Date: 2024-10-28T09:14:38+00:00

Actual source code: dsops.c
slepc-3.22.1 2024-10-28
Report Typos and Errors

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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: */
     10: /*
     11:    DS operations: DSSolve(), DSVectors(), etc
     12: */

     14: #include <slepc/private/dsimpl.h>

     16: /*@
     17:    DSGetLeadingDimension - Returns the leading dimension of the allocated
     18:    matrices.

     20:    Not Collective

     22:    Input Parameter:
     23: .  ds - the direct solver context

     25:    Output Parameter:
     26: .  ld - leading dimension (maximum allowed dimension for the matrices)

     28:    Level: advanced

     30: .seealso: DSAllocate(), DSSetDimensions()
     31: @*/
     32: PetscErrorCode DSGetLeadingDimension(DS ds,PetscInt *ld)
     33: {
     34:   PetscFunctionBegin;
     36:   PetscAssertPointer(ld,2);
     37:   *ld = ds->ld;
     38:   PetscFunctionReturn(PETSC_SUCCESS);
     39: }

     41: /*@
     42:    DSSetState - Change the state of the DS object.

     44:    Logically Collective

     46:    Input Parameters:
     47: +  ds    - the direct solver context
     48: -  state - the new state

     50:    Notes:
     51:    The state indicates that the dense system is in an initial state (raw),
     52:    in an intermediate state (such as tridiagonal, Hessenberg or
     53:    Hessenberg-triangular), in a condensed state (such as diagonal, Schur or
     54:    generalized Schur), or in a truncated state.

     56:    This function is normally used to return to the raw state when the
     57:    condensed structure is destroyed.

     59:    Level: advanced

     61: .seealso: DSGetState()
     62: @*/
     63: PetscErrorCode DSSetState(DS ds,DSStateType state)
     64: {
     65:   PetscFunctionBegin;
     68:   switch (state) {
     69:     case DS_STATE_RAW:
     70:     case DS_STATE_INTERMEDIATE:
     71:     case DS_STATE_CONDENSED:
     72:     case DS_STATE_TRUNCATED:
     73:       if (ds->state!=state) PetscCall(PetscInfo(ds,"State has changed from %s to %s\n",DSStateTypes[ds->state],DSStateTypes[state]));
     74:       ds->state = state;
     75:       break;
     76:     default:
     77:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Wrong state");
     78:   }
     79:   PetscFunctionReturn(PETSC_SUCCESS);
     80: }

     82: /*@
     83:    DSGetState - Returns the current state.

     85:    Not Collective

     87:    Input Parameter:
     88: .  ds - the direct solver context

     90:    Output Parameter:
     91: .  state - current state

     93:    Level: advanced

     95: .seealso: DSSetState()
     96: @*/
     97: PetscErrorCode DSGetState(DS ds,DSStateType *state)
     98: {
     99:   PetscFunctionBegin;
    101:   PetscAssertPointer(state,2);
    102:   *state = ds->state;
    103:   PetscFunctionReturn(PETSC_SUCCESS);
    104: }

    106: /*@
    107:    DSSetDimensions - Resize the matrices in the DS object.

    109:    Logically Collective

    111:    Input Parameters:
    112: +  ds - the direct solver context
    113: .  n  - the new size
    114: .  l  - number of locked (inactive) leading columns
    115: -  k  - intermediate dimension (e.g., position of arrow)

    117:    Notes:
    118:    The internal arrays are not reallocated.

    120:    Some DS types have additional dimensions, e.g. the number of columns
    121:    in DSSVD. For these, you should call a specific interface function.

    123:    Use PETSC_CURRENT to leave any of the values unchanged. Use PETSC_DETERMINE
    124:    to set n to the leading dimension, l to the minimum value (0), and k to n/2.

    126:    Level: intermediate

    128: .seealso: DSGetDimensions(), DSAllocate(), DSSVDSetDimensions()
    129: @*/
    130: PetscErrorCode DSSetDimensions(DS ds,PetscInt n,PetscInt l,PetscInt k)
    131: {
    132:   PetscInt       on,ol,ok;
    133:   PetscBool      issvd;

    135:   PetscFunctionBegin;
    137:   DSCheckAlloc(ds,1);
    141:   on = ds->n; ol = ds->l; ok = ds->k;
    142:   if (n == PETSC_DETERMINE) {
    143:     ds->n = ds->extrarow? ds->ld-1: ds->ld;
    144:   } else if (n != PETSC_CURRENT) {
    145:     PetscCheck(n>=0 && n<=ds->ld,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of n. Must be between 0 and ld");
    146:     PetscCall(PetscObjectTypeCompareAny((PetscObject)ds,&issvd,DSSVD,DSGSVD,""));  /* SVD and GSVD have extra column instead of extra row */
    147:     PetscCheck(!ds->extrarow || n<ds->ld || issvd,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"A value of n equal to ld leaves no room for extra row");
    148:     ds->n = n;
    149:   }
    150:   ds->t = ds->n;   /* truncated length equal to the new dimension */
    151:   if (l == PETSC_DETERMINE) {
    152:     ds->l = 0;
    153:   } else if (l != PETSC_CURRENT) {
    154:     PetscCheck(l>=0 && l<=ds->n,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of l. Must be between 0 and n");
    155:     ds->l = l;
    156:   }
    157:   if (k == PETSC_DETERMINE) {
    158:     ds->k = ds->n/2;
    159:   } else if (k != PETSC_CURRENT) {
    160:     PetscCheck(k>=0 || k<=ds->n,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of k. Must be between 0 and n");
    161:     ds->k = k;
    162:   }
    163:   if (on!=ds->n || ol!=ds->l || ok!=ds->k) PetscCall(PetscInfo(ds,"New dimensions are: n=%" PetscInt_FMT ", l=%" PetscInt_FMT ", k=%" PetscInt_FMT "\n",ds->n,ds->l,ds->k));
    164:   PetscFunctionReturn(PETSC_SUCCESS);
    165: }

    167: /*@
    168:    DSGetDimensions - Returns the current dimensions.

    170:    Not Collective

    172:    Input Parameter:
    173: .  ds - the direct solver context

    175:    Output Parameters:
    176: +  n  - the current size
    177: .  l  - number of locked (inactive) leading columns
    178: .  k  - intermediate dimension (e.g., position of arrow)
    179: -  t  - truncated length

    181:    Note:
    182:    The t parameter makes sense only if DSTruncate() has been called.
    183:    Otherwise its value equals n.

    185:    Some DS types have additional dimensions, e.g. the number of columns
    186:    in DSSVD. For these, you should call a specific interface function.

    188:    Level: intermediate

    190: .seealso: DSSetDimensions(), DSTruncate(), DSSVDGetDimensions()
    191: @*/
    192: PetscErrorCode DSGetDimensions(DS ds,PetscInt *n,PetscInt *l,PetscInt *k,PetscInt *t)
    193: {
    194:   PetscFunctionBegin;
    196:   DSCheckAlloc(ds,1);
    197:   if (n) *n = ds->n;
    198:   if (l) *l = ds->l;
    199:   if (k) *k = ds->k;
    200:   if (t) *t = ds->t;
    201:   PetscFunctionReturn(PETSC_SUCCESS);
    202: }

    204: /*@
    205:    DSTruncate - Truncates the system represented in the DS object.

    207:    Logically Collective

    209:    Input Parameters:
    210: +  ds   - the direct solver context
    211: .  n    - the new size
    212: -  trim - a flag to indicate if the factorization must be trimmed

    214:    Note:
    215:    The new size is set to n. Note that in some cases the new size could
    216:    be n+1 or n-1 to avoid breaking a 2x2 diagonal block (e.g. in real
    217:    Schur form). In cases where the extra row is meaningful, the first
    218:    n elements are kept as the extra row for the new system.

    220:    If the flag trim is turned on, it resets the locked and intermediate
    221:    dimensions to zero, see DSSetDimensions(), and sets the state to RAW.
    222:    It also cleans the extra row if being used.

    224:    The typical usage of trim=true is to truncate the Schur decomposition
    225:    at the end of a Krylov iteration. In this case, the state must be
    226:    changed to RAW so that DSVectors() computes eigenvectors from scratch.

    228:    Level: advanced

    230: .seealso: DSSetDimensions(), DSSetExtraRow(), DSStateType
    231: @*/
    232: PetscErrorCode DSTruncate(DS ds,PetscInt n,PetscBool trim)
    233: {
    234:   DSStateType    old;

    236:   PetscFunctionBegin;
    239:   DSCheckAlloc(ds,1);
    242:   PetscCheck(n>=ds->l && n<=ds->n,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of n (%" PetscInt_FMT "). Must be between l (%" PetscInt_FMT ") and n (%" PetscInt_FMT ")",n,ds->l,ds->n);
    243:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    244:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    245:   PetscUseTypeMethod(ds,truncate,n,trim);
    246:   PetscCall(PetscFPTrapPop());
    247:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    248:   PetscCall(PetscInfo(ds,"Decomposition %s to size n=%" PetscInt_FMT "\n",trim?"trimmed":"truncated",ds->n));
    249:   old = ds->state;
    250:   ds->state = trim? DS_STATE_RAW: DS_STATE_TRUNCATED;
    251:   if (old!=ds->state) PetscCall(PetscInfo(ds,"State has changed from %s to %s\n",DSStateTypes[old],DSStateTypes[ds->state]));
    252:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    253:   PetscFunctionReturn(PETSC_SUCCESS);
    254: }

    256: /*@
    257:    DSMatGetSize - Returns the numbers of rows and columns of one of the DS matrices.

    259:    Not Collective

    261:    Input Parameters:
    262: +  ds - the direct solver context
    263: -  t  - the requested matrix

    265:    Output Parameters:
    266: +  n  - the number of rows
    267: -  m  - the number of columns

    269:    Note:
    270:    This is equivalent to MatGetSize() on a matrix obtained with DSGetMat().

    272:    Level: developer

    274: .seealso: DSSetDimensions(), DSGetMat()
    275: @*/
    276: PetscErrorCode DSMatGetSize(DS ds,DSMatType t,PetscInt *m,PetscInt *n)
    277: {
    278:   PetscInt       rows,cols;

    280:   PetscFunctionBegin;
    283:   DSCheckValidMat(ds,t,2);
    284:   if (ds->ops->matgetsize) PetscUseTypeMethod(ds,matgetsize,t,&rows,&cols);
    285:   else {
    286:     if (ds->state==DS_STATE_TRUNCATED && t>=DS_MAT_Q) rows = ds->t;
    287:     else rows = (t==DS_MAT_A && ds->extrarow)? ds->n+1: ds->n;
    288:     if (t==DS_MAT_T) cols = PetscDefined(USE_COMPLEX)? 2: 3;
    289:     else if (t==DS_MAT_D) cols = 1;
    290:     else cols = ds->n;
    291:   }
    292:   if (m) *m = rows;
    293:   if (n) *n = cols;
    294:   PetscFunctionReturn(PETSC_SUCCESS);
    295: }

    297: /*@
    298:    DSMatIsHermitian - Checks if one of the DS matrices is known to be Hermitian.

    300:    Not Collective

    302:    Input Parameters:
    303: +  ds - the direct solver context
    304: -  t  - the requested matrix

    306:    Output Parameter:
    307: .  flg - the Hermitian flag

    309:    Note:
    310:    Does not check the matrix values directly. The flag is set according to the
    311:    problem structure. For instance, in DSHEP matrix A is Hermitian.

    313:    Level: developer

    315: .seealso: DSGetMat()
    316: @*/
    317: PetscErrorCode DSMatIsHermitian(DS ds,DSMatType t,PetscBool *flg)
    318: {
    319:   PetscFunctionBegin;
    322:   DSCheckValidMat(ds,t,2);
    323:   PetscAssertPointer(flg,3);
    324:   *flg = PETSC_FALSE;
    325:   PetscTryTypeMethod(ds,hermitian,t,flg);
    326:   PetscFunctionReturn(PETSC_SUCCESS);
    327: }

    329: PetscErrorCode DSGetTruncateSize_Default(DS ds,PetscInt l,PetscInt n,PetscInt *k)
    330: {
    331: #if !defined(PETSC_USE_COMPLEX)
    332:   PetscScalar val;
    333: #endif

    335:   PetscFunctionBegin;
    336: #if !defined(PETSC_USE_COMPLEX)
    337:   PetscCall(MatGetValue(ds->omat[DS_MAT_A],l+(*k),l+(*k)-1,&val));
    338:   if (val != 0.0) {
    339:     if (l+(*k)<n-1) (*k)++;
    340:     else (*k)--;
    341:   }
    342: #endif
    343:   PetscFunctionReturn(PETSC_SUCCESS);
    344: }

    346: /*@
    347:    DSGetTruncateSize - Gets the correct size to be used in DSTruncate()
    348:    to avoid breaking a 2x2 block.

    350:    Not Collective

    352:    Input Parameters:
    353: +  ds - the direct solver context
    354: .  l  - the size of the locked part (set to 0 to use ds->l)
    355: -  n  - the total matrix size (set to 0 to use ds->n)

    357:    Output Parameter:
    358: .  k  - the wanted truncation size (possibly modified)

    360:    Notes:
    361:    This should be called before DSTruncate() to make sure that the truncation
    362:    does not break a 2x2 block corresponding to a complex conjugate eigenvalue.

    364:    The total size is n (either user-provided or ds->n if 0 is passed). The
    365:    size where the truncation is intended is equal to l+k (where l can be
    366:    equal to the locked size ds->l if set to 0). Then if there is a 2x2 block
    367:    at the l+k limit, the value of k is increased (or decreased) by 1.

    369:    Level: advanced

    371: .seealso: DSTruncate(), DSSetDimensions()
    372: @*/
    373: PetscErrorCode DSGetTruncateSize(DS ds,PetscInt l,PetscInt n,PetscInt *k)
    374: {
    375:   PetscFunctionBegin;
    377:   DSCheckAlloc(ds,1);
    380:   PetscAssertPointer(k,4);
    381:   PetscUseTypeMethod(ds,gettruncatesize,l?l:ds->l,n?n:ds->n,k);
    382:   PetscFunctionReturn(PETSC_SUCCESS);
    383: }

    385: /*@
    386:    DSGetMat - Returns a sequential dense Mat object containing the requested
    387:    matrix.

    389:    Not Collective

    391:    Input Parameters:
    392: +  ds - the direct solver context
    393: -  m  - the requested matrix

    395:    Output Parameter:
    396: .  A  - Mat object

    398:    Notes:
    399:    The returned Mat has sizes equal to the current DS dimensions (nxm),
    400:    and contains the values that would be obtained with DSGetArray()
    401:    (not DSGetArrayReal()). If the DS was truncated, then the number of rows
    402:    is equal to the dimension prior to truncation, see DSTruncate().
    403:    The communicator is always PETSC_COMM_SELF.

    405:    It is implemented with MatDenseGetSubMatrix(), and when no longer needed
    406:    the user must call DSRestoreMat() which will invoke MatDenseRestoreSubMatrix().

    408:    For matrices DS_MAT_T and DS_MAT_D, this function will return a Mat object
    409:    that cannot be used directly for computations, since it uses compact storage
    410:    (three and one diagonals for T and D, respectively). In complex scalars, the
    411:    internal array stores real values, so it is sufficient with 2 columns for T.

    413:    Level: advanced

    415: .seealso: DSRestoreMat(), DSSetDimensions(), DSGetArray(), DSGetArrayReal(), DSTruncate()
    416: @*/
    417: PetscErrorCode DSGetMat(DS ds,DSMatType m,Mat *A)
    418: {
    419:   PetscInt  rows=0,cols=0;
    420:   PetscBool flg;

    422:   PetscFunctionBegin;
    424:   DSCheckAlloc(ds,1);
    425:   DSCheckValidMat(ds,m,2);
    426:   PetscAssertPointer(A,3);

    428:   PetscCall(DSMatGetSize(ds,m,&rows,&cols));
    429:   PetscCheck(rows && cols,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"Must call DSSetDimensions() first");
    430:   PetscCall(MatDenseGetSubMatrix(ds->omat[m],0,rows,0,cols,A));

    432:   /* set Hermitian flag */
    433:   PetscCall(DSMatIsHermitian(ds,m,&flg));
    434:   PetscCall(MatSetOption(*A,MAT_SYMMETRIC,flg));
    435:   PetscCall(MatSetOption(*A,MAT_HERMITIAN,flg));
    436:   PetscFunctionReturn(PETSC_SUCCESS);
    437: }

    439: /*@
    440:    DSRestoreMat - Restores the matrix after DSGetMat() was called.

    442:    Not Collective

    444:    Input Parameters:
    445: +  ds - the direct solver context
    446: .  m  - the requested matrix
    447: -  A  - the fetched Mat object

    449:    Note:
    450:    A call to this function must match a previous call of DSGetMat().

    452:    Level: advanced

    454: .seealso: DSGetMat(), DSRestoreArray(), DSRestoreArrayReal()
    455: @*/
    456: PetscErrorCode DSRestoreMat(DS ds,DSMatType m,Mat *A)
    457: {
    458:   PetscFunctionBegin;
    460:   DSCheckAlloc(ds,1);
    461:   DSCheckValidMat(ds,m,2);
    462:   PetscAssertPointer(A,3);

    464:   PetscCall(MatDenseRestoreSubMatrix(ds->omat[m],A));
    465:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    466:   PetscFunctionReturn(PETSC_SUCCESS);
    467: }

    469: /*@
    470:    DSGetMatAndColumn - Returns a sequential dense Mat object containing the requested
    471:    matrix and one of its columns as a Vec.

    473:    Not Collective

    475:    Input Parameters:
    476: +  ds  - the direct solver context
    477: .  m   - the requested matrix
    478: -  col - the requested column

    480:    Output Parameters:
    481: +  A   - Mat object
    482: -  v   - Vec object (the column)

    484:    Notes:
    485:    This calls DSGetMat() and then it extracts the selected column.
    486:    The user must call DSRestoreMatAndColumn() to recover the original state.
    487:    For matrices DS_MAT_T and DS_MAT_D, in complex scalars this function implies
    488:    copying from real values stored internally to scalar values in the Vec.

    490:    Level: advanced

    492: .seealso: DSRestoreMatAndColumn(), DSGetMat()
    493: @*/
    494: PetscErrorCode DSGetMatAndColumn(DS ds,DSMatType m,PetscInt col,Mat *A,Vec *v)
    495: {
    496:   PetscFunctionBegin;
    498:   DSCheckAlloc(ds,1);
    499:   DSCheckValidMat(ds,m,2);
    500:   PetscAssertPointer(A,4);
    501:   PetscAssertPointer(v,5);

    503:   PetscCall(DSGetMat(ds,m,A));
    504:   if (PetscDefined(USE_COMPLEX) && (m==DS_MAT_T || m==DS_MAT_D)) {
    505:     const PetscScalar *as;
    506:     PetscScalar       *vs;
    507:     PetscReal         *ar;
    508:     PetscInt          i,n,lda;
    509:     PetscCall(MatCreateVecs(*A,NULL,v));
    510:     PetscCall(VecGetSize(*v,&n));
    511:     PetscCall(MatDenseGetLDA(*A,&lda));
    512:     PetscCall(MatDenseGetArrayRead(*A,&as));
    513:     PetscCall(VecGetArrayWrite(*v,&vs));
    514:     ar = (PetscReal*)as;
    515:     for (i=0;i<n;i++) vs[i] = ar[i+col*lda];
    516:     PetscCall(VecRestoreArrayWrite(*v,&vs));
    517:     PetscCall(MatDenseRestoreArrayRead(*A,&as));
    518:   } else PetscCall(MatDenseGetColumnVec(*A,col,v));
    519:   PetscFunctionReturn(PETSC_SUCCESS);
    520: }

    522: /*@
    523:    DSRestoreMatAndColumn - Restores the matrix and vector after DSGetMatAndColumn()
    524:    was called.

    526:    Not Collective

    528:    Input Parameters:
    529: +  ds  - the direct solver context
    530: .  m   - the requested matrix
    531: .  col - the requested column
    532: .  A   - the fetched Mat object
    533: -  v   - the fetched Vec object

    535:    Note:
    536:    A call to this function must match a previous call of DSGetMatAndColumn().

    538:    Level: advanced

    540: .seealso: DSGetMatAndColumn(), DSRestoreMat()
    541: @*/
    542: PetscErrorCode DSRestoreMatAndColumn(DS ds,DSMatType m,PetscInt col,Mat *A,Vec *v)
    543: {
    544:   PetscFunctionBegin;
    546:   DSCheckAlloc(ds,1);
    547:   DSCheckValidMat(ds,m,2);
    548:   PetscAssertPointer(A,4);
    549:   PetscAssertPointer(v,5);

    551:   if (PetscDefined(USE_COMPLEX) && (m==DS_MAT_T || m==DS_MAT_D)) {
    552:     const PetscScalar *vs;
    553:     PetscScalar       *as;
    554:     PetscReal         *ar;
    555:     PetscInt          i,n,lda;
    556:     PetscCall(VecGetSize(*v,&n));
    557:     PetscCall(MatDenseGetLDA(*A,&lda));
    558:     PetscCall(MatDenseGetArray(*A,&as));
    559:     PetscCall(VecGetArrayRead(*v,&vs));
    560:     ar = (PetscReal*)as;
    561:     for (i=0;i<n;i++) ar[i+col*lda] = PetscRealPart(vs[i]);
    562:     PetscCall(VecRestoreArrayRead(*v,&vs));
    563:     PetscCall(MatDenseRestoreArray(*A,&as));
    564:     PetscCall(VecDestroy(v));
    565:   } else PetscCall(MatDenseRestoreColumnVec(*A,col,v));
    566:   PetscCall(DSRestoreMat(ds,m,A));
    567:   PetscFunctionReturn(PETSC_SUCCESS);
    568: }

    570: /*@C
    571:    DSGetArray - Returns a pointer to the internal array of one of the
    572:    matrices. You MUST call DSRestoreArray() when you no longer
    573:    need to access the array.

    575:    Not Collective

    577:    Input Parameters:
    578: +  ds - the direct solver context
    579: -  m  - the requested matrix

    581:    Output Parameter:
    582: .  a  - pointer to the values

    584:    Note:
    585:    To get read-only access, use DSGetMat() followed by MatDenseGetArrayRead().

    587:    Level: advanced

    589: .seealso: DSRestoreArray(), DSGetArrayReal()
    590: @*/
    591: PetscErrorCode DSGetArray(DS ds,DSMatType m,PetscScalar *a[])
    592: {
    593:   PetscFunctionBegin;
    595:   DSCheckAlloc(ds,1);
    596:   DSCheckValidMat(ds,m,2);
    597:   PetscAssertPointer(a,3);
    598:   PetscCall(MatDenseGetArray(ds->omat[m],a));
    599:   PetscFunctionReturn(PETSC_SUCCESS);
    600: }

    602: /*@C
    603:    DSRestoreArray - Restores the matrix after DSGetArray() was called.

    605:    Not Collective

    607:    Input Parameters:
    608: +  ds - the direct solver context
    609: .  m  - the requested matrix
    610: -  a  - pointer to the values

    612:    Level: advanced

    614: .seealso: DSGetArray(), DSGetArrayReal()
    615: @*/
    616: PetscErrorCode DSRestoreArray(DS ds,DSMatType m,PetscScalar *a[])
    617: {
    618:   PetscFunctionBegin;
    620:   DSCheckAlloc(ds,1);
    621:   DSCheckValidMat(ds,m,2);
    622:   PetscAssertPointer(a,3);
    623:   PetscCall(MatDenseRestoreArray(ds->omat[m],a));
    624:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    625:   PetscFunctionReturn(PETSC_SUCCESS);
    626: }

    628: /*@C
    629:    DSGetArrayReal - Returns a real pointer to the internal array of T or D.
    630:    You MUST call DSRestoreArrayReal() when you no longer need to access the array.

    632:    Not Collective

    634:    Input Parameters:
    635: +  ds - the direct solver context
    636: -  m  - the requested matrix

    638:    Output Parameter:
    639: .  a  - pointer to the values

    641:    Note:
    642:    This function can be used only for DS_MAT_T and DS_MAT_D. These matrices always
    643:    store real values, even in complex scalars, that is why the returned pointer is
    644:    PetscReal.

    646:    Level: advanced

    648: .seealso: DSRestoreArrayReal(), DSGetArray()
    649: @*/
    650: PetscErrorCode DSGetArrayReal(DS ds,DSMatType m,PetscReal *a[])
    651: {
    652: #if defined(PETSC_USE_COMPLEX)
    653:   PetscScalar *as;
    654: #endif

    656:   PetscFunctionBegin;
    658:   DSCheckAlloc(ds,1);
    659:   DSCheckValidMatReal(ds,m,2);
    660:   PetscAssertPointer(a,3);
    661: #if defined(PETSC_USE_COMPLEX)
    662:   PetscCall(MatDenseGetArray(ds->omat[m],&as));
    663:   *a = (PetscReal*)as;
    664: #else
    665:   PetscCall(MatDenseGetArray(ds->omat[m],a));
    666: #endif
    667:   PetscFunctionReturn(PETSC_SUCCESS);
    668: }

    670: /*@C
    671:    DSRestoreArrayReal - Restores the matrix after DSGetArrayReal() was called.

    673:    Not Collective

    675:    Input Parameters:
    676: +  ds - the direct solver context
    677: .  m  - the requested matrix
    678: -  a  - pointer to the values

    680:    Level: advanced

    682: .seealso: DSGetArrayReal(), DSGetArray()
    683: @*/
    684: PetscErrorCode DSRestoreArrayReal(DS ds,DSMatType m,PetscReal *a[])
    685: {
    686: #if defined(PETSC_USE_COMPLEX)
    687:   PetscScalar *as;
    688: #endif

    690:   PetscFunctionBegin;
    692:   DSCheckAlloc(ds,1);
    693:   DSCheckValidMatReal(ds,m,2);
    694:   PetscAssertPointer(a,3);
    695: #if defined(PETSC_USE_COMPLEX)
    696:   PetscCall(MatDenseRestoreArray(ds->omat[m],&as));
    697:   *a = NULL;
    698: #else
    699:   PetscCall(MatDenseRestoreArray(ds->omat[m],a));
    700: #endif
    701:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    702:   PetscFunctionReturn(PETSC_SUCCESS);
    703: }

    705: /*@
    706:    DSSolve - Solves the problem.

    708:    Logically Collective

    710:    Input Parameters:
    711: +  ds   - the direct solver context
    712: .  eigr - array to store the computed eigenvalues (real part)
    713: -  eigi - array to store the computed eigenvalues (imaginary part)

    715:    Note:
    716:    This call brings the dense system to condensed form. No ordering
    717:    of the eigenvalues is enforced (for this, call DSSort() afterwards).

    719:    Level: intermediate

    721: .seealso: DSSort(), DSStateType
    722: @*/
    723: PetscErrorCode DSSolve(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    724: {
    725:   PetscFunctionBegin;
    728:   DSCheckAlloc(ds,1);
    729:   PetscAssertPointer(eigr,2);
    730:   if (ds->state>=DS_STATE_CONDENSED) PetscFunctionReturn(PETSC_SUCCESS);
    731:   PetscCheck(ds->ops->solve[ds->method],PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The specified method number does not exist for this DS");
    732:   PetscCall(PetscInfo(ds,"Starting solve with problem sizes: n=%" PetscInt_FMT ", l=%" PetscInt_FMT ", k=%" PetscInt_FMT "\n",ds->n,ds->l,ds->k));
    733:   PetscCall(PetscLogEventBegin(DS_Solve,ds,0,0,0));
    734:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    735:   PetscUseTypeMethod(ds,solve[ds->method],eigr,eigi);
    736:   PetscCall(PetscFPTrapPop());
    737:   PetscCall(PetscLogEventEnd(DS_Solve,ds,0,0,0));
    738:   PetscCall(PetscInfo(ds,"State has changed from %s to CONDENSED\n",DSStateTypes[ds->state]));
    739:   ds->state = DS_STATE_CONDENSED;
    740:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    741:   PetscFunctionReturn(PETSC_SUCCESS);
    742: }

    744: /*@
    745:    DSSort - Sorts the result of DSSolve() according to a given sorting
    746:    criterion.

    748:    Logically Collective

    750:    Input Parameters:
    751: +  ds   - the direct solver context
    752: .  rr   - (optional) array containing auxiliary values (real part)
    753: -  ri   - (optional) array containing auxiliary values (imaginary part)

    755:    Input/Output Parameters:
    756: +  eigr - array containing the computed eigenvalues (real part)
    757: .  eigi - array containing the computed eigenvalues (imaginary part)
    758: -  k    - (optional) number of elements in the leading group

    760:    Notes:
    761:    This routine sorts the arrays provided in eigr and eigi, and also
    762:    sorts the dense system stored inside ds (assumed to be in condensed form).
    763:    The sorting criterion is specified with DSSetSlepcSC().

    765:    If arrays rr and ri are provided, then a (partial) reordering based on these
    766:    values rather than on the eigenvalues is performed. In symmetric problems
    767:    a total order is obtained (parameter k is ignored), but otherwise the result
    768:    is sorted only partially. In this latter case, it is only guaranteed that
    769:    all the first k elements satisfy the comparison with any of the last n-k
    770:    elements. The output value of parameter k is the final number of elements in
    771:    the first set.

    773:    Level: intermediate

    775: .seealso: DSSolve(), DSSetSlepcSC(), DSSortWithPermutation()
    776: @*/
    777: PetscErrorCode DSSort(DS ds,PetscScalar eigr[],PetscScalar eigi[],PetscScalar rr[],PetscScalar ri[],PetscInt *k)
    778: {
    779:   PetscInt       i;

    781:   PetscFunctionBegin;
    784:   DSCheckSolved(ds,1);
    785:   PetscAssertPointer(eigr,2);
    786:   if (rr) PetscAssertPointer(rr,4);
    787:   PetscCheck(ds->state<DS_STATE_TRUNCATED,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"Cannot sort a truncated DS");
    788:   PetscCheck(ds->sc,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"Must provide a sorting criterion first");
    789:   PetscCheck(!k || rr,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Argument k can only be used together with rr");

    791:   for (i=0;i<ds->n;i++) ds->perm[i] = i;   /* initialize to trivial permutation */
    792:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    793:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    794:   PetscUseTypeMethod(ds,sort,eigr,eigi,rr,ri,k);
    795:   PetscCall(PetscFPTrapPop());
    796:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    797:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    798:   PetscCall(PetscInfo(ds,"Finished sorting\n"));
    799:   PetscFunctionReturn(PETSC_SUCCESS);
    800: }

    802: /*@
    803:    DSSortWithPermutation - Reorders the result of DSSolve() according to a given
    804:    permutation.

    806:    Logically Collective

    808:    Input Parameters:
    809: +  ds   - the direct solver context
    810: -  perm - permutation that indicates the new ordering

    812:    Input/Output Parameters:
    813: +  eigr - array with the reordered eigenvalues (real part)
    814: -  eigi - array with the reordered eigenvalues (imaginary part)

    816:    Notes:
    817:    This routine reorders the arrays provided in eigr and eigi, and also the dense
    818:    system stored inside ds (assumed to be in condensed form). There is no sorting
    819:    criterion, as opposed to DSSort(). Instead, the new ordering is given in argument perm.

    821:    Level: advanced

    823: .seealso: DSSolve(), DSSort()
    824: @*/
    825: PetscErrorCode DSSortWithPermutation(DS ds,PetscInt perm[],PetscScalar eigr[],PetscScalar eigi[])
    826: {
    827:   PetscFunctionBegin;
    830:   DSCheckSolved(ds,1);
    831:   PetscAssertPointer(perm,2);
    832:   PetscAssertPointer(eigr,3);
    833:   PetscCheck(ds->state<DS_STATE_TRUNCATED,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"Cannot sort a truncated DS");

    835:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    836:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    837:   PetscUseTypeMethod(ds,sortperm,perm,eigr,eigi);
    838:   PetscCall(PetscFPTrapPop());
    839:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    840:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    841:   PetscCall(PetscInfo(ds,"Finished sorting\n"));
    842:   PetscFunctionReturn(PETSC_SUCCESS);
    843: }

    845: /*@
    846:    DSSynchronize - Make sure that all processes have the same data, performing
    847:    communication if necessary.

    849:    Collective

    851:    Input Parameter:
    852: .  ds   - the direct solver context

    854:    Input/Output Parameters:
    855: +  eigr - (optional) array with the computed eigenvalues (real part)
    856: -  eigi - (optional) array with the computed eigenvalues (imaginary part)

    858:    Notes:
    859:    When the DS has been created with a communicator with more than one process,
    860:    the internal data, especially the computed matrices, may diverge in the
    861:    different processes. This happens when using multithreaded BLAS and may
    862:    cause numerical issues in some ill-conditioned problems. This function
    863:    performs the necessary communication among the processes so that the
    864:    internal data is exactly equal in all of them.

    866:    Depending on the parallel mode as set with DSSetParallel(), this function
    867:    will either do nothing or synchronize the matrices computed by DSSolve()
    868:    and DSSort(). The arguments eigr and eigi are typically those used in the
    869:    calls to DSSolve() and DSSort().

    871:    Level: developer

    873: .seealso: DSSetParallel(), DSSolve(), DSSort()
    874: @*/
    875: PetscErrorCode DSSynchronize(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    876: {
    877:   PetscMPIInt    size;

    879:   PetscFunctionBegin;
    882:   DSCheckAlloc(ds,1);
    883:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ds),&size));
    884:   if (size>1 && ds->pmode==DS_PARALLEL_SYNCHRONIZED) {
    885:     PetscCall(PetscLogEventBegin(DS_Synchronize,ds,0,0,0));
    886:     PetscUseTypeMethod(ds,synchronize,eigr,eigi);
    887:     PetscCall(PetscLogEventEnd(DS_Synchronize,ds,0,0,0));
    888:     PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    889:     PetscCall(PetscInfo(ds,"Synchronization completed (%s)\n",DSParallelTypes[ds->pmode]));
    890:   }
    891:   PetscFunctionReturn(PETSC_SUCCESS);
    892: }

    894: /*@
    895:    DSVectors - Compute vectors associated to the dense system such
    896:    as eigenvectors.

    898:    Logically Collective

    900:    Input Parameters:
    901: +  ds  - the direct solver context
    902: -  mat - the matrix, used to indicate which vectors are required

    904:    Input/Output Parameter:
    905: .  j   - (optional) index of vector to be computed

    907:    Output Parameter:
    908: .  rnorm - (optional) computed residual norm

    910:    Notes:
    911:    Allowed values for mat are DS_MAT_X, DS_MAT_Y, DS_MAT_U and DS_MAT_V, to
    912:    compute right or left eigenvectors, or left or right singular vectors,
    913:    respectively.

    915:    If NULL is passed in argument j then all vectors are computed,
    916:    otherwise j indicates which vector must be computed. In real non-symmetric
    917:    problems, on exit the index j will be incremented when a complex conjugate
    918:    pair is found.

    920:    This function can be invoked after the dense problem has been solved,
    921:    to get the residual norm estimate of the associated Ritz pair. In that
    922:    case, the relevant information is returned in rnorm.

    924:    For computing eigenvectors, LAPACK's _trevc is used so the matrix must
    925:    be in (quasi-)triangular form, or call DSSolve() first.

    927:    Level: intermediate

    929: .seealso: DSSolve()
    930: @*/
    931: PetscErrorCode DSVectors(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    932: {
    933:   PetscFunctionBegin;
    936:   DSCheckAlloc(ds,1);
    938:   PetscCheck(mat<DS_NUM_MAT,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Invalid matrix");
    939:   PetscCheck(!rnorm || j,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"Must give a value of j");
    940:   if (!ds->omat[mat]) PetscCall(DSAllocateMat_Private(ds,mat));
    941:   if (!j) PetscCall(PetscInfo(ds,"Computing all vectors on %s\n",DSMatName[mat]));
    942:   PetscCall(PetscLogEventBegin(DS_Vectors,ds,0,0,0));
    943:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    944:   PetscUseTypeMethod(ds,vectors,mat,j,rnorm);
    945:   PetscCall(PetscFPTrapPop());
    946:   PetscCall(PetscLogEventEnd(DS_Vectors,ds,0,0,0));
    947:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    948:   PetscFunctionReturn(PETSC_SUCCESS);
    949: }

    951: /*@
    952:    DSUpdateExtraRow - Performs all necessary operations so that the extra
    953:    row gets up-to-date after a call to DSSolve().

    955:    Logically Collective

    957:    Input Parameters:
    958: .  ds - the direct solver context

    960:    Level: advanced

    962: .seealso: DSSolve(), DSSetExtraRow()
    963: @*/
    964: PetscErrorCode DSUpdateExtraRow(DS ds)
    965: {
    966:   PetscFunctionBegin;
    969:   DSCheckAlloc(ds,1);
    970:   PetscCheck(ds->extrarow,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONGSTATE,"Should have called DSSetExtraRow");
    971:   PetscCall(PetscInfo(ds,"Updating extra row\n"));
    972:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    973:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    974:   PetscUseTypeMethod(ds,update);
    975:   PetscCall(PetscFPTrapPop());
    976:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    977:   PetscFunctionReturn(PETSC_SUCCESS);
    978: }

    980: /*@
    981:    DSCond - Compute the condition number.

    983:    Logically Collective

    985:    Input Parameters:
    986: +  ds - the direct solver context
    987: -  cond - the computed condition number

    989:    Notes:
    990:    In standard eigenvalue problems, returns the inf-norm condition number of the first
    991:    matrix, computed as cond(A) = norm(A)*norm(inv(A)).

    993:    In GSVD problems, returns the maximum of cond(A) and cond(B), where cond(.) is
    994:    computed as the ratio of the largest and smallest singular values.

    996:    Does not take into account the extra row.

    998:    Level: advanced

    1000: .seealso: DSSolve(), DSSetExtraRow()
    1001: @*/
    1002: PetscErrorCode DSCond(DS ds,PetscReal *cond)
    1003: {
    1004:   PetscFunctionBegin;
    1007:   DSCheckAlloc(ds,1);
    1008:   PetscAssertPointer(cond,2);
    1009:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    1010:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1011:   PetscUseTypeMethod(ds,cond,cond);
    1012:   PetscCall(PetscFPTrapPop());
    1013:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    1014:   PetscCall(PetscInfo(ds,"Computed condition number = %g\n",(double)*cond));
    1015:   PetscFunctionReturn(PETSC_SUCCESS);
    1016: }

    1018: /*@
    1019:    DSTranslateHarmonic - Computes a translation of the dense system.

    1021:    Logically Collective

    1023:    Input Parameters:
    1024: +  ds      - the direct solver context
    1025: .  tau     - the translation amount
    1026: .  beta    - last component of vector b
    1027: -  recover - boolean flag to indicate whether to recover or not

    1029:    Output Parameters:
    1030: +  g       - the computed vector (optional)
    1031: -  gamma   - scale factor (optional)

    1033:    Notes:
    1034:    This function is intended for use in the context of Krylov methods only.
    1035:    It computes a translation of a Krylov decomposition in order to extract
    1036:    eigenpair approximations by harmonic Rayleigh-Ritz.
    1037:    The matrix is updated as A + g*b' where g = (A-tau*eye(n))'\b and
    1038:    vector b is assumed to be beta*e_n^T.

    1040:    The gamma factor is defined as sqrt(1+g'*g) and can be interpreted as
    1041:    the factor by which the residual of the Krylov decomposition is scaled.

    1043:    If the recover flag is activated, the computed translation undoes the
    1044:    translation done previously. In that case, parameter tau is ignored.

    1046:    Level: developer

    1048: .seealso: DSTranslateRKS()
    1049: @*/
    1050: PetscErrorCode DSTranslateHarmonic(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *g,PetscReal *gamma)
    1051: {
    1052:   PetscFunctionBegin;
    1055:   DSCheckAlloc(ds,1);
    1056:   if (recover) PetscCall(PetscInfo(ds,"Undoing the translation\n"));
    1057:   else PetscCall(PetscInfo(ds,"Computing the translation\n"));
    1058:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    1059:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1060:   PetscUseTypeMethod(ds,transharm,tau,beta,recover,g,gamma);
    1061:   PetscCall(PetscFPTrapPop());
    1062:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    1063:   ds->state = DS_STATE_RAW;
    1064:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    1065:   PetscFunctionReturn(PETSC_SUCCESS);
    1066: }

    1068: /*@
    1069:    DSTranslateRKS - Computes a modification of the dense system corresponding
    1070:    to an update of the shift in a rational Krylov method.

    1072:    Logically Collective

    1074:    Input Parameters:
    1075: +  ds    - the direct solver context
    1076: -  alpha - the translation amount

    1078:    Notes:
    1079:    This function is intended for use in the context of Krylov methods only.
    1080:    It takes the leading (k+1,k) submatrix of A, containing the truncated
    1081:    Rayleigh quotient of a Krylov-Schur relation computed from a shift
    1082:    sigma1 and transforms it to obtain a Krylov relation as if computed
    1083:    from a different shift sigma2. The new matrix is computed as
    1084:    1.0/alpha*(eye(k)-Q*inv(R)), where [Q,R]=qr(eye(k)-alpha*A) and
    1085:    alpha = sigma1-sigma2.

    1087:    Matrix Q is placed in DS_MAT_Q so that it can be used to update the
    1088:    Krylov basis.

    1090:    Level: developer

    1092: .seealso: DSTranslateHarmonic()
    1093: @*/
    1094: PetscErrorCode DSTranslateRKS(DS ds,PetscScalar alpha)
    1095: {
    1096:   PetscFunctionBegin;
    1099:   DSCheckAlloc(ds,1);
    1100:   PetscCall(PetscInfo(ds,"Translating with alpha=%g\n",(double)PetscRealPart(alpha)));
    1101:   PetscCall(DSSetCompact(ds,PETSC_FALSE));
    1102:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
    1103:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1104:   PetscUseTypeMethod(ds,transrks,alpha);
    1105:   PetscCall(PetscFPTrapPop());
    1106:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
    1107:   ds->state = DS_STATE_RAW;
    1108:   PetscCall(PetscObjectStateIncrease((PetscObject)ds));
    1109:   PetscFunctionReturn(PETSC_SUCCESS);
    1110: }