sics/sgfind.c

/*
  Space Group Info's (c) 1994-96 Ralf W. Grosse-Kunstleve
 */

#include <stdio.h>
#include <stdlib.h>


#define SGCOREDEF__
#include "sginfo.h"


static int InitialCBMxR(T_SgInfo * SgInfo,
                        const T_LatticeInfo ** NewLatticeInfo,
                        int *NewPointGroup,
                        int *IniCBMxR, int *IniInvCBMxR)
{
  int Code, NewPG, deterCCMx, fac, i;
  const T_LatticeInfo *NewLI;
  const int *CCMx;


  Code = SgInfo->LatticeInfo->Code;
  NewLI = SgInfo->LatticeInfo;
  NewPG = SgInfo->PointGroup;
  CCMx = CCMx_PP;

  switch (SgInfo->XtalSystem) {
  case XS_Triclinic:
    NewLI = LI_P;
    CCMx = SgInfo->CCMx_LP;
    break;

  case XS_Monoclinic:
  case XS_Tetragonal:
    switch (SgInfo->UniqueRefAxis) {
    case 'z':
      if (Code == 'C') {
        NewLI = LI_P;
        CCMx = SgInfo->CCMx_LP;
      } else if (Code == 'F') {
        NewLI = LI_I;
        CCMx = CCMx_FI_z;
      }
      break;
    case 'y':
      if (Code == 'B') {
        NewLI = LI_P;
        CCMx = SgInfo->CCMx_LP;
      } else if (Code == 'F') {
        NewLI = LI_I;
        CCMx = CCMx_FI_y;
      }
      break;
    case 'x':
      if (Code == 'A') {
        NewLI = LI_P;
        CCMx = SgInfo->CCMx_LP;
      } else if (Code == 'F') {
        NewLI = LI_I;
        CCMx = CCMx_FI_x;
      }
      break;
    default:
      goto ReturnError;
    }

    if (SgInfo->XtalSystem == XS_Tetragonal
        && SgInfo->LatticeInfo != NewLI) {
      if (NewPG == PG_4b2m)
        NewPG = PG_4bm2;
      else if (NewPG == PG_4bm2)
        NewPG = PG_4b2m;
    }

    break;

  case XS_Orthorhombic:
    break;

  case XS_Trigonal:
    NewLI = LI_P;
    CCMx = SgInfo->CCMx_LP;

    if (Code == 'R' || Code == 'S' || Code == 'T') {
      if (NewPG == PG_321)
        NewPG = PG_32;
      else if (NewPG == PG_3m1)
        NewPG = PG_3m;
      else if (NewPG == PG_3bm1)
        NewPG = PG_3bm;
    }

    break;

  case XS_Hexagonal:
    break;

  case XS_Cubic:
    break;

  default:
    goto ReturnError;
  }

  deterCCMx = deterRotMx(CCMx);
  if (deterCCMx < 1 || CRBF % deterCCMx)
    goto ReturnError;

  fac = CRBF / deterCCMx;

  InverseRotMx(CCMx, IniInvCBMxR);

  for (i = 0; i < 9; i++) {
    IniCBMxR[i] = CRBF * CCMx[i];
    IniInvCBMxR[i] *= fac;
  }

  *NewLatticeInfo = NewLI;
  *NewPointGroup = NewPG;

  return deterCCMx;

ReturnError:

  SetSgError("Internal Error: InitialCBMxR()");
  return -1;
}


static int CBR_RMx(int *RRMx,
                   const int *CBMxR, const int *RMx, const int *InvCBMxR)
{
  int i, BufMx[9];


  RotMxMultiply(BufMx, RMx, InvCBMxR);
  RotMxMultiply(RRMx, CBMxR, BufMx);

  for (i = 0; i < 9; i++) {
    if (RRMx[i] % (CRBF * CRBF)) {
      SetSgError("Internal Error: CBR_SMx()");
      return -1;
    }

    RRMx[i] /= (CRBF * CRBF);
  }

  return 0;
}


static void RotateCBMxR(const int *RMx, const int *InvRMx,
                        int *CBMxR, int *InvCBMxR)
{
  int i, BufMx[9];


  RotMxMultiply(BufMx, RMx, CBMxR);
  for (i = 0; i < 9; i++)
    CBMxR[i] = BufMx[i];

  /* matrix algebra: (A * B)^-1 = B^-1 * A^-1 */

  RotMxMultiply(BufMx, InvCBMxR, InvRMx);
  for (i = 0; i < 9; i++)
    InvCBMxR[i] = BufMx[i];
}


static int AlignUniqueAxis(const T_SgInfo * SgInfo,
                           const T_SgInfo * GenSgI,
                           int *CBMxR, int *InvCBMxR, const int **AlignRMx)
{
  int i, iListS, DirCode;
  int UAMx[9], RotEV[3];
  const int *RMx, *InvRMx, *lsmxR;
  T_RotMxInfo RMxI_S, *RMxI_G;


  if (GenSgI->nList < 2)
    goto ReturnError;

  RMxI_G = &GenSgI->ListRotMxInfo[1];

  if (abs(RMxI_G->Order) == 3)
    DirCode = 0;
  else
    DirCode = '=';

  iListS = FindSeitzMx(SgInfo, RMxI_G->Order, 1, 0, DirCode);
  if (iListS < 0) {
    if (SgInfo->Centric == 0)
      return 0;

    iListS = FindSeitzMx(SgInfo, -RMxI_G->Order, 1, 0, DirCode);
    if (iListS < 0)
      goto ReturnError;

    for (i = 0; i < 9; i++)
      UAMx[i] = -SgInfo->ListSeitzMx[iListS].s.R[i];

    lsmxR = UAMx;
  } else
    lsmxR = SgInfo->ListSeitzMx[iListS].s.R;

  if (CBR_RMx(UAMx, CBMxR, lsmxR, InvCBMxR) != 0)
    goto ReturnError;

  if (GetRotMxInfo(UAMx, &RMxI_S) != RMxI_G->Order)
    goto ReturnError;

  if (RMxI_S.DirCode != RMxI_G->DirCode)
    return 0;

  RMx = InvRMx = RMx_1_000;

  for (;;) {
    RotMx_t_Vector(RotEV, RMx, RMxI_S.EigenVector, 0);

    for (i = 0; i < 3; i++)
      if (RotEV[i] != RMxI_G->EigenVector[i])
        break;

    if (i == 3)
      break;

    if (RMxI_S.DirCode == '=') {
      if (RMx == RMx_1_000) {
        RMx = RMx_3_111;
        InvRMx = RMx_3i111;
      } else if (RMx == RMx_3_111) {
        RMx = RMx_3i111;
        InvRMx = RMx_3_111;
      } else
        goto ReturnError;
    } else if (RMxI_S.DirCode == '*') {
      if (RMx == RMx_1_000) {
        RMx = RMx_4_001;
        InvRMx = RMx_4i001;
      } else if (RMx == RMx_4_001) {
        RMx = RMx_2_001;
        InvRMx = RMx_2_001;
      } else if (RMx == RMx_2_001) {
        RMx = RMx_4i001;
        InvRMx = RMx_4_001;
      } else
        goto ReturnError;
    } else
      goto ReturnError;
  }

  if (RMx != RMx_1_000)
    RotateCBMxR(RMx, InvRMx, CBMxR, InvCBMxR);

  if (AlignRMx)
    *AlignRMx = RMx;

  return 1;

ReturnError:

  SetSgError("Internal Error: AlignUniqueAxis()");
  return -1;
}


static const T_RTMx *GetSMxWithSameRot(const int *WtdRotMx,
                                       const T_SgInfo * SgInfo,
                                       T_RTMx * BufMx)
{
  int iList, i;
  const T_RTMx *lsmx;


  lsmx = SgInfo->ListSeitzMx;

  for (iList = 0; iList < SgInfo->nList; iList++, lsmx++) {
    for (i = 0; i < 9; i++)
      if (WtdRotMx[i] != lsmx->s.R[i])
        break;

    if (i == 9)
      return lsmx;

    if (SgInfo->Centric != -1)
      continue;

    for (i = 0; i < 9; i++)
      if (WtdRotMx[i] != -lsmx->s.R[i])
        break;

    if (i == 9) {
      for (i = 0; i < 9; i++)
        BufMx->s.R[i] = -lsmx->s.R[i];

      for (i = 0; i < 3; i++) {
        BufMx->s.T[i] = -lsmx->s.T[i] % STBF;
        if (BufMx->s.T[i] < 0)
          BufMx->s.T[i] += STBF;
      }

      return BufMx;
    }
  }

  return NULL;
}


static int BuildFreeMx(const int *EigenVector, int Order, int *FreeMx)
{
  static const int GeneratorEigenVectors[] = {
    001, 0, 0, 1,
    010, 0, 1, 0,
    100, 1, 0, 0,
    110, 1, 1, 0,
    -110, 1, -1, 0,
    111, 1, 1, 1,
    0
  };

  int i;
  const int *gev;


  for (i = 0; i < 9; i++)
    FreeMx[i] = 0;

  if (Order == -1 || Order == -3 || Order == -4 || Order == -6)
    return 0;

  for (gev = GeneratorEigenVectors; *gev++ != 0; gev += 3) {
    for (i = 0; i < 3; i++)
      if (EigenVector[i] != gev[i])
        break;

    if (i == 3)
      break;
  }

  gev--;

  if (Order == -2) {
    switch (*gev) {
    case 001:
      FreeMx[0] = 1;
      FreeMx[4] = 1;
      return 0;
    case 010:
      FreeMx[8] = 1;
      FreeMx[0] = 1;
      return 0;
    case 100:
      FreeMx[4] = 1;
      FreeMx[8] = 1;
      return 0;
    case 110:
      FreeMx[1] = 1;
      FreeMx[4] = -1;
      FreeMx[8] = 1;
      return 1;
    case -110:
      FreeMx[1] = 1;
      FreeMx[4] = 1;
      FreeMx[8] = 1;
      return 1;
    default:
      break;
    }
  } else if (Order > 1) {
    switch (*gev) {
    case 001:
      FreeMx[8] = 1;
      return 0;
    case 010:
      FreeMx[4] = 1;
      return 0;
    case 100:
      FreeMx[0] = 1;
      return 0;
    case 110:
      FreeMx[0] = 1;
      FreeMx[3] = 1;
      return 1;
    case -110:
      FreeMx[0] = 1;
      FreeMx[3] = -1;
      return 1;
    case 111:
      FreeMx[0] = 1;
      FreeMx[3] = 1;
      FreeMx[6] = 1;
      return 1;
    default:
      break;
    }
  }

  SetSgError("Internal Error: BuildFreeMx()");
  return -1;
}


static int StartFixAxes(const T_SgInfo * SgInfo,
                        const T_SgInfo * GenSgI, const int *iGen,
                        T_RTMx * CBMx, T_RTMx * InvCBMx,
                        T_RTMx * SMxG, T_RTMx * SMxS_G,
                        int *FreeMx, int *TryAgain)
{
  int iG, Order, i;
  const int *EV;
  T_RTMx SMxG_S, BufMx;
  const T_RTMx *SMx;
  const T_RotMxInfo *RMxI_G;


  if (*iGen == -3)
    iG = 1;
  else
    iG = *iGen;

  if (iG == -1) {
    Order = -1;
    EV = NULL;
  } else {
    if (iG < 1 || iG >= GenSgI->nList)
      goto ReturnError;

    RMxI_G = &GenSgI->ListRotMxInfo[iG];
    Order = RMxI_G->Order;
    EV = RMxI_G->EigenVector;

    if (iG != *iGen) {
      Order *= -1;
      if (Order != *iGen)
        goto ReturnError;
    }
  }

  if (Order == -1) {
    if (GenSgI->Centric == -1) {
      InitSeitzMx(SMxG, -1);
    } else {
      for (iG = 1; iG < GenSgI->nList; iG++)
        if (GenSgI->ListRotMxInfo[iG].Order == -1)
          break;

      if (iG == GenSgI->nList)
        goto ReturnError;

      SMx = &GenSgI->ListSeitzMx[iG];

      for (i = 0; i < 12; i++)
        SMxG->a[i] = SMx->a[i];
    }
  } else {
    SMx = &GenSgI->ListSeitzMx[iG];

    if (iG == *iGen)
      for (i = 0; i < 12; i++)
        SMxG->a[i] = SMx->a[i];
    else {
      for (i = 0; i < 9; i++)
        SMxG->s.R[i] = -SMx->s.R[i];

      for (i = 0; i < 3; i++) {
        SMxG->s.T[i] = -SMx->s.T[i] % STBF;
        if (SMxG->s.T[i] < 0)
          SMxG->s.T[i] += STBF;
      }
    }
  }

  if (CB_SMx(&SMxG_S, InvCBMx, SMxG, CBMx) != 0)
    return -1;

  SMx = GetSMxWithSameRot(SMxG_S.s.R, SgInfo, &BufMx);
  if (SMx == NULL)
    return 0;

  if (CB_SMx(SMxS_G, CBMx, SMx, InvCBMx) != 0)
    return -1;

  for (i = 0; i < 9; i++)
    if (SMxS_G->s.R[i] != SMxG->s.R[i])
      goto ReturnError;

  *TryAgain = BuildFreeMx(EV, Order, FreeMx);
  if (*TryAgain < 0)
    return -1;

  return 1;

ReturnError:

  SetSgError("Internal Error: StartFixAxes()");
  return -1;
}


static int FindInvertableMx(const int *Mx, int *InvMx,
                            int *nActive, int *irActive, int *icActive)
{
  int Init, deterMx, i;


  if (*nActive == 0 || *nActive == 3)
    return 0;

  if (*nActive == -1) {
    Init = 1;

    deterMx = deterRotMx(Mx);
    if (deterMx) {
      InverseRotMx(Mx, InvMx);

      *nActive = 3;
      return deterMx;
    }
  } else
    Init = 0;

  if (Init || *nActive == 2) {
    for (;;) {
      if (Init) {
        irActive[0] = 0;
        irActive[1] = 1;
        icActive[0] = 0;
        icActive[1] = 1;
        Init = 0;
      } else {
        if (++icActive[1] == 3) {
          if (++icActive[0] == 2) {
            if (++irActive[1] == 3) {
              if (++irActive[0] == 2) {
                Init = 1;
                break;
              } else {
                irActive[1] = irActive[0] + 1;
                icActive[0] = 0;
                icActive[1] = 1;
              }
            } else {
              icActive[0] = 0;
              icActive[1] = 1;
            }
          } else {
            icActive[1] = icActive[0] + 1;
          }
        }
      }

      InvMx[0] = Mx[irActive[1] * 3 + icActive[1]];
      InvMx[1] = -Mx[irActive[0] * 3 + icActive[1]];
      InvMx[2] = -Mx[irActive[1] * 3 + icActive[0]];
      InvMx[3] = Mx[irActive[0] * 3 + icActive[0]];

      deterMx = InvMx[3] * InvMx[0] - InvMx[1] * InvMx[2];
      if (deterMx) {
        *nActive = 2;
        return deterMx;
      }
    }
  }

  if (*nActive == 2)
    return 0;

  if (Init)
    i = 0;
  else
    i = irActive[0] * 3 + icActive[0] + 1;

  for (; i < 9; i++) {
    if (Mx[i]) {
      irActive[0] = i / 3;
      icActive[0] = i % 3;
      *nActive = 1;
      return Mx[i];
    }
  }

  if (*nActive == 1)
    return 0;

  *nActive = 0;
  return 1;
}


static int SetInvCBMxT(const int *CBMxT, const int *InvCBMxR,
                       int *InvCBMxT)
{
  int i;


  RotMx_t_Vector(InvCBMxT, InvCBMxR, CBMxT, CRBF * CTBF);

  for (i = 0; i < 3; i++) {
    if (InvCBMxT[i] % CRBF) {
      SetSgError("Internal Error: SetInvCBMxT()");
      return -1;
    }

    if (InvCBMxT[i])
      InvCBMxT[i] = CTBF - InvCBMxT[i] / CRBF;
  }

  return 0;
}


static int FixAxes(const T_SgInfo * SgInfo,
                   const T_SgInfo * GenSgI, const int *iGen,
                   T_RTMx * CBMx, T_RTMx * InvCBMx,
                   int *FreeMx, int TryAgain)
{
  int i, NextTryAgain;
  int IniCBMxT[3], SingleFreeMx[9];
  T_RTMx SMxG, SMxS_G;
  int NextFreeMxBuf[9], R_I_FMxBuf[9];
  int R_I[9], *R_I_FMx, InvR_I_FMx[9], deterR_I_FMx;
  int S_G[3], CmpS_G[3], RedSh[3], Sh[3], *NextFreeMx;
  int nActive, irActive[3], icActive[3];
  int nTrV, iTrV;
  const int *TrV;


  if (FreeMx == NULL) {
    for (i = 0; i < 3; i++) {
      CBMx->s.T[i] = 0;
      InvCBMx->s.T[i] = 0;
    }
  }

  i = StartFixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx,
                   &SMxG, &SMxS_G, SingleFreeMx, &NextTryAgain);
  if (i != 1)
    return i;

  if (FreeMx) {
    RotMxMultiply(NextFreeMxBuf, SingleFreeMx, FreeMx);
    NextFreeMx = NextFreeMxBuf;
  } else
    NextFreeMx = SingleFreeMx;

  for (i = 0; i < 9; i++)
    R_I[i] = SMxG.s.R[i];

  for (i = 0; i < 9; i += 4)
    R_I[i] -= 1;

  if (FreeMx) {
    RotMxMultiply(R_I_FMxBuf, R_I, FreeMx);
    R_I_FMx = R_I_FMxBuf;
  } else
    R_I_FMx = R_I;

  for (i = 0; i < 3; i++)
    IniCBMxT[i] = CBMx->s.T[i];

  nActive = -1;

  for (;;) {
    deterR_I_FMx = FindInvertableMx(R_I_FMx, InvR_I_FMx,
                                    &nActive, irActive, icActive);
    if (deterR_I_FMx == 0)
      break;

    nTrV = GenSgI->LatticeInfo->nTrVector;
    TrV = GenSgI->LatticeInfo->TrVector;

    for (iTrV = 0; iTrV < nTrV; iTrV++, TrV += 3) {
      for (i = 0; i < 3; i++) {
        S_G[i] = (CTBF / STBF)
            * ((SMxS_G.s.T[i] - SMxG.s.T[i] - TrV[i]) % STBF);
        RedSh[i] = 0;
      }

      switch (nActive) {
      case 1:
        RedSh[icActive[0]] = S_G[irActive[0]];
        break;
      case 2:
        RedSh[icActive[0]] = InvR_I_FMx[0] * S_G[irActive[0]]
            + InvR_I_FMx[1] * S_G[irActive[1]];
        RedSh[icActive[1]] = InvR_I_FMx[2] * S_G[irActive[0]]
            + InvR_I_FMx[3] * S_G[irActive[1]];
        break;
      case 3:
        RotMx_t_Vector(RedSh, InvR_I_FMx, S_G, 0);
        break;
      default:
        break;
      }

      if (FreeMx) {
        RotMx_t_Vector(Sh, FreeMx, RedSh, 0);

        for (i = 0; i < 3; i++)
          Sh[i] %= (CTBF * abs(deterR_I_FMx));
      } else {
        for (i = 0; i < 3; i++)
          Sh[i] = RedSh[i] % (CTBF * abs(deterR_I_FMx));
      }

      RotMx_t_Vector(CmpS_G, R_I, Sh, 0);

      for (i = 0; i < 3; i++)
        if ((CmpS_G[i] -
             S_G[i] * deterR_I_FMx) % (CTBF * abs(deterR_I_FMx)))
          break;

      if (i < 3)
        continue;

      if (deterR_I_FMx != 1) {
        for (i = 0; i < 3; i++) {
          if (Sh[i] % abs(deterR_I_FMx))
            goto ReturnError;

          Sh[i] /= deterR_I_FMx;
        }
      }

      for (i = 0; i < 3; i++) {
        CBMx->s.T[i] = IniCBMxT[i] + Sh[i] % CTBF;
        if (CBMx->s.T[i] < 0)
          CBMx->s.T[i] += CTBF;
      }

      if (SetInvCBMxT(CBMx->s.T, InvCBMx->s.R, InvCBMx->s.T) != 0)
        return -1;

      if (iGen[1] == 0)
        return 1;

      i = FixAxes(SgInfo, GenSgI, &iGen[1], CBMx, InvCBMx,
                  NextFreeMx, NextTryAgain);
      if (i != 0)
        return i;
    }

    if (TryAgain == 0)
      break;
  }

  return 0;

ReturnError:

  SetSgError("Internal Error: FixAxes()");
  return -1;
}


static int CompleteCBMx(const T_SgInfo * SgInfo,
                        const T_LatticeInfo * NewLI,
                        const T_SgInfo * GenSgI, const int *IniCBMxR,
                        const int *IniInvCBMxR, T_RTMx * CBMx,
                        T_RTMx * InvCBMx)
{
  int iGen[5], i;


  if (SgInfo->XtalSystem == XS_Triclinic) {
    for (i = 0; i < 9; i++) {
      CBMx->s.R[i] = IniCBMxR[i];
      InvCBMx->s.R[i] = IniInvCBMxR[i];
    }

    if (GenSgI->PointGroup == PG_1) {
      for (i = 0; i < 3; i++) {
        CBMx->s.T[i] = 0;
        InvCBMx->s.T[i] = 0;
      }
      return 1;
    }

    iGen[0] = -1;
    iGen[1] = 0;

    return FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
  }

  if (SgInfo->XtalSystem == XS_Monoclinic) {
    int iCCs, BufRMx[9];
    int RMxCCs_Buf[9], RMxCCn_Buf[9], InvRMxCCn_Buf[9], RotLTrV[3];
    const int *RMxAA, *RMxCCs, *RMxCCn, *InvRMxCCn, *TrV;
    T_RTMx BufCBMx, BufInvCBMx;


    if (NewLI->nTrVector != 1 && NewLI->nTrVector != 2)
      goto ReturnError;

    for (i = 0; i < 9; i++) {
      BufCBMx.s.R[i] = IniCBMxR[i];
      BufInvCBMx.s.R[i] = IniInvCBMxR[i];
    }

    i = AlignUniqueAxis(SgInfo, GenSgI,
                        BufCBMx.s.R, BufInvCBMx.s.R, &RMxAA);
    if (i != 1)
      return i;

    if (GenSgI->nList < 2)
      goto ReturnError;

    for (i = 0; i < 9; i++) {
      RMxCCs_Buf[i] = RMx_2_110[i];
      RMxCCn_Buf[i] = RMx_3_001[i];
    }

    switch (GenSgI->ListRotMxInfo[1].RefAxis) {
    case 'z':
      break;
    case 'x':
      RotateRotMx(RMxCCs_Buf, RMx_3_111, RMx_3i111);
      RotateRotMx(RMxCCn_Buf, RMx_3_111, RMx_3i111);
      break;
    case 'y':
      RotateRotMx(RMxCCs_Buf, RMx_3i111, RMx_3_111);
      RotateRotMx(RMxCCn_Buf, RMx_3i111, RMx_3_111);
      break;
    default:
      goto ReturnError;
    }

    InverseRotMx(RMxCCn_Buf, InvRMxCCn_Buf);

    i = 0;
    iGen[i++] = 1;
    if (GenSgI->PointGroup == PG_2_m)
      iGen[i++] = -1;
    iGen[i] = 0;

    RMxCCs = RMx_1_000;

    for (iCCs = 0; iCCs < 2; iCCs++, RMxCCs = RMxCCs_Buf) {
      RMxCCn = InvRMxCCn = RMx_1_000;

      for (;;) {
        if (NewLI->nTrVector == 2) {
          RotMx_t_Vector(RotLTrV, RMxAA, &NewLI->TrVector[3], STBF);
          RotMx_t_Vector(BufRMx, RMxCCn, RotLTrV, STBF);
          RotMx_t_Vector(RotLTrV, RMxCCs, BufRMx, STBF);

          TrV = &GenSgI->LatticeInfo->TrVector[3];

          for (i = 0; i < 3; i++)
            if (RotLTrV[i] != TrV[i])
              break;
        }

        if (NewLI->nTrVector == 1 || i == 3) {
          RotMxMultiply(BufRMx, RMxCCn, BufCBMx.s.R);
          RotMxMultiply(CBMx->s.R, RMxCCs, BufRMx);

          RotMxMultiply(BufRMx, BufInvCBMx.s.R, InvRMxCCn);
          RotMxMultiply(InvCBMx->s.R, BufRMx, RMxCCs);

          i = FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
          if (i != 0)
            return i;
        }

        if (RMxCCn == RMx_1_000) {
          RMxCCn = RMxCCn_Buf;
          InvRMxCCn = InvRMxCCn_Buf;
        } else if (RMxCCn == RMxCCn_Buf) {
          RMxCCn = InvRMxCCn_Buf;
          InvRMxCCn = RMxCCn_Buf;
        } else {
          RMxCCn = NULL;
          break;
        }
      }
    }

    return 0;
  }

  for (i = 0; i < 9; i++) {
    CBMx->s.R[i] = IniCBMxR[i];
    InvCBMx->s.R[i] = IniInvCBMxR[i];
  }

  if (SgInfo->XtalSystem == XS_Orthorhombic) {
    int iNextBasis;
    int BufCBMxR[9], BufInvCBMxR[9];
    int NLTrV_Buf1[3], NLTrV_Buf2[3];
    const int *NLTrV, *GLTrV;


    if ((GenSgI->LatticeInfo->Code == 'I') != (NewLI->Code == 'I'))
      return 0;

    if (NewLI->Code == 'A' || NewLI->Code == 'B' || NewLI->Code == 'C') {
      NLTrV = &NewLI->TrVector[3];
      GLTrV = &GenSgI->LatticeInfo->TrVector[3];
    } else {
      NLTrV = NULL;
      GLTrV = NULL;
    }
    i = 0;
    iGen[i++] = 1;
    iGen[i++] = 2;
    if (GenSgI->PointGroup == PG_mmm)
      iGen[i++] = -1;
    iGen[i] = 0;

    for (iNextBasis = 0; iNextBasis < 6; iNextBasis++) {
      if (iNextBasis % 2) {
        RotMxMultiply(BufCBMxR, RMx_2_110, CBMx->s.R);
        RotMxMultiply(BufInvCBMxR, InvCBMx->s.R, RMx_2_110);

        for (i = 0; i < 9; i++) {
          CBMx->s.R[i] = BufCBMxR[i];
          InvCBMx->s.R[i] = BufInvCBMxR[i];
        }
      } else if (iNextBasis == 2) {
        RotMxMultiply(CBMx->s.R, RMx_3_111, IniCBMxR);
        RotMxMultiply(InvCBMx->s.R, IniInvCBMxR, RMx_3i111);
      } else if (iNextBasis) {
        RotMxMultiply(CBMx->s.R, RMx_3i111, IniCBMxR);
        RotMxMultiply(InvCBMx->s.R, IniInvCBMxR, RMx_3_111);
      }

      if (NLTrV) {
        if (iNextBasis % 2) {
          RotMx_t_Vector(NLTrV_Buf1, RMx_2_110, NLTrV, STBF);
          NLTrV = NLTrV_Buf1;
        } else if (iNextBasis == 2) {
          RotMx_t_Vector(NLTrV_Buf2, RMx_3_111, &NewLI->TrVector[3], STBF);
          NLTrV = NLTrV_Buf2;
        } else if (iNextBasis) {
          RotMx_t_Vector(NLTrV_Buf2, RMx_3i111, &NewLI->TrVector[3], STBF);
          NLTrV = NLTrV_Buf2;
        }

        for (i = 0; i < 3; i++)
          if (NLTrV[i] != GLTrV[i])
            break;

        if (i < 3)
          continue;
      }

      i = FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
      if (i != 0)
        return i;
    }
  }

  if (SgInfo->XtalSystem == XS_Tetragonal) {
    i = AlignUniqueAxis(SgInfo, GenSgI, CBMx->s.R, InvCBMx->s.R, NULL);
    if (i != 1)
      return -1;
    i = 0;
    iGen[i++] = 1;

    switch (GenSgI->PointGroup) {
    case PG_422:
    case PG_4mm:
    case PG_4b2m:
    case PG_4bm2:
    case PG_4_mmm:
      iGen[i++] = 2;
    }

    switch (GenSgI->PointGroup) {
    case PG_4_m:
    case PG_4_mmm:
      iGen[i++] = -1;
    }
    iGen[i] = 0;

    return FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
  }

  if (SgInfo->XtalSystem == XS_Trigonal) {
    i = AlignUniqueAxis(SgInfo, GenSgI, CBMx->s.R, InvCBMx->s.R, NULL);
    if (i != 1)
      return i;
    i = 0;

    switch (GenSgI->PointGroup) {
    case PG_3:
    case PG_312:
    case PG_32:
    case PG_3m1:
    case PG_3m:
      iGen[i++] = 1;
      break;
    case PG_3b:
    case PG_3bm1:
    case PG_3b1m:
    case PG_3bm:
      iGen[i++] = -3;
    }

    switch (GenSgI->PointGroup) {
    case PG_321:
    case PG_312:
    case PG_32:
    case PG_3m1:
    case PG_31m:
    case PG_3m:
    case PG_3bm1:
    case PG_3b1m:
    case PG_3bm:
      iGen[i++] = 2;
    }

    switch (GenSgI->PointGroup) {
    case PG_321:
    case PG_31m:
      iGen[i++] = 1;
    }
    iGen[i] = 0;

    return FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
  }

  if (SgInfo->XtalSystem == XS_Hexagonal) {
    i = AlignUniqueAxis(SgInfo, GenSgI, CBMx->s.R, InvCBMx->s.R, NULL);
    if (i != 1)
      return -1;
    i = 0;

    switch (GenSgI->PointGroup) {
    case PG_6bm2:
    case PG_6b2m:
      iGen[i++] = 2;
    }
    iGen[i++] = 1;

    switch (GenSgI->PointGroup) {
    case PG_622:
    case PG_6mm:
    case PG_6_mmm:
      iGen[i++] = 2;
    }

    switch (GenSgI->PointGroup) {
    case PG_6_m:
    case PG_6_mmm:
      iGen[i++] = -1;
    }
    iGen[i] = 0;

    return FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
  }

  if (SgInfo->XtalSystem == XS_Cubic) {
    i = 0;
    iGen[i++] = 3;
    iGen[i++] = 1;
    iGen[i++] = 2;
    if (GenSgI->PointGroup == PG_m3b || GenSgI->PointGroup == PG_m3bm)
      iGen[i++] = -1;
    iGen[i] = 0;

    return FixAxes(SgInfo, GenSgI, iGen, CBMx, InvCBMx, NULL, 0);
  }

  return 0;

ReturnError:

  SetSgError("Internal Error: CompleteCBMx()");
  return -1;
}


const T_TabSgName *FindReferenceSpaceGroup(T_SgInfo * SgInfo,
                                           T_RTMx * CBMx, T_RTMx * InvCBMx)
{
  int stat, NewPG, SgInfo_CI, OL_SgInfo, OL_GenSgI;
  const T_TabSgName *tsgn;
  T_SgInfo GenSgI;
  T_RTMx GenSgI_ListSeitzMx[5];
  T_RotMxInfo GenSgI_ListRotMxInfo[5];
  int iList, PrevSgNumber;
  int FacIniCBMxR;
  T_RotMxInfo *lrmxi;
  const T_LatticeInfo *NewLI;
  int IniCBMxR[9], IniInvCBMxR[9];


  GenSgI.MaxList = 5;
  GenSgI.ListSeitzMx = GenSgI_ListSeitzMx;
  GenSgI.ListRotMxInfo = GenSgI_ListRotMxInfo;

  FacIniCBMxR =
      InitialCBMxR(SgInfo, &NewLI, &NewPG, IniCBMxR, IniInvCBMxR);
  if (FacIniCBMxR < 0)
    return NULL;

  OL_SgInfo = SgInfo->OrderL;
  if (OL_SgInfo % FacIniCBMxR)
    goto ReturnError;

  OL_SgInfo /= FacIniCBMxR;

  SgInfo_CI = (SgInfo->Centric || SgInfo->InversionOffOrigin);

  PrevSgNumber = 0;

  for (tsgn = TabSgName; tsgn->HallSymbol; tsgn++) {
    if (tsgn->HallSymbol[1] == 'R')
      continue;

    if (VolAPointGroups[tsgn->SgNumber] != NewPG)
      continue;

    if (tsgn->SgNumber == PrevSgNumber)
      continue;

    PrevSgNumber = tsgn->SgNumber;

    InitSgInfo(&GenSgI);
    GenSgI.GenOption = -1;

    ParseHallSymbol(tsgn->HallSymbol, &GenSgI);

    if (SgError != NULL)
      return NULL;

    if (ApplyOriginShift(&GenSgI) < 0)
      return NULL;

    if (SgInfo_CI != (GenSgI.Centric || GenSgI.InversionOffOrigin))
      goto ReturnError;

    OL_GenSgI = GenSgI.LatticeInfo->nTrVector;

    if (SgInfo_CI)
      OL_GenSgI *= 2;

    lrmxi = &GenSgI.ListRotMxInfo[1];

    for (iList = 1; iList < GenSgI.nList; iList++, lrmxi++) {
      OL_GenSgI *= abs(lrmxi->Order);

      if ((lrmxi->Order == -1 || lrmxi->Order == -3)
          && GenSgI.Centric == 0 && GenSgI.InversionOffOrigin == 0)
        goto ReturnError;
    }

    if (OL_GenSgI == OL_SgInfo) {
      if (NewLI->nTrVector != GenSgI.LatticeInfo->nTrVector)
        goto ReturnError;

      GenSgI.PointGroup = NewPG;

#if DEBUG_FindConventionalSetting
      fprintf(stdout, "%s ?= %s (%d)\n",
              SgInfo->HallSymbol, tsgn->HallSymbol, tsgn->SgNumber);
#endif

      stat = CompleteCBMx(SgInfo, NewLI, &GenSgI,
                          IniCBMxR, IniInvCBMxR, CBMx, InvCBMx);
      if (stat < 0)
        return NULL;

      if (stat)
        return tsgn;
    }
  }

  SetSgError("Internal Error: Space Group not found");
  return NULL;

ReturnError:

  SetSgError("Internal Error: FindReferenceSpaceGroup()");
  return NULL;
}