From 0b8f90db6f06a3ee69e12475df688afa4c5f73c8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= <marek@necada.org>
Date: Mon, 25 Feb 2019 18:11:22 +0200
Subject: [PATCH] Move typedefs from wigner.h to qpms_types.h; new
 qpms_vswf_irot_elem_from_irot3 fun.

Former-commit-id: 0db6bbaade3993108c7227bfae67f5c22ab9df3e
---
 qpms/qpms_cdefs.pxd | 22 +++++++++++-----------
 qpms/qpms_types.h   | 26 ++++++++++++++++++++++++++
 qpms/wigner.c       | 14 +++++++++++++-
 qpms/wigner.h       | 32 ++++++++++++--------------------
 4 files changed, 62 insertions(+), 32 deletions(-)

diff --git a/qpms/qpms_cdefs.pxd b/qpms/qpms_cdefs.pxd
index bc203ca..1606e26 100644
--- a/qpms/qpms_cdefs.pxd
+++ b/qpms/qpms_cdefs.pxd
@@ -37,6 +37,17 @@ cdef extern from "qpms_types.h":
     ctypedef int qpms_lm_t
     ctypedef int qpms_l_t
     ctypedef int qpms_m_t
+    struct qpms_quat_t:
+        cdouble a
+        cdouble b
+    struct qpms_quat4d_t:
+        double c1
+        double ci
+        double cj
+        double ck
+    struct qpms_irot3_t:
+        qpms_quat_t rot
+        short det
     # maybe more if needed
 
 # Point generators from lattices.h
@@ -75,14 +86,6 @@ cdef extern from "lattices.h":
 ctypedef double complex cdouble
 
 cdef extern from "wigner.h":
-    struct qpms_quat_t:
-        cdouble a
-        cdouble b
-    struct qpms_quat4d_t:
-        double c1
-        double ci
-        double cj
-        double ck
     qpms_quat_t qpms_quat_2c_from_4d(qpms_quat4d_t q)
     qpms_quat4d_t qpms_quat_4d_from_2c(qpms_quat_t q)
     qpms_quat_t qpms_quat_mult(qpms_quat_t p, qpms_quat_t q)
@@ -97,9 +100,6 @@ cdef extern from "wigner.h":
     qpms_quat_t qpms_quat_pow(qpms_quat_t q, double exponent)
     cdouble qpms_wignerD_elem(qpms_quat_t q, qpms_l_t l,
                            qpms_m_t mp, qpms_m_t m)
-    struct qpms_irot3_t:
-        qpms_quat_t rot
-        short det
     qpms_irot3_t qpms_irot3_mult(qpms_irot3_t p, qpms_irot3_t q)
     qpms_irot3_t qpms_irot3_pow(qpms_irot3_t p, int n)
 
diff --git a/qpms/qpms_types.h b/qpms/qpms_types.h
index 34e34f7..6d34e46 100644
--- a/qpms/qpms_types.h
+++ b/qpms/qpms_types.h
@@ -254,6 +254,32 @@ typedef enum {
 	QPMS_COORDS_CART3 = 1024, ///< 3D cartesian.
 } qpms_coord_system_t;
 
+/// Quaternion type.
+/**
+ * Internaly represented as a pair of complex numbers,
+ * \f$ Q_a = Q_1 + iQ_z, Q_b = Q_y + i Q_x\f$.
+ *
+ * Check wigner.h for "methods".
+ */
+typedef struct qpms_quat_t {
+        complex double a, b;
+} qpms_quat_t;
+
+/// Quaternion type as four doubles.
+/** Check wigner.h for "methods".
+ */
+typedef struct qpms_quat4d_t {
+        double c1, ci, cj, ck;
+} qpms_quat4d_t;
+
+/// 3D improper rotations represented as a quaternion and a sign of the determinant.
+/** Check wigner.h for "methods".
+ */
+typedef struct qpms_irot3_t {
+        qpms_quat_t rot; ///< Quaternion representing the rotation part.
+        short det; ///< Determinant of the transformation (valid values are 1 (rotation) or -1 (improper rotation)
+} qpms_irot3_t;
+
 
 #define lmcheck(l,m) assert((l) >= 1 && abs(m) <= (l))
 #endif // QPMS_TYPES
diff --git a/qpms/wigner.c b/qpms/wigner.c
index 779e405..80cf86b 100644
--- a/qpms/wigner.c
+++ b/qpms/wigner.c
@@ -54,4 +54,16 @@ complex double qpms_wignerD_elem(const qpms_quat_t R,
   }
 }
 
-
+complex double qpms_vswf_irot_elem_from_irot3(const_qpms_irot3_t q,
+    qpms_l_t l, qpms_m_t mp, qpms_m_t m, bool pseudo) {
+#ifndef NDEBUG
+  qpms_irot3_checkdet(q);
+#endif
+  complex double res = qpms_wignerD_elem(q.rot, l, mp);
+  if (q.det == -1) {
+    res *= min1pow(l);
+    if (pseudo)
+      res *= -1;
+  }
+  return res;
+}
diff --git a/qpms/wigner.h b/qpms/wigner.h
index b575e68..f7e89e3 100644
--- a/qpms/wigner.h
+++ b/qpms/wigner.h
@@ -8,25 +8,6 @@
 
 #include "tiny_inlines.h"
 
-/// Quaternion type.
-/**
- * Internaly represented as a pair of complex numbers,
- * \f$ Q_a = Q_1 + iQ_z, Q_b = Q_y + i Q_x\f$.
- */
-typedef struct qpms_quat_t {
-	complex double a, b;
-} qpms_quat_t;
-
-/// Quaternion type as four doubles.
-typedef struct qpms_quat4d_t {
-	double c1, ci, cj, ck;
-} qpms_quat4d_t;
-
-/// 3D improper rotations represented as a quaternion and a sign of the determinant.
-typedef struct qpms_irot3_t {
-	qpms_quat_t rot; ///< Quaternion representing the rotation part.
-	short det; ///< Determinant of the transformation (valid values are 1 (rotation) or -1 (improper rotation)
-} qpms_irot3_t;
 
 /// Conversion from the 4*double to the 2*complex quaternion.
 // TODO is this really correct? 
@@ -134,7 +115,7 @@ static inline qpms_quat_t qpms_quat_pow(const qpms_quat_t q, const double expone
 	return qpms_quat_exp(qe);
 }
 
-/// Wigner D matrix element from a rotator quaternion for integer l.
+/// Wigner D matrix element from a rotator quaternion for integer \a l.
 /**
  * The D matrix are calculated using formulae (3), (4), (6), (7) from
  * http://moble.github.io/spherical_functions/WignerDMatrices.html
@@ -142,6 +123,17 @@ static inline qpms_quat_t qpms_quat_pow(const qpms_quat_t q, const double expone
 complex double qpms_wignerD_elem(qpms_quat_t q, qpms_l_t l,
 	       qpms_m_t	mp, qpms_m_t m);
 
+/// A VSWF representation element of the O(3) group.
+/**
+ * TODO more doc.
+ */
+complex double qpms_vswf_irot_elem_from_irot3(
+		const qpms_irot3_t q, ///< The O(3) element in the quaternion representation.
+		qpms_l_t l, qpms_m_t mp, qpms_m_t m,
+		bool pseudo ///< Determines the sign of improper rotations. True for magnetic waves, false otherwise.
+		);
+
+
 static inline int qpms_irot3_checkdet(const qpms_irot3_t p) {
 	if (p.det != 1 && p.det != -1) abort();
 	return 0;