#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <complex.h>
#include <string.h>

#include "../numeric/SU21-numeric.h"
#include "../numeric/SU21-numeric-base.c"

#define GOODPREFIX "a7p2N/a7p2N-5"

typedef struct {
  char Nam[MaxGenNameLength+1]; // Generator name
  char InvNam[MaxGenNameLength+1]; // Inverse generator name
  int Len; // ``Length'' of Generator
  Mtx_t Mtx; // matrix for generator
} Gen_t;

// $\exp(2\pi i/7)$, a seventh root of unity
#define ZZ (0.6234898018587335305300629+0.7818314824680298087044108*I)
// and its powers, the other seventh roots of unity
#define ZZ2 (ZZ*ZZ)
#define ZZ3 (ZZ*ZZ2)
#define ZZ4 (ZZ*ZZ3)
#define ZZ5 (ZZ*ZZ4)
#define ZZ6 (ZZ*ZZ5)

#define MaxNoGens 3
#define ActualNoGens 3
#define KSiz 1

void SetupGens(Elt_t GenElts[],int *NoGenElts_p);
void SetupK(Elt_t KElts[]);

int main(int argc,char *(argv[])) {
  // The generators as group elements
  Elt_t GenElts[2*ActualNoGens],KElts[KSiz];

  char *Prefix_p,FileNam[MAX_FILENAME_LEN]="../";
  int GenIx,GenEltIx,NoGenElts;
  size_t NamLen;
  Mtx_t MtxInv;

  FILE *GensFile;
  FILE *KFile;

  // Check that the prefix is right
  Prefix_p=getenv("PREFIX");
  assert(Prefix_p != NULL);
  assert(strncmp(Prefix_p,GOODPREFIX,50) == 0);

  // Open the output files
  {
    size_t len=strlen(Prefix_p);
    assert(3+len+5<MAX_FILENAME_LEN);
    strcpy(&FileNam[3],Prefix_p);
    strcpy(&FileNam[3]+len,"-Gens");
    printf("%s\n",FileNam);
    GensFile=fopen(FileNam,"w");
    assert(GensFile != NULL);
    strcpy(&FileNam[3]+len,"-K");
    printf("%s\n",FileNam);
    KFile=fopen(FileNam,"w");
    assert(KFile != NULL);
  }

  // Prepare the generators and write the generator file
  SetupGens(GenElts,&NoGenElts);
  fprintf(GensFile,"NoGenElts=%i\n",NoGenElts);
  for(GenEltIx=0;GenEltIx<NoGenElts;GenEltIx++)
    OutputElt(GensFile,GenElts[GenEltIx]);

  // Prepare K (the finite group) and write the K file
  SetupK(KElts);
  fprintf(KFile,"KSiz=%i\n",KSiz);
  for(GenEltIx=0;GenEltIx<KSiz;GenEltIx++)
    OutputElt(KFile,KElts[GenEltIx]);
}

// Prepare the generating elements
//
void SetupGens(Elt_t GenElts[],int *NoGenElts_p) {
  // The form with respect to which the original, given matrices are
  // unitary:
  Mtx_t FF0=
    {{ ZZ+1/ZZ, 0, 0},
     { 0, ZZ2+1/ZZ2, 0},
     { 0, 0, ZZ4+1/ZZ4}};

  // Matrix to conjugate them to be unitary with respect to
  // $\diag{1,1,-1}$
  Mtx_t ConjMtxInv, ConjMtx={
    {0, 0, SQRT(-CREAL(ZZ4+1/ZZ4))},
    {0, SQRT(-CREAL(ZZ2+1/ZZ2)), 0},
    {SQRT(CREAL(ZZ+1/ZZ)), 0, 0}};

  // The generators
  Gen_t Gens[MaxNoGens]={
    {"A","a",20,
     {
       {1/5.0*(6*ZZ5+2*ZZ4+4*ZZ3+4*ZZ2-ZZ),
	1/5.0*(-2*ZZ5-4*ZZ4+2*ZZ3-4*ZZ),
	1/5.0*(-ZZ5-ZZ4+3*ZZ3+2*ZZ2-4*ZZ-3)},
       {1/5.0*(-2*ZZ5-4*ZZ4-4*ZZ3-8*ZZ2-2*ZZ-4),
	1/5.0*(-4*ZZ5+2*ZZ3-5*ZZ2-2*ZZ-4),
	1/5.0*(-2*ZZ5-2*ZZ4-4*ZZ3-6*ZZ2-6*ZZ-2)},
       {1/5.0*(5*ZZ5-ZZ4+2*ZZ3+2*ZZ2+2*ZZ+5),
	1/5.0*(4*ZZ5-4*ZZ4+2*ZZ3+2*ZZ2),
	1/5.0*(-2*ZZ5-7*ZZ4-6*ZZ3-4*ZZ2-2*ZZ-6)}
     }
    },

    {"B","b",20,
     {
       {1/7.0*(6*ZZ5-3*ZZ4-6*ZZ3-3*ZZ2-ZZ),
	1/7.0*(-2*ZZ5-7*ZZ4-ZZ3-5*ZZ2-5*ZZ-1),
	1/7.0*(7*ZZ5+5*ZZ4+ZZ3+2*ZZ2+8*ZZ+5)},
       {1/7.0*(ZZ5+6*ZZ4+8*ZZ3+7*ZZ2+3*ZZ+3),
	1/7.0*(6*ZZ5+3*ZZ4+12*ZZ3+5*ZZ2+3*ZZ+6),
	1/7.0*(ZZ5-4*ZZ4-ZZ3-4*ZZ2-6*ZZ)},
       {1/14.0*(5*ZZ5-ZZ4+3*ZZ3-4*ZZ2-ZZ+12),
	1/7.0*(-8*ZZ5-ZZ4-7*ZZ3-5*ZZ2-2*ZZ-5),
	1/7.0*(-12*ZZ5-7*ZZ4-6*ZZ3-9*ZZ2-9*ZZ-6)}
     }
    },

    {"C","c",20,
     {
       {1/35.0*(-38*ZZ5-26*ZZ4-20*ZZ3+ZZ2+2*ZZ+4),
	1/35.0*(39*ZZ5+32*ZZ4-28*ZZ3+20*ZZ2+29*ZZ+13),
	1/35.0*(6*ZZ5+28*ZZ4+38*ZZ3+22*ZZ2+36*ZZ+52)},
       {1/35.0*(-39*ZZ5+2*ZZ4-10*ZZ3+9*ZZ2+17*ZZ+7),
	1/35.0*(20*ZZ5+21*ZZ4-18*ZZ3+22*ZZ2-6*ZZ+24),
	1/35.0*(28*ZZ5+48*ZZ4+67*ZZ3+57*ZZ2+60*ZZ+41)},
       {1/35.0*(-59*ZZ5-4*ZZ4-10*ZZ3-21*ZZ2+5*ZZ-37),
	1/35.0*(10*ZZ5+19*ZZ4-29*ZZ3+27*ZZ2+12*ZZ+17),
	1/35.0*(18*ZZ5+40*ZZ4+38*ZZ3+12*ZZ2+39*ZZ+42)}
     }
    }
  };

  int GenIx,GenEltIx;
  size_t NamLen;
  Mtx_t MtxInv;

  // Calculate the inverse of ConjMtx
  InvMtx(ConjMtxInv,ConjMtx);
  
  GenEltIx=0;
  for(GenIx=0;GenIx<ActualNoGens;GenIx++) {
    printf("Checking Generator %s\n",Gens[GenIx].Nam);
    // Check that the matrix is unitary with respect to FF0
    assert(CheckUnitary(Gens[GenIx].Mtx,FF0));
    // Calculate the conjugated matrix
    ConjugateMtx(GenElts[GenEltIx].Mtx,Gens[GenIx].Mtx,ConjMtx,ConjMtxInv);
    // and check that that is unitary relative to FF1
    assert(CheckUnitary(GenElts[GenEltIx].Mtx,FF1));
    InvMtx(MtxInv,GenElts[GenEltIx].Mtx);
    // Set up the generator name
    NamLen=strlen(Gens[GenIx].Nam);
    assert(NamLen>0 && NamLen<MaxGenNameLength);
    strcpy(GenElts[GenEltIx].Word,Gens[GenIx].Nam);
    // and ``length''
    GenElts[GenEltIx].Len=Gens[GenIx].Len;
    // and KIx and KStart
    GenElts[GenEltIx].KIx = -1;
    GenElts[GenEltIx].KStart = 0;

    FixUpElt(&GenElts[GenEltIx]);
    GenEltIx++;

    // Now do the inverse generator.  If the inverse name is empty, we
    // skip this.
    NamLen=strlen(Gens[GenIx].InvNam);
    if(NamLen>0) {
      // The matrix
      memcpy(&GenElts[GenEltIx].Mtx,MtxInv,sizeof(Mtx_t));
      assert(CheckUnitary(GenElts[GenEltIx].Mtx,FF1));
      // the inverse generator name
      assert(NamLen<MaxGenNameLength);
      strcpy(GenElts[GenEltIx].Word,Gens[GenIx].InvNam);
      // the length
      GenElts[GenEltIx].Len=Gens[GenIx].Len;
      // and KIx and KStart
      GenElts[GenEltIx].KIx = -1;
      GenElts[GenEltIx].KStart = 0;

      FixUpElt(&GenElts[GenEltIx]);
      GenEltIx++;
    }
  }
  *NoGenElts_p=GenEltIx;
}

// Set up the (trivial) finite group, K
//
void SetupK(Elt_t KElts[]) {
  // The identity element
  Gen_t IGen=
    {"1","",0,{{1,0,0},{0,1,0},0,0,1}};
  Elt_t *KElt_p;

  KElt_p=&KElts[0];

  // Set up the matrix
  memcpy(KElt_p->Mtx,IGen.Mtx,sizeof(Mtx_t));
  // the generator name
  assert(strlen(IGen.Nam)<MaxGenNameLength);
  strcpy(KElt_p->Word,IGen.Nam);
  // the ``length''
  KElt_p->Len = IGen.Len;
  // and KIx and KStart
  KElt_p->KIx = KElt_p->KStart = 0;
  FixUpElt(KElt_p);
}