| 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 | SLEPc eigensolver: "krylovschur" | ||
| 12 | |||
| 13 | Method: thick-restarted Lanczos for Linear Response eigenvalue problems | ||
| 14 | |||
| 15 | References: | ||
| 16 | |||
| 17 | [1] Z. Teng, R.-C. Li, "Convergence analysis of Lanczos-type methods for the | ||
| 18 | linear response eigenvalue problem", J. Comput. Appl. Math. 247, 2013. | ||
| 19 | |||
| 20 | [2] F. Alvarruiz, B. Mellado-Pinto, J. E. Roman, "Restarted Lanczos methods | ||
| 21 | for the linear response eigenvalue problem", in preparation, 2026. | ||
| 22 | |||
| 23 | */ | ||
| 24 | #include <slepc/private/epsimpl.h> | ||
| 25 | #include "krylovschur.h" | ||
| 26 | |||
| 27 | 7948 | static PetscErrorCode Orthog_Teng(Vec x,BV U,BV V,PetscInt j,PetscScalar *h,PetscScalar *c,PetscBool *breakdown) | |
| 28 | { | ||
| 29 | 7948 | PetscInt i; | |
| 30 | |||
| 31 |
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7948 | PetscFunctionBegin; |
| 32 |
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7948 | PetscCall(BVSetActiveColumns(U,0,j)); |
| 33 |
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7948 | PetscCall(BVSetActiveColumns(V,0,j)); |
| 34 | /* c = U^* x */ | ||
| 35 |
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7948 | PetscCall(BVDotVec(U,x,c)); |
| 36 | /* x = x-V*c */ | ||
| 37 |
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7948 | PetscCall(BVMultVec(V,-1.0,1.0,x,c)); |
| 38 | /* accumulate orthog coeffs into h */ | ||
| 39 |
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166936 | for (i=0;i<2*j;i++) h[i] += c[i]; |
| 40 |
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1436 | PetscFunctionReturn(PETSC_SUCCESS); |
| 41 | } | ||
| 42 | |||
| 43 | /* Orthogonalize vector x against first j vectors in U and V | ||
| 44 | v is column j-1 of V */ | ||
| 45 | 7948 | static PetscErrorCode OrthogonalizeVector_Teng(Vec x,BV U,BV V,PetscInt j,Vec u,PetscReal *beta,PetscInt k,PetscScalar *h,PetscBool *breakdown) | |
| 46 | { | ||
| 47 | 7948 | PetscReal alpha; | |
| 48 | 7948 | PetscInt i,l; | |
| 49 | |||
| 50 |
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7948 | PetscFunctionBegin; |
| 51 |
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7948 | PetscCall(PetscArrayzero(h,2*j)); |
| 52 | |||
| 53 | /* Local orthogonalization */ | ||
| 54 |
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7948 | l = j==k+1?0:j-2; /* 1st column to orthogonalize against */ |
| 55 |
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7948 | PetscCall(VecDotRealPart(x,u,&alpha)); |
| 56 |
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21568 | for (i=l;i<j-1;i++) h[i] = beta[i]; |
| 57 | 7948 | h[j-1] = alpha; | |
| 58 | /* x = x-V(:,l:j-1)*h(l:j-1) */ | ||
| 59 |
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7948 | PetscCall(BVSetActiveColumns(V,l,j)); |
| 60 |
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7948 | PetscCall(BVMultVec(V,-1.0,1.0,x,h+l)); |
| 61 | |||
| 62 | /* Full orthogonalization */ | ||
| 63 |
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7948 | PetscCall(Orthog_Teng(x,U,V,j,h,h+2*j,breakdown)); |
| 64 |
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1436 | PetscFunctionReturn(PETSC_SUCCESS); |
| 65 | } | ||
| 66 | |||
| 67 | 1132 | static PetscErrorCode EPSLREPLanczos_Teng(EPS eps,Mat K,Mat M,BV U,BV V,PetscReal *alpha,PetscReal *beta,PetscInt k,PetscInt *min,PetscBool *breakdown) | |
| 68 | { | ||
| 69 | 1132 | PetscInt j,m = *min; | |
| 70 | 1132 | Vec u,v,uh,vh; | |
| 71 | 1132 | PetscReal beta0; | |
| 72 | 1132 | PetscScalar *hwork,lhwork[100],gamma; | |
| 73 | |||
| 74 |
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1132 | PetscFunctionBegin; |
| 75 |
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1132 | if (4*m > 100) PetscCall(PetscMalloc1(4*m,&hwork)); |
| 76 | 1132 | else hwork = lhwork; | |
| 77 | |||
| 78 | /* Normalize initial vector */ | ||
| 79 |
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1132 | if (k==0) { |
| 80 |
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154 | if (eps->nini==0) PetscCall(BVSetRandomColumn(V,0)); |
| 81 |
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154 | PetscCall(BVGetColumn(U,0,&u)); |
| 82 |
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154 | PetscCall(BVGetColumn(V,0,&v)); |
| 83 |
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154 | PetscCall(MatMult(M,v,u)); |
| 84 |
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154 | PetscCall(VecDot(u,v,&gamma)); |
| 85 | 154 | beta0 = PetscSqrtReal(PetscRealPart(gamma)); /* TODO check beta_0=0 */ | |
| 86 |
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154 | PetscCall(VecScale(u,1.0/beta0)); |
| 87 |
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154 | PetscCall(VecScale(v,1.0/beta0)); |
| 88 |
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154 | PetscCall(BVRestoreColumn(U,0,&u)); |
| 89 |
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154 | PetscCall(BVRestoreColumn(V,0,&v)); |
| 90 | } | ||
| 91 | |||
| 92 |
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9080 | for (j=k;j<m;j++) { |
| 93 | /* j+1 columns (indices 0 to j) have been computed */ | ||
| 94 |
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7948 | PetscCall(BVGetColumn(U,j+1,&uh)); |
| 95 |
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7948 | PetscCall(BVGetColumn(V,j+1,&vh)); |
| 96 |
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7948 | PetscCall(BVGetColumn(U,j,&u)); |
| 97 |
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7948 | PetscCall(MatMult(K,u,vh)); |
| 98 |
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7948 | PetscCall(OrthogonalizeVector_Teng(vh,U,V,j+1,u,beta,k,hwork,breakdown)); |
| 99 | 7948 | alpha[j] = PetscRealPart(hwork[j]); | |
| 100 |
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7948 | PetscCall(MatMult(M,vh,uh)); |
| 101 |
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7948 | PetscCall(VecDot(uh,vh,&gamma)); |
| 102 | 7948 | beta[j] = PetscSqrtReal(PetscRealPart(gamma)); /* TODO check beta_j=0 */ | |
| 103 |
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7948 | PetscCall(VecScale(uh,1.0/beta[j])); |
| 104 |
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7948 | PetscCall(VecScale(vh,1.0/beta[j])); |
| 105 |
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7948 | PetscCall(BVRestoreColumn(U,j+1,&uh)); |
| 106 |
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7948 | PetscCall(BVRestoreColumn(V,j+1,&vh)); |
| 107 |
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7948 | PetscCall(BVRestoreColumn(U,j,&u)); |
| 108 | } | ||
| 109 |
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1132 | if (4*m > 100) PetscCall(PetscFree(hwork)); |
| 110 |
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212 | PetscFunctionReturn(PETSC_SUCCESS); |
| 111 | } | ||
| 112 | |||
| 113 | 154 | static PetscErrorCode EPSComputeVectors_LREP_Teng(EPS eps) | |
| 114 | { | ||
| 115 | 154 | Mat H; | |
| 116 | 154 | Vec u,v,w; | |
| 117 | 154 | BV U,V; | |
| 118 | 154 | IS is[2]; | |
| 119 | 154 | PetscInt k; | |
| 120 | 154 | PetscScalar lambda; | |
| 121 | 154 | PetscBool reduced; | |
| 122 | |||
| 123 |
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154 | PetscFunctionBegin; |
| 124 |
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154 | PetscCall(STGetMatrix(eps->st,0,&H)); |
| 125 |
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154 | PetscCall(MatNestGetISs(H,is,NULL)); |
| 126 |
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154 | PetscCall(SlepcCheckMatLREPReduced(H,&reduced)); |
| 127 |
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154 | PetscCall(BVGetSplitRows(eps->V,is[0],is[1],&V,&U)); |
| 128 |
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1242 | for (k=0;k<eps->nconv;k++) { |
| 129 |
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1088 | PetscCall(BVGetColumn(V,k,&v)); |
| 130 | /* approx eigenvector is [eigr[k]*v; u] */ | ||
| 131 | 1088 | lambda = eps->eigr[k]; | |
| 132 |
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1088 | PetscCall(STBackTransform(eps->st,1,&lambda,&eps->eigi[k])); |
| 133 |
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1088 | PetscCall(VecScale(v,lambda)); |
| 134 |
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1088 | PetscCall(BVRestoreColumn(V,k,&v)); |
| 135 | } | ||
| 136 |
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154 | if (!reduced) { |
| 137 | /* the eigenvector [v;u] = J*[y;x] where [y;x] is the reduced eigenvector | ||
| 138 | and J = 1/sqrt(2)[I I; I -I], i.e, v=1/sqrt(2)*(y+x) u=1/sqrt(2)*(y-x) */ | ||
| 139 |
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77 | PetscCall(BVCreateVec(V,&w)); |
| 140 |
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621 | for (k=0;k<eps->nconv;k++) { |
| 141 |
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544 | PetscCall(BVGetColumn(U,k,&u)); |
| 142 |
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544 | PetscCall(BVGetColumn(V,k,&v)); |
| 143 |
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544 | PetscCall(VecCopy(u,w)); |
| 144 |
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544 | PetscCall(VecCopy(v,u)); |
| 145 |
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544 | PetscCall(VecAXPY(u,-1.0,w)); |
| 146 |
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544 | PetscCall(VecAXPY(v,1.0,w)); |
| 147 |
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544 | PetscCall(BVRestoreColumn(U,k,&u)); |
| 148 |
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544 | PetscCall(BVRestoreColumn(V,k,&v)); |
| 149 | } | ||
| 150 |
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77 | PetscCall(VecDestroy(&w)); |
| 151 | } | ||
| 152 |
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154 | PetscCall(BVRestoreSplitRows(eps->V,is[0],is[1],&V,&U)); |
| 153 | /* Normalize eigenvectors */ | ||
| 154 |
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154 | PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv)); |
| 155 |
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154 | PetscCall(BVNormalize(eps->V,NULL)); |
| 156 |
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26 | PetscFunctionReturn(PETSC_SUCCESS); |
| 157 | } | ||
| 158 | |||
| 159 | 154 | PetscErrorCode EPSSetUp_KrylovSchur_LREP(EPS eps) | |
| 160 | { | ||
| 161 | 154 | EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data; | |
| 162 | 154 | PetscBool flg; | |
| 163 | |||
| 164 |
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154 | PetscFunctionBegin; |
| 165 |
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154 | PetscCheck((eps->problem_type==EPS_LREP),PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Problem type should be LREP"); |
| 166 |
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154 | EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION | EPS_FEATURE_BALANCE,PETSC_TRUE," with LREP structure"); |
| 167 |
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154 | PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd)); |
| 168 |
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154 | PetscCheck(eps->ncv<=eps->nev+eps->mpd,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd"); |
| 169 |
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298 | if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv)*((eps->stop==EPS_STOP_THRESHOLD)?10:1); |
| 170 | |||
| 171 |
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154 | PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&flg)); |
| 172 |
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154 | PetscCheck(flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Krylov-Schur LREP only supports shift ST"); |
| 173 |
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154 | if (!eps->which) eps->which = EPS_SMALLEST_MAGNITUDE; |
| 174 | |||
| 175 |
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154 | if (!ctx->keep) ctx->keep = 0.5; |
| 176 |
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154 | PetscCall(STSetStructured(eps->st,PETSC_FALSE)); |
| 177 | |||
| 178 |
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154 | PetscCall(EPSAllocateSolution(eps,1)); |
| 179 | /* Teng */ | ||
| 180 | 154 | eps->ops->solve = EPSSolve_KrylovSchur_LREP_Teng; | |
| 181 | 154 | eps->ops->computevectors = EPSComputeVectors_LREP_Teng; | |
| 182 |
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154 | PetscCall(DSSetType(eps->ds,DSHEP)); |
| 183 |
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154 | PetscCall(DSSetCompact(eps->ds,PETSC_TRUE)); |
| 184 |
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154 | PetscCall(DSSetExtraRow(eps->ds,PETSC_TRUE)); |
| 185 |
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154 | PetscCall(DSAllocate(eps->ds,eps->ncv+1)); |
| 186 |
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26 | PetscFunctionReturn(PETSC_SUCCESS); |
| 187 | } | ||
| 188 | |||
| 189 | 154 | PetscErrorCode EPSSolve_KrylovSchur_LREP_Teng(EPS eps) | |
| 190 | { | ||
| 191 | 154 | EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data; | |
| 192 | 154 | PetscInt i,k,l,ld,nv,nconv=0,nevsave,ma,na,Ma,Na; | |
| 193 | 154 | Mat H,Q,K,M,A,B; | |
| 194 | 154 | BV U,V; | |
| 195 | 154 | IS is[2]; | |
| 196 | 154 | PetscReal *a,*b,beta; | |
| 197 | 154 | PetscBool reduced,breakdown=PETSC_FALSE; | |
| 198 | 154 | const PetscScalar scal[] = { 1.0, -1.0 }; | |
| 199 | |||
| 200 |
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154 | PetscFunctionBegin; |
| 201 |
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154 | PetscCall(DSGetLeadingDimension(eps->ds,&ld)); |
| 202 | |||
| 203 | /* Extract matrix blocks */ | ||
| 204 |
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154 | PetscCall(STGetMatrix(eps->st,0,&H)); |
| 205 |
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154 | PetscCall(MatNestGetISs(H,is,NULL)); |
| 206 |
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154 | PetscCall(SlepcCheckMatLREPReduced(H,&reduced)); |
| 207 |
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154 | if (reduced) { |
| 208 |
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77 | PetscCall(MatNestGetSubMat(H,0,1,&K)); |
| 209 |
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77 | PetscCall(MatNestGetSubMat(H,1,0,&M)); |
| 210 | } else { | ||
| 211 |
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77 | PetscCall(MatNestGetSubMat(H,0,0,&A)); |
| 212 |
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77 | PetscCall(MatNestGetSubMat(H,0,1,&B)); |
| 213 |
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77 | PetscCall(MatGetSize(A,&Ma,&Na)); |
| 214 |
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77 | PetscCall(MatGetLocalSize(A,&ma,&na)); |
| 215 | /* K = A-B */ | ||
| 216 |
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77 | PetscCall(MatCreate(PetscObjectComm((PetscObject)A),&K)); |
| 217 |
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77 | PetscCall(MatSetSizes(K,ma,na,Ma,Na)); |
| 218 |
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77 | PetscCall(MatSetType(K,MATCOMPOSITE)); |
| 219 |
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77 | PetscCall(MatCompositeAddMat(K,A)); |
| 220 |
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77 | PetscCall(MatCompositeAddMat(K,B)); |
| 221 |
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77 | PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY)); |
| 222 |
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77 | PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY)); |
| 223 |
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77 | PetscCall(MatCompositeSetScalings(K,scal)); |
| 224 | /* M = A+B */ | ||
| 225 |
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77 | PetscCall(MatCreate(PetscObjectComm((PetscObject)A),&M)); |
| 226 |
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77 | PetscCall(MatSetSizes(M,ma,na,Ma,Na)); |
| 227 |
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77 | PetscCall(MatSetType(M,MATCOMPOSITE)); |
| 228 |
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77 | PetscCall(MatCompositeAddMat(M,A)); |
| 229 |
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77 | PetscCall(MatCompositeAddMat(M,B)); |
| 230 |
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77 | PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY)); |
| 231 |
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77 | PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY)); |
| 232 | } | ||
| 233 | |||
| 234 | /* Get the split bases */ | ||
| 235 |
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154 | PetscCall(BVGetSplitRows(eps->V,is[0],is[1],&V,&U)); |
| 236 | |||
| 237 | 154 | nevsave = eps->nev; | |
| 238 | 154 | eps->nev = (eps->nev+1)/2; | |
| 239 | 154 | l = 0; | |
| 240 | |||
| 241 | /* Restart loop */ | ||
| 242 | 154 | while (eps->reason == EPS_CONVERGED_ITERATING) { | |
| 243 | 1132 | eps->its++; | |
| 244 | |||
| 245 | /* Compute an nv-step Lanczos factorization */ | ||
| 246 | 1132 | nv = PetscMin(eps->nconv+eps->mpd,eps->ncv); | |
| 247 |
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1132 | PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l)); |
| 248 |
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1132 | PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&a)); |
| 249 | 1132 | b = a + ld; | |
| 250 |
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1132 | PetscCall(EPSLREPLanczos_Teng(eps,K,M,U,V,a,b,eps->nconv+l,&nv,&breakdown)); |
| 251 | 1132 | beta = b[nv-1]; | |
| 252 |
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1132 | PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&a)); |
| 253 |
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1132 | PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l)); |
| 254 |
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1132 | PetscCall(DSSetState(eps->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE)); |
| 255 |
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1132 | PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv)); |
| 256 | |||
| 257 | /* Solve projected problem */ | ||
| 258 |
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1132 | PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi)); |
| 259 |
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1132 | PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL)); |
| 260 |
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1132 | PetscCall(DSUpdateExtraRow(eps->ds)); |
| 261 |
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1132 | PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi)); |
| 262 | |||
| 263 | /* Check convergence */ | ||
| 264 |
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15884 | for (i=0;i<nv;i++) eps->eigr[i] = PetscSqrtReal(PetscRealPart(eps->eigr[i])); |
| 265 |
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1132 | PetscCall(EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,0.0,1.0,&k)); |
| 266 |
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1132 | EPSSetCtxThreshold(eps,eps->eigr,eps->eigi,eps->errest,k,nv); |
| 267 |
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1132 | PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx)); |
| 268 | 1132 | nconv = k; | |
| 269 | |||
| 270 | /* Update l */ | ||
| 271 |
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1132 | if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0; |
| 272 | 978 | else l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep)); | |
| 273 |
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1132 | if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */ |
| 274 |
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1132 | if (l) PetscCall(PetscInfo(eps,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l)); |
| 275 | |||
| 276 |
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1132 | if (eps->reason == EPS_CONVERGED_ITERATING) { |
| 277 |
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978 | PetscCheck(!breakdown,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Breakdown in LREP Krylov-Schur (beta=%g)",(double)beta); |
| 278 | /* Prepare the Rayleigh quotient for restart */ | ||
| 279 |
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978 | PetscCall(DSTruncate(eps->ds,k+l,PETSC_FALSE)); |
| 280 | } | ||
| 281 | /* Update the corresponding vectors | ||
| 282 | U(:,idx) = U*Q(:,idx), V(:,idx) = V*Q(:,idx) */ | ||
| 283 |
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1132 | PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&Q)); |
| 284 |
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1132 | PetscCall(BVMultInPlace(U,Q,eps->nconv,k+l)); |
| 285 |
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1132 | PetscCall(BVMultInPlace(V,Q,eps->nconv,k+l)); |
| 286 |
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1132 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&Q)); |
| 287 | |||
| 288 |
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1132 | if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) { |
| 289 |
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978 | PetscCall(BVCopyColumn(eps->V,nv,k+l)); |
| 290 |
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978 | if (eps->stop==EPS_STOP_THRESHOLD && nv-k<5) { /* reallocate */ |
| 291 | 10 | eps->ncv = eps->mpd+k; | |
| 292 |
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10 | PetscCall(BVRestoreSplitRows(eps->V,is[0],is[1],&V,&U)); |
| 293 |
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10 | PetscCall(EPSReallocateSolution(eps,eps->ncv+1)); |
| 294 |
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10 | PetscCall(BVGetSplitRows(eps->V,is[0],is[1],&V,&U)); |
| 295 |
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70 | for (i=nv;i<eps->ncv;i++) eps->perm[i] = i; |
| 296 |
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10 | PetscCall(DSReallocate(eps->ds,eps->ncv+1)); |
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10 | PetscCall(DSGetLeadingDimension(eps->ds,&ld)); |
| 298 | } | ||
| 299 | } | ||
| 300 | 1132 | eps->nconv = k; | |
| 301 |
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1286 | PetscCall(EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv)); |
| 302 | } | ||
| 303 | |||
| 304 | 154 | eps->nev = nevsave; | |
| 305 | |||
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154 | PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE)); |
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154 | PetscCall(BVRestoreSplitRows(eps->V,is[0],is[1],&V,&U)); |
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154 | if (!reduced) { |
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77 | PetscCall(MatDestroy(&K)); |
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77 | PetscCall(MatDestroy(&M)); |
| 311 | } | ||
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26 | PetscFunctionReturn(PETSC_SUCCESS); |
| 313 | } | ||
| 314 |