| 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 | LME routines related to the solution process | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/lmeimpl.h> /*I "slepclme.h" I*/ | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | /*@ | ||
| 18 | LMESolve - Solves the linear matrix equation. | ||
| 19 | |||
| 20 | Collective | ||
| 21 | |||
| 22 | Input Parameter: | ||
| 23 | . lme - the linear matrix equation solver context | ||
| 24 | |||
| 25 | Options Database Keys: | ||
| 26 | + -lme_view - print information about the solver once the solve is complete | ||
| 27 | . -lme_view_pre - print information about the solver before the solve starts | ||
| 28 | . -lme_view_mat_a - view the A matrix | ||
| 29 | . -lme_view_mat_b - view the B matrix | ||
| 30 | . -lme_view_mat_d - view the D matrix | ||
| 31 | . -lme_view_mat_e - view the E matrix | ||
| 32 | . -lme_view_rhs - view the right hand side of the equation | ||
| 33 | . -lme_view_solution - view the computed solution | ||
| 34 | - -lme_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 35 | |||
| 36 | Notes: | ||
| 37 | The matrix coefficients are specified with `LMESetCoefficients()`. The right-hand | ||
| 38 | side is specified with `LMESetRHS()`. The placeholder for the solution is specified | ||
| 39 | with `LMESetSolution()`. | ||
| 40 | |||
| 41 | All the command-line options listed above admit an optional argument specifying | ||
| 42 | the viewer type and options. For instance, use `-lme_view_mat_a binary:amatrix.bin` | ||
| 43 | to save the $A$ matrix to a binary file. | ||
| 44 | See `PetscObjectViewFromOptions()` for more details. | ||
| 45 | |||
| 46 | Level: beginner | ||
| 47 | |||
| 48 | .seealso: [](ch:lme), `LMECreate()`, `LMESetUp()`, `LMEDestroy()`, `LMESetTolerances()`, `LMESetCoefficients()`, `LMESetRHS()`, `LMESetSolution()` | ||
| 49 | @*/ | ||
| 50 | 499 | PetscErrorCode LMESolve(LME lme) | |
| 51 | { | ||
| 52 |
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499 | PetscFunctionBegin; |
| 53 |
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499 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 54 | |||
| 55 | /* call setup */ | ||
| 56 |
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499 | PetscCall(LMESetUp(lme)); |
| 57 | 499 | lme->its = 0; | |
| 58 | 499 | lme->errest = 0.0; | |
| 59 | |||
| 60 |
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499 | PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view_pre")); |
| 61 | |||
| 62 | /* call solver */ | ||
| 63 |
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499 | PetscCheck(lme->ops->solve[lme->problem_type],PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"The specified solver does not support equation type %s",LMEProblemTypes[lme->problem_type]); |
| 64 |
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499 | PetscCall(PetscLogEventBegin(LME_Solve,lme,0,0,0)); |
| 65 |
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499 | PetscUseTypeMethod(lme,solve[lme->problem_type]); |
| 66 |
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499 | PetscCall(PetscLogEventEnd(LME_Solve,lme,0,0,0)); |
| 67 | |||
| 68 |
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499 | PetscCheck(lme->reason,PetscObjectComm((PetscObject)lme),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 69 | |||
| 70 |
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499 | PetscCheck(!lme->errorifnotconverged || lme->reason>=0,PetscObjectComm((PetscObject)lme),PETSC_ERR_NOT_CONVERGED,"LMESolve has not converged"); |
| 71 | |||
| 72 | /* various viewers */ | ||
| 73 |
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499 | PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view")); |
| 74 |
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499 | PetscCall(LMEConvergedReasonViewFromOptions(lme)); |
| 75 |
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499 | PetscCall(MatViewFromOptions(lme->A,(PetscObject)lme,"-lme_view_mat_a")); |
| 76 |
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499 | if (lme->B) PetscCall(MatViewFromOptions(lme->B,(PetscObject)lme,"-lme_view_mat_b")); |
| 77 |
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499 | if (lme->D) PetscCall(MatViewFromOptions(lme->D,(PetscObject)lme,"-lme_view_mat_d")); |
| 78 |
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499 | if (lme->E) PetscCall(MatViewFromOptions(lme->E,(PetscObject)lme,"-lme_view_mat_e")); |
| 79 |
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499 | PetscCall(MatViewFromOptions(lme->C,(PetscObject)lme,"-lme_view_rhs")); |
| 80 |
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499 | PetscCall(MatViewFromOptions(lme->X,(PetscObject)lme,"-lme_view_solution")); |
| 81 |
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72 | PetscFunctionReturn(PETSC_SUCCESS); |
| 82 | } | ||
| 83 | |||
| 84 | /*@ | ||
| 85 | LMEGetIterationNumber - Gets the current iteration number. If the | ||
| 86 | call to `LMESolve()` is complete, then it returns the number of iterations | ||
| 87 | carried out by the solution method. | ||
| 88 | |||
| 89 | Not Collective | ||
| 90 | |||
| 91 | Input Parameter: | ||
| 92 | . lme - the linear matrix equation solver context | ||
| 93 | |||
| 94 | Output Parameter: | ||
| 95 | . its - number of iterations | ||
| 96 | |||
| 97 | Note: | ||
| 98 | During the $i$-th iteration this call returns $i-1$. If `LMESolve()` is | ||
| 99 | complete, then parameter `its` contains either the iteration number at | ||
| 100 | which convergence was successfully reached, or failure was detected. | ||
| 101 | Call `LMEGetConvergedReason()` to determine if the solver converged or | ||
| 102 | failed and why. | ||
| 103 | |||
| 104 | Level: intermediate | ||
| 105 | |||
| 106 | .seealso: [](ch:lme), `LMEGetConvergedReason()`, `LMESetTolerances()` | ||
| 107 | @*/ | ||
| 108 | 22 | PetscErrorCode LMEGetIterationNumber(LME lme,PetscInt *its) | |
| 109 | { | ||
| 110 |
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22 | PetscFunctionBegin; |
| 111 |
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22 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 112 |
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22 | PetscAssertPointer(its,2); |
| 113 | 22 | *its = lme->its; | |
| 114 |
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22 | PetscFunctionReturn(PETSC_SUCCESS); |
| 115 | } | ||
| 116 | |||
| 117 | /*@ | ||
| 118 | LMEGetConvergedReason - Gets the reason why the `LMESolve()` iteration was | ||
| 119 | stopped. | ||
| 120 | |||
| 121 | Not Collective | ||
| 122 | |||
| 123 | Input Parameter: | ||
| 124 | . lme - the linear matrix equation solver context | ||
| 125 | |||
| 126 | Output Parameter: | ||
| 127 | . reason - negative value indicates diverged, positive value converged, see | ||
| 128 | `LMEConvergedReason` for the possible values | ||
| 129 | |||
| 130 | Options Database Key: | ||
| 131 | . -lme_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 132 | |||
| 133 | Note: | ||
| 134 | If this routine is called before or doing the `LMESolve()` the value of | ||
| 135 | `LME_CONVERGED_ITERATING` is returned. | ||
| 136 | |||
| 137 | Level: intermediate | ||
| 138 | |||
| 139 | .seealso: [](ch:lme), `LMESetTolerances()`, `LMESolve()`, `LMEConvergedReason`, `LMESetErrorIfNotConverged()` | ||
| 140 | @*/ | ||
| 141 | 20 | PetscErrorCode LMEGetConvergedReason(LME lme,LMEConvergedReason *reason) | |
| 142 | { | ||
| 143 |
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20 | PetscFunctionBegin; |
| 144 |
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20 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 145 |
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20 | PetscAssertPointer(reason,2); |
| 146 | 20 | *reason = lme->reason; | |
| 147 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); |
| 148 | } | ||
| 149 | |||
| 150 | /*@ | ||
| 151 | LMEGetErrorEstimate - Returns the error estimate obtained during the solve. | ||
| 152 | |||
| 153 | Not Collective | ||
| 154 | |||
| 155 | Input Parameter: | ||
| 156 | . lme - the linear matrix equation solver context | ||
| 157 | |||
| 158 | Output Parameter: | ||
| 159 | . errest - the error estimate | ||
| 160 | |||
| 161 | Note: | ||
| 162 | This is the error estimated internally by the solver. The actual | ||
| 163 | error bound can be computed with `LMEComputeError()`. Note that some | ||
| 164 | solvers may not be able to provide an error estimate. | ||
| 165 | |||
| 166 | Level: advanced | ||
| 167 | |||
| 168 | .seealso: [](ch:lme), `LMEComputeError()` | ||
| 169 | @*/ | ||
| 170 | 52 | PetscErrorCode LMEGetErrorEstimate(LME lme,PetscReal *errest) | |
| 171 | { | ||
| 172 |
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52 | PetscFunctionBegin; |
| 173 |
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52 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 174 |
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52 | PetscAssertPointer(errest,2); |
| 175 | 52 | *errest = lme->errest; | |
| 176 |
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52 | PetscFunctionReturn(PETSC_SUCCESS); |
| 177 | } | ||
| 178 | |||
| 179 | /* | ||
| 180 | LMEComputeResidualNorm_Lyapunov - Computes the Frobenius norm of the residual matrix | ||
| 181 | associated with the Lyapunov equation. | ||
| 182 | */ | ||
| 183 | 52 | static PetscErrorCode LMEComputeResidualNorm_Lyapunov(LME lme,PetscReal *norm) | |
| 184 | { | ||
| 185 | 52 | PetscInt j,n,N,k,l,lda,ldb; | |
| 186 | 52 | PetscBLASInt n_,N_,k_,l_,lda_,ldb_; | |
| 187 | 52 | PetscScalar *Rarray,alpha=1.0,beta=0.0; | |
| 188 | 52 | const PetscScalar *A,*B; | |
| 189 | 52 | BV W,AX,X1,C1; | |
| 190 | 52 | Mat R,X1m,C1m; | |
| 191 | 52 | Vec v,w; | |
| 192 | 52 | VecScatter vscat; | |
| 193 | |||
| 194 |
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52 | PetscFunctionBegin; |
| 195 |
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52 | PetscCall(MatLRCGetMats(lme->C,NULL,&C1m,NULL,NULL)); |
| 196 |
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52 | PetscCall(MatLRCGetMats(lme->X,NULL,&X1m,NULL,NULL)); |
| 197 |
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52 | PetscCall(BVCreateFromMat(C1m,&C1)); |
| 198 |
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52 | PetscCall(BVSetFromOptions(C1)); |
| 199 |
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52 | PetscCall(BVCreateFromMat(X1m,&X1)); |
| 200 |
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52 | PetscCall(BVSetFromOptions(X1)); |
| 201 |
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52 | PetscCall(BVGetSizes(X1,&n,&N,&k)); |
| 202 |
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52 | PetscCall(BVGetSizes(C1,NULL,NULL,&l)); |
| 203 |
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52 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 204 |
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52 | PetscCall(PetscBLASIntCast(N,&N_)); |
| 205 |
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52 | PetscCall(PetscBLASIntCast(k,&k_)); |
| 206 |
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52 | PetscCall(PetscBLASIntCast(l,&l_)); |
| 207 | |||
| 208 | /* create W to store a redundant copy of a BV in each process */ | ||
| 209 |
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52 | PetscCall(BVCreate(PETSC_COMM_SELF,&W)); |
| 210 |
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52 | PetscCall(BVSetSizes(W,N,N,k)); |
| 211 |
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52 | PetscCall(BVSetFromOptions(W)); |
| 212 |
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52 | PetscCall(BVGetColumn(X1,0,&v)); |
| 213 |
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52 | PetscCall(VecScatterCreateToAll(v,&vscat,NULL)); |
| 214 |
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52 | PetscCall(BVRestoreColumn(X1,0,&v)); |
| 215 | |||
| 216 | /* create AX to hold the product A*X1 */ | ||
| 217 |
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52 | PetscCall(BVDuplicate(X1,&AX)); |
| 218 |
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52 | PetscCall(BVMatMult(X1,lme->A,AX)); |
| 219 | |||
| 220 | /* create dense matrix to hold the residual R=C1*C1'+AX*X1'+X1*AX' */ | ||
| 221 |
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52 | PetscCall(MatCreateDense(PetscObjectComm((PetscObject)lme),n,n,N,N,NULL,&R)); |
| 222 | |||
| 223 | /* R=C1*C1' */ | ||
| 224 |
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52 | PetscCall(MatDenseGetArrayWrite(R,&Rarray)); |
| 225 |
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156 | for (j=0;j<l;j++) { |
| 226 |
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104 | PetscCall(BVGetColumn(C1,j,&v)); |
| 227 |
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104 | PetscCall(BVGetColumn(W,j,&w)); |
| 228 |
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104 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 229 |
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104 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 230 |
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104 | PetscCall(BVRestoreColumn(C1,j,&v)); |
| 231 |
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104 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 232 | } | ||
| 233 |
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52 | if (n) { |
| 234 |
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52 | PetscCall(BVGetArrayRead(C1,&A)); |
| 235 |
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52 | PetscCall(BVGetLeadingDimension(C1,&lda)); |
| 236 |
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52 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 237 |
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52 | PetscCall(BVGetArrayRead(W,&B)); |
| 238 |
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52 | PetscCall(BVGetLeadingDimension(W,&ldb)); |
| 239 |
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52 | PetscCall(PetscBLASIntCast(ldb,&ldb_)); |
| 240 |
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52 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&l_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 241 |
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52 | PetscCall(BVRestoreArrayRead(C1,&A)); |
| 242 |
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52 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 243 | } | ||
| 244 | 52 | beta = 1.0; | |
| 245 | |||
| 246 | /* R+=AX*X1' */ | ||
| 247 |
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3687 | for (j=0;j<k;j++) { |
| 248 |
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3635 | PetscCall(BVGetColumn(X1,j,&v)); |
| 249 |
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3635 | PetscCall(BVGetColumn(W,j,&w)); |
| 250 |
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3635 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 251 |
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3635 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 252 |
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3635 | PetscCall(BVRestoreColumn(X1,j,&v)); |
| 253 |
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3635 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 254 | } | ||
| 255 |
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52 | if (n) { |
| 256 |
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52 | PetscCall(BVGetArrayRead(AX,&A)); |
| 257 |
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52 | PetscCall(BVGetLeadingDimension(AX,&lda)); |
| 258 |
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52 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 259 |
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52 | PetscCall(BVGetArrayRead(W,&B)); |
| 260 |
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52 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 261 |
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52 | PetscCall(BVRestoreArrayRead(AX,&A)); |
| 262 |
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52 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 263 | } | ||
| 264 | |||
| 265 | /* R+=X1*AX' */ | ||
| 266 |
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3687 | for (j=0;j<k;j++) { |
| 267 |
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3635 | PetscCall(BVGetColumn(AX,j,&v)); |
| 268 |
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3635 | PetscCall(BVGetColumn(W,j,&w)); |
| 269 |
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3635 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 270 |
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3635 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 271 |
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3635 | PetscCall(BVRestoreColumn(AX,j,&v)); |
| 272 |
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3635 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 273 | } | ||
| 274 |
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52 | if (n) { |
| 275 |
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52 | PetscCall(BVGetArrayRead(X1,&A)); |
| 276 |
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52 | PetscCall(BVGetLeadingDimension(AX,&lda)); |
| 277 |
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52 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 278 |
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52 | PetscCall(BVGetArrayRead(W,&B)); |
| 279 |
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52 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 280 |
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52 | PetscCall(BVRestoreArrayRead(X1,&A)); |
| 281 |
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52 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 282 | } | ||
| 283 |
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52 | PetscCall(MatDenseRestoreArrayWrite(R,&Rarray)); |
| 284 | |||
| 285 | /* compute ||R||_F */ | ||
| 286 |
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52 | PetscCall(MatNorm(R,NORM_FROBENIUS,norm)); |
| 287 | |||
| 288 |
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52 | PetscCall(BVDestroy(&W)); |
| 289 |
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52 | PetscCall(VecScatterDestroy(&vscat)); |
| 290 |
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52 | PetscCall(BVDestroy(&AX)); |
| 291 |
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52 | PetscCall(MatDestroy(&R)); |
| 292 |
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52 | PetscCall(BVDestroy(&C1)); |
| 293 |
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52 | PetscCall(BVDestroy(&X1)); |
| 294 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 295 | } | ||
| 296 | |||
| 297 | /*@ | ||
| 298 | LMEComputeError - Computes the error (based on the residual norm) associated | ||
| 299 | with the last equation solved. | ||
| 300 | |||
| 301 | Collective | ||
| 302 | |||
| 303 | Input Parameter: | ||
| 304 | . lme - the linear matrix equation solver context | ||
| 305 | |||
| 306 | Output Parameter: | ||
| 307 | . error - the error | ||
| 308 | |||
| 309 | Notes: | ||
| 310 | This function is not scalable (in terms of memory or parallel communication), | ||
| 311 | so it should not be called except in the case of small problem size. For | ||
| 312 | large equations, use `LMEGetErrorEstimate()`. | ||
| 313 | |||
| 314 | Level: advanced | ||
| 315 | |||
| 316 | .seealso: [](ch:lme), `LMESolve()`, `LMEGetErrorEstimate()` | ||
| 317 | @*/ | ||
| 318 | 52 | PetscErrorCode LMEComputeError(LME lme,PetscReal *error) | |
| 319 | { | ||
| 320 |
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52 | PetscFunctionBegin; |
| 321 |
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52 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 322 |
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52 | PetscAssertPointer(error,2); |
| 323 | |||
| 324 |
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52 | PetscCall(PetscLogEventBegin(LME_ComputeError,lme,0,0,0)); |
| 325 | /* compute residual norm */ | ||
| 326 |
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52 | switch (lme->problem_type) { |
| 327 | 52 | case LME_LYAPUNOV: | |
| 328 |
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52 | PetscCall(LMEComputeResidualNorm_Lyapunov(lme,error)); |
| 329 | 52 | break; | |
| 330 | ✗ | default: | |
| 331 | − | SETERRQ(PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"Not implemented for equation type %s",LMEProblemTypes[lme->problem_type]); | |
| 332 | } | ||
| 333 | |||
| 334 | /* compute error */ | ||
| 335 | /* currently we only support absolute error, so just return the norm */ | ||
| 336 |
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52 | PetscCall(PetscLogEventEnd(LME_ComputeError,lme,0,0,0)); |
| 337 |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 338 | } | ||
| 339 |