| 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 | Utility subroutines common to several impls | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/dsimpl.h> /*I "slepcds.h" I*/ | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | Compute the (real) Schur form of A. At the end, A is (quasi-)triangular and Q | ||
| 19 | contains the unitary matrix of Schur vectors. Eigenvalues are returned in wr,wi | ||
| 20 | */ | ||
| 21 | 39823 | PetscErrorCode DSSolve_NHEP_Private(DS ds,DSMatType mA,DSMatType mQ,PetscScalar *wr,PetscScalar *wi) | |
| 22 | { | ||
| 23 | 39823 | PetscScalar *work,*tau,*A,*Q; | |
| 24 | 39823 | PetscInt i,j; | |
| 25 | 39823 | PetscBLASInt ilo,lwork,info,n,k,ld; | |
| 26 | |||
| 27 |
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39823 | PetscFunctionBegin; |
| 28 |
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39823 | PetscCall(MatDenseGetArray(ds->omat[mA],&A)); |
| 29 |
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39823 | PetscCall(MatDenseGetArray(ds->omat[mQ],&Q)); |
| 30 |
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39823 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 31 |
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39823 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 32 |
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39823 | PetscCall(PetscBLASIntCast(ds->l+1,&ilo)); |
| 33 |
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39823 | PetscCall(PetscBLASIntCast(ds->k,&k)); |
| 34 |
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39823 | PetscCall(DSAllocateWork_Private(ds,ld+6*ld,0,0)); |
| 35 | 39823 | tau = ds->work; | |
| 36 | 39823 | work = ds->work+ld; | |
| 37 | 39823 | lwork = 6*ld; | |
| 38 | |||
| 39 | /* initialize orthogonal matrix */ | ||
| 40 |
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39823 | PetscCall(PetscArrayzero(Q,ld*ld)); |
| 41 |
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764051 | for (i=0;i<n;i++) Q[i+i*ld] = 1.0; |
| 42 |
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39823 | if (n==1) { /* quick return */ |
| 43 | 460 | wr[0] = A[0]; | |
| 44 |
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460 | if (wi) wi[0] = 0.0; |
| 45 |
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460 | PetscFunctionReturn(PETSC_SUCCESS); |
| 46 | } | ||
| 47 | |||
| 48 | /* reduce to upper Hessenberg form */ | ||
| 49 |
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39363 | if (ds->state<DS_STATE_INTERMEDIATE) { |
| 50 |
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26777 | PetscCallBLAS("LAPACKgehrd",LAPACKgehrd_(&n,&ilo,&n,A,&ld,tau,work,&lwork,&info)); |
| 51 |
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26777 | SlepcCheckLapackInfo("gehrd",info); |
| 52 |
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497946 | for (j=0;j<n-1;j++) { |
| 53 |
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5950127 | for (i=j+2;i<n;i++) { |
| 54 | 5478958 | Q[i+j*ld] = A[i+j*ld]; | |
| 55 | 5478958 | A[i+j*ld] = 0.0; | |
| 56 | } | ||
| 57 | } | ||
| 58 |
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26777 | PetscCallBLAS("LAPACKorghr",LAPACKorghr_(&n,&ilo,&n,Q,&ld,tau,work,&lwork,&info)); |
| 59 |
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26777 | SlepcCheckLapackInfo("orghr",info); |
| 60 | } | ||
| 61 | |||
| 62 | /* compute the (real) Schur form */ | ||
| 63 | #if !defined(PETSC_USE_COMPLEX) | ||
| 64 |
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19729 | PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,wi,Q,&ld,work,&lwork,&info)); |
| 65 |
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38633 | for (j=0;j<ds->l;j++) { |
| 66 |
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18904 | if (j==n-1 || A[j+1+j*ld] == 0.0) { |
| 67 | /* real eigenvalue */ | ||
| 68 | 17159 | wr[j] = A[j+j*ld]; | |
| 69 | 17159 | wi[j] = 0.0; | |
| 70 | } else { | ||
| 71 | /* complex eigenvalue */ | ||
| 72 | 1745 | wr[j] = A[j+j*ld]; | |
| 73 | 1745 | wr[j+1] = A[j+j*ld]; | |
| 74 | 1745 | wi[j] = PetscSqrtReal(PetscAbsReal(A[j+1+j*ld]))*PetscSqrtReal(PetscAbsReal(A[j+(j+1)*ld])); | |
| 75 | 1745 | wi[j+1] = -wi[j]; | |
| 76 | 1745 | j++; | |
| 77 | } | ||
| 78 | } | ||
| 79 | #else | ||
| 80 |
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19634 | PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,Q,&ld,work,&lwork,&info)); |
| 81 |
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347403 | if (wi) for (i=ds->l;i<n;i++) wi[i] = 0.0; |
| 82 | #endif | ||
| 83 |
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39363 | SlepcCheckLapackInfo("hseqr",info); |
| 84 |
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39363 | PetscCall(MatDenseRestoreArray(ds->omat[mA],&A)); |
| 85 |
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39363 | PetscCall(MatDenseRestoreArray(ds->omat[mQ],&Q)); |
| 86 |
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7578 | PetscFunctionReturn(PETSC_SUCCESS); |
| 87 | } | ||
| 88 | |||
| 89 | /* | ||
| 90 | Sort a Schur form represented by the (quasi-)triangular matrix T and | ||
| 91 | the unitary matrix Q, and return the sorted eigenvalues in wr,wi | ||
| 92 | */ | ||
| 93 | 43678 | PetscErrorCode DSSort_NHEP_Total(DS ds,DSMatType mT,DSMatType mQ,PetscScalar *wr,PetscScalar *wi) | |
| 94 | { | ||
| 95 | 43678 | PetscScalar re,*T,*Q; | |
| 96 | 43678 | PetscInt i,j,pos,result; | |
| 97 | 43678 | PetscBLASInt ifst,ilst,info,n,ld; | |
| 98 | #if !defined(PETSC_USE_COMPLEX) | ||
| 99 | 21911 | PetscScalar *work,im; | |
| 100 | #endif | ||
| 101 | |||
| 102 |
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43678 | PetscFunctionBegin; |
| 103 |
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43678 | PetscCall(MatDenseGetArray(ds->omat[mT],&T)); |
| 104 |
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43678 | PetscCall(MatDenseGetArray(ds->omat[mQ],&Q)); |
| 105 |
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43678 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 106 |
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43678 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 107 | #if !defined(PETSC_USE_COMPLEX) | ||
| 108 |
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21911 | PetscCall(DSAllocateWork_Private(ds,ld,0,0)); |
| 109 | 21911 | work = ds->work; | |
| 110 | #endif | ||
| 111 | /* selection sort */ | ||
| 112 |
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686116 | for (i=ds->l;i<n-1;i++) { |
| 113 | 642438 | re = wr[i]; | |
| 114 | #if !defined(PETSC_USE_COMPLEX) | ||
| 115 | 300077 | im = wi[i]; | |
| 116 | #endif | ||
| 117 | 642438 | pos = 0; | |
| 118 | 642438 | j=i+1; /* j points to the next eigenvalue */ | |
| 119 | #if !defined(PETSC_USE_COMPLEX) | ||
| 120 |
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300077 | if (im != 0) j=i+2; |
| 121 | #endif | ||
| 122 | /* find minimum eigenvalue */ | ||
| 123 |
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7557684 | for (;j<n;j++) { |
| 124 | #if !defined(PETSC_USE_COMPLEX) | ||
| 125 |
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3131940 | PetscCall(SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result)); |
| 126 | #else | ||
| 127 |
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3783306 | PetscCall(SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result)); |
| 128 | #endif | ||
| 129 |
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6915246 | if (result > 0) { |
| 130 | 2610035 | re = wr[j]; | |
| 131 | #if !defined(PETSC_USE_COMPLEX) | ||
| 132 | 1222242 | im = wi[j]; | |
| 133 | #endif | ||
| 134 | 2610035 | pos = j; | |
| 135 | } | ||
| 136 | #if !defined(PETSC_USE_COMPLEX) | ||
| 137 |
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3131940 | if (wi[j] != 0) j++; |
| 138 | #endif | ||
| 139 | } | ||
| 140 |
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642438 | if (pos) { |
| 141 | /* interchange blocks */ | ||
| 142 |
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436931 | PetscCall(PetscBLASIntCast(pos+1,&ifst)); |
| 143 |
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436931 | PetscCall(PetscBLASIntCast(i+1,&ilst)); |
| 144 | #if !defined(PETSC_USE_COMPLEX) | ||
| 145 |
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201607 | PetscCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info)); |
| 146 | #else | ||
| 147 |
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235324 | PetscCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info)); |
| 148 | #endif | ||
| 149 |
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436931 | SlepcCheckLapackInfo("trexc",info); |
| 150 | /* recover original eigenvalues from T matrix */ | ||
| 151 |
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5798775 | for (j=i;j<n;j++) { |
| 152 | 5361844 | wr[j] = T[j+j*ld]; | |
| 153 | #if !defined(PETSC_USE_COMPLEX) | ||
| 154 |
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2397764 | if (j<n-1 && T[j+1+j*ld] != 0.0) { |
| 155 | /* complex conjugate eigenvalue */ | ||
| 156 | 262242 | wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld]))*PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld])); | |
| 157 | 262242 | wr[j+1] = wr[j]; | |
| 158 | 262242 | wi[j+1] = -wi[j]; | |
| 159 | 262242 | j++; | |
| 160 | 2135522 | } else wi[j] = 0.0; | |
| 161 | #endif | ||
| 162 | } | ||
| 163 | } | ||
| 164 | #if !defined(PETSC_USE_COMPLEX) | ||
| 165 |
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300077 | if (wi[i] != 0) i++; |
| 166 | #endif | ||
| 167 | } | ||
| 168 |
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43678 | PetscCall(MatDenseRestoreArray(ds->omat[mT],&T)); |
| 169 |
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43678 | PetscCall(MatDenseRestoreArray(ds->omat[mQ],&Q)); |
| 170 |
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8432 | PetscFunctionReturn(PETSC_SUCCESS); |
| 171 | } | ||
| 172 | |||
| 173 | /* | ||
| 174 | Reorder a Schur form represented by T,Q according to a permutation perm, | ||
| 175 | and return the sorted eigenvalues in wr,wi | ||
| 176 | */ | ||
| 177 | 187 | PetscErrorCode DSSortWithPermutation_NHEP_Private(DS ds,PetscInt *perm,DSMatType mT,DSMatType mQ,PetscScalar *wr,PetscScalar *wi) | |
| 178 | { | ||
| 179 | 187 | PetscInt i,j,pos,inc=1; | |
| 180 | 187 | PetscBLASInt ifst,ilst,info,n,ld; | |
| 181 | 187 | PetscScalar *T,*Q; | |
| 182 | #if !defined(PETSC_USE_COMPLEX) | ||
| 183 | 75 | PetscScalar *work; | |
| 184 | #endif | ||
| 185 | |||
| 186 |
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187 | PetscFunctionBegin; |
| 187 |
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187 | PetscCall(MatDenseGetArray(ds->omat[mT],&T)); |
| 188 |
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187 | PetscCall(MatDenseGetArray(ds->omat[mQ],&Q)); |
| 189 |
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187 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 190 |
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187 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 191 | #if !defined(PETSC_USE_COMPLEX) | ||
| 192 |
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75 | PetscCall(DSAllocateWork_Private(ds,ld,0,0)); |
| 193 | 75 | work = ds->work; | |
| 194 | #endif | ||
| 195 |
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4223 | for (i=ds->l;i<n-1;i++) { |
| 196 | 4036 | pos = perm[i]; | |
| 197 | #if !defined(PETSC_USE_COMPLEX) | ||
| 198 |
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2100 | inc = (pos<n-1 && T[pos+1+pos*ld] != 0.0)? 2: 1; |
| 199 | #endif | ||
| 200 |
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4036 | if (pos!=i) { |
| 201 | #if !defined(PETSC_USE_COMPLEX) | ||
| 202 |
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445 | PetscCheck((T[pos+(pos-1)*ld]==0.0 || perm[i+1]==pos-1) && (pos==n-1 || (T[pos+1+pos*ld]==0.0 || perm[i+1]==pos+1)),PETSC_COMM_SELF,PETSC_ERR_FP,"Invalid permutation due to a 2x2 block at position %" PetscInt_FMT,pos); |
| 203 | #endif | ||
| 204 | /* interchange blocks */ | ||
| 205 |
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1352 | PetscCall(PetscBLASIntCast(pos+1,&ifst)); |
| 206 |
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1352 | PetscCall(PetscBLASIntCast(i+1,&ilst)); |
| 207 | #if !defined(PETSC_USE_COMPLEX) | ||
| 208 |
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445 | PetscCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info)); |
| 209 | #else | ||
| 210 |
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907 | PetscCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info)); |
| 211 | #endif | ||
| 212 |
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1352 | SlepcCheckLapackInfo("trexc",info); |
| 213 |
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13584 | for (j=i+1;j<n;j++) { |
| 214 |
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12232 | if (perm[j]>=i && perm[j]<pos) perm[j]+=inc; |
| 215 | } | ||
| 216 | 1352 | perm[i] = i; | |
| 217 |
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1352 | if (inc==2) perm[i+1] = i+1; |
| 218 | } | ||
| 219 |
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3646 | if (inc==2) i++; |
| 220 | } | ||
| 221 | /* recover original eigenvalues from T matrix */ | ||
| 222 |
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4365 | for (j=ds->l;j<n;j++) { |
| 223 | 4178 | wr[j] = T[j+j*ld]; | |
| 224 | #if !defined(PETSC_USE_COMPLEX) | ||
| 225 |
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2130 | if (j<n-1 && T[j+1+j*ld] != 0.0) { |
| 226 | /* complex conjugate eigenvalue */ | ||
| 227 | 140 | wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld]))*PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld])); | |
| 228 | 140 | wr[j+1] = wr[j]; | |
| 229 | 140 | wi[j+1] = -wi[j]; | |
| 230 | 140 | j++; | |
| 231 | 1990 | } else wi[j] = 0.0; | |
| 232 | #endif | ||
| 233 | } | ||
| 234 |
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187 | PetscCall(MatDenseRestoreArray(ds->omat[mT],&T)); |
| 235 |
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187 | PetscCall(MatDenseRestoreArray(ds->omat[mQ],&Q)); |
| 236 |
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48 | PetscFunctionReturn(PETSC_SUCCESS); |
| 237 | } | ||
| 238 |