Date: 2021-02-01T14:41:38+00:00

Actual source code: slepcsc.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

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

     11: #include <slepc/private/slepcimpl.h>
     12: #include <slepcrg.h>
     13: #include <slepcst.h>

     15: /*@
     16:    SlepcSCCompare - Compares two (possibly complex) values according
     17:    to a certain criterion.

     19:    Not Collective

     21:    Input Parameters:
     22: +  sc  - the sorting criterion context
     23: .  ar  - real part of the 1st value
     24: .  ai  - imaginary part of the 1st value
     25: .  br  - real part of the 2nd value
     26: -  bi  - imaginary part of the 2nd value

     28:    Output Parameter:
     29: .  res - result of comparison

     31:    Notes:
     32:    Returns an integer less than, equal to, or greater than zero if the first
     33:    value is considered to be respectively less than, equal to, or greater
     34:    than the second one.

     36:    Level: developer

     38: .seealso: SlepcSortEigenvalues(), SlepcSC
     39: @*/
     40: PetscErrorCode SlepcSCCompare(SlepcSC sc,PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *res)
     41: {
     43:   PetscScalar    re[2],im[2];
     44:   PetscInt       cin[2];
     45:   PetscBool      inside[2];

     49: #if defined(PETSC_USE_DEBUG)
     50:   if (!sc->comparison) SETERRQ(PETSC_COMM_SELF,1,"Undefined comparison function");
     51: #endif
     52:   re[0] = ar; re[1] = br;
     53:   im[0] = ai; im[1] = bi;
     54:   if (sc->map) {
     55:     (*sc->map)(sc->mapobj,2,re,im);
     56:   }
     57:   if (sc->rg) {
     58:     RGCheckInside(sc->rg,2,re,im,cin);
     59:     inside[0] = PetscNot(cin[0]<0);
     60:     inside[1] = PetscNot(cin[1]<0);
     61:     if (inside[0] && !inside[1]) *res = -1;
     62:     else if (!inside[0] && inside[1]) *res = 1;
     63:     else {
     64:       (*sc->comparison)(re[0],im[0],re[1],im[1],res,sc->comparisonctx);
     65:     }
     66:   } else {
     67:     (*sc->comparison)(re[0],im[0],re[1],im[1],res,sc->comparisonctx);
     68:   }
     69:   return(0);
     70: }

     72: /*@
     73:    SlepcSortEigenvalues - Sorts a list of eigenvalues according to the
     74:    sorting criterion specified in a SlepcSC context.

     76:    Not Collective

     78:    Input Parameters:
     79: +  sc   - the sorting criterion context
     80: .  n    - number of eigenvalues in the list
     81: .  eigr - pointer to the array containing the eigenvalues
     82: -  eigi - imaginary part of the eigenvalues (only when using real numbers)

     84:    Input/Output Parameter:
     85: .  perm - permutation array. Must be initialized to 0:n-1 on input.

     87:    Note:
     88:    The result is a list of indices in the original eigenvalue array
     89:    corresponding to the first n eigenvalues sorted in the specified
     90:    criterion.

     92:    Level: developer

     94: .seealso: SlepcSCCompare(), SlepcSC
     95: @*/
     96: PetscErrorCode SlepcSortEigenvalues(SlepcSC sc,PetscInt n,PetscScalar *eigr,PetscScalar *eigi,PetscInt *perm)
     97: {
     99:   PetscScalar    re,im;
    100:   PetscInt       i,j,result,tmp;

    107:   /* insertion sort */
    108:   for (i=n-1;i>=0;i--) {
    109:     re = eigr[perm[i]];
    110:     im = eigi[perm[i]];
    111:     j = i+1;
    112: #if !defined(PETSC_USE_COMPLEX)
    113:     if (im!=0) {
    114:       /* complex eigenvalue */
    115:       i--;
    116:       im = eigi[perm[i]];
    117:     }
    118: #endif
    119:     while (j<n) {
    120:       SlepcSCCompare(sc,re,im,eigr[perm[j]],eigi[perm[j]],&result);
    121:       if (result<=0) break;
    122: #if !defined(PETSC_USE_COMPLEX)
    123:       /* keep together every complex conjugated eigenpair */
    124:       if (!im) {
    125:         if (eigi[perm[j]] == 0.0) {
    126: #endif
    127:           tmp = perm[j-1]; perm[j-1] = perm[j]; perm[j] = tmp;
    128:           j++;
    129: #if !defined(PETSC_USE_COMPLEX)
    130:         } else {
    131:           tmp = perm[j-1]; perm[j-1] = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp;
    132:           j+=2;
    133:         }
    134:       } else {
    135:         if (eigi[perm[j]] == 0.0) {
    136:           tmp = perm[j-2]; perm[j-2] = perm[j]; perm[j] = perm[j-1]; perm[j-1] = tmp;
    137:           j++;
    138:         } else {
    139:           tmp = perm[j-2]; perm[j-2] = perm[j]; perm[j] = tmp;
    140:           tmp = perm[j-1]; perm[j-1] = perm[j+1]; perm[j+1] = tmp;
    141:           j+=2;
    142:         }
    143:       }
    144: #endif
    145:     }
    146:   }
    147:   return(0);
    148: }

    150: /*
    151:    SlepcMap_ST - Gateway function to call STBackTransform from outside ST.
    152: */
    153: PetscErrorCode SlepcMap_ST(PetscObject obj,PetscInt n,PetscScalar* eigr,PetscScalar* eigi)
    154: {

    158:   STBackTransform((ST)obj,n,eigr,eigi);
    159:   return(0);
    160: }

    162: PetscErrorCode SlepcCompareLargestMagnitude(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    163: {
    164:   PetscReal a,b;

    167:   a = SlepcAbsEigenvalue(ar,ai);
    168:   b = SlepcAbsEigenvalue(br,bi);
    169:   if (a<b) *result = 1;
    170:   else if (a>b) *result = -1;
    171:   else *result = 0;
    172:   return(0);
    173: }

    175: PetscErrorCode SlepcCompareSmallestMagnitude(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    176: {
    177:   PetscReal a,b;

    180:   a = SlepcAbsEigenvalue(ar,ai);
    181:   b = SlepcAbsEigenvalue(br,bi);
    182:   if (a>b) *result = 1;
    183:   else if (a<b) *result = -1;
    184:   else *result = 0;
    185:   return(0);
    186: }

    188: PetscErrorCode SlepcCompareLargestReal(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    189: {
    190:   PetscReal a,b;

    193:   a = PetscRealPart(ar);
    194:   b = PetscRealPart(br);
    195:   if (a<b) *result = 1;
    196:   else if (a>b) *result = -1;
    197:   else *result = 0;
    198:   return(0);
    199: }

    201: PetscErrorCode SlepcCompareSmallestReal(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    202: {
    203:   PetscReal a,b;

    206:   a = PetscRealPart(ar);
    207:   b = PetscRealPart(br);
    208:   if (a>b) *result = 1;
    209:   else if (a<b) *result = -1;
    210:   else *result = 0;
    211:   return(0);
    212: }

    214: PetscErrorCode SlepcCompareLargestImaginary(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    215: {
    216:   PetscReal a,b;

    219: #if defined(PETSC_USE_COMPLEX)
    220:   a = PetscImaginaryPart(ar);
    221:   b = PetscImaginaryPart(br);
    222: #else
    223:   a = PetscAbsReal(ai);
    224:   b = PetscAbsReal(bi);
    225: #endif
    226:   if (a<b) *result = 1;
    227:   else if (a>b) *result = -1;
    228:   else *result = 0;
    229:   return(0);
    230: }

    232: PetscErrorCode SlepcCompareSmallestImaginary(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    233: {
    234:   PetscReal a,b;

    237: #if defined(PETSC_USE_COMPLEX)
    238:   a = PetscImaginaryPart(ar);
    239:   b = PetscImaginaryPart(br);
    240: #else
    241:   a = PetscAbsReal(ai);
    242:   b = PetscAbsReal(bi);
    243: #endif
    244:   if (a>b) *result = 1;
    245:   else if (a<b) *result = -1;
    246:   else *result = 0;
    247:   return(0);
    248: }

    250: PetscErrorCode SlepcCompareTargetMagnitude(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    251: {
    252:   PetscReal   a,b;
    253:   PetscScalar *target = (PetscScalar*)ctx;

    256:   /* complex target only allowed if scalartype=complex */
    257:   a = SlepcAbsEigenvalue(ar-(*target),ai);
    258:   b = SlepcAbsEigenvalue(br-(*target),bi);
    259:   if (a>b) *result = 1;
    260:   else if (a<b) *result = -1;
    261:   else *result = 0;
    262:   return(0);
    263: }

    265: PetscErrorCode SlepcCompareTargetReal(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    266: {
    267:   PetscReal   a,b;
    268:   PetscScalar *target = (PetscScalar*)ctx;

    271:   a = PetscAbsReal(PetscRealPart(ar-(*target)));
    272:   b = PetscAbsReal(PetscRealPart(br-(*target)));
    273:   if (a>b) *result = 1;
    274:   else if (a<b) *result = -1;
    275:   else *result = 0;
    276:   return(0);
    277: }

    279: #if defined(PETSC_USE_COMPLEX)
    280: PetscErrorCode SlepcCompareTargetImaginary(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    281: {
    282:   PetscReal   a,b;
    283:   PetscScalar *target = (PetscScalar*)ctx;

    286:   a = PetscAbsReal(PetscImaginaryPart(ar-(*target)));
    287:   b = PetscAbsReal(PetscImaginaryPart(br-(*target)));
    288:   if (a>b) *result = 1;
    289:   else if (a<b) *result = -1;
    290:   else *result = 0;
    291:   return(0);
    292: }
    293: #endif

    295: /*
    296:    Used in the SVD for computing smallest singular values
    297:    from the cyclic matrix.
    298: */
    299: PetscErrorCode SlepcCompareSmallestPosReal(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *result,void *ctx)
    300: {
    301:   PetscReal a,b;
    302:   PetscBool aisright,bisright;

    305:   if (PetscRealPart(ar)>0.0) aisright = PETSC_TRUE;
    306:   else aisright = PETSC_FALSE;
    307:   if (PetscRealPart(br)>0.0) bisright = PETSC_TRUE;
    308:   else bisright = PETSC_FALSE;
    309:   if (aisright == bisright) { /* same sign */
    310:     a = SlepcAbsEigenvalue(ar,ai);
    311:     b = SlepcAbsEigenvalue(br,bi);
    312:     if (a>b) *result = 1;
    313:     else if (a<b) *result = -1;
    314:     else *result = 0;
    315:   } else if (aisright && !bisright) *result = -1; /* 'a' is on the right */
    316:   else *result = 1;  /* 'b' is on the right */
    317:   return(0);
    318: }