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Eigen  3.4.0
 
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Jacobi.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
5// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_JACOBI_H
12#define EIGEN_JACOBI_H
13
14namespace Eigen {
15
34template<typename Scalar> class JacobiRotation
35{
36 public:
37 typedef typename NumTraits<Scalar>::Real RealScalar;
38
40 EIGEN_DEVICE_FUNC
42
44 EIGEN_DEVICE_FUNC
45 JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
46
47 EIGEN_DEVICE_FUNC Scalar& c() { return m_c; }
48 EIGEN_DEVICE_FUNC Scalar c() const { return m_c; }
49 EIGEN_DEVICE_FUNC Scalar& s() { return m_s; }
50 EIGEN_DEVICE_FUNC Scalar s() const { return m_s; }
51
53 EIGEN_DEVICE_FUNC
55 {
56 using numext::conj;
57 return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
58 conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
59 }
60
62 EIGEN_DEVICE_FUNC
63 JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }
64
66 EIGEN_DEVICE_FUNC
67 JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }
68
69 template<typename Derived>
70 EIGEN_DEVICE_FUNC
71 bool makeJacobi(const MatrixBase<Derived>&, Index p, Index q);
72 EIGEN_DEVICE_FUNC
73 bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);
74
75 EIGEN_DEVICE_FUNC
76 void makeGivens(const Scalar& p, const Scalar& q, Scalar* r=0);
77
78 protected:
79 EIGEN_DEVICE_FUNC
80 void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type);
81 EIGEN_DEVICE_FUNC
82 void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type);
83
84 Scalar m_c, m_s;
85};
86
92template<typename Scalar>
93EIGEN_DEVICE_FUNC
94bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)
95{
96 using std::sqrt;
97 using std::abs;
98
99 RealScalar deno = RealScalar(2)*abs(y);
100 if(deno < (std::numeric_limits<RealScalar>::min)())
101 {
102 m_c = Scalar(1);
103 m_s = Scalar(0);
104 return false;
105 }
106 else
107 {
108 RealScalar tau = (x-z)/deno;
109 RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
110 RealScalar t;
111 if(tau>RealScalar(0))
112 {
113 t = RealScalar(1) / (tau + w);
114 }
115 else
116 {
117 t = RealScalar(1) / (tau - w);
118 }
119 RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
120 RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));
121 m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;
122 m_c = n;
123 return true;
124 }
125}
126
136template<typename Scalar>
137template<typename Derived>
138EIGEN_DEVICE_FUNC
140{
141 return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));
142}
143
160template<typename Scalar>
161EIGEN_DEVICE_FUNC
162void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r)
163{
164 makeGivens(p, q, r, typename internal::conditional<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>::type());
165}
166
167
168// specialization for complexes
169template<typename Scalar>
170EIGEN_DEVICE_FUNC
171void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
172{
173 using std::sqrt;
174 using std::abs;
175 using numext::conj;
176
177 if(q==Scalar(0))
178 {
179 m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);
180 m_s = 0;
181 if(r) *r = m_c * p;
182 }
183 else if(p==Scalar(0))
184 {
185 m_c = 0;
186 m_s = -q/abs(q);
187 if(r) *r = abs(q);
188 }
189 else
190 {
191 RealScalar p1 = numext::norm1(p);
192 RealScalar q1 = numext::norm1(q);
193 if(p1>=q1)
194 {
195 Scalar ps = p / p1;
196 RealScalar p2 = numext::abs2(ps);
197 Scalar qs = q / p1;
198 RealScalar q2 = numext::abs2(qs);
199
200 RealScalar u = sqrt(RealScalar(1) + q2/p2);
201 if(numext::real(p)<RealScalar(0))
202 u = -u;
203
204 m_c = Scalar(1)/u;
205 m_s = -qs*conj(ps)*(m_c/p2);
206 if(r) *r = p * u;
207 }
208 else
209 {
210 Scalar ps = p / q1;
211 RealScalar p2 = numext::abs2(ps);
212 Scalar qs = q / q1;
213 RealScalar q2 = numext::abs2(qs);
214
215 RealScalar u = q1 * sqrt(p2 + q2);
216 if(numext::real(p)<RealScalar(0))
217 u = -u;
218
219 p1 = abs(p);
220 ps = p/p1;
221 m_c = p1/u;
222 m_s = -conj(ps) * (q/u);
223 if(r) *r = ps * u;
224 }
225 }
226}
227
228// specialization for reals
229template<typename Scalar>
230EIGEN_DEVICE_FUNC
231void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)
232{
233 using std::sqrt;
234 using std::abs;
235 if(q==Scalar(0))
236 {
237 m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);
238 m_s = Scalar(0);
239 if(r) *r = abs(p);
240 }
241 else if(p==Scalar(0))
242 {
243 m_c = Scalar(0);
244 m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);
245 if(r) *r = abs(q);
246 }
247 else if(abs(p) > abs(q))
248 {
249 Scalar t = q/p;
250 Scalar u = sqrt(Scalar(1) + numext::abs2(t));
251 if(p<Scalar(0))
252 u = -u;
253 m_c = Scalar(1)/u;
254 m_s = -t * m_c;
255 if(r) *r = p * u;
256 }
257 else
258 {
259 Scalar t = p/q;
260 Scalar u = sqrt(Scalar(1) + numext::abs2(t));
261 if(q<Scalar(0))
262 u = -u;
263 m_s = -Scalar(1)/u;
264 m_c = -t * m_s;
265 if(r) *r = q * u;
266 }
267
268}
269
270/****************************************************************************************
271* Implementation of MatrixBase methods
272****************************************************************************************/
273
274namespace internal {
281template<typename VectorX, typename VectorY, typename OtherScalar>
282EIGEN_DEVICE_FUNC
283void apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j);
284}
285
292template<typename Derived>
293template<typename OtherScalar>
294EIGEN_DEVICE_FUNC
296{
297 RowXpr x(this->row(p));
298 RowXpr y(this->row(q));
299 internal::apply_rotation_in_the_plane(x, y, j);
300}
301
308template<typename Derived>
309template<typename OtherScalar>
310EIGEN_DEVICE_FUNC
312{
313 ColXpr x(this->col(p));
314 ColXpr y(this->col(q));
315 internal::apply_rotation_in_the_plane(x, y, j.transpose());
316}
317
318namespace internal {
319
320template<typename Scalar, typename OtherScalar,
321 int SizeAtCompileTime, int MinAlignment, bool Vectorizable>
322struct apply_rotation_in_the_plane_selector
323{
324 static EIGEN_DEVICE_FUNC
325 inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
326 {
327 for(Index i=0; i<size; ++i)
328 {
329 Scalar xi = *x;
330 Scalar yi = *y;
331 *x = c * xi + numext::conj(s) * yi;
332 *y = -s * xi + numext::conj(c) * yi;
333 x += incrx;
334 y += incry;
335 }
336 }
337};
338
339template<typename Scalar, typename OtherScalar,
340 int SizeAtCompileTime, int MinAlignment>
341struct apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,true /* vectorizable */>
342{
343 static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
344 {
345 enum {
346 PacketSize = packet_traits<Scalar>::size,
347 OtherPacketSize = packet_traits<OtherScalar>::size
348 };
349 typedef typename packet_traits<Scalar>::type Packet;
350 typedef typename packet_traits<OtherScalar>::type OtherPacket;
351
352 /*** dynamic-size vectorized paths ***/
353 if(SizeAtCompileTime == Dynamic && ((incrx==1 && incry==1) || PacketSize == 1))
354 {
355 // both vectors are sequentially stored in memory => vectorization
356 enum { Peeling = 2 };
357
358 Index alignedStart = internal::first_default_aligned(y, size);
359 Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
360
361 const OtherPacket pc = pset1<OtherPacket>(c);
362 const OtherPacket ps = pset1<OtherPacket>(s);
363 conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj;
364 conj_helper<OtherPacket,Packet,false,false> pm;
365
366 for(Index i=0; i<alignedStart; ++i)
367 {
368 Scalar xi = x[i];
369 Scalar yi = y[i];
370 x[i] = c * xi + numext::conj(s) * yi;
371 y[i] = -s * xi + numext::conj(c) * yi;
372 }
373
374 Scalar* EIGEN_RESTRICT px = x + alignedStart;
375 Scalar* EIGEN_RESTRICT py = y + alignedStart;
376
377 if(internal::first_default_aligned(x, size)==alignedStart)
378 {
379 for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)
380 {
381 Packet xi = pload<Packet>(px);
382 Packet yi = pload<Packet>(py);
383 pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
384 pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
385 px += PacketSize;
386 py += PacketSize;
387 }
388 }
389 else
390 {
391 Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);
392 for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)
393 {
394 Packet xi = ploadu<Packet>(px);
395 Packet xi1 = ploadu<Packet>(px+PacketSize);
396 Packet yi = pload <Packet>(py);
397 Packet yi1 = pload <Packet>(py+PacketSize);
398 pstoreu(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
399 pstoreu(px+PacketSize, padd(pm.pmul(pc,xi1),pcj.pmul(ps,yi1)));
400 pstore (py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
401 pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pm.pmul(ps,xi1)));
402 px += Peeling*PacketSize;
403 py += Peeling*PacketSize;
404 }
405 if(alignedEnd!=peelingEnd)
406 {
407 Packet xi = ploadu<Packet>(x+peelingEnd);
408 Packet yi = pload <Packet>(y+peelingEnd);
409 pstoreu(x+peelingEnd, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
410 pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
411 }
412 }
413
414 for(Index i=alignedEnd; i<size; ++i)
415 {
416 Scalar xi = x[i];
417 Scalar yi = y[i];
418 x[i] = c * xi + numext::conj(s) * yi;
419 y[i] = -s * xi + numext::conj(c) * yi;
420 }
421 }
422
423 /*** fixed-size vectorized path ***/
424 else if(SizeAtCompileTime != Dynamic && MinAlignment>0) // FIXME should be compared to the required alignment
425 {
426 const OtherPacket pc = pset1<OtherPacket>(c);
427 const OtherPacket ps = pset1<OtherPacket>(s);
428 conj_helper<OtherPacket,Packet,NumTraits<OtherPacket>::IsComplex,false> pcj;
429 conj_helper<OtherPacket,Packet,false,false> pm;
430 Scalar* EIGEN_RESTRICT px = x;
431 Scalar* EIGEN_RESTRICT py = y;
432 for(Index i=0; i<size; i+=PacketSize)
433 {
434 Packet xi = pload<Packet>(px);
435 Packet yi = pload<Packet>(py);
436 pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
437 pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
438 px += PacketSize;
439 py += PacketSize;
440 }
441 }
443 /*** non-vectorized path ***/
444 else
446 apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,false>::run(x,incrx,y,incry,size,c,s);
447 }
448 }
449};
450
451template<typename VectorX, typename VectorY, typename OtherScalar>
452EIGEN_DEVICE_FUNC
453void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j)
454{
455 typedef typename VectorX::Scalar Scalar;
456 const bool Vectorizable = (int(VectorX::Flags) & int(VectorY::Flags) & PacketAccessBit)
457 && (int(packet_traits<Scalar>::size) == int(packet_traits<OtherScalar>::size));
458
459 eigen_assert(xpr_x.size() == xpr_y.size());
460 Index size = xpr_x.size();
461 Index incrx = xpr_x.derived().innerStride();
462 Index incry = xpr_y.derived().innerStride();
463
464 Scalar* EIGEN_RESTRICT x = &xpr_x.derived().coeffRef(0);
465 Scalar* EIGEN_RESTRICT y = &xpr_y.derived().coeffRef(0);
466
467 OtherScalar c = j.c();
468 OtherScalar s = j.s();
469 if (c==OtherScalar(1) && s==OtherScalar(0))
470 return;
471
472 apply_rotation_in_the_plane_selector<
473 Scalar,OtherScalar,
474 VectorX::SizeAtCompileTime,
475 EIGEN_PLAIN_ENUM_MIN(evaluator<VectorX>::Alignment, evaluator<VectorY>::Alignment),
476 Vectorizable>::run(x,incrx,y,incry,size,c,s);
477}
478
479} // end namespace internal
480
481} // end namespace Eigen
482
483#endif // EIGEN_JACOBI_H
CoeffReturnType coeff(Index row, Index col) const
Definition: DenseCoeffsBase.h:97
Rotation given by a cosine-sine pair.
Definition: Jacobi.h:35
JacobiRotation()
Definition: Jacobi.h:41
JacobiRotation(const Scalar &c, const Scalar &s)
Definition: Jacobi.h:45
bool makeJacobi(const MatrixBase< Derived > &, Index p, Index q)
Definition: Jacobi.h:139
JacobiRotation adjoint() const
Definition: Jacobi.h:67
JacobiRotation transpose() const
Definition: Jacobi.h:63
JacobiRotation operator*(const JacobiRotation &other)
Definition: Jacobi.h:54
void makeGivens(const Scalar &p, const Scalar &q, Scalar *r=0)
Definition: Jacobi.h:162
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
const unsigned int PacketAccessBit
Definition: Constants.h:94
Namespace containing all symbols from the Eigen library.
Definition: Core:141
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_conjugate_op< typename Derived::Scalar >, const Derived > conj(const Eigen::ArrayBase< Derived > &x)
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const int Dynamic
Definition: Constants.h:22
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233