Date: 2022-03-31T04:46:10+00:00

Actual source code: sorti.c

      2: /*
      3:    This file contains routines for sorting integers. Values are sorted in place.
      4:    One can use src/sys/tests/ex52.c for benchmarking.
      5:  */
      6: #include <petsc/private/petscimpl.h>
      7: #include <petsc/private/hashseti.h>

      9: #define MEDIAN3(v,a,b,c)                                                        \
     10:   (v[a]<v[b]                                                                    \
     11:    ? (v[b]<v[c]                                                                 \
     12:       ? (b)                                                                     \
     13:       : (v[a]<v[c] ? (c) : (a)))                                                \
     14:    : (v[c]<v[b]                                                                 \
     15:       ? (b)                                                                     \
     16:       : (v[a]<v[c] ? (a) : (c))))

     18: #define MEDIAN(v,right) MEDIAN3(v,right/4,right/2,right/4*3)

     20: /* Swap one, two or three pairs. Each pair can have its own type */
     21: #define SWAP1(a,b,t1)               do {t1=a;a=b;b=t1;} while (0)
     22: #define SWAP2(a,b,c,d,t1,t2)        do {t1=a;a=b;b=t1; t2=c;c=d;d=t2;} while (0)
     23: #define SWAP3(a,b,c,d,e,f,t1,t2,t3) do {t1=a;a=b;b=t1; t2=c;c=d;d=t2; t3=e;e=f;f=t3;} while (0)

     25: /* Swap a & b, *c & *d. c, d, t2 are pointers to a type of size <siz> */
     26: #define SWAP2Data(a,b,c,d,t1,t2,siz)                                             \
     27:   do {                                                                           \
     28:     t1=a; a=b; b=t1;                                                             \
     29:     PetscMemcpy(t2,c,siz);                                              \
     30:     PetscMemcpy(c,d,siz);                                               \
     31:     PetscMemcpy(d,t2,siz);                                              \
     32:   } while (0)

     34: /*
     35:    Partition X[lo,hi] into two parts: X[lo,l) <= pivot; X[r,hi] > pivot

     37:    Input Parameters:
     38:     + X         - array to partition
     39:     . pivot     - a pivot of X[]
     40:     . t1        - temp variable for X
     41:     - lo,hi     - lower and upper bound of the array

     43:    Output Parameters:
     44:     + l,r       - of type PetscInt

     46:    Notes:
     47:     The TwoWayPartition2/3 variants also partition other arrays along with X.
     48:     These arrays can have different types, so they provide their own temp t2,t3
     49:  */
     50: #define TwoWayPartition1(X,pivot,t1,lo,hi,l,r)                                   \
     51:   do {                                                                           \
     52:     l = lo;                                                                      \
     53:     r = hi;                                                                      \
     54:     while (1) {                                                                  \
     55:       while (X[l] < pivot) l++;                                                  \
     56:       while (X[r] > pivot) r--;                                                  \
     57:       if (l >= r) {r++; break;}                                                  \
     58:       SWAP1(X[l],X[r],t1);                                                       \
     59:       l++;                                                                       \
     60:       r--;                                                                       \
     61:     }                                                                            \
     62:   } while (0)

     64: /*
     65:    Partition X[lo,hi] into two parts: X[lo,l) >= pivot; X[r,hi] < pivot

     67:    Input Parameters:
     68:     + X         - array to partition
     69:     . pivot     - a pivot of X[]
     70:     . t1        - temp variable for X
     71:     - lo,hi     - lower and upper bound of the array

     73:    Output Parameters:
     74:     + l,r       - of type PetscInt

     76:    Notes:
     77:     The TwoWayPartition2/3 variants also partition other arrays along with X.
     78:     These arrays can have different types, so they provide their own temp t2,t3
     79:  */
     80: #define TwoWayPartitionReverse1(X,pivot,t1,lo,hi,l,r)                            \
     81:   do {                                                                           \
     82:     l = lo;                                                                      \
     83:     r = hi;                                                                      \
     84:     while (1) {                                                                  \
     85:       while (X[l] > pivot) l++;                                                  \
     86:       while (X[r] < pivot) r--;                                                  \
     87:       if (l >= r) {r++; break;}                                                  \
     88:       SWAP1(X[l],X[r],t1);                                                       \
     89:       l++;                                                                       \
     90:       r--;                                                                       \
     91:     }                                                                            \
     92:   } while (0)

     94: #define TwoWayPartition2(X,Y,pivot,t1,t2,lo,hi,l,r)                              \
     95:   do {                                                                           \
     96:     l = lo;                                                                      \
     97:     r = hi;                                                                      \
     98:     while (1) {                                                                  \
     99:       while (X[l] < pivot) l++;                                                  \
    100:       while (X[r] > pivot) r--;                                                  \
    101:       if (l >= r) {r++; break;}                                                  \
    102:       SWAP2(X[l],X[r],Y[l],Y[r],t1,t2);                                          \
    103:       l++;                                                                       \
    104:       r--;                                                                       \
    105:     }                                                                            \
    106:   } while (0)

    108: #define TwoWayPartition3(X,Y,Z,pivot,t1,t2,t3,lo,hi,l,r)                         \
    109:   do {                                                                           \
    110:     l = lo;                                                                      \
    111:     r = hi;                                                                      \
    112:     while (1) {                                                                  \
    113:       while (X[l] < pivot) l++;                                                  \
    114:       while (X[r] > pivot) r--;                                                  \
    115:       if (l >= r) {r++; break;}                                                  \
    116:       SWAP3(X[l],X[r],Y[l],Y[r],Z[l],Z[r],t1,t2,t3);                             \
    117:       l++;                                                                       \
    118:       r--;                                                                       \
    119:     }                                                                            \
    120:   } while (0)

    122: /* Templates for similar functions used below */
    123: #define QuickSort1(FuncName,X,n,pivot,t1)                                        \
    124:   do {                                                                           \
    125:     PetscCount i,j,p,l,r,hi=n-1;                                                 \
    126:     if (n < 8) {                                                                 \
    127:       for (i=0; i<n; i++) {                                                      \
    128:         pivot = X[i];                                                            \
    129:         for (j=i+1; j<n; j++) {                                                  \
    130:           if (pivot > X[j]) {                                                    \
    131:             SWAP1(X[i],X[j],t1);                                                 \
    132:             pivot = X[i];                                                        \
    133:           }                                                                      \
    134:         }                                                                        \
    135:       }                                                                          \
    136:     } else {                                                                     \
    137:       p     = MEDIAN(X,hi);                                                      \
    138:       pivot = X[p];                                                              \
    139:       TwoWayPartition1(X,pivot,t1,0,hi,l,r);                                     \
    140:       FuncName(l,X);                                                    \
    141:       FuncName(hi-r+1,X+r);                                             \
    142:     }                                                                            \
    143:   } while (0)

    145: /* Templates for similar functions used below */
    146: #define QuickSortReverse1(FuncName,X,n,pivot,t1)                                 \
    147:   do {                                                                           \
    148:     PetscCount i,j,p,l,r,hi=n-1;                                                 \
    149:     if (n < 8) {                                                                 \
    150:       for (i=0; i<n; i++) {                                                      \
    151:         pivot = X[i];                                                            \
    152:         for (j=i+1; j<n; j++) {                                                  \
    153:           if (pivot < X[j]) {                                                    \
    154:             SWAP1(X[i],X[j],t1);                                                 \
    155:             pivot = X[i];                                                        \
    156:           }                                                                      \
    157:         }                                                                        \
    158:       }                                                                          \
    159:     } else {                                                                     \
    160:       p     = MEDIAN(X,hi);                                                      \
    161:       pivot = X[p];                                                              \
    162:       TwoWayPartitionReverse1(X,pivot,t1,0,hi,l,r);                              \
    163:       FuncName(l,X);                                                    \
    164:       FuncName(hi-r+1,X+r);                                             \
    165:     }                                                                            \
    166:   } while (0)

    168: #define QuickSort2(FuncName,X,Y,n,pivot,t1,t2)                                   \
    169:   do {                                                                           \
    170:     PetscCount i,j,p,l,r,hi=n-1;                                                 \
    171:     if (n < 8) {                                                                 \
    172:       for (i=0; i<n; i++) {                                                      \
    173:         pivot = X[i];                                                            \
    174:         for (j=i+1; j<n; j++) {                                                  \
    175:           if (pivot > X[j]) {                                                    \
    176:             SWAP2(X[i],X[j],Y[i],Y[j],t1,t2);                                    \
    177:             pivot = X[i];                                                        \
    178:           }                                                                      \
    179:         }                                                                        \
    180:       }                                                                          \
    181:     } else {                                                                     \
    182:       p     = MEDIAN(X,hi);                                                      \
    183:       pivot = X[p];                                                              \
    184:       TwoWayPartition2(X,Y,pivot,t1,t2,0,hi,l,r);                                \
    185:       FuncName(l,X,Y);                                                  \
    186:       FuncName(hi-r+1,X+r,Y+r);                                         \
    187:     }                                                                            \
    188:   } while (0)

    190: #define QuickSort3(FuncName,X,Y,Z,n,pivot,t1,t2,t3)                              \
    191:   do {                                                                           \
    192:     PetscCount i,j,p,l,r,hi=n-1;                                                 \
    193:     if (n < 8) {                                                                 \
    194:       for (i=0; i<n; i++) {                                                      \
    195:         pivot = X[i];                                                            \
    196:         for (j=i+1; j<n; j++) {                                                  \
    197:           if (pivot > X[j]) {                                                    \
    198:             SWAP3(X[i],X[j],Y[i],Y[j],Z[i],Z[j],t1,t2,t3);                       \
    199:             pivot = X[i];                                                        \
    200:           }                                                                      \
    201:         }                                                                        \
    202:       }                                                                          \
    203:     } else {                                                                     \
    204:       p     = MEDIAN(X,hi);                                                      \
    205:       pivot = X[p];                                                              \
    206:       TwoWayPartition3(X,Y,Z,pivot,t1,t2,t3,0,hi,l,r);                           \
    207:       FuncName(l,X,Y,Z);                                                \
    208:       FuncName(hi-r+1,X+r,Y+r,Z+r);                                     \
    209:     }                                                                            \
    210:   } while (0)

    212: /*@
    213:    PetscSortedInt - Determines whether the array is sorted.

    215:    Not Collective

    217:    Input Parameters:
    218: +  n  - number of values
    219: -  X  - array of integers

    221:    Output Parameters:
    222: .  sorted - flag whether the array is sorted

    224:    Level: intermediate

    226: .seealso: PetscSortInt(), PetscSortedMPIInt(), PetscSortedReal()
    227: @*/
    228: PetscErrorCode  PetscSortedInt(PetscInt n,const PetscInt X[],PetscBool *sorted)
    229: {
    232:   PetscSorted(n,X,*sorted);
    233:   return 0;
    234: }

    236: /*@
    237:    PetscSortInt - Sorts an array of integers in place in increasing order.

    239:    Not Collective

    241:    Input Parameters:
    242: +  n  - number of values
    243: -  X  - array of integers

    245:    Notes:
    246:    This function serves as an alternative to PetscIntSortSemiOrdered(), and may perform faster especially if the array
    247:    is completely random. There are exceptions to this and so it is __highly__ recommended that the user benchmark their
    248:    code to see which routine is fastest.

    250:    Level: intermediate

    252: .seealso: PetscIntSortSemiOrdered(), PetscSortReal(), PetscSortIntWithPermutation()
    253: @*/
    254: PetscErrorCode  PetscSortInt(PetscInt n,PetscInt X[])
    255: {
    256:   PetscInt pivot,t1;

    259:   QuickSort1(PetscSortInt,X,n,pivot,t1);
    260:   return 0;
    261: }

    263: /*@
    264:    PetscSortReverseInt - Sorts an array of integers in place in decreasing order.

    266:    Not Collective

    268:    Input Parameters:
    269: +  n  - number of values
    270: -  X  - array of integers

    272:    Level: intermediate

    274: .seealso: PetscIntSortSemiOrdered(), PetscSortInt(), PetscSortIntWithPermutation()
    275: @*/
    276: PetscErrorCode  PetscSortReverseInt(PetscInt n,PetscInt X[])
    277: {
    278:   PetscInt pivot,t1;

    281:   QuickSortReverse1(PetscSortReverseInt,X,n,pivot,t1);
    282:   return 0;
    283: }

    285: /*@
    286:    PetscSortedRemoveDupsInt - Removes all duplicate entries of a sorted input array

    288:    Not Collective

    290:    Input Parameters:
    291: +  n  - number of values
    292: -  X  - sorted array of integers

    294:    Output Parameter:
    295: .  n - number of non-redundant values

    297:    Level: intermediate

    299: .seealso: PetscSortInt()
    300: @*/
    301: PetscErrorCode  PetscSortedRemoveDupsInt(PetscInt *n,PetscInt X[])
    302: {
    303:   PetscInt i,s = 0,N = *n, b = 0;

    307:   for (i=0; i<N-1; i++) {
    308:     if (X[b+s+1] != X[b]) {
    309:       X[b+1] = X[b+s+1]; b++;
    310:     } else s++;
    311:   }
    312:   *n = N - s;
    313:   return 0;
    314: }

    316: /*@
    317:    PetscSortedCheckDupsInt - Checks if a sorted integer array has duplicates

    319:    Not Collective

    321:    Input Parameters:
    322: +  n  - number of values
    323: -  X  - sorted array of integers

    325:    Output Parameter:
    326: .  dups - True if the array has dups, otherwise false

    328:    Level: intermediate

    331: @*/
    332: PetscErrorCode  PetscSortedCheckDupsInt(PetscInt n,const PetscInt X[],PetscBool *flg)
    333: {
    334:   PetscInt i;

    337:   *flg = PETSC_FALSE;
    338:   for (i=0; i<n-1; i++) {
    339:     if (X[i+1] == X[i]) {
    340:       *flg = PETSC_TRUE;
    341:       break;
    342:     }
    343:   }
    344:   return 0;
    345: }

    347: /*@
    348:    PetscSortRemoveDupsInt - Sorts an array of integers in place in increasing order removes all duplicate entries

    350:    Not Collective

    352:    Input Parameters:
    353: +  n  - number of values
    354: -  X  - array of integers

    356:    Output Parameter:
    357: .  n - number of non-redundant values

    359:    Level: intermediate

    361: .seealso: PetscIntSortSemiOrdered(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortedRemoveDupsInt()
    362: @*/
    363: PetscErrorCode  PetscSortRemoveDupsInt(PetscInt *n,PetscInt X[])
    364: {
    366:   PetscSortInt(*n,X);
    367:   PetscSortedRemoveDupsInt(n,X);
    368:   return 0;
    369: }

    371: /*@
    372:   PetscFindInt - Finds integer in a sorted array of integers

    374:    Not Collective

    376:    Input Parameters:
    377: +  key - the integer to locate
    378: .  n   - number of values in the array
    379: -  X  - array of integers

    381:    Output Parameter:
    382: .  loc - the location if found, otherwise -(slot+1) where slot is the place the value would go

    384:    Level: intermediate

    386: .seealso: PetscIntSortSemiOrdered(), PetscSortInt(), PetscSortIntWithArray(), PetscSortRemoveDupsInt()
    387: @*/
    388: PetscErrorCode PetscFindInt(PetscInt key, PetscInt n, const PetscInt X[], PetscInt *loc)
    389: {
    390:   PetscInt lo = 0,hi = n;

    393:   if (!n) {*loc = -1; return 0;}
    396:   while (hi - lo > 1) {
    397:     PetscInt mid = lo + (hi - lo)/2;
    398:     if (key < X[mid]) hi = mid;
    399:     else               lo = mid;
    400:   }
    401:   *loc = key == X[lo] ? lo : -(lo + (key > X[lo]) + 1);
    402:   return 0;
    403: }

    405: /*@

    408:    Not Collective

    410:    Input Parameters:
    411: +  n  - number of values in the array
    412: -  X  - array of integers

    414:    Output Parameter:
    415: .  dups - True if the array has dups, otherwise false

    417:    Level: intermediate

    419: .seealso: PetscSortRemoveDupsInt(), PetscSortedCheckDupsInt()
    420: @*/
    422: {
    423:   PetscInt   i;
    424:   PetscHSetI ht;
    425:   PetscBool  missing;

    429:   *dups = PETSC_FALSE;
    430:   if (n > 1) {
    431:     PetscHSetICreate(&ht);
    432:     PetscHSetIResize(ht,n);
    433:     for (i=0; i<n; i++) {
    434:       PetscHSetIQueryAdd(ht,X[i],&missing);
    435:       if (!missing) {*dups = PETSC_TRUE; break;}
    436:     }
    437:     PetscHSetIDestroy(&ht);
    438:   }
    439:   return 0;
    440: }

    442: /*@
    443:   PetscFindMPIInt - Finds MPI integer in a sorted array of integers

    445:    Not Collective

    447:    Input Parameters:
    448: +  key - the integer to locate
    449: .  n   - number of values in the array
    450: -  X   - array of integers

    452:    Output Parameter:
    453: .  loc - the location if found, otherwise -(slot+1) where slot is the place the value would go

    455:    Level: intermediate

    457: .seealso: PetscMPIIntSortSemiOrdered(), PetscSortInt(), PetscSortIntWithArray(), PetscSortRemoveDupsInt()
    458: @*/
    459: PetscErrorCode PetscFindMPIInt(PetscMPIInt key, PetscInt n, const PetscMPIInt X[], PetscInt *loc)
    460: {
    461:   PetscInt lo = 0,hi = n;

    464:   if (!n) {*loc = -1; return 0;}
    467:   while (hi - lo > 1) {
    468:     PetscInt mid = lo + (hi - lo)/2;
    469:     if (key < X[mid]) hi = mid;
    470:     else               lo = mid;
    471:   }
    472:   *loc = key == X[lo] ? lo : -(lo + (key > X[lo]) + 1);
    473:   return 0;
    474: }

    476: /*@
    477:    PetscSortIntWithArray - Sorts an array of integers in place in increasing order;
    478:        changes a second array to match the sorted first array.

    480:    Not Collective

    482:    Input Parameters:
    483: +  n  - number of values
    484: .  X  - array of integers
    485: -  Y  - second array of integers

    487:    Level: intermediate

    489: .seealso: PetscIntSortSemiOrderedWithArray(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithCountArray()
    490: @*/
    491: PetscErrorCode  PetscSortIntWithArray(PetscInt n,PetscInt X[],PetscInt Y[])
    492: {
    493:   PetscInt pivot,t1,t2;

    495:   QuickSort2(PetscSortIntWithArray,X,Y,n,pivot,t1,t2);
    496:   return 0;
    497: }

    499: /*@
    500:    PetscSortIntWithArrayPair - Sorts an array of integers in place in increasing order;
    501:        changes a pair of integer arrays to match the sorted first array.

    503:    Not Collective

    505:    Input Parameters:
    506: +  n  - number of values
    507: .  X  - array of integers
    508: .  Y  - second array of integers (first array of the pair)
    509: -  Z  - third array of integers  (second array of the pair)

    511:    Level: intermediate

    513: .seealso: PetscSortReal(), PetscSortIntWithPermutation(), PetscSortIntWithArray(), PetscIntSortSemiOrdered(), PetscSortIntWithIntCountArrayPair()
    514: @*/
    515: PetscErrorCode  PetscSortIntWithArrayPair(PetscInt n,PetscInt X[],PetscInt Y[],PetscInt Z[])
    516: {
    517:   PetscInt pivot,t1,t2,t3;

    519:   QuickSort3(PetscSortIntWithArrayPair,X,Y,Z,n,pivot,t1,t2,t3);
    520:   return 0;
    521: }

    523: /*@
    524:    PetscSortIntWithCountArray - Sorts an array of integers in place in increasing order;
    525:        changes a second array to match the sorted first array.

    527:    Not Collective

    529:    Input Parameters:
    530: +  n  - number of values
    531: .  X  - array of integers
    532: -  Y  - second array of PetscCounts (signed integers)

    534:    Level: intermediate

    536: .seealso: PetscIntSortSemiOrderedWithArray(), PetscSortReal(), PetscSortIntPermutation(), PetscSortInt(), PetscSortIntWithArray()
    537: @*/
    538: PetscErrorCode  PetscSortIntWithCountArray(PetscCount n,PetscInt X[],PetscCount Y[])
    539: {
    540:   PetscInt   pivot,t1;
    541:   PetscCount t2;

    543:   QuickSort2(PetscSortIntWithCountArray,X,Y,n,pivot,t1,t2);
    544:   return 0;
    545: }

    547: /*@
    548:    PetscSortIntWithIntCountArrayPair - Sorts an array of integers in place in increasing order;
    549:        changes an integer array and a PetscCount array to match the sorted first array.

    551:    Not Collective

    553:    Input Parameters:
    554: +  n  - number of values
    555: .  X  - array of integers
    556: .  Y  - second array of integers (first array of the pair)
    557: -  Z  - third array of PetscCounts  (second array of the pair)

    559:    Level: intermediate

    561:    Notes:
    562:     Usually X, Y are matrix row/column indices, and Z is a permutation array and therefore Z's type is PetscCount to allow 2B+ nonzeros even with 32-bit PetscInt.

    564: .seealso: PetscSortReal(), PetscSortIntPermutation(), PetscSortIntWithArray(), PetscIntSortSemiOrdered(), PetscSortIntWithArrayPair()
    565: @*/
    566: PetscErrorCode  PetscSortIntWithIntCountArrayPair(PetscCount n,PetscInt X[],PetscInt Y[],PetscCount Z[])
    567: {
    568:   PetscInt   pivot,t1,t2; /* pivot is take from X[], so its type is still PetscInt */
    569:   PetscCount t3; /* temp for Z[] */

    571:   QuickSort3(PetscSortIntWithIntCountArrayPair,X,Y,Z,n,pivot,t1,t2,t3);
    572:   return 0;
    573: }

    575: /*@
    576:    PetscSortedMPIInt - Determines whether the array is sorted.

    578:    Not Collective

    580:    Input Parameters:
    581: +  n  - number of values
    582: -  X  - array of integers

    584:    Output Parameters:
    585: .  sorted - flag whether the array is sorted

    587:    Level: intermediate

    589: .seealso: PetscMPIIntSortSemiOrdered(), PetscSortMPIInt(), PetscSortedInt(), PetscSortedReal()
    590: @*/
    591: PetscErrorCode  PetscSortedMPIInt(PetscInt n,const PetscMPIInt X[],PetscBool *sorted)
    592: {
    593:   PetscSorted(n,X,*sorted);
    594:   return 0;
    595: }

    597: /*@
    598:    PetscSortMPIInt - Sorts an array of MPI integers in place in increasing order.

    600:    Not Collective

    602:    Input Parameters:
    603: +  n  - number of values
    604: -  X  - array of integers

    606:    Level: intermediate

    608:    Notes:
    609:    This function serves as an alternative to PetscMPIIntSortSemiOrdered(), and may perform faster especially if the array
    610:    is completely random. There are exceptions to this and so it is __highly__ recommended that the user benchmark their
    611:    code to see which routine is fastest.

    613: .seealso: PetscMPIIntSortSemiOrdered(), PetscSortReal(), PetscSortIntWithPermutation()
    614: @*/
    615: PetscErrorCode  PetscSortMPIInt(PetscInt n,PetscMPIInt X[])
    616: {
    617:   PetscMPIInt pivot,t1;

    619:   QuickSort1(PetscSortMPIInt,X,n,pivot,t1);
    620:   return 0;
    621: }

    623: /*@
    624:    PetscSortRemoveDupsMPIInt - Sorts an array of MPI integers in place in increasing order removes all duplicate entries

    626:    Not Collective

    628:    Input Parameters:
    629: +  n  - number of values
    630: -  X  - array of integers

    632:    Output Parameter:
    633: .  n - number of non-redundant values

    635:    Level: intermediate

    637: .seealso: PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt()
    638: @*/
    639: PetscErrorCode  PetscSortRemoveDupsMPIInt(PetscInt *n,PetscMPIInt X[])
    640: {
    641:   PetscInt s = 0,N = *n,b = 0;

    643:   PetscSortMPIInt(N,X);
    644:   for (PetscInt i=0; i<N-1; i++) {
    645:     if (X[b+s+1] != X[b]) {
    646:       X[b+1] = X[b+s+1]; b++;
    647:     } else s++;
    648:   }
    649:   *n = N - s;
    650:   return 0;
    651: }

    653: /*@
    654:    PetscSortMPIIntWithArray - Sorts an array of integers in place in increasing order;
    655:        changes a second array to match the sorted first array.

    657:    Not Collective

    659:    Input Parameters:
    660: +  n  - number of values
    661: .  X  - array of integers
    662: -  Y  - second array of integers

    664:    Level: intermediate

    666: .seealso: PetscMPIIntSortSemiOrderedWithArray(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt()
    667: @*/
    668: PetscErrorCode  PetscSortMPIIntWithArray(PetscMPIInt n,PetscMPIInt X[],PetscMPIInt Y[])
    669: {
    670:   PetscMPIInt pivot,t1,t2;

    672:   QuickSort2(PetscSortMPIIntWithArray,X,Y,n,pivot,t1,t2);
    673:   return 0;
    674: }

    676: /*@
    677:    PetscSortMPIIntWithIntArray - Sorts an array of MPI integers in place in increasing order;
    678:        changes a second array of Petsc intergers to match the sorted first array.

    680:    Not Collective

    682:    Input Parameters:
    683: +  n  - number of values
    684: .  X  - array of MPI integers
    685: -  Y  - second array of Petsc integers

    687:    Level: intermediate

    689:    Notes: this routine is useful when one needs to sort MPI ranks with other integer arrays.

    691: .seealso: PetscSortMPIIntWithArray(), PetscIntSortSemiOrderedWithArray(), PetscTimSortWithArray()
    692: @*/
    693: PetscErrorCode PetscSortMPIIntWithIntArray(PetscMPIInt n,PetscMPIInt X[],PetscInt Y[])
    694: {
    695:   PetscMPIInt pivot,t1;
    696:   PetscInt    t2;

    698:   QuickSort2(PetscSortMPIIntWithIntArray,X,Y,n,pivot,t1,t2);
    699:   return 0;
    700: }

    702: /*@
    703:    PetscSortIntWithScalarArray - Sorts an array of integers in place in increasing order;
    704:        changes a second SCALAR array to match the sorted first INTEGER array.

    706:    Not Collective

    708:    Input Parameters:
    709: +  n  - number of values
    710: .  X  - array of integers
    711: -  Y  - second array of scalars

    713:    Level: intermediate

    715: .seealso: PetscTimSortWithArray(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithArray()
    716: @*/
    717: PetscErrorCode  PetscSortIntWithScalarArray(PetscInt n,PetscInt X[],PetscScalar Y[])
    718: {
    719:   PetscInt    pivot,t1;
    720:   PetscScalar t2;

    722:   QuickSort2(PetscSortIntWithScalarArray,X,Y,n,pivot,t1,t2);
    723:   return 0;
    724: }

    726: /*@C
    727:    PetscSortIntWithDataArray - Sorts an array of integers in place in increasing order;
    728:        changes a second array to match the sorted first INTEGER array.  Unlike other sort routines, the user must
    729:        provide workspace (the size of an element in the data array) to use when sorting.

    731:    Not Collective

    733:    Input Parameters:
    734: +  n  - number of values
    735: .  X  - array of integers
    736: .  Y  - second array of data
    737: .  size - sizeof elements in the data array in bytes
    738: -  t2   - workspace of "size" bytes used when sorting

    740:    Level: intermediate

    742: .seealso: PetscTimSortWithArray(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithArray()
    743: @*/
    744: PetscErrorCode  PetscSortIntWithDataArray(PetscInt n,PetscInt X[],void *Y,size_t size,void *t2)
    745: {
    746:   char     *YY       = (char*)Y;
    747:   PetscInt  t1,pivot,hi = n-1;

    749:   if (n<8) {
    750:     for (PetscInt i=0; i<n; i++) {
    751:       pivot = X[i];
    752:       for (PetscInt j=i+1; j<n; j++) {
    753:         if (pivot > X[j]) {
    754:           SWAP2Data(X[i],X[j],YY+size*i,YY+size*j,t1,t2,size);
    755:           pivot = X[i];
    756:         }
    757:       }
    758:     }
    759:   } else {
    760:     /* Two way partition */
    761:     PetscInt l = 0,r = hi;

    763:     pivot = X[MEDIAN(X,hi)];
    764:     while (1) {
    765:       while (X[l] < pivot) l++;
    766:       while (X[r] > pivot) r--;
    767:       if (l >= r) {r++; break;}
    768:       SWAP2Data(X[l],X[r],YY+size*l,YY+size*r,t1,t2,size);
    769:       l++;
    770:       r--;
    771:     }
    772:     PetscSortIntWithDataArray(l,X,Y,size,t2);
    773:     PetscSortIntWithDataArray(hi-r+1,X+r,YY+size*r,size,t2);
    774:   }
    775:   return 0;
    776: }

    778: /*@
    779:    PetscMergeIntArray -     Merges two SORTED integer arrays, removes duplicate elements.

    781:    Not Collective

    783:    Input Parameters:
    784: +  an  - number of values in the first array
    785: .  aI  - first sorted array of integers
    786: .  bn  - number of values in the second array
    787: -  bI  - second array of integers

    789:    Output Parameters:
    790: +  n   - number of values in the merged array
    791: -  L   - merged sorted array, this is allocated if an array is not provided

    793:    Level: intermediate

    795: .seealso: PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithArray()
    796: @*/
    797: PetscErrorCode  PetscMergeIntArray(PetscInt an,const PetscInt aI[], PetscInt bn, const PetscInt bI[], PetscInt *n, PetscInt **L)
    798: {
    799:   PetscInt       *L_ = *L, ak, bk, k;

    801:   if (!L_) {
    802:     PetscMalloc1(an+bn, L);
    803:     L_   = *L;
    804:   }
    805:   k = ak = bk = 0;
    806:   while (ak < an && bk < bn) {
    807:     if (aI[ak] == bI[bk]) {
    808:       L_[k] = aI[ak];
    809:       ++ak;
    810:       ++bk;
    811:       ++k;
    812:     } else if (aI[ak] < bI[bk]) {
    813:       L_[k] = aI[ak];
    814:       ++ak;
    815:       ++k;
    816:     } else {
    817:       L_[k] = bI[bk];
    818:       ++bk;
    819:       ++k;
    820:     }
    821:   }
    822:   if (ak < an) {
    823:     PetscArraycpy(L_+k,aI+ak,an-ak);
    824:     k   += (an-ak);
    825:   }
    826:   if (bk < bn) {
    827:     PetscArraycpy(L_+k,bI+bk,bn-bk);
    828:     k   += (bn-bk);
    829:   }
    830:   *n = k;
    831:   return 0;
    832: }

    834: /*@
    835:    PetscMergeIntArrayPair -     Merges two SORTED integer arrays that share NO common values along with an additional array of integers.
    836:                                 The additional arrays are the same length as sorted arrays and are merged
    837:                                 in the order determined by the merging of the sorted pair.

    839:    Not Collective

    841:    Input Parameters:
    842: +  an  - number of values in the first array
    843: .  aI  - first sorted array of integers
    844: .  aJ  - first additional array of integers
    845: .  bn  - number of values in the second array
    846: .  bI  - second array of integers
    847: -  bJ  - second additional of integers

    849:    Output Parameters:
    850: +  n   - number of values in the merged array (== an + bn)
    851: .  L   - merged sorted array
    852: -  J   - merged additional array

    854:    Notes:
    855:     if L or J point to non-null arrays then this routine will assume they are of the approproate size and use them, otherwise this routine will allocate space for them
    856:    Level: intermediate

    858: .seealso: PetscIntSortSemiOrdered(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithArray()
    859: @*/
    860: PetscErrorCode  PetscMergeIntArrayPair(PetscInt an,const PetscInt aI[], const PetscInt aJ[], PetscInt bn, const PetscInt bI[], const PetscInt bJ[], PetscInt *n, PetscInt **L, PetscInt **J)
    861: {
    862:   PetscInt       n_, *L_, *J_, ak, bk, k;

    866:   n_ = an + bn;
    867:   *n = n_;
    868:   if (!*L) {
    869:     PetscMalloc1(n_, L);
    870:   }
    871:   L_ = *L;
    872:   if (!*J) {
    873:     PetscMalloc1(n_, J);
    874:   }
    875:   J_   = *J;
    876:   k = ak = bk = 0;
    877:   while (ak < an && bk < bn) {
    878:     if (aI[ak] <= bI[bk]) {
    879:       L_[k] = aI[ak];
    880:       J_[k] = aJ[ak];
    881:       ++ak;
    882:       ++k;
    883:     } else {
    884:       L_[k] = bI[bk];
    885:       J_[k] = bJ[bk];
    886:       ++bk;
    887:       ++k;
    888:     }
    889:   }
    890:   if (ak < an) {
    891:     PetscArraycpy(L_+k,aI+ak,an-ak);
    892:     PetscArraycpy(J_+k,aJ+ak,an-ak);
    893:     k   += (an-ak);
    894:   }
    895:   if (bk < bn) {
    896:     PetscArraycpy(L_+k,bI+bk,bn-bk);
    897:     PetscArraycpy(J_+k,bJ+bk,bn-bk);
    898:   }
    899:   return 0;
    900: }

    902: /*@
    903:    PetscMergeMPIIntArray -     Merges two SORTED integer arrays.

    905:    Not Collective

    907:    Input Parameters:
    908: +  an  - number of values in the first array
    909: .  aI  - first sorted array of integers
    910: .  bn  - number of values in the second array
    911: -  bI  - second array of integers

    913:    Output Parameters:
    914: +  n   - number of values in the merged array (<= an + bn)
    915: -  L   - merged sorted array, allocated if address of NULL pointer is passed

    917:    Level: intermediate

    919: .seealso: PetscIntSortSemiOrdered(), PetscSortReal(), PetscSortIntWithPermutation(), PetscSortInt(), PetscSortIntWithArray()
    920: @*/
    921: PetscErrorCode PetscMergeMPIIntArray(PetscInt an,const PetscMPIInt aI[],PetscInt bn,const PetscMPIInt bI[],PetscInt *n,PetscMPIInt **L)
    922: {
    923:   PetscInt       ai,bi,k;

    925:   if (!*L) PetscMalloc1((an+bn),L);
    926:   for (ai=0,bi=0,k=0; ai<an || bi<bn;) {
    927:     PetscInt t = -1;
    928:     for (; ai<an && (!bn || aI[ai] <= bI[bi]); ai++) (*L)[k++] = t = aI[ai];
    929:     for (; bi<bn && bI[bi] == t; bi++);
    930:     for (; bi<bn && (!an || bI[bi] <= aI[ai]); bi++) (*L)[k++] = t = bI[bi];
    931:     for (; ai<an && aI[ai] == t; ai++);
    932:   }
    933:   *n = k;
    934:   return 0;
    935: }

    937: /*@C
    938:    PetscProcessTree - Prepares tree data to be displayed graphically

    940:    Not Collective

    942:    Input Parameters:
    943: +  n  - number of values
    944: .  mask - indicates those entries in the tree, location 0 is always masked
    945: -  parentid - indicates the parent of each entry

    947:    Output Parameters:
    948: +  Nlevels - the number of levels
    949: .  Level - for each node tells its level
    950: .  Levelcnts - the number of nodes on each level
    951: .  Idbylevel - a list of ids on each of the levels, first level followed by second etc
    952: -  Column - for each id tells its column index

    954:    Level: developer

    956:    Notes:
    957:     This code is not currently used

    959: .seealso: PetscSortReal(), PetscSortIntWithPermutation()
    960: @*/
    961: PetscErrorCode  PetscProcessTree(PetscInt n,const PetscBool mask[],const PetscInt parentid[],PetscInt *Nlevels,PetscInt **Level,PetscInt **Levelcnt,PetscInt **Idbylevel,PetscInt **Column)
    962: {
    963:   PetscInt       i,j,cnt,nmask = 0,nlevels = 0,*level,*levelcnt,levelmax = 0,*workid,*workparentid,tcnt = 0,*idbylevel,*column;
    964:   PetscBool      done = PETSC_FALSE;

    967:   for (i=0; i<n; i++) {
    968:     if (mask[i]) continue;
    971:   }

    973:   for (i=0; i<n; i++) {
    974:     if (!mask[i]) nmask++;
    975:   }

    977:   /* determine the level in the tree of each node */
    978:   PetscCalloc1(n,&level);

    980:   level[0] = 1;
    981:   while (!done) {
    982:     done = PETSC_TRUE;
    983:     for (i=0; i<n; i++) {
    984:       if (mask[i]) continue;
    985:       if (!level[i] && level[parentid[i]]) level[i] = level[parentid[i]] + 1;
    986:       else if (!level[i]) done = PETSC_FALSE;
    987:     }
    988:   }
    989:   for (i=0; i<n; i++) {
    990:     level[i]--;
    991:     nlevels = PetscMax(nlevels,level[i]);
    992:   }

    994:   /* count the number of nodes on each level and its max */
    995:   PetscCalloc1(nlevels,&levelcnt);
    996:   for (i=0; i<n; i++) {
    997:     if (mask[i]) continue;
    998:     levelcnt[level[i]-1]++;
    999:   }
    1000:   for (i=0; i<nlevels;i++) levelmax = PetscMax(levelmax,levelcnt[i]);

    1002:   /* for each level sort the ids by the parent id */
    1003:   PetscMalloc2(levelmax,&workid,levelmax,&workparentid);
    1004:   PetscMalloc1(nmask,&idbylevel);
    1005:   for (j=1; j<=nlevels;j++) {
    1006:     cnt = 0;
    1007:     for (i=0; i<n; i++) {
    1008:       if (mask[i]) continue;
    1009:       if (level[i] != j) continue;
    1010:       workid[cnt]         = i;
    1011:       workparentid[cnt++] = parentid[i];
    1012:     }
    1013:     /*  PetscIntView(cnt,workparentid,0);
    1014:     PetscIntView(cnt,workid,0);
    1015:     PetscSortIntWithArray(cnt,workparentid,workid);
    1016:     PetscIntView(cnt,workparentid,0);
    1017:     PetscIntView(cnt,workid,0);*/
    1018:     PetscArraycpy(idbylevel+tcnt,workid,cnt);
    1019:     tcnt += cnt;
    1020:   }
    1022:   PetscFree2(workid,workparentid);

    1024:   /* for each node list its column */
    1025:   PetscMalloc1(n,&column);
    1026:   cnt = 0;
    1027:   for (j=0; j<nlevels; j++) {
    1028:     for (i=0; i<levelcnt[j]; i++) {
    1029:       column[idbylevel[cnt++]] = i;
    1030:     }
    1031:   }

    1033:   *Nlevels   = nlevels;
    1034:   *Level     = level;
    1035:   *Levelcnt  = levelcnt;
    1036:   *Idbylevel = idbylevel;
    1037:   *Column    = column;
    1038:   return 0;
    1039: }

    1041: /*@
    1042:   PetscParallelSortedInt - Check whether an integer array, distributed over a communicator, is globally sorted.

    1044:   Collective

    1046:   Input Parameters:
    1047: + comm - the MPI communicator
    1048: . n - the local number of integers
    1049: - keys - the local array of integers

    1051:   Output Parameters:
    1052: . is_sorted - whether the array is globally sorted

    1054:   Level: developer

    1056: .seealso: PetscParallelSortInt()
    1057: @*/
    1058: PetscErrorCode PetscParallelSortedInt(MPI_Comm comm, PetscInt n, const PetscInt keys[], PetscBool *is_sorted)
    1059: {
    1060:   PetscBool      sorted;
    1061:   PetscInt       i, min, max, prevmax;
    1062:   PetscMPIInt    rank;

    1064:   sorted = PETSC_TRUE;
    1065:   min    = PETSC_MAX_INT;
    1066:   max    = PETSC_MIN_INT;
    1067:   if (n) {
    1068:     min = keys[0];
    1069:     max = keys[0];
    1070:   }
    1071:   for (i = 1; i < n; i++) {
    1072:     if (keys[i] < keys[i - 1]) break;
    1073:     min = PetscMin(min,keys[i]);
    1074:     max = PetscMax(max,keys[i]);
    1075:   }
    1076:   if (i < n) sorted = PETSC_FALSE;
    1077:   prevmax = PETSC_MIN_INT;
    1078:   MPI_Exscan(&max, &prevmax, 1, MPIU_INT, MPI_MAX, comm);
    1079:   MPI_Comm_rank(comm, &rank);
    1080:   if (rank == 0) prevmax = PETSC_MIN_INT;
    1081:   if (prevmax > min) sorted = PETSC_FALSE;
    1082:   MPI_Allreduce(&sorted, is_sorted, 1, MPIU_BOOL, MPI_LAND, comm);
    1083:   return 0;
    1084: }