Whole translation matrix: it compiles; untested
Former-commit-id: 1465a1385a2f318148d7b3a21cbbf2c0391a13df
This commit is contained in:
Marek Nečada
parent
e2a2100b57
commit
2d88a1ef0d
202
qpms/qpms_c.pyx
202
qpms/qpms_c.pyx
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@ -166,21 +166,29 @@ cdef extern from "translations.h":
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cdouble qpms_trans_single_B_Taylor_ext(int m, int n, int mu, int nu,
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double r, double th, double ph, int r_ge_d, int J) nogil
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struct qpms_trans_calculator:
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pass
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int lMax
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size_t nelem
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cdouble** A_multipliers
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cdouble** B_multipliers
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enum qpms_normalization_t:
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pass
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qpms_trans_calculator* qpms_trans_calculator_init(int lMax, int nt) # should be qpms_normalization_t
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void qpms_trans_calculator_free(qpms_trans_calculator* c)
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cdouble qpms_trans_calculator_get_A_ext(const qpms_trans_calculator* c,
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int m, int n, int mu, int nu, double kdlj_r, double kdlj_th, double kdlj_phi,
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int r_ge_d, int J)
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int r_ge_d, int J) nogil
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cdouble qpms_trans_calculator_get_B_ext(const qpms_trans_calculator* c,
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int m, int n, int mu, int nu, double kdlj_r, double kdlj_th, double kdlj_phi,
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int r_ge_d, int J)
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int r_ge_d, int J) nogil
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int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator* c,
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cdouble *Adest, cdouble *Bdest,
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int m, int n, int mu, int nu, double kdlj_r, double kdlj_th, double kdlj_phi,
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int r_ge_d, int J)
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int r_ge_d, int J) nogil
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int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
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cdouble *Adest, cdouble *Bdest,
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size_t deststride, size_t srcstride,
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double kdlj_r, double kdlj_theta, double kdlj_phi,
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int r_ge_d, int J) nogil
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@ -436,6 +444,20 @@ trans_calculator_get_AB_loop_funcs[0] = trans_calculator_loop_E_C_DD_iiiidddii_A
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cdef void *trans_calculator_get_AB_elementwise_funcs[1]
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trans_calculator_get_AB_elementwise_funcs[0] = <void *>qpms_trans_calculator_get_AB_p_ext
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'''
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cdef extern from "numpy/ndarrayobject.h":
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struct PyArrayInterface:
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int itemsize
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np.npy_uintp *shape
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np.npy_uintp *strides
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void *data
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'''
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from libc.stdlib cimport malloc, free, calloc, abort
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cdef class trans_calculator:
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cdef qpms_trans_calculator* c
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cdef trans_calculator_get_X_data_t get_A_data[1]
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@ -509,6 +531,178 @@ cdef class trans_calculator:
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qpms_trans_calculator_free(self.c)
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# TODO Reference counts to get_A, get_B, get_AB?
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def lMax(self):
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return self.c[0].lMax
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def nelem(self):
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return self.c[0].nelem
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def get_AB_arrays(self, r, theta, phi, r_ge_d, int J,
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destaxis=None, srcaxis=None, expand=True):
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"""
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Returns arrays of translation coefficients, inserting two new nelem-sized axes
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(corresponding to the destination and source axes of the translation matrix,
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respectively).
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By default (expand==True), it inserts the new axes. or it can be provided with
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the resulting shape (with the corresponding axes dimensions equal to one).
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The provided axes positions are for the resulting array.
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If none axis positions are provided, destaxis and srcaxis will be the second-to-last
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and last, respectively.
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"""
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# TODO CHECK (and try to cast) INPUT ARRAY TYPES (now is done)
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# BIG FIXME: make skalars valid arguments, now r, theta, phi, r_ge_d have to be ndarrays
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cdef:
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int daxis, saxis, smallaxis, bigaxis, reslen, longest_axis, i, j, d, ax, errval
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np.npy_intp sstride, dstride, longi, longstride
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int *local_indices
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int *innerloop_shape
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char *r_p
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char *theta_p
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char *phi_p
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char *r_ge_d_p
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char *a_p
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char *b_p
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# Process the array shapes
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baseshape = np.broadcast.shape(r,theta,phi,r_ge_d)
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if not expand:
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reslen = len(baseshape)
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if reslen < 2:
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raise ValueError('Translation matrix arrays must have at least 2 dimensions!')
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daxis = (reslen-2) if destaxis is None else destaxis
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saxis = (reslen-1) if srcaxis is None else srcaxis
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if daxis < 0:
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daxis = reslen + daxis
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if saxis < 0:
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saxis = reslen + saxis
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if daxis < 0 or saxis < 0 or daxis >= reslen or saxis >= reslen or daxis == saxis:
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raise ValueError('invalid axes provided (destaxis = %d, srcaxis = %d, # of axes: %d'
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% (daxis, saxis, reslen))
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if baseshape[daxis] != 1 or baseshape[saxis] != 1:
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raise ValueError('dimension mismatch (input argument dimensions have to be 1 both at'
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'destaxis (==%d) and srcaxis (==%d) but are %d and %d' %
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(daxis, saxis, baseshape[daxis], baseshape[saxis]))
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resultshape = list(baseshape)
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else:
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reslen = len(baseshape)+2
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if destaxis is None:
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daxis = -2
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if srcaxis is None:
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saxis = -1
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if daxis < 0:
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daxis = reslen + daxis
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if saxis < 0:
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saxis = reslen + saxis
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if daxis < 0 or saxis < 0 or daxis >= reslen or saxis >= reslen or daxis == saxis:
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raise ValueError('invalid axes provided') # TODO better error formulation
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resultshape = list(baseshape)
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if daxis > saxis:
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smallaxis = saxis
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bigaxis = daxis
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else:
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smallaxis = daxis
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bixagis = saxis
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resultshape.insert(smallaxis,1)
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resultshape.insert(bigaxis,1)
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r = np.expand_dims(np.expand_dims(r.astype(np.float_, copy=False), smallaxis), bigaxis)
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theta = np.expand_dims(np.expand_dims(theta.astype(np.float_, copy=False), smallaxis), bigaxis)
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phi = np.expand_dims(np.expand_dims(phi.astype(np.float_, copy=False), smallaxis), bigaxis)
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r_ge_d = np.expand_dims(np.expand_dims(r_ge_d(np.bool_, copy=False), smallaxis), bigaxis)
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longestaxis = 0
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# FIxME: the whole thing with longest_axis will fail if none is longer than 1
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for i in range(reslen):
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if resultshape[i] > resultshape[longest_axis]:
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longestaxis = i
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innerloop_shape = <int *> malloc(reslen * sizeof(int))
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if innerloop_shape == NULL:
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abort()
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for i in range(reslen):
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innerloop_shape[i] = resultshape[i]
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innerloop_shape[longest_axis] = 1 # longest axis will be iterated in the outer (parallelized) loop. Therefore, longest axis, together with saxis and daxis, will not be iterated in the inner loop
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resultshape[daxis] = self.c[0].nelem
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resultshape[saxis] = self.c[0].nelem
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cdef np.ndarray r_c = np.broadcast_to(r,resultshape)
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cdef np.ndarray theta_c = np.broadcast_to(theta,resultshape)
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cdef np.ndarray phi_c = np.broadcast_to(phi,resultshape)
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cdef np.ndarray r_ge_d_c = np.broadcast_to(r_ge_d, resultshape)
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cdef np.ndarray a = np.empty(resultshape, dtype=complex)
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cdef np.ndarray b = np.empty(resultshape, dtype=complex)
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dstride = a.strides[daxis]
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sstride = a.strides[saxis]
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longstride = a.strides[longest_axis]
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# TODO write this in C (as a function) and parallelize there
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with nogil: #, parallel(): # FIXME rewrite this part in C
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local_indices = <int *> calloc(reslen, sizeof(int))
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if local_indices == NULL: abort()
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for longi in range(a.shape[longest_axis]): # outer loop (to be parallelized)
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# this might be done also in the inverse order, but this is more 'c-contiguous' way of incrementing the indices
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ax = reslen - 1
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while ax >= 0:
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# calculate the correct index/pointer for each array used. This can be further optimized from O(reslen * total size of the result array) to O(total size of the result array), but fick that now
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r_p = r_c.data + r_c.strides[longest_axis] * longi
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theta_p = theta_c.data + theta_c.strides[longest_axis] * longi
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phi_p = phi_c.data + phi_c.strides[longest_axis] * longi
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r_ge_d_p = r_ge_d_c.data + r_ge_d_c.strides[longest_axis] * longi
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a_p = a.data + a.strides[longest_axis] * longi
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b_p = b.data + b.strides[longest_axis] * longi
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for i in range(reslen):
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if i == longest_axis: continue
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r_p += r_c.strides[i] * local_indices[i]
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theta_p += theta_c.strides[i] * local_indices[i]
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phi_p += phi_c.strides[i] * local_indices[i]
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r_ge_d_p += r_ge_d_c.strides[i] * local_indices[i]
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if i == saxis or i == daxis: continue
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a_p += a.strides[i] * local_indices[i]
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b_p += b.strides[i] * local_indices[i]
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# perform the actual task here
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errval = qpms_trans_calculator_get_AB_arrays_ext(self.c,
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<cdouble*>a_p, <cdouble*>b_p,
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dstride // sizeof(cdouble), sstride // sizeof(cdouble),
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(<double*>r_p)[0], (<double*>theta_p)[0], (<double*>phi_p)[0], <int>((<np.npy_bool*>r_ge_d_p)[0]), J)
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if errval: abort()
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# increment the last index 'digit' (ax is now reslen-1; we don't have do-while loop in python)
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local_indices[ax] += 1
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while (local_indices[ax] == innerloop_shape[ax] and ax >= 0): # overflow to the next digit but stop when we reach below the last one
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local_indices[ax] = 0
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ax -= 1
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local_indices[ax] += 1
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if ax >= 0: # did not overflow, get back to the lowest index
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ax = reslen - 1
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for ax in range(a.ndim):
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if (ax == longest_axis or ax == daxis or ax == saxis):
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continue
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free(local_indices)
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free(innerloop_shape)
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# TODO make possible to access the attributes (to show normalization etc)
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@ -48,6 +48,12 @@ int main() {
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cabs(B - B2)/((cabs(B2) < cabs(B)) ? cabs(B2) : cabs(B))
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);
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}
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complex double A,B;
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// Test of zero R
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sph_t kdlj = {0, 1, 2};
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int m = -1, n = 1, mu = -1, nu = 1;
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qpms_trans_calculator_get_AB_p(c,&A,&B,m,n,mu,nu,kdlj,false,3);
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printf("A = %.6e+%.6ej, B = %.6e+%.6ej\n", creal(A),cimag(A),creal(B),cimag(B));
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qpms_trans_calculator_free(c);
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}
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@ -64,102 +64,102 @@ int qpms_sph_bessel_array(qpms_bessel_t typ, int lmax, double x, complex double
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complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) { // TODO make J enum
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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double costheta = cos(kdlj.theta);
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int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
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// N.B. -m !!!!!!
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double a1q[qmax+1];
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int err;
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gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
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double a1q0 = a1q[0];
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if (err) abort();
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int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
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// N.B. -m !!!!!!
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double a1q[qmax+1];
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int err;
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gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
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double a1q0 = a1q[0];
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if (err) abort();
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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int Pp_order = mu-m;
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//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
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assert(p >= abs(Pp_order));
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double a1q_n = a1q[q] / a1q0;
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double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
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if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
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complex double zp = bes[p];
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complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
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sum += summandq;
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}
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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int Pp_order = mu-m;
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//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
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assert(p >= abs(Pp_order));
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double a1q_n = a1q[q] / a1q0;
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double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
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if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
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complex double zp = bes[p];
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complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
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sum += summandq;
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}
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double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
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double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
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complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
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lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
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return (presum / prenormratio) * sum;
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complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
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lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
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return (presum / prenormratio) * sum;
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}
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complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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int err;
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if (mu == nu) {
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for (int q = 0; q <= q2max; ++q)
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a2q[q] = 0;
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a2q0 = 1;
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}
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else {
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gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
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a2q0 = a2q[0];
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}
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gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
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a3q0 = a3q[0];
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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int err;
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if (mu == nu) {
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for (int q = 0; q <= q2max; ++q)
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a2q[q] = 0;
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a2q0 = 1;
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}
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else {
|
||||
gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
|
||||
a2q0 = a2q[0];
|
||||
}
|
||||
gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
|
||||
a3q0 = a3q[0];
|
||||
|
||||
double leg[gsl_sf_legendre_array_n(n+nu+1)];
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
|
||||
complex double bes[n+nu+2];
|
||||
if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bes)) abort();
|
||||
double leg[gsl_sf_legendre_array_n(n+nu+1)];
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
|
||||
complex double bes[n+nu+2];
|
||||
if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bes)) abort();
|
||||
|
||||
complex double sum = 0;
|
||||
for (int q = 0; q <= Qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double a2q_n = a2q[q]/a2q0;
|
||||
double a3q_n = a3q[q]/a3q0;
|
||||
complex double zp_ = bes[p+1];
|
||||
int Pp_order_ = mu-m;
|
||||
//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
|
||||
assert(p+1 >= abs(Pp_order_));
|
||||
double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
|
||||
if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
|
||||
complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
|
||||
-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
|
||||
*min1pow(q) * zp_ * Pp_);
|
||||
sum += summandq;
|
||||
}
|
||||
complex double sum = 0;
|
||||
for (int q = 0; q <= Qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double a2q_n = a2q[q]/a2q0;
|
||||
double a3q_n = a3q[q]/a3q0;
|
||||
complex double zp_ = bes[p+1];
|
||||
int Pp_order_ = mu-m;
|
||||
//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
|
||||
assert(p+1 >= abs(Pp_order_));
|
||||
double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
|
||||
if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
|
||||
complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
|
||||
-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
|
||||
*min1pow(q) * zp_ * Pp_);
|
||||
sum += summandq;
|
||||
}
|
||||
|
||||
double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
|
||||
complex double presum = exp(exponent);
|
||||
presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
|
||||
(4*n)*(n+1)*(n+m+1));
|
||||
double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
|
||||
complex double presum = exp(exponent);
|
||||
presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
|
||||
(4*n)*(n+1)*(n+m+1));
|
||||
|
||||
// Taylor normalisation v2, proven to be equivalent
|
||||
complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
|
||||
// Taylor normalisation v2, proven to be equivalent
|
||||
complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
|
||||
|
||||
return (presum / prenormratio) * sum;
|
||||
return (presum / prenormratio) * sum;
|
||||
}
|
||||
|
||||
complex double qpms_trans_single_A_Taylor_ext(int m, int n, int mu, int nu,
|
||||
|
|
@ -223,9 +223,9 @@ static void qpms_trans_calculator_multipliers_A_Taylor(
|
|||
double a1q0 = a1q[0];
|
||||
|
||||
double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||||
+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||||
+lgamma(n+nu+1) - lgamma(2*(n+nu)+1)) - 0.5*( // ex-prenormratio
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
|
||||
+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||||
+lgamma(n+nu+1) - lgamma(2*(n+nu)+1)) - 0.5*( // ex-prenormratio
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
|
||||
double presum = exp(exponent);
|
||||
presum *= min1pow(m+n) * sqrt((2.*n+1)/(2.*nu+1)) / (4*n);
|
||||
|
||||
|
|
@ -236,7 +236,7 @@ static void qpms_trans_calculator_multipliers_A_Taylor(
|
|||
double a1q_n = a1q[q] / a1q0;
|
||||
// Assuming non_normalized legendre polynomials!
|
||||
double Ppfac = (Pp_order >= 0) ? 1 :
|
||||
min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||||
min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||||
double summandfac = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n;
|
||||
dest[q] = presum * summandfac * Ppfac;
|
||||
// FIXME I might not need complex here
|
||||
|
|
@ -260,7 +260,7 @@ static void qpms_trans_calculator_multipliers_A_Taylor(
|
|||
double a1q_n = a1q[q] / a1q0;
|
||||
//double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
|
||||
//complex double zp = bes[p];
|
||||
dest[q] = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n /* * zp * Pp*/;
|
||||
dest[q] = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n /* * zp * Pp*/;
|
||||
if (Pp_order < 0) dest[q] *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||||
//sum += summandq;
|
||||
}
|
||||
|
|
@ -290,25 +290,25 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
|
|||
double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
|
||||
int err;
|
||||
if (mu == nu) {
|
||||
for (int q = 0; q <= q2max; ++q)
|
||||
a2q[q] = 0;
|
||||
a2q0 = 1;
|
||||
}
|
||||
else {
|
||||
gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
|
||||
a2q0 = a2q[0];
|
||||
}
|
||||
gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
|
||||
a3q0 = a3q[0];
|
||||
for (int q = 0; q <= q2max; ++q)
|
||||
a2q[q] = 0;
|
||||
a2q0 = 1;
|
||||
}
|
||||
else {
|
||||
gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
|
||||
a2q0 = a2q[0];
|
||||
}
|
||||
gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
|
||||
a3q0 = a3q[0];
|
||||
|
||||
double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3)) - 0.5 * (
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)
|
||||
-lgamma(nu+mu+1));
|
||||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)
|
||||
-lgamma(nu+mu+1));
|
||||
complex double presum = exp(exponent);
|
||||
presum *= I * (min1pow(m+n) *sqrt((2.*n+1)/(2.*nu+1)) / (
|
||||
(4*n)*(n+1)*(n+m+1)));
|
||||
(4*n)*(n+1)*(n+m+1)));
|
||||
|
||||
for (int q = 0; q <= Qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
|
|
@ -367,8 +367,8 @@ qpms_trans_calculator
|
|||
qpms_y2mn_p(y,&m,&n);
|
||||
qpms_y2mn_p(yu,&mu,&nu);
|
||||
qmaxsum += 1 + (
|
||||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||||
= gaunt_q_max(-m,n,mu,nu));
|
||||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||||
= gaunt_q_max(-m,n,mu,nu));
|
||||
}
|
||||
c->A_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
|
||||
// calculate multiplier beginnings
|
||||
|
|
@ -382,7 +382,7 @@ qpms_trans_calculator
|
|||
qpms_y2mn_p(y, &m, &n);
|
||||
qpms_y2mn_p(yu, &mu, &nu);
|
||||
qpms_trans_calculator_multipliers_A(normalization,
|
||||
c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||||
c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||||
}
|
||||
|
||||
qmaxsum = 0;
|
||||
|
|
@ -392,8 +392,8 @@ qpms_trans_calculator
|
|||
qpms_y2mn_p(y,&m,&n);
|
||||
qpms_y2mn_p(yu,&mu,&nu);
|
||||
qmaxsum += 1 + (
|
||||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||||
= gaunt_q_max(-m,n+1,mu,nu));
|
||||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||||
= gaunt_q_max(-m,n+1,mu,nu));
|
||||
}
|
||||
c->B_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
|
||||
// calculate multiplier beginnings
|
||||
|
|
@ -407,41 +407,50 @@ qpms_trans_calculator
|
|||
qpms_y2mn_p(y, &m, &n);
|
||||
qpms_y2mn_p(yu, &mu, &nu);
|
||||
qpms_trans_calculator_multipliers_B(normalization,
|
||||
c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||||
c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||||
}
|
||||
|
||||
free(qmaxes);
|
||||
return c;
|
||||
}
|
||||
|
||||
complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
|
||||
static inline complex double qpms_trans_calculator_get_A_precalcbuf(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J,
|
||||
complex double *bessel_buf, double *legendre_buf) {
|
||||
const complex double *bessel_buf, const double *legendre_buf) {
|
||||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||||
size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
|
||||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||||
complex double sum = 0;
|
||||
for(size_t q = 0; q <= qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
|
||||
complex double zp = bessel_buf[p];
|
||||
complex double multiplier = c->A_multipliers[i][q];
|
||||
sum += Pp * zp * multiplier;
|
||||
}
|
||||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||||
return sum * eimf;
|
||||
}
|
||||
|
||||
complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J,
|
||||
complex double *bessel_buf, double *legendre_buf) {
|
||||
// This functions gets preallocated memory for bessel and legendre functions, but computes them itself
|
||||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
|
||||
// TODO warn?
|
||||
return NAN+I*NAN;
|
||||
|
||||
switch(c->normalization) {
|
||||
case QPMS_NORMALIZATION_TAYLOR:
|
||||
{
|
||||
double costheta = cos(kdlj.theta);
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,legendre_buf)) abort();
|
||||
if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bessel_buf)) abort();
|
||||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||||
size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
|
||||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||||
complex double sum = 0;
|
||||
for(size_t q = 0; q <= qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
|
||||
complex double zp = bessel_buf[p];
|
||||
complex double multiplier = c->A_multipliers[i][q];
|
||||
sum += Pp * zp * multiplier;
|
||||
}
|
||||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||||
return sum * eimf;
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bessel_buf)) abort();
|
||||
return qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
}
|
||||
break;
|
||||
default:
|
||||
|
|
@ -450,10 +459,30 @@ complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
|
|||
assert(0);
|
||||
}
|
||||
|
||||
complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
|
||||
static inline complex double qpms_trans_calculator_get_B_precalcbuf(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J,
|
||||
complex double *bessel_buf, double *legendre_buf) {
|
||||
const complex double *bessel_buf, const double *legendre_buf) {
|
||||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||||
size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
|
||||
assert(qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||||
complex double sum = 0;
|
||||
for(int q = 0; q <= qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
|
||||
complex double zp_ = bessel_buf[p+1];
|
||||
complex double multiplier = c->B_multipliers[i][q];
|
||||
sum += Pp_ * zp_ * multiplier;
|
||||
}
|
||||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||||
return sum * eimf;
|
||||
}
|
||||
|
||||
complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J,
|
||||
complex double *bessel_buf, double *legendre_buf) {
|
||||
// This functions gets preallocated memory for bessel and legendre functions, but computes them itself
|
||||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
|
||||
// TODO warn?
|
||||
|
|
@ -463,22 +492,10 @@ complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
|
|||
{
|
||||
double costheta = cos(kdlj.theta);
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
if (qpms_sph_bessel_array(J, n+nu+2, kdlj.r, bessel_buf)) abort();
|
||||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||||
size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
|
||||
assert(qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||||
complex double sum = 0;
|
||||
for(int q = 0; q <= qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
|
||||
complex double eimf = cexp(I * kdlj.phi);
|
||||
complex double zp_ = bessel_buf[p+1];
|
||||
complex double multiplier = c->B_multipliers[i][q];
|
||||
sum += Pp_ * zp_ * multiplier;
|
||||
}
|
||||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||||
return sum * eimf;
|
||||
return qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
}
|
||||
break;
|
||||
default:
|
||||
|
|
@ -504,35 +521,12 @@ int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
|
|||
{
|
||||
double costheta = cos(kdlj.theta);
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
if (qpms_sph_bessel_array(J, n+nu+2, kdlj.r, bessel_buf)) abort();
|
||||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||||
size_t Qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
|
||||
assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||||
complex double Bsum = 0;
|
||||
for(int q = 0; q <= Qmax; ++q) {
|
||||
int p = n+nu-2*q;
|
||||
double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
|
||||
complex double eimf = cexp(I * kdlj.phi);
|
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complex double zp_ = bessel_buf[p+1];
|
||||
complex double multiplier = c->B_multipliers[i][q];
|
||||
Bsum += Pp_ * zp_ * multiplier;
|
||||
}
|
||||
|
||||
size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
|
||||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
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complex double Asum = 0;
|
||||
for(size_t q = 0; q <= qmax; ++q) {
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||||
int p = n+nu-2*q;
|
||||
double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
|
||||
complex double zp = bessel_buf[p];
|
||||
complex double multiplier = c->A_multipliers[i][q];
|
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Asum += Pp * zp * multiplier;
|
||||
}
|
||||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||||
|
||||
*Adest = Asum * eimf;
|
||||
*Bdest = Bsum * eimf;
|
||||
*Adest = qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
*Bdest = qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
return 0;
|
||||
}
|
||||
break;
|
||||
|
|
@ -543,6 +537,53 @@ int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
|
|||
}
|
||||
|
||||
|
||||
|
||||
|
||||
int qpms_trans_calculator_get_AB_arrays_buf(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
size_t deststride, size_t srcstride,
|
||||
sph_t kdlj, bool r_ge_d, qpms_bessel_t J,
|
||||
complex double *bessel_buf, double *legendre_buf) {
|
||||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR) {
|
||||
for (size_t i = 0; i < c->nelem; ++i)
|
||||
for (size_t j = 0; j < c->nelem; ++j) {
|
||||
*(Adest + i*srcstride + j*deststride) = NAN+I*NAN;
|
||||
*(Bdest + i*srcstride + j*deststride) = NAN+I*NAN;
|
||||
}
|
||||
// TODO warn? different return value?
|
||||
return 0;
|
||||
}
|
||||
switch(c->normalization) {
|
||||
case QPMS_NORMALIZATION_TAYLOR:
|
||||
{
|
||||
double costheta = cos(kdlj.theta);
|
||||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,2*c->lMax+1,
|
||||
costheta,-1,legendre_buf)) abort();
|
||||
if (qpms_sph_bessel_array(J, 2*c->lMax+2, kdlj.r, bessel_buf)) abort();
|
||||
size_t desti = 0, srci = 0;
|
||||
for (int n = 1; n <= c->nelem; ++n) for (int m = -n; m <= n; ++m) {
|
||||
for (int nu = 1; nu <= c->nelem; ++nu) for (int mu = -nu; mu <= nu; ++mu) {
|
||||
assert(qpms_trans_calculator_index_mnmunu(c,m,n,mu,nu) == desti*c->nelem + srci);
|
||||
*(Adest + deststride * desti + srcstride * srci) =
|
||||
qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
*(Bdest + deststride * desti + srcstride * srci) =
|
||||
qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||||
++srci;
|
||||
}
|
||||
++desti;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
break;
|
||||
default:
|
||||
abort();
|
||||
}
|
||||
assert(0);
|
||||
}
|
||||
|
||||
complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J) {
|
||||
|
|
@ -565,12 +606,26 @@ int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
|
|||
complex double *Adest, complex double *Bdest,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
bool r_ge_d, qpms_bessel_t J) {
|
||||
double leg[gsl_sf_legendre_array_n(n+nu+1)];
|
||||
complex double bes[n+nu+2];
|
||||
double leg[gsl_sf_legendre_array_n(2*c->lMax+1)];
|
||||
complex double bes[2*c->lMax+2];
|
||||
return qpms_trans_calculator_get_AB_buf_p(c,Adest, Bdest,m,n,mu,nu,kdlj,r_ge_d,J,
|
||||
bes,leg);
|
||||
}
|
||||
|
||||
int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
size_t deststride, size_t srcstride,
|
||||
sph_t kdlj, bool r_ge_d, qpms_bessel_t J) {
|
||||
double leg[gsl_sf_legendre_array_n(c->lMax+c->lMax+1)];
|
||||
complex double bes[c->lMax+c->lMax+2];
|
||||
return qpms_trans_calculator_get_AB_arrays_buf(c,
|
||||
Adest, Bdest, deststride, srcstride,
|
||||
kdlj, r_ge_d, J,
|
||||
bes, leg);
|
||||
}
|
||||
|
||||
|
||||
|
||||
complex double qpms_trans_calculator_get_A_ext(const qpms_trans_calculator *c,
|
||||
int m, int n, int mu, int nu,
|
||||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||||
|
|
@ -596,3 +651,13 @@ int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
|
|||
return qpms_trans_calculator_get_AB_p(c,Adest,Bdest,m,n,mu,nu,kdlj,r_ge_d,J);
|
||||
}
|
||||
|
||||
int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
size_t deststride, size_t srcstride,
|
||||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||||
int r_ge_d, int J) {
|
||||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||||
return qpms_trans_calculator_get_AB_arrays(c,Adest,Bdest,deststride,srcstride,
|
||||
kdlj, r_ge_d, J);
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -60,7 +60,6 @@ complex double qpms_trans_calculator_get_B_ext(const qpms_trans_calculator *c,
|
|||
int m, int n, int mu, int nu, double kdlj_r,
|
||||
double kdlj_th, double kdlj_phi, int r_ge_d, int J);
|
||||
|
||||
|
||||
int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
int m, int n, int mu, int nu, sph_t kdlj,
|
||||
|
|
@ -70,5 +69,15 @@ int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
|
|||
int m, int n, int mu, int nu, double kdlj_r,
|
||||
double kdlj_th, double kdlj_phi, int r_ge_d, int J);
|
||||
|
||||
int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
size_t deststride, size_t srcstride,
|
||||
sph_t kdlj, bool r_ge_d, qpms_bessel_t J);
|
||||
int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
|
||||
complex double *Adest, complex double *Bdest,
|
||||
size_t deststride, size_t srcstride,
|
||||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||||
int r_ge_d, int J);
|
||||
|
||||
|
||||
#endif // QPMS_TRANSLATIONS_H
|
||||
|
|
|
|||
Loading…
Reference in New Issue