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
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
|
# -*- coding: utf-8 -*-
#cython: embedsignature=True, language_level=3
#cython: boundscheck=False, wraparound=False, cdivision=True, initializedcheck=False,
## This is for developping:
## cython: profile=True, warn.undeclared=True, warn.unused=True, warn.unused_result=False, warn.unused_arg=True
#
# Project: Fast Azimuthal Integration
# https://github.com/silx-kit/pyFAI
#
# Copyright (C) 2014-2020 European Synchrotron Radiation Facility, Grenoble, France
#
# Principal author: Zubair Nawaz <zubair.nawaz@gmail.com>
# Jérôme Kieffer (Jerome.Kieffer@ESRF.eu)
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# .
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# .
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
"""Module containing a re-implementation of bi-cubic spline evaluation from
scipy."""
__authors__ = ["Zubair Nawaz", "Jerome Kieffer"]
__contact__ = "Jerome.kieffer@esrf.fr"
__date__ = "15/12/2020"
__status__ = "stable"
__license__ = "MIT"
import numpy
from libc.stdint cimport int32_t
import cython
cimport cython
from cython.parallel import prange
# copied bisplev function from fitpack.bisplev
def bisplev(x, y, tck, dx=0, dy=0):
"""
Evaluate a bivariate B-spline and its derivatives.
Return a rank-2 array of spline function values (or spline derivative
values) at points given by the cross-product of the rank-1 arrays x and
y. In special cases, return an array or just a float if either x or y or
both are floats. Based on BISPEV from FITPACK.
See :func:`bisplrep` to generate the `tck` representation.
See also :func:`splprep`, :func:`splrep`, :func:`splint`, :func:`sproot`,
:func:`splev`, :func:`UnivariateSpline`, :func:`BivariateSpline`
References: [1]_, [2]_, [3]_.
.. [1] Dierckx P. : An algorithm for surface fitting
with spline functions
Ima J. Numer. Anal. 1 (1981) 267-283.
.. [2] Dierckx P. : An algorithm for surface fitting
with spline functions
report tw50, Dept. Computer Science,K.U.Leuven, 1980.
.. [3] Dierckx P. : Curve and surface fitting with splines,
Monographs on Numerical Analysis, Oxford University Press, 1993.
:param ndarray x: Rank-1 arrays specifying the domain over which to evaluate
the spline or its derivative.
:param ndarray y: Rank-1 arrays specifying the domain over which to evaluate
the spline or its derivative.
:param tuple tck: A sequence of length 5 returned by `bisplrep` containing
the knot locations, the coefficients, and the degree of the spline:
[tx, ty, c, kx, ky].
:param int dx: The orders of the partial derivatives in `x`.
This version does not implement derivatives.
:param int dy: The orders of the partial derivatives in `y`.
This version does not implement derivatives.
:rtype: ndarray
:return: The B-spline or its derivative evaluated over the set formed by
the cross-product of `x` and `y`.
"""
cdef:
int kx, ky
float[::1] tx, ty, c, cy_x, cy_y
tx = numpy.ascontiguousarray(tck[0], dtype=numpy.float32)
ty = numpy.ascontiguousarray(tck[1], dtype=numpy.float32)
c = numpy.ascontiguousarray(tck[2], dtype=numpy.float32)
kx = tck[3]
ky = tck[4]
if not (0 <= dx < kx):
raise ValueError("0 <= dx = %d < kx = %d must hold" % (dx, kx))
if not (0 <= dy < ky):
raise ValueError("0 <= dy = %d < ky = %d must hold" % (dy, ky))
x = numpy.atleast_1d(x)
y = numpy.atleast_1d(y)
if (len(x.shape) != 1) or (len(y.shape) != 1):
raise ValueError("First two entries should be rank-1 arrays.")
cy_x = numpy.ascontiguousarray(x, dtype=numpy.float32)
cy_y = numpy.ascontiguousarray(y, dtype=numpy.float32)
z = cy_bispev(tx, ty, c, kx, ky, cy_x, cy_y)
z.shape = len(y), len(x)
# Transpose again afterwards to retrieve a memory-contiguous object
if len(z) > 1:
return z.T
if len(z[0]) > 1:
return z[0]
return z[0][0]
cdef void fpbspl(float[::1]t,
int n,
int k,
float x,
int l,
float[::1] h,
float[::1] hh) nogil:
"""
subroutine fpbspl evaluates the (k+1) non-zero b-splines of
degree k at t(l) <= x < t(l+1) using the stable recurrence
relation of de boor and cox.
TODO: Unused argument 'n' !
"""
cdef int i, j
cdef float f
h[0] = 1.00
for j in range(1, k + 1):
for i in range(j):
hh[i] = h[i]
h[0] = 0.00
for i in range(j):
f = hh[i] / (t[l + i] - t[l + i - j])
h[i] = h[i] + f * (t[l + i] - x)
h[i + 1] = f * (x - t[l + i - j])
cdef void init_w(float[::1] t, int k, float[::1] x, int32_t[::1] lx, float[:, ::1] w) nogil:
"""
Initialize w array for a 1D array
:param t:
:param k: order of the spline
:param x: position of the evaluation
:param w:
"""
cdef:
int i, l1, l2, n, m, j
float arg, tb, te
float[::1] h, hh
tb = t[k]
with gil:
n = t.size
m = x.size
h = numpy.empty(6, dtype=numpy.float32)
hh = numpy.empty(5, dtype=numpy.float32)
te = t[n - k - 1]
l1 = k + 1
l2 = l1 + 1
for i in range(m):
arg = x[i]
if arg < tb:
arg = tb
if arg > te:
arg = te
while not (arg < t[l1] or l1 == (n - k - 1)):
l1 = l2
l2 = l1 + 1
fpbspl(t, n, k, arg, l1, h, hh)
lx[i] = l1 - k - 1
for j in range(k + 1):
w[i, j] = h[j]
cdef cy_bispev(float[::1] tx,
float[::1] ty,
float[::1] c,
int kx,
int ky,
float[::1] x,
float[::1] y):
"""
Actual implementation of bispev in Cython
:param tx: array of float size nx containing position of knots in x
:param ty: array of float size ny containing position of knots in y
"""
cdef:
#int nx = tx.shape[0]
int ny = ty.shape[0]
int mx = x.shape[0]
int my = y.shape[0]
int kx1 = kx + 1
int ky1 = ky + 1
#int nkx1 = nx - kx1
int nky1 = ny - ky1
# initializing scratch space
float[:, ::1] wx = numpy.empty((mx, kx1), dtype=numpy.float32)
float[:, ::1] wy = numpy.empty((my, ky1), dtype=numpy.float32)
int32_t[::1] lx = numpy.empty(mx, dtype=numpy.int32)
int32_t[::1] ly = numpy.empty(my, dtype=numpy.int32)
int i, j, i1, l2, j1
int size_z = mx * my
# initializing z and h
float[::1] z = numpy.zeros(size_z, dtype=numpy.float32)
float sp, err, tmp, a
with nogil:
# cannot be initialized in parallel, why ? segfaults on MacOSX
init_w(tx, kx, x, lx, wx)
init_w(ty, ky, y, ly, wy)
for j in prange(my):
for i in range(mx):
sp = 0.0
err = 0.0
for i1 in range(kx1):
for j1 in range(ky1):
# Implements Kahan summation
l2 = lx[i] * nky1 + ly[j] + i1 * nky1 + j1
a = c[l2] * wx[i, i1] * wy[j, j1] - err
tmp = sp + a
err = (tmp - sp) - a
sp = tmp
z[j * mx + i] += sp
return numpy.asarray(z)
|
