27 #ifndef __PROSHADE_MATHS__
28 #define __PROSHADE_MATHS__
34 extern void zgesdd_(
char* jobz,
int* m,
int* n, std::complex<double>* a,
int* lda,
double* s, std::complex<double>* u,
int* ldu, std::complex<double>* vt,
int* ldvt, std::complex<double>* work,
int* lwork,
double* rwork,
int* iwork,
int* info );
53 proshade_double radius;
54 proshade_double radiusMax;
55 proshade_double radiusMin;
56 proshade_unsign angularDim;
57 proshade_double representedAngle;
58 proshade_unsign sphereNumber;
60 proshade_double* axesValues;
61 std::vector< std::pair< proshade_unsign,proshade_unsign > > peaks;
63 ProSHADE_rotFun_sphere ( proshade_double rad, proshade_double radRange, proshade_unsign dim, proshade_double repAng, proshade_unsign sphNo );
73 std::vector<std::pair<proshade_unsign,proshade_unsign>>
getPeaks (
void );
80 void findAllPeaks ( proshade_signed noSmNeighbours, std::vector< proshade_double >* allHeights );
104 proshade_double a00, a01, a02, a03, a10, a11, a12, a13, a20, a21, a22, a23, a30, a31, a32, a33;
105 proshade_double xStartIndex, xRange, yStartIndex, yRange;
115 BicubicInterpolator ( proshade_double** areaToInterpolate, proshade_double xStart, proshade_double yStart )
118 this->xStartIndex = xStart;
119 this->yStartIndex = yStart;
126 this->a00 = areaToInterpolate[1][1];
127 this->a01 = - ( 0.5 * areaToInterpolate[1][0] ) +
128 ( 0.5 * areaToInterpolate[1][2] );
129 this->a02 = areaToInterpolate[1][0] -
130 ( 2.5 * areaToInterpolate[1][1] ) +
131 ( 2.0 * areaToInterpolate[1][2] ) -
132 ( 0.5 * areaToInterpolate[1][3] );
133 this->a03 = - ( 0.5 * areaToInterpolate[1][0] ) +
134 ( 1.5 * areaToInterpolate[1][1] ) -
135 ( 1.5 * areaToInterpolate[1][2] ) +
136 ( 0.5 * areaToInterpolate[1][3] );
137 this->a10 = - ( 0.5 * areaToInterpolate[0][1] ) +
138 ( 0.5 * areaToInterpolate[2][1] );
139 this->a11 = ( 0.25 * areaToInterpolate[0][0] ) -
140 ( 0.25 * areaToInterpolate[0][2] ) -
141 ( 0.25 * areaToInterpolate[2][0] ) +
142 ( 0.25 * areaToInterpolate[2][2] );
143 this->a12 = - ( 0.5 * areaToInterpolate[0][0] ) +
144 ( 1.25 * areaToInterpolate[0][1] ) -
145 areaToInterpolate[0][2] +
146 ( 0.25 * areaToInterpolate[0][3] ) +
147 ( 0.5 * areaToInterpolate[2][0] ) -
148 ( 1.25 * areaToInterpolate[2][1] ) +
149 areaToInterpolate[2][2] -
150 ( 0.25 * areaToInterpolate[2][3] );
151 this->a13 = ( 0.25 * areaToInterpolate[0][0] ) -
152 ( 0.75 * areaToInterpolate[0][1] ) +
153 ( 0.75 * areaToInterpolate[0][2] ) -
154 ( 0.25 * areaToInterpolate[0][3] ) -
155 ( 0.25 * areaToInterpolate[2][0] ) +
156 ( 0.75 * areaToInterpolate[2][1] ) -
157 ( 0.75 * areaToInterpolate[2][2] ) +
158 ( 0.25 * areaToInterpolate[2][3] );
159 this->a20 = areaToInterpolate[0][1] -
160 ( 2.5 * areaToInterpolate[1][1] ) +
161 ( 2.0 * areaToInterpolate[2][1] ) -
162 ( 0.5 * areaToInterpolate[3][1] );
163 this->a21 = - ( 0.5 * areaToInterpolate[0][0] ) +
164 ( 0.5 * areaToInterpolate[0][2] ) +
165 ( 1.25 * areaToInterpolate[1][0] ) -
166 ( 1.25 * areaToInterpolate[1][2] ) -
167 areaToInterpolate[2][0] + areaToInterpolate[2][2] +
168 ( 0.25 * areaToInterpolate[3][0] ) -
169 ( 0.25 * areaToInterpolate[3][2] );
170 this->a22 = areaToInterpolate[0][0] -
171 ( 2.5 * areaToInterpolate[0][1] ) +
172 ( 2.0 * areaToInterpolate[0][2] ) -
173 ( 0.5 * areaToInterpolate[0][3] ) -
174 ( 2.5 * areaToInterpolate[1][0] ) +
175 ( 6.25 * areaToInterpolate[1][1] ) -
176 ( 5.0 * areaToInterpolate[1][2] ) +
177 ( 1.25 * areaToInterpolate[1][3] ) +
178 ( 2.0 * areaToInterpolate[2][0] ) -
179 ( 5.0 * areaToInterpolate[2][1] ) +
180 ( 4.0 * areaToInterpolate[2][2] ) -
181 areaToInterpolate[2][3] -
182 ( 0.5 * areaToInterpolate[3][0] ) +
183 ( 1.25 * areaToInterpolate[3][1] ) -
184 areaToInterpolate[3][2] +
185 ( 0.25 * areaToInterpolate[3][3] );
186 this->a23 = - ( 0.5 * areaToInterpolate[0][0] ) +
187 ( 1.5 * areaToInterpolate[0][1] ) -
188 ( 1.5 * areaToInterpolate[0][2] ) +
189 ( 0.5 * areaToInterpolate[0][3] ) +
190 ( 1.25 * areaToInterpolate[1][0] ) -
191 ( 3.75 * areaToInterpolate[1][1] ) +
192 ( 3.75 * areaToInterpolate[1][2] ) -
193 ( 1.25 * areaToInterpolate[1][3] ) -
194 areaToInterpolate[2][0] +
195 ( 3.0 * areaToInterpolate[2][1] ) -
196 ( 3.0 * areaToInterpolate[2][2] ) +
197 areaToInterpolate[2][3] +
198 ( 0.25 * areaToInterpolate[3][0] ) -
199 ( 0.75 * areaToInterpolate[3][1] ) +
200 ( 0.75 * areaToInterpolate[3][2] ) -
201 ( 0.25 * areaToInterpolate[3][3] );
202 this->a30 = - ( 0.5 * areaToInterpolate[0][1] ) +
203 ( 1.5 * areaToInterpolate[1][1] ) -
204 ( 1.5 * areaToInterpolate[2][1] ) +
205 ( 0.5*areaToInterpolate[3][1] );
206 this->a31 = ( 0.25 * areaToInterpolate[0][0] ) -
207 ( 0.25 * areaToInterpolate[0][2] ) -
208 ( 0.75 * areaToInterpolate[1][0] ) +
209 ( 0.75 * areaToInterpolate[1][2] ) +
210 ( 0.75 * areaToInterpolate[2][0] ) -
211 ( 0.75 * areaToInterpolate[2][2] ) -
212 ( 0.25 * areaToInterpolate[3][0] ) +
213 ( 0.25 * areaToInterpolate[3][2] );
214 this->a32 = - ( 0.5 * areaToInterpolate[0][0] ) +
215 ( 1.25 * areaToInterpolate[0][1] ) -
216 areaToInterpolate[0][2] +
217 ( 0.25 * areaToInterpolate[0][3] ) +
218 ( 1.5 * areaToInterpolate[1][0] ) -
219 ( 3.75 * areaToInterpolate[1][1] ) +
220 ( 3.0 * areaToInterpolate[1][2] ) -
221 ( 0.75 * areaToInterpolate[1][3] ) -
222 ( 1.5 * areaToInterpolate[2][0] ) +
223 ( 3.75 * areaToInterpolate[2][1] ) -
224 ( 3.0 * areaToInterpolate[2][2] ) +
225 ( 0.75 * areaToInterpolate[2][3] ) +
226 ( 0.5 * areaToInterpolate[3][0] ) -
227 ( 1.25 * areaToInterpolate[3][1] ) +
228 areaToInterpolate[3][2] -
229 ( 0.25 * areaToInterpolate[3][3] );
230 this->a33 = ( 0.25 * areaToInterpolate[0][0] ) -
231 ( 0.75 * areaToInterpolate[0][1] ) +
232 ( 0.75 * areaToInterpolate[0][2] ) -
233 ( 0.25 * areaToInterpolate[0][3] ) -
234 ( 0.75 * areaToInterpolate[1][0] ) +
235 ( 2.25 * areaToInterpolate[1][1] ) -
236 ( 2.25 * areaToInterpolate[1][2] ) +
237 ( 0.75 * areaToInterpolate[1][3] ) +
238 ( 0.75 * areaToInterpolate[2][0] ) -
239 ( 2.25 * areaToInterpolate[2][1] ) +
240 ( 2.25 * areaToInterpolate[2][2] ) -
241 ( 0.75 * areaToInterpolate[2][3] ) -
242 ( 0.25 * areaToInterpolate[3][0] ) +
243 ( 0.75 * areaToInterpolate[3][1] ) -
244 ( 0.75 * areaToInterpolate[3][2] ) +
245 ( 0.25 * areaToInterpolate[3][3] );
263 proshade_double
getValue ( proshade_double x, proshade_double y )
266 if ( ( ( x < this->xStartIndex ) || ( x > ( this->xStartIndex + this->xRange ) ) ) ||
267 ( ( y < this->yStartIndex ) || ( y > ( this->yStartIndex + this->yRange ) ) ) )
269 if ( ( x < this->xStartIndex ) || ( x > ( this->xStartIndex + this->xRange ) ) ) { std::cout <<
"PROBLEM WITH LAT" << std::endl; }
270 if ( ( y < this->yStartIndex ) || ( y > ( this->yStartIndex + this->yRange ) ) ) { std::cout <<
"PROBLEM WITH LON" << std::endl; }
272 throw ProSHADE_exception (
"Requested bicubic interpolation outside of pre-computed\n : square.",
"ES00064", __FILE__, __LINE__, __func__,
"The supplied x or y value(s) is outside of the range of\n : the bi-cubic interpolator's pre-computed square. Please\n : make sure the start values were correctly supplied when\n : the constructor was called or create a new interpolator\n : for these values." );
276 proshade_double unitSquareX = ( x - this->xStartIndex ) / this->xRange;
277 proshade_double unitSquareY = ( y - this->yStartIndex ) / this->yRange;
280 proshade_double x2 = std::pow ( unitSquareX, 2.0 );
281 proshade_double x3 = std::pow ( unitSquareX, 3.0 );
282 proshade_double y2 = std::pow ( unitSquareY, 2.0 );
283 proshade_double y3 = std::pow ( unitSquareY, 3.0 );
286 return ( ( this->a00 + this->a01 * unitSquareY + this->a02 * y2 + this->a03 * y3 ) +
287 ( this->a10 + this->a11 * unitSquareY + this->a12 * y2 + this->a13 * y3 ) * unitSquareX +
288 ( this->a20 + this->a21 * unitSquareY + this->a22 * y2 + this->a23 * y3 ) * x2 +
289 ( this->a30 + this->a31 * unitSquareY + this->a32 * y2 + this->a33 * y3 ) * x3 );
293 void complexMultiplication ( proshade_double* r1, proshade_double* i1, proshade_double* r2, proshade_double* i2,
294 proshade_double* retReal, proshade_double* retImag );
296 proshade_double* retReal, proshade_double* retImag );
299 void vectorMeanAndSD ( std::vector<proshade_double>* vec, proshade_double*& ret );
301 void arrayMedianAndIQR ( proshade_double* vec, proshade_unsign vecSize, proshade_double*& ret );
302 proshade_double
pearsonCorrCoeff ( proshade_double* valSet1, proshade_double* valSet2, proshade_unsign length );
304 proshade_unsign taylorSeriesCap );
305 void getGLPolyAtZero ( proshade_unsign order, proshade_double *polyValue, proshade_double *deriValue );
306 void getGLFirstEvenRoot ( proshade_double polyAtZero, proshade_unsign order, proshade_double *abscAtZero,
307 proshade_double *weighAtZero, proshade_unsign taylorSeriesCap );
308 proshade_double
evaluateGLSeries ( proshade_double *series, proshade_double target, proshade_unsign terms );
309 proshade_double
advanceGLPolyValue ( proshade_double from, proshade_double to, proshade_double valAtFrom,
310 proshade_unsign noSteps, proshade_unsign taylorSeriesCap );
312 proshade_unsign taylorSeriesCap );
314 proshade_double* abscissas, proshade_double* weights, proshade_double integralOverRange,
315 proshade_double maxSphereDists );
317 proshade_double* abscissas, proshade_double* weights, proshade_double integralOverRange,
318 proshade_double maxSphereDists, proshade_double* retReal, proshade_double* retImag );
321 void getEulerZXZFromSOFTPosition ( proshade_signed band, proshade_signed x, proshade_signed y, proshade_signed z, proshade_double* eulerAlpha,
322 proshade_double* eulerBeta, proshade_double* eulerGamma );
323 void getSOFTPositionFromEulerZXZ ( proshade_signed band, proshade_double eulerAlpha, proshade_double eulerBeta, proshade_double eulerGamma,
324 proshade_double* x, proshade_double* y, proshade_double* z );
326 void getAxisAngleFromRotationMatrix ( proshade_double* rotMat, proshade_double* x, proshade_double* y, proshade_double* z, proshade_double* ang );
327 void getAxisAngleFromRotationMatrix ( std::vector< proshade_double >* rotMat, proshade_double* x, proshade_double* y, proshade_double* z, proshade_double* ang );
329 void getEulerZXZFromRotMatrix ( proshade_double* rotMat, proshade_double* eA, proshade_double* eB, proshade_double* eG );
330 void getEulerZXZFromAngleAxis ( proshade_double axX, proshade_double axY, proshade_double axZ, proshade_double axAng, proshade_double* eA,
331 proshade_double* eB, proshade_double* eG, proshade_unsign angDim );
333 proshade_double* eB, proshade_double* eG, proshade_signed angDim );
334 void multiplyTwoSquareMatrices ( proshade_double* A, proshade_double* B, proshade_double* res, proshade_unsign dim = 3 );
336 proshade_double
normalDistributionValue ( proshade_double mean, proshade_double standardDev, proshade_double value );
337 proshade_double
computeDotProduct ( proshade_double* x1, proshade_double* y1, proshade_double* z1, proshade_double* x2, proshade_double* y2,
338 proshade_double* z2 );
339 proshade_double
computeDotProduct ( proshade_double x1, proshade_double y1, proshade_double z1, proshade_double x2, proshade_double y2,
340 proshade_double z2 );
341 proshade_double*
computeCrossProduct ( proshade_double* x1, proshade_double* y1, proshade_double* z1, proshade_double* x2, proshade_double* y2,
342 proshade_double* z2 );
347 proshade_double*
findRotMatMatchingVectors ( proshade_double x1, proshade_double y1, proshade_double z1, proshade_double x2, proshade_double y2,
348 proshade_double z2 );
349 std::vector < proshade_double >
findVectorFromTwoVAndTwoD ( proshade_double x1, proshade_double y1, proshade_double z1, proshade_double x2, proshade_double y2,
350 proshade_double z2, proshade_double dot1, proshade_double dot2 );
351 std::vector < proshade_double >
findVectorFromThreeVAndThreeD ( proshade_double x1, proshade_double y1, proshade_double z1, proshade_double x2, proshade_double y2,
352 proshade_double z2, proshade_double x3, proshade_double y3, proshade_double z3, proshade_double dot1,
353 proshade_double dot2, proshade_double dot3 );
354 std::vector< proshade_double >
multiplyGroupElementMatrices ( std::vector< proshade_double >* el1, std::vector< proshade_double >* el2 );
355 bool rotationMatrixSimilarity ( std::vector< proshade_double >* mat1, std::vector< proshade_double >* mat2, proshade_double tolerance = 0.1 );
356 bool vectorOrientationSimilarity ( proshade_double a1, proshade_double a2, proshade_double a3, proshade_double b1, proshade_double b2,
357 proshade_double b3, proshade_double tolerance = 0.1 );
359 proshade_double b3, proshade_double tolerance = 0.1 );
360 void optimiseAxisBiCubicInterpolation ( proshade_double* bestLattitude, proshade_double* bestLongitude, proshade_double* bestSum, std::vector<proshade_unsign>* sphereList,
361 std::vector<ProSHADE_internal_spheres::ProSHADE_rotFun_sphere*>* sphereMappedRotFun, proshade_double step = 0.05 );
363 std::vector<ProSHADE_internal_maths::BicubicInterpolator*>* interpols, std::vector<ProSHADE_internal_spheres::ProSHADE_rotFun_sphere*>* sphereMappedRotFun );
365 std::vector<ProSHADE_internal_maths::BicubicInterpolator*>* interpols, std::vector<ProSHADE_internal_spheres::ProSHADE_rotFun_sphere*>* sphereMappedRotFun );
367 std::vector<ProSHADE_internal_maths::BicubicInterpolator*>* interpols, std::vector<ProSHADE_internal_spheres::ProSHADE_rotFun_sphere*>* sphereMappedRotFun );
369 std::vector<ProSHADE_internal_maths::BicubicInterpolator*>* interpols, std::vector<ProSHADE_internal_spheres::ProSHADE_rotFun_sphere*>* sphereMappedRotFun );
370 bool isAxisUnique ( std::vector< proshade_double* >* CSymList, proshade_double* axis, proshade_double tolerance = 0.1,
bool improve =
false );
371 bool isAxisUnique ( std::vector< proshade_double* >* CSymList, proshade_double X, proshade_double Y, proshade_double Z, proshade_double fold, proshade_double tolerance );
372 std::vector< proshade_unsign >
findAllPrimes ( proshade_unsign upTo );