Simbody  3.5
MatrixBase.h
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1 #ifndef SimTK_SIMMATRIX_MATRIXBASE_H_
2 #define SimTK_SIMMATRIX_MATRIXBASE_H_
3 
4 /* -------------------------------------------------------------------------- *
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26 
31 namespace SimTK {
32 
33 //==============================================================================
34 // MATRIX BASE
35 //==============================================================================
67 // ----------------------------------------------------------------------------
68 template <class ELT> class MatrixBase {
69 public:
70  // These typedefs are handy, but despite appearances you cannot
71  // treat a MatrixBase as a composite numerical type. That is,
72  // CNT<MatrixBase> will not compile, or if it does it won't be
73  // meaningful.
74 
75  typedef ELT E;
76  typedef typename CNT<E>::TNeg ENeg;
78  typedef typename CNT<E>::TReal EReal;
79  typedef typename CNT<E>::TImag EImag;
80  typedef typename CNT<E>::TComplex EComplex;
81  typedef typename CNT<E>::THerm EHerm;
82  typedef typename CNT<E>::TPosTrans EPosTrans;
83 
84  typedef typename CNT<E>::TAbs EAbs;
85  typedef typename CNT<E>::TStandard EStandard;
86  typedef typename CNT<E>::TInvert EInvert;
87  typedef typename CNT<E>::TNormalize ENormalize;
88  typedef typename CNT<E>::TSqHermT ESqHermT;
89  typedef typename CNT<E>::TSqTHerm ESqTHerm;
90 
91  typedef typename CNT<E>::Scalar EScalar;
92  typedef typename CNT<E>::Number ENumber;
93  typedef typename CNT<E>::StdNumber EStdNumber;
94  typedef typename CNT<E>::Precision EPrecision;
96 
97  typedef EScalar Scalar; // the underlying Scalar type
98  typedef ENumber Number; // negator removed from Scalar
99  typedef EStdNumber StdNumber; // conjugate goes to complex
100  typedef EPrecision Precision; // complex removed from StdNumber
101  typedef EScalarNormSq ScalarNormSq; // type of scalar^2
102 
103  typedef MatrixBase<E> T;
111 
116  typedef MatrixBase<ESqHermT> TSqHermT; // ~Mat*Mat
117  typedef MatrixBase<ESqTHerm> TSqTHerm; // Mat*~Mat
118 
120  const MatrixCharacter& getMatrixCharacter() const {return helper.getMatrixCharacter();}
121 
124  void commitTo(const MatrixCommitment& mc)
125  { helper.commitTo(mc); }
126 
127  // This gives the resulting matrix type when (m(i,j) op P) is applied to each element.
128  // It will have element types which are the regular composite result of E op P.
129  template <class P> struct EltResult {
130  typedef MatrixBase<typename CNT<E>::template Result<P>::Mul> Mul;
131  typedef MatrixBase<typename CNT<E>::template Result<P>::Dvd> Dvd;
132  typedef MatrixBase<typename CNT<E>::template Result<P>::Add> Add;
133  typedef MatrixBase<typename CNT<E>::template Result<P>::Sub> Sub;
134  };
135 
137  int nrow() const {return helper.nrow();}
139  int ncol() const {return helper.ncol();}
140 
148  ptrdiff_t nelt() const {return helper.nelt();}
149 
152 
153  enum {
155  CppNScalarsPerElement = sizeof(E) / sizeof(Scalar)
156  };
157 
162 
165  MatrixBase(int m, int n)
167 
173  explicit MatrixBase(const MatrixCommitment& commitment)
174  : helper(NScalarsPerElement,CppNScalarsPerElement,commitment) {}
175 
176 
181  MatrixBase(const MatrixCommitment& commitment, int m, int n)
182  : helper(NScalarsPerElement,CppNScalarsPerElement,commitment,m,n) {}
183 
186  : helper(b.helper.getCharacterCommitment(),
187  b.helper, typename MatrixHelper<Scalar>::DeepCopy()) { }
188 
191  MatrixBase(const TNeg& b)
192  : helper(b.helper.getCharacterCommitment(),
193  b.helper, typename MatrixHelper<Scalar>::DeepCopy()) { }
194 
198  helper.copyAssign(b.helper);
199  return *this;
200  }
201  MatrixBase& operator=(const MatrixBase& b) { return copyAssign(b); }
202 
203 
213  helper.writableViewAssign(const_cast<MatrixHelper<Scalar>&>(src.helper));
214  return *this;
215  }
216 
217  // default destructor
218 
225  MatrixBase(const MatrixCommitment& commitment, int m, int n, const ELT& initialValue)
226  : helper(NScalarsPerElement, CppNScalarsPerElement, commitment, m, n)
227  { helper.fillWith(reinterpret_cast<const Scalar*>(&initialValue)); }
228 
239  MatrixBase(const MatrixCommitment& commitment, int m, int n,
240  const ELT* cppInitialValuesByRow)
241  : helper(NScalarsPerElement, CppNScalarsPerElement, commitment, m, n)
242  { helper.copyInByRowsFromCpp(reinterpret_cast<const Scalar*>(cppInitialValuesByRow)); }
243 
255 
257  MatrixBase(const MatrixCommitment& commitment,
258  const MatrixCharacter& character,
259  int spacing, const Scalar* data) // read only data
261  commitment, character, spacing, data) {}
262 
264  MatrixBase(const MatrixCommitment& commitment,
265  const MatrixCharacter& character,
266  int spacing, Scalar* data) // writable data
268  commitment, character, spacing, data) {}
270 
271  // Create a new MatrixBase from an existing helper. Both shallow and deep copies are possible.
272  MatrixBase(const MatrixCommitment& commitment,
273  MatrixHelper<Scalar>& source,
274  const typename MatrixHelper<Scalar>::ShallowCopy& shallow)
275  : helper(commitment, source, shallow) {}
276  MatrixBase(const MatrixCommitment& commitment,
277  const MatrixHelper<Scalar>& source,
278  const typename MatrixHelper<Scalar>::ShallowCopy& shallow)
279  : helper(commitment, source, shallow) {}
280  MatrixBase(const MatrixCommitment& commitment,
281  const MatrixHelper<Scalar>& source,
282  const typename MatrixHelper<Scalar>::DeepCopy& deep)
283  : helper(commitment, source, deep) {}
284 
288  void clear() {helper.clear();}
289 
290  MatrixBase& operator*=(const StdNumber& t) { helper.scaleBy(t); return *this; }
291  MatrixBase& operator/=(const StdNumber& t) { helper.scaleBy(StdNumber(1)/t); return *this; }
292  MatrixBase& operator+=(const MatrixBase& r) { helper.addIn(r.helper); return *this; }
293  MatrixBase& operator-=(const MatrixBase& r) { helper.subIn(r.helper); return *this; }
294 
295  template <class EE> MatrixBase(const MatrixBase<EE>& b)
296  : helper(MatrixCommitment(),b.helper, typename MatrixHelper<Scalar>::DeepCopy()) { }
297 
298  template <class EE> MatrixBase& operator=(const MatrixBase<EE>& b)
299  { helper = b.helper; return *this; }
300  template <class EE> MatrixBase& operator+=(const MatrixBase<EE>& b)
301  { helper.addIn(b.helper); return *this; }
302  template <class EE> MatrixBase& operator-=(const MatrixBase<EE>& b)
303  { helper.subIn(b.helper); return *this; }
304 
315  MatrixBase& operator=(const ELT& t) {
316  setToZero(); updDiag().setTo(t);
317  return *this;
318  }
319 
325  template <class S> inline MatrixBase&
326  scalarAssign(const S& s) {
327  setToZero(); updDiag().setTo(s);
328  return *this;
329  }
330 
334  template <class S> inline MatrixBase&
335  scalarAddInPlace(const S& s) {
336  updDiag().elementwiseAddScalarInPlace(s);
337  }
338 
339 
343  template <class S> inline MatrixBase&
344  scalarSubtractInPlace(const S& s) {
345  updDiag().elementwiseSubtractScalarInPlace(s);
346  }
347 
350  template <class S> inline MatrixBase&
352  negateInPlace();
353  updDiag().elementwiseAddScalarInPlace(s); // yes, add
354  }
355 
362  template <class S> inline MatrixBase&
363  scalarMultiplyInPlace(const S&);
364 
368  template <class S> inline MatrixBase&
370 
377  template <class S> inline MatrixBase&
378  scalarDivideInPlace(const S&);
379 
383  template <class S> inline MatrixBase&
384  scalarDivideFromLeftInPlace(const S&);
385 
386 
389  template <class EE> inline MatrixBase&
391 
394  template <class EE> inline void
395  rowScale(const VectorBase<EE>& r, typename EltResult<EE>::Mul& out) const;
396 
397  template <class EE> inline typename EltResult<EE>::Mul
398  rowScale(const VectorBase<EE>& r) const {
399  typename EltResult<EE>::Mul out(nrow(), ncol()); rowScale(r,out); return out;
400  }
401 
404  template <class EE> inline MatrixBase&
406 
407  template <class EE> inline void
408  colScale(const VectorBase<EE>& c, typename EltResult<EE>::Mul& out) const;
409 
410  template <class EE> inline typename EltResult<EE>::Mul
411  colScale(const VectorBase<EE>& c) const {
412  typename EltResult<EE>::Mul out(nrow(), ncol()); colScale(c,out); return out;
413  }
414 
415 
420  template <class ER, class EC> inline MatrixBase&
422 
423  template <class ER, class EC> inline void
424  rowAndColScale(const VectorBase<ER>& r, const VectorBase<EC>& c,
425  typename EltResult<typename VectorBase<ER>::template EltResult<EC>::Mul>::Mul& out) const;
426 
427  template <class ER, class EC> inline typename EltResult<typename VectorBase<ER>::template EltResult<EC>::Mul>::Mul
428  rowAndColScale(const VectorBase<ER>& r, const VectorBase<EC>& c) const {
429  typename EltResult<typename VectorBase<ER>::template EltResult<EC>::Mul>::Mul
430  out(nrow(), ncol());
431  rowAndColScale(r,c,out); return out;
432  }
433 
441  template <class S> inline MatrixBase&
442  elementwiseAssign(const S& s);
443 
446  { return elementwiseAssign<Real>(Real(s)); }
447 
450 
451  void elementwiseInvert(MatrixBase<typename CNT<E>::TInvert>& out) const;
452 
455  elementwiseInvert(out);
456  return out;
457  }
458 
466  template <class S> inline MatrixBase&
467  elementwiseAddScalarInPlace(const S& s);
468 
469  template <class S> inline void
470  elementwiseAddScalar(const S& s, typename EltResult<S>::Add&) const;
471 
472  template <class S> inline typename EltResult<S>::Add
473  elementwiseAddScalar(const S& s) const {
474  typename EltResult<S>::Add out(nrow(), ncol());
475  elementwiseAddScalar(s,out);
476  return out;
477  }
478 
486  template <class S> inline MatrixBase&
488 
489  template <class S> inline void
490  elementwiseSubtractScalar(const S& s, typename EltResult<S>::Sub&) const;
491 
492  template <class S> inline typename EltResult<S>::Sub
493  elementwiseSubtractScalar(const S& s) const {
494  typename EltResult<S>::Sub out(nrow(), ncol());
496  return out;
497  }
498 
507  template <class S> inline MatrixBase&
509 
510  template <class S> inline void
512  const S&,
514 
515  template <class S> inline typename MatrixBase<S>::template EltResult<E>::Sub
516  elementwiseSubtractFromScalar(const S& s) const {
517  typename MatrixBase<S>::template EltResult<E>::Sub out(nrow(), ncol());
518  elementwiseSubtractFromScalar<S>(s,out);
519  return out;
520  }
521 
523  template <class EE> inline MatrixBase&
525 
526  template <class EE> inline void
527  elementwiseMultiply(const MatrixBase<EE>&, typename EltResult<EE>::Mul&) const;
528 
529  template <class EE> inline typename EltResult<EE>::Mul
531  typename EltResult<EE>::Mul out(nrow(), ncol());
532  elementwiseMultiply<EE>(m,out);
533  return out;
534  }
535 
537  template <class EE> inline MatrixBase&
539 
540  template <class EE> inline void
542  const MatrixBase<EE>&,
544 
545  template <class EE> inline typename MatrixBase<EE>::template EltResult<E>::Mul
547  typename EltResult<EE>::Mul out(nrow(), ncol());
548  elementwiseMultiplyFromLeft<EE>(m,out);
549  return out;
550  }
551 
553  template <class EE> inline MatrixBase&
555 
556  template <class EE> inline void
557  elementwiseDivide(const MatrixBase<EE>&, typename EltResult<EE>::Dvd&) const;
558 
559  template <class EE> inline typename EltResult<EE>::Dvd
561  typename EltResult<EE>::Dvd out(nrow(), ncol());
562  elementwiseDivide<EE>(m,out);
563  return out;
564  }
565 
567  template <class EE> inline MatrixBase&
569 
570  template <class EE> inline void
572  const MatrixBase<EE>&,
574 
575  template <class EE> inline typename MatrixBase<EE>::template EltResult<EE>::Dvd
577  typename MatrixBase<EE>::template EltResult<E>::Dvd out(nrow(), ncol());
578  elementwiseDivideFromLeft<EE>(m,out);
579  return out;
580  }
581 
583  MatrixBase& setTo(const ELT& t) {helper.fillWith(reinterpret_cast<const Scalar*>(&t)); return *this;}
584  MatrixBase& setToNaN() {helper.fillWithScalar(CNT<StdNumber>::getNaN()); return *this;}
585  MatrixBase& setToZero() {helper.fillWithScalar(StdNumber(0)); return *this;}
586 
587  // View creating operators.
588  inline RowVectorView_<ELT> row(int i) const; // select a row
589  inline RowVectorView_<ELT> updRow(int i);
590  inline VectorView_<ELT> col(int j) const; // select a column
591  inline VectorView_<ELT> updCol(int j);
592 
593  RowVectorView_<ELT> operator[](int i) const {return row(i);}
595  VectorView_<ELT> operator()(int j) const {return col(j);}
596  VectorView_<ELT> operator()(int j) {return updCol(j);}
597 
598  // Select a block.
599  inline MatrixView_<ELT> block(int i, int j, int m, int n) const;
600  inline MatrixView_<ELT> updBlock(int i, int j, int m, int n);
601 
602  MatrixView_<ELT> operator()(int i, int j, int m, int n) const
603  { return block(i,j,m,n); }
604  MatrixView_<ELT> operator()(int i, int j, int m, int n)
605  { return updBlock(i,j,m,n); }
606 
607  // Hermitian transpose.
608  inline MatrixView_<EHerm> transpose() const;
610 
613 
616  inline VectorView_<ELT> diag() const;
619  inline VectorView_<ELT> updDiag();
623 
624  // Create a view of the real or imaginary elements. TODO
625  //inline MatrixView_<EReal> real() const;
626  //inline MatrixView_<EReal> updReal();
627  //inline MatrixView_<EImag> imag() const;
628  //inline MatrixView_<EImag> updImag();
629 
630  // Overload "real" and "imag" for both read and write as a nod to convention. TODO
631  //MatrixView_<EReal> real() {return updReal();}
632  //MatrixView_<EReal> imag() {return updImag();}
633 
634  // TODO: this routine seems ill-advised but I need it for the IVM port at the moment
635  TInvert invert() const { // return a newly-allocated inverse; dump negator
636  TInvert m(*this);
637  m.helper.invertInPlace();
638  return m; // TODO - bad: makes an extra copy
639  }
640 
641  void invertInPlace() {helper.invertInPlace();}
642 
644  void dump(const char* msg=0) const {
645  helper.dump(msg);
646  }
647 
656  const ELT& getElt(int i, int j) const { return *reinterpret_cast<const ELT*>(helper.getElt(i,j)); }
657  ELT& updElt(int i, int j) { return *reinterpret_cast< ELT*>(helper.updElt(i,j)); }
658 
659  const ELT& operator()(int i, int j) const {return getElt(i,j);}
660  ELT& operator()(int i, int j) {return updElt(i,j);}
661 
666  void getAnyElt(int i, int j, ELT& value) const
667  { helper.getAnyElt(i,j,reinterpret_cast<Scalar*>(&value)); }
668  ELT getAnyElt(int i, int j) const {ELT e; getAnyElt(i,j,e); return e;}
669 
672  // TODO: very slow! Should be optimized at least for the case
673  // where ELT is a Scalar.
674  ScalarNormSq scalarNormSqr() const {
675  const int nr=nrow(), nc=ncol();
676  ScalarNormSq sum(0);
677  for(int j=0;j<nc;++j)
678  for (int i=0; i<nr; ++i)
679  sum += CNT<E>::scalarNormSqr((*this)(i,j));
680  return sum;
681  }
682 
686  // TODO: very slow! Should be optimized at least for the case
687  // where ELT is a Scalar.
688  void abs(TAbs& mabs) const {
689  const int nr=nrow(), nc=ncol();
690  mabs.resize(nr,nc);
691  for(int j=0;j<nc;++j)
692  for (int i=0; i<nr; ++i)
693  mabs(i,j) = CNT<E>::abs((*this)(i,j));
694  }
695 
699  TAbs abs() const { TAbs mabs; abs(mabs); return mabs; }
700 
711  TStandard standardize() const {
712  const int nr=nrow(), nc=ncol();
713  TStandard mstd(nr, nc);
714  for(int j=0;j<nc;++j)
715  for (int i=0; i<nr; ++i)
716  mstd(i,j) = CNT<E>::standardize((*this)(i,j));
717  return mstd;
718  }
719 
723  ScalarNormSq normSqr() const { return scalarNormSqr(); }
724  // TODO -- not good; unnecessary overflow
725  typename CNT<ScalarNormSq>::TSqrt
727 
731  typename CNT<ScalarNormSq>::TSqrt
732  normRMS() const {
733  if (!CNT<ELT>::IsScalar)
734  SimTK_THROW1(Exception::Cant, "normRMS() only defined for scalar elements");
735  if (nelt() == 0)
736  return typename CNT<ScalarNormSq>::TSqrt(0);
738  }
739 
742  const int cols = ncol();
743  RowVector_<ELT> row(cols);
744  for (int j = 0; j < cols; ++j)
745  helper.colSum(j, reinterpret_cast<Scalar*>(&row[j]));
746  return row;
747  }
749  RowVector_<ELT> sum() const {return colSum();}
750 
753  const int rows = nrow();
754  Vector_<ELT> col(rows);
755  for (int i = 0; i < rows; ++i)
756  helper.rowSum(i, reinterpret_cast<Scalar*>(&col[i]));
757  return col;
758  }
759 
760  //TODO: make unary +/- return a self-view so they won't reallocate?
761  const MatrixBase& operator+() const {return *this; }
762  const TNeg& negate() const {return *reinterpret_cast<const TNeg*>(this); }
763  TNeg& updNegate() {return *reinterpret_cast<TNeg*>(this); }
764 
765  const TNeg& operator-() const {return negate();}
766  TNeg& operator-() {return updNegate();}
767 
768  MatrixBase& negateInPlace() {(*this) *= EPrecision(-1); return *this;}
769 
774  MatrixBase& resize(int m, int n) { helper.resize(m,n); return *this; }
780  MatrixBase& resizeKeep(int m, int n) { helper.resizeKeep(m,n); return *this; }
781 
782  // This prevents shape changes in a Matrix that would otherwise allow it. No harm if is
783  // are called on a Matrix that is locked already; it always succeeds.
784  void lockShape() {helper.lockShape();}
785 
786  // This allows shape changes again for a Matrix which was constructed to allow them
787  // but had them locked with the above routine. No harm if this is called on a Matrix
788  // that is already unlocked, but it is not allowed to call this on a Matrix which
789  // *never* allowed resizing. An exception will be thrown in that case.
790  void unlockShape() {helper.unlockShape();}
791 
792  // An assortment of handy conversions
793  const MatrixView_<ELT>& getAsMatrixView() const { return *reinterpret_cast<const MatrixView_<ELT>*>(this); }
794  MatrixView_<ELT>& updAsMatrixView() { return *reinterpret_cast< MatrixView_<ELT>*>(this); }
795  const Matrix_<ELT>& getAsMatrix() const { return *reinterpret_cast<const Matrix_<ELT>*>(this); }
796  Matrix_<ELT>& updAsMatrix() { return *reinterpret_cast< Matrix_<ELT>*>(this); }
797 
799  { assert(ncol()==1); return *reinterpret_cast<const VectorView_<ELT>*>(this); }
801  { assert(ncol()==1); return *reinterpret_cast< VectorView_<ELT>*>(this); }
802  const Vector_<ELT>& getAsVector() const
803  { assert(ncol()==1); return *reinterpret_cast<const Vector_<ELT>*>(this); }
805  { assert(ncol()==1); return *reinterpret_cast< Vector_<ELT>*>(this); }
807  { assert(ncol()==1); return *reinterpret_cast<const VectorBase<ELT>*>(this); }
809  { assert(ncol()==1); return *reinterpret_cast< VectorBase<ELT>*>(this); }
810 
812  { assert(nrow()==1); return *reinterpret_cast<const RowVectorView_<ELT>*>(this); }
814  { assert(nrow()==1); return *reinterpret_cast< RowVectorView_<ELT>*>(this); }
816  { assert(nrow()==1); return *reinterpret_cast<const RowVector_<ELT>*>(this); }
818  { assert(nrow()==1); return *reinterpret_cast< RowVector_<ELT>*>(this); }
820  { assert(nrow()==1); return *reinterpret_cast<const RowVectorBase<ELT>*>(this); }
822  { assert(nrow()==1); return *reinterpret_cast< RowVectorBase<ELT>*>(this); }
823 
824  // Access to raw data. We have to return the raw data
825  // pointer as pointer-to-scalar because we may pack the elements tighter
826  // than a C++ array would.
827 
832 
836  int getPackedSizeofElement() const {return NScalarsPerElement*sizeof(Scalar);}
837 
838  bool hasContiguousData() const {return helper.hasContiguousData();}
839  ptrdiff_t getContiguousScalarDataLength() const {
840  return helper.getContiguousDataLength();
841  }
842  const Scalar* getContiguousScalarData() const {
843  return helper.getContiguousData();
844  }
846  return helper.updContiguousData();
847  }
848  void replaceContiguousScalarData(Scalar* newData, ptrdiff_t length, bool takeOwnership) {
849  helper.replaceContiguousData(newData,length,takeOwnership);
850  }
851  void replaceContiguousScalarData(const Scalar* newData, ptrdiff_t length) {
852  helper.replaceContiguousData(newData,length);
853  }
854  void swapOwnedContiguousScalarData(Scalar* newData, ptrdiff_t length, Scalar*& oldData) {
855  helper.swapOwnedContiguousData(newData,length,oldData);
856  }
857 
862  explicit MatrixBase(MatrixHelperRep<Scalar>* hrep) : helper(hrep) {}
863 
864 protected:
865  const MatrixHelper<Scalar>& getHelper() const {return helper;}
866  MatrixHelper<Scalar>& updHelper() {return helper;}
867 
868 private:
869  MatrixHelper<Scalar> helper; // this is just one pointer
870 
871  template <class EE> friend class MatrixBase;
872 
873  // ============================= Unimplemented =============================
874  // This routine is useful for implementing friendlier Matrix expressions and operators.
875  // It maps closely to the Level-3 BLAS family of pxxmm() routines like sgemm(). The
876  // operation performed assumes that "this" is the result, and that "this" has
877  // already been sized correctly to receive the result. We'll compute
878  // this = beta*this + alpha*A*B
879  // If beta is 0 then "this" can be uninitialized. If alpha is 0 we promise not
880  // to look at A or B. The routine can work efficiently even if A and/or B are transposed
881  // by their views, so an expression like
882  // C += s * ~A * ~B
883  // can be performed with the single equivalent call
884  // C.matmul(1., s, Tr(A), Tr(B))
885  // where Tr(A) indicates a transposed view of the original A.
886  // The ultimate efficiency of this call depends on the data layout and views which
887  // are used for the three matrices.
888  // NOTE: neither A nor B can be the same matrix as 'this', nor views of the same data
889  // which would expose elements of 'this' that will be modified by this operation.
890  template <class ELT_A, class ELT_B>
891  MatrixBase& matmul(const StdNumber& beta, // applied to 'this'
892  const StdNumber& alpha, const MatrixBase<ELT_A>& A, const MatrixBase<ELT_B>& B)
893  {
894  helper.matmul(beta,alpha,A.helper,B.helper);
895  return *this;
896  }
897 
898 };
899 
900 } //namespace SimTK
901 
902 #endif // SimTK_SIMMATRIX_MATRIXBASE_H_
Here we define class MatrixHelper<S>, the scalar-type templatized helper class for the more general...
Definition: MatrixHelper.h:79
VectorView_< ELT > operator()(int j) const
Definition: MatrixBase.h:595
void unlockShape()
Definition: MatrixBase.h:790
CNT< E >::Precision EPrecision
Definition: MatrixBase.h:94
MatrixBase & setToNaN()
Definition: MatrixBase.h:584
MatrixView_< ELT > operator()(int i, int j, int m, int n)
Definition: MatrixBase.h:604
K::ScalarNormSq ScalarNormSq
Definition: CompositeNumericalTypes.h:166
Vector_< ELT > & updAsVector()
Definition: MatrixBase.h:804
const VectorView_< ELT > & getAsVectorView() const
Definition: MatrixBase.h:798
const MatrixCharacter & getMatrixCharacter() const
Definition: MatrixBase.h:120
MatrixBase< ESqTHerm > TSqTHerm
Definition: MatrixBase.h:117
MatrixBase(const MatrixCommitment &commitment, int m, int n, const ELT *cppInitialValuesByRow)
Initializing constructor with the initially-allocated elements initialized from a C++ array of elemen...
Definition: MatrixBase.h:239
EScalarNormSq ScalarNormSq
Definition: MatrixBase.h:101
const TNeg & negate() const
Definition: MatrixBase.h:762
K::TReal TReal
Definition: CompositeNumericalTypes.h:141
MatrixBase & copyAssign(const MatrixBase &b)
Copy assignment is a deep copy but behavior depends on type of lhs: if view, rhs must match...
Definition: MatrixBase.h:197
MatrixBase< EStandard > TStandard
Definition: MatrixBase.h:113
CNT< E >::TNormalize ENormalize
Definition: MatrixBase.h:87
const VectorBase< ELT > & getAsVectorBase() const
Definition: MatrixBase.h:806
This is the vector class intended to appear in user code for large, variable size column vectors...
Definition: BigMatrix.h:171
This is a dataless rehash of the MatrixBase class to specialize it for RowVectors.
Definition: BigMatrix.h:165
CNT< E >::TImag EImag
Definition: MatrixBase.h:79
const MatrixCommitment & getCharacterCommitment() const
Definition: MatrixBase.h:119
This is the top-level SimTK namespace into which all SimTK names are placed to avoid collision with o...
Definition: Assembler.h:37
EltResult< EE >::Mul colScale(const VectorBase< EE > &c) const
Definition: MatrixBase.h:411
CNT< E >::TNeg ENeg
Definition: MatrixBase.h:76
K::TSqrt TSqrt
Definition: CompositeNumericalTypes.h:154
VectorBase< ELT > & updAsVectorBase()
Definition: MatrixBase.h:808
MatrixHelper< Scalar > & updHelper()
Definition: MatrixBase.h:866
MatrixBase & elementwiseSubtractScalarInPlace(const S &s)
Set M(i,j)-=s for every element of M and some value s.
CNT< E >::TStandard EStandard
Definition: MatrixBase.h:85
Definition: MatrixBase.h:129
static TSqrt sqrt(const K &t)
Definition: CompositeNumericalTypes.h:239
void commitTo(const MatrixCommitment &mc)
Change the handle commitment for this matrix handle; only allowed if the handle is currently clear...
Definition: MatrixBase.h:124
CNT< E >::THerm EHerm
Definition: MatrixBase.h:81
ScalarNormSq normSqr() const
This is the scalar Frobenius norm, and its square.
Definition: MatrixBase.h:723
RowVectorView_< ELT > row(int i) const
Definition: BigMatrix.h:270
const MatrixCharacter & getMatrixCharacter() const
MatrixBase< typename CNT< E >::TInvert > elementwiseInvert() const
Definition: MatrixBase.h:453
K::Scalar Scalar
Definition: CompositeNumericalTypes.h:160
void elementwiseDivide(const MatrixBase< EE > &, typename EltResult< EE >::Dvd &) const
A MatrixCharacter is a set containing a value for each of the matrix characteristics except element t...
Definition: MatrixCharacteristics.h:597
K::TNormalize TNormalize
Definition: CompositeNumericalTypes.h:158
TStandard standardize() const
Return a Matrix of the same shape and contents as this one but with the element type converted to one...
Definition: MatrixBase.h:711
MatrixBase()
The default constructor builds a 0x0 matrix managed by a helper that understands how many scalars the...
Definition: MatrixBase.h:161
CNT< E >::TComplex EComplex
Definition: MatrixBase.h:80
MatrixBase & elementwiseDivideFromLeftInPlace(const MatrixBase< EE > &)
M(i,j) = R(i,j) / M(i,j); R must have same dimensions as this.
MatrixBase & rowAndColScaleInPlace(const VectorBase< ER > &r, const VectorBase< EC > &c)
M = diag(r) * M * diag(c); r must have nrow() elements; must have ncol() elements.
MatrixBase & elementwiseMultiplyFromLeftInPlace(const MatrixBase< EE > &)
M(i,j) = R(i,j) * M(i,j); R must have same dimensions as this.
MatrixBase & elementwiseAssign(const S &s)
Set M(i,j)=s for every element of M and some value s.
MatrixView_< EHerm > operator~()
Definition: MatrixBase.h:612
void replaceContiguousScalarData(const Scalar *newData, ptrdiff_t length)
Definition: MatrixBase.h:851
VectorView_< ELT > updCol(int j)
Definition: BigMatrix.h:261
MatrixBase & operator/=(const StdNumber &t)
Definition: MatrixBase.h:291
CNT< ScalarNormSq >::TSqrt normRMS() const
We only allow RMS norm if the elements are scalars.
Definition: MatrixBase.h:732
void replaceContiguousScalarData(Scalar *newData, ptrdiff_t length, bool takeOwnership)
Definition: MatrixBase.h:848
MatrixBase & resizeKeep(int m, int n)
Change the size of this matrix, retaining as much of the old data as will fit.
Definition: MatrixBase.h:780
Scalar * updContiguousScalarData()
Definition: MatrixBase.h:845
MatrixBase< EHerm > THerm
Definition: MatrixBase.h:109
K::TImag TImag
Definition: CompositeNumericalTypes.h:142
CNT< E >::Number ENumber
Definition: MatrixBase.h:92
Definition: Exception.h:297
RowVectorView_< ELT > updRow(int i)
Definition: BigMatrix.h:279
ELT & updElt(int i, int j)
Definition: MatrixBase.h:657
ELT E
Definition: MatrixBase.h:75
int getNScalarsPerElement() const
This is the number of consecutive scalars used to represent one element of type ELT.
Definition: MatrixBase.h:831
ptrdiff_t getContiguousScalarDataLength() const
Definition: MatrixBase.h:839
MatrixBase & viewAssign(const MatrixBase &src)
View assignment is a shallow copy, meaning that we disconnect the MatrixBase from whatever it used to...
Definition: MatrixBase.h:212
TNeg & operator-()
Definition: MatrixBase.h:766
EltResult< S >::Sub elementwiseSubtractScalar(const S &s) const
Definition: MatrixBase.h:493
EltResult< typename VectorBase< ER >::template EltResult< EC >::Mul >::Mul rowAndColScale(const VectorBase< ER > &r, const VectorBase< EC > &c) const
Definition: MatrixBase.h:428
MatrixBase(const MatrixCommitment &commitment, const MatrixCharacter &character, int spacing, const Scalar *data)
Construct a read-only view of pre-existing data.
Definition: MatrixBase.h:257
MatrixBase(const MatrixCommitment &commitment, MatrixHelper< Scalar > &source, const typename MatrixHelper< Scalar >::ShallowCopy &shallow)
Definition: MatrixBase.h:272
void elementwiseMultiplyFromLeft(const MatrixBase< EE > &, typename MatrixBase< EE >::template EltResult< E >::Mul &) const
Definition: BigMatrix.h:484
void elementwiseDivideFromLeft(const MatrixBase< EE > &, typename MatrixBase< EE >::template EltResult< E >::Dvd &) const
Definition: BigMatrix.h:533
VectorView_< ELT > operator()(int j)
Definition: MatrixBase.h:596
MatrixBase(const MatrixCommitment &commitment, int m, int n)
This constructor takes a handle commitment and allocates the default matrix for that kind of commitme...
Definition: MatrixBase.h:181
SimTK_Real Real
This is the default compiled-in floating point type for SimTK, either float or double.
Definition: SimTKcommon/include/SimTKcommon/internal/common.h:593
MatrixBase & scalarMultiplyInPlace(const S &)
Set M(i,j) = M(i,j)*S for some "scalar" S.
CNT< E >::TWithoutNegator EWithoutNegator
Definition: MatrixBase.h:77
MatrixBase & operator-=(const MatrixBase &r)
Definition: MatrixBase.h:293
MatrixBase & operator*=(const StdNumber &t)
Definition: MatrixBase.h:290
Matrix_< ELT > & updAsMatrix()
Definition: MatrixBase.h:796
static TStandard standardize(const K &t)
Definition: CompositeNumericalTypes.h:241
CNT< ScalarNormSq >::TSqrt norm() const
Definition: MatrixBase.h:726
void getAnyElt(int i, int j, ELT &value) const
This returns a copy of the element value for any position in the logical matrix, regardless of whethe...
Definition: MatrixBase.h:666
void abs(TAbs &mabs) const
abs() is elementwise absolute value; that is, the return value has the same dimension as this Matrix ...
Definition: MatrixBase.h:688
const Matrix_< ELT > & getAsMatrix() const
Definition: MatrixBase.h:795
const RowVector_< ELT > & getAsRowVector() const
Definition: MatrixBase.h:815
(Advanced) This class is identical to RowVector_ except that it has shallow (reference) copy and assi...
Definition: BigMatrix.h:173
CNT< E >::TInvert EInvert
Definition: MatrixBase.h:86
RowVectorView_< ELT > operator[](int i)
Definition: MatrixBase.h:594
MatrixBase< typename CNT< E >::template Result< P >::Sub > Sub
Definition: MatrixBase.h:133
RowVector_< ELT > & updAsRowVector()
Definition: MatrixBase.h:817
K::TSqTHerm TSqTHerm
Definition: CompositeNumericalTypes.h:147
MatrixBase< EComplex > TComplex
Definition: MatrixBase.h:108
CNT< E >::StdNumber EStdNumber
Definition: MatrixBase.h:93
MatrixView_< EHerm > transpose() const
Definition: BigMatrix.h:222
MatrixView_< ELT > updBlock(int i, int j, int m, int n)
Definition: BigMatrix.h:211
EltResult< S >::Add elementwiseAddScalar(const S &s) const
Definition: MatrixBase.h:473
VectorView_< ELT > diag()
This non-const version of diag() is an alternate name for updDiag() available for historical reasons...
Definition: MatrixBase.h:622
int nrow() const
Return the number of rows m in the logical shape of this matrix.
Definition: MatrixBase.h:137
RowVector_< ELT > colSum() const
Form the column sums of this matrix, returned as a RowVector.
Definition: MatrixBase.h:741
MatrixBase< EImag > TImag
Definition: MatrixBase.h:107
void elementwiseSubtractScalar(const S &s, typename EltResult< S >::Sub &) const
K::Precision Precision
Definition: CompositeNumericalTypes.h:164
TNeg & updNegate()
Definition: MatrixBase.h:763
Vector_< ELT > rowSum() const
Form the row sums of this matrix, returned as a Vector.
Definition: MatrixBase.h:752
MatrixBase< E > TPosTrans
Definition: MatrixBase.h:110
(Advanced) This class is identical to Matrix_ except that it has shallow (reference) copy and assignm...
Definition: BigMatrix.h:167
void dump(const char *msg=0) const
Matlab-compatible debug output.
Definition: MatrixBase.h:644
ScalarNormSq scalarNormSqr() const
Scalar norm square is sum( squares of all scalars ).
Definition: MatrixBase.h:674
RowVector_< ELT > sum() const
Alternate name for colSum(); behaves like the Matlab function sum().
Definition: MatrixBase.h:749
EltResult< EE >::Mul elementwiseMultiply(const MatrixBase< EE > &m) const
Definition: MatrixBase.h:530
MatrixBase & elementwiseAssign(int s)
Overloaded to allow an integer argument, which is converted to Real.
Definition: MatrixBase.h:445
K::TInvert TInvert
Definition: CompositeNumericalTypes.h:157
MatrixBase & scalarAddInPlace(const S &s)
Add a scalar to M&#39;s diagonal.
Definition: MatrixBase.h:335
const RowVectorBase< ELT > & getAsRowVectorBase() const
Definition: MatrixBase.h:819
MatrixView_< ELT > block(int i, int j, int m, int n) const
Definition: BigMatrix.h:200
CNT< E >::TSqHermT ESqHermT
Definition: MatrixBase.h:88
MatrixView_< EHerm > updTranspose()
Definition: BigMatrix.h:230
CNT< E >::TReal EReal
Definition: MatrixBase.h:78
VectorView_< ELT > updDiag()
Select main diagonal (of largest leading square if rectangular) and return it as a writable view of t...
Definition: BigMatrix.h:245
MatrixBase(const MatrixCommitment &commitment, const MatrixCharacter &character, int spacing, Scalar *data)
Construct a writable view of pre-existing data.
Definition: MatrixBase.h:264
ENumber Number
Definition: MatrixBase.h:98
MatrixBase & scalarSubtractFromLeftInPlace(const S &s)
Set M(i,i) = S - M(i,i), M(i,j) = -M(i,j) for i!=j.
Definition: MatrixBase.h:351
MatrixBase< typename CNT< E >::template Result< P >::Add > Add
Definition: MatrixBase.h:132
RowVectorBase< ELT > & updAsRowVectorBase()
Definition: MatrixBase.h:821
MatrixBase(const TNeg &b)
Implicit conversion from matrix with negated elements (otherwise this is just like the copy construct...
Definition: MatrixBase.h:191
MatrixBase< typename CNT< E >::template Result< P >::Dvd > Dvd
Definition: MatrixBase.h:131
MatrixBase< E > T
Definition: MatrixBase.h:103
#define SimTK_THROW1(exc, a1)
Definition: Exception.h:311
void rowScale(const VectorBase< EE > &r, typename EltResult< EE >::Mul &out) const
Return type is a new matrix which will have the same dimensions as &#39;this&#39; but will have element types...
MatrixBase< EInvert > TInvert
Definition: MatrixBase.h:114
const ELT & getElt(int i, int j) const
Element selection for stored elements.
Definition: MatrixBase.h:656
MatrixBase< ENormalize > TNormalize
Definition: MatrixBase.h:115
CNT< E >::TPosTrans EPosTrans
Definition: MatrixBase.h:82
MatrixBase< EAbs > TAbs
Definition: MatrixBase.h:112
void lockShape()
Definition: MatrixBase.h:784
K::TPosTrans TPosTrans
Definition: CompositeNumericalTypes.h:145
EStdNumber StdNumber
Definition: MatrixBase.h:99
TInvert invert() const
Definition: MatrixBase.h:635
MatrixBase< EWithoutNegator > TWithoutNegator
Definition: MatrixBase.h:105
Definition: MatrixBase.h:155
MatrixBase< EReal > TReal
Definition: MatrixBase.h:106
bool isResizeable() const
Return true if either dimension of this Matrix is resizable.
Definition: MatrixBase.h:151
EltResult< EE >::Mul rowScale(const VectorBase< EE > &r) const
Definition: MatrixBase.h:398
const TNeg & operator-() const
Definition: MatrixBase.h:765
const MatrixView_< ELT > & getAsMatrixView() const
Definition: MatrixBase.h:793
MatrixBase & elementwiseInvertInPlace()
Set M(i,j) = M(i,j)^-1.
Definition: BigMatrix.h:361
MatrixBase & rowScaleInPlace(const VectorBase< EE > &)
M = diag(r) * M; r must have nrow() elements.
const Vector_< ELT > & getAsVector() const
Definition: MatrixBase.h:802
This is the matrix class intended to appear in user code for large, variable size matrices...
Definition: BigMatrix.h:168
int getPackedSizeofElement() const
This is like sizeof(ELT), but returning the number of bytes we use to store the element which may be ...
Definition: MatrixBase.h:836
CNT< E >::TSqTHerm ESqTHerm
Definition: MatrixBase.h:89
MatrixView_< EHerm > operator~() const
Definition: MatrixBase.h:611
MatrixBase & elementwiseAddScalarInPlace(const S &s)
Set M(i,j)+=s for every element of M and some value s.
MatrixBase & operator+=(const MatrixBase &r)
Definition: MatrixBase.h:292
K::StdNumber StdNumber
Definition: CompositeNumericalTypes.h:163
ELT getAnyElt(int i, int j) const
Definition: MatrixBase.h:668
void colScale(const VectorBase< EE > &c, typename EltResult< EE >::Mul &out) const
MatrixBase & operator=(const MatrixBase< EE > &b)
Definition: MatrixBase.h:298
void elementwiseMultiply(const MatrixBase< EE > &, typename EltResult< EE >::Mul &) const
MatrixBase & setToZero()
Definition: MatrixBase.h:585
MatrixBase< S >::template EltResult< E >::Sub elementwiseSubtractFromScalar(const S &s) const
Definition: MatrixBase.h:516
MatrixBase(const MatrixCommitment &commitment, int m, int n, const ELT &initialValue)
Initializing constructor with all of the initially-allocated elements initialized to the same value...
Definition: MatrixBase.h:225
void elementwiseAddScalar(const S &s, typename EltResult< S >::Add &) const
Specialized information about Composite Numerical Types which allows us to define appropriate templat...
Definition: CompositeNumericalTypes.h:136
const RowVectorView_< ELT > & getAsRowVectorView() const
Definition: MatrixBase.h:811
MatrixBase & operator-=(const MatrixBase< EE > &b)
Definition: MatrixBase.h:302
void invertInPlace()
Definition: MatrixBase.h:641
MatrixBase(const MatrixCommitment &commitment)
This constructor takes a handle commitment and allocates the default matrix for that kind of commitme...
Definition: MatrixBase.h:173
CNT< E >::ScalarNormSq EScalarNormSq
Definition: MatrixBase.h:95
MatrixBase & scalarDivideInPlace(const S &)
Set M(i,j) = M(i,j)/S for some "scalar" S.
MatrixBase< EE >::template EltResult< EE >::Dvd elementwiseDivideFromLeft(const MatrixBase< EE > &m) const
Definition: MatrixBase.h:576
VectorView_< ELT > diag() const
Select main diagonal (of largest leading square if rectangular) and return it as a read-only view of ...
Definition: BigMatrix.h:238
MatrixBase & operator=(const MatrixBase &b)
Definition: MatrixBase.h:201
MatrixBase(int m, int n)
This constructor allocates the default matrix a completely uncommitted matrix commitment, given particular initial dimensions.
Definition: MatrixBase.h:165
const MatrixHelper< Scalar > & getHelper() const
Definition: MatrixBase.h:865
CNT< E >::TAbs EAbs
Definition: MatrixBase.h:84
K::TNeg TNeg
Definition: CompositeNumericalTypes.h:139
This is a dataless rehash of the MatrixBase class to specialize it for Vectors.
Definition: BigMatrix.h:164
MatrixBase & scalarDivideFromLeftInPlace(const S &)
Set M(i,j) = S/M(i,j) for some "scalar" S.
K::TStandard TStandard
Definition: CompositeNumericalTypes.h:156
Definition: MatrixBase.h:154
K::TWithoutNegator TWithoutNegator
Definition: CompositeNumericalTypes.h:140
CNT< E >::Scalar EScalar
Definition: MatrixBase.h:91
const Scalar * getContiguousScalarData() const
Definition: MatrixBase.h:842
RowVectorView_< ELT > operator[](int i) const
Definition: MatrixBase.h:593
Represents a variable size row vector; much less common than the column vector type Vector_...
Definition: BigMatrix.h:174
void commitTo(const MatrixCommitment &)
A MatrixCommitment provides a set of acceptable matrix characteristics.
Definition: MatrixCharacteristics.h:832
VectorView_< ELT > & updAsVectorView()
Definition: MatrixBase.h:800
void swapOwnedContiguousScalarData(Scalar *newData, ptrdiff_t length, Scalar *&oldData)
Definition: MatrixBase.h:854
MatrixBase< EE >::template EltResult< E >::Mul elementwiseMultiplyFromLeft(const MatrixBase< EE > &m) const
Definition: MatrixBase.h:546
MatrixBase(MatrixHelperRep< Scalar > *hrep)
Helper rep-stealing constructor.
Definition: MatrixBase.h:862
ptrdiff_t nelt() const
Return the number of elements in the logical shape of this matrix.
Definition: MatrixBase.h:148
void elementwiseSubtractFromScalar(const S &, typename MatrixBase< S >::template EltResult< E >::Sub &) const
Definition: BigMatrix.h:435
TAbs abs() const
abs() with the result as a function return.
Definition: MatrixBase.h:699
bool isResizeable() const
Definition: MatrixCharacteristics.h:925
MatrixBase & elementwiseDivideInPlace(const MatrixBase< EE > &)
M(i,j) /= R(i,j); R must have same dimensions as this.
MatrixBase(const MatrixCommitment &commitment, const MatrixHelper< Scalar > &source, const typename MatrixHelper< Scalar >::ShallowCopy &shallow)
Definition: MatrixBase.h:276
K::TComplex TComplex
Definition: CompositeNumericalTypes.h:143
This is the common base class for Simbody&#39;s Vector_ and Matrix_ classes for handling large...
Definition: BigMatrix.h:163
K::Number Number
Definition: CompositeNumericalTypes.h:162
MatrixBase & operator=(const ELT &t)
Matrix assignment to an element sets only the *diagonal* elements to the indicated value; everything ...
Definition: MatrixBase.h:315
static TAbs abs(const K &t)
Definition: CompositeNumericalTypes.h:240
MatrixBase & scalarAssign(const S &s)
Set M&#39;s diagonal elements to a "scalar" value S, and all off-diagonal elements to zero...
Definition: MatrixBase.h:326
MatrixBase(const MatrixBase< EE > &b)
Definition: MatrixBase.h:295
MatrixBase & elementwiseMultiplyInPlace(const MatrixBase< EE > &)
M(i,j) *= R(i,j); R must have same dimensions as this.
MatrixBase & colScaleInPlace(const VectorBase< EE > &)
M = M * diag(c); c must have ncol() elements.
void clear()
This restores the MatrixBase to the state it would be in had it been constructed specifying only its ...
Definition: MatrixBase.h:288
MatrixBase< ENeg > TNeg
Definition: MatrixBase.h:104
int ncol() const
Return the number of columns n in the logical shape of this matrix.
Definition: MatrixBase.h:139
MatrixBase & setTo(const ELT &t)
Fill every element in current allocation with given element (or NaN or 0).
Definition: MatrixBase.h:583
RowVectorView_< ELT > & updAsRowVectorView()
Definition: MatrixBase.h:813
MatrixBase & operator+=(const MatrixBase< EE > &b)
Definition: MatrixBase.h:300
K::TSqHermT TSqHermT
Definition: CompositeNumericalTypes.h:146
EltResult< EE >::Dvd elementwiseDivide(const MatrixBase< EE > &m) const
Definition: MatrixBase.h:560
MatrixBase & resize(int m, int n)
Change the size of this matrix.
Definition: MatrixBase.h:774
bool hasContiguousData() const
Definition: MatrixBase.h:838
MatrixBase & scalarMultiplyFromLeftInPlace(const S &)
Set M(i,j) = S * M(i,j) for some "scalar" S.
void rowAndColScale(const VectorBase< ER > &r, const VectorBase< EC > &c, typename EltResult< typename VectorBase< ER >::template EltResult< EC >::Mul >::Mul &out) const
Definition: BigMatrix.h:337
MatrixBase< typename CNT< E >::template Result< P >::Mul > Mul
Definition: MatrixBase.h:130
MatrixBase & negateInPlace()
Definition: MatrixBase.h:768
MatrixBase(const MatrixCommitment &commitment, const MatrixHelper< Scalar > &source, const typename MatrixHelper< Scalar >::DeepCopy &deep)
Definition: MatrixBase.h:280
(Advanced) This class is identical to Vector_ except that it has shallow (reference) copy and assignm...
Definition: BigMatrix.h:170
ELT & operator()(int i, int j)
Definition: MatrixBase.h:660
MatrixBase & elementwiseSubtractFromScalarInPlace(const S &s)
Set M(i,j) = s - M(i,j) for every element of M and some value s.
K::THerm THerm
Definition: CompositeNumericalTypes.h:144
MatrixView_< ELT > & updAsMatrixView()
Definition: MatrixBase.h:794
const MatrixCommitment & getCharacterCommitment() const
MatrixView_< ELT > operator()(int i, int j, int m, int n) const
Definition: MatrixBase.h:602
const ELT & operator()(int i, int j) const
Definition: MatrixBase.h:659
MatrixBase & scalarSubtractInPlace(const S &s)
Subtract a scalar from M&#39;s diagonal.
Definition: MatrixBase.h:344
MatrixBase(const MatrixBase &b)
Copy constructor is a deep copy (not appropriate for views!).
Definition: MatrixBase.h:185
EPrecision Precision
Definition: MatrixBase.h:100
EScalar Scalar
Definition: MatrixBase.h:97
MatrixBase< ESqHermT > TSqHermT
Definition: MatrixBase.h:116
K::TAbs TAbs
Definition: CompositeNumericalTypes.h:155
VectorView_< ELT > col(int j) const
Definition: BigMatrix.h:252
const MatrixBase & operator+() const
Definition: MatrixBase.h:761