Line data Source code
1 : #include <gmock/gmock.h>
2 : #include <gtest/gtest.h>
3 : #include <cfloat>
4 : #include <cmath>
5 : #include <limits>
6 :
7 : #include "threeterm.hpp"
8 :
9 : #define epsilon DBL_EPSILON
10 : using namespace testing;
11 : using namespace std;
12 :
13 2 : TEST(ThreeTermAnalysisOf,
14 : TaylorSeriesAtNegativeOneRealPoleAtOneWithScalingTenthAlphaOne)
15 : {
16 : // t =-1.0;
17 : // x[0] = 1.0/(1.0-t);
18 :
19 1 : double a{1.0};
20 1 : double time{-1.0};
21 1 : double scale{0.1};
22 : vector<double> coeffs{0.5,
23 : 0.025,
24 : 0.00125,
25 : 6.25e-05,
26 : 3.125e-06,
27 : 1.5625e-07,
28 : 7.8125e-09,
29 : 3.90625e-10,
30 : 1.953125e-11,
31 : 9.765625e-13,
32 : 4.8828125e-14,
33 : 2.44140625e-15,
34 : 1.220703125e-16,
35 : 6.103515625e-18,
36 : 3.0517578125e-19,
37 : 1.52587890625e-20,
38 : 7.62939453125001e-22,
39 : 3.814697265625e-23,
40 : 1.9073486328125e-24,
41 : 9.53674316406251e-26,
42 : 4.76837158203126e-27,
43 : 2.38418579101563e-28,
44 : 1.19209289550781e-29,
45 : 5.96046447753907e-31,
46 : 2.98023223876954e-32,
47 : 1.49011611938477e-33,
48 : 7.45058059692384e-35,
49 : 3.72529029846192e-36,
50 : 1.86264514923096e-37,
51 2 : 9.3132257461548e-39};
52 1 : double rc{0.0}, order{0.0};
53 :
54 1 : double err = threeterm(coeffs, scale, rc, order);
55 :
56 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
57 1 : EXPECT_THAT(rc, DoubleNear(a - time, 9.68115e-14));
58 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.1887e-12));
59 1 : EXPECT_THAT(coeffs.size(), Eq(30));
60 1 : }
61 :
62 2 : TEST(ThreeTermAnalysisOf,
63 : TaylorSeriesAtZeroOneRealPoleAtOneWithScalingTenthAlphaOne)
64 : {
65 : // t = 0.0;
66 : // x[0] = 1.0/(1.0-t);
67 :
68 1 : double a{1.0};
69 1 : double time{0.0};
70 1 : double scale{0.1};
71 : vector<double> coeffs{1, 0.1, 0.01, 0.001, 0.0001, 1e-05, 1e-06, 1e-07,
72 : 1e-08, 1e-09, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15,
73 : 1e-16, 1e-17, 1e-18, 1e-19, 1e-20, 1e-21, 1e-22, 1e-23,
74 2 : 1e-24, 1e-25, 1e-26, 1e-27, 1e-28, 1e-29};
75 1 : double rc{0.0}, order{0.0};
76 :
77 1 : double err = threeterm(coeffs, scale, rc, order);
78 :
79 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
80 1 : EXPECT_THAT(rc, DoubleNear(a - time, 4.44090e-16));
81 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.35448e-14));
82 1 : EXPECT_THAT(coeffs.size(), Eq(30));
83 1 : }
84 :
85 2 : TEST(ThreeTermAnalysisOf,
86 : TaylorSeriesAtPTNineOneRealPoleAtOneWithScalingTenthAlphaOne)
87 : {
88 : // t = 0.9;
89 : // x[0] = 1.0/(1.0-t);
90 :
91 1 : double a{1.0};
92 1 : double time{0.9};
93 1 : double scale{0.1};
94 : vector<double> coeffs{10,
95 : 10,
96 : 10,
97 : 10,
98 : 10,
99 : 10,
100 : 10,
101 : 10,
102 : 10,
103 : 10,
104 : 10,
105 : 10,
106 : 10,
107 : 10,
108 : 10,
109 : 10,
110 : 10,
111 : 10.0000000000001,
112 : 10.0000000000001,
113 : 10.0000000000001,
114 : 10.0000000000001,
115 : 10.0000000000001,
116 : 10.0000000000001,
117 : 10.0000000000001,
118 : 10.0000000000001,
119 : 10.0000000000001,
120 : 10.0000000000001,
121 : 10.0000000000001,
122 : 10.0000000000001,
123 2 : 10.0000000000001};
124 1 : double rc{0.0}, order{0.0};
125 :
126 1 : double err = threeterm(coeffs, scale, rc, order);
127 :
128 1 : EXPECT_THAT(err, DoubleNear(0.0, 8.52652e-14));
129 1 : EXPECT_THAT(rc, DoubleNear(a - time, 8.52652e-14));
130 1 : EXPECT_THAT(order, DoubleNear(1.0, 2.93099e-14));
131 1 : EXPECT_THAT(coeffs.size(), Eq(30));
132 1 : }
133 :
134 2 : TEST(ThreeTermAnalysisOf,
135 : TaylorSeriesAtOnePT0001RealPoleAtOneWithScalingTenthAlphaOne)
136 : {
137 : // t = 1.0001;
138 : // x[0] = 1.0/(1.0-t);
139 :
140 1 : double a{1.0};
141 1 : double time{1.0001};
142 1 : double scale{0.1};
143 : vector<double> coeffs{
144 : -10000.0000000011, 10000000.0000022, -10000000000.0033,
145 : 10000000000004.4, -1.00000000000055e+16, 1.00000000000066e+19,
146 : -1.00000000000077e+22, 1.00000000000088e+25, -1.00000000000099e+28,
147 : 1.0000000000011e+31, -1.00000000000121e+34, 1.00000000000132e+37,
148 : -1.00000000000143e+40, 1.00000000000154e+43, -1.00000000000165e+46,
149 : 1.00000000000176e+49, -1.00000000000187e+52, 1.00000000000198e+55,
150 : -1.00000000000209e+58, 1.0000000000022e+61, -1.00000000000231e+64,
151 : 1.00000000000242e+67, -1.00000000000253e+70, 1.00000000000264e+73,
152 : -1.00000000000275e+76, 1.00000000000286e+79, -1.00000000000297e+82,
153 2 : 1.00000000000308e+85, -1.00000000000319e+88, 1.00000000000331e+91};
154 1 : double rc{0.0}, order{0.0};
155 :
156 1 : double err = threeterm(coeffs, scale, rc, order);
157 :
158 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.7213e+58));
159 1 : EXPECT_THAT(rc, DoubleNear(a - time, epsilon));
160 1 : EXPECT_THAT(order, DoubleNear(1.0, 8.03569e-12));
161 1 : EXPECT_THAT(coeffs.size(), Eq(30));
162 1 : }
163 :
164 2 : TEST(ThreeTermAnalysisOf,
165 : TaylorSeriesAtOnePT9RealPoleAtOneWithScalingTenthAlphaOne)
166 : {
167 : // t = 1.9;
168 : // x[0] = 1.0/(1.0-t);
169 :
170 1 : double a{1.0};
171 1 : double time{1.9};
172 1 : double scale{0.1};
173 : vector<double> coeffs{
174 : -1.11111111111111, 0.123456790123457, -0.0137174211248285,
175 : 0.00152415790275873, -0.000169350878084303, 1.88167642315892e-05,
176 : -2.09075158128769e-06, 2.32305731254188e-07, -2.5811747917132e-08,
177 : 2.86797199079245e-09, -3.18663554532494e-10, 3.54070616147216e-11,
178 : -3.93411795719128e-12, 4.37124217465698e-13, -4.85693574961887e-14,
179 : 5.3965952773543e-15, -5.99621697483812e-16, 6.66246330537568e-17,
180 : -7.40273700597298e-18, 8.22526333996998e-19, -9.13918148885554e-20,
181 : 1.01546460987284e-20, -1.12829401096982e-21, 1.25366001218869e-22,
182 : -1.39295556909854e-23, 1.54772841010949e-24, -1.71969823345499e-25,
183 2 : 1.91077581494999e-26, -2.12308423883332e-27, 2.35898248759258e-28};
184 1 : double rc{0.0}, order{0.0};
185 :
186 1 : double err = threeterm(coeffs, scale, rc, order);
187 :
188 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
189 1 : EXPECT_THAT(rc, DoubleNear(a - time, 8.54872e-14));
190 1 : EXPECT_THAT(order, DoubleNear(1.0, 2.19869e-12));
191 1 : EXPECT_THAT(coeffs.size(), Eq(30));
192 1 : }
193 :
194 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtThreePoleAtOneWithScalingTenthAlphaOne)
195 : {
196 : // t = 3.0;
197 : // x[0] = 1.0/(1.0-t);
198 :
199 1 : double a{1.0};
200 1 : double time{3.0};
201 1 : double scale{0.1};
202 : vector<double> coeffs{-0.5,
203 : 0.025,
204 : -0.00125,
205 : 6.25e-05,
206 : -3.125e-06,
207 : 1.5625e-07,
208 : -7.8125e-09,
209 : 3.90625e-10,
210 : -1.953125e-11,
211 : 9.765625e-13,
212 : -4.8828125e-14,
213 : 2.44140625e-15,
214 : -1.220703125e-16,
215 : 6.103515625e-18,
216 : -3.0517578125e-19,
217 : 1.52587890625e-20,
218 : -7.62939453125001e-22,
219 : 3.814697265625e-23,
220 : -1.9073486328125e-24,
221 : 9.53674316406251e-26,
222 : -4.76837158203126e-27,
223 : 2.38418579101563e-28,
224 : -1.19209289550781e-29,
225 : 5.96046447753907e-31,
226 : -2.98023223876954e-32,
227 : 1.49011611938477e-33,
228 : -7.45058059692384e-35,
229 : 3.72529029846192e-36,
230 : -1.86264514923096e-37,
231 2 : 9.3132257461548e-39};
232 1 : double rc{0.0}, order{0.0};
233 :
234 1 : double err = threeterm(coeffs, scale, rc, order);
235 :
236 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
237 1 : EXPECT_THAT(rc, DoubleNear(a - time, 9.68115e-14));
238 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.1887e-12));
239 1 : EXPECT_THAT(coeffs.size(), Eq(30));
240 1 : }
241 :
242 2 : TEST(ThreeTermAnalysisOf,
243 : TaylorSeriesAtNegativeOneRealPoleAtOneWithScalingOneAlphaOne)
244 : {
245 : // t =-1.0;
246 : // x[0] = 1.0/(1.0-t);
247 :
248 1 : double a{1.0};
249 1 : double time{-1.0};
250 1 : double scale{1.0};
251 : vector<double> coeffs{
252 : 5.000000000000000e-01, 2.500000000000000e-01, 1.250000000000000e-01,
253 : 6.250000000000000e-02, 3.125000000000000e-02, 1.562500000000000e-02,
254 : 7.812500000000000e-03, 3.906250000000000e-03, 1.953125000000000e-03,
255 : 9.765625000000000e-04, 4.882812500000000e-04, 2.441406250000000e-04,
256 : 1.220703125000000e-04, 6.103515625000000e-05, 3.051757812500000e-05,
257 : 1.525878906250000e-05, 7.629394531250000e-06, 3.814697265625000e-06,
258 : 1.907348632812500e-06, 9.536743164062500e-07, 4.768371582031250e-07,
259 : 2.384185791015625e-07, 1.192092895507813e-07, 5.960464477539063e-08,
260 : 2.980232238769531e-08, 1.490116119384766e-08, 7.450580596923828e-09,
261 2 : 3.725290298461914e-09, 1.862645149230957e-09, 9.313225746154785e-10};
262 1 : double rc{0.0}, order{0.0};
263 :
264 1 : double err = threeterm(coeffs, scale, rc, order);
265 :
266 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
267 1 : EXPECT_THAT(rc, DoubleNear(a - time, 1.06582e-14));
268 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.33005e-13));
269 1 : EXPECT_THAT(coeffs.size(), Eq(30));
270 1 : }
271 :
272 2 : TEST(ThreeTermAnalysisOf,
273 : TaylorSeriesAtZeroOneRealPoleAtOneWithScalingOneAlphaOne)
274 : {
275 : // t = 0.0;
276 : // x[0] = 1.0/(1.0-t);
277 :
278 1 : double a{1.0};
279 1 : double time{0.0};
280 1 : double scale{1.0};
281 : vector<double> coeffs{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
282 2 : 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
283 1 : double rc{0.0}, order{0.0};
284 :
285 1 : double err = threeterm(coeffs, scale, rc, order);
286 :
287 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.06582e-14));
288 1 : EXPECT_THAT(rc, DoubleNear(a - time, 6.66134e-16));
289 1 : EXPECT_THAT(order, DoubleNear(1.0, 2.4758e-14));
290 1 : EXPECT_THAT(coeffs.size(), Eq(30));
291 1 : }
292 :
293 2 : TEST(ThreeTermAnalysisOf,
294 : TaylorSeriesAtPTNineOneRealPoleAtOneWithScalingOneAlphaOne)
295 : {
296 : // t = 0.9;
297 : // x[0] = 1.0/(1.0-t);
298 :
299 1 : double a{1.0};
300 1 : double time{0.9};
301 1 : double scale{1.0};
302 : vector<double> coeffs{
303 : 1.000000000000000e+01, 1.000000000000000e+02, 1.000000000000001e+03,
304 : 1.000000000000001e+04, 1.000000000000001e+05, 1.000000000000001e+06,
305 : 1.000000000000002e+07, 1.000000000000002e+08, 1.000000000000002e+09,
306 : 1.000000000000002e+10, 1.000000000000002e+11, 1.000000000000003e+12,
307 : 1.000000000000003e+13, 1.000000000000003e+14, 1.000000000000003e+15,
308 : 1.000000000000004e+16, 1.000000000000004e+17, 1.000000000000004e+18,
309 : 1.000000000000004e+19, 1.000000000000005e+20, 1.000000000000005e+21,
310 : 1.000000000000005e+22, 1.000000000000005e+23, 1.000000000000005e+24,
311 : 1.000000000000006e+25, 1.000000000000006e+26, 1.000000000000006e+27,
312 2 : 1.000000000000006e+28, 1.000000000000007e+29, 1.000000000000007e+30};
313 1 : double rc{0.0}, order{0.0};
314 :
315 1 : double err = threeterm(coeffs, scale, rc, order);
316 :
317 1 : EXPECT_THAT(err, DoubleNear(0.0, 2.25486e+10));
318 1 : EXPECT_THAT(rc, DoubleNear(a - time, 2.98373e-15));
319 1 : EXPECT_THAT(order, DoubleNear(1.0, 8.77743e-13));
320 1 : EXPECT_THAT(coeffs.size(), Eq(30));
321 1 : }
322 :
323 2 : TEST(ThreeTermAnalysisOf,
324 : TaylorSeriesAtOnePT0001RealPoleAtOneWithScalingOneAlphaOne)
325 : {
326 : // t = 1.0001;
327 : // x[0] = 1.0/(1.0-t);
328 :
329 1 : double a{1.0};
330 1 : double time{1.0001};
331 1 : double scale{1.0};
332 : vector<double> coeffs{
333 : -1.000000000000110e+04, 1.000000000000220e+08, -1.000000000000330e+12,
334 : 1.000000000000440e+16, -1.000000000000551e+20, 1.000000000000661e+24,
335 : -1.000000000000771e+28, 1.000000000000881e+32, -1.000000000000991e+36,
336 : 1.000000000001101e+40, -1.000000000001211e+44, 1.000000000001321e+48,
337 : -1.000000000001431e+52, 1.000000000001542e+56, -1.000000000001652e+60,
338 : 1.000000000001762e+64, -1.000000000001872e+68, 1.000000000001982e+72,
339 : -1.000000000002092e+76, 1.000000000002202e+80, -1.000000000002312e+84,
340 : 1.000000000002422e+88, -1.000000000002533e+92, 1.000000000002643e+96,
341 : -1.000000000002753e+100, 1.000000000002863e+104, -1.000000000002973e+108,
342 2 : 1.000000000003083e+112, -1.000000000003193e+116, 1.000000000003303e+120};
343 1 : double rc{0.0}, order{0.0};
344 :
345 1 : double err = threeterm(coeffs, scale, rc, order);
346 :
347 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.85268e+78));
348 1 : EXPECT_THAT(rc, DoubleNear(a - time, epsilon));
349 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.5100e-14));
350 1 : EXPECT_THAT(coeffs.size(), Eq(30));
351 1 : }
352 :
353 2 : TEST(ThreeTermAnalysisOf,
354 : TaylorSeriesAtOnePT9RealPoleAtOneWithScalingOneAlphaOne)
355 : {
356 : // t = 1.9;
357 : // x[0] = 1.0/(1.0-t);
358 :
359 1 : double a{1.0};
360 1 : double time{1.9};
361 1 : double scale{1.0};
362 : vector<double> coeffs{
363 : -1.111111111111111e+00, 1.234567901234568e+00, -1.371742112482853e+00,
364 : 1.524157902758726e+00, -1.693508780843029e+00, 1.881676423158922e+00,
365 : -2.090751581287691e+00, 2.323057312541879e+00, -2.581174791713199e+00,
366 : 2.867971990792444e+00, -3.186635545324938e+00, 3.540706161472154e+00,
367 : -3.934117957191282e+00, 4.371242174656981e+00, -4.856935749618868e+00,
368 : 5.396595277354298e+00, -5.996216974838109e+00, 6.662463305375677e+00,
369 : -7.402737005972976e+00, 8.225263339969974e+00, -9.139181488855527e+00,
370 : 1.015464609872837e+01, -1.128294010969818e+01, 1.253660012188687e+01,
371 : -1.392955569098542e+01, 1.547728410109491e+01, -1.719698233454990e+01,
372 2 : 1.910775814949989e+01, -2.123084238833321e+01, 2.358982487592579e+01};
373 1 : double rc{0.0}, order{0.0};
374 :
375 1 : double err = threeterm(coeffs, scale, rc, order);
376 :
377 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.98952e-13));
378 1 : EXPECT_THAT(rc, DoubleNear(a - time, 9.99201e-16));
379 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.77636e-14));
380 1 : EXPECT_THAT(coeffs.size(), Eq(30));
381 1 : }
382 :
383 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtThreePoleAtOneWithScalingOneAlphaOne)
384 : {
385 : // t = 3.0;
386 : // x[0] = 1.0/(1.0-t);
387 :
388 1 : double a{1.0};
389 1 : double time{3.0};
390 1 : double scale{1.0};
391 : vector<double> coeffs{
392 : -5.000000000000000e-01, 2.500000000000000e-01, -1.250000000000000e-01,
393 : 6.250000000000000e-02, -3.125000000000000e-02, 1.562500000000000e-02,
394 : -7.812500000000000e-03, 3.906250000000000e-03, -1.953125000000000e-03,
395 : 9.765625000000000e-04, -4.882812500000000e-04, 2.441406250000000e-04,
396 : -1.220703125000000e-04, 6.103515625000000e-05, -3.051757812500000e-05,
397 : 1.525878906250000e-05, -7.629394531250000e-06, 3.814697265625000e-06,
398 : -1.907348632812500e-06, 9.536743164062500e-07, -4.768371582031250e-07,
399 : 2.384185791015625e-07, -1.192092895507813e-07, 5.960464477539063e-08,
400 : -2.980232238769531e-08, 1.490116119384766e-08, -7.450580596923828e-09,
401 2 : 3.725290298461914e-09, -1.862645149230957e-09, 9.313225746154785e-10};
402 1 : double rc{0.0}, order{0.0};
403 :
404 1 : double err = threeterm(coeffs, scale, rc, order);
405 :
406 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
407 1 : EXPECT_THAT(rc, DoubleNear(a - time, 1.06582e-14));
408 1 : EXPECT_THAT(order, DoubleNear(1.0, 1.33005e-13));
409 1 : EXPECT_THAT(coeffs.size(), Eq(30));
410 1 : }
411 :
412 : // Requires TOL=1e-1
413 2 : TEST(ThreeTermAnalysisOf,
414 : TaylorSeriesAtNegativeOnePoleAtOneWithScalingTenthAlphaTwo)
415 : {
416 : // t =-1.0;
417 : // x[0] = 1.0/((1.0-t)*(1.0-t));
418 :
419 1 : double a{1.0};
420 1 : double time{-1.0};
421 1 : double scale{0.1};
422 : vector<double> coeffs{0.25,
423 : 0.025,
424 : 0.001875,
425 : 0.000125,
426 : 7.8125e-06,
427 : 4.6875e-07,
428 : 2.734375e-08,
429 : 1.5625e-09,
430 : 8.78906250000001e-11,
431 : 4.8828125e-12,
432 : 2.685546875e-13,
433 : 1.46484375e-14,
434 : 7.9345703125e-16,
435 : 4.2724609375e-17,
436 : 2.288818359375e-18,
437 : 1.220703125e-19,
438 : 6.48498535156251e-21,
439 : 3.4332275390625e-22,
440 : 1.81198120117188e-23,
441 : 9.53674316406251e-25,
442 : 5.00679016113282e-26,
443 : 2.62260437011719e-27,
444 : 1.37090682983399e-28,
445 : 7.15255737304688e-30,
446 : 3.72529029846192e-31,
447 : 1.9371509552002e-32,
448 : 1.00582838058472e-33,
449 : 5.21540641784669e-35,
450 : 2.70083546638489e-36,
451 2 : 1.39698386192322e-37};
452 1 : double rc{0.0}, order{0.0};
453 :
454 1 : double err = threeterm(coeffs, scale, rc, order);
455 :
456 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
457 1 : EXPECT_THAT(rc, DoubleNear(a - time, 2.0096e-13));
458 1 : EXPECT_THAT(order, DoubleNear(2.0, 2.49401e-12));
459 1 : EXPECT_THAT(coeffs.size(), Eq(30));
460 1 : }
461 :
462 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtZeroPoleAtOneWithScalingTenthAlphaTwo)
463 : {
464 : // t = 0.0;
465 : // x[0] = 1.0/((1.0-t)*(1.0-t));
466 :
467 1 : double a{1.0};
468 1 : double time{0.0};
469 1 : double scale{0.1};
470 : vector<double> coeffs{1, 0.2, 0.03,
471 : 0.004, 0.0005, 6e-05,
472 : 7e-06, 8e-07, 9.00000000000001e-08,
473 : 1e-08, 1.1e-09, 1.2e-10,
474 : 1.3e-11, 1.4e-12, 1.5e-13,
475 : 1.6e-14, 1.7e-15, 1.8e-16,
476 : 1.9e-17, 2e-18, 2.1e-19,
477 : 2.2e-20, 2.3e-21, 2.4e-22,
478 : 2.5e-23, 2.6e-24, 2.7e-25,
479 2 : 2.8e-26, 2.9e-27, 3e-28};
480 1 : double rc{0.0}, order{0.0};
481 :
482 1 : double err = threeterm(coeffs, scale, rc, order);
483 :
484 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
485 1 : EXPECT_THAT(rc, DoubleNear(a - time, 3.77476e-15));
486 1 : EXPECT_THAT(order, DoubleNear(2.0, 9.32588e-14));
487 1 : EXPECT_THAT(coeffs.size(), Eq(30));
488 1 : }
489 :
490 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtPT9PoleAtOneWithScalingTenthAlphaTwo)
491 : {
492 : // t = 0.9;
493 : // x[0] = 1.0/((1.0-t)*(1.0-t));
494 :
495 1 : double a{1.0};
496 1 : double time{0.9};
497 1 : double scale{0.1};
498 : vector<double> coeffs{100,
499 : 200,
500 : 300,
501 : 400.000000000001,
502 : 500.000000000001,
503 : 600.000000000002,
504 : 700.000000000002,
505 : 800.000000000003,
506 : 900.000000000004,
507 : 1000,
508 : 1100.00000000001,
509 : 1200.00000000001,
510 : 1300.00000000001,
511 : 1400.00000000001,
512 : 1500.00000000001,
513 : 1600.00000000001,
514 : 1700.00000000001,
515 : 1800.00000000001,
516 : 1900.00000000002,
517 : 2000.00000000002,
518 : 2100.00000000002,
519 : 2200.00000000002,
520 : 2300.00000000003,
521 : 2400.00000000003,
522 : 2500.00000000003,
523 : 2600.00000000004,
524 : 2700.00000000004,
525 : 2800.00000000004,
526 : 2900.00000000005,
527 2 : 3000.00000000005};
528 1 : double rc{0.0}, order{0.0};
529 :
530 1 : double err = threeterm(coeffs, scale, rc, order);
531 :
532 1 : EXPECT_THAT(err, DoubleNear(0.0, 2.03727e-10));
533 1 : EXPECT_THAT(rc, DoubleNear(a - time, 2.77556e-16));
534 1 : EXPECT_THAT(order, DoubleNear(2.0, 7.50511e-14));
535 1 : EXPECT_THAT(coeffs.size(), Eq(30));
536 1 : }
537 :
538 2 : TEST(ThreeTermAnalysisOf,
539 : TaylorSeriesAtNegativeOnePoleAtOneWithScalingOneAlphaTwo)
540 : {
541 : // t =-1.0;
542 : // x[0] = 1.0/((1.0-t)*(1.0-t));
543 :
544 1 : double a{1.0};
545 1 : double time{-1.0};
546 1 : double scale{1.0};
547 : vector<double> coeffs{
548 : 2.500000000000000e-01, 2.500000000000000e-01, 1.875000000000000e-01,
549 : 1.250000000000000e-01, 7.812500000000000e-02, 4.687500000000000e-02,
550 : 2.734375000000000e-02, 1.562500000000000e-02, 8.789062500000000e-03,
551 : 4.882812500000000e-03, 2.685546875000000e-03, 1.464843750000000e-03,
552 : 7.934570312500000e-04, 4.272460937500000e-04, 2.288818359375000e-04,
553 : 1.220703125000000e-04, 6.484985351562500e-05, 3.433227539062500e-05,
554 : 1.811981201171875e-05, 9.536743164062500e-06, 5.006790161132813e-06,
555 : 2.622604370117188e-06, 1.370906829833984e-06, 7.152557373046875e-07,
556 : 3.725290298461914e-07, 1.937150955200195e-07, 1.005828380584717e-07,
557 2 : 5.215406417846680e-08, 2.700835466384888e-08, 1.396983861923218e-08};
558 1 : double rc{0.0}, order{0.0};
559 :
560 1 : double err = threeterm(coeffs, scale, rc, order);
561 :
562 1 : EXPECT_THAT(err, DoubleNear(0.0, epsilon));
563 1 : EXPECT_THAT(rc, DoubleNear(a - time, 6.66134e-15));
564 1 : EXPECT_THAT(order, DoubleNear(2.0, 8.34888e-14));
565 1 : EXPECT_THAT(coeffs.size(), Eq(30));
566 1 : }
567 :
568 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtZeroPoleAtOneWithScalingOneAlphaTwo)
569 : {
570 : // t = 0.0;
571 : // x[0] = 1.0/((1.0-t)*(1.0-t));
572 :
573 1 : double a{1.0};
574 1 : double time{0.0};
575 1 : double scale{1.0};
576 : vector<double> coeffs{1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
577 : 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
578 2 : 21, 22, 23, 24, 25, 26, 27, 28, 29, 30};
579 1 : double rc{0.0}, order{0.0};
580 :
581 1 : double err = threeterm(coeffs, scale, rc, order);
582 :
583 1 : EXPECT_THAT(err, DoubleNear(0.0, 3.97904e-13));
584 1 : EXPECT_THAT(rc, DoubleNear(a - time, 1.11023e-15));
585 1 : EXPECT_THAT(order, DoubleNear(2.0, 4.17444e-14));
586 1 : EXPECT_THAT(coeffs.size(), Eq(30));
587 1 : }
588 :
589 2 : TEST(ThreeTermAnalysisOf, TaylorSeriesAtPT9PoleAtOneWithScalingOneAlphaTwo)
590 : {
591 : // t = 0.9;
592 : // x[0] = 1.0/((1.0-t)*(1.0-t));
593 :
594 1 : double a{1.0};
595 1 : double time{0.9};
596 1 : double scale{1.0};
597 : vector<double> coeffs{
598 : 1.000000000000001e+02, 2.000000000000002e+03, 3.000000000000004e+04,
599 : 4.000000000000006e+05, 5.000000000000010e+06, 6.000000000000015e+07,
600 : 7.000000000000021e+08, 8.000000000000028e+09, 9.000000000000035e+10,
601 : 1.000000000000004e+12, 1.100000000000005e+13, 1.200000000000006e+14,
602 : 1.300000000000008e+15, 1.400000000000009e+16, 1.500000000000010e+17,
603 : 1.600000000000010e+18, 1.700000000000012e+19, 1.800000000000013e+20,
604 : 1.900000000000014e+21, 2.000000000000016e+22, 2.100000000000018e+23,
605 : 2.200000000000020e+24, 2.300000000000022e+25, 2.400000000000025e+26,
606 : 2.500000000000028e+27, 2.600000000000031e+28, 2.700000000000035e+29,
607 2 : 2.800000000000039e+30, 2.900000000000042e+31, 3.000000000000046e+32};
608 1 : double rc{0.0}, order{0.0};
609 :
610 1 : double err = threeterm(coeffs, scale, rc, order);
611 :
612 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.71799e+12));
613 1 : EXPECT_THAT(rc, DoubleNear(a - time, 1.27676e-15));
614 1 : EXPECT_THAT(order, DoubleNear(2.0, 3.61711e-13));
615 1 : EXPECT_THAT(coeffs.size(), Eq(30));
616 1 : }
617 :
618 2 : TEST(
619 : ThreeTermAnalysisOf,
620 : TaylorSeriesAtNegativePT3WithScalingTenthForComplexConjugatePolesAtPMOneFifthAlphaOne)
621 : {
622 : // t =-0.3;
623 : // x[0] = 1.0/(1.0+25.0*t*t);
624 :
625 1 : double a{1.0 / 5.0};
626 1 : double time{-0.3};
627 1 : double scale{0.1};
628 : vector<double> coeffs{3.0769230769230771e-01, 1.4201183431952663e-01,
629 : 4.1875284478834776e-02, 8.4030671194986195e-03,
630 : 6.5716294139668780e-04, -3.4308380547065328e-04,
631 : -2.0889736724773902e-04, -7.0023107539675438e-05,
632 : -1.6249329076177969e-05, -2.1132974551840289e-06,
633 : 2.7458033423644587e-07, 2.8929072773866954e-07,
634 : 1.1239723324581319e-07, 2.9622513210477662e-08,
635 : 5.0259881551579064e-09, 4.1031978497675339e-11,
636 : -3.6767663724398882e-10, -1.7285321553550831e-10,
637 : -5.1495588920697002e-11, -1.0470793691436441e-11,
638 : -8.7147486368628090e-13, 4.0322650071682737e-13,
639 : 2.5314106676824962e-13, 8.5816915376359253e-14,
640 : 2.0135417345377379e-14, 2.6919683612234631e-15,
641 : -3.0643132138743080e-16, -3.4850432996523446e-16,
642 2 : -1.3727651218492121e-16, -3.6550364857253289e-17};
643 1 : double rc{0.0}, order{0.0};
644 :
645 1 : double err = threeterm(coeffs, scale, rc, order);
646 :
647 : // Model is wrong, as it should be. However there are no difficulties
648 : // executing this test case
649 1 : EXPECT_THAT(err, DoubleNear(0.0, 1.54316e-12));
650 1 : EXPECT_THAT(rc, DoubleNear(a - time, 0.545748));
651 1 : EXPECT_THAT(order, DoubleNear(1.0, 26.5676));
652 1 : EXPECT_THAT(coeffs.size(), Eq(30));
653 1 : }
654 :
655 2 : TEST(ThreeTermAnalysisOf, TestRCThree)
656 : {
657 1 : double rc = std::numeric_limits<double>::quiet_NaN();
658 2 : EXPECT_THROW(testRCThree(rc), std::exception);
659 1 : }
660 :
661 2 : TEST(ThreeTermAnalysisOf, TestOrder)
662 : {
663 1 : double order = std::numeric_limits<double>::quiet_NaN();
664 2 : EXPECT_THROW(testOrder(order), std::exception);
665 1 : }
666 :
667 : // WARNING Rc and order can be accurate, but backward error can be large near
668 : // singularity WARNING Error model wrong for complex-conjugate comparison
669 : //
670 : // Exceptions (Hard to think of a test)
671 : // Top-line comparison
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