Actual source code: sortd.c

      1: /*
      2:    This file contains routines for sorting doubles.  Values are sorted in place.
      3:    These are provided because the general sort routines incur a great deal
      4:    of overhead in calling the comparison routines.

      6:  */
      7: #include <petscsys.h>
      8: #include <petsc/private/petscimpl.h>

     10: #define SWAP(a, b, t) \
     11:   do { \
     12:     t = a; \
     13:     a = b; \
     14:     b = t; \
     15:   } while (0)

     17: /*@
     18:   PetscSortedReal - Determines whether the array of `PetscReal` is sorted.

     20:   Not Collective

     22:   Input Parameters:
     23: + n - number of values
     24: - X - array of integers

     26:   Output Parameter:
     27: . sorted - flag whether the array is sorted

     29:   Level: intermediate

     31: .seealso: `PetscSortReal()`, `PetscSortedInt()`, `PetscSortedMPIInt()`
     32: @*/
     33: PetscErrorCode PetscSortedReal(PetscCount n, const PetscReal X[], PetscBool *sorted)
     34: {
     35:   PetscFunctionBegin;
     36:   PetscSorted(n, X, *sorted);
     37:   PetscFunctionReturn(PETSC_SUCCESS);
     38: }

     40: /* A simple version of quicksort; taken from Kernighan and Ritchie, page 87 */
     41: static PetscErrorCode PetscSortReal_Private(PetscReal *v, PetscCount right)
     42: {
     43:   PetscCount i, last;
     44:   PetscReal  vl, tmp;

     46:   PetscFunctionBegin;
     47:   if (right <= 1) {
     48:     if (right == 1) {
     49:       if (v[0] > v[1]) SWAP(v[0], v[1], tmp);
     50:     }
     51:     PetscFunctionReturn(PETSC_SUCCESS);
     52:   }
     53:   SWAP(v[0], v[right / 2], tmp);
     54:   vl   = v[0];
     55:   last = 0;
     56:   for (i = 1; i <= right; i++) {
     57:     if (v[i] < vl) {
     58:       last++;
     59:       SWAP(v[last], v[i], tmp);
     60:     }
     61:   }
     62:   SWAP(v[0], v[last], tmp);
     63:   PetscCall(PetscSortReal_Private(v, last - 1));
     64:   PetscCall(PetscSortReal_Private(v + last + 1, right - (last + 1)));
     65:   PetscFunctionReturn(PETSC_SUCCESS);
     66: }

     68: /*@
     69:   PetscSortReal - Sorts an array of `PetscReal` in place in increasing order.

     71:   Not Collective

     73:   Input Parameters:
     74: + n - number of values
     75: - v - array of doubles

     77:   Level: intermediate

     79:   Note:
     80:   This function serves as an alternative to `PetscRealSortSemiOrdered()`, and may perform faster especially if the array
     81:   is completely random. There are exceptions to this and so it is __highly__ recommended that the user benchmark their
     82:   code to see which routine is fastest.

     84: .seealso: `PetscRealSortSemiOrdered()`, `PetscSortInt()`, `PetscSortRealWithPermutation()`, `PetscSortRealWithArrayInt()`
     85: @*/
     86: PetscErrorCode PetscSortReal(PetscCount n, PetscReal v[])
     87: {
     88:   PetscFunctionBegin;
     89:   PetscAssertPointer(v, 2);
     90:   if (n < 8) {
     91:     PetscReal tmp, vk;
     92:     for (PetscCount k = 0; k < n; k++) {
     93:       vk = v[k];
     94:       for (PetscCount j = k + 1; j < n; j++) {
     95:         if (vk > v[j]) {
     96:           SWAP(v[k], v[j], tmp);
     97:           vk = v[k];
     98:         }
     99:       }
    100:     }
    101:   } else {
    102:     PetscInt N;

    104:     PetscCall(PetscIntCast(n, &N));
    105:     PetscCall(PetscSortReal_Private(v, N - 1));
    106:   }
    107:   PetscFunctionReturn(PETSC_SUCCESS);
    108: }

    110: #define SWAP2ri(a, b, c, d, rt, it) \
    111:   do { \
    112:     rt = a; \
    113:     a  = b; \
    114:     b  = rt; \
    115:     it = c; \
    116:     c  = d; \
    117:     d  = it; \
    118:   } while (0)

    120: /* modified from PetscSortIntWithArray_Private */
    121: static PetscErrorCode PetscSortRealWithArrayInt_Private(PetscReal *v, PetscInt *V, PetscCount right)
    122: {
    123:   PetscCount i, last;
    124:   PetscInt   itmp;
    125:   PetscReal  rvl, rtmp;

    127:   PetscFunctionBegin;
    128:   if (right <= 1) {
    129:     if (right == 1) {
    130:       if (v[0] > v[1]) SWAP2ri(v[0], v[1], V[0], V[1], rtmp, itmp);
    131:     }
    132:     PetscFunctionReturn(PETSC_SUCCESS);
    133:   }
    134:   SWAP2ri(v[0], v[right / 2], V[0], V[right / 2], rtmp, itmp);
    135:   rvl  = v[0];
    136:   last = 0;
    137:   for (i = 1; i <= right; i++) {
    138:     if (v[i] < rvl) {
    139:       last++;
    140:       SWAP2ri(v[last], v[i], V[last], V[i], rtmp, itmp);
    141:     }
    142:   }
    143:   SWAP2ri(v[0], v[last], V[0], V[last], rtmp, itmp);
    144:   PetscCall(PetscSortRealWithArrayInt_Private(v, V, last - 1));
    145:   PetscCall(PetscSortRealWithArrayInt_Private(v + last + 1, V + last + 1, right - (last + 1)));
    146:   PetscFunctionReturn(PETSC_SUCCESS);
    147: }
    148: /*@
    149:   PetscSortRealWithArrayInt - Sorts an array of `PetscReal` in place in increasing order;
    150:   changes a second `PetscInt` array to match the sorted first array.

    152:   Not Collective

    154:   Input Parameters:
    155: + n  - number of values
    156: . Ii - array of integers
    157: - r  - second array of integers

    159:   Level: intermediate

    161: .seealso: `PetscSortReal()`
    162: @*/
    163: PetscErrorCode PetscSortRealWithArrayInt(PetscCount n, PetscReal r[], PetscInt Ii[])
    164: {
    165:   PetscCount j, k;
    166:   PetscInt   itmp;
    167:   PetscReal  rk, rtmp;

    169:   PetscFunctionBegin;
    170:   PetscAssertPointer(r, 2);
    171:   PetscAssertPointer(Ii, 3);
    172:   if (n < 8) {
    173:     for (k = 0; k < n; k++) {
    174:       rk = r[k];
    175:       for (j = k + 1; j < n; j++) {
    176:         if (rk > r[j]) {
    177:           SWAP2ri(r[k], r[j], Ii[k], Ii[j], rtmp, itmp);
    178:           rk = r[k];
    179:         }
    180:       }
    181:     }
    182:   } else {
    183:     PetscCall(PetscSortRealWithArrayInt_Private(r, Ii, n - 1));
    184:   }
    185:   PetscFunctionReturn(PETSC_SUCCESS);
    186: }

    188: /*@
    189:   PetscFindReal - Finds a `PetscReal` in a sorted array of `PetscReal`s

    191:   Not Collective

    193:   Input Parameters:
    194: + key - the value to locate
    195: . n   - number of values in the array
    196: . t   - array of values
    197: - eps - tolerance used to compare

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

    202:   Level: intermediate

    204: .seealso: `PetscSortReal()`, `PetscSortRealWithArrayInt()`
    205: @*/
    206: PetscErrorCode PetscFindReal(PetscReal key, PetscCount n, const PetscReal t[], PetscReal eps, PetscInt *loc)
    207: {
    208:   PetscInt lo = 0, hi;

    210:   PetscFunctionBegin;
    211:   PetscAssertPointer(loc, 5);
    212:   if (!n) {
    213:     *loc = -1;
    214:     PetscFunctionReturn(PETSC_SUCCESS);
    215:   }
    216:   PetscAssertPointer(t, 3);
    217:   PetscCall(PetscIntCast(n, &hi));
    218:   while (hi - lo > 1) {
    219:     PetscInt mid = lo + (hi - lo) / 2;
    220:     PetscAssert(t[lo] <= t[mid] && t[mid] <= t[hi - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input array was not sorted: (%g, %g, %g)", (double)t[lo], (double)t[mid], (double)t[hi - 1]);
    221:     if (key < t[mid]) hi = mid;
    222:     else lo = mid;
    223:   }
    224:   *loc = (PetscAbsReal(key - t[lo]) < eps) ? lo : -(lo + (key > t[lo]) + 1);
    225:   PetscFunctionReturn(PETSC_SUCCESS);
    226: }

    228: /*@
    229:   PetscSortRemoveDupsReal - Sorts an array of `PetscReal` in place in increasing order and removes all duplicate entries

    231:   Not Collective

    233:   Input Parameters:
    234: + n - initial number of values
    235: - v - array of values

    237:   Note:
    238:   On output both `n` and `v` are modified with non-redundant values.

    240:   Level: intermediate

    242: .seealso: `PetscSortReal()`, `PetscSortRemoveDupsInt()`
    243: @*/
    244: PetscErrorCode PetscSortRemoveDupsReal(PetscInt *n, PetscReal v[])
    245: {
    246:   PetscInt i, s = 0, N = *n, b = 0;

    248:   PetscFunctionBegin;
    249:   PetscCall(PetscSortReal(N, v));
    250:   for (i = 0; i < N - 1; i++) {
    251:     if (v[b + s + 1] != v[b]) {
    252:       v[b + 1] = v[b + s + 1];
    253:       b++;
    254:     } else s++;
    255:   }
    256:   *n = N - s;
    257:   PetscFunctionReturn(PETSC_SUCCESS);
    258: }

    260: /*@
    261:   PetscSortSplit - Quick-sort split of an array of `PetscScalar`s in place.

    263:   Not Collective

    265:   Input Parameters:
    266: + ncut - splitting index
    267: - n    - number of values to sort

    269:   Input/Output Parameters:
    270: + a   - array of values, on output the values are permuted such that its elements satisfy:
    271:            abs(a[i]) >= abs(a[ncut-1]) for i < ncut and
    272:            abs(a[i]) <= abs(a[ncut-1]) for i >= ncut
    273: - idx - index for array a, on output permuted accordingly

    275:   Level: intermediate

    277: .seealso: `PetscSortInt()`, `PetscSortRealWithPermutation()`
    278: @*/
    279: PetscErrorCode PetscSortSplit(PetscInt ncut, PetscInt n, PetscScalar a[], PetscInt idx[])
    280: {
    281:   PetscInt    i, mid, last, itmp, j, first;
    282:   PetscScalar d, tmp;
    283:   PetscReal   abskey;

    285:   PetscFunctionBegin;
    286:   first = 0;
    287:   last  = n - 1;
    288:   if (ncut < first || ncut > last) PetscFunctionReturn(PETSC_SUCCESS);

    290:   while (1) {
    291:     mid    = first;
    292:     d      = a[mid];
    293:     abskey = PetscAbsScalar(d);
    294:     i      = last;
    295:     for (j = first + 1; j <= i; ++j) {
    296:       d = a[j];
    297:       if (PetscAbsScalar(d) >= abskey) {
    298:         ++mid;
    299:         /* interchange */
    300:         tmp      = a[mid];
    301:         itmp     = idx[mid];
    302:         a[mid]   = a[j];
    303:         idx[mid] = idx[j];
    304:         a[j]     = tmp;
    305:         idx[j]   = itmp;
    306:       }
    307:     }

    309:     /* interchange */
    310:     tmp        = a[mid];
    311:     itmp       = idx[mid];
    312:     a[mid]     = a[first];
    313:     idx[mid]   = idx[first];
    314:     a[first]   = tmp;
    315:     idx[first] = itmp;

    317:     /* test for while loop */
    318:     if (mid == ncut) break;
    319:     else if (mid > ncut) last = mid - 1;
    320:     else first = mid + 1;
    321:   }
    322:   PetscFunctionReturn(PETSC_SUCCESS);
    323: }

    325: /*@
    326:   PetscSortSplitReal - Quick-sort split of an array of `PetscReal`s in place.

    328:   Not Collective

    330:   Input Parameters:
    331: + ncut - splitting index
    332: - n    - number of values to sort

    334:   Input/Output Parameters:
    335: + a   - array of values, on output the values are permuted such that its elements satisfy:
    336:            abs(a[i]) >= abs(a[ncut-1]) for i < ncut and
    337:            abs(a[i]) <= abs(a[ncut-1]) for i >= ncut
    338: - idx - index for array a, on output permuted accordingly

    340:   Level: intermediate

    342: .seealso: `PetscSortInt()`, `PetscSortRealWithPermutation()`
    343: @*/
    344: PetscErrorCode PetscSortSplitReal(PetscInt ncut, PetscInt n, PetscReal a[], PetscInt idx[])
    345: {
    346:   PetscInt  i, mid, last, itmp, j, first;
    347:   PetscReal d, tmp;
    348:   PetscReal abskey;

    350:   PetscFunctionBegin;
    351:   first = 0;
    352:   last  = n - 1;
    353:   if (ncut < first || ncut > last) PetscFunctionReturn(PETSC_SUCCESS);

    355:   while (1) {
    356:     mid    = first;
    357:     d      = a[mid];
    358:     abskey = PetscAbsReal(d);
    359:     i      = last;
    360:     for (j = first + 1; j <= i; ++j) {
    361:       d = a[j];
    362:       if (PetscAbsReal(d) >= abskey) {
    363:         ++mid;
    364:         /* interchange */
    365:         tmp      = a[mid];
    366:         itmp     = idx[mid];
    367:         a[mid]   = a[j];
    368:         idx[mid] = idx[j];
    369:         a[j]     = tmp;
    370:         idx[j]   = itmp;
    371:       }
    372:     }

    374:     /* interchange */
    375:     tmp        = a[mid];
    376:     itmp       = idx[mid];
    377:     a[mid]     = a[first];
    378:     idx[mid]   = idx[first];
    379:     a[first]   = tmp;
    380:     idx[first] = itmp;

    382:     /* test for while loop */
    383:     if (mid == ncut) break;
    384:     else if (mid > ncut) last = mid - 1;
    385:     else first = mid + 1;
    386:   }
    387:   PetscFunctionReturn(PETSC_SUCCESS);
    388: }