| 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[] = "A quadratic eigenproblem defined using shell matrices.\n\n" | ||
| 12 | "The command line options are:\n" | ||
| 13 | " -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n"; | ||
| 14 | |||
| 15 | #include <slepcpep.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | User-defined routines | ||
| 19 | */ | ||
| 20 | PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y); | ||
| 21 | PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag); | ||
| 22 | PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y); | ||
| 23 | PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag); | ||
| 24 | PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y); | ||
| 25 | PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag); | ||
| 26 | |||
| 27 | 30 | int main(int argc,char **argv) | |
| 28 | { | ||
| 29 | 30 | Mat M,C,K,A[3]; /* problem matrices */ | |
| 30 | 30 | PEP pep; /* polynomial eigenproblem solver context */ | |
| 31 | 30 | PEPType type; | |
| 32 | 30 | PetscInt N,n=10,nev; | |
| 33 | 30 | PetscMPIInt size; | |
| 34 | 30 | PetscBool terse; | |
| 35 | 30 | ST st; | |
| 36 | |||
| 37 |
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30 | PetscFunctionBeginUser; |
| 38 |
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30 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 39 |
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30 | PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); |
| 40 |
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30 | PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only"); |
| 41 | |||
| 42 |
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30 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
| 43 | 30 | N = n*n; | |
| 44 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n)); |
| 45 | |||
| 46 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 47 | Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0 | ||
| 48 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 49 | |||
| 50 | /* K is the 2-D Laplacian */ | ||
| 51 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K)); |
| 52 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Laplacian2D)); |
| 53 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Laplacian2D)); |
| 54 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Laplacian2D)); |
| 55 | |||
| 56 | /* C is the zero matrix */ | ||
| 57 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&C)); |
| 58 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Zero)); |
| 59 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Zero)); |
| 60 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Zero)); |
| 61 | |||
| 62 | /* M is the identity matrix */ | ||
| 63 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&M)); |
| 64 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Identity)); |
| 65 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Identity)); |
| 66 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Identity)); |
| 67 | |||
| 68 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 69 | Create the eigensolver and set various options | ||
| 70 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 71 | |||
| 72 | /* | ||
| 73 | Create eigensolver context | ||
| 74 | */ | ||
| 75 |
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30 | PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep)); |
| 76 | |||
| 77 | /* | ||
| 78 | Set matrices and problem type | ||
| 79 | */ | ||
| 80 | 30 | A[0] = K; A[1] = C; A[2] = M; | |
| 81 |
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30 | PetscCall(PEPSetOperators(pep,3,A)); |
| 82 |
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30 | PetscCall(PEPGetST(pep,&st)); |
| 83 |
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30 | PetscCall(STSetMatMode(st,ST_MATMODE_SHELL)); |
| 84 | |||
| 85 | /* | ||
| 86 | Set solver parameters at runtime | ||
| 87 | */ | ||
| 88 |
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30 | PetscCall(PEPSetFromOptions(pep)); |
| 89 | |||
| 90 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 91 | Solve the eigensystem | ||
| 92 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 93 | |||
| 94 |
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30 | PetscCall(PEPSolve(pep)); |
| 95 | |||
| 96 | /* | ||
| 97 | Optional: Get some information from the solver and display it | ||
| 98 | */ | ||
| 99 |
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30 | PetscCall(PEPGetType(pep,&type)); |
| 100 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type)); |
| 101 |
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30 | PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL)); |
| 102 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev)); |
| 103 | |||
| 104 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 105 | Display solution and clean up | ||
| 106 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 107 | |||
| 108 | /* show detailed info unless -terse option is given by user */ | ||
| 109 |
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30 | PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse)); |
| 110 |
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30 | if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL)); |
| 111 | else { | ||
| 112 | ✗ | PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL)); | |
| 113 | ✗ | PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD)); | |
| 114 | ✗ | PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD)); | |
| 115 | ✗ | PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD)); | |
| 116 | } | ||
| 117 |
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30 | PetscCall(PEPDestroy(&pep)); |
| 118 |
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30 | PetscCall(MatDestroy(&M)); |
| 119 |
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30 | PetscCall(MatDestroy(&C)); |
| 120 |
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30 | PetscCall(MatDestroy(&K)); |
| 121 |
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30 | PetscCall(SlepcFinalize()); |
| 122 | return 0; | ||
| 123 | } | ||
| 124 | |||
| 125 | /* | ||
| 126 | Compute the matrix vector multiplication y<---T*x where T is a nx by nx | ||
| 127 | tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and | ||
| 128 | DU on the superdiagonal. | ||
| 129 | */ | ||
| 130 | 48630 | static void tv(int nx,const PetscScalar *x,PetscScalar *y) | |
| 131 | { | ||
| 132 | 48630 | PetscScalar dd,dl,du; | |
| 133 | 48630 | int j; | |
| 134 | |||
| 135 | 48630 | dd = 4.0; | |
| 136 | 48630 | dl = -1.0; | |
| 137 | 48630 | du = -1.0; | |
| 138 | |||
| 139 | 48630 | y[0] = dd*x[0] + du*x[1]; | |
| 140 |
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437670 | for (j=1;j<nx-1;j++) |
| 141 | 389040 | y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1]; | |
| 142 | 48630 | y[nx-1] = dl*x[nx-2] + dd*x[nx-1]; | |
| 143 | 48630 | } | |
| 144 | |||
| 145 | /* | ||
| 146 | Matrix-vector product subroutine for the 2D Laplacian. | ||
| 147 | |||
| 148 | The matrix used is the 2 dimensional discrete Laplacian on unit square with | ||
| 149 | zero Dirichlet boundary condition. | ||
| 150 | |||
| 151 | Computes y <-- A*x, where A is the block tridiagonal matrix | ||
| 152 | |||
| 153 | | T -I | | ||
| 154 | |-I T -I | | ||
| 155 | A = | -I T | | ||
| 156 | | ... -I| | ||
| 157 | | -I T| | ||
| 158 | |||
| 159 | The subroutine TV is called to compute y<--T*x. | ||
| 160 | */ | ||
| 161 | 4863 | PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y) | |
| 162 | { | ||
| 163 | 4863 | void *ctx; | |
| 164 | 4863 | int nx,lo,i,j; | |
| 165 | 4863 | const PetscScalar *px; | |
| 166 | 4863 | PetscScalar *py; | |
| 167 | |||
| 168 |
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4863 | PetscFunctionBeginUser; |
| 169 |
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4863 | PetscCall(MatShellGetContext(A,&ctx)); |
| 170 | 4863 | nx = *(int*)ctx; | |
| 171 |
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4863 | PetscCall(VecGetArrayRead(x,&px)); |
| 172 |
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4863 | PetscCall(VecGetArray(y,&py)); |
| 173 | |||
| 174 | 4863 | tv(nx,&px[0],&py[0]); | |
| 175 |
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58356 | for (i=0;i<nx;i++) py[i] -= px[nx+i]; |
| 176 | |||
| 177 |
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43767 | for (j=2;j<nx;j++) { |
| 178 | 38904 | lo = (j-1)*nx; | |
| 179 | 38904 | tv(nx,&px[lo],&py[lo]); | |
| 180 |
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466848 | for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i]; |
| 181 | } | ||
| 182 | |||
| 183 | 4863 | lo = (nx-1)*nx; | |
| 184 | 4863 | tv(nx,&px[lo],&py[lo]); | |
| 185 |
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58356 | for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i]; |
| 186 | |||
| 187 |
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4863 | PetscCall(VecRestoreArrayRead(x,&px)); |
| 188 |
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4863 | PetscCall(VecRestoreArray(y,&py)); |
| 189 |
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973 | PetscFunctionReturn(PETSC_SUCCESS); |
| 190 | } | ||
| 191 | |||
| 192 | 20 | PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag) | |
| 193 | { | ||
| 194 |
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20 | PetscFunctionBeginUser; |
| 195 |
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20 | PetscCall(VecSet(diag,4.0)); |
| 196 |
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4 | PetscFunctionReturn(PETSC_SUCCESS); |
| 197 | } | ||
| 198 | |||
| 199 | /* | ||
| 200 | Matrix-vector product subroutine for the Null matrix. | ||
| 201 | */ | ||
| 202 | 4863 | PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y) | |
| 203 | { | ||
| 204 |
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4863 | PetscFunctionBeginUser; |
| 205 |
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4863 | PetscCall(VecSet(y,0.0)); |
| 206 |
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973 | PetscFunctionReturn(PETSC_SUCCESS); |
| 207 | } | ||
| 208 | |||
| 209 | 20 | PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag) | |
| 210 | { | ||
| 211 |
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20 | PetscFunctionBeginUser; |
| 212 |
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20 | PetscCall(VecSet(diag,0.0)); |
| 213 |
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4 | PetscFunctionReturn(PETSC_SUCCESS); |
| 214 | } | ||
| 215 | |||
| 216 | /* | ||
| 217 | Matrix-vector product subroutine for the Identity matrix. | ||
| 218 | */ | ||
| 219 | 2990 | PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y) | |
| 220 | { | ||
| 221 |
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2990 | PetscFunctionBeginUser; |
| 222 |
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2990 | PetscCall(VecCopy(x,y)); |
| 223 |
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598 | PetscFunctionReturn(PETSC_SUCCESS); |
| 224 | } | ||
| 225 | |||
| 226 | 30 | PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag) | |
| 227 | { | ||
| 228 |
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30 | PetscFunctionBeginUser; |
| 229 |
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30 | PetscCall(VecSet(diag,1.0)); |
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6 | PetscFunctionReturn(PETSC_SUCCESS); |
| 231 | } | ||
| 232 | |||
| 233 | /*TEST | ||
| 234 | |||
| 235 | test: | ||
| 236 | suffix: 1 | ||
| 237 | args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse | ||
| 238 | filter: grep -v Solution | sed -e "s/2.7996[1-8]i/2.79964i/g" | sed -e "s/2.7570[5-9]i/2.75708i/g" | sed -e "s/0.00000-2.79964i, 0.00000+2.79964i/0.00000+2.79964i, 0.00000-2.79964i/" | sed -e "s/0.00000-2.75708i, 0.00000+2.75708i/0.00000+2.75708i, 0.00000-2.75708i/" | ||
| 239 | |||
| 240 | TEST*/ | ||
| 241 |