Date: 2017-05-17T08:24:37+00:00

Actual source code: dshep.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: #include <slepc/private/dsimpl.h>
     23: #include <slepcblaslapack.h>

     27: PetscErrorCode DSAllocate_HEP(DS ds,PetscInt ld)
     28: {

     32:   DSAllocateMat_Private(ds,DS_MAT_A);
     33:   DSAllocateMat_Private(ds,DS_MAT_Q);
     34:   DSAllocateMatReal_Private(ds,DS_MAT_T);
     35:   PetscFree(ds->perm);
     36:   PetscMalloc1(ld,&ds->perm);
     37:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     38:   return(0);
     39: }

     41: /*   0       l           k                 n-1
     42:     -----------------------------------------
     43:     |*       .           .                  |
     44:     |  *     .           .                  |
     45:     |    *   .           .                  |
     46:     |      * .           .                  |
     47:     |. . . . o           o                  |
     48:     |          o         o                  |
     49:     |            o       o                  |
     50:     |              o     o                  |
     51:     |                o   o                  |
     52:     |                  o o                  |
     53:     |. . . . o o o o o o o x                |
     54:     |                    x x x              |
     55:     |                      x x x            |
     56:     |                        x x x          |
     57:     |                          x x x        |
     58:     |                            x x x      |
     59:     |                              x x x    |
     60:     |                                x x x  |
     61:     |                                  x x x|
     62:     |                                    x x|
     63:     -----------------------------------------
     64: */

     68: static PetscErrorCode DSSwitchFormat_HEP(DS ds,PetscBool tocompact)
     69: {
     71:   PetscReal      *T = ds->rmat[DS_MAT_T];
     72:   PetscScalar    *A = ds->mat[DS_MAT_A];
     73:   PetscInt       i,n=ds->n,k=ds->k,ld=ds->ld;

     76:   if (tocompact) { /* switch from dense (arrow) to compact storage */
     77:     PetscMemzero(T,3*ld*sizeof(PetscReal));
     78:     for (i=0;i<k;i++) {
     79:       T[i] = PetscRealPart(A[i+i*ld]);
     80:       T[i+ld] = PetscRealPart(A[k+i*ld]);
     81:     }
     82:     for (i=k;i<n-1;i++) {
     83:       T[i] = PetscRealPart(A[i+i*ld]);
     84:       T[i+ld] = PetscRealPart(A[i+1+i*ld]);
     85:     }
     86:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
     87:     if (ds->extrarow) T[n-1+ld] = PetscRealPart(A[n+(n-1)*ld]);
     88:   } else { /* switch from compact (arrow) to dense storage */
     89:     PetscMemzero(A,ld*ld*sizeof(PetscScalar));
     90:     for (i=0;i<k;i++) {
     91:       A[i+i*ld] = T[i];
     92:       A[k+i*ld] = T[i+ld];
     93:       A[i+k*ld] = T[i+ld];
     94:     }
     95:     A[k+k*ld] = T[k];
     96:     for (i=k+1;i<n;i++) {
     97:       A[i+i*ld] = T[i];
     98:       A[i-1+i*ld] = T[i-1+ld];
     99:       A[i+(i-1)*ld] = T[i-1+ld];
    100:     }
    101:     if (ds->extrarow) A[n+(n-1)*ld] = T[n-1+ld];
    102:   }
    103:   return(0);
    104: }

    108: PetscErrorCode DSView_HEP(DS ds,PetscViewer viewer)
    109: {
    110:   PetscErrorCode    ierr;
    111:   PetscViewerFormat format;
    112:   PetscInt          i,j,r,c,rows;
    113:   PetscReal         value;
    114:   const char        *methodname[] = {
    115:                      "Implicit QR method (_steqr)",
    116:                      "Relatively Robust Representations (_stevr)",
    117:                      "Divide and Conquer method (_stedc)",
    118:                      "Block Divide and Conquer method (dsbtdc)"
    119:   };
    120:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

    123:   PetscViewerGetFormat(viewer,&format);
    124:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    125:     if (ds->bs>1) {
    126:       PetscViewerASCIIPrintf(viewer,"block size: %D\n",ds->bs);
    127:     }
    128:     if (ds->method>=nmeth) {
    129:       PetscViewerASCIIPrintf(viewer,"solving the problem with: INVALID METHOD\n");
    130:     } else {
    131:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
    132:     }
    133:     return(0);
    134:   }
    135:   if (ds->compact) {
    136:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    137:     rows = ds->extrarow? ds->n+1: ds->n;
    138:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
    139:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",rows,ds->n);
    140:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
    141:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
    142:       for (i=0;i<ds->n;i++) {
    143:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_T]+i));
    144:       }
    145:       for (i=0;i<rows-1;i++) {
    146:         r = PetscMax(i+2,ds->k+1);
    147:         c = i+1;
    148:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",r,c,*(ds->rmat[DS_MAT_T]+ds->ld+i));
    149:         if (i<ds->n-1 && ds->k<ds->n) { /* do not print vertical arrow when k=n */
    150:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",c,r,*(ds->rmat[DS_MAT_T]+ds->ld+i));
    151:         }
    152:       }
    153:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
    154:     } else {
    155:       for (i=0;i<rows;i++) {
    156:         for (j=0;j<ds->n;j++) {
    157:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    158:           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));
    159:           else if (i==j+1 && i>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+i-1);
    160:           else if (i+1==j && j>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+j-1);
    161:           else value = 0.0;
    162:           PetscViewerASCIIPrintf(viewer," %18.16e ",value);
    163:         }
    164:         PetscViewerASCIIPrintf(viewer,"\n");
    165:       }
    166:     }
    167:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    168:     PetscViewerFlush(viewer);
    169:   } else {
    170:     DSViewMat(ds,viewer,DS_MAT_A);
    171:   }
    172:   if (ds->state>DS_STATE_INTERMEDIATE) {
    173:     DSViewMat(ds,viewer,DS_MAT_Q);
    174:   }
    175:   return(0);
    176: }

    180: PetscErrorCode DSVectors_HEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    181: {
    182:   PetscScalar    *Q = ds->mat[DS_MAT_Q];
    183:   PetscInt       ld = ds->ld,i;

    187:   switch (mat) {
    188:     case DS_MAT_X:
    189:     case DS_MAT_Y:
    190:       if (j) {
    191:         if (ds->state>=DS_STATE_CONDENSED) {
    192:           PetscMemcpy(ds->mat[mat]+(*j)*ld,Q+(*j)*ld,ld*sizeof(PetscScalar));
    193:         } else {
    194:           PetscMemzero(ds->mat[mat]+(*j)*ld,ld*sizeof(PetscScalar));
    195:           *(ds->mat[mat]+(*j)+(*j)*ld) = 1.0;
    196:         }
    197:       } else {
    198:         if (ds->state>=DS_STATE_CONDENSED) {
    199:           PetscMemcpy(ds->mat[mat],Q,ld*ld*sizeof(PetscScalar));
    200:         } else {
    201:           PetscMemzero(ds->mat[mat],ld*ld*sizeof(PetscScalar));
    202:           for (i=0;i<ds->n;i++) *(ds->mat[mat]+i+i*ld) = 1.0;
    203:         }
    204:       }
    205:       if (rnorm && j) *rnorm = PetscAbsScalar(Q[ds->n-1+(*j)*ld]);
    206:       break;
    207:     case DS_MAT_U:
    208:     case DS_MAT_VT:
    209:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    210:       break;
    211:     default:
    212:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    213:   }
    214:   return(0);
    215: }

    219: PetscErrorCode DSNormalize_HEP(DS ds,DSMatType mat,PetscInt col)
    220: {
    222:   switch (mat) {
    223:     case DS_MAT_X:
    224:     case DS_MAT_Y:
    225:     case DS_MAT_Q:
    226:       /* All the matrices resulting from DSVectors and DSSolve are already normalized */
    227:       break;
    228:     case DS_MAT_U:
    229:     case DS_MAT_VT:
    230:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    231:       break;
    232:     default:
    233:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    234:   }
    235:   return(0);
    236: }

    240: /*
    241:   ARROWTRIDIAG reduces a symmetric arrowhead matrix of the form

    243:                 [ d 0 0 0 e ]
    244:                 [ 0 d 0 0 e ]
    245:             A = [ 0 0 d 0 e ]
    246:                 [ 0 0 0 d e ]
    247:                 [ e e e e d ]

    249:   to tridiagonal form

    251:                 [ d e 0 0 0 ]
    252:                 [ e d e 0 0 ]
    253:    T = Q'*A*Q = [ 0 e d e 0 ],
    254:                 [ 0 0 e d e ]
    255:                 [ 0 0 0 e d ]

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

    261:   Arguments
    262:   =========

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

    267:   D       (input/output) DOUBLE PRECISION array, dimension (N)
    268:           On entry, the diagonal entries of the matrix A to be
    269:           reduced.
    270:           On exit, the diagonal entries of the reduced matrix T.

    272:   E       (input/output) DOUBLE PRECISION array, dimension (N-1)
    273:           On entry, the off-diagonal entries of the matrix A to be
    274:           reduced.
    275:           On exit, the subdiagonal entries of the reduced matrix T.

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

    280:   LDQ     (input) INTEGER
    281:           The leading dimension of the array Q.

    283:   Note
    284:   ====
    285:   Based on Fortran code contributed by Daniel Kressner
    286: */
    287: static PetscErrorCode ArrowTridiag(PetscBLASInt n,PetscReal *d,PetscReal *e,PetscScalar *Q,PetscBLASInt ld)
    288: {
    289: #if defined(SLEPC_MISSING_LAPACK_LARTG)
    291:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARTG - Lapack routine is unavailable");
    292: #else
    293:   PetscBLASInt i,j,j2,one=1;
    294:   PetscReal    c,s,p,off,temp;

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

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

    301:     /* Eliminate entry e(j) by a rotation in the planes (j,j+1) */
    302:     temp = e[j+1];
    303:     PetscStackCallBLAS("LAPACKlartg",LAPACKlartg_(&temp,&e[j],&c,&s,&e[j+1]));
    304:     s = -s;

    306:     /* Apply rotation to diagonal elements */
    307:     temp   = d[j+1];
    308:     e[j]   = c*s*(temp-d[j]);
    309:     d[j+1] = s*s*d[j] + c*c*temp;
    310:     d[j]   = c*c*d[j] + s*s*temp;

    312:     /* Apply rotation to Q */
    313:     j2 = j+2;
    314:     PetscStackCallBLAS("BLASrot",BLASrot_(&j2,Q+j*ld,&one,Q+(j+1)*ld,&one,&c,&s));

    316:     /* Chase newly introduced off-diagonal entry to the top left corner */
    317:     for (i=j-1;i>=0;i--) {
    318:       off  = -s*e[i];
    319:       e[i] = c*e[i];
    320:       temp = e[i+1];
    321:       PetscStackCallBLAS("LAPACKlartg",LAPACKlartg_(&temp,&off,&c,&s,&e[i+1]));
    322:       s = -s;
    323:       temp = (d[i]-d[i+1])*s - 2.0*c*e[i];
    324:       p = s*temp;
    325:       d[i+1] += p;
    326:       d[i] -= p;
    327:       e[i] = -e[i] - c*temp;
    328:       j2 = j+2;
    329:       PetscStackCallBLAS("BLASrot",BLASrot_(&j2,Q+i*ld,&one,Q+(i+1)*ld,&one,&c,&s));
    330:     }
    331:   }
    332:   return(0);
    333: #endif
    334: }

    338: /*
    339:    Reduce to tridiagonal form by means of ArrowTridiag.
    340: */
    341: static PetscErrorCode DSIntermediate_HEP(DS ds)
    342: {
    343: #if defined(SLEPC_MISSING_LAPACK_SYTRD) || defined(SLEPC_MISSING_LAPACK_ORGTR)
    345:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SYTRD/ORGTR - Lapack routine is unavailable");
    346: #else
    348:   PetscInt       i;
    349:   PetscBLASInt   n1,n2,n3,lwork,info,l,n,ld,off;
    350:   PetscScalar    *A,*Q,*work,*tau;
    351:   PetscReal      *d,*e;

    354:   PetscBLASIntCast(ds->n,&n);
    355:   PetscBLASIntCast(ds->l,&l);
    356:   PetscBLASIntCast(ds->ld,&ld);
    357:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
    358:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
    359:   n3 = n1+n2;
    360:   off = l+l*ld;
    361:   A  = ds->mat[DS_MAT_A];
    362:   Q  = ds->mat[DS_MAT_Q];
    363:   d  = ds->rmat[DS_MAT_T];
    364:   e  = ds->rmat[DS_MAT_T]+ld;
    365:   PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
    366:   for (i=0;i<n;i++) Q[i+i*ld] = 1.0;

    368:   if (ds->compact) {

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

    372:   } else {

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

    376:     if (ds->state<DS_STATE_INTERMEDIATE) {
    377:       DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
    378:       DSAllocateWork_Private(ds,ld+ld*ld,0,0);
    379:       tau  = ds->work;
    380:       work = ds->work+ld;
    381:       lwork = ld*ld;
    382:       PetscStackCallBLAS("LAPACKsytrd",LAPACKsytrd_("L",&n3,Q+off,&ld,d+l,e+l,tau,work,&lwork,&info));
    383:       if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xSYTRD %d",info);
    384:       PetscStackCallBLAS("LAPACKorgtr",LAPACKorgtr_("L",&n3,Q+off,&ld,tau,work,&lwork,&info));
    385:       if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGTR %d",info);
    386:     } else {
    387:       /* copy tridiagonal to d,e */
    388:       for (i=l;i<n;i++) d[i] = PetscRealPart(A[i+i*ld]);
    389:       for (i=l;i<n-1;i++) e[i] = PetscRealPart(A[(i+1)+i*ld]);
    390:     }
    391:   }
    392:   return(0);
    393: #endif
    394: }

    398: PetscErrorCode DSSort_HEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    399: {
    401:   PetscInt       n,l,i,*perm,ld=ds->ld;
    402:   PetscScalar    *A;
    403:   PetscReal      *d;

    406:   if (!ds->sc) return(0);
    407:   n = ds->n;
    408:   l = ds->l;
    409:   A = ds->mat[DS_MAT_A];
    410:   d = ds->rmat[DS_MAT_T];
    411:   perm = ds->perm;
    412:   if (!rr) {
    413:     DSSortEigenvaluesReal_Private(ds,d,perm);
    414:   } else {
    415:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
    416:   }
    417:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
    418:   DSPermuteColumns_Private(ds,l,n,DS_MAT_Q,perm);
    419:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
    420:   if (!ds->compact) {
    421:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
    422:   }
    423:   return(0);
    424: }

    428: PetscErrorCode DSUpdateExtraRow_HEP(DS ds)
    429: {
    431:   PetscInt       i;
    432:   PetscBLASInt   n,ld,incx=1;
    433:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
    434:   PetscReal      *e,beta;

    437:   PetscBLASIntCast(ds->n,&n);
    438:   PetscBLASIntCast(ds->ld,&ld);
    439:   A  = ds->mat[DS_MAT_A];
    440:   Q  = ds->mat[DS_MAT_Q];
    441:   e  = ds->rmat[DS_MAT_T]+ld;

    443:   if (ds->compact) {
    444:     beta = e[n-1];   /* in compact, we assume all entries are zero except the last one */
    445:     for (i=0;i<n;i++) e[i] = PetscRealPart(beta*Q[n-1+i*ld]);
    446:     ds->k = n;
    447:   } else {
    448:     DSAllocateWork_Private(ds,2*ld,0,0);
    449:     x = ds->work;
    450:     y = ds->work+ld;
    451:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    452:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    453:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    454:     ds->k = n;
    455:   }
    456:   return(0);
    457: }

    461: PetscErrorCode DSSolve_HEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    462: {
    463: #if defined(PETSC_MISSING_LAPACK_STEQR)
    465:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEQR - Lapack routine is unavailable");
    466: #else
    468:   PetscInt       i;
    469:   PetscBLASInt   n1,n2,n3,info,l,n,ld,off;
    470:   PetscScalar    *Q,*A;
    471:   PetscReal      *d,*e;

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

    487:   /* Reduce to tridiagonal form */
    488:   DSIntermediate_HEP(ds);

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

    493:   DSAllocateWork_Private(ds,0,2*ld,0);
    494:   PetscStackCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n3,d+l,e+l,Q+off,&ld,ds->rwork,&info));
    495:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xSTEQR %d",info);
    496:   for (i=l;i<n;i++) wr[i] = d[i];

    498:   /* Create diagonal matrix as a result */
    499:   if (ds->compact) {
    500:     PetscMemzero(e,(n-1)*sizeof(PetscReal));
    501:   } else {
    502:     for (i=l;i<n;i++) {
    503:       PetscMemzero(A+l+i*ld,(n-l)*sizeof(PetscScalar));
    504:     }
    505:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
    506:   }

    508:   /* Set zero wi */
    509:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
    510:   return(0);
    511: #endif
    512: }

    516: PetscErrorCode DSSolve_HEP_MRRR(DS ds,PetscScalar *wr,PetscScalar *wi)
    517: {
    518: #if defined(SLEPC_MISSING_LAPACK_STEVR)
    520:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEVR - Lapack routine is unavailable");
    521: #else
    523:   PetscInt       i;
    524:   PetscBLASInt   n1,n2,n3,lwork,liwork,info,l,n,m,ld,off,il,iu,*isuppz;
    525:   PetscScalar    *A,*Q,*W=NULL,one=1.0,zero=0.0;
    526:   PetscReal      *d,*e,abstol=0.0,vl,vu;
    527: #if defined(PETSC_USE_COMPLEX)
    528:   PetscInt       j;
    529:   PetscReal      *ritz;
    530: #endif

    533:   if (ds->bs>1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This method is not prepared for bs>1");
    534:   PetscBLASIntCast(ds->n,&n);
    535:   PetscBLASIntCast(ds->l,&l);
    536:   PetscBLASIntCast(ds->ld,&ld);
    537:   PetscBLASIntCast(ds->k-l+1,&n1); /* size of leading block, excl. locked */
    538:   PetscBLASIntCast(n-ds->k-1,&n2); /* size of trailing block */
    539:   n3 = n1+n2;
    540:   off = l+l*ld;
    541:   A  = ds->mat[DS_MAT_A];
    542:   Q  = ds->mat[DS_MAT_Q];
    543:   d  = ds->rmat[DS_MAT_T];
    544:   e  = ds->rmat[DS_MAT_T]+ld;

    546:   /* Reduce to tridiagonal form */
    547:   DSIntermediate_HEP(ds);

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

    552:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* Q contains useful info */
    553:     DSAllocateMat_Private(ds,DS_MAT_W);
    554:     DSCopyMatrix_Private(ds,DS_MAT_W,DS_MAT_Q);
    555:     W = ds->mat[DS_MAT_W];
    556:   }
    557: #if defined(PETSC_USE_COMPLEX)
    558:   DSAllocateMatReal_Private(ds,DS_MAT_Q);
    559: #endif
    560:   lwork = 20*ld;
    561:   liwork = 10*ld;
    562:   DSAllocateWork_Private(ds,0,lwork+ld,liwork+2*ld);
    563:   isuppz = ds->iwork+liwork;
    564: #if defined(PETSC_USE_COMPLEX)
    565:   ritz = ds->rwork+lwork;
    566:   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));
    567:   for (i=l;i<n;i++) wr[i] = ritz[i];
    568: #else
    569:   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));
    570: #endif
    571:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack DSTEVR %d",info);
    572: #if defined(PETSC_USE_COMPLEX)
    573:   for (i=l;i<n;i++)
    574:     for (j=l;j<n;j++)
    575:       Q[i+j*ld] = (ds->rmat[DS_MAT_Q])[i+j*ld];
    576: #endif
    577:   if (ds->state<DS_STATE_INTERMEDIATE) {  /* accumulate previous Q */
    578:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n3,&n3,&n3,&one,W+off,&ld,Q+off,&ld,&zero,A+off,&ld));
    579:     DSCopyMatrix_Private(ds,DS_MAT_Q,DS_MAT_A);
    580:   }
    581:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);

    583:   /* Create diagonal matrix as a result */
    584:   if (ds->compact) {
    585:     PetscMemzero(e,(n-1)*sizeof(PetscReal));
    586:   } else {
    587:     for (i=l;i<n;i++) {
    588:       PetscMemzero(A+l+i*ld,(n-l)*sizeof(PetscScalar));
    589:     }
    590:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
    591:   }

    593:   /* Set zero wi */
    594:   if (wi) for (i=l;i<n;i++) wi[i] = 0.0;
    595:   return(0);
    596: #endif
    597: }

    601: PetscErrorCode DSSolve_HEP_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
    602: {
    603: #if defined(SLEPC_MISSING_LAPACK_STEDC)
    605:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STEDC - Lapack routine is unavailable");
    606: #else
    608:   PetscInt       i;
    609:   PetscBLASInt   n1,info,l,ld,off,lrwork,liwork;
    610:   PetscScalar    *Q,*A;
    611:   PetscReal      *d,*e;
    612: #if defined(PETSC_USE_COMPLEX)
    613:   PetscBLASInt   lwork;
    614:   PetscInt       j;
    615: #endif

    618:   if (ds->bs>1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This method is not prepared for bs>1");
    619:   PetscBLASIntCast(ds->l,&l);
    620:   PetscBLASIntCast(ds->ld,&ld);
    621:   PetscBLASIntCast(ds->n-ds->l,&n1);
    622:   off = l+l*ld;
    623:   Q  = ds->mat[DS_MAT_Q];
    624:   A  = ds->mat[DS_MAT_A];
    625:   d  = ds->rmat[DS_MAT_T];
    626:   e  = ds->rmat[DS_MAT_T]+ld;

    628:   /* Reduce to tridiagonal form */
    629:   DSIntermediate_HEP(ds);

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

    634:   lrwork = 5*n1*n1+3*n1+1;
    635:   liwork = 5*n1*n1+6*n1+6;
    636: #if !defined(PETSC_USE_COMPLEX)
    637:   DSAllocateWork_Private(ds,0,lrwork,liwork);
    638:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
    639: #else
    640:   lwork = ld*ld;
    641:   DSAllocateWork_Private(ds,lwork,lrwork,liwork);
    642:   PetscStackCallBLAS("LAPACKstedc",LAPACKstedc_("V",&n1,d+l,e+l,Q+off,&ld,ds->work,&lwork,ds->rwork,&lrwork,ds->iwork,&liwork,&info));
    643:   /* Fixing Lapack bug*/
    644:   for (j=ds->l;j<ds->n;j++)
    645:     for (i=0;i<ds->l;i++) Q[i+j*ld] = 0.0;
    646: #endif
    647:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xSTEDC %d",info);
    648:   for (i=l;i<ds->n;i++) wr[i] = d[i];

    650:   /* Create diagonal matrix as a result */
    651:   if (ds->compact) {
    652:     PetscMemzero(e,(ds->n-1)*sizeof(PetscReal));
    653:   } else {
    654:     for (i=l;i<ds->n;i++) {
    655:       PetscMemzero(A+l+i*ld,(ds->n-l)*sizeof(PetscScalar));
    656:     }
    657:     for (i=l;i<ds->n;i++) A[i+i*ld] = d[i];
    658:   }

    660:   /* Set zero wi */
    661:   if (wi) for (i=l;i<ds->n;i++) wi[i] = 0.0;
    662:   return(0);
    663: #endif
    664: }

    666: #if !defined(PETSC_USE_COMPLEX)
    669: PetscErrorCode DSSolve_HEP_BDC(DS ds,PetscScalar *wr,PetscScalar *wi)
    670: {
    672:   PetscBLASInt   i,j,k,m,n,info,nblks,bs,ld,lde,lrwork,liwork,*ksizes,*iwork,mingapi;
    673:   PetscScalar    *Q,*A;
    674:   PetscReal      *D,*E,*d,*e,tol=PETSC_MACHINE_EPSILON/2,tau1=1e-16,tau2=1e-18,*rwork,mingap;

    677:   if (ds->l>0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This method is not prepared for l>1");
    678:   if (ds->compact) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for compact storage");
    679:   PetscBLASIntCast(ds->ld,&ld);
    680:   PetscBLASIntCast(ds->bs,&bs);
    681:   PetscBLASIntCast(ds->n,&n);
    682:   nblks = n/bs;
    683:   Q  = ds->mat[DS_MAT_Q];
    684:   A  = ds->mat[DS_MAT_A];
    685:   d  = ds->rmat[DS_MAT_T];
    686:   e  = ds->rmat[DS_MAT_T]+ld;
    687:   lrwork = 4*n*n+60*n+1;
    688:   liwork = 5*n+5*nblks-1;
    689:   lde = 2*bs+1;
    690:   DSAllocateWork_Private(ds,bs*n+lde*lde*(nblks-1),lrwork,nblks+liwork);
    691:   D      = ds->work;
    692:   E      = ds->work+bs*n;
    693:   rwork  = ds->rwork;
    694:   ksizes = ds->iwork;
    695:   iwork  = ds->iwork+nblks;
    696:   PetscMemzero(iwork,liwork*sizeof(PetscBLASInt));

    698:   /* Copy matrix to block tridiagonal format */
    699:   j=0;
    700:   for (i=0;i<nblks;i++) {
    701:     ksizes[i]=bs;
    702:     for (k=0;k<bs;k++)
    703:       for (m=0;m<bs;m++)
    704:         D[k+m*bs+i*bs*bs] = PetscRealPart(A[j+k+(j+m)*n]);
    705:     j = j + bs;
    706:   }
    707:   j=0;
    708:   for (i=0;i<nblks-1;i++) {
    709:     for (k=0;k<bs;k++)
    710:       for (m=0;m<bs;m++)
    711:         E[k+m*lde+i*lde*lde] = PetscRealPart(A[j+bs+k+(j+m)*n]);
    712:     j = j + bs;
    713:   }

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

    720:   /* Create diagonal matrix as a result */
    721:   if (ds->compact) {
    722:     PetscMemzero(e,(ds->n-1)*sizeof(PetscReal));
    723:   } else {
    724:     for (i=0;i<ds->n;i++) {
    725:       PetscMemzero(A+i*ld,ds->n*sizeof(PetscScalar));
    726:     }
    727:     for (i=0;i<ds->n;i++) A[i+i*ld] = wr[i];
    728:   }

    730:   /* Set zero wi */
    731:   if (wi) for (i=0;i<ds->n;i++) wi[i] = 0.0;
    732:   return(0);
    733: }
    734: #endif

    738: PetscErrorCode DSTruncate_HEP(DS ds,PetscInt n)
    739: {
    740:   PetscInt       i,ld=ds->ld,l=ds->l;
    741:   PetscScalar    *A;

    744:   if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
    745:   A = ds->mat[DS_MAT_A];
    746:   if (!ds->compact && ds->extrarow && ds->k==ds->n) {
    747:     for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
    748:   }
    749:   if (ds->extrarow) ds->k = n;
    750:   else ds->k = 0;
    751:   ds->n = n;
    752:   return(0);
    753: }

    757: PetscErrorCode DSCond_HEP(DS ds,PetscReal *cond)
    758: {
    759: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRI) || defined(SLEPC_MISSING_LAPACK_LANGE)
    761:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI/LANGE - Lapack routines are unavailable");
    762: #else
    764:   PetscScalar    *work;
    765:   PetscReal      *rwork;
    766:   PetscBLASInt   *ipiv;
    767:   PetscBLASInt   lwork,info,n,ld;
    768:   PetscReal      hn,hin;
    769:   PetscScalar    *A;

    772:   PetscBLASIntCast(ds->n,&n);
    773:   PetscBLASIntCast(ds->ld,&ld);
    774:   lwork = 8*ld;
    775:   DSAllocateWork_Private(ds,lwork,ld,ld);
    776:   work  = ds->work;
    777:   rwork = ds->rwork;
    778:   ipiv  = ds->iwork;
    779:   DSSwitchFormat_HEP(ds,PETSC_FALSE);

    781:   /* use workspace matrix W to avoid overwriting A */
    782:   DSAllocateMat_Private(ds,DS_MAT_W);
    783:   A = ds->mat[DS_MAT_W];
    784:   PetscMemcpy(A,ds->mat[DS_MAT_A],sizeof(PetscScalar)*ds->ld*ds->ld);

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

    789:   /* norm of inv(A) */
    790:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
    791:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRF %d",info);
    792:   PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
    793:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRI %d",info);
    794:   hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);

    796:   *cond = hn*hin;
    797:   return(0);
    798: #endif
    799: }

    803: PetscErrorCode DSTranslateRKS_HEP(DS ds,PetscScalar alpha)
    804: {
    805: #if defined(PETSC_MISSING_LAPACK_GEQRF) || defined(PETSC_MISSING_LAPACK_ORGQR)
    807:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEQRF/ORGQR - Lapack routines are unavailable");
    808: #else
    810:   PetscInt       i,j,k=ds->k;
    811:   PetscScalar    *Q,*A,*R,*tau,*work;
    812:   PetscBLASInt   ld,n1,n0,lwork,info;

    815:   PetscBLASIntCast(ds->ld,&ld);
    816:   DSAllocateWork_Private(ds,ld*ld,0,0);
    817:   tau = ds->work;
    818:   work = ds->work+ld;
    819:   PetscBLASIntCast(ld*(ld-1),&lwork);
    820:   DSAllocateMat_Private(ds,DS_MAT_W);
    821:   A  = ds->mat[DS_MAT_A];
    822:   Q  = ds->mat[DS_MAT_Q];
    823:   R  = ds->mat[DS_MAT_W];
    824:   /* Copy I+alpha*A */
    825:   PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
    826:   PetscMemzero(R,ld*ld*sizeof(PetscScalar));
    827:   for (i=0;i<k;i++) {
    828:     Q[i+i*ld] = 1.0 + alpha*A[i+i*ld];
    829:     Q[k+i*ld] = alpha*A[k+i*ld];
    830:   }
    831:   /* Compute qr */
    832:   PetscBLASIntCast(k+1,&n1);
    833:   PetscBLASIntCast(k,&n0);
    834:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&n1,&n0,Q,&ld,tau,work,&lwork,&info));
    835:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
    836:   /* Copy R from Q */
    837:   for (j=0;j<k;j++)
    838:     for (i=0;i<=j;i++)
    839:       R[i+j*ld] = Q[i+j*ld];
    840:   /* Compute orthogonal matrix in Q */
    841:   PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&n1,&n1,&n0,Q,&ld,tau,work,&lwork,&info));
    842:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGQR %d",info);
    843:   /* Compute the updated matrix of projected problem */
    844:   for (j=0;j<k;j++)
    845:     for (i=0;i<k+1;i++)
    846:       A[j*ld+i] = Q[i*ld+j];
    847:   alpha = -1.0/alpha;
    848:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&n1,&n0,&alpha,R,&ld,A,&ld));
    849:   for (i=0;i<k;i++)
    850:     A[ld*i+i]-=alpha;
    851:   return(0);
    852: #endif
    853: }

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