| 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 | 556 | PetscErrorCode SVDComputeVectors_Left(SVD svd) | |
| 22 | { | ||
| 23 | 556 | Vec tl,omega2,u,v,w; | |
| 24 | 556 | PetscInt i,oldsize; | |
| 25 | 556 | VecType vtype; | |
| 26 | 556 | const PetscScalar* varray; | |
| 27 | |||
| 28 |
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556 | PetscFunctionBegin; |
| 29 |
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556 | if (!svd->leftbasis) { |
| 30 | /* generate left singular vectors on U */ | ||
| 31 |
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396 | if (!svd->U) PetscCall(SVDGetBV(svd,NULL,&svd->U)); |
| 32 |
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396 | PetscCall(BVGetSizes(svd->U,NULL,NULL,&oldsize)); |
| 33 |
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396 | if (!oldsize) { |
| 34 |
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346 | if (!((PetscObject)svd->U)->type_name) PetscCall(BVSetType(svd->U,((PetscObject)svd->V)->type_name)); |
| 35 |
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346 | PetscCall(MatCreateVecsEmpty(svd->A,NULL,&tl)); |
| 36 |
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346 | PetscCall(BVSetSizesFromVec(svd->U,tl,svd->ncv)); |
| 37 |
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346 | PetscCall(VecDestroy(&tl)); |
| 38 | } | ||
| 39 |
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396 | PetscCall(BVSetActiveColumns(svd->V,0,svd->nconv)); |
| 40 |
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396 | PetscCall(BVSetActiveColumns(svd->U,0,svd->nconv)); |
| 41 |
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396 | 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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396 | PetscCall(BVOrthogonalize(svd->U,NULL)); |
| 58 |
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396 | 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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1869 | for (i=0;i<svd->nconv;i++) { |
| 66 | 1808 | svd->sign[i] = PetscRealPart(varray[i]); | |
| 67 |
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1808 | 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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112 | PetscFunctionReturn(PETSC_SUCCESS); |
| 74 | } | ||
| 75 | |||
| 76 | 24274 | PetscErrorCode SVDComputeVectors(SVD svd) | |
| 77 | { | ||
| 78 |
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24274 | PetscFunctionBegin; |
| 79 |
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24274 | SVDCheckSolved(svd,1); |
| 80 |
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24274 | if (svd->state==SVD_STATE_SOLVED) PetscTryTypeMethod(svd,computevectors); |
| 81 | 24274 | svd->state = SVD_STATE_VECTORS; | |
| 82 |
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24274 | PetscFunctionReturn(PETSC_SUCCESS); |
| 83 | } | ||
| 84 | |||
| 85 | /*@ | ||
| 86 | SVDSolve - Solves the singular value problem. | ||
| 87 | |||
| 88 | Collective | ||
| 89 | |||
| 90 | Input Parameter: | ||
| 91 | . svd - the singular value solver context | ||
| 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/divergence, 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 | The problem matrices are specified with `SVDSetOperators()`. | ||
| 107 | |||
| 108 | `SVDSolve()` will return without generating an error regardless of whether | ||
| 109 | all requested solutions were computed or not. Call `SVDGetConverged()` to get the | ||
| 110 | actual number of computed solutions, and `SVDGetConvergedReason()` to determine if | ||
| 111 | the solver converged or failed and why. | ||
| 112 | |||
| 113 | All the command-line options listed above admit an optional argument specifying | ||
| 114 | the viewer type and options. For instance, use `-svd_view_mat0 binary:amatrix.bin` | ||
| 115 | to save the $A$ matrix to a binary file, `-svd_view_values draw` to draw the computed | ||
| 116 | singular values graphically, or `-svd_error_relative :myerr.m:ascii_matlab` to save | ||
| 117 | the errors in a file that can be executed in Matlab. | ||
| 118 | See `PetscObjectViewFromOptions()` for more details. | ||
| 119 | |||
| 120 | Level: beginner | ||
| 121 | |||
| 122 | .seealso: [](ch:svd), `SVDCreate()`, `SVDSetUp()`, `SVDDestroy()`, `SVDSetOperators()`, `SVDGetConverged()`, `SVDGetConvergedReason()` | ||
| 123 | @*/ | ||
| 124 | 2766 | PetscErrorCode SVDSolve(SVD svd) | |
| 125 | { | ||
| 126 | 2766 | PetscInt i,m,n,*workperm; | |
| 127 | |||
| 128 |
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2766 | PetscFunctionBegin; |
| 129 |
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2766 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 130 |
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2766 | if (svd->state>=SVD_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 131 |
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2766 | PetscCall(PetscLogEventBegin(SVD_Solve,svd,0,0,0)); |
| 132 | |||
| 133 | /* call setup */ | ||
| 134 |
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2766 | PetscCall(SVDSetUp(svd)); |
| 135 | |||
| 136 | /* safeguard for matrices with zero rows or columns */ | ||
| 137 |
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2766 | PetscCall(MatGetSize(svd->OP,&m,&n)); |
| 138 |
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2766 | if (m == 0 || n == 0) { |
| 139 | ✗ | svd->nconv = 0; | |
| 140 | ✗ | svd->reason = SVD_CONVERGED_TOL; | |
| 141 | ✗ | svd->state = SVD_STATE_SOLVED; | |
| 142 | ✗ | PetscFunctionReturn(PETSC_SUCCESS); | |
| 143 | } | ||
| 144 | |||
| 145 | 2766 | svd->its = 0; | |
| 146 | 2766 | svd->nconv = 0; | |
| 147 |
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61199 | for (i=0;i<svd->ncv;i++) { |
| 148 | 58433 | svd->sigma[i] = 0.0; | |
| 149 | 58433 | svd->errest[i] = 0.0; | |
| 150 | 58433 | svd->perm[i] = i; | |
| 151 | } | ||
| 152 |
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2766 | PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view_pre")); |
| 153 | |||
| 154 |
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2766 | switch (svd->problem_type) { |
| 155 | 1519 | case SVD_STANDARD: | |
| 156 |
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1519 | PetscUseTypeMethod(svd,solve); |
| 157 | break; | ||
| 158 | 985 | case SVD_GENERALIZED: | |
| 159 |
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985 | PetscUseTypeMethod(svd,solveg); |
| 160 | break; | ||
| 161 | 262 | case SVD_HYPERBOLIC: | |
| 162 |
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262 | PetscUseTypeMethod(svd,solveh); |
| 163 | break; | ||
| 164 | } | ||
| 165 | 2766 | svd->state = SVD_STATE_SOLVED; | |
| 166 | |||
| 167 | /* sort singular triplets */ | ||
| 168 |
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2766 | if (svd->which == SVD_SMALLEST) PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm)); |
| 169 | else { | ||
| 170 |
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2446 | PetscCall(PetscMalloc1(svd->nconv,&workperm)); |
| 171 |
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35507 | for (i=0;i<svd->nconv;i++) workperm[i] = i; |
| 172 |
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2446 | PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm)); |
| 173 |
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35507 | for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1]; |
| 174 |
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2446 | PetscCall(PetscFree(workperm)); |
| 175 | } | ||
| 176 |
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2766 | PetscCall(PetscLogEventEnd(SVD_Solve,svd,0,0,0)); |
| 177 | |||
| 178 | /* various viewers */ | ||
| 179 |
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2766 | PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view")); |
| 180 |
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2766 | PetscCall(SVDConvergedReasonViewFromOptions(svd)); |
| 181 |
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2766 | PetscCall(SVDErrorViewFromOptions(svd)); |
| 182 |
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2766 | PetscCall(SVDValuesViewFromOptions(svd)); |
| 183 |
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2766 | PetscCall(SVDVectorsViewFromOptions(svd)); |
| 184 |
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2766 | PetscCall(MatViewFromOptions(svd->OP,(PetscObject)svd,"-svd_view_mat0")); |
| 185 |
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2766 | if (svd->isgeneralized) PetscCall(MatViewFromOptions(svd->OPb,(PetscObject)svd,"-svd_view_mat1")); |
| 186 |
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2766 | if (svd->ishyperbolic) PetscCall(VecViewFromOptions(svd->omega,(PetscObject)svd,"-svd_view_signature")); |
| 187 | |||
| 188 | /* Remove the initial subspaces */ | ||
| 189 | 2766 | svd->nini = 0; | |
| 190 | 2766 | svd->ninil = 0; | |
| 191 |
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2766 | PetscFunctionReturn(PETSC_SUCCESS); |
| 192 | } | ||
| 193 | |||
| 194 | /*@ | ||
| 195 | SVDGetIterationNumber - Gets the current iteration number. If the | ||
| 196 | call to `SVDSolve()` is complete, then it returns the number of iterations | ||
| 197 | carried out by the solution method. | ||
| 198 | |||
| 199 | Not Collective | ||
| 200 | |||
| 201 | Input Parameter: | ||
| 202 | . svd - the singular value solver context | ||
| 203 | |||
| 204 | Output Parameter: | ||
| 205 | . its - number of iterations | ||
| 206 | |||
| 207 | Note: | ||
| 208 | During the $i$-th iteration this call returns $i-1$. If `SVDSolve()` is | ||
| 209 | complete, then parameter `its` contains either the iteration number at | ||
| 210 | which convergence was successfully reached, or failure was detected. | ||
| 211 | Call `SVDGetConvergedReason()` to determine if the solver converged or | ||
| 212 | failed and why. | ||
| 213 | |||
| 214 | Level: intermediate | ||
| 215 | |||
| 216 | .seealso: [](ch:svd), `SVDGetConvergedReason()`, `SVDSetTolerances()` | ||
| 217 | @*/ | ||
| 218 | 718 | PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its) | |
| 219 | { | ||
| 220 |
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718 | PetscFunctionBegin; |
| 221 |
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718 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 222 |
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718 | PetscAssertPointer(its,2); |
| 223 | 718 | *its = svd->its; | |
| 224 |
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718 | PetscFunctionReturn(PETSC_SUCCESS); |
| 225 | } | ||
| 226 | |||
| 227 | /*@ | ||
| 228 | SVDGetConvergedReason - Gets the reason why the `SVDSolve()` iteration was | ||
| 229 | stopped. | ||
| 230 | |||
| 231 | Not Collective | ||
| 232 | |||
| 233 | Input Parameter: | ||
| 234 | . svd - the singular value solver context | ||
| 235 | |||
| 236 | Output Parameter: | ||
| 237 | . reason - negative value indicates diverged, positive value converged, see | ||
| 238 | `SVDConvergedReason` for the possible values | ||
| 239 | |||
| 240 | Options Database Key: | ||
| 241 | . -svd_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 242 | |||
| 243 | Note: | ||
| 244 | If this routine is called before or doing the `SVDSolve()` the value of | ||
| 245 | `SVD_CONVERGED_ITERATING` is returned. | ||
| 246 | |||
| 247 | Level: intermediate | ||
| 248 | |||
| 249 | .seealso: [](ch:svd), `SVDSetTolerances()`, `SVDSolve()`, `SVDConvergedReason` | ||
| 250 | @*/ | ||
| 251 | 171 | PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason) | |
| 252 | { | ||
| 253 |
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171 | PetscFunctionBegin; |
| 254 |
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171 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 255 |
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171 | PetscAssertPointer(reason,2); |
| 256 |
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171 | SVDCheckSolved(svd,1); |
| 257 | 171 | *reason = svd->reason; | |
| 258 |
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171 | PetscFunctionReturn(PETSC_SUCCESS); |
| 259 | } | ||
| 260 | |||
| 261 | /*@ | ||
| 262 | SVDGetConverged - Gets the number of converged singular values. | ||
| 263 | |||
| 264 | Not Collective | ||
| 265 | |||
| 266 | Input Parameter: | ||
| 267 | . svd - the singular value solver context | ||
| 268 | |||
| 269 | Output Parameter: | ||
| 270 | . nconv - number of converged singular values | ||
| 271 | |||
| 272 | Notes: | ||
| 273 | This function should be called after `SVDSolve()` has finished. | ||
| 274 | |||
| 275 | The value `nconv` may be different from the number of requested solutions | ||
| 276 | `nsv`, but not larger than `ncv`, see `SVDSetDimensions()`. | ||
| 277 | |||
| 278 | Level: beginner | ||
| 279 | |||
| 280 | .seealso: [](ch:svd), `SVDSetDimensions()`, `SVDSolve()`, `SVDGetSingularTriplet()` | ||
| 281 | @*/ | ||
| 282 | 1215 | PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv) | |
| 283 | { | ||
| 284 |
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1215 | PetscFunctionBegin; |
| 285 |
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1215 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 286 |
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1215 | PetscAssertPointer(nconv,2); |
| 287 |
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1215 | SVDCheckSolved(svd,1); |
| 288 | 1215 | *nconv = svd->nconv; | |
| 289 |
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1215 | PetscFunctionReturn(PETSC_SUCCESS); |
| 290 | } | ||
| 291 | |||
| 292 | /*@ | ||
| 293 | SVDGetSingularTriplet - Gets the `i`-th triplet of the singular value decomposition | ||
| 294 | as computed by `SVDSolve()`. The solution consists in the singular value and its left | ||
| 295 | and right singular vectors. | ||
| 296 | |||
| 297 | Collective | ||
| 298 | |||
| 299 | Input Parameters: | ||
| 300 | + svd - the singular value solver context | ||
| 301 | - i - index of the solution | ||
| 302 | |||
| 303 | Output Parameters: | ||
| 304 | + sigma - singular value | ||
| 305 | . u - left singular vector | ||
| 306 | - v - right singular vector | ||
| 307 | |||
| 308 | Note: | ||
| 309 | Both `u` or `v` can be `NULL` if singular vectors are not required. | ||
| 310 | Otherwise, the caller must provide valid `Vec` objects, i.e., | ||
| 311 | they must be created by the calling program with e.g. `MatCreateVecs()`. | ||
| 312 | |||
| 313 | The index `i` should be a value between 0 and `nconv`-1 (see `SVDGetConverged()`). | ||
| 314 | Singular triplets are indexed according to the ordering criterion established | ||
| 315 | with `SVDSetWhichSingularTriplets()`. | ||
| 316 | |||
| 317 | In the case of GSVD, the solution consists in three vectors $u$, $v$, $x$ that are | ||
| 318 | returned as follows. Vector $x$ is returned in the right singular vector | ||
| 319 | (argument `v`) and has length equal to the number of columns of $A$ and $B$. | ||
| 320 | The other two vectors are returned stacked on top of each other $[u^*,v^*]^*$ in | ||
| 321 | the left singular vector argument `u`, with length equal to $m+n$ (number of rows | ||
| 322 | of $A$ plus number of rows of $B$). | ||
| 323 | |||
| 324 | Level: beginner | ||
| 325 | |||
| 326 | .seealso: [](ch:svd), `SVDSolve()`, `SVDGetConverged()`, `SVDSetWhichSingularTriplets()` | ||
| 327 | @*/ | ||
| 328 | 35257 | PetscErrorCode SVDGetSingularTriplet(SVD svd,PetscInt i,PetscReal *sigma,Vec u,Vec v) | |
| 329 | { | ||
| 330 | 35257 | PetscInt M,N; | |
| 331 | 35257 | Vec w; | |
| 332 | |||
| 333 |
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35257 | PetscFunctionBegin; |
| 334 |
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35257 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 335 |
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35257 | PetscValidLogicalCollectiveInt(svd,i,2); |
| 336 |
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35257 | SVDCheckSolved(svd,1); |
| 337 |
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35257 | if (u) { PetscValidHeaderSpecific(u,VEC_CLASSID,4); PetscCheckSameComm(svd,1,u,4); } |
| 338 |
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35257 | if (v) { PetscValidHeaderSpecific(v,VEC_CLASSID,5); PetscCheckSameComm(svd,1,v,5); } |
| 339 |
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35257 | PetscCheck(i>=0,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 340 |
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35257 | PetscCheck(i<svd->nconv,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see SVDGetConverged()"); |
| 341 |
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35257 | if (sigma) *sigma = svd->sigma[svd->perm[i]]; |
| 342 |
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35257 | if (u || v) { |
| 343 |
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24264 | if (!svd->isgeneralized) { |
| 344 |
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18217 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 345 |
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18217 | if (M<N) { w = u; u = v; v = w; } |
| 346 | } | ||
| 347 |
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24264 | PetscCall(SVDComputeVectors(svd)); |
| 348 |
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24264 | if (u) PetscCall(BVCopyVec(svd->U,svd->perm[i],u)); |
| 349 |
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24264 | if (v) PetscCall(BVCopyVec(svd->V,svd->perm[i],v)); |
| 350 | } | ||
| 351 |
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7801 | PetscFunctionReturn(PETSC_SUCCESS); |
| 352 | } | ||
| 353 | |||
| 354 | /* | ||
| 355 | SVDComputeResidualNorms_Standard - Computes the norms of the left and | ||
| 356 | right residuals associated with the i-th computed singular triplet. | ||
| 357 | |||
| 358 | Input Parameters: | ||
| 359 | sigma - singular value | ||
| 360 | u,v - singular vectors | ||
| 361 | x,y - two work vectors with the same dimensions as u,v | ||
| 362 | */ | ||
| 363 | 5908 | static PetscErrorCode SVDComputeResidualNorms_Standard(SVD svd,PetscReal sigma,Vec u,Vec v,Vec x,Vec y,PetscReal *norm1,PetscReal *norm2) | |
| 364 | { | ||
| 365 | 5908 | PetscInt M,N; | |
| 366 | |||
| 367 |
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5908 | PetscFunctionBegin; |
| 368 | /* norm1 = ||A*v-sigma*u||_2 */ | ||
| 369 |
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5908 | if (norm1) { |
| 370 |
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5908 | PetscCall(MatMult(svd->OP,v,x)); |
| 371 |
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5908 | PetscCall(VecAXPY(x,-sigma,u)); |
| 372 |
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5908 | PetscCall(VecNorm(x,NORM_2,norm1)); |
| 373 | } | ||
| 374 | /* norm2 = ||A^T*u-sigma*v||_2 */ | ||
| 375 |
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5908 | if (norm2) { |
| 376 |
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5908 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 377 |
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5908 | if (M<N) PetscCall(MatMult(svd->A,u,y)); |
| 378 |
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5181 | else PetscCall(MatMult(svd->AT,u,y)); |
| 379 |
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5908 | PetscCall(VecAXPY(y,-sigma,v)); |
| 380 |
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5908 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 381 | } | ||
| 382 |
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927 | PetscFunctionReturn(PETSC_SUCCESS); |
| 383 | } | ||
| 384 | |||
| 385 | /* | ||
| 386 | SVDComputeResidualNorms_Generalized - In GSVD, compute the residual norms | ||
| 387 | norm1 = ||s^2*A'*u-c*B'*B*x||_2 and norm2 = ||c^2*B'*v-s*A'*A*x||_2. | ||
| 388 | |||
| 389 | Input Parameters: | ||
| 390 | sigma - singular value | ||
| 391 | uv - left singular vectors [u;v] | ||
| 392 | x - right singular vector | ||
| 393 | y,z - two work vectors with the same dimension as x | ||
| 394 | */ | ||
| 395 | 4077 | static PetscErrorCode SVDComputeResidualNorms_Generalized(SVD svd,PetscReal sigma,Vec uv,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2) | |
| 396 | { | ||
| 397 | 4077 | Vec u,v,ax,bx,nest,aux[2]; | |
| 398 | 4077 | PetscReal c,s; | |
| 399 | |||
| 400 |
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4077 | PetscFunctionBegin; |
| 401 |
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4077 | PetscCall(MatCreateVecs(svd->OP,NULL,&u)); |
| 402 |
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4077 | PetscCall(MatCreateVecs(svd->OPb,NULL,&v)); |
| 403 | 4077 | aux[0] = u; | |
| 404 | 4077 | aux[1] = v; | |
| 405 |
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4077 | PetscCall(VecCreateNest(PetscObjectComm((PetscObject)svd),2,NULL,aux,&nest)); |
| 406 |
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4077 | PetscCall(VecCopy(uv,nest)); |
| 407 | |||
| 408 | 4077 | s = 1.0/PetscSqrtReal(1.0+sigma*sigma); | |
| 409 | 4077 | c = sigma*s; | |
| 410 | |||
| 411 | /* norm1 = ||s^2*A'*u-c*B'*B*x||_2 */ | ||
| 412 |
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4077 | if (norm1) { |
| 413 |
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4077 | PetscCall(VecDuplicate(v,&bx)); |
| 414 |
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4077 | PetscCall(MatMultHermitianTranspose(svd->OP,u,z)); |
| 415 |
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4077 | PetscCall(MatMult(svd->OPb,x,bx)); |
| 416 |
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4077 | PetscCall(MatMultHermitianTranspose(svd->OPb,bx,y)); |
| 417 |
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4077 | PetscCall(VecAXPBY(y,s*s,-c,z)); |
| 418 |
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4077 | PetscCall(VecNorm(y,NORM_2,norm1)); |
| 419 |
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4077 | PetscCall(VecDestroy(&bx)); |
| 420 | } | ||
| 421 | /* norm2 = ||c^2*B'*v-s*A'*A*x||_2 */ | ||
| 422 |
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4077 | if (norm2) { |
| 423 |
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4077 | PetscCall(VecDuplicate(u,&ax)); |
| 424 |
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4077 | PetscCall(MatMultHermitianTranspose(svd->OPb,v,z)); |
| 425 |
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4077 | PetscCall(MatMult(svd->OP,x,ax)); |
| 426 |
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4077 | PetscCall(MatMultHermitianTranspose(svd->OP,ax,y)); |
| 427 |
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4077 | PetscCall(VecAXPBY(y,c*c,-s,z)); |
| 428 |
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4077 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 429 |
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4077 | PetscCall(VecDestroy(&ax)); |
| 430 | } | ||
| 431 | |||
| 432 |
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4077 | PetscCall(VecDestroy(&v)); |
| 433 |
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4077 | PetscCall(VecDestroy(&u)); |
| 434 |
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4077 | PetscCall(VecDestroy(&nest)); |
| 435 |
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807 | PetscFunctionReturn(PETSC_SUCCESS); |
| 436 | } | ||
| 437 | |||
| 438 | /* | ||
| 439 | SVDComputeResidualNorms_Hyperbolic - Computes the norms of the left and | ||
| 440 | right residuals associated with the i-th computed singular triplet. | ||
| 441 | |||
| 442 | Input Parameters: | ||
| 443 | sigma - singular value | ||
| 444 | sign - corresponding element of the signature Omega2 | ||
| 445 | u,v - singular vectors | ||
| 446 | x,y,z - three work vectors with the same dimensions as u,v,u | ||
| 447 | */ | ||
| 448 | 4166 | static PetscErrorCode SVDComputeResidualNorms_Hyperbolic(SVD svd,PetscReal sigma,PetscReal sign,Vec u,Vec v,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2) | |
| 449 | { | ||
| 450 | 4166 | PetscInt M,N; | |
| 451 | |||
| 452 |
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4166 | PetscFunctionBegin; |
| 453 | /* norm1 = ||A*v-sigma*u||_2 */ | ||
| 454 |
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4166 | if (norm1) { |
| 455 |
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4166 | PetscCall(MatMult(svd->OP,v,x)); |
| 456 |
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4166 | PetscCall(VecAXPY(x,-sigma,u)); |
| 457 |
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4166 | PetscCall(VecNorm(x,NORM_2,norm1)); |
| 458 | } | ||
| 459 | /* norm2 = ||A^T*Omega*u-sigma*sign*v||_2 */ | ||
| 460 |
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4166 | if (norm2) { |
| 461 |
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4166 | PetscCall(MatGetSize(svd->OP,&M,&N)); |
| 462 |
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4166 | PetscCall(VecPointwiseMult(z,u,svd->omega)); |
| 463 |
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4166 | if (M<N) PetscCall(MatMult(svd->A,z,y)); |
| 464 |
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3878 | else PetscCall(MatMult(svd->AT,z,y)); |
| 465 |
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4166 | PetscCall(VecAXPY(y,-sigma*sign,v)); |
| 466 |
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4166 | PetscCall(VecNorm(y,NORM_2,norm2)); |
| 467 | } | ||
| 468 |
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1274 | PetscFunctionReturn(PETSC_SUCCESS); |
| 469 | } | ||
| 470 | |||
| 471 | /*@ | ||
| 472 | SVDComputeError - Computes the error (based on the residual norm) associated | ||
| 473 | with the `i`-th singular triplet. | ||
| 474 | |||
| 475 | Collective | ||
| 476 | |||
| 477 | Input Parameters: | ||
| 478 | + svd - the singular value solver context | ||
| 479 | . i - the solution index | ||
| 480 | - type - the type of error to compute, see `SVDErrorType` | ||
| 481 | |||
| 482 | Output Parameter: | ||
| 483 | . error - the error | ||
| 484 | |||
| 485 | Notes: | ||
| 486 | The error can be computed in various ways, all of them based on the residual | ||
| 487 | norm obtained as $\sqrt{\eta_1^2+\eta_2^2}$ with $\eta_1 = \|Av-\sigma u\|_2$ and | ||
| 488 | $\eta_2 = \|A^*u-\sigma v\|_2$, where $(\sigma,u,v)$ is the approximate singular | ||
| 489 | triplet. | ||
| 490 | |||
| 491 | In the case of the GSVD, the two components of the residual norm are | ||
| 492 | $\eta_1 = \|s^2 A^*u-cB^*Bx\|_2$ and $\eta_2 = ||c^2 B^*v-sA^*Ax||_2$, where | ||
| 493 | $(\sigma,u,v,x)$ is the approximate generalized singular quadruple, with | ||
| 494 | $\sigma=c/s$. | ||
| 495 | |||
| 496 | Level: beginner | ||
| 497 | |||
| 498 | .seealso: [](ch:svd), `SVDErrorType`, `SVDSolve()` | ||
| 499 | @*/ | ||
| 500 | 14151 | PetscErrorCode SVDComputeError(SVD svd,PetscInt i,SVDErrorType type,PetscReal *error) | |
| 501 | { | ||
| 502 | 14151 | PetscReal sigma,norm1,norm2,c,s; | |
| 503 | 14151 | Vec u=NULL,v=NULL,x=NULL,y=NULL,z=NULL; | |
| 504 | 14151 | PetscReal vecnorm=1.0; | |
| 505 | |||
| 506 |
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14151 | PetscFunctionBegin; |
| 507 |
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14151 | PetscValidHeaderSpecific(svd,SVD_CLASSID,1); |
| 508 |
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14151 | PetscValidLogicalCollectiveInt(svd,i,2); |
| 509 |
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14151 | PetscValidLogicalCollectiveEnum(svd,type,3); |
| 510 |
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14151 | PetscAssertPointer(error,4); |
| 511 |
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14151 | SVDCheckSolved(svd,1); |
| 512 | |||
| 513 | /* allocate work vectors */ | ||
| 514 |
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14151 | switch (svd->problem_type) { |
| 515 | 5908 | case SVD_STANDARD: | |
| 516 |
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5908 | PetscCall(SVDSetWorkVecs(svd,2,2)); |
| 517 | 5908 | u = svd->workl[0]; | |
| 518 | 5908 | v = svd->workr[0]; | |
| 519 | 5908 | x = svd->workl[1]; | |
| 520 | 5908 | y = svd->workr[1]; | |
| 521 | 5908 | break; | |
| 522 | 4077 | case SVD_GENERALIZED: | |
| 523 |
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4077 | PetscCall(SVDSetWorkVecs(svd,1,3)); |
| 524 | 4077 | u = svd->workl[0]; | |
| 525 | 4077 | v = svd->workr[0]; | |
| 526 | 4077 | x = svd->workr[1]; | |
| 527 | 4077 | y = svd->workr[2]; | |
| 528 | 4077 | break; | |
| 529 | 4166 | case SVD_HYPERBOLIC: | |
| 530 |
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4166 | PetscCall(SVDSetWorkVecs(svd,3,2)); |
| 531 | 4166 | u = svd->workl[0]; | |
| 532 | 4166 | v = svd->workr[0]; | |
| 533 | 4166 | x = svd->workl[1]; | |
| 534 | 4166 | y = svd->workr[1]; | |
| 535 | 4166 | z = svd->workl[2]; | |
| 536 | 4166 | break; | |
| 537 | } | ||
| 538 | |||
| 539 | /* compute residual norm */ | ||
| 540 |
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14151 | PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v)); |
| 541 |
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14151 | switch (svd->problem_type) { |
| 542 | 5908 | case SVD_STANDARD: | |
| 543 |
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5908 | PetscCall(SVDComputeResidualNorms_Standard(svd,sigma,u,v,x,y,&norm1,&norm2)); |
| 544 | break; | ||
| 545 | 4077 | case SVD_GENERALIZED: | |
| 546 |
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4077 | PetscCall(SVDComputeResidualNorms_Generalized(svd,sigma,u,v,x,y,&norm1,&norm2)); |
| 547 | break; | ||
| 548 | 4166 | case SVD_HYPERBOLIC: | |
| 549 |
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4166 | PetscCall(SVDComputeResidualNorms_Hyperbolic(svd,sigma,svd->sign[svd->perm[i]],u,v,x,y,z,&norm1,&norm2)); |
| 550 | break; | ||
| 551 | } | ||
| 552 | 14151 | *error = SlepcAbs(norm1,norm2); | |
| 553 | |||
| 554 | /* compute 2-norm of eigenvector of the cyclic form */ | ||
| 555 |
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14151 | if (type!=SVD_ERROR_ABSOLUTE) { |
| 556 |
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14017 | switch (svd->problem_type) { |
| 557 | 5774 | case SVD_STANDARD: | |
| 558 | 5774 | vecnorm = PETSC_SQRT2; | |
| 559 | 5774 | break; | |
| 560 | 4077 | case SVD_GENERALIZED: | |
| 561 |
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4077 | PetscCall(VecNorm(v,NORM_2,&vecnorm)); |
| 562 | 4077 | vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm); | |
| 563 | 4077 | break; | |
| 564 | 4166 | case SVD_HYPERBOLIC: | |
| 565 |
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4166 | PetscCall(VecNorm(u,NORM_2,&vecnorm)); |
| 566 | 4166 | vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm); | |
| 567 | 4166 | break; | |
| 568 | } | ||
| 569 | 13 | } | |
| 570 | |||
| 571 | /* compute error */ | ||
| 572 |
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14030 | switch (type) { |
| 573 | case SVD_ERROR_ABSOLUTE: | ||
| 574 | break; | ||
| 575 | 5700 | case SVD_ERROR_RELATIVE: | |
| 576 |
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5700 | if (svd->isgeneralized) { |
| 577 | ✗ | s = 1.0/PetscSqrtReal(1.0+sigma*sigma); | |
| 578 | ✗ | c = sigma*s; | |
| 579 | ✗ | norm1 /= c*vecnorm; | |
| 580 | ✗ | norm2 /= s*vecnorm; | |
| 581 | ✗ | *error = PetscMax(norm1,norm2); | |
| 582 | 5700 | } else *error /= sigma*vecnorm; | |
| 583 | break; | ||
| 584 | 8317 | case SVD_ERROR_NORM: | |
| 585 |
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8317 | if (!svd->nrma) PetscCall(MatNorm(svd->OP,NORM_INFINITY,&svd->nrma)); |
| 586 |
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8317 | if (svd->isgeneralized && !svd->nrmb) PetscCall(MatNorm(svd->OPb,NORM_INFINITY,&svd->nrmb)); |
| 587 |
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8317 | *error /= PetscMax(svd->nrma,svd->nrmb)*vecnorm; |
| 588 | 8317 | break; | |
| 589 | ✗ | default: | |
| 590 | − | SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 591 | } | ||
| 592 |
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3008 | PetscFunctionReturn(PETSC_SUCCESS); |
| 593 | } | ||
| 594 |