"Basis fields" for finite systems

qpms/qpms_c.pyx

@@ -1066,6 +1066,7 @@ cdef class _ScatteringSystemAtOmegaK:
                 results[i,2] = res.z
         return results.reshape(evalpos.shape)
 
+    @boundscheck(False)
     def scattered_field_basis(self, evalpos, btyp=QPMS_HANKEL_PLUS):
         # TODO examples
         """Evaluate scattered field "basis" (periodic system)
@@ -1237,7 +1238,6 @@ cdef class _ScatteringSystemAtOmega:
 
     @boundscheck(False)
     def scattered_E(self, scatcoeffvector_full, evalpos, blochvector=None, btyp=QPMS_HANKEL_PLUS, bint alt=False): 
-        # FIXME TODO this obviously does not work for periodic systems
         """Evaluate electric field for a given excitation coefficient vector
 
         Parameters
@@ -1288,6 +1288,56 @@ cdef class _ScatteringSystemAtOmega:
                 results[i,2] = res.z
         return results.reshape(evalpos.shape)
 
+    @boundscheck(False)
+    def scattered_field_basis(self, evalpos, blochvector=None, btyp=QPMS_HANKEL_PLUS):
+        # TODO examples
+        """Evaluate scattered field "basis" 
+
+        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.
+        blochvector: array_like or None
+            Bloch vector, must be supplied (non-None) for periodic systems, else None.
+        btyp: BesselType, optional
+            Kind of the waves. Defaults to BesselType.HANKEL_PLUS.
+
+        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_scatsysw_scattered_field_basis(res, self.ssw, 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))
+    
 
 cdef class ScatteringMatrix:
     '''

qpms/qpms_cdefs.pxd

@@ -708,6 +708,10 @@ 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_scatsys_scattered_field_basis(ccart3_t *target, const qpms_scatsys_t *ss,
+            qpms_bessel_t btyp, cdouble wavenumber, cart3_t where) nogil
+    qpms_errno_t qpms_scatsysw_scattered_field_basis(ccart3_t *target, const qpms_scatsys_at_omega_t *ssw,
+            qpms_bessel_t btyp, 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

@@ -2049,6 +2049,38 @@ ccart3_t qpms_scatsysw_scattered_E(const qpms_scatsys_at_omega_t *ssw,
       cvf, where);
 }
 
+qpms_errno_t qpms_scatsys_scattered_field_basis(
+    ccart3_t *target,
+    const qpms_scatsys_t *ss,
+    const qpms_bessel_t btyp,
+    const complex double k,
+    const cart3_t where
+    ) {
+  qpms_ss_ensure_nonperiodic_a(ss, "qpms_scatsyswk_scattered_field_basis()");
+  QPMS_UNTESTED;
+  csphvec_t *vswfs_sph; //Single particle contributions in spherical coordinates
+  QPMS_CRASHING_CALLOC(vswfs_sph, ss->max_bspecn, sizeof(*vswfs_sph));
+
+  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 csph_t kr = sph_cscale(k, cart2sph(
+          cart3_substract(where, particle_pos)));
+    QPMS_ENSURE_SUCCESS(qpms_uvswf_fill(vswfs_sph, bspec, kr, btyp));
+    for(size_t i = 0; i < bspec->n; ++i)
+      target[ss->fecv_pstarts[pi] + i] = csphvec2ccart_csph(vswfs_sph[i], kr);
+  }
+  
+  free(vswfs_sph);
+  return QPMS_SUCCESS;
+}
+
+qpms_errno_t qpms_scatsysw_scattered_field_basis(
+    ccart3_t *target, const qpms_scatsys_at_omega_t *ssw, 
+    const qpms_bessel_t btyp, const cart3_t where) {
+  return qpms_scatsys_scattered_field_basis(target, ssw->ss, btyp, 
+        ssw->wavenumber, where);
+}
 
 #define DIPSPECN 3 // We have three basis vectors
 // Evaluates the regular electric dipole waves in the origin. The returned

qpms/scatsystem.h

@@ -706,7 +706,7 @@ complex double *qpms_scatsys_incident_field_vector_irrep_packed(
  *
  * \return Complex electric field at the point defined by \a evalpoint.
  * 
- * \see qpms_scatsysw_scattered_E()
+ * \see qpms_scatsysw_scattered_E(), qpms_scatsys_scattered_field_basis()
  *
  * \see qpms_scatsyswk_scattered_E() for periodic systems.
  *
@@ -727,7 +727,7 @@ ccart3_t qpms_scatsys_scattered_E(
  *
  * \return Complex electric field at the point defined by \a evalpoint.
  * 
- * \see qpms_scatsys_scattered_E()
+ * \see qpms_scatsys_scattered_E(), qpms_scatsysw_scattered_field_basis()
  *
  * \see qpms_scatsyswk_scattered_E() for periodic systems.
  */
@@ -738,6 +738,43 @@ ccart3_t qpms_scatsysw_scattered_E(
 		cart3_t evalpoint ///< A point \f$ \vect r \f$, at which the field is evaluated.
 		);
 
+/// Evaluates a "basis" for electric field at a given point.
+/**
+ * This function evaluates all the included VSWFs from the particles in the system, evaluated 
+ * at a given point. Taking a linear combination of these with the coefficients \a scattcoeff_full[]
+ * would be equivalent to the result of qpms_scatsys_scattered_E().
+ *
+ * \see qpms_scatsysw_scattered_field_basis()
+ *
+ * \see qpms_scatsyswk_scattered_field_basis() for periodic systems.
+ *
+ */
+qpms_errno_t qpms_scatsys_scattered_field_basis(
+		ccart3_t *target, ///< Target array of length \a ss->fecv_size
+		const qpms_scatsys_t *ss,
+		qpms_bessel_t typ, ///< Bessel function kind to use (for scattered fields, use QPMS_HANKEL_PLUS).
+		complex double wavenumber, ///< Wavenumber of the background medium.
+		cart3_t evalpoint ///< A point \f$ \vect r \f$, at which the field is evaluated.
+		);
+
+/// Evaluates a "basis" for electric field at a given point.
+/**
+ * This function evaluates all the included VSWFs from the particles in the system, evaluated 
+ * at a given point. Taking a linear combination of these with the coefficients \a scattcoeff_full[]
+ * would be equivalent to the result of qpms_scatsysw_scattered_E().
+ *
+ * \see qpms_scatsys_scattered_field_basis()
+ *
+ * \see qpms_scatsyswk_scattered_field_basis() for periodic systems.
+ *
+ */
+qpms_errno_t qpms_scatsysw_scattered_field_basis(
+		ccart3_t *target, ///< Target array of length \a ss->fecv_size
+		const qpms_scatsys_at_omega_t *ssw,
+		qpms_bessel_t typ, ///< Bessel function kind to use (for scattered fields, use QPMS_HANKEL_PLUS).
+		cart3_t evalpoint ///< A point \f$ \vect r \f$, at which the field is evaluated.
+		);
+
 /// Evaluates scattered electric field at a point, given a full vector of scattered field coefficients.
 /**
  * This is an alternative implementation of qpms_scatsys_scattered_E(), and should give the same results