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
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_SPARSEMATRIX_H
#define EIGEN_SPARSEMATRIX_H
/** \ingroup Sparse_Module
*
* \class SparseMatrix
*
* \brief The main sparse matrix class
*
* This class implements a sparse matrix using the very common compressed row/column storage
* scheme.
*
* \param _Scalar the scalar type, i.e. the type of the coefficients
* \param _Options Union of bit flags controlling the storage scheme. Currently the only possibility
* is RowMajor. The default is 0 which means column-major.
*
* See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
*
*/
template<typename _Scalar, int _Options>
struct ei_traits<SparseMatrix<_Scalar, _Options> >
{
typedef _Scalar Scalar;
enum {
RowsAtCompileTime = Dynamic,
ColsAtCompileTime = Dynamic,
MaxRowsAtCompileTime = Dynamic,
MaxColsAtCompileTime = Dynamic,
Flags = SparseBit | _Options,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
SupportedAccessPatterns = InnerRandomAccessPattern
};
};
template<typename _Scalar, int _Options>
class SparseMatrix
: public SparseMatrixBase<SparseMatrix<_Scalar, _Options> >
{
public:
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseMatrix)
EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, +=)
EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, -=)
// FIXME: why are these operator already alvailable ???
// EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(SparseMatrix, *=)
// EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(SparseMatrix, /=)
typedef MappedSparseMatrix<Scalar,Flags> Map;
using Base::IsRowMajor;
protected:
typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;
int m_outerSize;
int m_innerSize;
int* m_outerIndex;
CompressedStorage<Scalar> m_data;
public:
inline int rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
inline int cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
inline int innerSize() const { return m_innerSize; }
inline int outerSize() const { return m_outerSize; }
inline int innerNonZeros(int j) const { return m_outerIndex[j+1]-m_outerIndex[j]; }
inline const Scalar* _valuePtr() const { return &m_data.value(0); }
inline Scalar* _valuePtr() { return &m_data.value(0); }
inline const int* _innerIndexPtr() const { return &m_data.index(0); }
inline int* _innerIndexPtr() { return &m_data.index(0); }
inline const int* _outerIndexPtr() const { return m_outerIndex; }
inline int* _outerIndexPtr() { return m_outerIndex; }
inline Scalar coeff(int row, int col) const
{
const int outer = IsRowMajor ? row : col;
const int inner = IsRowMajor ? col : row;
return m_data.atInRange(m_outerIndex[outer], m_outerIndex[outer+1], inner);
}
inline Scalar& coeffRef(int row, int col)
{
const int outer = IsRowMajor ? row : col;
const int inner = IsRowMajor ? col : row;
int start = m_outerIndex[outer];
int end = m_outerIndex[outer+1];
ei_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
ei_assert(end>start && "coeffRef cannot be called on a zero coefficient");
const int id = m_data.searchLowerIndex(start,end-1,inner);
ei_assert((id<end) && (m_data.index(id)==inner) && "coeffRef cannot be called on a zero coefficient");
return m_data.value(id);
}
public:
class InnerIterator;
/** Removes all non zeros */
inline void setZero()
{
m_data.clear();
memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(int));
}
/** \returns the number of non zero coefficients */
inline int nonZeros() const { return m_data.size(); }
/** \deprecated use setZero() and reserve()
* Initializes the filling process of \c *this.
* \param reserveSize approximate number of nonzeros
* Note that the matrix \c *this is zero-ed.
*/
EIGEN_DEPRECATED void startFill(int reserveSize = 1000)
{
setZero();
m_data.reserve(reserveSize);
}
/** Preallocates \a reserveSize non zeros */
inline void reserve(int reserveSize)
{
m_data.reserve(reserveSize);
}
/** \deprecated use insert()
*/
EIGEN_DEPRECATED Scalar& fill(int row, int col)
{
const int outer = IsRowMajor ? row : col;
const int inner = IsRowMajor ? col : row;
if (m_outerIndex[outer+1]==0)
{
// we start a new inner vector
int i = outer;
while (i>=0 && m_outerIndex[i]==0)
{
m_outerIndex[i] = m_data.size();
--i;
}
m_outerIndex[outer+1] = m_outerIndex[outer];
}
else
{
ei_assert(m_data.index(m_data.size()-1)<inner && "wrong sorted insertion");
}
// std::cerr << size_t(m_outerIndex[outer+1]) << " == " << m_data.size() << "\n";
assert(size_t(m_outerIndex[outer+1]) == m_data.size());
int id = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
m_data.append(0, inner);
return m_data.value(id);
}
//--- low level purely coherent filling ---
inline Scalar& insertBack(int outer, int inner)
{
ei_assert(size_t(m_outerIndex[outer+1]) == m_data.size() && "wrong sorted insertion");
ei_assert( (m_outerIndex[outer+1]-m_outerIndex[outer]==0 || m_data.index(m_data.size()-1)<inner) && "wrong sorted insertion");
int id = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
m_data.append(0, inner);
return m_data.value(id);
}
inline void startVec(int outer)
{
ei_assert(m_outerIndex[outer]==int(m_data.size()) && "you must call startVec on each inner vec");
ei_assert(m_outerIndex[outer+1]==0 && "you must call startVec on each inner vec");
m_outerIndex[outer+1] = m_outerIndex[outer];
}
//---
/** \deprecated use insert()
* Like fill() but with random inner coordinates.
*/
EIGEN_DEPRECATED Scalar& fillrand(int row, int col)
{
return insert(row,col);
}
/** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
* The non zero coefficient must \b not already exist.
*
* \warning This function can be extremely slow if the non zero coefficients
* are not inserted in a coherent order.
*
* After an insertion session, you should call the finalize() function.
*/
EIGEN_DONT_INLINE Scalar& insert(int row, int col)
{
const int outer = IsRowMajor ? row : col;
const int inner = IsRowMajor ? col : row;
int previousOuter = outer;
if (m_outerIndex[outer+1]==0)
{
// we start a new inner vector
while (previousOuter>=0 && m_outerIndex[previousOuter]==0)
{
m_outerIndex[previousOuter] = m_data.size();
--previousOuter;
}
m_outerIndex[outer+1] = m_outerIndex[outer];
}
// here we have to handle the tricky case where the outerIndex array
// starts with: [ 0 0 0 0 0 1 ...] and we are inserting in, e.g.,
// the 2nd inner vector...
bool isLastVec = (!(previousOuter==-1 && m_data.size()!=0))
&& (size_t(m_outerIndex[outer+1]) == m_data.size());
size_t startId = m_outerIndex[outer];
// FIXME let's make sure sizeof(long int) == sizeof(size_t)
size_t id = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
float reallocRatio = 1;
if (m_data.allocatedSize()<=m_data.size())
{
// if there is no preallocated memory, let's reserve a minimum of 32 elements
if (m_data.size()==0)
{
m_data.reserve(32);
}
else
{
// we need to reallocate the data, to reduce multiple reallocations
// we use a smart resize algorithm based on the current filling ratio
// in addition, we use float to avoid integers overflows
float nnzEstimate = float(m_outerIndex[outer])*float(m_outerSize)/float(outer+1);
reallocRatio = (nnzEstimate-float(m_data.size()))/float(m_data.size());
// furthermore we bound the realloc ratio to:
// 1) reduce multiple minor realloc when the matrix is almost filled
// 2) avoid to allocate too much memory when the matrix is almost empty
reallocRatio = std::min(std::max(reallocRatio,1.5f),8.f);
}
}
m_data.resize(m_data.size()+1,reallocRatio);
if (!isLastVec)
{
if (previousOuter==-1)
{
// oops wrong guess.
// let's correct the outer offsets
for (int k=0; k<=(outer+1); ++k)
m_outerIndex[k] = 0;
int k=outer+1;
while(m_outerIndex[k]==0)
m_outerIndex[k++] = 1;
while (k<=m_outerSize && m_outerIndex[k]!=0)
m_outerIndex[k++]++;
id = 0;
--k;
k = m_outerIndex[k]-1;
while (k>0)
{
m_data.index(k) = m_data.index(k-1);
m_data.value(k) = m_data.value(k-1);
k--;
}
}
else
{
// we are not inserting into the last inner vec
// update outer indices:
int j = outer+2;
while (j<=m_outerSize && m_outerIndex[j]!=0)
m_outerIndex[j++]++;
--j;
// shift data of last vecs:
int k = m_outerIndex[j]-1;
while (k>=int(id))
{
m_data.index(k) = m_data.index(k-1);
m_data.value(k) = m_data.value(k-1);
k--;
}
}
}
while ( (id > startId) && (m_data.index(id-1) > inner) )
{
m_data.index(id) = m_data.index(id-1);
m_data.value(id) = m_data.value(id-1);
--id;
}
m_data.index(id) = inner;
return (m_data.value(id) = 0);
}
EIGEN_DEPRECATED void endFill() { finalize(); }
/** Must be called after inserting a set of non zero entries.
*/
inline void finalize()
{
int size = m_data.size();
int i = m_outerSize;
// find the last filled column
while (i>=0 && m_outerIndex[i]==0)
--i;
++i;
while (i<=m_outerSize)
{
m_outerIndex[i] = size;
++i;
}
}
void prune(Scalar reference, RealScalar epsilon = precision<RealScalar>())
{
int k = 0;
for (int j=0; j<m_outerSize; ++j)
{
int previousStart = m_outerIndex[j];
m_outerIndex[j] = k;
int end = m_outerIndex[j+1];
for (int i=previousStart; i<end; ++i)
{
if (!ei_isMuchSmallerThan(m_data.value(i), reference, epsilon))
{
m_data.value(k) = m_data.value(i);
m_data.index(k) = m_data.index(i);
++k;
}
}
}
m_outerIndex[m_outerSize] = k;
m_data.resize(k,0);
}
/** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero
* \sa resizeNonZeros(int), reserve(), setZero()
*/
void resize(int rows, int cols)
{
const int outerSize = IsRowMajor ? rows : cols;
m_innerSize = IsRowMajor ? cols : rows;
m_data.clear();
if (m_outerSize != outerSize || m_outerSize==0)
{
delete[] m_outerIndex;
m_outerIndex = new int [outerSize+1];
m_outerSize = outerSize;
}
memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(int));
}
void resizeNonZeros(int size)
{
m_data.resize(size);
}
inline SparseMatrix()
: m_outerSize(-1), m_innerSize(0), m_outerIndex(0)
{
resize(0, 0);
}
inline SparseMatrix(int rows, int cols)
: m_outerSize(0), m_innerSize(0), m_outerIndex(0)
{
resize(rows, cols);
}
template<typename OtherDerived>
inline SparseMatrix(const SparseMatrixBase<OtherDerived>& other)
: m_outerSize(0), m_innerSize(0), m_outerIndex(0)
{
*this = other.derived();
}
inline SparseMatrix(const SparseMatrix& other)
: Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0)
{
*this = other.derived();
}
inline void swap(SparseMatrix& other)
{
//EIGEN_DBG_SPARSE(std::cout << "SparseMatrix:: swap\n");
std::swap(m_outerIndex, other.m_outerIndex);
std::swap(m_innerSize, other.m_innerSize);
std::swap(m_outerSize, other.m_outerSize);
m_data.swap(other.m_data);
}
inline SparseMatrix& operator=(const SparseMatrix& other)
{
// std::cout << "SparseMatrix& operator=(const SparseMatrix& other)\n";
if (other.isRValue())
{
swap(other.const_cast_derived());
}
else
{
resize(other.rows(), other.cols());
memcpy(m_outerIndex, other.m_outerIndex, (m_outerSize+1)*sizeof(int));
m_data = other.m_data;
}
return *this;
}
template<typename OtherDerived>
inline SparseMatrix& operator=(const SparseMatrixBase<OtherDerived>& other)
{
const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
if (needToTranspose)
{
// two passes algorithm:
// 1 - compute the number of coeffs per dest inner vector
// 2 - do the actual copy/eval
// Since each coeff of the rhs has to be evaluated twice, let's evauluate it if needed
//typedef typename ei_nested<OtherDerived,2>::type OtherCopy;
typedef typename ei_eval<OtherDerived>::type OtherCopy;
typedef typename ei_cleantype<OtherCopy>::type _OtherCopy;
OtherCopy otherCopy(other.derived());
resize(other.rows(), other.cols());
Eigen::Map<VectorXi>(m_outerIndex,outerSize()).setZero();
// pass 1
// FIXME the above copy could be merged with that pass
for (int j=0; j<otherCopy.outerSize(); ++j)
for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
++m_outerIndex[it.index()];
// prefix sum
int count = 0;
VectorXi positions(outerSize());
for (int j=0; j<outerSize(); ++j)
{
int tmp = m_outerIndex[j];
m_outerIndex[j] = count;
positions[j] = count;
count += tmp;
}
m_outerIndex[outerSize()] = count;
// alloc
m_data.resize(count);
// pass 2
for (int j=0; j<otherCopy.outerSize(); ++j)
for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
{
int pos = positions[it.index()]++;
m_data.index(pos) = j;
m_data.value(pos) = it.value();
}
return *this;
}
else
{
// there is no special optimization
return SparseMatrixBase<SparseMatrix>::operator=(other.derived());
}
}
friend std::ostream & operator << (std::ostream & s, const SparseMatrix& m)
{
EIGEN_DBG_SPARSE(
s << "Nonzero entries:\n";
for (int i=0; i<m.nonZeros(); ++i)
{
s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
}
s << std::endl;
s << std::endl;
s << "Column pointers:\n";
for (int i=0; i<m.outerSize(); ++i)
{
s << m.m_outerIndex[i] << " ";
}
s << " $" << std::endl;
s << std::endl;
);
s << static_cast<const SparseMatrixBase<SparseMatrix>&>(m);
return s;
}
/** Destructor */
inline ~SparseMatrix()
{
delete[] m_outerIndex;
}
/** Overloaded for performance */
Scalar sum() const;
};
template<typename Scalar, int _Options>
class SparseMatrix<Scalar,_Options>::InnerIterator
{
public:
InnerIterator(const SparseMatrix& mat, int outer)
: m_matrix(mat), m_outer(outer), m_id(mat.m_outerIndex[outer]), m_start(m_id), m_end(mat.m_outerIndex[outer+1])
{}
template<unsigned int Added, unsigned int Removed>
InnerIterator(const Flagged<SparseMatrix,Added,Removed>& mat, int outer)
: m_matrix(mat._expression()), m_outer(outer), m_id(m_matrix.m_outerIndex[outer]),
m_start(m_id), m_end(m_matrix.m_outerIndex[outer+1])
{}
inline InnerIterator& operator++() { m_id++; return *this; }
inline Scalar value() const { return m_matrix.m_data.value(m_id); }
inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.m_data.value(m_id)); }
inline int index() const { return m_matrix.m_data.index(m_id); }
inline int row() const { return IsRowMajor ? m_outer : index(); }
inline int col() const { return IsRowMajor ? index() : m_outer; }
inline operator bool() const { return (m_id < m_end) && (m_id>=m_start); }
protected:
const SparseMatrix& m_matrix;
const int m_outer;
int m_id;
const int m_start;
const int m_end;
};
#endif // EIGEN_SPARSEMATRIX_H
|