| 142 |
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20 | PetscCall(PetscFree(ctx)); |
| 143 |
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20 | PetscCall(SlepcFinalize()); |
| 144 | return 0; | ||
| 145 | } | ||
| 146 | |||
| 147 | /* | ||
| 148 | Matrix-vector y = R*x. | ||
| 149 | |||
| 150 | R = pentadiag{a,b,c,conj(b),conj(a)} | ||
| 151 | */ | ||
| 152 | 1780 | PetscErrorCode MatMult_R(Mat R,Vec x,Vec y) | |
| 153 | { | ||
| 154 | 1780 | CTX_SHELL *ctx; | |
| 155 | 1780 | PetscInt n,i; | |
| 156 | 1780 | const PetscScalar *px; | |
| 157 | 1780 | PetscScalar *py; | |
| 158 | |||
| 159 |
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1780 | PetscFunctionBeginUser; |
| 160 |
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1780 | PetscCall(MatShellGetContext(R,&ctx)); |
| 161 |
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1780 | PetscCall(MatGetSize(R,NULL,&n)); |
| 162 |
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1780 | PetscCall(VecGetArrayRead(x,&px)); |
| 163 |
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1780 | PetscCall(VecGetArray(y,&py)); |
| 164 |
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44500 | for (i=0;i<n;i++) { |
| 165 | 42720 | py[i] = ctx->c*px[i]; | |
| 166 |
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42720 | if (i>1) py[i] += ctx->a*px[i-2]; |
| 167 |
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42720 | if (i>0) py[i] += ctx->b*px[i-1]; |
| 168 |
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42720 | if (i<n-1) py[i] += PetscConj(ctx->b)*px[i+1]; |
| 169 |
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42720 | if (i<n-2) py[i] += PetscConj(ctx->a)*px[i+2]; |
| 170 | } | ||
| 171 |
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1780 | PetscCall(VecRestoreArrayRead(x,&px)); |
| 172 |
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1780 | PetscCall(VecRestoreArray(y,&py)); |
| 173 |
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356 | PetscFunctionReturn(PETSC_SUCCESS); |
| 174 | } | ||
| 175 | |||
| 176 | /* | ||
| 177 | Matrix-vector y = R^T*x. | ||
| 178 | |||
| 179 | Only needed to compute the residuals. | ||
| 180 | */ | ||
| 181 | 80 | PetscErrorCode MatMultTranspose_R(Mat R,Vec x,Vec y) | |
| 182 | { | ||
| 183 | 80 | Vec w; | |
| 184 | |||
| 185 |
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80 | PetscFunctionBeginUser; |
| 186 |
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80 | PetscCall(VecDuplicate(x,&w)); |
| 187 |
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80 | PetscCall(VecCopy(x,w)); |
| 188 |
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80 | PetscCall(VecConjugate(w)); |
| 189 |
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80 | PetscCall(MatMult_R(R,w,y)); |
| 190 |
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80 | PetscCall(VecConjugate(y)); |
| 191 |
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80 | PetscCall(VecDestroy(&w)); |
| 192 |
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16 | PetscFunctionReturn(PETSC_SUCCESS); |
| 193 | } | ||
| 194 | |||
| 195 | /* | ||
| 196 | Matrix-vector y = C*x. | ||
| 197 | |||
| 198 | C = tridiag{b,d,b} | ||
| 199 | */ | ||
| 200 | 1780 | PetscErrorCode MatMult_C(Mat C,Vec x,Vec y) | |
| 201 | { | ||
| 202 | 1780 | CTX_SHELL *ctx; | |
| 203 | 1780 | PetscInt n,i; | |
| 204 | 1780 | const PetscScalar *px; | |
| 205 | 1780 | PetscScalar *py; | |
| 206 | |||
| 207 |
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1780 | PetscFunctionBeginUser; |
| 208 |
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1780 | PetscCall(MatShellGetContext(C,&ctx)); |
| 209 |
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1780 | PetscCall(MatGetSize(C,NULL,&n)); |
| 210 |
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1780 | PetscCall(VecGetArrayRead(x,&px)); |
| 211 |
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1780 | PetscCall(VecGetArray(y,&py)); |
| 212 |
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44500 | for (i=0;i<n;i++) { |
| 213 | 42720 | py[i] = ctx->d*px[i]; | |
| 214 |
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42720 | if (i>0) py[i] += ctx->b*px[i-1]; |
| 215 |
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42720 | if (i<n-1) py[i] += ctx->b*px[i+1]; |
| 216 | } | ||
| 217 |
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1780 | PetscCall(VecRestoreArrayRead(x,&px)); |
| 218 |
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1780 | PetscCall(VecRestoreArray(y,&py)); |
| 219 |
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356 | PetscFunctionReturn(PETSC_SUCCESS); |
| 220 | } | ||
| 221 | |||
| 222 | /* | ||
| 223 | Matrix-vector y = C^H*x. | ||
| 224 | |||
| 225 | Only needed to compute the residuals. | ||
| 226 | */ | ||
| 227 | 40 | PetscErrorCode MatMultHermitianTranspose_C(Mat C,Vec x,Vec y) | |
| 228 | { | ||
| 229 | 40 | Vec w; | |
| 230 | |||
| 231 |
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40 | PetscFunctionBeginUser; |
| 232 |
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40 | PetscCall(VecDuplicate(x,&w)); |
| 233 |
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40 | PetscCall(VecCopy(x,w)); |
| 234 |
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40 | PetscCall(VecConjugate(w)); |
| 235 |
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40 | PetscCall(MatMult_C(C,w,y)); |
| 236 |
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40 | PetscCall(VecConjugate(y)); |
| 237 |
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40 | PetscCall(VecDestroy(&w)); |
| 238 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 239 | } | ||
| 240 | |||
| 241 | /*TEST | ||
| 242 | |||
| 243 | testset: | ||
| 244 | args: -eps_nev 4 -eps_ncv 16 -eps_krylovschur_bse_type {{shao gruning}} -terse -checkorthog | ||
| 245 | filter: sed -e "s/17496/17495/g" | sed -e "s/32172/32173/g" | sed -e "s/38566/38567/g" | ||
| 246 | test: | ||
| 247 | suffix: 1 | ||
| 248 | requires: complex | ||
| 249 | test: | ||
| 250 | suffix: 1_real | ||
| 251 | requires: !complex | ||
| 252 | |||
| 253 | TEST*/ | ||
| 254 |