1 /////////////////////////////////////////////////////////////////////////////
2 // einspline: a library for creating and evaluating B-splines //
3 // Copyright (C) 2007 Kenneth P. Esler, Jr. //
4 // //
5 // This program is free software; you can redistribute it and/or modify //
6 // it under the terms of the GNU General Public License as published by //
7 // the Free Software Foundation; either version 2 of the License, or //
8 // (at your option) any later version. //
9 // //
10 // This program is distributed in the hope that it will be useful, //
11 // but WITHOUT ANY WARRANTY; without even the implied warranty of //
12 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
13 // GNU General Public License for more details. //
14 // //
15 // You should have received a copy of the GNU General Public License //
16 // along with this program; if not, write to the Free Software //
17 // Foundation, Inc., 51 Franklin Street, Fifth Floor, //
18 // Boston, MA 02110-1301 USA //
19 /////////////////////////////////////////////////////////////////////////////
20
21 #ifndef NUBSPLINE_EVAL_STD_Z_H
22 #define NUBSPLINE_EVAL_STD_Z_H
23
24 #include <math.h>
25 #include <stdio.h>
26 #include "nubspline_structs.h"
27
28 /************************************************************/
29 /* 1D single-precision, real evaulation functions */
30 /************************************************************/
31
32 /* Value only */
33 inline void
eval_NUBspline_1d_z(NUBspline_1d_z * restrict spline,double x,complex_double * restrict val)34 eval_NUBspline_1d_z (NUBspline_1d_z * restrict spline,
35 double x, complex_double* restrict val)
36 {
37 double bfuncs[4];
38 int i = get_NUBasis_funcs_d (spline->x_basis, x, bfuncs);
39 complex_double* restrict coefs = spline->coefs;
40 *val = (coefs[i+0]*bfuncs[0] +coefs[i+1]*bfuncs[1] +
41 coefs[i+2]*bfuncs[2] +coefs[i+3]*bfuncs[3]);
42 }
43
44 /* Value and first derivative */
45 inline void
eval_NUBspline_1d_z_vg(NUBspline_1d_z * restrict spline,double x,complex_double * restrict val,complex_double * restrict grad)46 eval_NUBspline_1d_z_vg (NUBspline_1d_z * restrict spline, double x,
47 complex_double* restrict val, complex_double* restrict grad)
48 {
49 double bfuncs[4], dbfuncs[4];
50 int i = get_NUBasis_dfuncs_d (spline->x_basis, x, bfuncs, dbfuncs);
51 complex_double* restrict coefs = spline->coefs;
52 *val = (coefs[i+0]* bfuncs[0] + coefs[i+1]* bfuncs[1] +
53 coefs[i+2]* bfuncs[2] + coefs[i+3]* bfuncs[3]);
54 *grad = (coefs[i+0]*dbfuncs[0] + coefs[i+1]*dbfuncs[1] +
55 coefs[i+2]*dbfuncs[2] + coefs[i+3]*dbfuncs[3]);
56 }
57
58 /* Value, first derivative, and second derivative */
59 inline void
eval_NUBspline_1d_z_vgl(NUBspline_1d_z * restrict spline,double x,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict lapl)60 eval_NUBspline_1d_z_vgl (NUBspline_1d_z * restrict spline, double x,
61 complex_double* restrict val, complex_double* restrict grad,
62 complex_double* restrict lapl)
63 {
64 double bfuncs[4], dbfuncs[4], d2bfuncs[4];
65 int i = get_NUBasis_d2funcs_d (spline->x_basis, x, bfuncs, dbfuncs, d2bfuncs);
66 complex_double* restrict coefs = spline->coefs;
67 *val = (coefs[i+0]* bfuncs[0] + coefs[i+1]* bfuncs[1] +
68 coefs[i+2]* bfuncs[2] + coefs[i+3]* bfuncs[3]);
69 *grad = (coefs[i+0]* dbfuncs[0] + coefs[i+1]* dbfuncs[1] +
70 coefs[i+2]* dbfuncs[2] + coefs[i+3]* dbfuncs[3]);
71 *lapl = (coefs[i+0]*d2bfuncs[0] + coefs[i+1]*d2bfuncs[1] +
72 coefs[i+2]*d2bfuncs[2] + coefs[i+3]*d2bfuncs[3]);
73
74 }
75
76 inline void
eval_NUBspline_1d_z_vgh(NUBspline_1d_z * restrict spline,double x,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict hess)77 eval_NUBspline_1d_z_vgh (NUBspline_1d_z * restrict spline, double x,
78 complex_double* restrict val, complex_double* restrict grad,
79 complex_double* restrict hess)
80 {
81 eval_NUBspline_1d_z_vgl (spline, x, val, grad, hess);
82 }
83
84 /************************************************************/
85 /* 2D single-precision, real evaulation functions */
86 /************************************************************/
87
88 /* Value only */
89 inline void
eval_NUBspline_2d_z(NUBspline_2d_z * restrict spline,double x,double y,complex_double * restrict val)90 eval_NUBspline_2d_z (NUBspline_2d_z * restrict spline,
91 double x, double y, complex_double* restrict val)
92 {
93 double a[4], b[4];
94 int ix = get_NUBasis_funcs_d (spline->x_basis, x, a);
95 int iy = get_NUBasis_funcs_d (spline->y_basis, y, b);
96
97 complex_double* restrict coefs = spline->coefs;
98
99 int xs = spline->x_stride;
100 #define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
101 *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
102 a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
103 a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
104 a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
105 #undef C
106
107 }
108
109
110 /* Value and gradient */
111 inline void
eval_NUBspline_2d_z_vg(NUBspline_2d_z * restrict spline,double x,double y,complex_double * restrict val,complex_double * restrict grad)112 eval_NUBspline_2d_z_vg (NUBspline_2d_z * restrict spline,
113 double x, double y,
114 complex_double* restrict val, complex_double* restrict grad)
115 {
116 double a[4], b[4], da[4], db[4];
117 int ix = get_NUBasis_dfuncs_d (spline->x_basis, x, a, da);
118 int iy = get_NUBasis_dfuncs_d (spline->y_basis, y, b, db);
119
120 complex_double* restrict coefs = spline->coefs;
121
122 int xs = spline->x_stride;
123 #define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
124 *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
125 a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
126 a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
127 a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
128 grad[0] = (da[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
129 da[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
130 da[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
131 da[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
132 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
133 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
134 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
135 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
136 #undef C
137 }
138
139 /* Value, gradient, and laplacian */
140 inline void
eval_NUBspline_2d_z_vgl(NUBspline_2d_z * restrict spline,double x,double y,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict lapl)141 eval_NUBspline_2d_z_vgl (NUBspline_2d_z * restrict spline,
142 double x, double y, complex_double* restrict val,
143 complex_double* restrict grad, complex_double* restrict lapl)
144 {
145 double a[4], b[4], da[4], db[4], d2a[4], d2b[4];
146 complex_double bc[4];
147 int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
148 int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
149
150 complex_double* restrict coefs = spline->coefs;
151
152 int xs = spline->x_stride;
153 #define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
154 bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
155 bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
156 bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
157 bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
158 *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
159 grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
160 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
161 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
162 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
163 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
164 *lapl = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]+
165 a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
166 a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
167 a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
168 a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
169
170 #undef C
171 }
172
173 /* Value, gradient, and Hessian */
174 inline void
eval_NUBspline_2d_z_vgh(NUBspline_2d_z * restrict spline,double x,double y,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict hess)175 eval_NUBspline_2d_z_vgh (NUBspline_2d_z * restrict spline,
176 double x, double y, complex_double* restrict val,
177 complex_double* restrict grad, complex_double* restrict hess)
178 {
179 double a[4], b[4], da[4], db[4], d2a[4], d2b[4];
180 complex_double bc[4];
181 int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
182 int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
183
184 complex_double* restrict coefs = spline->coefs;
185
186 int xs = spline->x_stride;
187 #define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
188 bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
189 bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
190 bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
191 bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
192 *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
193 grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
194 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
195 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
196 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
197 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
198 hess[0] = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]);
199 hess[1] = (da[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
200 da[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
201 da[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
202 da[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
203 hess[3] = (a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
204 a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
205 a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
206 a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
207 hess[2] = hess[1];
208
209 #undef C
210 }
211
212
213 /************************************************************/
214 /* 3D single-precision, real evaulation functions */
215 /************************************************************/
216
217 /* Value only */
218 inline void
eval_NUBspline_3d_z(NUBspline_3d_z * restrict spline,double x,double y,double z,complex_double * restrict val)219 eval_NUBspline_3d_z (NUBspline_3d_z * restrict spline,
220 double x, double y, double z,
221 complex_double* restrict val)
222 {
223
224 double a[4], b[4], c[4];
225 int ix = get_NUBasis_funcs_d (spline->x_basis, x, a);
226 int iy = get_NUBasis_funcs_d (spline->y_basis, y, b);
227 int iz = get_NUBasis_funcs_d (spline->z_basis, z, c);
228 complex_double* restrict coefs = spline->coefs;
229
230 int xs = spline->x_stride;
231 int ys = spline->y_stride;
232 #define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
233 *val = (a[0]*(b[0]*(P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3])+
234 b[1]*(P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3])+
235 b[2]*(P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3])+
236 b[3]*(P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]))+
237 a[1]*(b[0]*(P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3])+
238 b[1]*(P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3])+
239 b[2]*(P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3])+
240 b[3]*(P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]))+
241 a[2]*(b[0]*(P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3])+
242 b[1]*(P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3])+
243 b[2]*(P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3])+
244 b[3]*(P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]))+
245 a[3]*(b[0]*(P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3])+
246 b[1]*(P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3])+
247 b[2]*(P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3])+
248 b[3]*(P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3])));
249 #undef P
250
251 }
252
253 /* Value and gradient */
254 inline void
eval_NUBspline_3d_z_vg(NUBspline_3d_z * restrict spline,double x,double y,double z,complex_double * restrict val,complex_double * restrict grad)255 eval_NUBspline_3d_z_vg (NUBspline_3d_z * restrict spline,
256 double x, double y, double z,
257 complex_double* restrict val, complex_double* restrict grad)
258 {
259 double a[4], b[4], c[4], da[4], db[4], dc[4];
260 complex_double cP[16], bcP[4], dbcP[4];
261 int ix = get_NUBasis_dfuncs_d (spline->x_basis, x, a, da);
262 int iy = get_NUBasis_dfuncs_d (spline->y_basis, y, b, db);
263 int iz = get_NUBasis_dfuncs_d (spline->z_basis, z, c, dc);
264 complex_double* restrict coefs = spline->coefs;
265
266 int xs = spline->x_stride;
267 int ys = spline->y_stride;
268 #define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
269 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
270 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
271 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
272 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
273 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
274 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
275 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
276 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
277 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
278 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
279 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
280 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
281 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
282 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
283 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
284 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
285
286 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
287 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
288 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
289 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
290
291 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
292 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
293 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
294 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
295
296 *val = ( a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3]);
297 grad[0] = (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
298 grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
299 grad[2] =
300 (a[0]*(b[0]*(P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3])+
301 b[1]*(P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3])+
302 b[2]*(P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3])+
303 b[3]*(P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]))+
304 a[1]*(b[0]*(P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3])+
305 b[1]*(P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3])+
306 b[2]*(P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3])+
307 b[3]*(P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]))+
308 a[2]*(b[0]*(P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3])+
309 b[1]*(P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3])+
310 b[2]*(P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3])+
311 b[3]*(P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]))+
312 a[3]*(b[0]*(P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3])+
313 b[1]*(P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3])+
314 b[2]*(P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3])+
315 b[3]*(P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3])));
316 #undef P
317
318 }
319
320
321
322 /* Value, gradient, and laplacian */
323 inline void
eval_NUBspline_3d_z_vgl(NUBspline_3d_z * restrict spline,double x,double y,double z,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict lapl)324 eval_NUBspline_3d_z_vgl (NUBspline_3d_z * restrict spline,
325 double x, double y, double z,
326 complex_double* restrict val, complex_double* restrict grad,
327 complex_double* restrict lapl)
328 {
329 double a[4], b[4], c[4], da[4], db[4], dc[4],
330 d2a[4], d2b[4], d2c[4];
331 complex_double cP[16], dcP[16], bcP[4], dbcP[4], d2bcP[4], bdcP[4];
332
333 int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
334 int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
335 int iz = get_NUBasis_d2funcs_d (spline->z_basis, z, c, dc, d2c);
336
337 complex_double* restrict coefs = spline->coefs;
338 int xs = spline->x_stride;
339 int ys = spline->y_stride;
340 #define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
341 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
342 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
343 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
344 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
345 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
346 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
347 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
348 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
349 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
350 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
351 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
352 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
353 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
354 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
355 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
356 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
357
358 dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
359 dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
360 dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
361 dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
362 dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
363 dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
364 dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
365 dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
366 dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
367 dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
368 dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
369 dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
370 dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
371 dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
372 dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
373 dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
374
375 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
376 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
377 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
378 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
379
380 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
381 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
382 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
383 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
384
385 bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
386 bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
387 bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
388 bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
389
390 d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
391 d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
392 d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
393 d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
394
395
396 *val =
397 ( a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3]);
398
399 grad[0] =
400 (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
401 grad[1] =
402 (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
403 grad[2] =
404 (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
405
406 *lapl = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3])
407 + (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]) +
408 (a[0]*(b[0]*(P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3])+
409 b[1]*(P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3])+
410 b[2]*(P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3])+
411 b[3]*(P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]))+
412 a[1]*(b[0]*(P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3])+
413 b[1]*(P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3])+
414 b[2]*(P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3])+
415 b[3]*(P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]))+
416 a[2]*(b[0]*(P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3])+
417 b[1]*(P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3])+
418 b[2]*(P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3])+
419 b[3]*(P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]))+
420 a[3]*(b[0]*(P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3])+
421 b[1]*(P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3])+
422 b[2]*(P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3])+
423 b[3]*(P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3])));
424 #undef P
425
426 }
427
428
429
430
431
432 /* Value, gradient, and Hessian */
433 inline void
eval_NUBspline_3d_z_vgh(NUBspline_3d_z * restrict spline,double x,double y,double z,complex_double * restrict val,complex_double * restrict grad,complex_double * restrict hess)434 eval_NUBspline_3d_z_vgh (NUBspline_3d_z * restrict spline,
435 double x, double y, double z,
436 complex_double* restrict val, complex_double* restrict grad, complex_double* restrict hess)
437 {
438 double a[4], b[4], c[4], da[4], db[4], dc[4],
439 d2a[4], d2b[4], d2c[4];
440 complex_double cP[16], dcP[16], d2cP[16], bcP[4], dbcP[4],
441 d2bcP[4], dbdcP[4], bd2cP[4], bdcP[4];
442 int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
443 int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
444 int iz = get_NUBasis_d2funcs_d (spline->z_basis, z, c, dc, d2c);
445
446 int xs = spline->x_stride;
447 int ys = spline->y_stride;
448 complex_double* restrict coefs = spline->coefs;
449 #define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
450 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
451 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
452 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
453 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
454 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
455 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
456 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
457 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
458 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
459 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
460 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
461 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
462 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
463 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
464 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
465 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
466
467 dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
468 dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
469 dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
470 dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
471 dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
472 dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
473 dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
474 dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
475 dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
476 dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
477 dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
478 dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
479 dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
480 dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
481 dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
482 dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
483
484 d2cP[ 0] = (P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3]);
485 d2cP[ 1] = (P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3]);
486 d2cP[ 2] = (P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3]);
487 d2cP[ 3] = (P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]);
488 d2cP[ 4] = (P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3]);
489 d2cP[ 5] = (P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3]);
490 d2cP[ 6] = (P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3]);
491 d2cP[ 7] = (P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]);
492 d2cP[ 8] = (P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3]);
493 d2cP[ 9] = (P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3]);
494 d2cP[10] = (P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3]);
495 d2cP[11] = (P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]);
496 d2cP[12] = (P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3]);
497 d2cP[13] = (P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3]);
498 d2cP[14] = (P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3]);
499 d2cP[15] = (P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3]);
500
501 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
502 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
503 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
504 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
505
506 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
507 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
508 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
509 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
510
511 bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
512 bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
513 bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
514 bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
515
516 bd2cP[0] = ( b[0]*d2cP[ 0] + b[1]*d2cP[ 1] + b[2]*d2cP[ 2] + b[3]*d2cP[ 3]);
517 bd2cP[1] = ( b[0]*d2cP[ 4] + b[1]*d2cP[ 5] + b[2]*d2cP[ 6] + b[3]*d2cP[ 7]);
518 bd2cP[2] = ( b[0]*d2cP[ 8] + b[1]*d2cP[ 9] + b[2]*d2cP[10] + b[3]*d2cP[11]);
519 bd2cP[3] = ( b[0]*d2cP[12] + b[1]*d2cP[13] + b[2]*d2cP[14] + b[3]*d2cP[15]);
520
521 d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
522 d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
523 d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
524 d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
525
526 dbdcP[0] = ( db[0]*dcP[ 0] + db[1]*dcP[ 1] + db[2]*dcP[ 2] + db[3]*dcP[ 3]);
527 dbdcP[1] = ( db[0]*dcP[ 4] + db[1]*dcP[ 5] + db[2]*dcP[ 6] + db[3]*dcP[ 7]);
528 dbdcP[2] = ( db[0]*dcP[ 8] + db[1]*dcP[ 9] + db[2]*dcP[10] + db[3]*dcP[11]);
529 dbdcP[3] = ( db[0]*dcP[12] + db[1]*dcP[13] + db[2]*dcP[14] + db[3]*dcP[15]);
530
531 *val = a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3];
532 grad[0] = (da[0] *bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
533 grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
534 grad[2] = (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
535 // d2x
536 hess[0] = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3]);
537 // dx dy
538 hess[1] = (da[0]*dbcP[0] + da[1]*dbcP[1] + da[1]*dbcP[1] + da[1]*dbcP[1]);
539 hess[3] = hess[1];
540 // dx dz;
541 hess[2] = (da[0]*bdcP[0] + da[1]*bdcP[1] + da[1]*bdcP[1] + da[1]*bdcP[1]);
542 hess[6] = hess[2];
543 // d2y
544 hess[4] = (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]);
545 // dy dz
546 hess[5] = (a[0]*dbdcP[0] + a[1]*dbdcP[1] + a[2]*dbdcP[2] + a[3]*dbdcP[3]);
547 hess[7] = hess[5];
548 // d2z
549 hess[8] = (a[0]*bd2cP[0] + a[1]*bd2cP[1] + a[2]*bd2cP[2] + a[3]*bd2cP[3]);
550 #undef P
551
552 }
553
554 #endif
555