| 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 | SVD routines related to the solution process | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/svdimpl.h> /*I "slepcsvd.h" I*/ | ||
| 15 | #include <slepc/private/bvimpl.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | SVDComputeVectors_Left - Compute left singular vectors as U=A*V. | ||
| 19 | Only done if the leftbasis flag is false. Assumes V is available. | ||
| 20 | */ | ||
| 21 | 563 | PetscErrorCode SVDComputeVectors_Left(SVD svd) | |
| 22 | { | ||
| 23 | 563 | Vec tl,omega2,u,v,w; | |
| 24 | 563 | PetscInt i,oldsize; | |
| 25 | 563 | VecType vtype; | |
| 26 | 563 | const PetscScalar* varray; | |
| 27 | |||
| 28 |
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563 | PetscFunctionBegin; |
| 29 |
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563 | if (!svd->leftbasis) { |
| 30 | /* generate left singular vectors on U */ | ||
| 31 |
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392 | if (!svd->U) PetscCall(SVDGetBV(svd,NULL,&svd->U)); |
| 32 |
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392 | PetscCall(BVGetSizes(svd->U,NULL,NULL,&oldsize)); |
| 33 |
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392 | if (!oldsize) { |
| 34 |
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342 | if (!((PetscObject)svd->U)->type_name) PetscCall(BVSetType(svd->U,((PetscObject)svd->V)->type_name)); |
| 35 |
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342 | PetscCall(MatCreateVecsEmpty(svd->A,NULL,&tl)); |
| 36 |
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342 | PetscCall(BVSetSizesFromVec(svd->U,tl,svd->ncv)); |
| 37 |
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342 | PetscCall(VecDestroy(&tl)); |
| 38 | } | ||
| 39 |
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392 | PetscCall(BVSetActiveColumns(svd->V,0,svd->nconv)); |
| 40 |
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392 | PetscCall(BVSetActiveColumns(svd->U,0,svd->nconv)); |
| 41 |
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392 | if (!svd->ishyperbolic) PetscCall(BVMatMult(svd->V,svd->A,svd->U)); |
| 42 |
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79 | else if (svd->swapped) { /* compute right singular vectors as V=A'*Omega*U */ |
| 43 |
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18 | PetscCall(MatCreateVecs(svd->A,&w,NULL)); |
| 44 |
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534 | for (i=0;i<svd->nconv;i++) { |
| 45 |
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516 | PetscCall(BVGetColumn(svd->V,i,&v)); |
| 46 |
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516 | PetscCall(BVGetColumn(svd->U,i,&u)); |
| 47 |
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516 | PetscCall(VecPointwiseMult(w,v,svd->omega)); |
| 48 |
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516 | PetscCall(MatMult(svd->A,w,u)); |
| 49 |
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516 | PetscCall(BVRestoreColumn(svd->V,i,&v)); |
| 50 |
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516 | PetscCall(BVRestoreColumn(svd->U,i,&u)); |
| 51 | } | ||
| 52 |
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18 | PetscCall(VecDestroy(&w)); |
| 53 | } else { /* compute left singular vectors as usual U=A*V, and set-up Omega-orthogonalization of U */ | ||
| 54 |
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61 | PetscCall(BV_SetMatrixDiagonal(svd->U,svd->omega,svd->A)); |
| 55 |
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61 | PetscCall(BVMatMult(svd->V,svd->A,svd->U)); |
| 56 | } | ||
| 57 |
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392 | PetscCall(BVOrthogonalize(svd->U,NULL)); |
| 58 |
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392 | if (svd->ishyperbolic && !svd->swapped) { /* store signature after Omega-orthogonalization */ |
| 59 |
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61 | PetscCall(MatGetVecType(svd->A,&vtype)); |
| 60 |
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61 | PetscCall(VecCreate(PETSC_COMM_SELF,&omega2)); |
| 61 |
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61 | PetscCall(VecSetSizes(omega2,svd->nconv,svd->nconv)); |
| 62 |
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61 | PetscCall(VecSetType(omega2,vtype)); |
| 63 |
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61 | PetscCall(BVGetSignature(svd->U,omega2)); |
| 64 |
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61 | PetscCall(VecGetArrayRead(omega2,&varray)); |
| 65 |
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1877 | for (i=0;i<svd->nconv;i++) { |
| 66 | 1816 | svd->sign[i] = PetscRealPart(varray[i]); | |
| 67 |
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1816 | if (PetscRealPart(varray[i])<0.0) PetscCall(BVScaleColumn(svd->U,i,-1.0)); |
| 68 | } | ||
| 69 |
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61 | PetscCall(VecRestoreArrayRead(omega2,&varray)); |
| 70 |
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61 | PetscCall(VecDestroy(&omega2)); |
| 71 | } | ||
| 72 | } | ||
| 73 |
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113 | PetscFunctionReturn(PETSC_SUCCESS); |
| 74 | } | ||
| 75 | |||
| 76 | 24287 | PetscErrorCode SVDComputeVectors(SVD svd) | |
| 77 | { | ||
| 78 |
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24287 | PetscFunctionBegin; |
| 79 |
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24287 | SVDCheckSolved(svd,1); |
| 80 |
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24287 | if (svd->state==SVD_STATE_SOLVED) PetscTryTypeMethod(svd,computevectors); |
| 81 | 24287 | svd->state = SVD_STATE_VECTORS; | |
| 82 |
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24287 | PetscFunctionReturn(PETSC_SUCCESS); |
| 83 | } | ||
| 84 | |||
| 85 | /*@ | ||
| 86 | SVDSolve - Solves the singular value problem. | ||
| 87 | |||
| 88 | Collective | ||
| 89 | |||
| 90 | Input Parameter: | ||
| 91 | . svd - singular value solver context obtained from SVDCreate() | ||
| 92 | |||
| 93 | Options Database Keys: | ||
| 94 | + -svd_view - print information about the solver used | ||
| 95 | . -svd_view_mat0 - view the first matrix (A) | ||
| 96 | . -svd_view_mat1 - view the second matrix (B) | ||
| 97 | . -svd_view_signature - view the signature matrix (omega) | ||
| 98 | . -svd_view_vectors - view the computed singular vectors | ||
| 99 | . -svd_view_values - view the computed singular values | ||
| 100 | . -svd_converged_reason - print reason for convergence, and number of iterations | ||
| 101 | . -svd_error_absolute - print absolute errors of each singular triplet | ||
| 102 | . -svd_error_relative - print relative errors of each singular triplet | ||
| 103 | - -svd_error_norm - print errors relative to the matrix norms of each singular triplet | ||
| 104 | |||
| 105 | Notes: | ||
| 106 | All the command-line options listed above admit an optional argument specifying | ||
| 107 | the viewer type and options. For instance, use '-svd_view_mat0 binary:amatrix.bin' | ||
| 108 | to save the A matrix to a binary file, '-svd_view_values draw' to draw the computed | ||
| 109 | singular values graphically, or '-svd_error_relative :myerr.m:ascii_matlab' to save | ||
| 110 | the errors in a file that can be executed in Matlab. | ||
| 111 | |||
| 112 | Level: beginner | ||
| 113 | |||
| 114 | .seealso: SVDCreate(), SVDSetUp(), SVDDestroy() | ||
| 115 | @*/ | ||
| 116 | 2773 | PetscErrorCode SVDSolve(SVD svd) | |
| 117 | { | ||
| 118 | 2773 | PetscInt i,m,n,*workperm; | |
| 119 | |||
| 120 |
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2773 | PetscFunctionBegin; |
| 121 |
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2773 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 122 |
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2773 | if (svd->state>=SVD_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 123 |
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2773 | PetscCall(PetscLogEventBegin(SVD_Solve,svd,0,0,0)); |
| 124 | |||
| 125 | /* call setup */ | ||
| 126 |
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2773 | PetscCall(SVDSetUp(svd)); |
| 127 | |||
| 128 | /* safeguard for matrices with zero rows or columns */ | ||
| 129 |
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2773 | PetscCall(MatGetSize(svd->OP,&m,&n)); |
| 130 |
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2773 | if (m == 0 || n == 0) { |
| 131 | ✗ | svd->nconv = 0; | |
| 132 | ✗ | svd->reason = SVD_CONVERGED_TOL; | |
| 133 | ✗ | svd->state = SVD_STATE_SOLVED; | |
| 134 | ✗ | PetscFunctionReturn(PETSC_SUCCESS); | |
| 135 | } | ||
| 136 | |||
| 137 | 2773 | svd->its = 0; | |
| 138 | 2773 | svd->nconv = 0; | |
| 139 |
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61325 | for (i=0;i<svd->ncv;i++) { |
| 140 | 58552 | svd->sigma[i] = 0.0; | |
| 141 | 58552 | svd->errest[i] = 0.0; | |
| 142 | 58552 | svd->perm[i] = i; | |
| 143 | } | ||
| 144 |
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2773 | PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view_pre")); |
| 145 | |||
| 146 |
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2773 | switch (svd->problem_type) { |
| 147 | 1526 | case SVD_STANDARD: | |
| 148 |
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1526 | PetscUseTypeMethod(svd,solve); |
| 149 | break; | ||
| 150 | 985 | case SVD_GENERALIZED: | |
| 151 |
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985 | PetscUseTypeMethod(svd,solveg); |
| 152 | break; | ||
| 153 | 262 | case SVD_HYPERBOLIC: | |
| 154 |
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262 | PetscUseTypeMethod(svd,solveh); |
| 155 | break; | ||
| 156 | } | ||
| 157 | 2773 | svd->state = SVD_STATE_SOLVED; | |
| 158 | |||
| 159 | /* sort singular triplets */ | ||
| 160 |
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2773 | if (svd->which == SVD_SMALLEST) PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm)); |
| 161 | else { | ||
| 162 |
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2453 | PetscCall(PetscMalloc1(svd->nconv,&workperm)); |
| 163 |
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35568 | for (i=0;i<svd->nconv;i++) workperm[i] = i; |
| 164 |
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2453 | PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm)); |
| 165 |
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35568 | for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1]; |
| 166 |
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2453 | PetscCall(PetscFree(workperm)); |
| 167 | } | ||
| 168 |
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2773 | PetscCall(PetscLogEventEnd(SVD_Solve,svd,0,0,0)); |
| 169 | |||
| 170 | /* various viewers */ | ||
| 171 |
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2773 | PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view")); |
| 172 |
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2773 | PetscCall(SVDConvergedReasonViewFromOptions(svd)); |
| 173 |
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2773 | PetscCall(SVDErrorViewFromOptions(svd)); |
| 174 |
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2773 | PetscCall(SVDValuesViewFromOptions(svd)); |
| 175 |
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2773 | PetscCall(SVDVectorsViewFromOptions(svd)); |
| 176 |
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2773 | PetscCall(MatViewFromOptions(svd->OP,(PetscObject)svd,"-svd_view_mat0")); |
| 177 |
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2773 | if (svd->isgeneralized) PetscCall(MatViewFromOptions(svd->OPb,(PetscObject)svd,"-svd_view_mat1")); |
| 178 |
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2773 | if (svd->ishyperbolic) PetscCall(VecViewFromOptions(svd->omega,(PetscObject)svd,"-svd_view_signature")); |
| 179 | |||
| 180 | /* Remove the initial subspaces */ | ||
| 181 | 2773 | svd->nini = 0; | |
| 182 | 2773 | svd->ninil = 0; | |
| 183 |
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2773 | PetscFunctionReturn(PETSC_SUCCESS); |
| 184 | } | ||
| 185 | |||
| 186 | /*@ | ||
| 187 | SVDGetIterationNumber - Gets the current iteration number. If the | ||
| 188 | call to SVDSolve() is complete, then it returns the number of iterations | ||
| 189 | carried out by the solution method. | ||
| 190 | |||
| 191 | Not Collective | ||
| 192 | |||
| 193 | Input Parameter: | ||
| 194 | . svd - the singular value solver context | ||
| 195 | |||
| 196 | Output Parameter: | ||
| 197 | . its - number of iterations | ||
| 198 | |||
| 199 | Note: | ||
| 200 | During the i-th iteration this call returns i-1. If SVDSolve() is | ||
| 201 | complete, then parameter "its" contains either the iteration number at | ||
| 202 | which convergence was successfully reached, or failure was detected. | ||
| 203 | Call SVDGetConvergedReason() to determine if the solver converged or | ||
| 204 | failed and why. | ||
| 205 | |||
| 206 | Level: intermediate | ||
| 207 | |||
| 208 | .seealso: SVDGetConvergedReason(), SVDSetTolerances() | ||
| 209 | @*/ | ||
| 210 | 729 | PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its) | |
| 211 | { | ||
| 212 |
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729 | PetscFunctionBegin; |
| 213 |
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729 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 214 |
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729 | PetscAssertPointer(its,2); |
| 215 | 729 | *its = svd->its; | |
| 216 |
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729 | PetscFunctionReturn(PETSC_SUCCESS); |
| 217 | } | ||
| 218 | |||
| 219 | /*@ | ||
| 220 | SVDGetConvergedReason - Gets the reason why the SVDSolve() iteration was | ||
| 221 | stopped. | ||
| 222 | |||
| 223 | Not Collective | ||
| 224 | |||
| 225 | Input Parameter: | ||
| 226 | . svd - the singular value solver context | ||
| 227 | |||
| 228 | Output Parameter: | ||
| 229 | . reason - negative value indicates diverged, positive value converged | ||
| 230 | (see SVDConvergedReason) | ||
| 231 | |||
| 232 | Options Database Key: | ||
| 233 | . -svd_converged_reason - print the reason to a viewer | ||
| 234 | |||
| 235 | Notes: | ||
| 236 | Possible values for reason are | ||
| 237 | + SVD_CONVERGED_TOL - converged up to tolerance | ||
| 238 | . SVD_CONVERGED_USER - converged due to a user-defined condition | ||
| 239 | . SVD_CONVERGED_MAXIT - reached the maximum number of iterations with SVD_CONV_MAXIT criterion | ||
| 240 | . SVD_DIVERGED_ITS - required more than max_it iterations to reach convergence | ||
| 241 | . SVD_DIVERGED_BREAKDOWN - generic breakdown in method | ||
| 242 | - SVD_DIVERGED_SYMMETRY_LOST - underlying indefinite eigensolver was not able to keep symmetry | ||
| 243 | |||
| 244 | Can only be called after the call to SVDSolve() is complete. | ||
| 245 | |||
| 246 | Level: intermediate | ||
| 247 | |||
| 248 | .seealso: SVDSetTolerances(), SVDSolve(), SVDConvergedReason | ||
| 249 | @*/ | ||
| 250 | 171 | PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason) | |
| 251 | { | ||
| 252 |
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171 | PetscFunctionBegin; |
| 253 |
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171 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 254 |
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171 | PetscAssertPointer(reason,2); |
| 255 |
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171 | SVDCheckSolved(svd,1); |
| 256 | 171 | *reason = svd->reason; | |
| 257 |
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171 | PetscFunctionReturn(PETSC_SUCCESS); |
| 258 | } | ||
| 259 | |||
| 260 | /*@ | ||
| 261 | SVDGetConverged - Gets the number of converged singular values. | ||
| 262 | |||
| 263 | Not Collective | ||
| 264 | |||
| 265 | Input Parameter: | ||
| 266 | . svd - the singular value solver context | ||
| 267 | |||
| 268 | Output Parameter: | ||
| 269 | . nconv - number of converged singular values | ||
| 270 | |||
| 271 | Note: | ||
| 272 | This function should be called after SVDSolve() has finished. | ||
| 273 | |||
| 274 | Level: beginner | ||
| 275 | |||
| 276 | .seealso: SVDSetDimensions(), SVDSolve(), SVDGetSingularTriplet() | ||
| 277 | @*/ | ||
| 278 | 1213 | PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv) | |
| 279 | { | ||
| 280 |
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1213 | PetscFunctionBegin; |
| 281 |
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1213 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 282 |
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1213 | PetscAssertPointer(nconv,2); |
| 283 |
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1213 | SVDCheckSolved(svd,1); |
| 284 | 1213 | *nconv = svd->nconv; | |
| 285 |
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1213 | PetscFunctionReturn(PETSC_SUCCESS); |
| 286 | } | ||
| 287 | |||
| 288 | /*@ | ||
| 289 | SVDGetSingularTriplet - Gets the i-th triplet of the singular value decomposition | ||
| 290 | as computed by SVDSolve(). The solution consists in the singular value and its left | ||
| 291 | and right singular vectors. | ||
| 292 | |||
| 293 | Collective | ||
| 294 | |||
| 295 | Input Parameters: | ||
| 296 | + svd - singular value solver context | ||
| 297 | - i - index of the solution | ||
| 298 | |||
| 299 | Output Parameters: | ||
| 300 | + sigma - singular value | ||
| 301 | . u - left singular vector | ||
| 302 | - v - right singular vector | ||
| 303 | |||
| 304 | Note: | ||
| 305 | Both u or v can be NULL if singular vectors are not required. | ||
| 306 | Otherwise, the caller must provide valid Vec objects, i.e., | ||
| 307 | they must be created by the calling program with e.g. MatCreateVecs(). | ||
| 308 | |||
| 309 | The index i should be a value between 0 and nconv-1 (see SVDGetConverged()). | ||
| 310 | Singular triplets are indexed according to the ordering criterion established | ||
| 311 | with SVDSetWhichSingularTriplets(). | ||
| 312 | |||
| 313 | In the case of GSVD, the solution consists in three vectors u,v,x that are | ||
| 314 | returned as follows. Vector x is returned in the right singular vector | ||
| 315 | (argument v) and has length equal to the number of columns of A and B. | ||
| 316 | The other two vectors are returned stacked on top of each other [u;v] in | ||
| 317 | the left singular vector argument, with length equal to m+n (number of rows | ||
| 318 | of A plus number of rows of B). | ||
| 319 | |||
| 320 | Level: beginner | ||
| 321 | |||
| 322 | .seealso: SVDSolve(), SVDGetConverged(), SVDSetWhichSingularTriplets() | ||
| 323 | @*/ | ||
| 324 | 35303 | PetscErrorCode SVDGetSingularTriplet(SVD svd,PetscInt i,PetscReal *sigma,Vec u,Vec v) | |
| 325 | { | ||
| 326 | 35303 | PetscInt M,N; | |
| 327 | 35303 | Vec w; | |
| 328 | |||
| 329 |
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35303 | PetscFunctionBegin; |
| 330 |
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35303 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 331 |
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35303 | PetscValidLogicalCollectiveInt(svd,i,2); |
| 332 |
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35303 | SVDCheckSolved(svd,1); |
| 333 |
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35303 | if (u) { PetscValidHeaderSpecific(u,VEC_CLASSID,4); PetscCheckSameComm(svd,1,u,4); } |
| 334 |
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35303 | if (v) { PetscValidHeaderSpecific(v,VEC_CLASSID,5); PetscCheckSameComm(svd,1,v,5); } |
| 335 |
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35303 | PetscCheck(i>=0,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 336 |
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35303 | PetscCheck(i<svd->nconv,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see SVDGetConverged()"); |
| 337 |
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35303 | if (sigma) *sigma = svd->sigma[svd->perm[i]]; |
| 338 |
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35303 | if (u || v) { |
| 339 |
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24277 | if (!svd->isgeneralized) { |
| 340 |
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18244 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 341 |
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18244 | if (M<N) { w = u; u = v; v = w; } |
| 342 | } | ||
| 343 |
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24277 | PetscCall(SVDComputeVectors(svd)); |
| 344 |
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24277 | if (u) PetscCall(BVCopyVec(svd->U,svd->perm[i],u)); |
| 345 |
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24277 | if (v) PetscCall(BVCopyVec(svd->V,svd->perm[i],v)); |
| 346 | } | ||
| 347 |
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7795 | PetscFunctionReturn(PETSC_SUCCESS); |
| 348 | } | ||
| 349 | |||
| 350 | /* | ||
| 351 | SVDComputeResidualNorms_Standard - Computes the norms of the left and | ||
| 352 | right residuals associated with the i-th computed singular triplet. | ||
| 353 | |||
| 354 | Input Parameters: | ||
| 355 | sigma - singular value | ||
| 356 | u,v - singular vectors | ||
| 357 | x,y - two work vectors with the same dimensions as u,v | ||
| 358 | */ | ||
| 359 | 5945 | static PetscErrorCode SVDComputeResidualNorms_Standard(SVD svd,PetscReal sigma,Vec u,Vec v,Vec x,Vec y,PetscReal *norm1,PetscReal *norm2) | |
| 360 | { | ||
| 361 | 5945 | PetscInt M,N; | |
| 362 | |||
| 363 |
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5945 | PetscFunctionBegin; |
| 364 | /* norm1 = ||A*v-sigma*u||_2 */ | ||
| 365 |
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5945 | if (norm1) { |
| 366 |
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5945 | PetscCall(MatMult(svd->OP,v,x)); |
| 367 |
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5945 | PetscCall(VecAXPY(x,-sigma,u)); |
| 368 |
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5945 | PetscCall(VecNorm(x,NORM_2,norm1)); |
| 369 | } | ||
| 370 | /* norm2 = ||A^T*u-sigma*v||_2 */ | ||
| 371 |
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5945 | if (norm2) { |
| 372 |
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5945 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 373 |
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5945 | if (M<N) PetscCall(MatMult(svd->A,u,y)); |
| 374 |
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5218 | else PetscCall(MatMult(svd->AT,u,y)); |
| 375 |
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5945 | PetscCall(VecAXPY(y,-sigma,v)); |
| 376 |
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5945 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 377 | } | ||
| 378 |
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932 | PetscFunctionReturn(PETSC_SUCCESS); |
| 379 | } | ||
| 380 | |||
| 381 | /* | ||
| 382 | SVDComputeResidualNorms_Generalized - In GSVD, compute the residual norms | ||
| 383 | norm1 = ||s^2*A'*u-c*B'*B*x||_2 and norm2 = ||c^2*B'*v-s*A'*A*x||_2. | ||
| 384 | |||
| 385 | Input Parameters: | ||
| 386 | sigma - singular value | ||
| 387 | uv - left singular vectors [u;v] | ||
| 388 | x - right singular vector | ||
| 389 | y,z - two work vectors with the same dimension as x | ||
| 390 | */ | ||
| 391 | 4063 | static PetscErrorCode SVDComputeResidualNorms_Generalized(SVD svd,PetscReal sigma,Vec uv,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2) | |
| 392 | { | ||
| 393 | 4063 | Vec u,v,ax,bx,nest,aux[2]; | |
| 394 | 4063 | PetscReal c,s; | |
| 395 | |||
| 396 |
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4063 | PetscFunctionBegin; |
| 397 |
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4063 | PetscCall(MatCreateVecs(svd->OP,NULL,&u)); |
| 398 |
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4063 | PetscCall(MatCreateVecs(svd->OPb,NULL,&v)); |
| 399 | 4063 | aux[0] = u; | |
| 400 | 4063 | aux[1] = v; | |
| 401 |
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4063 | PetscCall(VecCreateNest(PetscObjectComm((PetscObject)svd),2,NULL,aux,&nest)); |
| 402 |
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4063 | PetscCall(VecCopy(uv,nest)); |
| 403 | |||
| 404 | 4063 | s = 1.0/PetscSqrtReal(1.0+sigma*sigma); | |
| 405 | 4063 | c = sigma*s; | |
| 406 | |||
| 407 | /* norm1 = ||s^2*A'*u-c*B'*B*x||_2 */ | ||
| 408 |
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4063 | if (norm1) { |
| 409 |
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4063 | PetscCall(VecDuplicate(v,&bx)); |
| 410 |
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4063 | PetscCall(MatMultHermitianTranspose(svd->OP,u,z)); |
| 411 |
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4063 | PetscCall(MatMult(svd->OPb,x,bx)); |
| 412 |
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4063 | PetscCall(MatMultHermitianTranspose(svd->OPb,bx,y)); |
| 413 |
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4063 | PetscCall(VecAXPBY(y,s*s,-c,z)); |
| 414 |
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4063 | PetscCall(VecNorm(y,NORM_2,norm1)); |
| 415 |
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4063 | PetscCall(VecDestroy(&bx)); |
| 416 | } | ||
| 417 | /* norm2 = ||c^2*B'*v-s*A'*A*x||_2 */ | ||
| 418 |
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4063 | if (norm2) { |
| 419 |
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4063 | PetscCall(VecDuplicate(u,&ax)); |
| 420 |
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4063 | PetscCall(MatMultHermitianTranspose(svd->OPb,v,z)); |
| 421 |
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4063 | PetscCall(MatMult(svd->OP,x,ax)); |
| 422 |
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4063 | PetscCall(MatMultHermitianTranspose(svd->OP,ax,y)); |
| 423 |
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4063 | PetscCall(VecAXPBY(y,c*c,-s,z)); |
| 424 |
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4063 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 425 |
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4063 | PetscCall(VecDestroy(&ax)); |
| 426 | } | ||
| 427 | |||
| 428 |
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4063 | PetscCall(VecDestroy(&v)); |
| 429 |
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4063 | PetscCall(VecDestroy(&u)); |
| 430 |
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4063 | PetscCall(VecDestroy(&nest)); |
| 431 |
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802 | PetscFunctionReturn(PETSC_SUCCESS); |
| 432 | } | ||
| 433 | |||
| 434 | /* | ||
| 435 | SVDComputeResidualNorms_Hyperbolic - Computes the norms of the left and | ||
| 436 | right residuals associated with the i-th computed singular triplet. | ||
| 437 | |||
| 438 | Input Parameters: | ||
| 439 | sigma - singular value | ||
| 440 | sign - corresponding element of the signature Omega2 | ||
| 441 | u,v - singular vectors | ||
| 442 | x,y,z - three work vectors with the same dimensions as u,v,u | ||
| 443 | */ | ||
| 444 | 4176 | static PetscErrorCode SVDComputeResidualNorms_Hyperbolic(SVD svd,PetscReal sigma,PetscReal sign,Vec u,Vec v,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2) | |
| 445 | { | ||
| 446 | 4176 | PetscInt M,N; | |
| 447 | |||
| 448 |
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4176 | PetscFunctionBegin; |
| 449 | /* norm1 = ||A*v-sigma*u||_2 */ | ||
| 450 |
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4176 | if (norm1) { |
| 451 |
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4176 | PetscCall(MatMult(svd->OP,v,x)); |
| 452 |
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4176 | PetscCall(VecAXPY(x,-sigma,u)); |
| 453 |
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4176 | PetscCall(VecNorm(x,NORM_2,norm1)); |
| 454 | } | ||
| 455 | /* norm2 = ||A^T*Omega*u-sigma*sign*v||_2 */ | ||
| 456 |
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4176 | if (norm2) { |
| 457 |
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4176 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 458 |
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4176 | PetscCall(VecPointwiseMult(z,u,svd->omega)); |
| 459 |
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4176 | if (M<N) PetscCall(MatMult(svd->A,z,y)); |
| 460 |
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3888 | else PetscCall(MatMult(svd->AT,z,y)); |
| 461 |
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4176 | PetscCall(VecAXPY(y,-sigma*sign,v)); |
| 462 |
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4176 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 463 | } | ||
| 464 |
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1276 | PetscFunctionReturn(PETSC_SUCCESS); |
| 465 | } | ||
| 466 | |||
| 467 | /*@ | ||
| 468 | SVDComputeError - Computes the error (based on the residual norm) associated | ||
| 469 | with the i-th singular triplet. | ||
| 470 | |||
| 471 | Collective | ||
| 472 | |||
| 473 | Input Parameters: | ||
| 474 | + svd - the singular value solver context | ||
| 475 | . i - the solution index | ||
| 476 | - type - the type of error to compute | ||
| 477 | |||
| 478 | Output Parameter: | ||
| 479 | . error - the error | ||
| 480 | |||
| 481 | Notes: | ||
| 482 | The error can be computed in various ways, all of them based on the residual | ||
| 483 | norm obtained as sqrt(n1^2+n2^2) with n1 = ||A*v-sigma*u||_2 and | ||
| 484 | n2 = ||A^T*u-sigma*v||_2, where sigma is the singular value, u is the left | ||
| 485 | singular vector and v is the right singular vector. | ||
| 486 | |||
| 487 | In the case of the GSVD, the two components of the residual norm are | ||
| 488 | n1 = ||s^2*A'*u-c*B'*B*x||_2 and n2 = ||c^2*B'*v-s*A'*A*x||_2, where [u;v] | ||
| 489 | are the left singular vectors and x is the right singular vector, with | ||
| 490 | sigma=c/s. | ||
| 491 | |||
| 492 | Level: beginner | ||
| 493 | |||
| 494 | .seealso: SVDErrorType, SVDSolve() | ||
| 495 | @*/ | ||
| 496 | 14184 | PetscErrorCode SVDComputeError(SVD svd,PetscInt i,SVDErrorType type,PetscReal *error) | |
| 497 | { | ||
| 498 | 14184 | PetscReal sigma,norm1,norm2,c,s; | |
| 499 | 14184 | Vec u=NULL,v=NULL,x=NULL,y=NULL,z=NULL; | |
| 500 | 14184 | PetscReal vecnorm=1.0; | |
| 501 | |||
| 502 |
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14184 | PetscFunctionBegin; |
| 503 |
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14184 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 504 |
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14184 | PetscValidLogicalCollectiveInt(svd,i,2); |
| 505 |
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14184 | PetscValidLogicalCollectiveEnum(svd,type,3); |
| 506 |
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14184 | PetscAssertPointer(error,4); |
| 507 |
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14184 | SVDCheckSolved(svd,1); |
| 508 | |||
| 509 | /* allocate work vectors */ | ||
| 510 |
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14184 | switch (svd->problem_type) { |
| 511 | 5945 | case SVD_STANDARD: | |
| 512 |
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5945 | PetscCall(SVDSetWorkVecs(svd,2,2)); |
| 513 | 5945 | u = svd->workl[0]; | |
| 514 | 5945 | v = svd->workr[0]; | |
| 515 | 5945 | x = svd->workl[1]; | |
| 516 | 5945 | y = svd->workr[1]; | |
| 517 | 5945 | break; | |
| 518 | 4063 | case SVD_GENERALIZED: | |
| 519 |
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4063 | PetscCall(SVDSetWorkVecs(svd,1,3)); |
| 520 | 4063 | u = svd->workl[0]; | |
| 521 | 4063 | v = svd->workr[0]; | |
| 522 | 4063 | x = svd->workr[1]; | |
| 523 | 4063 | y = svd->workr[2]; | |
| 524 | 4063 | break; | |
| 525 | 4176 | case SVD_HYPERBOLIC: | |
| 526 |
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4176 | PetscCall(SVDSetWorkVecs(svd,3,2)); |
| 527 | 4176 | u = svd->workl[0]; | |
| 528 | 4176 | v = svd->workr[0]; | |
| 529 | 4176 | x = svd->workl[1]; | |
| 530 | 4176 | y = svd->workr[1]; | |
| 531 | 4176 | z = svd->workl[2]; | |
| 532 | 4176 | break; | |
| 533 | } | ||
| 534 | |||
| 535 | /* compute residual norm */ | ||
| 536 |
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14184 | PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v)); |
| 537 |
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14184 | switch (svd->problem_type) { |
| 538 | 5945 | case SVD_STANDARD: | |
| 539 |
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5945 | PetscCall(SVDComputeResidualNorms_Standard(svd,sigma,u,v,x,y,&norm1,&norm2)); |
| 540 | break; | ||
| 541 | 4063 | case SVD_GENERALIZED: | |
| 542 |
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4063 | PetscCall(SVDComputeResidualNorms_Generalized(svd,sigma,u,v,x,y,&norm1,&norm2)); |
| 543 | break; | ||
| 544 | 4176 | case SVD_HYPERBOLIC: | |
| 545 |
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4176 | PetscCall(SVDComputeResidualNorms_Hyperbolic(svd,sigma,svd->sign[svd->perm[i]],u,v,x,y,z,&norm1,&norm2)); |
| 546 | break; | ||
| 547 | } | ||
| 548 | 14184 | *error = SlepcAbs(norm1,norm2); | |
| 549 | |||
| 550 | /* compute 2-norm of eigenvector of the cyclic form */ | ||
| 551 |
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14184 | if (type!=SVD_ERROR_ABSOLUTE) { |
| 552 |
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14050 | switch (svd->problem_type) { |
| 553 | 5811 | case SVD_STANDARD: | |
| 554 | 5811 | vecnorm = PETSC_SQRT2; | |
| 555 | 5811 | break; | |
| 556 | 4063 | case SVD_GENERALIZED: | |
| 557 |
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4063 | PetscCall(VecNorm(v,NORM_2,&vecnorm)); |
| 558 | 4063 | vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm); | |
| 559 | 4063 | break; | |
| 560 | 4176 | case SVD_HYPERBOLIC: | |
| 561 |
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4176 | PetscCall(VecNorm(u,NORM_2,&vecnorm)); |
| 562 | 4176 | vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm); | |
| 563 | 4176 | break; | |
| 564 | } | ||
| 565 | 26 | } | |
| 566 | |||
| 567 | /* compute error */ | ||
| 568 |
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14076 | switch (type) { |
| 569 | case SVD_ERROR_ABSOLUTE: | ||
| 570 | break; | ||
| 571 | 5737 | case SVD_ERROR_RELATIVE: | |
| 572 |
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5737 | if (svd->isgeneralized) { |
| 573 | ✗ | s = 1.0/PetscSqrtReal(1.0+sigma*sigma); | |
| 574 | ✗ | c = sigma*s; | |
| 575 | ✗ | norm1 /= c*vecnorm; | |
| 576 | ✗ | norm2 /= s*vecnorm; | |
| 577 | ✗ | *error = PetscMax(norm1,norm2); | |
| 578 | 5737 | } else *error /= sigma*vecnorm; | |
| 579 | break; | ||
| 580 | 8313 | case SVD_ERROR_NORM: | |
| 581 |
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8313 | if (!svd->nrma) PetscCall(MatNorm(svd->OP,NORM_INFINITY,&svd->nrma)); |
| 582 |
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8313 | if (svd->isgeneralized && !svd->nrmb) PetscCall(MatNorm(svd->OPb,NORM_INFINITY,&svd->nrmb)); |
| 583 |
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8313 | *error /= PetscMax(svd->nrma,svd->nrmb)*vecnorm; |
| 584 | 8313 | break; | |
| 585 | ✗ | default: | |
| 586 | ✗ | SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 587 | } | ||
| 588 |
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3010 | PetscFunctionReturn(PETSC_SUCCESS); |
| 589 | } | ||
| 590 |