1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
# Copyright (c) 2012, Jaydeep P. Bardhan
# Copyright (c) 2012, Matthew G. Knepley
# Copyright (c) 2014, Janani Padmanabhan
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification,
# are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
# CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
# INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
# OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
# OF SUCH DAMAGE.
import cython
cimport sf_error
from libc.math cimport sqrt, fabs, pow
from libc.stdlib cimport malloc, free
from numpy.math cimport NAN, PI
cdef extern from "lapack_defs.h":
void c_dstevr(char *jobz, char *range, int *n, double *d, double *e,
double *vl, double *vu, int *il, int *iu, double *abstol,
int *m, double *w, double *z, int *ldz, int *isuppz,
double *work, int *lwork, int *iwork, int *liwork, int *info) nogil
@cython.wraparound(False)
@cython.boundscheck(False)
@cython.cdivision(True)
cdef inline double* lame_coefficients(double h2, double k2, int n, int p,
void **bufferp, double signm,
double signn) nogil:
if n < 0:
sf_error.error("ellip_harm", sf_error.ARG, "invalid value for n")
return NULL
if p < 1 or p > 2*n + 1:
sf_error.error("ellip_harm", sf_error.ARG, "invalid value for p")
return NULL
if fabs(signm) != 1 or fabs(signn) != 1:
sf_error.error("ellip_harm", sf_error.ARG, "invalid signm or signn")
return NULL
cdef double s2, alpha, beta, gamma, lamba_romain, pp, psi, t1, tol, vl, vu
cdef int r, tp, j, size, i, info, lwork, liwork, c, iu
cdef char t
r = n/2
alpha = h2
beta = k2 - h2
gamma = alpha - beta
if p - 1 < r + 1:
t, tp, size = 'K', p, r + 1
elif p - 1 < (n - r) + (r + 1):
t, tp, size = 'L', p - (r + 1), n - r
elif p - 1 < (n - r) + (n - r) + (r + 1):
t, tp, size = 'M', p - (n - r) - (r + 1), n - r
elif p - 1 < 2*n + 1:
t, tp, size = 'N', p - (n - r) - (n - r) - (r + 1), r
lwork = 60*size
liwork = 30*size
tol = 0.0
vl = 0
vu = 0
cdef void *buffer = malloc((sizeof(double)*(7*size + lwork))
+ (sizeof(int)*(2*size + liwork)))
bufferp[0] = buffer
if not buffer:
sf_error.error("ellip_harm", sf_error.NO_RESULT, "failed to allocate memory")
return NULL
cdef double *g = <double *>buffer
cdef double *d = g + size
cdef double *f = d + size
cdef double *ss = f + size
cdef double *w = ss + size
cdef double *dd = w + size
cdef double *eigv = dd + size
cdef double *work = eigv + size
cdef int *iwork = <int *>(work + lwork)
cdef int *isuppz = iwork + liwork
if t == 'K':
for j in range(0, r + 1):
g[j] = (-(2*j + 2)*(2*j + 1)*beta)
if n%2:
f[j] = (-alpha*(2*(r- (j + 1)) + 2)*(2*((j + 1) + r) + 1))
d[j] = ((2*r + 1)*(2*r + 2) - 4*j*j)*alpha + (2*j + 1)*(2*j + 1)*beta
else:
f[j] = (-alpha*(2*(r - (j + 1)) + 2)*(2*(r + (j + 1)) - 1))
d[j] = 2*r*(2*r + 1)*alpha - 4*j*j*gamma
elif t == 'L':
for j in range(0, n - r):
g[j] = (-(2*j + 2)*(2*j + 3)*beta)
if n%2:
f[j] = (-alpha*(2*(r- (j + 1)) + 2)*(2*((j + 1) + r) + 1))
d[j] = (2*r + 1)*(2*r + 2)*alpha - (2*j + 1)*(2*j + 1)*gamma
else:
f[j] = (-alpha*(2*(r - (j + 1)))*(2*(r+(j + 1)) + 1))
d[j] = (2*r*(2*r + 1) - (2*j + 1)*(2*j + 1))*alpha + (2*j + 2)*(2*j + 2)*beta
elif t == 'M':
for j in range(0, n - r):
g[j] = (-(2*j + 2)*(2*j + 1)*beta)
if n%2:
f[j] = (-alpha*(2*(r - (j + 1)) + 2)*(2*((j + 1) + r) + 1))
d[j] = ((2*r + 1)*(2*r + 2) - (2*j + 1)*(2*j + 1))*alpha + 4*j*j*beta
else:
f[j] = (-alpha*(2*(r - (j + 1)))*(2*(r+(j + 1)) + 1))
d[j] = 2*r*(2*r + 1)*alpha - (2*j + 1)*(2*j + 1)*gamma
elif t == 'N':
for j in range(0, r):
g[j] = (-(2*j + 2)*(2*j + 3)*beta)
if n%2:
f[j] = (-alpha*(2*(r- (j + 1)))*(2*((j + 1) + r) + 3))
d[j] = (2*r + 1)*(2*r + 2)*alpha - (2*j + 2)*(2*j + 2)*gamma
else:
f[j] = (-alpha*(2*(r - (j + 1)))*(2*(r+(j + 1)) + 1))
d[j] = 2*r*(2*r + 1)*alpha - (2*j + 2)*(2*j +2)*alpha + (2*j + 1)*(2*j + 1)*beta
for i in range(0, size):
if i == 0:
ss[i] = 1
else:
ss[i] = sqrt(g[i - 1]/f[i - 1])*ss[i - 1]
for i in range(0, size-1):
dd[i] = g[i]*ss[i]/ss[i+1]
c_dstevr("V", "I", &size, d, dd, &vl, &vu, &tp, &tp, &tol, &c, w, eigv,
&size, isuppz, work, &lwork, iwork, &liwork, &info)
if info != 0:
sf_error.error("ellip_harm", sf_error.NO_RESULT, "failed to allocate memory")
return NULL
for i in range(0, size):
eigv[i] /= ss[i]
for i in range(0, size):
eigv[i] = eigv[i]/(eigv[size - 1]/pow(-h2, size - 1))
return eigv
@cython.wraparound(False)
@cython.boundscheck(False)
@cython.cdivision(True)
cdef inline double ellip_harm_eval(double h2, double k2, int n, int p,
double s, double *eigv, double signm,
double signn) nogil:
cdef int size, tp, r, j
cdef double s2, pp, lambda_romain, psi
s2 = s*s
r = n/2
if p - 1 < r + 1:
size, psi = r + 1, pow(s, n - 2*r)
elif p - 1 < (n - r) + (r + 1):
size, psi = n - r, pow(s, 1 - n + 2*r)*signm*sqrt(fabs(s2 - h2))
elif p - 1 < (n - r) + (n - r) + (r + 1):
size, psi = n - r, pow(s, 1 - n + 2*r)*signn*sqrt(fabs(s2 - k2))
elif p - 1 < 2*n + 1:
size, psi = r, pow(s, n - 2*r)*signm*signn*sqrt(fabs((s2 - h2)*(s2 - k2)))
lambda_romain = 1.0 - <double>s2/<double>h2
pp = eigv[size - 1]
for j in range(size - 2, -1, -1):
pp = pp*lambda_romain + eigv[j]
pp = pp*psi
return pp
cdef inline double ellip_harmonic(double h2, double k2, int n, int p, double s,
double signm, double signn) nogil:
cdef double result
cdef double *eigv
cdef void *bufferp
eigv = lame_coefficients(h2, k2, n, p, &bufferp, signm, signn)
if not eigv:
free(bufferp)
return NAN
result = ellip_harm_eval(h2, k2, n, p, s, eigv, signm, signn)
free(bufferp)
return result
|
