Infinite periodic system scattered field "bases"

qpms/cyewaldtest.pyx

@@ -5,7 +5,7 @@ import numpy as np
 cdef extern from "ewald.h":
     void ewald3_2_sigma_long_Delta(cdouble *target, double *err,  int maxn, cdouble x, int xbranch, cdouble z)
     void ewald3_2_sigma_long_Delta_series(cdouble *target, double *err,  int maxn, cdouble x, int xbranch, cdouble z)
-    void ewald3_2_sigma_long_Delta_recurrent(cdouble *target, double *err,  int maxn, cdouble x, int xbranch, cdouble z)
+    void ewald3_2_sigma_long_Delta_recurrent(cdouble *target, double *err,  int maxn, cdouble x, int xbranch, cdouble z, bint bigimz)
     int complex_gamma_inc_e(double a, cdouble x, int xbranch, qpms_csf_result *result)
 
 def e32_Delta(int maxn, cdouble x, cdouble z, int xbranch = 0, get_err=True, method='auto'):
@@ -17,7 +17,9 @@ def e32_Delta(int maxn, cdouble x, cdouble z, int xbranch = 0, get_err=True, met
         err_np = np.empty((maxn+1,), order='C')
         err_view = err_np
     if method == 'recurrent':
-        ewald3_2_sigma_long_Delta_recurrent(&target_view[0], &err_view[0] if get_err else NULL, maxn, x, xbranch, z)
+        ewald3_2_sigma_long_Delta_recurrent(&target_view[0], &err_view[0] if get_err else NULL, maxn, x, xbranch, z, False)
+    if method == 'recurrent_bigimz':
+        ewald3_2_sigma_long_Delta_recurrent(&target_view[0], &err_view[0] if get_err else NULL, maxn, x, xbranch, z, True)
     elif method == 'series':
         ewald3_2_sigma_long_Delta_series(&target_view[0], &err_view[0] if get_err else NULL, maxn, x, xbranch, z)
     else:

qpms/qpms_c.pyx

@@ -1036,8 +1036,8 @@ cdef class _ScatteringSystemAtOmegaK:
 
         Returns
         -------
-        array_like of complex, with the same shape as `evalpos`
+        ndarray of complex, with the same shape as `evalpos`
-            Electric field at the positions given in `evalpos`.
+            Electric field at the positions given in `evalpos`, in cartesian coordinates.
         """
         if(btyp != QPMS_HANKEL_PLUS):
             raise NotImplementedError("Only first kind Bessel function-based fields are supported")
@@ -1062,6 +1062,51 @@ cdef class _ScatteringSystemAtOmegaK:
                 results[i,1] = res.y
                 results[i,2] = res.z
         return results.reshape(evalpos.shape)
+
+    def scattered_field_basis(self, evalpos, btyp=QPMS_HANKEL_PLUS):
+        # TODO examples
+        """Evaluate scattered field "basis" (periodic system)
+
+        This function enables the evaluation of "scattered" fields
+        generated by the system for many different excitation 
+        coefficients vectors, without the expensive re-evaluation of the respective
+        translation operators for each excitation coefficient vector.
+
+        Parameters
+        ----------
+        evalpos: array_like of floats and shape (..., 3)
+            Evaluation points in cartesian coordinates.
+
+        Returns
+        ------- 
+        ndarray of complex, with the shape `evalpos.shape[:-1] + (self.fecv_size, 3)`
+            "Basis" fields at the positions given in `evalpos`, in cartesian coordinates.
+        """
+        if(btyp != QPMS_HANKEL_PLUS):
+            raise NotImplementedError("Only first kind Bessel function-based fields are supported")
+        cdef qpms_bessel_t btyp_c = BesselType(btyp)
+        cdef Py_ssize_t fecv_size = self.fecv_size
+        evalpos = np.array(evalpos, dtype=float, copy=False)
+        if evalpos.shape[-1] != 3:
+            raise ValueError("Last dimension of evalpos has to be 3")
+        cdef np.ndarray[double,ndim=2] evalpos_a = evalpos.reshape(-1,3)
+        cdef np.ndarray[complex, ndim=3] results = np.empty((evalpos_a.shape[0], fecv_size, 3), dtype=complex)
+        cdef ccart3_t *res
+        res = <ccart3_t *> malloc(fecv_size*sizeof(ccart3_t))
+        cdef cart3_t pos
+        cdef Py_ssize_t i, j
+        with nogil, wraparound(False), parallel():
+            for i in prange(evalpos_a.shape[0]):
+                pos.x = evalpos_a[i,0]
+                pos.y = evalpos_a[i,1]
+                pos.z = evalpos_a[i,2]
+                qpms_scatsyswk_scattered_field_basis(res, &self.sswk, btyp_c, pos)
+                for j in range(fecv_size):
+                    results[i,j,0] = res[j].x
+                    results[i,j,1] = res[j].y
+                    results[i,j,2] = res[j].z
+        free(res)
+        return results.reshape(evalpos.shape[:-1] + (self.fecv_size, 3))
     
     property fecv_size: 
         def __get__(self): return self.ssw_pyref.ss_pyref.fecv_size

qpms/qpms_cdefs.pxd

@@ -705,6 +705,8 @@ cdef extern from "scatsystem.h":
             const cdouble *f_excitation_vector_full, cart3_t where) nogil
     ccart3_t qpms_scatsyswk_scattered_E(const qpms_scatsys_at_omega_k_t *sswk, qpms_bessel_t btyp,
             const cdouble *f_excitation_vector_full, cart3_t where) nogil
+    qpms_errno_t qpms_scatsyswk_scattered_field_basis(ccart3_t *target, const qpms_scatsys_at_omega_k_t *sswk,
+            qpms_bessel_t btyp, cart3_t where) nogil
     double qpms_ss_adjusted_eta(const qpms_scatsys_t *ss, cdouble wavenumber, const double *wavevector) nogil
 
 

qpms/scatsystem.c

@@ -2186,6 +2186,86 @@ ccart3_t qpms_scatsyswk_scattered_E(const qpms_scatsys_at_omega_k_t *sswk,
   return res;
 }
 
+qpms_errno_t qpms_scatsyswk_scattered_field_basis(
+    ccart3_t *target,
+    const qpms_scatsys_at_omega_k_t *sswk,
+    const qpms_bessel_t btyp,
+    const cart3_t where
+    ) {
+  QPMS_UNTESTED;
+  if (btyp != QPMS_HANKEL_PLUS) 
+    QPMS_NOT_IMPLEMENTED("Only scattered field with first kind Hankel functions currently implemented.");
+  const qpms_scatsys_t *ss = sswk->ssw->ss;
+  if (ss->lattice_dimension != 2)
+    QPMS_NOT_IMPLEMENTED("Only 2D-periodic lattices implemented");
+  //ccart3_t res = {0,0,0};
+  //ccart3_t res_kc = {0,0,0}; // kahan sum compensation
+
+  static const int dipspecn = 3; // We have three basis vectors
+  // bspec containing only electric dipoles
+  const qpms_vswf_set_spec_t dipspec = {
+    .n = dipspecn,
+    .ilist = (qpms_uvswfi_t[]){
+      qpms_tmn2uvswfi(QPMS_VSWF_ELECTRIC, -1, 1),
+      qpms_tmn2uvswfi(QPMS_VSWF_ELECTRIC,  0, 1),
+      qpms_tmn2uvswfi(QPMS_VSWF_ELECTRIC, +1, 1),
+    },
+    .lMax=1, .lMax_M=0, .lMax_N=1, .lMax_L=-1,
+    .capacity=0,
+    .norm = ss->c->normalisation,
+  };
+
+  ccart3_t regdipoles_0[dipspecn]; {
+    const sph_t origin_sph = {.r = 0, .theta = M_PI_2, .phi=0}; // Should work with any theta/phi (TESTWORTHY)
+    csphvec_t regdipoles_0_sph[dipspecn];
+    QPMS_ENSURE_SUCCESS(qpms_uvswf_fill(regdipoles_0_sph, &dipspec,
+          sph2csph(origin_sph), QPMS_BESSEL_REGULAR));
+    for(int i = 0; i < dipspecn; ++i)
+      regdipoles_0[i] = csphvec2ccart(regdipoles_0_sph[i], origin_sph);
+  }
+
+  complex double *s; // Translation matrix
+  QPMS_CRASHING_MALLOC(s, ss->max_bspecn * sizeof(*s) * dipspec.n);
+
+  memset(target, 0, ss->fecv_size * sizeof(*target));
+
+  for (qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
+    const qpms_vswf_set_spec_t *bspec = qpms_ss_bspec_pi(ss, pi);
+    const cart3_t particle_pos = ss->p[pi].pos;
+    //const complex double *particle_cv = cvf + ss->fecv_pstarts[pi];
+
+    const cart3_t origin_cart = {0, 0, 0};
+
+    QPMS_ASSERT(sswk->k[2] == 0); // At least not implemented now
+    QPMS_ASSERT(ss->per.lattice_basis[0].z == 0);
+    QPMS_ASSERT(ss->per.lattice_basis[1].z == 0);
+    
+    // Same choices as in qpms_ss_ppair_W32xy; TODO make it more dynamic
+    const double maxR = sqrt(ss->per.unitcell_volume) * 64;
+    const double maxK = 2048 * 2 * M_PI / maxR;
+
+    QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_e32(
+          ss->c, s, NULL, 
+          &dipspec, 1, bspec, dipspecn,
+          sswk->eta, sswk->ssw->wavenumber,
+          cart3xy2cart2(ss->per.lattice_basis[0]), cart3xy2cart2(ss->per.lattice_basis[1]),
+          cart2_from_double_array(sswk->k), cart3_substract(where, particle_pos) /*CHECKSIGN*/, 
+          maxR, maxK));
+
+    for(size_t i = 0; i < bspec->n; ++i)
+      for(size_t j = 0; j < dipspecn; ++j){
+        target[ss->fecv_pstarts[pi] + i] = ccart3_add(target[ss->fecv_pstarts[pi] + i],
+                                                      ccart3_scale(s[dipspecn*i+j], regdipoles_0[j]));
+        //ccart3_t summand = ccart3_scale(particle_cv[i] * s[dipspecn*i+j], regdipoles_0[j]);
+        //ckahanadd(&(res.x), &(res_kc.x), summand.x);
+        //ckahanadd(&(res.y), &(res_kc.y), summand.y);
+        //ckahanadd(&(res.z), &(res_kc.z), summand.z);
+      }
+  }
+  free(s);
+  return QPMS_SUCCESS;
+}
+
 #if 0
 ccart3_t qpms_scatsys_scattered_E_irrep(const qpms_scatsys_t *ss,
    qpms_iri_t iri, const complex double *cvr, cart3_t where) {

qpms/scatsystem.h

@@ -785,11 +785,24 @@ ccart3_t qpms_scatsysw_scattered_E__alt(
  */
 ccart3_t qpms_scatsyswk_scattered_E(
 		const qpms_scatsys_at_omega_k_t *sswk,
-		qpms_bessel_t typ, ///< Bessel function kind to use (for scattered fields, use QPMS_HANKEL_PLUS).
+		qpms_bessel_t typ, ///< Bessel function kind to use (only QPMS_HANKEL_PLUS is currently supported).
 		const complex double *scatcoeff_full, ///< Full vector of the scattered field coefficients \f$ \wckcout \f$.
 		cart3_t evalpoint ///< A point \f$ \vect r \f$, at which the field is evaluated.
 		);
 
+/// Evaluates "scattered" field basis functions in a periodic system.
+/**
+ *
+ * \see qpms_uvswf_fill() evaluates a set of VSWF basis functions (for finite systems).
+ */
+qpms_errno_t qpms_scatsyswk_scattered_field_basis(
+		ccart3_t *target, ///< Target array of size sswk->ssw->ss->fecv_size
+		const qpms_scatsys_at_omega_k_t *sswk,
+		qpms_bessel_t typ, ///< Bessel function kind to use (only QPMS_HANKEL_PLUS is currently supponted).
+		cart3_t evalpoint ///< A point \f$ \vect r \f$, at which the basis is evaluated.
+		);
+
+
 /// Adjusted Ewadl parameter to avoid high-frequency breakdown.
 // TODO DOC
 double qpms_ss_adjusted_eta(const qpms_scatsys_t *ss, complex double wavenumber, const double wavevector[3]);