| 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 - linear matrix equation solver context obtained from LMECreate() | ||
| 24 | |||
| 25 | Options Database Keys: | ||
| 26 | + -lme_view - print information about the solver used | ||
| 27 | . -lme_view_mat binary - save the matrix to the default binary viewer | ||
| 28 | . -lme_view_rhs binary - save right hand side to the default binary viewer | ||
| 29 | . -lme_view_solution binary - save computed solution to the default binary viewer | ||
| 30 | - -lme_converged_reason - print reason for convergence, and number of iterations | ||
| 31 | |||
| 32 | Notes: | ||
| 33 | The matrix coefficients are specified with LMESetCoefficients(). | ||
| 34 | The right-hand side is specified with LMESetRHS(). | ||
| 35 | The placeholder for the solution is specified with LMESetSolution(). | ||
| 36 | |||
| 37 | Level: beginner | ||
| 38 | |||
| 39 | .seealso: LMECreate(), LMESetUp(), LMEDestroy(), LMESetTolerances(), LMESetCoefficients(), LMESetRHS(), LMESetSolution() | ||
| 40 | @*/ | ||
| 41 | 497 | PetscErrorCode LMESolve(LME lme) | |
| 42 | { | ||
| 43 |
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497 | PetscFunctionBegin; |
| 44 |
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497 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 45 | |||
| 46 | /* call setup */ | ||
| 47 |
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497 | PetscCall(LMESetUp(lme)); |
| 48 | 497 | lme->its = 0; | |
| 49 | 497 | lme->errest = 0.0; | |
| 50 | |||
| 51 |
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497 | PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view_pre")); |
| 52 | |||
| 53 | /* call solver */ | ||
| 54 |
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497 | 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]); |
| 55 |
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497 | PetscCall(PetscLogEventBegin(LME_Solve,lme,0,0,0)); |
| 56 |
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497 | PetscUseTypeMethod(lme,solve[lme->problem_type]); |
| 57 |
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497 | PetscCall(PetscLogEventEnd(LME_Solve,lme,0,0,0)); |
| 58 | |||
| 59 |
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497 | PetscCheck(lme->reason,PetscObjectComm((PetscObject)lme),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 60 | |||
| 61 |
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497 | PetscCheck(!lme->errorifnotconverged || lme->reason>=0,PetscObjectComm((PetscObject)lme),PETSC_ERR_NOT_CONVERGED,"LMESolve has not converged"); |
| 62 | |||
| 63 | /* various viewers */ | ||
| 64 |
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497 | PetscCall(LMEViewFromOptions(lme,NULL,"-lme_view")); |
| 65 |
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497 | PetscCall(LMEConvergedReasonViewFromOptions(lme)); |
| 66 |
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497 | PetscCall(MatViewFromOptions(lme->A,(PetscObject)lme,"-lme_view_mat")); |
| 67 |
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497 | PetscCall(MatViewFromOptions(lme->C,(PetscObject)lme,"-lme_view_rhs")); |
| 68 |
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497 | PetscCall(MatViewFromOptions(lme->X,(PetscObject)lme,"-lme_view_solution")); |
| 69 |
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71 | PetscFunctionReturn(PETSC_SUCCESS); |
| 70 | } | ||
| 71 | |||
| 72 | /*@ | ||
| 73 | LMEGetIterationNumber - Gets the current iteration number. If the | ||
| 74 | call to LMESolve() is complete, then it returns the number of iterations | ||
| 75 | carried out by the solution method. | ||
| 76 | |||
| 77 | Not Collective | ||
| 78 | |||
| 79 | Input Parameter: | ||
| 80 | . lme - the linear matrix equation solver context | ||
| 81 | |||
| 82 | Output Parameter: | ||
| 83 | . its - number of iterations | ||
| 84 | |||
| 85 | Note: | ||
| 86 | During the i-th iteration this call returns i-1. If LMESolve() is | ||
| 87 | complete, then parameter "its" contains either the iteration number at | ||
| 88 | which convergence was successfully reached, or failure was detected. | ||
| 89 | Call LMEGetConvergedReason() to determine if the solver converged or | ||
| 90 | failed and why. | ||
| 91 | |||
| 92 | Level: intermediate | ||
| 93 | |||
| 94 | .seealso: LMEGetConvergedReason(), LMESetTolerances() | ||
| 95 | @*/ | ||
| 96 | 22 | PetscErrorCode LMEGetIterationNumber(LME lme,PetscInt *its) | |
| 97 | { | ||
| 98 |
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22 | PetscFunctionBegin; |
| 99 |
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22 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 100 |
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22 | PetscAssertPointer(its,2); |
| 101 | 22 | *its = lme->its; | |
| 102 |
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22 | PetscFunctionReturn(PETSC_SUCCESS); |
| 103 | } | ||
| 104 | |||
| 105 | /*@ | ||
| 106 | LMEGetConvergedReason - Gets the reason why the LMESolve() iteration was | ||
| 107 | stopped. | ||
| 108 | |||
| 109 | Not Collective | ||
| 110 | |||
| 111 | Input Parameter: | ||
| 112 | . lme - the linear matrix equation solver context | ||
| 113 | |||
| 114 | Output Parameter: | ||
| 115 | . reason - negative value indicates diverged, positive value converged | ||
| 116 | |||
| 117 | Notes: | ||
| 118 | |||
| 119 | Possible values for reason are | ||
| 120 | + LME_CONVERGED_TOL - converged up to tolerance | ||
| 121 | . LME_DIVERGED_ITS - required more than max_it iterations to reach convergence | ||
| 122 | - LME_DIVERGED_BREAKDOWN - generic breakdown in method | ||
| 123 | |||
| 124 | Can only be called after the call to LMESolve() is complete. | ||
| 125 | |||
| 126 | Level: intermediate | ||
| 127 | |||
| 128 | .seealso: LMESetTolerances(), LMESolve(), LMEConvergedReason, LMESetErrorIfNotConverged() | ||
| 129 | @*/ | ||
| 130 | 20 | PetscErrorCode LMEGetConvergedReason(LME lme,LMEConvergedReason *reason) | |
| 131 | { | ||
| 132 |
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20 | PetscFunctionBegin; |
| 133 |
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20 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 134 |
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20 | PetscAssertPointer(reason,2); |
| 135 | 20 | *reason = lme->reason; | |
| 136 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); |
| 137 | } | ||
| 138 | |||
| 139 | /*@ | ||
| 140 | LMEGetErrorEstimate - Returns the error estimate obtained during solve. | ||
| 141 | |||
| 142 | Not Collective | ||
| 143 | |||
| 144 | Input Parameter: | ||
| 145 | . lme - linear matrix equation solver context | ||
| 146 | |||
| 147 | Output Parameter: | ||
| 148 | . errest - the error estimate | ||
| 149 | |||
| 150 | Notes: | ||
| 151 | This is the error estimated internally by the solver. The actual | ||
| 152 | error bound can be computed with LMEComputeError(). Note that some | ||
| 153 | solvers may not be able to provide an error estimate. | ||
| 154 | |||
| 155 | Level: advanced | ||
| 156 | |||
| 157 | .seealso: LMEComputeError() | ||
| 158 | @*/ | ||
| 159 | 50 | PetscErrorCode LMEGetErrorEstimate(LME lme,PetscReal *errest) | |
| 160 | { | ||
| 161 |
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50 | PetscFunctionBegin; |
| 162 |
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50 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 163 |
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50 | PetscAssertPointer(errest,2); |
| 164 | 50 | *errest = lme->errest; | |
| 165 |
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50 | PetscFunctionReturn(PETSC_SUCCESS); |
| 166 | } | ||
| 167 | |||
| 168 | /* | ||
| 169 | LMEComputeResidualNorm_Lyapunov - Computes the Frobenius norm of the residual matrix | ||
| 170 | associated with the Lyapunov equation. | ||
| 171 | */ | ||
| 172 | 50 | static PetscErrorCode LMEComputeResidualNorm_Lyapunov(LME lme,PetscReal *norm) | |
| 173 | { | ||
| 174 | 50 | PetscInt j,n,N,k,l,lda,ldb; | |
| 175 | 50 | PetscBLASInt n_,N_,k_,l_,lda_,ldb_; | |
| 176 | 50 | PetscScalar *Rarray,alpha=1.0,beta=0.0; | |
| 177 | 50 | const PetscScalar *A,*B; | |
| 178 | 50 | BV W,AX,X1,C1; | |
| 179 | 50 | Mat R,X1m,C1m; | |
| 180 | 50 | Vec v,w; | |
| 181 | 50 | VecScatter vscat; | |
| 182 | |||
| 183 |
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50 | PetscFunctionBegin; |
| 184 |
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50 | PetscCall(MatLRCGetMats(lme->C,NULL,&C1m,NULL,NULL)); |
| 185 |
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50 | PetscCall(MatLRCGetMats(lme->X,NULL,&X1m,NULL,NULL)); |
| 186 |
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50 | PetscCall(BVCreateFromMat(C1m,&C1)); |
| 187 |
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50 | PetscCall(BVSetFromOptions(C1)); |
| 188 |
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50 | PetscCall(BVCreateFromMat(X1m,&X1)); |
| 189 |
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50 | PetscCall(BVSetFromOptions(X1)); |
| 190 |
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50 | PetscCall(BVGetSizes(X1,&n,&N,&k)); |
| 191 |
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50 | PetscCall(BVGetSizes(C1,NULL,NULL,&l)); |
| 192 |
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50 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 193 |
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50 | PetscCall(PetscBLASIntCast(N,&N_)); |
| 194 |
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50 | PetscCall(PetscBLASIntCast(k,&k_)); |
| 195 |
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50 | PetscCall(PetscBLASIntCast(l,&l_)); |
| 196 | |||
| 197 | /* create W to store a redundant copy of a BV in each process */ | ||
| 198 |
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50 | PetscCall(BVCreate(PETSC_COMM_SELF,&W)); |
| 199 |
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50 | PetscCall(BVSetSizes(W,N,N,k)); |
| 200 |
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50 | PetscCall(BVSetFromOptions(W)); |
| 201 |
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50 | PetscCall(BVGetColumn(X1,0,&v)); |
| 202 |
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50 | PetscCall(VecScatterCreateToAll(v,&vscat,NULL)); |
| 203 |
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50 | PetscCall(BVRestoreColumn(X1,0,&v)); |
| 204 | |||
| 205 | /* create AX to hold the product A*X1 */ | ||
| 206 |
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50 | PetscCall(BVDuplicate(X1,&AX)); |
| 207 |
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50 | PetscCall(BVMatMult(X1,lme->A,AX)); |
| 208 | |||
| 209 | /* create dense matrix to hold the residual R=C1*C1'+AX*X1'+X1*AX' */ | ||
| 210 |
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50 | PetscCall(MatCreateDense(PetscObjectComm((PetscObject)lme),n,n,N,N,NULL,&R)); |
| 211 | |||
| 212 | /* R=C1*C1' */ | ||
| 213 |
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50 | PetscCall(MatDenseGetArrayWrite(R,&Rarray)); |
| 214 |
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150 | for (j=0;j<l;j++) { |
| 215 |
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100 | PetscCall(BVGetColumn(C1,j,&v)); |
| 216 |
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100 | PetscCall(BVGetColumn(W,j,&w)); |
| 217 |
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100 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 218 |
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100 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 219 |
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100 | PetscCall(BVRestoreColumn(C1,j,&v)); |
| 220 |
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100 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 221 | } | ||
| 222 |
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50 | if (n) { |
| 223 |
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50 | PetscCall(BVGetArrayRead(C1,&A)); |
| 224 |
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50 | PetscCall(BVGetLeadingDimension(C1,&lda)); |
| 225 |
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50 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 226 |
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50 | PetscCall(BVGetArrayRead(W,&B)); |
| 227 |
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50 | PetscCall(BVGetLeadingDimension(W,&ldb)); |
| 228 |
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50 | PetscCall(PetscBLASIntCast(ldb,&ldb_)); |
| 229 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&l_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 230 |
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50 | PetscCall(BVRestoreArrayRead(C1,&A)); |
| 231 |
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50 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 232 | } | ||
| 233 | 50 | beta = 1.0; | |
| 234 | |||
| 235 | /* R+=AX*X1' */ | ||
| 236 |
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3517 | for (j=0;j<k;j++) { |
| 237 |
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3467 | PetscCall(BVGetColumn(X1,j,&v)); |
| 238 |
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3467 | PetscCall(BVGetColumn(W,j,&w)); |
| 239 |
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3467 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 240 |
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3467 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 241 |
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3467 | PetscCall(BVRestoreColumn(X1,j,&v)); |
| 242 |
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3467 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 243 | } | ||
| 244 |
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50 | if (n) { |
| 245 |
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50 | PetscCall(BVGetArrayRead(AX,&A)); |
| 246 |
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50 | PetscCall(BVGetLeadingDimension(AX,&lda)); |
| 247 |
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50 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 248 |
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50 | PetscCall(BVGetArrayRead(W,&B)); |
| 249 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 250 |
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50 | PetscCall(BVRestoreArrayRead(AX,&A)); |
| 251 |
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50 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 252 | } | ||
| 253 | |||
| 254 | /* R+=X1*AX' */ | ||
| 255 |
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3517 | for (j=0;j<k;j++) { |
| 256 |
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3467 | PetscCall(BVGetColumn(AX,j,&v)); |
| 257 |
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3467 | PetscCall(BVGetColumn(W,j,&w)); |
| 258 |
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3467 | PetscCall(VecScatterBegin(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 259 |
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3467 | PetscCall(VecScatterEnd(vscat,v,w,INSERT_VALUES,SCATTER_FORWARD)); |
| 260 |
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3467 | PetscCall(BVRestoreColumn(AX,j,&v)); |
| 261 |
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3467 | PetscCall(BVRestoreColumn(W,j,&w)); |
| 262 | } | ||
| 263 |
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50 | if (n) { |
| 264 |
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50 | PetscCall(BVGetArrayRead(X1,&A)); |
| 265 |
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50 | PetscCall(BVGetLeadingDimension(AX,&lda)); |
| 266 |
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50 | PetscCall(PetscBLASIntCast(lda,&lda_)); |
| 267 |
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50 | PetscCall(BVGetArrayRead(W,&B)); |
| 268 |
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50 | PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&n_,&N_,&k_,&alpha,(PetscScalar*)A,&lda_,(PetscScalar*)B,&ldb_,&beta,Rarray,&n_)); |
| 269 |
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50 | PetscCall(BVRestoreArrayRead(X1,&A)); |
| 270 |
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50 | PetscCall(BVRestoreArrayRead(W,&B)); |
| 271 | } | ||
| 272 |
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50 | PetscCall(MatDenseRestoreArrayWrite(R,&Rarray)); |
| 273 | |||
| 274 | /* compute ||R||_F */ | ||
| 275 |
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50 | PetscCall(MatNorm(R,NORM_FROBENIUS,norm)); |
| 276 | |||
| 277 |
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50 | PetscCall(BVDestroy(&W)); |
| 278 |
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50 | PetscCall(VecScatterDestroy(&vscat)); |
| 279 |
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50 | PetscCall(BVDestroy(&AX)); |
| 280 |
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50 | PetscCall(MatDestroy(&R)); |
| 281 |
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50 | PetscCall(BVDestroy(&C1)); |
| 282 |
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50 | PetscCall(BVDestroy(&X1)); |
| 283 |
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9 | PetscFunctionReturn(PETSC_SUCCESS); |
| 284 | } | ||
| 285 | |||
| 286 | /*@ | ||
| 287 | LMEComputeError - Computes the error (based on the residual norm) associated | ||
| 288 | with the last equation solved. | ||
| 289 | |||
| 290 | Collective | ||
| 291 | |||
| 292 | Input Parameter: | ||
| 293 | . lme - the linear matrix equation solver context | ||
| 294 | |||
| 295 | Output Parameter: | ||
| 296 | . error - the error | ||
| 297 | |||
| 298 | Notes: | ||
| 299 | This function is not scalable (in terms of memory or parallel communication), | ||
| 300 | so it should not be called except in the case of small problem size. For | ||
| 301 | large equations, use LMEGetErrorEstimate(). | ||
| 302 | |||
| 303 | Level: advanced | ||
| 304 | |||
| 305 | .seealso: LMESolve(), LMEGetErrorEstimate() | ||
| 306 | @*/ | ||
| 307 | 50 | PetscErrorCode LMEComputeError(LME lme,PetscReal *error) | |
| 308 | { | ||
| 309 |
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50 | PetscFunctionBegin; |
| 310 |
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50 | PetscValidHeaderSpecific(lme,LME_CLASSID,1); |
| 311 |
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50 | PetscAssertPointer(error,2); |
| 312 | |||
| 313 |
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50 | PetscCall(PetscLogEventBegin(LME_ComputeError,lme,0,0,0)); |
| 314 | /* compute residual norm */ | ||
| 315 |
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50 | switch (lme->problem_type) { |
| 316 | 50 | case LME_LYAPUNOV: | |
| 317 |
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50 | PetscCall(LMEComputeResidualNorm_Lyapunov(lme,error)); |
| 318 | 50 | break; | |
| 319 | ✗ | default: | |
| 320 | ✗ | SETERRQ(PetscObjectComm((PetscObject)lme),PETSC_ERR_SUP,"Not implemented for equation type %s",LMEProblemTypes[lme->problem_type]); | |
| 321 | } | ||
| 322 | |||
| 323 | /* compute error */ | ||
| 324 | /* currently we only support absolute error, so just return the norm */ | ||
| 325 |
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50 | PetscCall(PetscLogEventEnd(LME_ComputeError,lme,0,0,0)); |
| 326 |
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9 | PetscFunctionReturn(PETSC_SUCCESS); |
| 327 | } | ||
| 328 |