| 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 | #include <slepc/private/dsimpl.h> | ||
| 12 | #include <slepcblaslapack.h> | ||
| 13 | |||
| 14 | 2876 | static PetscErrorCode DSAllocate_HEP(DS ds,PetscInt ld) | |
| 15 | { | ||
| 16 |
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2876 | PetscFunctionBegin; |
| 17 |
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2876 | if (!ds->compact) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A)); |
| 18 |
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2876 | PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q)); |
| 19 |
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2876 | PetscCall(DSAllocateMat_Private(ds,DS_MAT_T)); |
| 20 |
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2876 | PetscCall(PetscFree(ds->perm)); |
| 21 |
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2876 | PetscCall(PetscMalloc1(ld,&ds->perm)); |
| 22 |
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690 | PetscFunctionReturn(PETSC_SUCCESS); |
| 23 | } | ||
| 24 | |||
| 25 | /* 0 l k n-1 | ||
| 26 | ----------------------------------------- | ||
| 27 | |* . . | | ||
| 28 | | * . . | | ||
| 29 | | * . . | | ||
| 30 | | * . . | | ||
| 31 | |. . . . o o | | ||
| 32 | | o o | | ||
| 33 | | o o | | ||
| 34 | | o o | | ||
| 35 | | o o | | ||
| 36 | | o o | | ||
| 37 | |. . . . o o o o o o o x | | ||
| 38 | | x x x | | ||
| 39 | | x x x | | ||
| 40 | | x x x | | ||
| 41 | | x x x | | ||
| 42 | | x x x | | ||
| 43 | | x x x | | ||
| 44 | | x x x | | ||
| 45 | | x x x| | ||
| 46 | | x x| | ||
| 47 | ----------------------------------------- | ||
| 48 | */ | ||
| 49 | |||
| 50 | 1020 | static PetscErrorCode DSSwitchFormat_HEP(DS ds) | |
| 51 | { | ||
| 52 | 1020 | PetscReal *T; | |
| 53 | 1020 | PetscScalar *A; | |
| 54 | 1020 | PetscInt i,n=ds->n,k=ds->k,ld=ds->ld; | |
| 55 | |||
| 56 |
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1020 | PetscFunctionBegin; |
| 57 | /* switch from compact (arrow) to dense storage */ | ||
| 58 |
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1020 | PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_A],&A)); |
| 59 |
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1020 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T)); |
| 60 |
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1020 | PetscCall(PetscArrayzero(A,ld*ld)); |
| 61 |
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1020 | for (i=0;i<k;i++) { |
| 62 | ✗ | A[i+i*ld] = T[i]; | |
| 63 | ✗ | A[k+i*ld] = T[i+ld]; | |
| 64 | ✗ | A[i+k*ld] = T[i+ld]; | |
| 65 | } | ||
| 66 | 1020 | A[k+k*ld] = T[k]; | |
| 67 |
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17825 | for (i=k+1;i<n;i++) { |
| 68 | 16805 | A[i+i*ld] = T[i]; | |
| 69 | 16805 | A[i-1+i*ld] = T[i-1+ld]; | |
| 70 | 16805 | A[i+(i-1)*ld] = T[i-1+ld]; | |
| 71 | } | ||
| 72 |
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1020 | if (ds->extrarow) A[n+(n-1)*ld] = T[n-1+ld]; |
| 73 |
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1020 | PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_A],&A)); |
| 74 |
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1020 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T)); |
| 75 |
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238 | PetscFunctionReturn(PETSC_SUCCESS); |
| 76 | } | ||
| 77 | |||
| 78 | 167 | static PetscErrorCode DSView_HEP(DS ds,PetscViewer viewer) | |
| 79 | { | ||
| 80 | 167 | PetscViewerFormat format; | |
| 81 | 167 | PetscInt i,j,r,c,rows; | |
| 82 | 167 | PetscReal *T,value; | |
| 83 | 167 | const char *methodname[] = { | |
| 84 | "Implicit QR method (_steqr)", | ||
| 85 | "Relatively Robust Representations (_stevr)", | ||
| 86 | "Divide and Conquer method (_stedc)", | ||
| 87 | "Block Divide and Conquer method (dsbtdc)" | ||
| 88 | }; | ||
| 89 | 167 | const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname); | |
| 90 | |||
| 91 |
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167 | PetscFunctionBegin; |
| 92 |
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167 | PetscCall(PetscViewerGetFormat(viewer,&format)); |
| 93 |
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167 | if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) { |
| 94 |
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119 | if (ds->bs>1) PetscCall(PetscViewerASCIIPrintf(viewer,"block size: %" PetscInt_FMT "\n",ds->bs)); |
| 95 |
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119 | if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method])); |
| 96 |
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119 | PetscFunctionReturn(PETSC_SUCCESS); |
| 97 | } | ||
| 98 |
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48 | if (ds->compact) { |
| 99 |
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48 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T)); |
| 100 |
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48 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 101 |
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48 | rows = ds->extrarow? ds->n+1: ds->n; |
| 102 |
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48 | if (format == PETSC_VIEWER_ASCII_MATLAB) { |
| 103 |
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48 | PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,ds->n)); |
| 104 |
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48 | PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",3*ds->n)); |
| 105 |
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48 | PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n")); |
| 106 |
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480 | for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)T[i])); |
| 107 |
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456 | for (i=0;i<rows-1;i++) { |
| 108 |
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408 | r = PetscMax(i+2,ds->k+1); |
| 109 | 408 | c = i+1; | |
| 110 |
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408 | PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",r,c,(double)T[i+ds->ld])); |
| 111 |
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408 | if (i<ds->n-1 && ds->k<ds->n) { /* do not print vertical arrow when k=n */ |
| 112 |
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384 | PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",c,r,(double)T[i+ds->ld])); |
| 113 | } | ||
| 114 | } | ||
| 115 |
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48 | PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T])); |
| 116 | } else { | ||
| 117 | ✗ | for (i=0;i<rows;i++) { | |
| 118 | ✗ | for (j=0;j<ds->n;j++) { | |
| 119 | ✗ | if (i==j) value = T[i]; | |
| 120 | ✗ | else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = T[PetscMin(i,j)+ds->ld]; | |
| 121 | ✗ | else if (i==j+1 && i>ds->k) value = T[i-1+ds->ld]; | |
| 122 | ✗ | else if (i+1==j && j>ds->k) value = T[j-1+ds->ld]; | |
| 123 | else value = 0.0; | ||
| 124 | ✗ | PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value)); | |
| 125 | } | ||
| 126 | ✗ | PetscCall(PetscViewerASCIIPrintf(viewer,"\n")); | |
| 127 | } | ||
| 128 | } | ||
| 129 |
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48 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 130 |
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48 | PetscCall(PetscViewerFlush(viewer)); |
| 131 |
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48 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T)); |
| 132 | ✗ | } else PetscCall(DSViewMat(ds,viewer,DS_MAT_A)); | |
| 133 |
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48 | if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_Q)); |
| 134 |
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12 | PetscFunctionReturn(PETSC_SUCCESS); |
| 135 | } | ||
| 136 | |||
| 137 | 192973 | static PetscErrorCode DSVectors_HEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm) | |
| 138 | { | ||
| 139 | 192973 | PetscScalar *Z; | |
| 140 | 192973 | const PetscScalar *Q; | |
| 141 | 192973 | PetscInt ld = ds->ld; | |
| 142 | |||
| 143 |
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192973 | PetscFunctionBegin; |
| 144 |
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192973 | switch (mat) { |
| 145 | 192973 | case DS_MAT_X: | |
| 146 | case DS_MAT_Y: | ||
| 147 |
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192973 | if (j) { |
| 148 |
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192485 | PetscCall(MatDenseGetArray(ds->omat[mat],&Z)); |
| 149 |
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192485 | if (ds->state>=DS_STATE_CONDENSED) { |
| 150 |
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192485 | PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q)); |
| 151 |
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192485 | PetscCall(PetscArraycpy(Z+(*j)*ld,Q+(*j)*ld,ld)); |
| 152 |
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192485 | if (rnorm) *rnorm = PetscAbsScalar(Q[ds->n-1+(*j)*ld]); |
| 153 |
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192485 | PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q)); |
| 154 | } else { | ||
| 155 | ✗ | PetscCall(PetscArrayzero(Z+(*j)*ld,ld)); | |
| 156 | ✗ | Z[(*j)+(*j)*ld] = 1.0; | |
| 157 | ✗ | if (rnorm) *rnorm = 0.0; | |
| 158 | } | ||
| 159 |
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192485 | PetscCall(MatDenseRestoreArray(ds->omat[mat],&Z)); |
| 160 | } else { | ||
| 161 |
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488 | if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatCopy(ds->omat[DS_MAT_Q],ds->omat[mat],SAME_NONZERO_PATTERN)); |
| 162 | ✗ | else PetscCall(DSSetIdentity(ds,mat)); | |
| 163 | } | ||
| 164 | 46655 | break; | |
| 165 | ✗ | case DS_MAT_U: | |
| 166 | case DS_MAT_V: | ||
| 167 | ✗ | SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet"); | |
| 168 | ✗ | default: | |
| 169 | ✗ | SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter"); | |
| 170 | } | ||
| 171 |
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46655 | PetscFunctionReturn(PETSC_SUCCESS); |
| 172 | } | ||
| 173 | |||
| 174 | /* | ||
| 175 | ARROWTRIDIAG reduces a symmetric arrowhead matrix of the form | ||
| 176 | |||
| 177 | [ d 0 0 0 e ] | ||
| 178 | [ 0 d 0 0 e ] | ||
| 179 | A = [ 0 0 d 0 e ] | ||
| 180 | [ 0 0 0 d e ] | ||
| 181 | [ e e e e d ] | ||
| 182 | |||
| 183 | to tridiagonal form | ||
| 184 | |||
| 185 | [ d e 0 0 0 ] | ||
| 186 | [ e d e 0 0 ] | ||
| 187 | T = Q'*A*Q = [ 0 e d e 0 ], | ||
| 188 | [ 0 0 e d e ] | ||
| 189 | [ 0 0 0 e d ] | ||
| 190 | |||
| 191 | where Q is an orthogonal matrix. Rutishauser's algorithm is used to | ||
| 192 | perform the reduction, which requires O(n**2) flops. The accumulation | ||
| 193 | of the orthogonal factor Q, however, requires O(n**3) flops. | ||
| 194 | |||
| 195 | Arguments | ||
| 196 | ========= | ||
| 197 | |||
| 198 | N (input) INTEGER | ||
| 199 | The order of the matrix A. N >= 0. | ||
| 200 | |||
| 201 | D (input/output) DOUBLE PRECISION array, dimension (N) | ||
| 202 | On entry, the diagonal entries of the matrix A to be | ||
| 203 | reduced. | ||
| 204 | On exit, the diagonal entries of the reduced matrix T. | ||
| 205 | |||
| 206 | E (input/output) DOUBLE PRECISION array, dimension (N-1) | ||
| 207 | On entry, the off-diagonal entries of the matrix A to be | ||
| 208 | reduced. | ||
| 209 | On exit, the subdiagonal entries of the reduced matrix T. | ||
| 210 | |||
| 211 | Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) | ||
| 212 | On exit, the orthogonal matrix Q. | ||
| 213 | |||
| 214 | LDQ (input) INTEGER | ||
| 215 | The leading dimension of the array Q. | ||
| 216 | |||
| 217 | Note | ||
| 218 | ==== | ||
| 219 | Based on Fortran code contributed by Daniel Kressner | ||
| 220 | */ | ||
| 221 | 20327 | PetscErrorCode DSArrowTridiag(PetscBLASInt n,PetscReal *d,PetscReal *e,PetscScalar *Q,PetscBLASInt ld) | |
| 222 | { | ||
| 223 | 20327 | PetscBLASInt i,j,j2,one=1; | |
| 224 | 20327 | PetscReal c,s,p,off,temp; | |
| 225 | |||
| 226 |
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20327 | PetscFunctionBegin; |
| 227 |
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20327 | if (n<=2) PetscFunctionReturn(PETSC_SUCCESS); |
| 228 | |||
| 229 |
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160075 | for (j=0;j<n-2;j++) { |
| 230 | |||
| 231 | /* Eliminate entry e(j) by a rotation in the planes (j,j+1) */ | ||
| 232 | 139858 | temp = e[j+1]; | |
| 233 |
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139858 | PetscCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&e[j],&c,&s,&e[j+1])); |
| 234 | 139858 | s = -s; | |
| 235 | |||
| 236 | /* Apply rotation to diagonal elements */ | ||
| 237 | 139858 | temp = d[j+1]; | |
| 238 | 139858 | e[j] = c*s*(temp-d[j]); | |
| 239 | 139858 | d[j+1] = s*s*d[j] + c*c*temp; | |
| 240 | 139858 | d[j] = c*c*d[j] + s*s*temp; | |
| 241 | |||
| 242 | /* Apply rotation to Q */ | ||
| 243 | 139858 | j2 = j+2; | |
| 244 |
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139858 | PetscCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+j*ld,&one,Q+(j+1)*ld,&one,&c,&s)); |
| 245 | |||
| 246 | /* Chase newly introduced off-diagonal entry to the top left corner */ | ||
| 247 |
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890008 | for (i=j-1;i>=0;i--) { |
| 248 | 750150 | off = -s*e[i]; | |
| 249 | 750150 | e[i] = c*e[i]; | |
| 250 | 750150 | temp = e[i+1]; | |
| 251 |
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750150 | PetscCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&off,&c,&s,&e[i+1])); |
| 252 | 750150 | s = -s; | |
| 253 | 750150 | temp = (d[i]-d[i+1])*s - 2.0*c*e[i]; | |
| 254 | 750150 | p = s*temp; | |
| 255 | 750150 | d[i+1] += p; | |
| 256 | 750150 | d[i] -= p; | |
| 257 | 750150 | e[i] = -e[i] - c*temp; | |
| 258 |
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750150 | PetscCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+i*ld,&one,Q+(i+1)*ld,&one,&c,&s)); |
| 259 | } | ||
| 260 | } | ||
| 261 |
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5011 | PetscFunctionReturn(PETSC_SUCCESS); |
| 262 | } | ||
| 263 | |||
| 264 | /* | ||
| 265 | Reduce to tridiagonal form by means of DSArrowTridiag. | ||
| 266 | */ | ||
| 267 | 84099 | static PetscErrorCode DSIntermediate_HEP(DS ds) | |
| 268 | { | ||
| 269 | 84099 | PetscInt i; | |
| 270 | 84099 | PetscBLASInt n1 = 0,n2,lwork,info,l = 0,n = 0,ld,off; | |
| 271 | 84099 | PetscScalar *Q,*work,*tau; | |
| 272 | 84099 | const PetscScalar *A; | |
| 273 | 84099 | PetscReal *d,*e; | |
| 274 | 84099 | Mat At,Qt; /* trailing submatrices */ | |
| 275 | |||
| 276 |
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84099 | PetscFunctionBegin; |
| 277 |
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84099 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 278 |
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84099 | PetscCall(PetscBLASIntCast(ds->l,&l)); |
| 279 |
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84099 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 280 |
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84099 | PetscCall(PetscBLASIntCast(PetscMax(0,ds->k-l+1),&n1)); /* size of leading block, excl. locked */ |
| 281 | 84099 | n2 = n-l; /* n2 = n1 + size of trailing block */ | |
| 282 | 84099 | off = l+l*ld; | |
| 283 |
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84099 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 284 | 84099 | e = d+ld; | |
| 285 |
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84099 | PetscCall(DSSetIdentity(ds,DS_MAT_Q)); |
| 286 |
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84099 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 287 | |||
| 288 |
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84099 | if (ds->compact) { |
| 289 | |||
| 290 |
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27880 | if (ds->state<DS_STATE_INTERMEDIATE) PetscCall(DSArrowTridiag(n1,d+l,e+l,Q+off,ld)); |
| 291 | |||
| 292 | } else { | ||
| 293 | |||
| 294 |
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56219 | PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A)); |
| 295 |
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57741 | for (i=0;i<l;i++) { d[i] = PetscRealPart(A[i+i*ld]); e[i] = 0.0; } |
| 296 | |||
| 297 |
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56219 | if (ds->state<DS_STATE_INTERMEDIATE) { |
| 298 |
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56219 | PetscCall(MatDenseGetSubMatrix(ds->omat[DS_MAT_A],ds->l,ds->n,ds->l,ds->n,&At)); |
| 299 |
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56219 | PetscCall(MatDenseGetSubMatrix(ds->omat[DS_MAT_Q],ds->l,ds->n,ds->l,ds->n,&Qt)); |
| 300 |
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56219 | PetscCall(MatCopy(At,Qt,SAME_NONZERO_PATTERN)); |
| 301 |
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56219 | PetscCall(MatDenseRestoreSubMatrix(ds->omat[DS_MAT_A],&At)); |
| 302 |
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56219 | PetscCall(MatDenseRestoreSubMatrix(ds->omat[DS_MAT_Q],&Qt)); |
| 303 |
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56219 | PetscCall(DSAllocateWork_Private(ds,ld+ld*ld,0,0)); |
| 304 | 56219 | tau = ds->work; | |
| 305 | 56219 | work = ds->work+ld; | |
| 306 | 56219 | lwork = ld*ld; | |
| 307 |
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56219 | PetscCallBLAS("LAPACKsytrd",LAPACKsytrd_("L",&n2,Q+off,&ld,d+l,e+l,tau,work,&lwork,&info)); |
| 308 |
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56219 | SlepcCheckLapackInfo("sytrd",info); |
| 309 |
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56219 | PetscCallBLAS("LAPACKorgtr",LAPACKorgtr_("L",&n2,Q+off,&ld,tau,work,&lwork,&info)); |
| 310 |
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56219 | SlepcCheckLapackInfo("orgtr",info); |
| 311 | } else { | ||
| 312 | /* copy tridiagonal to d,e */ | ||
| 313 | ✗ | for (i=l;i<n;i++) d[i] = PetscRealPart(A[i+i*ld]); | |
| 314 | ✗ | for (i=l;i<n-1;i++) e[i] = PetscRealPart(A[(i+1)+i*ld]); | |
| 315 | } | ||
| 316 |
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56219 | PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A)); |
| 317 | } | ||
| 318 |
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84099 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 319 |
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84099 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 320 |
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20462 | PetscFunctionReturn(PETSC_SUCCESS); |
| 321 | } | ||
| 322 | |||
| 323 | 137150 | static PetscErrorCode DSSort_HEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k) | |
| 324 | { | ||
| 325 | 137150 | PetscInt n,l,i,*perm,ld=ds->ld; | |
| 326 | 137150 | PetscScalar *A; | |
| 327 | 137150 | PetscReal *d; | |
| 328 | |||
| 329 |
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137150 | PetscFunctionBegin; |
| 330 |
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137150 | if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS); |
| 331 | 137150 | n = ds->n; | |
| 332 | 137150 | l = ds->l; | |
| 333 |
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137150 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 334 | 137150 | perm = ds->perm; | |
| 335 |
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137150 | if (!rr) PetscCall(DSSortEigenvaluesReal_Private(ds,d,perm)); |
| 336 |
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107421 | else PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE)); |
| 337 |
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1821761 | for (i=l;i<n;i++) wr[i] = d[perm[i]]; |
| 338 |
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137150 | PetscCall(DSPermuteColumns_Private(ds,l,n,n,DS_MAT_Q,perm)); |
| 339 |
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1821761 | for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]); |
| 340 |
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137150 | if (!ds->compact) { |
| 341 |
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109270 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 342 |
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1356039 | for (i=l;i<n;i++) A[i+i*ld] = wr[i]; |
| 343 |
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109270 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 344 | } | ||
| 345 |
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137150 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 346 |
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33358 | PetscFunctionReturn(PETSC_SUCCESS); |
| 347 | } | ||
| 348 | |||
| 349 | 19799 | static PetscErrorCode DSUpdateExtraRow_HEP(DS ds) | |
| 350 | { | ||
| 351 | 19799 | PetscInt i; | |
| 352 | 19799 | PetscBLASInt n,ld,incx=1; | |
| 353 | 19799 | PetscScalar *A,*x,*y,one=1.0,zero=0.0; | |
| 354 | 19799 | PetscReal *T,*e,beta; | |
| 355 | 19799 | const PetscScalar *Q; | |
| 356 | |||
| 357 |
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19799 | PetscFunctionBegin; |
| 358 |
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19799 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 359 |
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19799 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 360 |
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19799 | PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q)); |
| 361 |
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19799 | if (ds->compact) { |
| 362 |
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19775 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T)); |
| 363 | 19775 | e = T+ld; | |
| 364 | 19775 | beta = e[n-1]; /* in compact, we assume all entries are zero except the last one */ | |
| 365 |
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363208 | for (i=0;i<n;i++) e[i] = PetscRealPart(beta*Q[n-1+i*ld]); |
| 366 |
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19775 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T)); |
| 367 | 19775 | ds->k = n; | |
| 368 | } else { | ||
| 369 |
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24 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 370 |
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24 | PetscCall(DSAllocateWork_Private(ds,2*ld,0,0)); |
| 371 | 24 | x = ds->work; | |
| 372 | 24 | y = ds->work+ld; | |
| 373 |
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312 | for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]); |
| 374 |
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24 | PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx)); |
| 375 |
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312 | for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]); |
| 376 | 24 | ds->k = n; | |
| 377 |
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24 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 378 | } | ||
| 379 |
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19799 | PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q)); |
| 380 |
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4806 | PetscFunctionReturn(PETSC_SUCCESS); |
| 381 | } | ||
| 382 | |||
| 383 | 84035 | static PetscErrorCode DSSolve_HEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi) | |
| 384 | { | ||
| 385 | 84035 | PetscInt i; | |
| 386 | 84035 | PetscBLASInt n1,info,l = 0,n = 0,ld,off; | |
| 387 | 84035 | PetscScalar *Q,*A; | |
| 388 | 84035 | PetscReal *d,*e; | |
| 389 | |||
| 390 |
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84035 | PetscFunctionBegin; |
| 391 |
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84035 | PetscCheck(ds->bs==1,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1"); |
| 392 |
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84035 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 393 |
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84035 | PetscCall(PetscBLASIntCast(ds->l,&l)); |
| 394 |
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84035 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 395 | 84035 | n1 = n-l; /* n1 = size of leading block, excl. locked + size of trailing block */ | |
| 396 | 84035 | off = l+l*ld; | |
| 397 |
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84035 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 398 | 84035 | e = d+ld; | |
| 399 | |||
| 400 | /* Reduce to tridiagonal form */ | ||
| 401 |
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84035 | PetscCall(DSIntermediate_HEP(ds)); |
| 402 | |||
| 403 | /* Solve the tridiagonal eigenproblem */ | ||
| 404 |
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148820 | for (i=0;i<l;i++) wr[i] = d[i]; |
| 405 | |||
| 406 |
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84035 | PetscCall(DSAllocateWork_Private(ds,0,2*ld,0)); |
| 407 |
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84035 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 408 |
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84035 | PetscCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n1,d+l,e+l,Q+off,&ld,ds->rwork,&info)); |
| 409 |
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84035 | SlepcCheckLapackInfo("steqr",info); |
| 410 |
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84035 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 411 |
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1175253 | for (i=l;i<n;i++) wr[i] = d[i]; |
| 412 | |||
| 413 | /* Create diagonal matrix as a result */ | ||
| 414 |
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84035 | if (ds->compact) PetscCall(PetscArrayzero(e,n-1)); |
| 415 | else { | ||
| 416 |
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56187 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 417 |
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709787 | for (i=l;i<n;i++) PetscCall(PetscArrayzero(A+l+i*ld,n-l)); |
| 418 |
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709787 | for (i=l;i<n;i++) A[i+i*ld] = d[i]; |
| 419 |
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56187 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 420 | } | ||
| 421 |
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84035 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 422 | |||
| 423 | /* Set zero wi */ | ||
| 424 |
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1037232 | if (wi) for (i=l;i<n;i++) wi[i] = 0.0; |
| 425 |
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20446 | PetscFunctionReturn(PETSC_SUCCESS); |
| 426 | } | ||
| 427 | |||
| 428 | 32 | static PetscErrorCode DSSolve_HEP_MRRR(DS ds,PetscScalar *wr,PetscScalar *wi) | |
| 429 | { | ||
| 430 | 32 | Mat At,Qt; /* trailing submatrices */ | |
| 431 | 32 | PetscInt i; | |
| 432 | 32 | PetscBLASInt n1 = 0,n2 = 0,n3,lrwork,liwork,info,l = 0,n = 0,m = 0,ld,off,il,iu,*isuppz; | |
| 433 | 32 | PetscScalar *A,*Q,*W=NULL,one=1.0,zero=0.0; | |
| 434 | 32 | PetscReal *d,*e,abstol=0.0,vl,vu; | |
| 435 | #if defined(PETSC_USE_COMPLEX) | ||
| 436 | 16 | PetscInt j; | |
| 437 | 16 | PetscReal *Qr,*ritz; | |
| 438 | #endif | ||
| 439 | |||
| 440 |
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32 | PetscFunctionBegin; |
| 441 |
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32 | PetscCheck(ds->bs==1,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1"); |
| 442 |
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32 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 443 |
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32 | PetscCall(PetscBLASIntCast(ds->l,&l)); |
| 444 |
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32 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 445 |
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32 | PetscCall(PetscBLASIntCast(ds->k-l+1,&n1)); /* size of leading block, excl. locked */ |
| 446 |
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32 | PetscCall(PetscBLASIntCast(n-ds->k-1,&n2)); /* size of trailing block */ |
| 447 | 32 | n3 = n1+n2; | |
| 448 | 32 | off = l+l*ld; | |
| 449 |
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32 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 450 | 32 | e = d+ld; | |
| 451 | |||
| 452 | /* Reduce to tridiagonal form */ | ||
| 453 |
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32 | PetscCall(DSIntermediate_HEP(ds)); |
| 454 | |||
| 455 | /* Solve the tridiagonal eigenproblem */ | ||
| 456 |
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64 | for (i=0;i<l;i++) wr[i] = d[i]; |
| 457 | |||
| 458 |
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32 | if (ds->state<DS_STATE_INTERMEDIATE) { /* Q contains useful info */ |
| 459 |
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32 | PetscCall(DSAllocateMat_Private(ds,DS_MAT_W)); |
| 460 |
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32 | PetscCall(MatCopy(ds->omat[DS_MAT_Q],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN)); |
| 461 | } | ||
| 462 |
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32 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 463 | 32 | lrwork = 20*ld; | |
| 464 | 32 | liwork = 10*ld; | |
| 465 | #if defined(PETSC_USE_COMPLEX) | ||
| 466 |
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16 | PetscCall(DSAllocateWork_Private(ds,0,lrwork+ld+ld*ld,liwork+2*ld)); |
| 467 | #else | ||
| 468 |
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16 | PetscCall(DSAllocateWork_Private(ds,0,lrwork+ld,liwork+2*ld)); |
| 469 | #endif | ||
| 470 | 32 | isuppz = ds->iwork+liwork; | |
| 471 | #if defined(PETSC_USE_COMPLEX) | ||
| 472 | 16 | ritz = ds->rwork+lrwork; | |
| 473 | 16 | Qr = ds->rwork+lrwork+ld; | |
| 474 |
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16 | PetscCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,ritz+l,Qr+off,&ld,isuppz,ds->rwork,&lrwork,ds->iwork,&liwork,&info)); |
| 475 |
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168 | for (i=l;i<n;i++) wr[i] = ritz[i]; |
| 476 | #else | ||
| 477 |
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16 | PetscCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,wr+l,Q+off,&ld,isuppz,ds->rwork,&lrwork,ds->iwork,&liwork,&info)); |
| 478 | #endif | ||
| 479 |
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32 | SlepcCheckLapackInfo("stevr",info); |
| 480 | #if defined(PETSC_USE_COMPLEX) | ||
| 481 |
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168 | for (i=l;i<n;i++) |
| 482 |
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1696 | for (j=l;j<n;j++) |
| 483 | 1544 | Q[i+j*ld] = Qr[i+j*ld]; | |
| 484 | #endif | ||
| 485 |
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32 | if (ds->state<DS_STATE_INTERMEDIATE) { /* accumulate previous Q */ |
| 486 |
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32 | if (ds->compact) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A)); |
| 487 |
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32 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 488 |
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32 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W)); |
| 489 |
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32 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n3,&n3,&n3,&one,W+off,&ld,Q+off,&ld,&zero,A+off,&ld)); |
| 490 |
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32 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 491 |
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32 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W)); |
| 492 |
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32 | PetscCall(MatDenseGetSubMatrix(ds->omat[DS_MAT_A],ds->l,ds->n,ds->l,ds->n,&At)); |
| 493 |
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32 | PetscCall(MatDenseGetSubMatrix(ds->omat[DS_MAT_Q],ds->l,ds->n,ds->l,ds->n,&Qt)); |
| 494 |
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32 | PetscCall(MatCopy(At,Qt,SAME_NONZERO_PATTERN)); |
| 495 |
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32 | PetscCall(MatDenseRestoreSubMatrix(ds->omat[DS_MAT_A],&At)); |
| 496 |
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32 | PetscCall(MatDenseRestoreSubMatrix(ds->omat[DS_MAT_Q],&Qt)); |
| 497 | } | ||
| 498 |
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32 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 499 |
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336 | for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]); |
| 500 | |||
| 501 | /* Create diagonal matrix as a result */ | ||
| 502 |
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32 | if (ds->compact) PetscCall(PetscArrayzero(e,n-1)); |
| 503 | else { | ||
| 504 |
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16 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 505 |
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208 | for (i=l;i<n;i++) PetscCall(PetscArrayzero(A+l+i*ld,n-l)); |
| 506 |
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208 | for (i=l;i<n;i++) A[i+i*ld] = d[i]; |
| 507 |
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16 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 508 | } | ||
| 509 |
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32 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 510 | |||
| 511 | /* Set zero wi */ | ||
| 512 |
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32 | if (wi) for (i=l;i<n;i++) wi[i] = 0.0; |
| 513 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 514 | } | ||
| 515 | |||
| 516 | 32 | static PetscErrorCode DSSolve_HEP_DC(DS ds,PetscScalar *wr,PetscScalar *wi) | |
| 517 | { | ||
| 518 | 32 | PetscInt i; | |
| 519 | 32 | PetscBLASInt n1,info,l = 0,ld,off,lrwork,liwork; | |
| 520 | 32 | PetscScalar *Q,*A; | |
| 521 | 32 | PetscReal *d,*e; | |
| 522 | #if defined(PETSC_USE_COMPLEX) | ||
| 523 | 16 | PetscBLASInt lwork; | |
| 524 | 16 | PetscInt j; | |
| 525 | #endif | ||
| 526 | |||
| 527 |
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32 | PetscFunctionBegin; |
| 528 |
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32 | PetscCheck(ds->bs==1,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1"); |
| 529 |
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32 | PetscCall(PetscBLASIntCast(ds->l,&l)); |
| 530 |
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32 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 531 |
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32 | PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1)); |
| 532 | 32 | off = l+l*ld; | |
| 533 |
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32 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 534 | 32 | e = d+ld; | |
| 535 | |||
| 536 | /* Reduce to tridiagonal form */ | ||
| 537 |
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32 | PetscCall(DSIntermediate_HEP(ds)); |
| 538 | |||
| 539 | /* Solve the tridiagonal eigenproblem */ | ||
| 540 |
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64 | for (i=0;i<l;i++) wr[i] = d[i]; |
| 541 | |||
| 542 | 32 | lrwork = 5*n1*n1+3*n1+1; | |
| 543 | 32 | liwork = 5*n1*n1+6*n1+6; | |
| 544 |
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32 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 545 | #if !defined(PETSC_USE_COMPLEX) | ||
| 546 |
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16 | PetscCall(DSAllocateWork_Private(ds,0,lrwork,liwork)); |
| 547 |
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16 | PetscCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->rwork,&lrwork,ds->iwork,&liwork,&info)); |
| 548 | #else | ||
| 549 | 16 | lwork = ld*ld; | |
| 550 |
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16 | PetscCall(DSAllocateWork_Private(ds,lwork,lrwork,liwork)); |
| 551 |
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16 | PetscCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->work,&lwork,ds->rwork,&lrwork,ds->iwork,&liwork,&info)); |
| 552 | /* Fixing Lapack bug*/ | ||
| 553 |
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168 | for (j=ds->l;j<ds->n;j++) |
| 554 |
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264 | for (i=0;i<ds->l;i++) Q[i+j*ld] = 0.0; |
| 555 | #endif | ||
| 556 |
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32 | SlepcCheckLapackInfo("stedc",info); |
| 557 |
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32 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 558 |
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336 | for (i=l;i<ds->n;i++) wr[i] = d[i]; |
| 559 | |||
| 560 | /* Create diagonal matrix as a result */ | ||
| 561 |
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32 | if (ds->compact) PetscCall(PetscArrayzero(e,ds->n-1)); |
| 562 | else { | ||
| 563 |
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16 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 564 |
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208 | for (i=l;i<ds->n;i++) PetscCall(PetscArrayzero(A+l+i*ld,ds->n-l)); |
| 565 |
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208 | for (i=l;i<ds->n;i++) A[i+i*ld] = d[i]; |
| 566 |
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16 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 567 | } | ||
| 568 |
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32 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 569 | |||
| 570 | /* Set zero wi */ | ||
| 571 |
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32 | if (wi) for (i=l;i<ds->n;i++) wi[i] = 0.0; |
| 572 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 573 | } | ||
| 574 | |||
| 575 | #if !defined(PETSC_USE_COMPLEX) | ||
| 576 | 8 | static PetscErrorCode DSSolve_HEP_BDC(DS ds,PetscScalar *wr,PetscScalar *wi) | |
| 577 | { | ||
| 578 | 8 | PetscBLASInt i,j,k,m,n = 0,info,nblks,bs = 0,ld = 0,lde,lrwork,liwork,*ksizes,*iwork,mingapi; | |
| 579 | 8 | PetscScalar *Q,*A; | |
| 580 | 8 | PetscReal *D,*E,*d,*e,tol=PETSC_MACHINE_EPSILON/2,tau1=1e-16,tau2=1e-18,*rwork,mingap; | |
| 581 | |||
| 582 |
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8 | PetscFunctionBegin; |
| 583 |
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8 | PetscCheck(ds->l==0,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for l>1"); |
| 584 |
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8 | PetscCheck(!ds->compact,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for compact storage"); |
| 585 |
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8 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 586 |
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8 | PetscCall(PetscBLASIntCast(ds->bs,&bs)); |
| 587 |
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8 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 588 | 8 | nblks = n/bs; | |
| 589 |
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8 | PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d)); |
| 590 | 8 | e = d+ld; | |
| 591 | 8 | lrwork = 4*n*n+60*n+1; | |
| 592 | 8 | liwork = 5*n+5*nblks-1; | |
| 593 | 8 | lde = 2*bs+1; | |
| 594 |
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8 | PetscCall(DSAllocateWork_Private(ds,bs*n+lde*lde*(nblks-1),lrwork,nblks+liwork)); |
| 595 | 8 | D = ds->work; | |
| 596 | 8 | E = ds->work+bs*n; | |
| 597 | 8 | rwork = ds->rwork; | |
| 598 | 8 | ksizes = ds->iwork; | |
| 599 | 8 | iwork = ds->iwork+nblks; | |
| 600 |
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8 | PetscCall(PetscArrayzero(iwork,liwork)); |
| 601 | |||
| 602 | /* Copy matrix to block tridiagonal format */ | ||
| 603 |
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8 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 604 | j=0; | ||
| 605 |
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44 | for (i=0;i<nblks;i++) { |
| 606 | 36 | ksizes[i]=bs; | |
| 607 |
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144 | for (k=0;k<bs;k++) |
| 608 |
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432 | for (m=0;m<bs;m++) |
| 609 | 324 | D[k+m*bs+i*bs*bs] = PetscRealPart(A[j+k+(j+m)*n]); | |
| 610 | 36 | j = j + bs; | |
| 611 | } | ||
| 612 | j=0; | ||
| 613 |
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36 | for (i=0;i<nblks-1;i++) { |
| 614 |
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112 | for (k=0;k<bs;k++) |
| 615 |
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336 | for (m=0;m<bs;m++) |
| 616 | 252 | E[k+m*lde+i*lde*lde] = PetscRealPart(A[j+bs+k+(j+m)*n]); | |
| 617 | 28 | j = j + bs; | |
| 618 | } | ||
| 619 |
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8 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 620 | |||
| 621 | /* Solve the block tridiagonal eigenproblem */ | ||
| 622 |
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8 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 623 |
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8 | PetscCall(BDC_dsbtdc_("D","A",n,nblks,ksizes,D,bs,bs,E,lde,lde,tol,tau1,tau2,d,Q,n,rwork,lrwork,iwork,liwork,&mingap,&mingapi,&info,1,1)); |
| 624 |
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8 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 625 |
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116 | for (i=0;i<ds->n;i++) wr[i] = d[i]; |
| 626 | |||
| 627 | /* Create diagonal matrix as a result */ | ||
| 628 |
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8 | if (ds->compact) PetscCall(PetscArrayzero(e,ds->n-1)); |
| 629 | else { | ||
| 630 |
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8 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 631 |
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116 | for (i=0;i<ds->n;i++) PetscCall(PetscArrayzero(A+i*ld,ds->n)); |
| 632 |
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116 | for (i=0;i<ds->n;i++) A[i+i*ld] = wr[i]; |
| 633 |
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8 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 634 | } | ||
| 635 |
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8 | PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d)); |
| 636 | |||
| 637 | /* Set zero wi */ | ||
| 638 |
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8 | if (wi) for (i=0;i<ds->n;i++) wi[i] = 0.0; |
| 639 |
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2 | PetscFunctionReturn(PETSC_SUCCESS); |
| 640 | } | ||
| 641 | #endif | ||
| 642 | |||
| 643 | 19867 | static PetscErrorCode DSTruncate_HEP(DS ds,PetscInt n,PetscBool trim) | |
| 644 | { | ||
| 645 | 19867 | PetscInt i,ld=ds->ld,l=ds->l; | |
| 646 | 19867 | PetscScalar *A; | |
| 647 | |||
| 648 |
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19867 | PetscFunctionBegin; |
| 649 |
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19867 | if (!ds->compact && ds->extrarow) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 650 |
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19867 | if (trim) { |
| 651 |
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2170 | if (!ds->compact && ds->extrarow) { /* clean extra row */ |
| 652 | ✗ | for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0; | |
| 653 | } | ||
| 654 | 2170 | ds->l = 0; | |
| 655 | 2170 | ds->k = 0; | |
| 656 | 2170 | ds->n = n; | |
| 657 | 2170 | ds->t = ds->n; /* truncated length equal to the new dimension */ | |
| 658 | } else { | ||
| 659 |
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17697 | if (!ds->compact && ds->extrarow && ds->k==ds->n) { |
| 660 | /* copy entries of extra row to the new position, then clean last row */ | ||
| 661 | ✗ | for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld]; | |
| 662 | ✗ | for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0; | |
| 663 | } | ||
| 664 |
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17697 | ds->k = (ds->extrarow)? n: 0; |
| 665 | 17697 | ds->t = ds->n; /* truncated length equal to previous dimension */ | |
| 666 | 17697 | ds->n = n; | |
| 667 | } | ||
| 668 |
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19867 | if (!ds->compact && ds->extrarow) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
| 669 |
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4821 | PetscFunctionReturn(PETSC_SUCCESS); |
| 670 | } | ||
| 671 | |||
| 672 | #if !defined(PETSC_HAVE_MPIUNI) | ||
| 673 | 16 | static PetscErrorCode DSSynchronize_HEP(DS ds,PetscScalar eigr[],PetscScalar eigi[]) | |
| 674 | { | ||
| 675 | 16 | PetscInt ld=ds->ld,l=ds->l,k=0,kr=0; | |
| 676 | 16 | PetscMPIInt n,rank,off=0,size,ldn,ld3; | |
| 677 | 16 | PetscScalar *A,*Q; | |
| 678 | 16 | PetscReal *T; | |
| 679 | |||
| 680 |
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16 | PetscFunctionBegin; |
| 681 |
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16 | if (ds->compact) kr = 3*ld; |
| 682 | ✗ | else k = (ds->n-l)*ld; | |
| 683 |
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16 | if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld; |
| 684 |
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16 | if (eigr) k += (ds->n-l); |
| 685 |
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16 | PetscCall(DSAllocateWork_Private(ds,k+kr,0,0)); |
| 686 |
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16 | PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size)); |
| 687 |
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16 | PetscCall(PetscMPIIntCast(ds->n-l,&n)); |
| 688 |
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16 | PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn)); |
| 689 |
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16 | PetscCall(PetscMPIIntCast(ld*3,&ld3)); |
| 690 |
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16 | if (ds->compact) PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T)); |
| 691 | ✗ | else PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); | |
| 692 |
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16 | if (ds->state>DS_STATE_RAW) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q)); |
| 693 |
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16 | PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank)); |
| 694 |
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16 | if (!rank) { |
| 695 |
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8 | if (ds->compact) PetscCallMPI(MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds))); |
| 696 | ✗ | else PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds))); | |
| 697 |
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8 | if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds))); |
| 698 |
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8 | if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds))); |
| 699 | } | ||
| 700 |
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32 | PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds))); |
| 701 |
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16 | if (rank) { |
| 702 |
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|
8 | if (ds->compact) PetscCallMPI(MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds))); |
| 703 | ✗ | else PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds))); | |
| 704 |
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8 | if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds))); |
| 705 |
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8 | if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds))); |
| 706 | } | ||
| 707 |
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|
16 | if (ds->compact) PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T)); |
| 708 | ✗ | else PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); | |
| 709 |
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16 | if (ds->state>DS_STATE_RAW) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q)); |
| 710 |
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|
4 | PetscFunctionReturn(PETSC_SUCCESS); |
| 711 | } | ||
| 712 | #endif | ||
| 713 | |||
| 714 | 1020 | static PetscErrorCode DSCond_HEP(DS ds,PetscReal *cond) | |
| 715 | { | ||
| 716 | 1020 | PetscScalar *work; | |
| 717 | 1020 | PetscReal *rwork; | |
| 718 | 1020 | PetscBLASInt *ipiv; | |
| 719 | 1020 | PetscBLASInt lwork,info,n,ld; | |
| 720 | 1020 | PetscReal hn,hin; | |
| 721 | 1020 | PetscScalar *A; | |
| 722 | |||
| 723 |
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1020 | PetscFunctionBegin; |
| 724 |
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1020 | PetscCall(PetscBLASIntCast(ds->n,&n)); |
| 725 |
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1020 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 726 | 1020 | lwork = 8*ld; | |
| 727 |
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1020 | PetscCall(DSAllocateWork_Private(ds,lwork,ld,ld)); |
| 728 | 1020 | work = ds->work; | |
| 729 | 1020 | rwork = ds->rwork; | |
| 730 | 1020 | ipiv = ds->iwork; | |
| 731 |
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1020 | if (ds->compact) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A)); |
| 732 |
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1020 | PetscCall(DSSwitchFormat_HEP(ds)); |
| 733 | |||
| 734 | /* use workspace matrix W to avoid overwriting A */ | ||
| 735 |
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1020 | PetscCall(DSAllocateMat_Private(ds,DS_MAT_W)); |
| 736 |
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1020 | PetscCall(MatCopy(ds->omat[DS_MAT_A],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN)); |
| 737 |
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1020 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&A)); |
| 738 | |||
| 739 | /* norm of A */ | ||
| 740 | 1020 | hn = LAPACKlange_("I",&n,&n,A,&ld,rwork); | |
| 741 | |||
| 742 | /* norm of inv(A) */ | ||
| 743 |
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1020 | PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info)); |
| 744 |
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1020 | SlepcCheckLapackInfo("getrf",info); |
| 745 |
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1020 | PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info)); |
| 746 |
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1020 | SlepcCheckLapackInfo("getri",info); |
| 747 | 1020 | hin = LAPACKlange_("I",&n,&n,A,&ld,rwork); | |
| 748 |
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1020 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&A)); |
| 749 | |||
| 750 | 1020 | *cond = hn*hin; | |
| 751 |
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1020 | PetscFunctionReturn(PETSC_SUCCESS); |
| 752 | } | ||
| 753 | |||
| 754 | 101 | static PetscErrorCode DSTranslateRKS_HEP(DS ds,PetscScalar alpha) | |
| 755 | { | ||
| 756 | 101 | PetscInt i,j,k=ds->k; | |
| 757 | 101 | PetscScalar *Q,*A,*R,*tau,*work; | |
| 758 | 101 | PetscBLASInt ld,n1,n0,lwork,info; | |
| 759 | |||
| 760 |
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101 | PetscFunctionBegin; |
| 761 |
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101 | PetscCall(PetscBLASIntCast(ds->ld,&ld)); |
| 762 |
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101 | PetscCall(DSAllocateWork_Private(ds,ld*ld,0,0)); |
| 763 | 101 | tau = ds->work; | |
| 764 | 101 | work = ds->work+ld; | |
| 765 |
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101 | PetscCall(PetscBLASIntCast(ld*(ld-1),&lwork)); |
| 766 |
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101 | PetscCall(DSAllocateMat_Private(ds,DS_MAT_W)); |
| 767 |
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101 | PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A)); |
| 768 |
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101 | PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_Q],&Q)); |
| 769 |
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101 | PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&R)); |
| 770 | |||
| 771 | /* copy I+alpha*A */ | ||
| 772 |
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101 | PetscCall(PetscArrayzero(Q,ld*ld)); |
| 773 |
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101 | PetscCall(PetscArrayzero(R,ld*ld)); |
| 774 |
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1492 | for (i=0;i<k;i++) { |
| 775 | 1391 | Q[i+i*ld] = 1.0 + alpha*A[i+i*ld]; | |
| 776 | 1391 | Q[k+i*ld] = alpha*A[k+i*ld]; | |
| 777 | } | ||
| 778 | |||
| 779 | /* compute qr */ | ||
| 780 |
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101 | PetscCall(PetscBLASIntCast(k+1,&n1)); |
| 781 |
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101 | PetscCall(PetscBLASIntCast(k,&n0)); |
| 782 |
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101 | PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&n1,&n0,Q,&ld,tau,work,&lwork,&info)); |
| 783 |
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101 | SlepcCheckLapackInfo("geqrf",info); |
| 784 | |||
| 785 | /* copy R from Q */ | ||
| 786 |
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1492 | for (j=0;j<k;j++) |
| 787 |
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11901 | for (i=0;i<=j;i++) |
| 788 | 10510 | R[i+j*ld] = Q[i+j*ld]; | |
| 789 | |||
| 790 | /* compute orthogonal matrix in Q */ | ||
| 791 |
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101 | PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&n1,&n1,&n0,Q,&ld,tau,work,&lwork,&info)); |
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101 | SlepcCheckLapackInfo("orgqr",info); |
| 793 | |||
| 794 | /* compute the updated matrix of projected problem */ | ||
| 795 |
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1492 | for (j=0;j<k;j++) |
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22411 | for (i=0;i<k+1;i++) |
| 797 | 21020 | A[j*ld+i] = Q[i*ld+j]; | |
| 798 | 101 | alpha = -1.0/alpha; | |
| 799 |
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101 | PetscCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&n1,&n0,&alpha,R,&ld,A,&ld)); |
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1492 | for (i=0;i<k;i++) |
| 801 | 1391 | A[ld*i+i] -= alpha; | |
| 802 | |||
| 803 |
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101 | PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A)); |
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101 | PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_Q],&Q)); |
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101 | PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&R)); |
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23 | PetscFunctionReturn(PETSC_SUCCESS); |
| 807 | } | ||
| 808 | |||
| 809 | 187543 | static PetscErrorCode DSHermitian_HEP(DS ds,DSMatType m,PetscBool *flg) | |
| 810 | { | ||
| 811 |
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187543 | PetscFunctionBegin; |
| 812 |
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187543 | if (m==DS_MAT_A && !ds->extrarow) *flg = PETSC_TRUE; |
| 813 | 130788 | else *flg = PETSC_FALSE; | |
| 814 |
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187543 | PetscFunctionReturn(PETSC_SUCCESS); |
| 815 | } | ||
| 816 | |||
| 817 | 546 | static PetscErrorCode DSSetCompact_HEP(DS ds,PetscBool comp) | |
| 818 | { | ||
| 819 |
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546 | PetscFunctionBegin; |
| 820 |
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546 | if (!comp) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A)); |
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130 | PetscFunctionReturn(PETSC_SUCCESS); |
| 822 | } | ||
| 823 | |||
| 824 | 39 | static PetscErrorCode DSReallocate_HEP(DS ds,PetscInt ld) | |
| 825 | { | ||
| 826 | 39 | PetscInt i,*perm=ds->perm; | |
| 827 | |||
| 828 |
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39 | PetscFunctionBegin; |
| 829 |
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897 | for (i=0;i<DS_NUM_MAT;i++) { |
| 830 |
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858 | if (!ds->compact && i==DS_MAT_A) continue; |
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858 | if (i!=DS_MAT_Q && i!=DS_MAT_T) PetscCall(MatDestroy(&ds->omat[i])); |
| 832 | } | ||
| 833 | |||
| 834 |
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39 | if (!ds->compact) PetscCall(DSReallocateMat_Private(ds,DS_MAT_A,ld)); |
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39 | PetscCall(DSReallocateMat_Private(ds,DS_MAT_Q,ld)); |
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39 | PetscCall(DSReallocateMat_Private(ds,DS_MAT_T,ld)); |
| 837 | |||
| 838 |
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39 | PetscCall(PetscMalloc1(ld,&ds->perm)); |
| 839 |
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39 | PetscCall(PetscArraycpy(ds->perm,perm,ds->ld)); |
| 840 |
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39 | PetscCall(PetscFree(perm)); |
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10 | PetscFunctionReturn(PETSC_SUCCESS); |
| 842 | } | ||
| 843 | |||
| 844 | /*MC | ||
| 845 | DSHEP - Dense Hermitian Eigenvalue Problem. | ||
| 846 | |||
| 847 | Notes: | ||
| 848 | The problem is expressed as $AX = X\Lambda$, where $A$ is real symmetric | ||
| 849 | (or complex Hermitian). $\Lambda$ is a diagonal matrix whose diagonal | ||
| 850 | elements are the arguments of `DSSolve()`. After solve, $A$ is overwritten | ||
| 851 | with $\Lambda$. | ||
| 852 | |||
| 853 | In the intermediate state $A$ is reduced to tridiagonal form. In compact | ||
| 854 | storage format, the symmetric tridiagonal matrix is stored in $T$. | ||
| 855 | |||
| 856 | Used DS matrices: | ||
| 857 | + `DS_MAT_A` - problem matrix (used only if `compact=PETSC_FALSE`) | ||
| 858 | . `DS_MAT_T` - symmetric tridiagonal matrix | ||
| 859 | - `DS_MAT_Q` - orthogonal/unitary transformation that reduces to tridiagonal form | ||
| 860 | (intermediate step) or matrix of orthogonal eigenvectors, which is equal to $X$ | ||
| 861 | |||
| 862 | Implemented methods: | ||
| 863 | + 0 - Implicit QR (`_steqr`) | ||
| 864 | . 1 - Multiple Relatively Robust Representations (`_stevr`) | ||
| 865 | . 2 - Divide and Conquer (`_stedc`) | ||
| 866 | - 3 - Block Divide and Conquer (real scalars only) | ||
| 867 | |||
| 868 | Level: beginner | ||
| 869 | |||
| 870 | .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`, `DSSetCompact()` | ||
| 871 | M*/ | ||
| 872 | 2800 | SLEPC_EXTERN PetscErrorCode DSCreate_HEP(DS ds) | |
| 873 | { | ||
| 874 |
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2800 | PetscFunctionBegin; |
| 875 | 2800 | ds->ops->allocate = DSAllocate_HEP; | |
| 876 | 2800 | ds->ops->view = DSView_HEP; | |
| 877 | 2800 | ds->ops->vectors = DSVectors_HEP; | |
| 878 | 2800 | ds->ops->solve[0] = DSSolve_HEP_QR; | |
| 879 | 2800 | ds->ops->solve[1] = DSSolve_HEP_MRRR; | |
| 880 | 2800 | ds->ops->solve[2] = DSSolve_HEP_DC; | |
| 881 | #if !defined(PETSC_USE_COMPLEX) | ||
| 882 | 1407 | ds->ops->solve[3] = DSSolve_HEP_BDC; | |
| 883 | #endif | ||
| 884 | 2800 | ds->ops->sort = DSSort_HEP; | |
| 885 | 2800 | ds->ops->truncate = DSTruncate_HEP; | |
| 886 | 2800 | ds->ops->update = DSUpdateExtraRow_HEP; | |
| 887 | 2800 | ds->ops->cond = DSCond_HEP; | |
| 888 | 2800 | ds->ops->transrks = DSTranslateRKS_HEP; | |
| 889 | 2800 | ds->ops->hermitian = DSHermitian_HEP; | |
| 890 | #if !defined(PETSC_HAVE_MPIUNI) | ||
| 891 | 2800 | ds->ops->synchronize = DSSynchronize_HEP; | |
| 892 | #endif | ||
| 893 | 2800 | ds->ops->setcompact = DSSetCompact_HEP; | |
| 894 | 2800 | ds->ops->reallocate = DSReallocate_HEP; | |
| 895 |
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2800 | PetscFunctionReturn(PETSC_SUCCESS); |
| 896 | } | ||
| 897 |