| 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 | BV routines related to Krylov decompositions | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/bvimpl.h> /*I "slepcbv.h" I*/ | ||
| 15 | |||
| 16 | /*@ | ||
| 17 | BVMatArnoldi - Computes an Arnoldi factorization associated with a matrix. | ||
| 18 | |||
| 19 | Collective | ||
| 20 | |||
| 21 | Input Parameters: | ||
| 22 | + V - basis vectors context | ||
| 23 | . A - the matrix | ||
| 24 | . H - (optional) the upper Hessenberg matrix | ||
| 25 | . k - number of locked columns | ||
| 26 | - m - dimension of the Arnoldi basis, may be modified | ||
| 27 | |||
| 28 | Output Parameters: | ||
| 29 | + beta - (optional) norm of last vector before normalization | ||
| 30 | - breakdown - (optional) flag indicating that breakdown occurred | ||
| 31 | |||
| 32 | Notes: | ||
| 33 | Computes an m-step Arnoldi factorization for matrix A. The first k columns | ||
| 34 | are assumed to be locked and therefore they are not modified. On exit, the | ||
| 35 | following relation is satisfied | ||
| 36 | |||
| 37 | $ A * V - V * H = beta*v_m * e_m^T | ||
| 38 | |||
| 39 | where the columns of V are the Arnoldi vectors (which are orthonormal), H is | ||
| 40 | an upper Hessenberg matrix, e_m is the m-th vector of the canonical basis. | ||
| 41 | On exit, beta contains the norm of V[m] before normalization. | ||
| 42 | |||
| 43 | The breakdown flag indicates that orthogonalization failed, see | ||
| 44 | BVOrthonormalizeColumn(). In that case, on exit m contains the index of | ||
| 45 | the column that failed. | ||
| 46 | |||
| 47 | The values of k and m are not restricted to the active columns of V. | ||
| 48 | |||
| 49 | To create an Arnoldi factorization from scratch, set k=0 and make sure the | ||
| 50 | first column contains the normalized initial vector. | ||
| 51 | |||
| 52 | Level: advanced | ||
| 53 | |||
| 54 | .seealso: BVMatLanczos(), BVSetActiveColumns(), BVOrthonormalizeColumn() | ||
| 55 | @*/ | ||
| 56 | 26341 | PetscErrorCode BVMatArnoldi(BV V,Mat A,Mat H,PetscInt k,PetscInt *m,PetscReal *beta,PetscBool *breakdown) | |
| 57 | { | ||
| 58 | 26341 | PetscScalar *h; | |
| 59 | 26341 | const PetscScalar *a; | |
| 60 | 26341 | PetscInt j,ldh,rows,cols; | |
| 61 | 26341 | PetscBool lindep=PETSC_FALSE; | |
| 62 | 26341 | Vec buf; | |
| 63 | |||
| 64 |
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26341 | PetscFunctionBegin; |
| 65 |
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26341 | PetscValidHeaderSpecific(V,BV_CLASSID,1); |
| 66 |
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26341 | PetscValidHeaderSpecific(A,MAT_CLASSID,2); |
| 67 |
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26341 | PetscValidLogicalCollectiveInt(V,k,4); |
| 68 |
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26341 | PetscAssertPointer(m,5); |
| 69 |
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26341 | PetscValidLogicalCollectiveInt(V,*m,5); |
| 70 |
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26341 | PetscValidType(V,1); |
| 71 |
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26341 | BVCheckSizes(V,1); |
| 72 |
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26341 | PetscValidType(A,2); |
| 73 |
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26341 | PetscCheckSameComm(V,1,A,2); |
| 74 | |||
| 75 |
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26341 | PetscCheck(k>=0 && k<=V->m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument k has wrong value %" PetscInt_FMT ", should be between 0 and %" PetscInt_FMT,k,V->m); |
| 76 |
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26341 | PetscCheck(*m>0 && *m<=V->m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument m has wrong value %" PetscInt_FMT ", should be between 1 and %" PetscInt_FMT,*m,V->m); |
| 77 |
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26341 | PetscCheck(*m>k,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument m should be at least equal to k+1"); |
| 78 |
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26341 | if (H) { |
| 79 |
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26341 | PetscValidHeaderSpecific(H,MAT_CLASSID,3); |
| 80 |
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26341 | PetscValidType(H,3); |
| 81 |
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26341 | PetscCheckTypeName(H,MATSEQDENSE); |
| 82 |
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26341 | PetscCall(MatGetSize(H,&rows,&cols)); |
| 83 |
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26341 | PetscCall(MatDenseGetLDA(H,&ldh)); |
| 84 |
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26341 | PetscCheck(rows>=*m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Matrix H has %" PetscInt_FMT " rows, should have at least %" PetscInt_FMT,rows,*m); |
| 85 |
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26341 | PetscCheck(cols>=*m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Matrix H has %" PetscInt_FMT " columns, should have at least %" PetscInt_FMT,cols,*m); |
| 86 | } | ||
| 87 | |||
| 88 |
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407188 | for (j=k;j<*m;j++) { |
| 89 |
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381363 | PetscCall(BVMatMultColumn(V,A,j)); |
| 90 |
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381363 | if (PetscUnlikely(j==V->N-1)) PetscCall(BV_OrthogonalizeColumn_Safe(V,j+1,NULL,beta,&lindep)); /* safeguard in case the full basis is requested */ |
| 91 |
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381055 | else PetscCall(BVOrthonormalizeColumn(V,j+1,PETSC_FALSE,beta,&lindep)); |
| 92 |
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381363 | if (PetscUnlikely(lindep)) { |
| 93 | 516 | *m = j+1; | |
| 94 | 516 | break; | |
| 95 | } | ||
| 96 | } | ||
| 97 |
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26341 | if (breakdown) *breakdown = lindep; |
| 98 |
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26341 | if (lindep) PetscCall(PetscInfo(V,"Arnoldi finished early at m=%" PetscInt_FMT "\n",*m)); |
| 99 | |||
| 100 |
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26341 | if (H) { |
| 101 |
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26341 | PetscCall(MatDenseGetArray(H,&h)); |
| 102 |
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26341 | PetscCall(BVGetBufferVec(V,&buf)); |
| 103 |
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26341 | PetscCall(VecGetArrayRead(buf,&a)); |
| 104 |
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381363 | for (j=k;j<*m-1;j++) PetscCall(PetscArraycpy(h+j*ldh,a+V->nc+(j+1)*(V->nc+V->m),j+2)); |
| 105 |
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26341 | PetscCall(PetscArraycpy(h+(*m-1)*ldh,a+V->nc+(*m)*(V->nc+V->m),*m)); |
| 106 |
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26341 | if (ldh>*m) h[(*m)+(*m-1)*ldh] = a[V->nc+(*m)+(*m)*(V->nc+V->m)]; |
| 107 |
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26341 | PetscCall(VecRestoreArrayRead(buf,&a)); |
| 108 |
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26341 | PetscCall(MatDenseRestoreArray(H,&h)); |
| 109 | } | ||
| 110 | |||
| 111 |
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26341 | PetscCall(PetscObjectStateIncrease((PetscObject)V)); |
| 112 |
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26341 | PetscFunctionReturn(PETSC_SUCCESS); |
| 113 | } | ||
| 114 | |||
| 115 | /*@ | ||
| 116 | BVMatLanczos - Computes a Lanczos factorization associated with a matrix. | ||
| 117 | |||
| 118 | Collective | ||
| 119 | |||
| 120 | Input Parameters: | ||
| 121 | + V - basis vectors context | ||
| 122 | . A - the matrix | ||
| 123 | . T - (optional) the tridiagonal matrix | ||
| 124 | . k - number of locked columns | ||
| 125 | - m - dimension of the Lanczos basis, may be modified | ||
| 126 | |||
| 127 | Output Parameters: | ||
| 128 | + beta - (optional) norm of last vector before normalization | ||
| 129 | - breakdown - (optional) flag indicating that breakdown occurred | ||
| 130 | |||
| 131 | Notes: | ||
| 132 | Computes an m-step Lanczos factorization for matrix A, with full | ||
| 133 | reorthogonalization. At each Lanczos step, the corresponding Lanczos | ||
| 134 | vector is orthogonalized with respect to all previous Lanczos vectors. | ||
| 135 | This is equivalent to computing an m-step Arnoldi factorization and | ||
| 136 | exploting symmetry of the operator. | ||
| 137 | |||
| 138 | The first k columns are assumed to be locked and therefore they are | ||
| 139 | not modified. On exit, the following relation is satisfied | ||
| 140 | |||
| 141 | $ A * V - V * T = beta*v_m * e_m^T | ||
| 142 | |||
| 143 | where the columns of V are the Lanczos vectors (which are B-orthonormal), | ||
| 144 | T is a real symmetric tridiagonal matrix, and e_m is the m-th vector of | ||
| 145 | the canonical basis. On exit, beta contains the B-norm of V[m] before | ||
| 146 | normalization. The T matrix is stored in a special way, its first column | ||
| 147 | contains the diagonal elements, and its second column the off-diagonal | ||
| 148 | ones. In complex scalars, the elements are stored as PetscReal and thus | ||
| 149 | occupy only the first column of the Mat object. This is the same storage | ||
| 150 | scheme used in matrix DS_MAT_T obtained with DSGetMat(). | ||
| 151 | |||
| 152 | The breakdown flag indicates that orthogonalization failed, see | ||
| 153 | BVOrthonormalizeColumn(). In that case, on exit m contains the index of | ||
| 154 | the column that failed. | ||
| 155 | |||
| 156 | The values of k and m are not restricted to the active columns of V. | ||
| 157 | |||
| 158 | To create a Lanczos factorization from scratch, set k=0 and make sure the | ||
| 159 | first column contains the normalized initial vector. | ||
| 160 | |||
| 161 | Level: advanced | ||
| 162 | |||
| 163 | .seealso: BVMatArnoldi(), BVSetActiveColumns(), BVOrthonormalizeColumn(), DSGetMat() | ||
| 164 | @*/ | ||
| 165 | 23395 | PetscErrorCode BVMatLanczos(BV V,Mat A,Mat T,PetscInt k,PetscInt *m,PetscReal *beta,PetscBool *breakdown) | |
| 166 | { | ||
| 167 | 23395 | PetscScalar *t; | |
| 168 | 23395 | const PetscScalar *a; | |
| 169 | 23395 | PetscReal *alpha,*betat; | |
| 170 | 23395 | PetscInt j,ldt,rows,cols,mincols=PetscDefined(USE_COMPLEX)?1:2; | |
| 171 | 23395 | PetscBool lindep=PETSC_FALSE; | |
| 172 | 23395 | Vec buf; | |
| 173 | |||
| 174 |
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23395 | PetscFunctionBegin; |
| 175 |
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23395 | PetscValidHeaderSpecific(V,BV_CLASSID,1); |
| 176 |
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23395 | PetscValidHeaderSpecific(A,MAT_CLASSID,2); |
| 177 |
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23395 | PetscValidLogicalCollectiveInt(V,k,4); |
| 178 |
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23395 | PetscAssertPointer(m,5); |
| 179 |
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23395 | PetscValidLogicalCollectiveInt(V,*m,5); |
| 180 |
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23395 | PetscValidType(V,1); |
| 181 |
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23395 | BVCheckSizes(V,1); |
| 182 |
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23395 | PetscValidType(A,2); |
| 183 |
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23395 | PetscCheckSameComm(V,1,A,2); |
| 184 | |||
| 185 |
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23395 | PetscCheck(k>=0 || k<=V->m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument k has wrong value %" PetscInt_FMT ", should be between 0 and %" PetscInt_FMT,k,V->m); |
| 186 |
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23395 | PetscCheck(*m>0 || *m<=V->m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument m has wrong value %" PetscInt_FMT ", should be between 1 and %" PetscInt_FMT,*m,V->m); |
| 187 |
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23395 | PetscCheck(*m>k,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_OUTOFRANGE,"Argument m should be at least equal to k+1"); |
| 188 |
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23395 | if (T) { |
| 189 |
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23395 | PetscValidHeaderSpecific(T,MAT_CLASSID,3); |
| 190 |
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23395 | PetscValidType(T,3); |
| 191 |
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23395 | PetscCheckTypeName(T,MATSEQDENSE); |
| 192 |
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23395 | PetscCall(MatGetSize(T,&rows,&cols)); |
| 193 |
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23395 | PetscCall(MatDenseGetLDA(T,&ldt)); |
| 194 |
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23395 | PetscCheck(rows>=*m,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Matrix T has %" PetscInt_FMT " rows, should have at least %" PetscInt_FMT,rows,*m); |
| 195 |
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23395 | PetscCheck(cols>=mincols,PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Matrix T has %" PetscInt_FMT " columns, should have at least %" PetscInt_FMT,cols,mincols); |
| 196 | } | ||
| 197 | |||
| 198 |
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278389 | for (j=k;j<*m;j++) { |
| 199 |
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255194 | PetscCall(BVMatMultColumn(V,A,j)); |
| 200 |
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255194 | if (PetscUnlikely(j==V->N-1)) PetscCall(BV_OrthogonalizeColumn_Safe(V,j+1,NULL,beta,&lindep)); /* safeguard in case the full basis is requested */ |
| 201 |
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254994 | else PetscCall(BVOrthonormalizeColumn(V,j+1,PETSC_FALSE,beta,&lindep)); |
| 202 |
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255194 | if (PetscUnlikely(lindep)) { |
| 203 | 200 | *m = j+1; | |
| 204 | 200 | break; | |
| 205 | } | ||
| 206 | } | ||
| 207 |
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23395 | if (breakdown) *breakdown = lindep; |
| 208 |
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23395 | if (lindep) PetscCall(PetscInfo(V,"Lanczos finished early at m=%" PetscInt_FMT "\n",*m)); |
| 209 | |||
| 210 |
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23395 | if (T) { |
| 211 |
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23395 | PetscCall(MatDenseGetArray(T,&t)); |
| 212 | 23395 | alpha = (PetscReal*)t; | |
| 213 | 23395 | betat = alpha+ldt; | |
| 214 |
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23395 | PetscCall(BVGetBufferVec(V,&buf)); |
| 215 |
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23395 | PetscCall(VecGetArrayRead(buf,&a)); |
| 216 |
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278589 | for (j=k;j<*m;j++) { |
| 217 | 255194 | alpha[j] = PetscRealPart(a[V->nc+j+(j+1)*(V->nc+V->m)]); | |
| 218 | 255194 | betat[j] = PetscRealPart(a[V->nc+j+1+(j+1)*(V->nc+V->m)]); | |
| 219 | } | ||
| 220 |
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23395 | PetscCall(VecRestoreArrayRead(buf,&a)); |
| 221 |
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23395 | PetscCall(MatDenseRestoreArray(T,&t)); |
| 222 | } | ||
| 223 | |||
| 224 |
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23395 | PetscCall(PetscObjectStateIncrease((PetscObject)V)); |
| 225 |
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23395 | PetscFunctionReturn(PETSC_SUCCESS); |
| 226 | } | ||
| 227 |