Actual source code: dshep.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: PetscErrorCode DSAllocate_HEP(DS ds,PetscInt ld)
     15: {

     19:   DSAllocateMat_Private(ds,DS_MAT_A);
     20:   DSAllocateMat_Private(ds,DS_MAT_Q);
     21:   DSAllocateMatReal_Private(ds,DS_MAT_T);
     22:   PetscFree(ds->perm);
     23:   PetscMalloc1(ld,&ds->perm);
     24:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     25:   return(0);
     26: }

     28: /*   0       l           k                 n-1
     29:     -----------------------------------------
     30:     |*       .           .                  |
     31:     |  *     .           .                  |
     32:     |    *   .           .                  |
     33:     |      * .           .                  |
     34:     |. . . . o           o                  |
     35:     |          o         o                  |
     36:     |            o       o                  |
     37:     |              o     o                  |
     38:     |                o   o                  |
     39:     |                  o o                  |
     40:     |. . . . o o o o o o o x                |
     41:     |                    x x x              |
     42:     |                      x x x            |
     43:     |                        x x x          |
     44:     |                          x x x        |
     45:     |                            x x x      |
     46:     |                              x x x    |
     47:     |                                x x x  |
     48:     |                                  x x x|
     49:     |                                    x x|
     50:     -----------------------------------------
     51: */

     53: static PetscErrorCode DSSwitchFormat_HEP(DS ds,PetscBool tocompact)
     54: {
     56:   PetscReal      *T = ds->rmat[DS_MAT_T];
     57:   PetscScalar    *A = ds->mat[DS_MAT_A];
     58:   PetscInt       i,n=ds->n,k=ds->k,ld=ds->ld;

     61:   if (tocompact) { /* switch from dense (arrow) to compact storage */
     62:     PetscMemzero(T,3*ld*sizeof(PetscReal));
     63:     for (i=0;i<k;i++) {
     64:       T[i] = PetscRealPart(A[i+i*ld]);
     65:       T[i+ld] = PetscRealPart(A[k+i*ld]);
     66:     }
     67:     for (i=k;i<n-1;i++) {
     68:       T[i]    = PetscRealPart(A[i+i*ld]);
     69:       T[i+ld] = PetscRealPart(A[i+1+i*ld]);
     70:     }
     71:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
     72:     if (ds->extrarow) T[n-1+ld] = PetscRealPart(A[n+(n-1)*ld]);
     73:   } else { /* switch from compact (arrow) to dense storage */
     74:     PetscMemzero(A,ld*ld*sizeof(PetscScalar));
     75:     for (i=0;i<k;i++) {
     76:       A[i+i*ld] = T[i];
     77:       A[k+i*ld] = T[i+ld];
     78:       A[i+k*ld] = T[i+ld];
     79:     }
     80:     A[k+k*ld] = T[k];
     81:     for (i=k+1;i<n;i++) {
     82:       A[i+i*ld]     = T[i];
     83:       A[i-1+i*ld]   = T[i-1+ld];
     84:       A[i+(i-1)*ld] = T[i-1+ld];
     85:     }
     86:     if (ds->extrarow) A[n+(n-1)*ld] = T[n-1+ld];
     87:   }
     88:   return(0);
     89: }

     91: PetscErrorCode DSView_HEP(DS ds,PetscViewer viewer)
     92: {
     93:   PetscErrorCode    ierr;
     94:   PetscViewerFormat format;
     95:   PetscInt          i,j,r,c,rows;
     96:   PetscReal         value;
     97:   const char        *methodname[] = {
     98:                      "Implicit QR method (_steqr)",
     99:                      "Relatively Robust Representations (_stevr)",
    100:                      "Divide and Conquer method (_stedc)",
    101:                      "Block Divide and Conquer method (dsbtdc)"
    102:   };
    103:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

    106:   PetscViewerGetFormat(viewer,&format);
    107:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    108:     if (ds->bs>1) {
    109:       PetscViewerASCIIPrintf(viewer,"block size: %D\n",ds->bs);
    110:     }
    111:     if (ds->method<nmeth) {
    112:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
    113:     }
    114:     return(0);
    115:   }
    116:   if (ds->compact) {
    117:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    118:     rows = ds->extrarow? ds->n+1: ds->n;
    119:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
    120:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",rows,ds->n);
    121:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
    122:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
    123:       for (i=0;i<ds->n;i++) {
    124:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
    125:       }
    126:       for (i=0;i<rows-1;i++) {
    127:         r = PetscMax(i+2,ds->k+1);
    128:         c = i+1;
    129:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",r,c,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    130:         if (i<ds->n-1 && ds->k<ds->n) { /* do not print vertical arrow when k=n */
    131:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",c,r,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    132:         }
    133:       }
    134:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
    135:     } else {
    136:       for (i=0;i<rows;i++) {
    137:         for (j=0;j<ds->n;j++) {
    138:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    139:           else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
    140:           else if (i==j+1 && i>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+i-1);
    141:           else if (i+1==j && j>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+j-1);
    142:           else value = 0.0;
    143:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    144:         }
    145:         PetscViewerASCIIPrintf(viewer,"\n");
    146:       }
    147:     }
    148:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    149:     PetscViewerFlush(viewer);
    150:   } else {
    151:     DSViewMat(ds,viewer,DS_MAT_A);
    152:   }
    153:   if (ds->state>DS_STATE_INTERMEDIATE) {
    154:     DSViewMat(ds,viewer,DS_MAT_Q);
    155:   }
    156:   return(0);
    157: }

    159: PetscErrorCode DSVectors_HEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    160: {
    161:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    162:   PetscInt       ld = ds->ld,i;

    166:   switch (mat) {
    167:     case DS_MAT_X:
    168:     case DS_MAT_Y:
    169:       if (j) {
    170:         if (ds->state>=DS_STATE_CONDENSED) {
    171:           PetscMemcpy(ds->mat[mat]+(*j)*ld,Q+(*j)*ld,ld*sizeof(PetscScalar));
    172:         } else {
    173:           PetscMemzero(ds->mat[mat]+(*j)*ld,ld*sizeof(PetscScalar));
    174:           *(ds->mat[mat]+(*j)+(*j)*ld) = 1.0;
    175:         }
    176:       } else {
    177:         if (ds->state>=DS_STATE_CONDENSED) {
    178:           PetscMemcpy(ds->mat[mat],Q,ld*ld*sizeof(PetscScalar));
    179:         } else {
    180:           PetscMemzero(ds->mat[mat],ld*ld*sizeof(PetscScalar));
    181:           for (i=0;i<ds->n;i++) *(ds->mat[mat]+i+i*ld) = 1.0;
    182:         }
    183:       }
    184:       if (rnorm && j) *rnorm = PetscAbsScalar(Q[ds->n-1+(*j)*ld]);
    185:       break;
    186:     case DS_MAT_U:
    187:     case DS_MAT_VT:
    188:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    189:       break;
    190:     default:
    191:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    192:   }
    193:   return(0);
    194: }

    196: /*
    197:   ARROWTRIDIAG reduces a symmetric arrowhead matrix of the form

    199:                 [ d 0 0 0 e ]
    200:                 [ 0 d 0 0 e ]
    201:             A = [ 0 0 d 0 e ]
    202:                 [ 0 0 0 d e ]
    203:                 [ e e e e d ]

    205:   to tridiagonal form

    207:                 [ d e 0 0 0 ]
    208:                 [ e d e 0 0 ]
    209:    T = Q'*A*Q = [ 0 e d e 0 ],
    210:                 [ 0 0 e d e ]
    211:                 [ 0 0 0 e d ]

    213:   where Q is an orthogonal matrix. Rutishauser's algorithm is used to
    214:   perform the reduction, which requires O(n**2) flops. The accumulation
    215:   of the orthogonal factor Q, however, requires O(n**3) flops.

    217:   Arguments
    218:   =========

    220:   N       (input) INTEGER
    221:           The order of the matrix A.  N >= 0.

    223:   D       (input/output) DOUBLE PRECISION array, dimension (N)
    224:           On entry, the diagonal entries of the matrix A to be
    225:           reduced.
    226:           On exit, the diagonal entries of the reduced matrix T.

    228:   E       (input/output) DOUBLE PRECISION array, dimension (N-1)
    229:           On entry, the off-diagonal entries of the matrix A to be
    230:           reduced.
    231:           On exit, the subdiagonal entries of the reduced matrix T.

    233:   Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
    234:           On exit, the orthogonal matrix Q.

    236:   LDQ     (input) INTEGER
    237:           The leading dimension of the array Q.

    239:   Note
    240:   ====
    241:   Based on Fortran code contributed by Daniel Kressner
    242: */
    243: static PetscErrorCode ArrowTridiag(PetscBLASInt n,PetscReal *d,PetscReal *e,PetscScalar *Q,PetscBLASInt ld)
    244: {
    245: #if defined(SLEPC_MISSING_LAPACK_LARTG)
    247:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARTG - Lapack routine is unavailable");
    248: #else
    249:   PetscBLASInt i,j,j2,one=1;
    250:   PetscReal    c,s,p,off,temp;

    253:   if (n<=2) return(0);

    255:   for (j=0;j<n-2;j++) {

    257:     /* Eliminate entry e(j) by a rotation in the planes (j,j+1) */
    258:     temp = e[j+1];
    259:     PetscStackCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&e[j],&c,&s,&e[j+1]));
    260:     s = -s;

    262:     /* Apply rotation to diagonal elements */
    263:     temp   = d[j+1];
    264:     e[j]   = c*s*(temp-d[j]);
    265:     d[j+1] = s*s*d[j] + c*c*temp;
    266:     d[j]   = c*c*d[j] + s*s*temp;

    268:     /* Apply rotation to Q */
    269:     j2 = j+2;
    270:     PetscStackCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+j*ld,&one,Q+(j+1)*ld,&one,&c,&s));

    272:     /* Chase newly introduced off-diagonal entry to the top left corner */
    273:     for (i=j-1;i>=0;i--) {
    274:       off  = -s*e[i];
    275:       e[i] = c*e[i];
    276:       temp = e[i+1];
    277:       PetscStackCallBLAS("LAPACKlartg",LAPACKREALlartg_(&temp,&off,&c,&s,&e[i+1]));
    278:       s = -s;
    279:       temp = (d[i]-d[i+1])*s - 2.0*c*e[i];
    280:       p = s*temp;
    281:       d[i+1] += p;
    282:       d[i] -= p;
    283:       e[i] = -e[i] - c*temp;
    284:       j2 = j+2;
    285:       PetscStackCallBLAS("BLASrot",BLASMIXEDrot_(&j2,Q+i*ld,&one,Q+(i+1)*ld,&one,&c,&s));
    286:     }
    287:   }
    288:   return(0);
    289: #endif
    290: }

    292: /*
    293:    Reduce to tridiagonal form by means of ArrowTridiag.
    294: */
    295: static PetscErrorCode DSIntermediate_HEP(DS ds)
    296: {
    297: #if defined(SLEPC_MISSING_LAPACK_SYTRD) || defined(SLEPC_MISSING_LAPACK_ORGTR)
    299:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SYTRD/ORGTR - Lapack routine is unavailable");
    300: #else
    302:   PetscInt       i;
    303:   PetscBLASInt   n1,n2,n3,lwork,info,l,n,ld,off;
    304:   PetscScalar    *A,*Q,*work,*tau;
    305:   PetscReal      *d,*e;

    308:   PetscBLASIntCast(ds->n,&n);
    309:   PetscBLASIntCast(ds->l,&l);
    310:   PetscBLASIntCast(ds->ld,&ld);
    311:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
    312:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
    313:   n3 = n1+n2;
    314:   off = l+l*ld;
    315:   A  = ds->mat[DS_MAT_A];
    316:   Q  = ds->mat[DS_MAT_Q];
    317:   d  = ds->rmat[DS_MAT_T];
    318:   e  = ds->rmat[DS_MAT_T]+ld;
    319:   PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
    320:   for (i=0;i<n;i++) Q[i+i*ld] = 1.0;

    322:   if (ds->compact) {

    324:     if (ds->state<DS_STATE_INTERMEDIATE) ArrowTridiag(n1,d+l,e+l,Q+off,ld);

    326:   } else {

    328:     for (i=0;i<l;i++) { d[i] = PetscRealPart(A[i+i*ld]); e[i] = 0.0; }

    330:     if (ds->state<DS_STATE_INTERMEDIATE) {
    331:       DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
    332:       DSAllocateWork_Private(ds,ld+ld*ld,0,0);
    333:       tau  = ds->work;
    334:       work = ds->work+ld;
    335:       lwork = ld*ld;
    336:       PetscStackCallBLAS("LAPACKsytrd",LAPACKsytrd_("L",&n3,Q+off,&ld,d+l,e+l,tau,work,&lwork,&info));
    337:       SlepcCheckLapackInfo("sytrd",info);
    338:       PetscStackCallBLAS("LAPACKorgtr",LAPACKorgtr_("L",&n3,Q+off,&ld,tau,work,&lwork,&info));
    339:       SlepcCheckLapackInfo("orgtr",info);
    340:     } else {
    341:       /* copy tridiagonal to d,e */
    342:       for (i=l;i<n;i++)   d[i] = PetscRealPart(A[i+i*ld]);
    343:       for (i=l;i<n-1;i++) e[i] = PetscRealPart(A[(i+1)+i*ld]);
    344:     }
    345:   }
    346:   return(0);
    347: #endif
    348: }

    350: PetscErrorCode DSSort_HEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    351: {
    353:   PetscInt       n,l,i,*perm,ld=ds->ld;
    354:   PetscScalar    *A;
    355:   PetscReal      *d;

    358:   if (!ds->sc) return(0);
    359:   n = ds->n;
    360:   l = ds->l;
    361:   A = ds->mat[DS_MAT_A];
    362:   d = ds->rmat[DS_MAT_T];
    363:   perm = ds->perm;
    364:   if (!rr) {
    365:     DSSortEigenvaluesReal_Private(ds,d,perm);
    366:   } else {
    367:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
    368:   }
    369:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
    370:   DSPermuteColumns_Private(ds,l,n,DS_MAT_Q,perm);
    371:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
    372:   if (!ds->compact) {
    373:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
    374:   }
    375:   return(0);
    376: }

    378: PetscErrorCode DSUpdateExtraRow_HEP(DS ds)
    379: {
    381:   PetscInt       i;
    382:   PetscBLASInt   n,ld,incx=1;
    383:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
    384:   PetscReal      *e,beta;

    387:   PetscBLASIntCast(ds->n,&n);
    388:   PetscBLASIntCast(ds->ld,&ld);
    389:   A  = ds->mat[DS_MAT_A];
    390:   Q  = ds->mat[DS_MAT_Q];
    391:   e  = ds->rmat[DS_MAT_T]+ld;

    393:   if (ds->compact) {
    394:     beta = e[n-1];   /* in compact, we assume all entries are zero except the last one */
    395:     for (i=0;i<n;i++) e[i] = PetscRealPart(beta*Q[n-1+i*ld]);
    396:     ds->k = n;
    397:   } else {
    398:     DSAllocateWork_Private(ds,2*ld,0,0);
    399:     x = ds->work;
    400:     y = ds->work+ld;
    401:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    402:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    403:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    404:     ds->k = n;
    405:   }
    406:   return(0);
    407: }

    409: PetscErrorCode DSSolve_HEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    410: {
    411: #if defined(PETSC_MISSING_LAPACK_STEQR)
    413:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEQR - Lapack routine is unavailable");
    414: #else
    416:   PetscInt       i;
    417:   PetscBLASInt   n1,n2,n3,info,l,n,ld,off;
    418:   PetscScalar    *Q,*A;
    419:   PetscReal      *d,*e;

    422:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
    423:   PetscBLASIntCast(ds->n,&n);
    424:   PetscBLASIntCast(ds->l,&l);
    425:   PetscBLASIntCast(ds->ld,&ld);
    426:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
    427:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
    428:   n3 = n1+n2;
    429:   off = l+l*ld;
    430:   Q  = ds->mat[DS_MAT_Q];
    431:   A  = ds->mat[DS_MAT_A];
    432:   d  = ds->rmat[DS_MAT_T];
    433:   e  = ds->rmat[DS_MAT_T]+ld;

    435:   /* Reduce to tridiagonal form */
    436:   DSIntermediate_HEP(ds);

    438:   /* Solve the tridiagonal eigenproblem */
    439:   for (i=0;i<l;i++) wr[i] = d[i];

    441:   DSAllocateWork_Private(ds,0,2*ld,0);
    442:   PetscStackCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n3,d+l,e+l,Q+off,&ld,ds->rwork,&info));
    443:   SlepcCheckLapackInfo("steqr",info);
    444:   for (i=l;i<n;i++) wr[i] = d[i];

    446:   /* Create diagonal matrix as a result */
    447:   if (ds->compact) {
    448:     PetscMemzero(e,(n-1)*sizeof(PetscReal));
    449:   } else {
    450:     for (i=l;i<n;i++) {
    451:       PetscMemzero(A+l+i*ld,(n-l)*sizeof(PetscScalar));
    452:     }
    453:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
    454:   }

    456:   /* Set zero wi */
    457:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
    458:   return(0);
    459: #endif
    460: }

    462: PetscErrorCode DSSolve_HEP_MRRR(DS ds,PetscScalar *wr,PetscScalar *wi)
    463: {
    464: #if defined(SLEPC_MISSING_LAPACK_STEVR)
    466:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEVR - Lapack routine is unavailable");
    467: #else
    469:   PetscInt       i;
    470:   PetscBLASInt   n1,n2,n3,lwork,liwork,info,l,n,m,ld,off,il,iu,*isuppz;
    471:   PetscScalar    *A,*Q,*W=NULL,one=1.0,zero=0.0;
    472:   PetscReal      *d,*e,abstol=0.0,vl,vu;
    473: #if defined(PETSC_USE_COMPLEX)
    474:   PetscInt       j;
    475:   PetscReal      *ritz;
    476: #endif

    479:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
    480:   PetscBLASIntCast(ds->n,&n);
    481:   PetscBLASIntCast(ds->l,&l);
    482:   PetscBLASIntCast(ds->ld,&ld);
    483:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
    484:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
    485:   n3 = n1+n2;
    486:   off = l+l*ld;
    487:   A  = ds->mat[DS_MAT_A];
    488:   Q  = ds->mat[DS_MAT_Q];
    489:   d  = ds->rmat[DS_MAT_T];
    490:   e  = ds->rmat[DS_MAT_T]+ld;

    492:   /* Reduce to tridiagonal form */
    493:   DSIntermediate_HEP(ds);

    495:   /* Solve the tridiagonal eigenproblem */
    496:   for (i=0;i<l;i++) wr[i] = d[i];

    498:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* Q contains useful info */
    499:     DSAllocateMat_Private(ds,DS_MAT_W);
    500:     DSCopyMatrix_Private(ds,DS_MAT_W,DS_MAT_Q);
    501:     W = ds->mat[DS_MAT_W];
    502:   }
    503: #if defined(PETSC_USE_COMPLEX)
    504:   DSAllocateMatReal_Private(ds,DS_MAT_Q);
    505: #endif
    506:   lwork = 20*ld;
    507:   liwork = 10*ld;
    508:   DSAllocateWork_Private(ds,0,lwork+ld,liwork+2*ld);
    509:   isuppz = ds->iwork+liwork;
    510: #if defined(PETSC_USE_COMPLEX)
    511:   ritz = ds->rwork+lwork;
    512:   PetscStackCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,ritz+l,ds->rmat[DS_MAT_Q]+off,&ld,isuppz,ds->rwork,&lwork,ds->iwork,&liwork,&info));
    513:   for (i=l;i<n;i++) wr[i] = ritz[i];
    514: #else
    515:   PetscStackCallBLAS("LAPACKstevr",LAPACKstevr_("V","A",&n3,d+l,e+l,&vl,&vu,&il,&iu,&abstol,&m,wr+l,Q+off,&ld,isuppz,ds->rwork,&lwork,ds->iwork,&liwork,&info));
    516: #endif
    517:   SlepcCheckLapackInfo("stevr",info);
    518: #if defined(PETSC_USE_COMPLEX)
    519:   for (i=l;i<n;i++)
    520:     for (j=l;j<n;j++)
    521:       Q[i+j*ld] = (ds->rmat[DS_MAT_Q])[i+j*ld];
    522: #endif
    523:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* accumulate previous Q */
    524:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n3,&n3,&n3,&one,W+off,&ld,Q+off,&ld,&zero,A+off,&ld));
    525:     DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
    526:   }
    527:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);

    529:   /* Create diagonal matrix as a result */
    530:   if (ds->compact) {
    531:     PetscMemzero(e,(n-1)*sizeof(PetscReal));
    532:   } else {
    533:     for (i=l;i<n;i++) {
    534:       PetscMemzero(A+l+i*ld,(n-l)*sizeof(PetscScalar));
    535:     }
    536:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
    537:   }

    539:   /* Set zero wi */
    540:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
    541:   return(0);
    542: #endif
    543: }

    545: PetscErrorCode DSSolve_HEP_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
    546: {
    547: #if defined(SLEPC_MISSING_LAPACK_STEDC)
    549:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEDC - Lapack routine is unavailable");
    550: #else
    552:   PetscInt       i;
    553:   PetscBLASInt   n1,info,l,ld,off,lrwork,liwork;
    554:   PetscScalar    *Q,*A;
    555:   PetscReal      *d,*e;
    556: #if defined(PETSC_USE_COMPLEX)
    557:   PetscBLASInt   lwork;
    558:   PetscInt       j;
    559: #endif

    562:   if (ds->bs>1) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for bs>1");
    563:   PetscBLASIntCast(ds->l,&l);
    564:   PetscBLASIntCast(ds->ld,&ld);
    565:   PetscBLASIntCast(ds->n-ds->l,&n1);
    566:   off = l+l*ld;
    567:   Q  = ds->mat[DS_MAT_Q];
    568:   A  = ds->mat[DS_MAT_A];
    569:   d  = ds->rmat[DS_MAT_T];
    570:   e  = ds->rmat[DS_MAT_T]+ld;

    572:   /* Reduce to tridiagonal form */
    573:   DSIntermediate_HEP(ds);

    575:   /* Solve the tridiagonal eigenproblem */
    576:   for (i=0;i<l;i++) wr[i] = d[i];

    578:   lrwork = 5*n1*n1+3*n1+1;
    579:   liwork = 5*n1*n1+6*n1+6;
    580: #if !defined(PETSC_USE_COMPLEX)
    581:   DSAllocateWork_Private(ds,0,lrwork,liwork);
    582:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
    583: #else
    584:   lwork = ld*ld;
    585:   DSAllocateWork_Private(ds,lwork,lrwork,liwork);
    586:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->work,&lwork,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
    587:   /* Fixing Lapack bug*/
    588:   for (j=ds->l;j<ds->n;j++)
    589:     for (i=0;i<ds->l;i++) Q[i+j*ld] = 0.0;
    590: #endif
    591:   SlepcCheckLapackInfo("stedc",info);
    592:   for (i=l;i<ds->n;i++) wr[i] = d[i];

    594:   /* Create diagonal matrix as a result */
    595:   if (ds->compact) {
    596:     PetscMemzero(e,(ds->n-1)*sizeof(PetscReal));
    597:   } else {
    598:     for (i=l;i<ds->n;i++) {
    599:       PetscMemzero(A+l+i*ld,(ds->n-l)*sizeof(PetscScalar));
    600:     }
    601:     for (i=l;i<ds->n;i++) A[i+i*ld] = d[i];
    602:   }

    604:   /* Set zero wi */
    605:   if (wi) for (i=l;i<ds->n;i++) wi[i] = 0.0;
    606:   return(0);
    607: #endif
    608: }

    610: #if !defined(PETSC_USE_COMPLEX)
    611: PetscErrorCode DSSolve_HEP_BDC(DS ds,PetscScalar *wr,PetscScalar *wi)
    612: {
    614:   PetscBLASInt   i,j,k,m,n,info,nblks,bs,ld,lde,lrwork,liwork,*ksizes,*iwork,mingapi;
    615:   PetscScalar    *Q,*A;
    616:   PetscReal      *D,*E,*d,*e,tol=PETSC_MACHINE_EPSILON/2,tau1=1e-16,tau2=1e-18,*rwork,mingap;

    619:   if (ds->l>0) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"This method is not prepared for l>1");
    620:   if (ds->compact) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for compact storage");
    621:   PetscBLASIntCast(ds->ld,&ld);
    622:   PetscBLASIntCast(ds->bs,&bs);
    623:   PetscBLASIntCast(ds->n,&n);
    624:   nblks = n/bs;
    625:   Q  = ds->mat[DS_MAT_Q];
    626:   A  = ds->mat[DS_MAT_A];
    627:   d  = ds->rmat[DS_MAT_T];
    628:   e  = ds->rmat[DS_MAT_T]+ld;
    629:   lrwork = 4*n*n+60*n+1;
    630:   liwork = 5*n+5*nblks-1;
    631:   lde = 2*bs+1;
    632:   DSAllocateWork_Private(ds,bs*n+lde*lde*(nblks-1),lrwork,nblks+liwork);
    633:   D      = ds->work;
    634:   E      = ds->work+bs*n;
    635:   rwork  = ds->rwork;
    636:   ksizes = ds->iwork;
    637:   iwork  = ds->iwork+nblks;
    638:   PetscMemzero(iwork,liwork*sizeof(PetscBLASInt));

    640:   /* Copy matrix to block tridiagonal format */
    641:   j=0;
    642:   for (i=0;i<nblks;i++) {
    643:     ksizes[i]=bs;
    644:     for (k=0;k<bs;k++)
    645:       for (m=0;m<bs;m++)
    646:         D[k+m*bs+i*bs*bs] = PetscRealPart(A[j+k+(j+m)*n]);
    647:     j = j + bs;
    648:   }
    649:   j=0;
    650:   for (i=0;i<nblks-1;i++) {
    651:     for (k=0;k<bs;k++)
    652:       for (m=0;m<bs;m++)
    653:         E[k+m*lde+i*lde*lde] = PetscRealPart(A[j+bs+k+(j+m)*n]);
    654:     j = j + bs;
    655:   }

    657:   /* Solve the block tridiagonal eigenproblem */
    658:   BDC_dsbtdc_("D","A",n,nblks,ksizes,D,bs,bs,E,lde,lde,tol,tau1,tau2,d,
    659:            Q,n,rwork,lrwork,iwork,liwork,&mingap,&mingapi,&info,1,1);
    660:   for (i=0;i<ds->n;i++) wr[i] = d[i];

    662:   /* Create diagonal matrix as a result */
    663:   if (ds->compact) {
    664:     PetscMemzero(e,(ds->n-1)*sizeof(PetscReal));
    665:   } else {
    666:     for (i=0;i<ds->n;i++) {
    667:       PetscMemzero(A+i*ld,ds->n*sizeof(PetscScalar));
    668:     }
    669:     for (i=0;i<ds->n;i++) A[i+i*ld] = wr[i];
    670:   }

    672:   /* Set zero wi */
    673:   if (wi) for (i=0;i<ds->n;i++) wi[i] = 0.0;
    674:   return(0);
    675: }
    676: #endif

    678: PetscErrorCode DSTruncate_HEP(DS ds,PetscInt n)
    679: {
    680:   PetscInt    i,ld=ds->ld,l=ds->l;
    681:   PetscScalar *A;

    684:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
    685:   A = ds->mat[DS_MAT_A];
    686:   if (!ds->compact && ds->extrarow && ds->k==ds->n) {
    687:     for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
    688:   }
    689:   if (ds->extrarow) ds->k = n;
    690:   else ds->k = 0;
    691:   ds->n = n;
    692:   return(0);
    693: }

    695: PetscErrorCode DSSynchronize_HEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    696: {
    698:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
    699:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;

    702:   if (ds->compact) kr = 3*ld;
    703:   else k = (ds->n-l)*ld;
    704:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    705:   if (eigr) k += (ds->n-l);
    706:   if (eigi) k += (ds->n-l);
    707:   DSAllocateWork_Private(ds,k+kr,0,0);
    708:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
    709:   PetscMPIIntCast(ds->n-l,&n);
    710:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    711:   PetscMPIIntCast(ld*3,&ld3);
    712:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    713:   if (!rank) {
    714:     if (ds->compact) {
    715:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    716:     } else {
    717:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    718:     }
    719:     if (ds->state>DS_STATE_RAW) {
    720:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    721:     }
    722:     if (eigr) {
    723:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    724:     }
    725:     if (eigi) {
    726:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    727:     }
    728:   }
    729:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    730:   if (rank) {
    731:     if (ds->compact) {
    732:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    733:     } else {
    734:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    735:     }
    736:     if (ds->state>DS_STATE_RAW) {
    737:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    738:     }
    739:     if (eigr) {
    740:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    741:     }
    742:     if (eigi) {
    743:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    744:     }
    745:   }
    746:   return(0);
    747: }

    749: PetscErrorCode DSCond_HEP(DS ds,PetscReal *cond)
    750: {
    751: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRI) || defined(SLEPC_MISSING_LAPACK_LANGE)
    753:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI/LANGE - Lapack routines are unavailable");
    754: #else
    756:   PetscScalar    *work;
    757:   PetscReal      *rwork;
    758:   PetscBLASInt   *ipiv;
    759:   PetscBLASInt   lwork,info,n,ld;
    760:   PetscReal      hn,hin;
    761:   PetscScalar    *A;

    764:   PetscBLASIntCast(ds->n,&n);
    765:   PetscBLASIntCast(ds->ld,&ld);
    766:   lwork = 8*ld;
    767:   DSAllocateWork_Private(ds,lwork,ld,ld);
    768:   work  = ds->work;
    769:   rwork = ds->rwork;
    770:   ipiv  = ds->iwork;
    771:   DSSwitchFormat_HEP(ds,PETSC_FALSE);

    773:   /* use workspace matrix W to avoid overwriting A */
    774:   DSAllocateMat_Private(ds,DS_MAT_W);
    775:   A = ds->mat[DS_MAT_W];
    776:   PetscMemcpy(A,ds->mat[DS_MAT_A],sizeof(PetscScalar)*ds->ld*ds->ld);

    778:   /* norm of A */
    779:   hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);

    781:   /* norm of inv(A) */
    782:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
    783:   SlepcCheckLapackInfo("getrf",info);
    784:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
    785:   SlepcCheckLapackInfo("getri",info);
    786:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

    788:   *cond = hn*hin;
    789:   return(0);
    790: #endif
    791: }

    793: PetscErrorCode DSTranslateRKS_HEP(DS ds,PetscScalar alpha)
    794: {
    795: #if defined(PETSC_MISSING_LAPACK_GEQRF) || defined(PETSC_MISSING_LAPACK_ORGQR)
    797:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEQRF/ORGQR - Lapack routines are unavailable");
    798: #else
    800:   PetscInt       i,j,k=ds->k;
    801:   PetscScalar    *Q,*A,*R,*tau,*work;
    802:   PetscBLASInt   ld,n1,n0,lwork,info;

    805:   PetscBLASIntCast(ds->ld,&ld);
    806:   DSAllocateWork_Private(ds,ld*ld,0,0);
    807:   tau = ds->work;
    808:   work = ds->work+ld;
    809:   PetscBLASIntCast(ld*(ld-1),&lwork);
    810:   DSAllocateMat_Private(ds,DS_MAT_W);
    811:   A  = ds->mat[DS_MAT_A];
    812:   Q  = ds->mat[DS_MAT_Q];
    813:   R  = ds->mat[DS_MAT_W];

    815:   /* copy I+alpha*A */
    816:   PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
    817:   PetscMemzero(R,ld*ld*sizeof(PetscScalar));
    818:   for (i=0;i<k;i++) {
    819:     Q[i+i*ld] = 1.0 + alpha*A[i+i*ld];
    820:     Q[k+i*ld] = alpha*A[k+i*ld];
    821:   }

    823:   /* compute qr */
    824:   PetscBLASIntCast(k+1,&n1);
    825:   PetscBLASIntCast(k,&n0);
    826:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&n1,&n0,Q,&ld,tau,work,&lwork,&info));
    827:   SlepcCheckLapackInfo("geqrf",info);

    829:   /* copy R from Q */
    830:   for (j=0;j<k;j++)
    831:     for (i=0;i<=j;i++)
    832:       R[i+j*ld] = Q[i+j*ld];

    834:   /* compute orthogonal matrix in Q */
    835:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&n1,&n1,&n0,Q,&ld,tau,work,&lwork,&info));
    836:   SlepcCheckLapackInfo("orgqr",info);

    838:   /* compute the updated matrix of projected problem */
    839:   for (j=0;j<k;j++)
    840:     for (i=0;i<k+1;i++)
    841:       A[j*ld+i] = Q[i*ld+j];
    842:   alpha = -1.0/alpha;
    843:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&n1,&n0,&alpha,R,&ld,A,&ld));
    844:   for (i=0;i<k;i++)
    845:     A[ld*i+i] -= alpha;
    846:   return(0);
    847: #endif
    848: }

    850: PetscErrorCode DSHermitian_HEP(DS ds,DSMatType m,PetscBool *flg)
    851: {
    853:   if (m==DS_MAT_A && !ds->extrarow) *flg = PETSC_TRUE;
    854:   else *flg = PETSC_FALSE;
    855:   return(0);
    856: }

    858: PETSC_EXTERN PetscErrorCode DSCreate_HEP(DS ds)
    859: {
    861:   ds->ops->allocate      = DSAllocate_HEP;
    862:   ds->ops->view          = DSView_HEP;
    863:   ds->ops->vectors       = DSVectors_HEP;
    864:   ds->ops->solve[0]      = DSSolve_HEP_QR;
    865:   ds->ops->solve[1]      = DSSolve_HEP_MRRR;
    866:   ds->ops->solve[2]      = DSSolve_HEP_DC;
    867: #if !defined(PETSC_USE_COMPLEX)
    868:   ds->ops->solve[3]      = DSSolve_HEP_BDC;
    869: #endif
    870:   ds->ops->sort          = DSSort_HEP;
    871:   ds->ops->synchronize   = DSSynchronize_HEP;
    872:   ds->ops->truncate      = DSTruncate_HEP;
    873:   ds->ops->update        = DSUpdateExtraRow_HEP;
    874:   ds->ops->cond          = DSCond_HEP;
    875:   ds->ops->transrks      = DSTranslateRKS_HEP;
    876:   ds->ops->hermitian     = DSHermitian_HEP;
    877:   return(0);
    878: }