qpms/symmetries.c

   1 #include "symmetries.h"
   2 #include "tiny_inlines.h"
   3 #include "indexing.h"
   4 #include "quaternions.h"
   5 #include "qpms_error.h"
   6
   7 // TODO at some point, maybe support also other norms.
   8 // (perhaps just use qpms_normalisation_t_factor() at the right places)
   9 static inline void check_norm_compat(const qpms_vswf_set_spec_t *s)
  10 {
  11   switch (s->norm & QPMS_NORMALISATION_NORM_BITS) {
  12     case QPMS_NORMALISATION_NORM_POWER:
  13       break;
  14     case QPMS_NORMALISATION_NORM_SPHARM:
  15       break;
  16     default:
  17       QPMS_NOT_IMPLEMENTED("At the moment, only spherical harmonics of spherical harmonics or power normalisations implemented.");
  18   }
  19 }
  20
  21
  22 static inline void ONLY_EIMF_IMPLEMENTED(const qpms_normalisation_t norm)
  23 {
  24         if (norm & QPMS_NORMALISATION_SPHARM_REAL)
  25                 QPMS_NOT_IMPLEMENTED("Support for real spherical harmonics not implemented yet.");
  26 }
  27
  28
  29 // Used in the functions below to ensure memory allocation and checks for bspec validity
  30 static inline complex double *ensure_alloc(complex double *target,
  31     const qpms_vswf_set_spec_t *bspec) {
  32   check_norm_compat(bspec);
  33   const size_t n = bspec->n;
  34   if (target == NULL)
  35     QPMS_CRASHING_MALLOC(target, n * n * sizeof(complex double));
  36   return target;
  37 }
  38
  39
  40 complex double *qpms_zflip_uvswi_dense(
  41     complex double *target,
  42     const qpms_vswf_set_spec_t *bspec)
  43 {
  44   check_norm_compat(bspec);
  45   target = ensure_alloc(target, bspec);
  46   const size_t n = bspec->n;
  47
  48   for (size_t row = 0; row < n; row++) {
  49     qpms_vswf_type_t rt;
  50     qpms_l_t rl;
  51     qpms_m_t rm;
  52     qpms_uvswfi2tmn(bspec->ilist[row], &rt, &rm, &rl);
  53     for (size_t col = 0; col < n; col++) {
  54       qpms_vswf_type_t ct;
  55       qpms_l_t cl;
  56       qpms_m_t cm;
  57       if(qpms_uvswfi2tmn(bspec->ilist[col], &ct, &cm, &cl)) abort();
  58       if (rl == cl && rm == cm && rt == ct)
  59         switch(rt) {
  60           case QPMS_VSWF_ELECTRIC:
  61           case QPMS_VSWF_LONGITUDINAL:
  62             target[n*row + col] = min1pow(cm + cl);
  63             break;
  64           case QPMS_VSWF_MAGNETIC:
  65             target[n*row + col] = -min1pow(cm + cl);
  66             break;
  67           default:
  68             abort();
  69         }
  70       else target[n*row + col] = 0;
  71     }
  72   }
  73   return target;
  74 }
  75
  76 complex double *qpms_yflip_uvswi_dense(
  77     complex double *target,
  78     const qpms_vswf_set_spec_t *bspec)
  79 {
  80   check_norm_compat(bspec);
  81   ONLY_EIMF_IMPLEMENTED(bspec->norm);
  82   target = ensure_alloc(target, bspec);
  83   const size_t n = bspec->n;
  84
  85   for (size_t row = 0; row < n; row++) {
  86     qpms_vswf_type_t rt;
  87     qpms_l_t rl;
  88     qpms_m_t rm;
  89     qpms_uvswfi2tmn(bspec->ilist[row], &rt, &rm, &rl);
  90     for (size_t col = 0; col < n; col++) {
  91       qpms_vswf_type_t ct;
  92       qpms_l_t cl;
  93       qpms_m_t cm;
  94       if(qpms_uvswfi2tmn(bspec->ilist[col], &ct, &cm, &cl)) abort();
  95       if (rl == cl && rm == -cm && rt == ct)
  96         switch(rt) {
  97           case QPMS_VSWF_ELECTRIC:
  98           case QPMS_VSWF_LONGITUDINAL:
  99             target[n*row + col] = min1pow(rm);
 100             break;
 101           case QPMS_VSWF_MAGNETIC:
 102             target[n*row + col] = -min1pow(rm);
 103             break;
 104           default:
 105             abort();
 106         }
 107       else target[n*row + col] = 0;
 108     }
 109   }
 110   return target;
 111 }
 112
 113 complex double *qpms_xflip_uvswi_dense(
 114     complex double *target,
 115     const qpms_vswf_set_spec_t *bspec)
 116 {
 117   check_norm_compat(bspec);
 118   ONLY_EIMF_IMPLEMENTED(bspec->norm);
 119   target = ensure_alloc(target, bspec);
 120   const size_t n = bspec->n;
 121
 122   for (size_t row = 0; row < n; row++) {
 123     qpms_vswf_type_t rt;
 124     qpms_l_t rl;
 125     qpms_m_t rm;
 126     qpms_uvswfi2tmn(bspec->ilist[row], &rt, &rm, &rl);
 127     for (size_t col = 0; col < n; col++) {
 128       qpms_vswf_type_t ct;
 129       qpms_l_t cl;
 130       qpms_m_t cm;
 131       if(qpms_uvswfi2tmn(bspec->ilist[col], &ct, &cm, &cl)) abort();
 132       if (rl == cl && rm == -cm && rt == ct)
 133         switch(rt) {
 134           case QPMS_VSWF_ELECTRIC:
 135           case QPMS_VSWF_LONGITUDINAL:
 136             target[n*row + col] = 1;
 137             break;
 138           case QPMS_VSWF_MAGNETIC:
 139             target[n*row + col] = -1;
 140             break;
 141           default:
 142             abort();
 143         }
 144       else target[n*row + col] = 0;
 145     }
 146   }
 147   return target;
 148 }
 149
 150 // Dense matrix representation of a rotation around the z-axis
 151 complex double *qpms_zrot_uvswi_dense(
 152                 complex double *target, ///< If NULL, a new array is allocated.
 153                 const qpms_vswf_set_spec_t *bspec,
 154                 double phi ///< Rotation angle
 155                 )
 156 {
 157   QPMS_UNTESTED; // not sure about the C.-S. phase. Don't forget documenting it as well.
 158   check_norm_compat(bspec);
 159   ONLY_EIMF_IMPLEMENTED(bspec->norm);
 160   target = ensure_alloc(target, bspec);
 161   const size_t n = bspec->n;
 162
 163   for (size_t row = 0; row < n; row++) {
 164     qpms_vswf_type_t rt;
 165     qpms_l_t rl;
 166     qpms_m_t rm;
 167     qpms_uvswfi2tmn(bspec->ilist[row], &rt, &rm, &rl);
 168     for (size_t col = 0; col < n; col++) {
 169       qpms_vswf_type_t ct;
 170       qpms_l_t cl;
 171       qpms_m_t cm;
 172       if(qpms_uvswfi2tmn(bspec->ilist[col], &ct, &cm, &cl)) abort();
 173       if (rl == cl && rm == cm && rt == ct) // TODO COMPARE WITH PYTHON
 174         target[n*row + col] = cexp(/* - ?*/I * rm * phi);
 175       else target[n*row + col] = 0;
 176     }
 177   }
 178   return target;
 179 }
 180
 181 // Dense matrix representation of a "rational" rotation around the z-axis
 182 /* Just for convenience. Corresponds to the angle \f$ \phi = 2\piw/N \f$.
 183  */
 184 complex double *qpms_zrot_rational_uvswi_dense(
 185                 complex double *target, ///< If NULL, a new array is allocated.
 186                 const qpms_vswf_set_spec_t *bspec,
 187                 int N,
 188                 int w
 189 )
 190 {
 191   double phi = 2 * M_PI * w / N;
 192   return qpms_zrot_uvswi_dense(target, bspec, phi);
 193 }
 194
 195 complex double *qpms_irot3_uvswfi_dense(
 196     complex double *target,
 197     const qpms_vswf_set_spec_t *bspec,
 198     const qpms_irot3_t t)
 199 {
 200   QPMS_UNTESTED; // not sure about the C.-S. phase. Don't forget documenting it as well.
 201   check_norm_compat(bspec);
 202   ONLY_EIMF_IMPLEMENTED(bspec->norm);
 203   target = ensure_alloc(target, bspec);
 204   const size_t n = bspec->n;
 205
 206   for (size_t row = 0; row < n; row++) {
 207     qpms_vswf_type_t rt;
 208     qpms_l_t rl;
 209     qpms_m_t rm;
 210     qpms_uvswfi2tmn(bspec->ilist[row], &rt, &rm, &rl);
 211     for (size_t col = 0; col < n; col++) {
 212       qpms_vswf_type_t ct;
 213       qpms_l_t cl;
 214       qpms_m_t cm;
 215       if(qpms_uvswfi2tmn(bspec->ilist[col], &ct, &cm, &cl)) abort();
 216       if (rl == cl && rt == ct)
 217         // TODO qpms_vswf_irot_elem_from_irot3 might be slow and not too accurate for large l
 218         target[n*row + col] = // Checkme rm and cm order
 219           qpms_vswf_irot_elem_from_irot3(t,
 220               rl, rm /* CHECKME here */, cm /* and here */,
 221               rt == QPMS_VSWF_MAGNETIC);
 222       else target[n*row + col] = 0;
 223     }
 224   }
 225   return target;
 226 }
 227
 228 size_t qpms_zero_roundoff_clean(double *arr, size_t nmemb, double atol) {
 229   size_t changed = 0;
 230   for(size_t i = 0; i < nmemb; ++i)
 231     if(fabs(arr[i]) <= atol) {
 232       arr[i] = 0;
 233       ++changed;
 234     }
 235   return changed;
 236 }
 237
 238 size_t qpms_czero_roundoff_clean(complex double *arr, size_t nmemb, double atol) {
 239   size_t changed = 0;
 240   for(size_t i = 0; i < nmemb; ++i) {
 241     if(fabs(creal(arr[i])) <= atol) {
 242       arr[i] = I*cimag(arr[i]);
 243       ++changed;
 244     }
 245     if(fabs(cimag(arr[i])) <= atol) {
 246       arr[i] = creal(arr[i]);
 247       ++changed;
 248     }
 249   }
 250 }
 251