OpenVDB 7.0.0

ConjGradient.h
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1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3
8
9 #ifndef OPENVDB_MATH_CONJGRADIENT_HAS_BEEN_INCLUDED
10 #define OPENVDB_MATH_CONJGRADIENT_HAS_BEEN_INCLUDED
11
12 #include <openvdb/Exceptions.h>
13 #include <openvdb/Types.h>
14 #include <openvdb/util/logging.h>
15 #include <openvdb/util/NullInterrupter.h>
16 #include "Math.h" // for Abs(), isZero(), Max(), Sqrt()
17 #include <tbb/parallel_for.h>
18 #include <tbb/parallel_reduce.h>
19 #include <algorithm> // for std::lower_bound()
20 #include <cassert>
21 #include <cmath> // for std::isfinite()
22 #include <limits>
23 #include <sstream>
24 #include <string>
25
26
27 namespace openvdb {
28 OPENVDB_USE_VERSION_NAMESPACE
29 namespace OPENVDB_VERSION_NAME {
30 namespace math {
31 namespace pcg {
32
33 using SizeType = Index32;
34
35 using SizeRange = tbb::blocked_range<SizeType>;
36
37 template<typename ValueType> class Vector;
38
39 template<typename ValueType, SizeType STENCIL_SIZE> class SparseStencilMatrix;
40
41 template<typename ValueType> class Preconditioner;
42 template<typename MatrixType> class JacobiPreconditioner;
43 template<typename MatrixType> class IncompleteCholeskyPreconditioner;
44
46 struct State {
47 bool success;
48 int iterations;
49 double relativeError;
50 double absoluteError;
51 };
52
53
55 template<typename ValueType>
56 inline State
57 terminationDefaults()
58 {
59 State s;
60 s.success = false;
61 s.iterations = 50;
62 s.relativeError = 1.0e-6;
63 s.absoluteError = std::numeric_limits<ValueType>::epsilon() * 100.0;
64 return s;
65 }
66
67
69
70
90 template<typename PositiveDefMatrix>
91 inline State
92 solve(
93 const PositiveDefMatrix& A,
94 const Vector<typename PositiveDefMatrix::ValueType>& b,
95 Vector<typename PositiveDefMatrix::ValueType>& x,
96 Preconditioner<typename PositiveDefMatrix::ValueType>& preconditioner,
97 const State& termination = terminationDefaults<typename PositiveDefMatrix::ValueType>());
98
99
122 template<typename PositiveDefMatrix, typename Interrupter>
123 inline State
124 solve(
125 const PositiveDefMatrix& A,
126 const Vector<typename PositiveDefMatrix::ValueType>& b,
127 Vector<typename PositiveDefMatrix::ValueType>& x,
128 Preconditioner<typename PositiveDefMatrix::ValueType>& preconditioner,
129 Interrupter& interrupter,
130 const State& termination = terminationDefaults<typename PositiveDefMatrix::ValueType>());
131
132
134
135
137 template<typename T>
138 class Vector
139 {
140 public:
141 using ValueType = T;
142 using Ptr = SharedPtr<Vector>;
143
145 Vector(): mData(nullptr), mSize(0) {}
147 Vector(SizeType n): mData(new T[n]), mSize(n) {}
149 Vector(SizeType n, const ValueType& val): mData(new T[n]), mSize(n) { this->fill(val); }
150
151 ~Vector() { mSize = 0; delete[] mData; mData = nullptr; }
152
154 Vector(const Vector&);
156 Vector& operator=(const Vector&);
157
159 SizeType size() const { return mSize; }
161 bool empty() const { return (mSize == 0); }
162
165 void resize(SizeType n);
166
168 void swap(Vector& other) { std::swap(mData, other.mData); std::swap(mSize, other.mSize); }
169
171 void fill(const ValueType& value);
172
174 template<typename Scalar> void scale(const Scalar& s);
176 template<typename Scalar> Vector& operator*=(const Scalar& s) { this->scale(s); return *this; }
178
180 ValueType dot(const Vector&) const;
181
183 ValueType infNorm() const;
185 ValueType l2Norm() const { return Sqrt(this->dot(*this)); }
186
188 bool isFinite() const;
189
192 template<typename OtherValueType>
193 bool eq(const Vector<OtherValueType>& other,
194 ValueType eps = Tolerance<ValueType>::value()) const;
195
197 std::string str() const;
198
200 inline T& at(SizeType i) { return mData[i]; }
202 inline const T& at(SizeType i) const { return mData[i]; }
203 inline T& operator[](SizeType i) { return this->at(i); }
204 inline const T& operator[](SizeType i) const { return this->at(i); }
206
208 inline T* data() { return mData; }
210 inline const T* data() const { return mData; }
211 inline const T* constData() const { return mData; }
213
214 private:
215 // Functor for use with tbb::parallel_for()
216 template<typename Scalar> struct ScaleOp;
217 struct DeterministicDotProductOp;
218 // Functors for use with tbb::parallel_reduce()
219 template<typename OtherValueType> struct EqOp;
220 struct InfNormOp;
221 struct IsFiniteOp;
222
223 T* mData;
224 SizeType mSize;
225 };
226
227 using VectorS = Vector<float>;
228 using VectorD = Vector<double>;
229
230
232
233
236 template<typename ValueType_, SizeType STENCIL_SIZE>
237 class SparseStencilMatrix
238 {
239 public:
240 using ValueType = ValueType_;
241 using VectorType = Vector<ValueType>;
242 using Ptr = SharedPtr<SparseStencilMatrix>;
243
244 class ConstValueIter;
245 class ConstRow;
246 class RowEditor;
247
248 static const ValueType sZeroValue;
249
251 SparseStencilMatrix(SizeType n);
252
254 SparseStencilMatrix(const SparseStencilMatrix&);
255
257 SizeType numRows() const { return mNumRows; }
259 SizeType size() const { return mNumRows; }
261
265 void setValue(SizeType row, SizeType col, const ValueType&);
266
268 const ValueType& getValue(SizeType row, SizeType col) const;
272 const ValueType& operator()(SizeType row, SizeType col) const;
274
276 ConstRow getConstRow(SizeType row) const;
277
279 RowEditor getRowEditor(SizeType row);
280
282 template<typename Scalar> void scale(const Scalar& s);
284 template<typename Scalar>
285 SparseStencilMatrix& operator*=(const Scalar& s) { this->scale(s); return *this; }
287
291 template<typename VecValueType>
292 void vectorMultiply(const Vector<VecValueType>& inVec, Vector<VecValueType>& resultVec) const;
293
298 template<typename VecValueType>
299 void vectorMultiply(const VecValueType* inVec, VecValueType* resultVec) const;
300
303 template<typename OtherValueType>
304 bool eq(const SparseStencilMatrix<OtherValueType, STENCIL_SIZE>& other,
305 ValueType eps = Tolerance<ValueType>::value()) const;
306
308 bool isFinite() const;
309
311 std::string str() const;
312
313 private:
314 struct RowData {
315 RowData(ValueType* v, SizeType* c, SizeType& s): mVals(v), mCols(c), mSize(s) {}
316 ValueType* mVals; SizeType* mCols; SizeType& mSize;
317 };
318
319 struct ConstRowData {
320 ConstRowData(const ValueType* v, const SizeType* c, const SizeType& s):
321 mVals(v), mCols(c), mSize(s) {}
322 const ValueType* mVals; const SizeType* mCols; const SizeType& mSize;
323 };
324
326 template<typename DataType_ = RowData>
327 class RowBase
328 {
329 public:
330 using DataType = DataType_;
331
332 static SizeType capacity() { return STENCIL_SIZE; }
333
334 RowBase(const DataType& data): mData(data) {}
335
336 bool empty() const { return (mData.mSize == 0); }
337 const SizeType& size() const { return mData.mSize; }
338
339 const ValueType& getValue(SizeType columnIdx, bool& active) const;
340 const ValueType& getValue(SizeType columnIdx) const;
341
343 ConstValueIter cbegin() const;
344
347 template<typename OtherDataType>
348 bool eq(const RowBase<OtherDataType>& other,
349 ValueType eps = Tolerance<ValueType>::value()) const;
350
354 template<typename VecValueType>
355 VecValueType dot(const VecValueType* inVec, SizeType vecSize) const;
356
358 template<typename VecValueType>
359 VecValueType dot(const Vector<VecValueType>& inVec) const;
360
362 std::string str() const;
363
364 protected:
365 friend class ConstValueIter;
366
367 const ValueType& value(SizeType i) const { return mData.mVals[i]; }
368 SizeType column(SizeType i) const { return mData.mCols[i]; }
369
374 SizeType find(SizeType columnIdx) const;
375
376 DataType mData;
377 };
378
379 using ConstRowBase = RowBase<ConstRowData>;
380
381 public:
383 class ConstValueIter
384 {
385 public:
386 const ValueType& operator*() const
387 {
388 if (mData.mSize == 0) return SparseStencilMatrix::sZeroValue;
389 return mData.mVals[mCursor];
390 }
391
392 SizeType column() const { return mData.mCols[mCursor]; }
393
394 void increment() { mCursor++; }
395 ConstValueIter& operator++() { increment(); return *this; }
396 operator bool() const { return (mCursor < mData.mSize); }
397
398 void reset() { mCursor = 0; }
399
400 private:
401 friend class SparseStencilMatrix;
402 ConstValueIter(const RowData& d): mData(d.mVals, d.mCols, d.mSize), mCursor(0) {}
403 ConstValueIter(const ConstRowData& d): mData(d), mCursor(0) {}
404
405 const ConstRowData mData;
406 SizeType mCursor;
407 };
408
409
411 class ConstRow: public ConstRowBase
412 {
413 public:
414 ConstRow(const ValueType* valueHead, const SizeType* columnHead, const SizeType& rowSize);
415 }; // class ConstRow
416
417
419 class RowEditor: public RowBase<>
420 {
421 public:
422 RowEditor(ValueType* valueHead, SizeType* columnHead, SizeType& rowSize, SizeType colSize);
423
425 void clear();
426
429 SizeType setValue(SizeType column, const ValueType& value);
430
432 template<typename Scalar> void scale(const Scalar&);
434 template<typename Scalar>
435 RowEditor& operator*=(const Scalar& s) { this->scale(s); return *this; }
437
438 private:
439 const SizeType mNumColumns; // used only for bounds checking
440 }; // class RowEditor
441
442 private:
443 // Functors for use with tbb::parallel_for()
444 struct MatrixCopyOp;
445 template<typename VecValueType> struct VecMultOp;
446 template<typename Scalar> struct RowScaleOp;
447
448 // Functors for use with tbb::parallel_reduce()
449 struct IsFiniteOp;
450 template<typename OtherValueType> struct EqOp;
451
452 const SizeType mNumRows;
453 std::unique_ptr<ValueType[]> mValueArray;
454 std::unique_ptr<SizeType[]> mColumnIdxArray;
455 std::unique_ptr<SizeType[]> mRowSizeArray;
456 }; // class SparseStencilMatrix
457
458
460
461
463 template<typename T>
464 class Preconditioner
465 {
466 public:
467 using ValueType = T;
468 using Ptr = SharedPtr<Preconditioner>;
469
470 template<SizeType STENCIL_SIZE> Preconditioner(const SparseStencilMatrix<T, STENCIL_SIZE>&) {}
471 virtual ~Preconditioner() = default;
472
473 virtual bool isValid() const { return true; }
474
479 virtual void apply(const Vector<T>& r, Vector<T>& z) = 0;
480 };
481
482
484
485
486 namespace internal {
487
488 // Functor for use with tbb::parallel_for() to copy data from one array to another
489 template<typename T>
490 struct CopyOp
491 {
492 CopyOp(const T* from_, T* to_): from(from_), to(to_) {}
493
494 void operator()(const SizeRange& range) const {
495 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) to[n] = from[n];
496 }
497
498 const T* from;
499 T* to;
500 };
501
502
503 // Functor for use with tbb::parallel_for() to fill an array with a constant value
504 template<typename T>
505 struct FillOp
506 {
507 FillOp(T* data_, const T& val_): data(data_), val(val_) {}
508
509 void operator()(const SizeRange& range) const {
510 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) data[n] = val;
511 }
512
513 T* data;
514 const T val;
515 };
516
517
518 // Functor for use with tbb::parallel_for() that computes a * x + y
519 template<typename T>
520 struct LinearOp
521 {
522 LinearOp(const T& a_, const T* x_, const T* y_, T* out_): a(a_), x(x_), y(y_), out(out_) {}
523
524 void operator()(const SizeRange& range) const {
525 if (isExactlyEqual(a, T(1))) {
526 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) out[n] = x[n] + y[n];
527 } else if (isExactlyEqual(a, T(-1))) {
528 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) out[n] = -x[n] + y[n];
529 } else {
530 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) out[n] = a * x[n] + y[n];
531 }
532 }
533
534 const T a, *x, *y;
535 T* out;
536 };
537
538 } // namespace internal
539
540
542
543
544 inline std::ostream&
545 operator<<(std::ostream& os, const State& state)
546 {
547 os << (state.success ? "succeeded with " : "")
548 << "rel. err. " << state.relativeError << ", abs. err. " << state.absoluteError
549 << " after " << state.iterations << " iteration" << (state.iterations == 1 ? "" : "s");
550 return os;
551 }
552
553
555
556
557 template<typename T>
558 inline
559 Vector<T>::Vector(const Vector& other): mData(new T[other.mSize]), mSize(other.mSize)
560 {
561 tbb::parallel_for(SizeRange(0, mSize),
562 internal::CopyOp<T>(/*from=*/other.mData, /*to=*/mData));
563 }
564
565
566 template<typename T>
567 inline
568 Vector<T>& Vector<T>::operator=(const Vector<T>& other)
569 {
570 // Update the internal storage to the correct size
571
572 if (mSize != other.mSize) {
573 mSize = other.mSize;
574 delete[] mData;
575 mData = new T[mSize];
576 }
577
578 // Deep copy the data
579 tbb::parallel_for(SizeRange(0, mSize),
580 internal::CopyOp<T>(/*from=*/other.mData, /*to=*/mData));
581
582 return *this;
583 }
584
585
586 template<typename T>
587 inline void
588 Vector<T>::resize(SizeType n)
589 {
590 if (n != mSize) {
591 if (mData) delete[] mData;
592 mData = new T[n];
593 mSize = n;
594 }
595 }
596
597
598 template<typename T>
599 inline void
600 Vector<T>::fill(const ValueType& value)
601 {
602 tbb::parallel_for(SizeRange(0, mSize), internal::FillOp<T>(mData, value));
603 }
604
605
606 template<typename T>
607 template<typename Scalar>
608 struct Vector<T>::ScaleOp
609 {
610 ScaleOp(T* data_, const Scalar& s_): data(data_), s(s_) {}
611
612 void operator()(const SizeRange& range) const {
613 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) data[n] *= s;
614 }
615
616 T* data;
617 const Scalar s;
618 };
619
620
621 template<typename T>
622 template<typename Scalar>
623 inline void
624 Vector<T>::scale(const Scalar& s)
625 {
626 tbb::parallel_for(SizeRange(0, mSize), ScaleOp<Scalar>(mData, s));
627 }
628
629
630 template<typename T>
631 struct Vector<T>::DeterministicDotProductOp
632 {
633 DeterministicDotProductOp(const T* a_, const T* b_,
634 const SizeType binCount_, const SizeType arraySize_, T* reducetmp_):
635 a(a_), b(b_), binCount(binCount_), arraySize(arraySize_), reducetmp(reducetmp_) {}
636
637 void operator()(const SizeRange& range) const
638 {
639 const SizeType binSize = arraySize / binCount;
640
641 // Iterate over bins (array segments)
642 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
643 const SizeType begin = n * binSize;
644 const SizeType end = (n == binCount-1) ? arraySize : begin + binSize;
645
646 // Compute the partial sum for this array segment
647 T sum = zeroVal<T>();
648 for (SizeType i = begin; i < end; ++i) { sum += a[i] * b[i]; }
649 // Store the partial sum
650 reducetmp[n] = sum;
651 }
652 }
653
654
655 const T* a;
656 const T* b;
657 const SizeType binCount;
658 const SizeType arraySize;
659 T* reducetmp;
660 };
661
662 template<typename T>
663 inline T
664 Vector<T>::dot(const Vector<T>& other) const
665 {
666 assert(this->size() == other.size());
667
668 const T* aData = this->data();
669 const T* bData = other.data();
670
671 SizeType arraySize = this->size();
672
673 T result = zeroVal<T>();
674
675 if (arraySize < 1024) {
676
677 // Compute the dot product in serial for small arrays
678
679 for (SizeType n = 0; n < arraySize; ++n) {
680 result += aData[n] * bData[n];
681 }
682
683 } else {
684
685 // Compute the dot product by segmenting the arrays into
686 // a predetermined number of sub arrays in parallel and
687 // accumulate the finial result in series.
688
689 const SizeType binCount = 100;
690 T partialSums[100];
691
692 tbb::parallel_for(SizeRange(0, binCount),
693 DeterministicDotProductOp(aData, bData, binCount, arraySize, partialSums));
694
695 for (SizeType n = 0; n < binCount; ++n) {
696 result += partialSums[n];
697 }
698 }
699
700 return result;
701 }
702
703
704 template<typename T>
705 struct Vector<T>::InfNormOp
706 {
707 InfNormOp(const T* data_): data(data_) {}
708
709 T operator()(const SizeRange& range, T maxValue) const
710 {
711 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
712 maxValue = Max(maxValue, Abs(data[n]));
713 }
714 return maxValue;
715 }
716
717 const T* data;
718 };
719
720
721 template<typename T>
722 inline T
723 Vector<T>::infNorm() const
724 {
725 // Parallelize over the elements of this vector.
726 T result = tbb::parallel_reduce(SizeRange(0, this->size()), /*seed=*/zeroVal<T>(),
727 InfNormOp(this->data()), /*join=*/[](T max1, T max2) { return Max(max1, max2); });
728 return result;
729 }
730
731
732 template<typename T>
733 struct Vector<T>::IsFiniteOp
734 {
735 IsFiniteOp(const T* data_): data(data_) {}
736
737 bool operator()(const SizeRange& range, bool finite) const
738 {
739 if (finite) {
740 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
741 if (!std::isfinite(data[n])) return false;
742 }
743 }
744 return finite;
745 }
746
747 const T* data;
748 };
749
750
751 template<typename T>
752 inline bool
753 Vector<T>::isFinite() const
754 {
755 // Parallelize over the elements of this vector.
756 bool finite = tbb::parallel_reduce(SizeRange(0, this->size()), /*seed=*/true,
757 IsFiniteOp(this->data()),
758 /*join=*/[](bool finite1, bool finite2) { return (finite1 && finite2); });
759 return finite;
760 }
761
762
763 template<typename T>
764 template<typename OtherValueType>
765 struct Vector<T>::EqOp
766 {
767 EqOp(const T* a_, const OtherValueType* b_, T e): a(a_), b(b_), eps(e) {}
768
769 bool operator()(const SizeRange& range, bool equal) const
770 {
771 if (equal) {
772 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
773 if (!isApproxEqual(a[n], b[n], eps)) return false;
774 }
775 }
776 return equal;
777 }
778
779 const T* a;
780 const OtherValueType* b;
781 const T eps;
782 };
783
784
785 template<typename T>
786 template<typename OtherValueType>
787 inline bool
788 Vector<T>::eq(const Vector<OtherValueType>& other, ValueType eps) const
789 {
790 if (this->size() != other.size()) return false;
791 bool equal = tbb::parallel_reduce(SizeRange(0, this->size()), /*seed=*/true,
792 EqOp<OtherValueType>(this->data(), other.data(), eps),
793 /*join=*/[](bool eq1, bool eq2) { return (eq1 && eq2); });
794 return equal;
795 }
796
797
798 template<typename T>
799 inline std::string
800 Vector<T>::str() const
801 {
802 std::ostringstream ostr;
803 ostr << "[";
804 std::string sep;
805 for (SizeType n = 0, N = this->size(); n < N; ++n) {
806 ostr << sep << (*this)[n];
807 sep = ", ";
808 }
809 ostr << "]";
810 return ostr.str();
811 }
812
813
815
816
817 template<typename ValueType, SizeType STENCIL_SIZE>
818 const ValueType SparseStencilMatrix<ValueType, STENCIL_SIZE>::sZeroValue = zeroVal<ValueType>();
819
820
821 template<typename ValueType, SizeType STENCIL_SIZE>
822 inline
823 SparseStencilMatrix<ValueType, STENCIL_SIZE>::SparseStencilMatrix(SizeType numRows)
824 : mNumRows(numRows)
825 , mValueArray(new ValueType[mNumRows * STENCIL_SIZE])
826 , mColumnIdxArray(new SizeType[mNumRows * STENCIL_SIZE])
827 , mRowSizeArray(new SizeType[mNumRows])
828 {
829 // Initialize the matrix to a null state by setting the size of each row to zero.
830 tbb::parallel_for(SizeRange(0, mNumRows),
831 internal::FillOp<SizeType>(mRowSizeArray.get(), /*value=*/0));
832 }
833
834
835 template<typename ValueType, SizeType STENCIL_SIZE>
836 struct SparseStencilMatrix<ValueType, STENCIL_SIZE>::MatrixCopyOp
837 {
838 MatrixCopyOp(const SparseStencilMatrix& from_, SparseStencilMatrix& to_):
839 from(&from_), to(&to_) {}
840
841 void operator()(const SizeRange& range) const
842 {
843 const ValueType* fromVal = from->mValueArray.get();
844 const SizeType* fromCol = from->mColumnIdxArray.get();
845 ValueType* toVal = to->mValueArray.get();
846 SizeType* toCol = to->mColumnIdxArray.get();
847 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
848 toVal[n] = fromVal[n];
849 toCol[n] = fromCol[n];
850 }
851 }
852
853 const SparseStencilMatrix* from; SparseStencilMatrix* to;
854 };
855
856
857 template<typename ValueType, SizeType STENCIL_SIZE>
858 inline
859 SparseStencilMatrix<ValueType, STENCIL_SIZE>::SparseStencilMatrix(const SparseStencilMatrix& other)
860 : mNumRows(other.mNumRows)
861 , mValueArray(new ValueType[mNumRows * STENCIL_SIZE])
862 , mColumnIdxArray(new SizeType[mNumRows * STENCIL_SIZE])
863 , mRowSizeArray(new SizeType[mNumRows])
864 {
865 SizeType size = mNumRows * STENCIL_SIZE;
866
867 // Copy the value and column index arrays from the other matrix to this matrix.
868 tbb::parallel_for(SizeRange(0, size), MatrixCopyOp(/*from=*/other, /*to=*/*this));
869
870 // Copy the row size array from the other matrix to this matrix.
871 tbb::parallel_for(SizeRange(0, mNumRows),
872 internal::CopyOp<SizeType>(/*from=*/other.mRowSizeArray.get(), /*to=*/mRowSizeArray.get()));
873 }
874
875
876 template<typename ValueType, SizeType STENCIL_SIZE>
877 inline void
878 SparseStencilMatrix<ValueType, STENCIL_SIZE>::setValue(SizeType row, SizeType col,
879 const ValueType& val)
880 {
881 assert(row < mNumRows);
882 this->getRowEditor(row).setValue(col, val);
883 }
884
885
886 template<typename ValueType, SizeType STENCIL_SIZE>
887 inline const ValueType&
888 SparseStencilMatrix<ValueType, STENCIL_SIZE>::getValue(SizeType row, SizeType col) const
889 {
890 assert(row < mNumRows);
891 return this->getConstRow(row).getValue(col);
892 }
893
894
895 template<typename ValueType, SizeType STENCIL_SIZE>
896 inline const ValueType&
897 SparseStencilMatrix<ValueType, STENCIL_SIZE>::operator()(SizeType row, SizeType col) const
898 {
899 return this->getValue(row,col);
900 }
901
902
903 template<typename ValueType, SizeType STENCIL_SIZE>
904 template<typename Scalar>
905 struct SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowScaleOp
906 {
907 RowScaleOp(SparseStencilMatrix& m, const Scalar& s_): mat(&m), s(s_) {}
908
909 void operator()(const SizeRange& range) const
910 {
911 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
912 RowEditor row = mat->getRowEditor(n);
913 row.scale(s);
914 }
915 }
916
917 SparseStencilMatrix* mat;
918 const Scalar s;
919 };
920
921
922 template<typename ValueType, SizeType STENCIL_SIZE>
923 template<typename Scalar>
924 inline void
925 SparseStencilMatrix<ValueType, STENCIL_SIZE>::scale(const Scalar& s)
926 {
927 // Parallelize over the rows in the matrix.
928 tbb::parallel_for(SizeRange(0, mNumRows), RowScaleOp<Scalar>(*this, s));
929 }
930
931
932 template<typename ValueType, SizeType STENCIL_SIZE>
933 template<typename VecValueType>
934 struct SparseStencilMatrix<ValueType, STENCIL_SIZE>::VecMultOp
935 {
936 VecMultOp(const SparseStencilMatrix& m, const VecValueType* i, VecValueType* o):
937 mat(&m), in(i), out(o) {}
938
939 void operator()(const SizeRange& range) const
940 {
941 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
942 ConstRow row = mat->getConstRow(n);
943 out[n] = row.dot(in, mat->numRows());
944 }
945 }
946
947 const SparseStencilMatrix* mat;
948 const VecValueType* in;
949 VecValueType* out;
950 };
951
952
953 template<typename ValueType, SizeType STENCIL_SIZE>
954 template<typename VecValueType>
955 inline void
956 SparseStencilMatrix<ValueType, STENCIL_SIZE>::vectorMultiply(
957 const Vector<VecValueType>& inVec, Vector<VecValueType>& resultVec) const
958 {
959 if (inVec.size() != mNumRows) {
960 OPENVDB_THROW(ArithmeticError, "matrix and input vector have incompatible sizes ("
961 << mNumRows << "x" << mNumRows << " vs. " << inVec.size() << ")");
962 }
963 if (resultVec.size() != mNumRows) {
964 OPENVDB_THROW(ArithmeticError, "matrix and result vector have incompatible sizes ("
965 << mNumRows << "x" << mNumRows << " vs. " << resultVec.size() << ")");
966 }
967
968 vectorMultiply(inVec.data(), resultVec.data());
969 }
970
971
972 template<typename ValueType, SizeType STENCIL_SIZE>
973 template<typename VecValueType>
974 inline void
975 SparseStencilMatrix<ValueType, STENCIL_SIZE>::vectorMultiply(
976 const VecValueType* inVec, VecValueType* resultVec) const
977 {
978 // Parallelize over the rows in the matrix.
979 tbb::parallel_for(SizeRange(0, mNumRows),
980 VecMultOp<VecValueType>(*this, inVec, resultVec));
981 }
982
983
984 template<typename ValueType, SizeType STENCIL_SIZE>
985 template<typename OtherValueType>
986 struct SparseStencilMatrix<ValueType, STENCIL_SIZE>::EqOp
987 {
988 EqOp(const SparseStencilMatrix& a_,
989 const SparseStencilMatrix<OtherValueType, STENCIL_SIZE>& b_, ValueType e):
990 a(&a_), b(&b_), eps(e) {}
991
992 bool operator()(const SizeRange& range, bool equal) const
993 {
994 if (equal) {
995 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
996 if (!a->getConstRow(n).eq(b->getConstRow(n), eps)) return false;
997 }
998 }
999 return equal;
1000 }
1001
1002 const SparseStencilMatrix* a;
1003 const SparseStencilMatrix<OtherValueType, STENCIL_SIZE>* b;
1004 const ValueType eps;
1005 };
1006
1007
1008 template<typename ValueType, SizeType STENCIL_SIZE>
1009 template<typename OtherValueType>
1010 inline bool
1011 SparseStencilMatrix<ValueType, STENCIL_SIZE>::eq(
1012 const SparseStencilMatrix<OtherValueType, STENCIL_SIZE>& other, ValueType eps) const
1013 {
1014 if (this->numRows() != other.numRows()) return false;
1015 bool equal = tbb::parallel_reduce(SizeRange(0, this->numRows()), /*seed=*/true,
1016 EqOp<OtherValueType>(*this, other, eps),
1017 /*join=*/[](bool eq1, bool eq2) { return (eq1 && eq2); });
1018 return equal;
1019 }
1020
1021
1022 template<typename ValueType, SizeType STENCIL_SIZE>
1023 struct SparseStencilMatrix<ValueType, STENCIL_SIZE>::IsFiniteOp
1024 {
1025 IsFiniteOp(const SparseStencilMatrix& m): mat(&m) {}
1026
1027 bool operator()(const SizeRange& range, bool finite) const
1028 {
1029 if (finite) {
1030 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
1031 const ConstRow row = mat->getConstRow(n);
1032 for (ConstValueIter it = row.cbegin(); it; ++it) {
1033 if (!std::isfinite(*it)) return false;
1034 }
1035 }
1036 }
1037 return finite;
1038 }
1039
1040 const SparseStencilMatrix* mat;
1041 };
1042
1043
1044 template<typename ValueType, SizeType STENCIL_SIZE>
1045 inline bool
1046 SparseStencilMatrix<ValueType, STENCIL_SIZE>::isFinite() const
1047 {
1048 // Parallelize over the rows of this matrix.
1049 bool finite = tbb::parallel_reduce(SizeRange(0, this->numRows()), /*seed=*/true,
1050 IsFiniteOp(*this), /*join=*/[](bool finite1, bool finite2) { return (finite1&&finite2); });
1051 return finite;
1052 }
1053
1054
1055 template<typename ValueType, SizeType STENCIL_SIZE>
1056 inline std::string
1057 SparseStencilMatrix<ValueType, STENCIL_SIZE>::str() const
1058 {
1059 std::ostringstream ostr;
1060 for (SizeType n = 0, N = this->size(); n < N; ++n) {
1061 ostr << n << ": " << this->getConstRow(n).str() << "\n";
1062 }
1063 return ostr.str();
1064 }
1065
1066
1067 template<typename ValueType, SizeType STENCIL_SIZE>
1068 inline typename SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowEditor
1069 SparseStencilMatrix<ValueType, STENCIL_SIZE>::getRowEditor(SizeType i)
1070 {
1071 assert(i < mNumRows);
1072 const SizeType head = i * STENCIL_SIZE;
1073 return RowEditor(&mValueArray[head], &mColumnIdxArray[head], mRowSizeArray[i], mNumRows);
1074 }
1075
1076
1077 template<typename ValueType, SizeType STENCIL_SIZE>
1078 inline typename SparseStencilMatrix<ValueType, STENCIL_SIZE>::ConstRow
1079 SparseStencilMatrix<ValueType, STENCIL_SIZE>::getConstRow(SizeType i) const
1080 {
1081 assert(i < mNumRows);
1082 const SizeType head = i * STENCIL_SIZE; // index for this row into main storage
1083 return ConstRow(&mValueArray[head], &mColumnIdxArray[head], mRowSizeArray[i]);
1084 }
1085
1086
1087 template<typename ValueType, SizeType STENCIL_SIZE>
1088 template<typename DataType>
1089 inline SizeType
1090 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::find(SizeType columnIdx) const
1091 {
1092 if (this->empty()) return mData.mSize;
1093
1094 // Get a pointer to the first column index that is equal to or greater than the given index.
1095 // (This assumes that the data is sorted by column.)
1096 const SizeType* colPtr = std::lower_bound(mData.mCols, mData.mCols + mData.mSize, columnIdx);
1097 // Return the offset of the pointer from the beginning of the array.
1098 return static_cast<SizeType>(colPtr - mData.mCols);
1099 }
1100
1101
1102 template<typename ValueType, SizeType STENCIL_SIZE>
1103 template<typename DataType>
1104 inline const ValueType&
1105 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::getValue(
1106 SizeType columnIdx, bool& active) const
1107 {
1108 active = false;
1109 SizeType idx = this->find(columnIdx);
1110 if (idx < this->size() && this->column(idx) == columnIdx) {
1111 active = true;
1112 return this->value(idx);
1113 }
1114 return SparseStencilMatrix::sZeroValue;
1115 }
1116
1117 template<typename ValueType, SizeType STENCIL_SIZE>
1118 template<typename DataType>
1119 inline const ValueType&
1120 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::getValue(SizeType columnIdx) const
1121 {
1122 SizeType idx = this->find(columnIdx);
1123 if (idx < this->size() && this->column(idx) == columnIdx) {
1124 return this->value(idx);
1125 }
1126 return SparseStencilMatrix::sZeroValue;
1127 }
1128
1129
1130 template<typename ValueType, SizeType STENCIL_SIZE>
1131 template<typename DataType>
1132 inline typename SparseStencilMatrix<ValueType, STENCIL_SIZE>::ConstValueIter
1133 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::cbegin() const
1134 {
1135 return ConstValueIter(mData);
1136 }
1137
1138
1139 template<typename ValueType, SizeType STENCIL_SIZE>
1140 template<typename DataType>
1141 template<typename OtherDataType>
1142 inline bool
1143 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::eq(
1144 const RowBase<OtherDataType>& other, ValueType eps) const
1145 {
1146 if (this->size() != other.size()) return false;
1147 for (ConstValueIter it = cbegin(), oit = other.cbegin(); it || oit; ++it, ++oit) {
1148 if (it.column() != oit.column()) return false;
1149 if (!isApproxEqual(*it, *oit, eps)) return false;
1150 }
1151 return true;
1152 }
1153
1154
1155 template<typename ValueType, SizeType STENCIL_SIZE>
1156 template<typename DataType>
1157 template<typename VecValueType>
1158 inline VecValueType
1159 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::dot(
1160 const VecValueType* inVec, SizeType vecSize) const
1161 {
1162 VecValueType result = zeroVal<VecValueType>();
1163 for (SizeType idx = 0, N = std::min(vecSize, this->size()); idx < N; ++idx) {
1164 result += static_cast<VecValueType>(this->value(idx) * inVec[this->column(idx)]);
1165 }
1166 return result;
1167 }
1168
1169 template<typename ValueType, SizeType STENCIL_SIZE>
1170 template<typename DataType>
1171 template<typename VecValueType>
1172 inline VecValueType
1173 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::dot(
1174 const Vector<VecValueType>& inVec) const
1175 {
1176 return dot(inVec.data(), inVec.size());
1177 }
1178
1179
1180 template<typename ValueType, SizeType STENCIL_SIZE>
1181 template<typename DataType>
1182 inline std::string
1183 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowBase<DataType>::str() const
1184 {
1185 std::ostringstream ostr;
1186 std::string sep;
1187 for (SizeType n = 0, N = this->size(); n < N; ++n) {
1188 ostr << sep << "(" << this->column(n) << ", " << this->value(n) << ")";
1189 sep = ", ";
1190 }
1191 return ostr.str();
1192 }
1193
1194
1195 template<typename ValueType, SizeType STENCIL_SIZE>
1196 inline
1197 SparseStencilMatrix<ValueType, STENCIL_SIZE>::ConstRow::ConstRow(
1198 const ValueType* valueHead, const SizeType* columnHead, const SizeType& rowSize):
1199 ConstRowBase(ConstRowData(const_cast<ValueType*>(valueHead),
1200 const_cast<SizeType*>(columnHead), const_cast<SizeType&>(rowSize)))
1201 {
1202 }
1203
1204
1205 template<typename ValueType, SizeType STENCIL_SIZE>
1206 inline
1207 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowEditor::RowEditor(
1208 ValueType* valueHead, SizeType* columnHead, SizeType& rowSize, SizeType colSize):
1209 RowBase<>(RowData(valueHead, columnHead, rowSize)), mNumColumns(colSize)
1210 {
1211 }
1212
1213
1214 template<typename ValueType, SizeType STENCIL_SIZE>
1215 inline void
1216 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowEditor::clear()
1217 {
1218 // Note: since mSize is a reference, this modifies the underlying matrix.
1219 RowBase<>::mData.mSize = 0;
1220 }
1221
1222
1223 template<typename ValueType, SizeType STENCIL_SIZE>
1224 inline SizeType
1225 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowEditor::setValue(
1226 SizeType column, const ValueType& value)
1227 {
1228 assert(column < mNumColumns);
1229
1230 RowData& data = RowBase<>::mData;
1231
1232 // Get the offset of the first column index that is equal to or greater than
1233 // the column to be modified.
1234 SizeType offset = this->find(column);
1235
1236 if (offset < data.mSize && data.mCols[offset] == column) {
1237 // If the column already exists, just update its value.
1238 data.mVals[offset] = value;
1239 return data.mSize;
1240 }
1241
1242 // Check that it is safe to add a new column.
1243 assert(data.mSize < this->capacity());
1244
1245 if (offset >= data.mSize) {
1246 // The new column's index is larger than any existing index. Append the new column.
1247 data.mVals[data.mSize] = value;
1248 data.mCols[data.mSize] = column;
1249 } else {
1250 // Insert the new column at the computed offset after shifting subsequent columns.
1251 for (SizeType i = data.mSize; i > offset; --i) {
1252 data.mVals[i] = data.mVals[i - 1];
1253 data.mCols[i] = data.mCols[i - 1];
1254 }
1255 data.mVals[offset] = value;
1256 data.mCols[offset] = column;
1257 }
1258 ++data.mSize;
1259
1260 return data.mSize;
1261 }
1262
1263
1264 template<typename ValueType, SizeType STENCIL_SIZE>
1265 template<typename Scalar>
1266 inline void
1267 SparseStencilMatrix<ValueType, STENCIL_SIZE>::RowEditor::scale(const Scalar& s)
1268 {
1269 for (int idx = 0, N = this->size(); idx < N; ++idx) {
1270 RowBase<>::mData.mVals[idx] *= s;
1271 }
1272 }
1273
1274
1276
1277
1279 template<typename MatrixType>
1280 class JacobiPreconditioner: public Preconditioner<typename MatrixType::ValueType>
1281 {
1282 private:
1283 struct InitOp;
1284 struct ApplyOp;
1285
1286 public:
1287 using ValueType = typename MatrixType::ValueType;
1288 using BaseType = Preconditioner<ValueType>;
1289 using VectorType = Vector<ValueType>;
1290 using Ptr = SharedPtr<JacobiPreconditioner>;
1291
1292 JacobiPreconditioner(const MatrixType& A): BaseType(A), mDiag(A.numRows())
1293 {
1294 // Initialize vector mDiag with the values from the matrix diagonal.
1295 tbb::parallel_for(SizeRange(0, A.numRows()), InitOp(A, mDiag.data()));
1296 }
1297
1298 ~JacobiPreconditioner() override = default;
1299
1300 void apply(const Vector<ValueType>& r, Vector<ValueType>& z) override
1301 {
1302 const SizeType size = mDiag.size();
1303
1304 assert(r.size() == z.size());
1305 assert(r.size() == size);
1306
1307 tbb::parallel_for(SizeRange(0, size), ApplyOp(mDiag.data(), r.data(), z.data()));
1308 }
1309
1311 bool isFinite() const { return mDiag.isFinite(); }
1312
1313 private:
1314 // Functor for use with tbb::parallel_for()
1315 struct InitOp
1316 {
1317 InitOp(const MatrixType& m, ValueType* v): mat(&m), vec(v) {}
1318 void operator()(const SizeRange& range) const {
1319 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
1320 const ValueType val = mat->getValue(n, n);
1321 assert(!isApproxZero(val, ValueType(0.0001)));
1322 vec[n] = static_cast<ValueType>(1.0 / val);
1323 }
1324 }
1325 const MatrixType* mat; ValueType* vec;
1326 };
1327
1328 // Functor for use with tbb::parallel_reduce()
1329 struct ApplyOp
1330 {
1331 ApplyOp(const ValueType* x_, const ValueType* y_, ValueType* out_):
1332 x(x_), y(y_), out(out_) {}
1333 void operator()(const SizeRange& range) const {
1334 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) out[n] = x[n] * y[n];
1335 }
1336 const ValueType *x, *y; ValueType* out;
1337 };
1338
1339 // The Jacobi preconditioner is a diagonal matrix
1340 VectorType mDiag;
1341 }; // class JacobiPreconditioner
1342
1343
1345 template<typename MatrixType>
1346 class IncompleteCholeskyPreconditioner: public Preconditioner<typename MatrixType::ValueType>
1347 {
1348 private:
1349 struct CopyToLowerOp;
1350 struct TransposeOp;
1351
1352 public:
1353 using ValueType = typename MatrixType::ValueType;
1354 using BaseType = Preconditioner<ValueType>;
1355 using VectorType = Vector<ValueType>;
1356 using Ptr = SharedPtr<IncompleteCholeskyPreconditioner>;
1357 using TriangularMatrix = SparseStencilMatrix<ValueType, 4>;
1358 using TriangleConstRow = typename TriangularMatrix::ConstRow;
1359 using TriangleRowEditor = typename TriangularMatrix::RowEditor;
1360
1361 IncompleteCholeskyPreconditioner(const MatrixType& matrix)
1362 : BaseType(matrix)
1363 , mLowerTriangular(matrix.numRows())
1364 , mUpperTriangular(matrix.numRows())
1365 , mTempVec(matrix.numRows())
1366 {
1367 // Size of matrix
1368 const SizeType numRows = mLowerTriangular.numRows();
1369
1370 // Copy the upper triangular part to the lower triangular part.
1371 tbb::parallel_for(SizeRange(0, numRows), CopyToLowerOp(matrix, mLowerTriangular));
1372
1373 // Build the Incomplete Cholesky Matrix
1374 //
1375 // Algorithm:
1376 //
1377 // for (k = 0; k < size; ++k) {
1378 // A(k,k) = sqrt(A(k,k));
1379 // for (i = k +1, i < size; ++i) {
1380 // if (A(i,k) == 0) continue;
1381 // A(i,k) = A(i,k) / A(k,k);
1382 // }
1383 // for (j = k+1; j < size; ++j) {
1384 // for (i = j; i < size; ++i) {
1385 // if (A(i,j) == 0) continue;
1386 // A(i,j) -= A(i,k)*A(j,k);
1387 // }
1388 // }
1389 // }
1390
1391 mPassedCompatibilityCondition = true;
1392
1393 for (SizeType k = 0; k < numRows; ++k) {
1394
1395 TriangleConstRow crow_k = mLowerTriangular.getConstRow(k);
1396 ValueType diagonalValue = crow_k.getValue(k);
1397
1398 // Test if the matrix build has failed.
1399 if (diagonalValue < 1.e-5) {
1400 mPassedCompatibilityCondition = false;
1401 break;
1402 }
1403
1404 diagonalValue = Sqrt(diagonalValue);
1405
1406 TriangleRowEditor row_k = mLowerTriangular.getRowEditor(k);
1407 row_k.setValue(k, diagonalValue);
1408
1409 // Exploit the fact that the matrix is symmetric.
1410 typename MatrixType::ConstRow srcRow = matrix.getConstRow(k);
1411 typename MatrixType::ConstValueIter citer = srcRow.cbegin();
1412 for ( ; citer; ++citer) {
1413 SizeType ii = citer.column();
1414 if (ii < k+1) continue; // look above diagonal
1415
1416 TriangleRowEditor row_ii = mLowerTriangular.getRowEditor(ii);
1417
1418 row_ii.setValue(k, *citer / diagonalValue);
1419 }
1420
1421 // for (j = k+1; j < size; ++j) replaced by row iter below
1422 citer.reset(); // k,j entries
1423 for ( ; citer; ++citer) {
1424 SizeType j = citer.column();
1425 if (j < k+1) continue;
1426
1427 TriangleConstRow row_j = mLowerTriangular.getConstRow(j);
1428 ValueType a_jk = row_j.getValue(k); // a_jk is non zero if a_kj is non zero
1429
1430 // Entry (i,j) is non-zero if matrix(j,i) is nonzero
1431
1432 typename MatrixType::ConstRow mask = matrix.getConstRow(j);
1433 typename MatrixType::ConstValueIter maskIter = mask.cbegin();
1434 for ( ; maskIter; ++maskIter) {
1435 SizeType i = maskIter.column();
1436 if (i < j) continue;
1437
1438 TriangleConstRow crow_i = mLowerTriangular.getConstRow(i);
1439 ValueType a_ij = crow_i.getValue(j);
1440 ValueType a_ik = crow_i.getValue(k);
1441 TriangleRowEditor row_i = mLowerTriangular.getRowEditor(i);
1442 a_ij -= a_ik * a_jk;
1443
1444 row_i.setValue(j, a_ij);
1445 }
1446 }
1447 }
1448
1449 // Build the transpose of the IC matrix: mUpperTriangular
1450 tbb::parallel_for(SizeRange(0, numRows),
1451 TransposeOp(matrix, mLowerTriangular, mUpperTriangular));
1452 }
1453
1454 ~IncompleteCholeskyPreconditioner() override = default;
1455
1456 bool isValid() const override { return mPassedCompatibilityCondition; }
1457
1458 void apply(const Vector<ValueType>& rVec, Vector<ValueType>& zVec) override
1459 {
1460 if (!mPassedCompatibilityCondition) {
1461 OPENVDB_THROW(ArithmeticError, "invalid Cholesky decomposition");
1462 }
1463
1464 // Solve mUpperTriangular * mLowerTriangular * rVec = zVec;
1465
1466 SizeType size = mLowerTriangular.numRows();
1467
1468 zVec.fill(zeroVal<ValueType>());
1469 ValueType* zData = zVec.data();
1470
1471 if (size == 0) return;
1472
1473 assert(rVec.size() == size);
1474 assert(zVec.size() == size);
1475
1476 // Allocate a temp vector
1477 mTempVec.fill(zeroVal<ValueType>());
1478 ValueType* tmpData = mTempVec.data();
1479 const ValueType* rData = rVec.data();
1480
1481 // Solve mLowerTriangular * tmp = rVec;
1482 for (SizeType i = 0; i < size; ++i) {
1483 typename TriangularMatrix::ConstRow row = mLowerTriangular.getConstRow(i);
1484 ValueType diagonal = row.getValue(i);
1485 ValueType dot = row.dot(mTempVec);
1486 tmpData[i] = (rData[i] - dot) / diagonal;
1487 if (!std::isfinite(tmpData[i])) {
1488 OPENVDB_LOG_DEBUG_RUNTIME("1 diagonal was " << diagonal);
1489 OPENVDB_LOG_DEBUG_RUNTIME("1a diagonal " << row.getValue(i));
1490 }
1491 }
1492
1493 // Solve mUpperTriangular * zVec = tmp;
1494 for (SizeType ii = 0; ii < size; ++ii) {
1495 SizeType i = size - 1 - ii;
1496 typename TriangularMatrix::ConstRow row = mUpperTriangular.getConstRow(i);
1497 ValueType diagonal = row.getValue(i);
1498 ValueType dot = row.dot(zVec);
1499 zData[i] = (tmpData[i] - dot) / diagonal;
1500 if (!std::isfinite(zData[i])) {
1501 OPENVDB_LOG_DEBUG_RUNTIME("2 diagonal was " << diagonal);
1502 }
1503 }
1504 }
1505
1506 const TriangularMatrix& lowerMatrix() const { return mLowerTriangular; }
1507 const TriangularMatrix& upperMatrix() const { return mUpperTriangular; }
1508
1509 private:
1510 // Functor for use with tbb::parallel_for()
1511 struct CopyToLowerOp
1512 {
1513 CopyToLowerOp(const MatrixType& m, TriangularMatrix& l): mat(&m), lower(&l) {}
1514 void operator()(const SizeRange& range) const {
1515 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
1516 typename TriangularMatrix::RowEditor outRow = lower->getRowEditor(n);
1517 outRow.clear();
1518 typename MatrixType::ConstRow inRow = mat->getConstRow(n);
1519 for (typename MatrixType::ConstValueIter it = inRow.cbegin(); it; ++it) {
1520 if (it.column() > n) continue; // skip above diagonal
1521 outRow.setValue(it.column(), *it);
1522 }
1523 }
1524 }
1525 const MatrixType* mat; TriangularMatrix* lower;
1526 };
1527
1528 // Functor for use with tbb::parallel_for()
1529 struct TransposeOp
1530 {
1531 TransposeOp(const MatrixType& m, const TriangularMatrix& l, TriangularMatrix& u):
1532 mat(&m), lower(&l), upper(&u) {}
1533 void operator()(const SizeRange& range) const {
1534 for (SizeType n = range.begin(), N = range.end(); n < N; ++n) {
1535 typename TriangularMatrix::RowEditor outRow = upper->getRowEditor(n);
1536 outRow.clear();
1537 // Use the fact that matrix is symmetric.
1538 typename MatrixType::ConstRow inRow = mat->getConstRow(n);
1539 for (typename MatrixType::ConstValueIter it = inRow.cbegin(); it; ++it) {
1540 const SizeType column = it.column();
1541 if (column < n) continue; // only set upper triangle
1542 outRow.setValue(column, lower->getValue(column, n));
1543 }
1544 }
1545 }
1546 const MatrixType* mat; const TriangularMatrix* lower; TriangularMatrix* upper;
1547 };
1548
1549 TriangularMatrix mLowerTriangular;
1550 TriangularMatrix mUpperTriangular;
1551 Vector<ValueType> mTempVec;
1552 bool mPassedCompatibilityCondition;
1553 }; // class IncompleteCholeskyPreconditioner
1554
1555
1557
1558
1559 namespace internal {
1560
1562 template<typename T>
1563 inline void
1564 axpy(const T& a, const T* xVec, const T* yVec, T* resultVec, SizeType size)
1565 {
1566 tbb::parallel_for(SizeRange(0, size), LinearOp<T>(a, xVec, yVec, resultVec));
1567 }
1568
1570 template<typename T>
1571 inline void
1572 axpy(const T& a, const Vector<T>& xVec, const Vector<T>& yVec, Vector<T>& result)
1573 {
1574 assert(xVec.size() == yVec.size());
1575 assert(xVec.size() == result.size());
1576 axpy(a, xVec.data(), yVec.data(), result.data(), xVec.size());
1577 }
1578
1579
1581 template<typename MatrixOperator, typename VecValueType>
1582 inline void
1583 computeResidual(const MatrixOperator& A, const VecValueType* x,
1584 const VecValueType* b, VecValueType* r)
1585 {
1586 // Compute r = A * x.
1587 A.vectorMultiply(x, r);
1588 // Compute r = b - r.
1589 tbb::parallel_for(SizeRange(0, A.numRows()), LinearOp<VecValueType>(-1.0, r, b, r));
1590 }
1591
1593 template<typename MatrixOperator, typename T>
1594 inline void
1595 computeResidual(const MatrixOperator& A, const Vector<T>& x, const Vector<T>& b, Vector<T>& r)
1596 {
1597 assert(x.size() == b.size());
1598 assert(x.size() == r.size());
1599 assert(x.size() == A.numRows());
1600
1601 computeResidual(A, x.data(), b.data(), r.data());
1602 }
1603
1604 } // namespace internal
1605
1606
1608
1609
1610 template<typename PositiveDefMatrix>
1611 inline State
1612 solve(
1613 const PositiveDefMatrix& Amat,
1614 const Vector<typename PositiveDefMatrix::ValueType>& bVec,
1615 Vector<typename PositiveDefMatrix::ValueType>& xVec,
1616 Preconditioner<typename PositiveDefMatrix::ValueType>& precond,
1617 const State& termination)
1618 {
1619 util::NullInterrupter interrupter;
1620 return solve(Amat, bVec, xVec, precond, interrupter, termination);
1621 }
1622
1623
1624 template<typename PositiveDefMatrix, typename Interrupter>
1625 inline State
1626 solve(
1627 const PositiveDefMatrix& Amat,
1628 const Vector<typename PositiveDefMatrix::ValueType>& bVec,
1629 Vector<typename PositiveDefMatrix::ValueType>& xVec,
1630 Preconditioner<typename PositiveDefMatrix::ValueType>& precond,
1631 Interrupter& interrupter,
1632 const State& termination)
1633 {
1634 using ValueType = typename PositiveDefMatrix::ValueType;
1635 using VectorType = Vector<ValueType>;
1636
1637 State result;
1638 result.success = false;
1639 result.iterations = 0;
1640 result.relativeError = 0.0;
1641 result.absoluteError = 0.0;
1642
1643 const SizeType size = Amat.numRows();
1644 if (size == 0) {
1645 OPENVDB_LOG_WARN("pcg::solve(): matrix has dimension zero");
1646 return result;
1647 }
1648 if (size != bVec.size()) {
1649 OPENVDB_THROW(ArithmeticError, "A and b have incompatible sizes"
1650 << size << "x" << size << " vs. " << bVec.size() << ")");
1651 }
1652 if (size != xVec.size()) {
1653 OPENVDB_THROW(ArithmeticError, "A and x have incompatible sizes"
1654 << size << "x" << size << " vs. " << xVec.size() << ")");
1655 }
1656
1657 // Temp vectors
1658 VectorType zVec(size); // transformed residual (M^-1 r)
1659 VectorType pVec(size); // search direction
1660 VectorType qVec(size); // A * p
1661
1662 // Compute norm of B (the source)
1663 const ValueType tmp = bVec.infNorm();
1664 const ValueType infNormOfB = isZero(tmp) ? ValueType(1) : tmp;
1665
1666 // Compute rVec: residual = b - Ax.
1667 VectorType rVec(size); // vector of residuals
1668
1669 internal::computeResidual(Amat, xVec, bVec, rVec);
1670
1671 assert(rVec.isFinite());
1672
1673 // Normalize the residual norm with the source norm and look for early out.
1674 result.absoluteError = static_cast<double>(rVec.infNorm());
1675 result.relativeError = static_cast<double>(result.absoluteError / infNormOfB);
1676 if (result.relativeError <= termination.relativeError) {
1677 result.success = true;
1678 return result;
1679 }
1680
1681 // Iterations of the CG solve
1682
1683 ValueType rDotZPrev(1); // inner product of <z,r>
1684
1685 // Keep track of the minimum error to monitor convergence.
1686 ValueType minL2Error = std::numeric_limits<ValueType>::max();
1687 ValueType l2Error;
1688
1689 int iteration = 0;
1690 for ( ; iteration < termination.iterations; ++iteration) {
1691
1692 if (interrupter.wasInterrupted()) {
1693 OPENVDB_THROW(RuntimeError, "conjugate gradient solver was interrupted");
1694 }
1695
1696 OPENVDB_LOG_DEBUG_RUNTIME("pcg::solve() " << result);
1697
1698 result.iterations = iteration + 1;
1699
1700 // Apply preconditioner to residual
1701 // z_{k} = M^-1 r_{k}
1702 precond.apply(rVec, zVec);
1703
1704 // <r,z>
1705 const ValueType rDotZ = rVec.dot(zVec);
1706 assert(std::isfinite(rDotZ));
1707
1708 if (0 == iteration) {
1709 // Initialize
1710 pVec = zVec;
1711 } else {
1712 const ValueType beta = rDotZ / rDotZPrev;
1713 // p = beta * p + z
1714 internal::axpy(beta, pVec, zVec, /*result */pVec);
1715 }
1716
1717 // q_{k} = A p_{k}
1718 Amat.vectorMultiply(pVec, qVec);
1719
1720 // alpha = <r_{k-1}, z_{k-1}> / <p_{k},q_{k}>
1721 const ValueType pAp = pVec.dot(qVec);
1722 assert(std::isfinite(pAp));
1723
1724 const ValueType alpha = rDotZ / pAp;
1725 rDotZPrev = rDotZ;
1726
1727 // x_{k} = x_{k-1} + alpha * p_{k}
1728 internal::axpy(alpha, pVec, xVec, /*result=*/xVec);
1729
1730 // r_{k} = r_{k-1} - alpha_{k-1} A p_{k}
1731 internal::axpy(-alpha, qVec, rVec, /*result=*/rVec);
1732
1733 // update tolerances
1734 l2Error = rVec.l2Norm();
1735 minL2Error = Min(l2Error, minL2Error);
1736
1737 result.absoluteError = static_cast<double>(rVec.infNorm());
1738 result.relativeError = static_cast<double>(result.absoluteError / infNormOfB);
1739
1740 if (l2Error > 2 * minL2Error) {
1741 // The solution started to diverge.
1742 result.success = false;
1743 break;
1744 }
1745 if (!std::isfinite(result.absoluteError)) {
1746 // Total divergence of solution
1747 result.success = false;
1748 break;
1749 }
1750 if (result.absoluteError <= termination.absoluteError) {
1751 // Convergence
1752 result.success = true;
1753 break;
1754 }
1755 if (result.relativeError <= termination.relativeError) {
1756 // Convergence
1757 result.success = true;
1758 break;
1759 }
1760 }
1761 OPENVDB_LOG_DEBUG_RUNTIME("pcg::solve() " << result);
1762
1763 return result;
1764 }
1765
1766 } // namespace pcg
1767 } // namespace math
1768 } // namespace OPENVDB_VERSION_NAME
1769 } // namespace openvdb
1770
1771 #endif // OPENVDB_MATH_CONJGRADIENT_HAS_BEEN_INCLUDED
openvdb::v7_0::math::pcg::Vector::operator[]
T & operator[](SizeType i)
Definition: ConjGradient.h:203
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::reducetmp
T * reducetmp
Definition: ConjGradient.h:659
openvdb::v7_0::math::pcg::Vector< ValueType >::Ptr
SharedPtr< Vector > Ptr
Definition: ConjGradient.h:142
openvdb::v7_0::math::pcg::SparseStencilMatrix::VectorType
Vector< ValueType > VectorType
Definition: ConjGradient.h:241
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter::operator++
ConstValueIter & operator++()
Definition: ConjGradient.h:395
openvdb::v7_0::math::pcg::State
Information about the state of a conjugate gradient solution.
Definition: ConjGradient.h:46
openvdb::v7_0::math::pcg::Vector::IsFiniteOp::data
const T * data
Definition: ConjGradient.h:747
openvdb::v7_0::math::pcg::internal::LinearOp
Definition: ConjGradient.h:520
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::a
const T * a
Definition: ConjGradient.h:655
openvdb::v7_0::math::pcg::Vector
Lightweight, variable-length vector.
Definition: ConjGradient.h:37
openvdb::v7_0::math::pcg::internal::CopyOp::from
const T * from
Definition: ConjGradient.h:498
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter::column
SizeType column() const
Definition: ConjGradient.h:392
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter::operator*
const ValueType & operator*() const
Definition: ConjGradient.h:386
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::b
const T * b
Definition: ConjGradient.h:656
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor::RowEditor
RowEditor(ValueType *valueHead, SizeType *columnHead, SizeType &rowSize, SizeType colSize)
Definition: ConjGradient.h:1207
openvdb::v7_0::math::pcg::SparseStencilMatrix::str
std::string str() const
Return a string representation of this matrix.
Definition: ConjGradient.h:1057
openvdb::v7_0::math::pcg::internal::CopyOp::CopyOp
CopyOp(const T *from_, T *to_)
Definition: ConjGradient.h:492
openvdb::v7_0::math::pcg::Preconditioner< MatrixType::ValueType >::Ptr
SharedPtr< Preconditioner > Ptr
Definition: ConjGradient.h:468
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor::clear
void clear()
Set the number of entries in this row to zero.
Definition: ConjGradient.h:1216
openvdb::v7_0::math::pcg::Vector::~Vector
~Vector()
Definition: ConjGradient.h:151
openvdb::v7_0::math::pcg::Preconditioner
Base class for conjugate gradient preconditioners.
Definition: ConjGradient.h:41
openvdb::v7_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:351
openvdb::v7_0::math::pcg::internal::computeResidual
void computeResidual(const MatrixOperator &A, const VecValueType *x, const VecValueType *b, VecValueType *r)
Compute r = b − Ax.
Definition: ConjGradient.h:1583
openvdb::v7_0::math::pcg::Vector< ValueType >::ValueType
ValueType ValueType
Definition: ConjGradient.h:141
Types.h
openvdb::v7_0::math::pcg::SparseStencilMatrix::MatrixCopyOp::operator()
void operator()(const SizeRange &range) const
Definition: ConjGradient.h:841
openvdb::v7_0::math::pcg::SparseStencilMatrix< OtherValueType, STENCIL_SIZE >::Ptr
SharedPtr< SparseStencilMatrix > Ptr
Definition: ConjGradient.h:242
openvdb::v7_0::math::pcg::internal::CopyOp::operator()
void operator()(const SizeRange &range) const
Definition: ConjGradient.h:494
openvdb::v7_0::math::pcg::internal::CopyOp
Definition: ConjGradient.h:490
openvdb::v7_0::math::pcg::SparseStencilMatrix::operator()
const ValueType & operator()(SizeType row, SizeType col) const
Definition: ConjGradient.h:897
openvdb::v7_0::math::pcg::Vector::IsFiniteOp::IsFiniteOp
IsFiniteOp(const T *data_)
Definition: ConjGradient.h:735
openvdb::v7_0::math::isFinite
bool isFinite(const float x)
Return true if x is finite.
Definition: Math.h:319
openvdb::v7_0::math::pcg::SparseStencilMatrix::numRows
SizeType numRows() const
Return the number of rows in this matrix.
Definition: ConjGradient.h:258
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::lowerMatrix
const TriangularMatrix & lowerMatrix() const
Definition: ConjGradient.h:1506
openvdb::v7_0::math::pcg::Vector::Vector
Vector(SizeType n)
Construct a vector of n elements, with uninitialized values.
Definition: ConjGradient.h:147
openvdb::v7_0::math::pcg::internal::LinearOp::y
const T * y
Definition: ConjGradient.h:534
openvdb::v7_0::math::pcg::State::iterations
int iterations
Definition: ConjGradient.h:48
openvdb::v7_0::math::pcg::Vector::Vector
Vector(SizeType n, const ValueType &val)
Construct a vector of n elements and initialize each element to the given value.
Definition: ConjGradient.h:149
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::DeterministicDotProductOp
DeterministicDotProductOp(const T *a_, const T *b_, const SizeType binCount_, const SizeType arraySize_, T *reducetmp_)
Definition: ConjGradient.h:633
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter::increment
void increment()
Definition: ConjGradient.h:394
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor::operator*=
RowEditor & operator*=(const Scalar &s)
Definition: ConjGradient.h:435
openvdb::v7_0::math::pcg::Vector::at
const T & at(SizeType i) const
Definition: ConjGradient.h:202
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstRow
Read-only accessor to a row of this matrix.
Definition: ConjGradient.h:411
openvdb::v7_0::math::pcg::JacobiPreconditioner::isFinite
bool isFinite() const
Return true if all values along the diagonal are finite.
Definition: ConjGradient.h:1311
openvdb::v7_0::math::pcg::Vector::InfNormOp::InfNormOp
InfNormOp(const T *data_)
Definition: ConjGradient.h:707
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::TriangleRowEditor
typename TriangularMatrix::RowEditor TriangleRowEditor
Definition: ConjGradient.h:1359
openvdb::v7_0::math::pcg::internal::LinearOp::operator()
void operator()(const SizeRange &range) const
Definition: ConjGradient.h:524
openvdb::v7_0::math::pcg::internal::computeResidual
void computeResidual(const MatrixOperator &A, const Vector< T > &x, const Vector< T > &b, Vector< T > &r)
Compute r = b − Ax.
Definition: ConjGradient.h:1595
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter::reset
void reset()
Definition: ConjGradient.h:398
openvdb::v7_0::math::pcg::Vector::InfNormOp::data
const T * data
Definition: ConjGradient.h:717
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp
Definition: ConjGradient.h:631
openvdb::v7_0::math::pcg::Vector::Vector
Vector()
Construct an empty vector.
Definition: ConjGradient.h:145
openvdb::v7_0::math::Max
const Type & Max(const Type &a, const Type &b)
Return the maximum of two values.
Definition: Math.h:542
openvdb::v7_0::math::pcg::terminationDefaults
State terminationDefaults()
Return default termination conditions for a conjugate gradient solver.
Definition: ConjGradient.h:57
openvdb::v7_0::math::pcg::internal::axpy
void axpy(const T &a, const Vector< T > &xVec, const Vector< T > &yVec, Vector< T > &result)
Compute ax + y.
Definition: ConjGradient.h:1572
openvdb::v7_0::SharedPtr
std::shared_ptr< T > SharedPtr
Definition: Types.h:91
openvdb::v7_0::math::pcg::Vector::str
std::string str() const
Return a string representation of this vector.
Definition: ConjGradient.h:800
openvdb::v7_0::math::pcg::internal::LinearOp::LinearOp
LinearOp(const T &a_, const T *x_, const T *y_, T *out_)
Definition: ConjGradient.h:522
openvdb::v7_0::math::pcg::Vector::fill
void fill(const ValueType &value)
Set all elements of this vector to value.
Definition: ConjGradient.h:600
openvdb::v7_0::math::pcg::JacobiPreconditioner::apply
void apply(const Vector< ValueType > &r, Vector< ValueType > &z) override
Apply this preconditioner to a residue vector: z = M−1r
Definition: ConjGradient.h:1300
openvdb::v7_0::math::pcg::Vector::InfNormOp::operator()
T operator()(const SizeRange &range, T maxValue) const
Definition: ConjGradient.h:709
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::arraySize
const SizeType arraySize
Definition: ConjGradient.h:658
openvdb::v7_0::math::pcg::internal::CopyOp::to
T * to
Definition: ConjGradient.h:499
openvdb::v7_0::math::pcg::SizeType
Index32 SizeType
Definition: ConjGradient.h:33
openvdb::v7_0::math::pcg::Vector::constData
const T * constData() const
Definition: ConjGradient.h:211
openvdb::v7_0::math::pcg::SparseStencilMatrix::IsFiniteOp::IsFiniteOp
IsFiniteOp(const SparseStencilMatrix &m)
Definition: ConjGradient.h:1025
openvdb::v7_0::math::pcg::Preconditioner::Preconditioner
Preconditioner(const SparseStencilMatrix< T, STENCIL_SIZE > &)
Definition: ConjGradient.h:470
openvdb::v7_0::math::pcg::Vector::empty
bool empty() const
Return true if this vector has no elements.
Definition: ConjGradient.h:161
openvdb::v7_0::util::NullInterrupter
Dummy NOOP interrupter class defining interface.
Definition: NullInterrupter.h:25
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor::scale
void scale(const Scalar &)
Scale all of the entries in this row.
Definition: ConjGradient.h:1267
openvdb::v7_0::math::pcg::JacobiPreconditioner::Ptr
SharedPtr< JacobiPreconditioner > Ptr
Definition: ConjGradient.h:1290
openvdb::v7_0::math::Abs
Coord Abs(const Coord &xyz)
Definition: Coord.h:515
openvdb::v7_0::math::Tolerance
Tolerance for floating-point comparison.
Definition: Math.h:90
openvdb::v7_0::math::pcg::SparseStencilMatrix::ConstValueIter
Iterator over the stored values in a row of this matrix.
Definition: ConjGradient.h:383
openvdb::v7_0::math::pcg::solve
State solve(const PositiveDefMatrix &A, const Vector< typename PositiveDefMatrix::ValueType > &b, Vector< typename PositiveDefMatrix::ValueType > &x, Preconditioner< typename PositiveDefMatrix::ValueType > &preconditioner, const State &termination=terminationDefaults< typename PositiveDefMatrix::ValueType >())
Solve Ax = b via the preconditioned conjugate gradient method.
Definition: ConjGradient.h:1612
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v7_0::math::pcg::operator<<
std::ostream & operator<<(std::ostream &os, const State &state)
Definition: ConjGradient.h:545
OPENVDB_LOG_DEBUG_RUNTIME
#define OPENVDB_LOG_DEBUG_RUNTIME(message)
Log a debugging message in both debug and optimized builds.
Definition: logging.h:267
openvdb::v7_0::math::pcg::Vector::l2Norm
ValueType l2Norm() const
Return the L2 norm of this vector.
Definition: ConjGradient.h:185
openvdb::v7_0::math::pcg::Vector::size
SizeType size() const
Return the number of elements in this vector.
Definition: ConjGradient.h:159
openvdb::v7_0::math::pcg::internal::FillOp::data
T * data
Definition: ConjGradient.h:513
openvdb::v7_0::math::pcg::JacobiPreconditioner
Diagonal preconditioner.
Definition: ConjGradient.h:42
openvdb::v7_0::math::pcg::SparseStencilMatrix::MatrixCopyOp::MatrixCopyOp
MatrixCopyOp(const SparseStencilMatrix &from_, SparseStencilMatrix &to_)
Definition: ConjGradient.h:838
openvdb::v7_0::math::pcg::internal::FillOp::FillOp
FillOp(T *data_, const T &val_)
Definition: ConjGradient.h:507
openvdb::v7_0::math::pcg::State::success
bool success
Definition: ConjGradient.h:47
openvdb::v7_0::math::pcg::Vector::data
T * data()
Return a pointer to this vector's elements.
Definition: ConjGradient.h:209
openvdb::v7_0::math::pcg::JacobiPreconditioner::ValueType
typename MatrixType::ValueType ValueType
Definition: ConjGradient.h:1287
openvdb::v7_0::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:106
openvdb::v7_0::math::pcg::SizeRange
tbb::blocked_range< SizeType > SizeRange
Definition: ConjGradient.h:35
openvdb::v7_0::math::pcg::Vector::InfNormOp
Definition: ConjGradient.h:705
openvdb::v7_0::math::pcg::internal::axpy
void axpy(const T &a, const T *xVec, const T *yVec, T *resultVec, SizeType size)
Compute ax + y.
Definition: ConjGradient.h:1564
NullInterrupter.h
openvdb::v7_0::math::pcg::internal::FillOp
Definition: ConjGradient.h:505
openvdb::v7_0::math::pcg::SparseStencilMatrix< OtherValueType, STENCIL_SIZE >::ValueType
OtherValueType ValueType
Definition: ConjGradient.h:240
openvdb::v7_0::math::pcg::State::absoluteError
double absoluteError
Definition: ConjGradient.h:50
openvdb::v7_0::math::pcg::internal::FillOp::val
const T val
Definition: ConjGradient.h:514
openvdb::v7_0::math::pcg::SparseStencilMatrix::IsFiniteOp::operator()
bool operator()(const SizeRange &range, bool finite) const
Definition: ConjGradient.h:1027
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner
Preconditioner using incomplete Cholesky factorization.
Definition: ConjGradient.h:43
openvdb::v7_0::math::Min
const Type & Min(const Type &a, const Type &b)
Return the minimum of two values.
Definition: Math.h:603
openvdb::v7_0::math::pcg::SparseStencilMatrix::size
SizeType size() const
Definition: ConjGradient.h:259
openvdb::v7_0::math::pcg::Vector::operator*=
Vector & operator*=(const Scalar &s)
Definition: ConjGradient.h:176
openvdb::v7_0::RuntimeError
Definition: Exceptions.h:63
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:154
openvdb::v7_0::math::Sqrt
float Sqrt(float x)
Return the square root of a floating-point value.
Definition: Math.h:708
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::TriangleConstRow
typename TriangularMatrix::ConstRow TriangleConstRow
Definition: ConjGradient.h:1358
openvdb::v7_0::math::pcg::solve
State solve(const PositiveDefMatrix &A, const Vector< typename PositiveDefMatrix::ValueType > &b, Vector< typename PositiveDefMatrix::ValueType > &x, Preconditioner< typename PositiveDefMatrix::ValueType > &preconditioner, Interrupter &interrupter, const State &termination=terminationDefaults< typename PositiveDefMatrix::ValueType >())
Solve Ax = b via the preconditioned conjugate gradient method.
Definition: ConjGradient.h:1626
openvdb::v7_0::math::isApproxZero
bool isApproxZero(const Type &x)
Return true if x is equal to zero to within the default floating-point comparison tolerance.
Definition: Math.h:293
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::Ptr
SharedPtr< IncompleteCholeskyPreconditioner > Ptr
Definition: ConjGradient.h:1356
openvdb::v7_0::math::pcg::SparseStencilMatrix::sZeroValue
static const ValueType sZeroValue
Definition: ConjGradient.h:246
openvdb::v7_0::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:102
openvdb::v7_0::math::pcg::Preconditioner< MatrixType::ValueType >::ValueType
MatrixType::ValueType ValueType
Definition: ConjGradient.h:467
openvdb::v7_0::math::pcg::SparseStencilMatrix::IsFiniteOp::mat
const SparseStencilMatrix * mat
Definition: ConjGradient.h:1040
openvdb::v7_0::math::pcg::Preconditioner::isValid
virtual bool isValid() const
Definition: ConjGradient.h:473
openvdb::v7_0::math::pcg::Vector::operator[]
const T & operator[](SizeType i) const
Definition: ConjGradient.h:204
openvdb::v7_0::math::pcg::SparseStencilMatrix::IsFiniteOp
Definition: ConjGradient.h:1023
openvdb::v7_0::math::pcg::SparseStencilMatrix::MatrixCopyOp
Definition: ConjGradient.h:836
openvdb::v7_0::math::pcg::JacobiPreconditioner::JacobiPreconditioner
JacobiPreconditioner(const MatrixType &A)
Definition: ConjGradient.h:1292
logging.h
openvdb::v7_0::math::pcg::SparseStencilMatrix::MatrixCopyOp::to
SparseStencilMatrix * to
Definition: ConjGradient.h:853
openvdb::v7_0::math::pcg::Vector::IsFiniteOp::operator()
bool operator()(const SizeRange &range, bool finite) const
Definition: ConjGradient.h:737
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::apply
void apply(const Vector< ValueType > &rVec, Vector< ValueType > &zVec) override
Apply this preconditioner to a residue vector: z = M−1r
Definition: ConjGradient.h:1458
openvdb::v7_0::math::pcg::Vector::IsFiniteOp
Definition: ConjGradient.h:733
openvdb::v7_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:388
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
openvdb::v7_0::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:620
openvdb::v7_0::Index32
uint32_t Index32
Definition: Types.h:29
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor
Read/write accessor to a row of this matrix.
Definition: ConjGradient.h:419
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::isValid
bool isValid() const override
Definition: ConjGradient.h:1456
openvdb::v7_0::math::pcg::SparseStencilMatrix::operator*=
SparseStencilMatrix & operator*=(const Scalar &s)
Definition: ConjGradient.h:285
openvdb::v7_0::math::pcg::internal::FillOp::operator()
void operator()(const SizeRange &range) const
Definition: ConjGradient.h:509
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::ValueType
typename MatrixType::ValueType ValueType
Definition: ConjGradient.h:1353
openvdb::v7_0::math::pcg::SparseStencilMatrix::RowEditor::setValue
SizeType setValue(SizeType column, const ValueType &value)
Set the value of the entry in the specified column.
Definition: ConjGradient.h:1225
openvdb
Definition: Exceptions.h:13
openvdb::v7_0::math::pcg::Vector::swap
void swap(Vector &other)
Swap internal storage with another vector, which need not be the same size.
Definition: ConjGradient.h:168
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::IncompleteCholeskyPreconditioner
IncompleteCholeskyPreconditioner(const MatrixType &matrix)
Definition: ConjGradient.h:1361
openvdb::v7_0::math::pcg::internal::LinearOp::out
T * out
Definition: ConjGradient.h:535
openvdb::v7_0::math::pcg::State::relativeError
double relativeError
Definition: ConjGradient.h:49
openvdb::v7_0::points::index::State
State
Definition: IndexIterator.h:39
openvdb::v7_0::math::pcg::SparseStencilMatrix
Sparse, square matrix representing a 3D stencil operator of size STENCIL_SIZE.
Definition: ConjGradient.h:39
openvdb::v7_0::math::pcg::Vector::data
const T * data() const
Definition: ConjGradient.h:210
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
Exceptions.h
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::binCount
const SizeType binCount
Definition: ConjGradient.h:657
openvdb::v7_0::math::pcg::Vector::DeterministicDotProductOp::operator()
void operator()(const SizeRange &range) const
Definition: ConjGradient.h:637
openvdb::v7_0::ArithmeticError
Definition: Exceptions.h:56
openvdb::v7_0::math::pcg::IncompleteCholeskyPreconditioner::upperMatrix
const TriangularMatrix & upperMatrix() const
Definition: ConjGradient.h:1507
OPENVDB_LOG_WARN
#define OPENVDB_LOG_WARN(message)
Log a warning message of the form 'someVar << "some text" << ...'.
Definition: logging.h:253
openvdb::v7_0::math::isZero
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:281