MPQC  2.3.1
matrix.h
1 //
2 // matrix.h
3 //
4 // Copyright (C) 1996 Limit Point Systems, Inc.
5 //
6 // Author: Curtis Janssen <cljanss@limitpt.com>
7 // Maintainer: LPS
8 //
9 // This file is part of the SC Toolkit.
10 //
11 // The SC Toolkit is free software; you can redistribute it and/or modify
12 // it under the terms of the GNU Library General Public License as published by
13 // the Free Software Foundation; either version 2, or (at your option)
14 // any later version.
15 //
16 // The SC Toolkit is distributed in the hope that it will be useful,
17 // but WITHOUT ANY WARRANTY; without even the implied warranty of
18 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 // GNU Library General Public License for more details.
20 //
21 // You should have received a copy of the GNU Library General Public License
22 // along with the SC Toolkit; see the file COPYING.LIB. If not, write to
23 // the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
24 //
25 // The U.S. Government is granted a limited license as per AL 91-7.
26 //
27 
28 #ifndef _math_scmat_matrix_h
29 #define _math_scmat_matrix_h
30 #ifdef __GNUC__
31 #pragma interface
32 #endif
33 
34 #include <iostream>
35 
36 #include <math/scmat/abstract.h>
37 
38 namespace sc {
39 
40 class SCVectordouble;
41 class SCMatrixdouble;
42 class SymmSCMatrixdouble;
43 class DiagSCMatrixdouble;
44 
45 class SCMatrixBlockIter;
46 class SCMatrixRectBlock;
47 class SCMatrixLTriBlock;
48 class SCMatrixDiagBlock;
49 class SCVectorSimpleBlock;
50 
51 class RefSCMatrix;
52 class RefSymmSCMatrix;
55 class RefSCVector: public Ref<SCVector> {
56  // standard overrides
57  public:
60  RefSCVector();
62  RefSCVector(const RefSCVector& v);
64  RefSCVector(SCVector *v);
65  // don't allow automatic conversion from any reference to a
66  // described class
67  ~RefSCVector();
69  RefSCVector& operator=(SCVector* v);
71  RefSCVector& operator=(const RefSCVector& v);
72 
73  // vector specific members
74  public:
77  RefSCVector(const RefSCDimension& dim,const Ref<SCMatrixKit>&);
78 
80  SCVectordouble operator()(int) const;
82  SCVectordouble operator[](int) const;
84  RefSCVector operator+(const RefSCVector&a) const;
86  RefSCVector operator-(const RefSCVector&a) const;
88  RefSCVector operator*(double) const;
90  RefSCMatrix outer_product(const RefSCVector& v) const;
92  RefSymmSCMatrix symmetric_outer_product() const;
93 
94  void set_element(int i,double val) const;
95  void accumulate_element(int i,double val) const;
96  double get_element(int) const;
97  int n() const;
98  RefSCDimension dim() const;
99  Ref<SCMatrixKit> kit() const;
100  RefSCVector clone() const;
101  RefSCVector copy() const;
102  double maxabs() const;
103  double scalar_product(const RefSCVector&) const;
104  double dot(const RefSCVector&) const;
105  void normalize() const;
106  void randomize() const;
107  void assign(const RefSCVector& v) const;
108  void assign(double val) const;
109  void assign(const double* v) const;
110  void convert(double*) const;
111  void scale(double val) const;
112  void accumulate(const RefSCVector& v) const;
113  void accumulate_product(const RefSymmSCMatrix&, const RefSCVector&);
114  void accumulate_product(const RefSCMatrix&, const RefSCVector&);
115  void element_op(const Ref<SCElementOp>& op) const;
116  void element_op(const Ref<SCElementOp2>&,
117  const RefSCVector&) const;
118  void element_op(const Ref<SCElementOp3>&,
119  const RefSCVector&,
120  const RefSCVector&) const;
121  void print(std::ostream&out) const;
122  void print(const char*title=0,
123  std::ostream&out=ExEnv::out0(), int precision=10) const;
124  void save(StateOut&);
126  void restore(StateIn&);
127 };
128 RefSCVector operator*(double,const RefSCVector&);
129 
130 class RefSymmSCMatrix;
131 class RefDiagSCMatrix;
135 class RefSCMatrix: public Ref<SCMatrix> {
136  // standard overrides
137  public:
140  RefSCMatrix();
142  RefSCMatrix(const RefSCMatrix& m);
144  RefSCMatrix(SCMatrix* m);
145  ~RefSCMatrix();
147  RefSCMatrix& operator=(SCMatrix* m);
149  RefSCMatrix& operator=(const RefSCMatrix& m);
150 
151  // matrix specific members
152  public:
155  RefSCMatrix(const RefSCDimension& d1,const RefSCDimension& d2,
156  const Ref<SCMatrixKit>&);
157 
159  RefSCVector operator*(const RefSCVector&) const;
160 
162  RefSCMatrix operator*(const RefSCMatrix&) const;
163  RefSCMatrix operator*(const RefSymmSCMatrix&) const;
164  RefSCMatrix operator*(const RefDiagSCMatrix&) const;
165 
167  RefSCMatrix operator*(double) const;
168 
170  RefSCMatrix operator+(const RefSCMatrix&) const;
172  RefSCMatrix operator-(const RefSCMatrix&) const;
173 
175  RefSCMatrix t() const;
177  RefSCMatrix i() const;
179  RefSCMatrix gi() const;
180 
183  RefSCMatrix clone() const;
184  RefSCMatrix copy() const;
185 
186  RefSCMatrix get_subblock(int br, int er, int bc, int ec);
187  void assign_subblock(const RefSCMatrix&, int br, int er, int bc, int ec,
188  int source_br = 0, int source_bc = 0);
189  void accumulate_subblock(const RefSCMatrix&, int, int, int, int,
190  int source_br = 0, int source_bc = 0);
191  RefSCVector get_row(int) const;
192  RefSCVector get_column(int) const;
193  void assign_row(const RefSCVector&, int) const;
194  void assign_column(const RefSCVector&, int) const;
195  void accumulate_row(const RefSCVector&, int) const;
196  void accumulate_column(const RefSCVector&, int) const;
197 
198  void accumulate_outer_product(const RefSCVector&,const RefSCVector&) const;
199  void accumulate_product(const RefSCMatrix&,const RefSCMatrix&) const;
200  void assign(const RefSCMatrix&) const;
201  void scale(double) const;
202  void randomize() const;
203  void assign(double) const;
204  void assign(const double*) const;
205  void assign(const double**) const;
206  void convert(double*) const;
207  void convert(double**) const;
208  void accumulate(const RefSCMatrix&) const;
209  void accumulate(const RefSymmSCMatrix&) const;
210  void accumulate(const RefDiagSCMatrix&) const;
211  void element_op(const Ref<SCElementOp>&) const;
212  void element_op(const Ref<SCElementOp2>&,
213  const RefSCMatrix&) const;
214  void element_op(const Ref<SCElementOp3>&,
215  const RefSCMatrix&,
216  const RefSCMatrix&) const;
217  int nrow() const;
218  int ncol() const;
219  RefSCDimension rowdim() const;
220  RefSCDimension coldim() const;
221  Ref<SCMatrixKit> kit() const;
222  void set_element(int,int,double) const;
223  void accumulate_element(int,int,double) const;
224  double get_element(int,int) const;
225  void print(std::ostream&) const;
226  void print(const char*title=0,
227  std::ostream&out=ExEnv::out0(), int =10) const;
228  double trace() const;
229  void save(StateOut&);
231  void restore(StateIn&);
232 
237  void svd(const RefSCMatrix &U,
238  const RefDiagSCMatrix &sigma,
239  const RefSCMatrix &V);
241  double solve_lin(const RefSCVector& v) const;
243  double determ() const;
245  SCMatrixdouble operator()(int i,int j) const;
246 
250  int nblock() const;
254  RefSCMatrix block(int i) const;
255 };
257 RefSCMatrix operator*(double,const RefSCMatrix&);
258 
261 class RefSymmSCMatrix: public Ref<SymmSCMatrix> {
262  // standard overrides
263  public:
266  RefSymmSCMatrix();
268  RefSymmSCMatrix(const RefSymmSCMatrix& m);
270  RefSymmSCMatrix(SymmSCMatrix *m);
271  ~RefSymmSCMatrix();
273  RefSymmSCMatrix& operator=(SymmSCMatrix* m);
275  RefSymmSCMatrix& operator=(const RefSymmSCMatrix& m);
276 
277  // matrix specific members
278  public:
281  RefSymmSCMatrix(const RefSCDimension& d,const Ref<SCMatrixKit>&);
283  RefSCMatrix operator*(const RefSCMatrix&) const;
284  RefSCMatrix operator*(const RefSymmSCMatrix&) const;
286  RefSCVector operator*(const RefSCVector&a) const;
287  RefSymmSCMatrix operator*(double) const;
289  RefSymmSCMatrix operator+(const RefSymmSCMatrix&) const;
290  RefSymmSCMatrix operator-(const RefSymmSCMatrix&) const;
292  RefSymmSCMatrix i() const;
294  RefSymmSCMatrix gi() const;
297  RefSymmSCMatrix clone() const;
298  RefSymmSCMatrix copy() const;
299  void set_element(int,int,double) const;
300  void accumulate_element(int,int,double) const;
301  double get_element(int,int) const;
302 
303  RefSCMatrix get_subblock(int br, int er, int bc, int ec);
304  RefSymmSCMatrix get_subblock(int br, int er);
305  void assign_subblock(const RefSCMatrix&, int br, int er, int bc, int ec);
306  void assign_subblock(const RefSymmSCMatrix&, int br, int er);
307  void accumulate_subblock(const RefSCMatrix&, int, int, int, int);
308  void accumulate_subblock(const RefSymmSCMatrix&, int, int);
309  RefSCVector get_row(int);
310  void assign_row(const RefSCVector&, int);
311  void accumulate_row(const RefSCVector&, int);
312 
313  void accumulate_symmetric_outer_product(const RefSCVector&) const;
314  double scalar_product(const RefSCVector&) const;
315  void accumulate_symmetric_product(const RefSCMatrix&) const;
316  void accumulate_symmetric_sum(const RefSCMatrix&) const;
318  void accumulate_transform(const RefSCMatrix&a,const RefSymmSCMatrix&b,
319  SCMatrix::Transform = SCMatrix::NormalTransform) const;
320  void accumulate_transform(const RefSCMatrix&a,const RefDiagSCMatrix&b,
321  SCMatrix::Transform = SCMatrix::NormalTransform) const;
322  void accumulate_transform(const RefSymmSCMatrix&a,
323  const RefSymmSCMatrix&b) const;
324 
325  void randomize() const;
326  void assign(const RefSymmSCMatrix&) const;
327  void scale(double) const;
328  void assign(double) const;
329  void assign(const double*) const;
330  void assign(const double**) const;
331  void convert(double*) const;
332  void convert(double**) const;
333  void accumulate(const RefSymmSCMatrix&) const;
334  void element_op(const Ref<SCElementOp>&) const;
335  void element_op(const Ref<SCElementOp2>&,
336  const RefSymmSCMatrix&) const;
337  void element_op(const Ref<SCElementOp3>&,
338  const RefSymmSCMatrix&,
339  const RefSymmSCMatrix&) const;
340  double trace() const;
341  int n() const;
342  RefSCDimension dim() const;
343  Ref<SCMatrixKit> kit() const;
344  void print(std::ostream&) const;
345  void print(const char*title=0,
346  std::ostream&out=ExEnv::out0(), int =10) const;
347  void save(StateOut&);
349  void restore(StateIn&);
350 
352  double solve_lin(const RefSCVector&) const;
354  double determ() const;
356  RefDiagSCMatrix eigvals() const;
358  RefSCMatrix eigvecs() const;
362  void diagonalize(const RefDiagSCMatrix& eigvals,
363  const RefSCMatrix& eigvecs) const;
365  SymmSCMatrixdouble operator()(int i,int j) const;
369  int nblock() const;
373  RefSymmSCMatrix block(int i) const;
374 };
376 RefSymmSCMatrix operator*(double,const RefSymmSCMatrix&);
377 
380 class RefDiagSCMatrix: public Ref<DiagSCMatrix> {
381  // standard overrides
382  public:
385  RefDiagSCMatrix();
387  RefDiagSCMatrix(const RefDiagSCMatrix& m);
389  RefDiagSCMatrix(DiagSCMatrix *m);
390  ~RefDiagSCMatrix();
392  RefDiagSCMatrix& operator=(DiagSCMatrix* m);
394  RefDiagSCMatrix& operator=(const RefDiagSCMatrix & m);
395 
396  // matrix specific members
397  public:
400  RefDiagSCMatrix(const RefSCDimension&,const Ref<SCMatrixKit>&);
402  RefSCMatrix operator*(const RefSCMatrix&) const;
403  RefDiagSCMatrix operator*(double) const;
405  RefDiagSCMatrix operator+(const RefDiagSCMatrix&) const;
406  RefDiagSCMatrix operator-(const RefDiagSCMatrix&) const;
408  RefDiagSCMatrix i() const;
410  RefDiagSCMatrix gi() const;
413  RefDiagSCMatrix clone() const;
414  RefDiagSCMatrix copy() const;
415  void set_element(int,double) const;
416  void accumulate_element(int,double) const;
417  double get_element(int) const;
418  void randomize() const;
419  void assign(const RefDiagSCMatrix&) const;
420  void scale(double) const;
421  void assign(double) const;
422  void assign(const double*) const;
423  void convert(double*) const;
424  void accumulate(const RefDiagSCMatrix&) const;
425  void element_op(const Ref<SCElementOp>&) const;
426  void element_op(const Ref<SCElementOp2>&,
427  const RefDiagSCMatrix&) const;
428  void element_op(const Ref<SCElementOp3>&,
429  const RefDiagSCMatrix&,
430  const RefDiagSCMatrix&) const;
431  int n() const;
432  RefSCDimension dim() const;
433  Ref<SCMatrixKit> kit() const;
434  double trace() const;
435  void print(std::ostream&) const;
436  void print(const char*title=0,
437  std::ostream&out=ExEnv::out0(), int =10) const;
438  void save(StateOut&);
440  void restore(StateIn&);
442  double determ() const;
444  DiagSCMatrixdouble operator()(int i) const;
448  int nblock() const;
452  RefDiagSCMatrix block(int i) const;
453 };
455 RefDiagSCMatrix operator*(double,const RefDiagSCMatrix&);
456 
457 class SCVectordouble {
458  friend class RefSCVector;
459  private:
460  RefSCVector vector;
461  int i;
462 
463  SCVectordouble(SCVector*,int);
464  public:
465  SCVectordouble(const SCVectordouble&);
466  ~SCVectordouble();
467  double operator=(double a);
468  double operator=(const SCVectordouble&);
469  operator double();
470  double val() const;
471 };
472 
473 class SCMatrixdouble {
474  friend class RefSCMatrix;
475  private:
476  RefSCMatrix matrix;
477  int i;
478  int j;
479 
480  SCMatrixdouble(SCMatrix*,int,int);
481  public:
482  SCMatrixdouble(const SCMatrixdouble&);
483  ~SCMatrixdouble();
484  double operator=(double a);
485  double operator=(const SCMatrixdouble&);
486  operator double();
487  double val() const;
488 };
489 
490 class SymmSCMatrixdouble {
491  friend class RefSymmSCMatrix;
492  private:
493  RefSymmSCMatrix matrix;
494  int i;
495  int j;
496 
497  SymmSCMatrixdouble(SymmSCMatrix*,int,int);
498  public:
499  SymmSCMatrixdouble(const SCMatrixdouble&);
500  ~SymmSCMatrixdouble();
501  double operator=(double a);
502  double operator=(const SymmSCMatrixdouble&);
503  operator double();
504  double val() const;
505 };
506 
507 class DiagSCMatrixdouble {
508  friend class RefDiagSCMatrix;
509  private:
510  RefDiagSCMatrix matrix;
511  int i;
512  int j;
513 
514  DiagSCMatrixdouble(DiagSCMatrix*,int,int);
515  public:
516  DiagSCMatrixdouble(const SCMatrixdouble&);
517  ~DiagSCMatrixdouble();
518  double operator=(double a);
519  double operator=(const DiagSCMatrixdouble&);
520  operator double();
521  double val() const;
522 };
523 
524 }
525 
526 #ifdef INLINE_FUNCTIONS
527 #include <math/scmat/matrix_i.h>
528 #endif
529 
530 #endif
531 
532 // Local Variables:
533 // mode: c++
534 // c-file-style: "CLJ"
535 // End:
sc::RefSCMatrix::i
RefSCMatrix i() const
Return the inverse of this.
sc::RefSymmSCMatrix::determ
double determ() const
Returns the determinant of the referenced matrix.
sc::RefSCMatrix::operator+
RefSCMatrix operator+(const RefSCMatrix &) const
Matrix addition.
sc::RefSymmSCMatrix::diagonalize
void diagonalize(const RefDiagSCMatrix &eigvals, const RefSCMatrix &eigvecs) const
Sets eigvals to the eigenvalues and eigvecs to the eigenvalues and eigenvectors of the referenced mat...
sc::RefDiagSCMatrix::i
RefDiagSCMatrix i() const
Return the inverse of this.
sc::SCVector
The SCVector class is the abstract base class for double valued vectors.
Definition: abstract.h:97
sc::RefSymmSCMatrix::restore
void restore(StateIn &)
Restores the matrix from StateIn object. The matrix must have been initialized already.
sc::SymmSCMatrixdouble
Definition: matrix.h:490
sc::RefSymmSCMatrix
The RefSymmSCMatrix class is a smart pointer to an SCSymmSCMatrix specialization.
Definition: matrix.h:261
sc::RefSymmSCMatrix::i
RefSymmSCMatrix i() const
Return the inverse of this.
sc::RefSCMatrix::nblock
int nblock() const
If this matrix is blocked return the number of blocks.
sc::RefSCMatrix
The RefSCMatrix class is a smart pointer to an SCMatrix specialization.
Definition: matrix.h:135
sc::RefSymmSCMatrix::operator+
RefSymmSCMatrix operator+(const RefSymmSCMatrix &) const
Matrix addition and subtraction.
sc::Ref
A template class that maintains references counts.
Definition: ref.h:332
sc::RefDiagSCMatrix::clone
RefDiagSCMatrix clone() const
These call the SCMatrix members of the same name after checking for references to 0.
sc::RefSCMatrix::clone
RefSCMatrix clone() const
These call the SCMatrix members of the same name after checking for references to 0.
sc::DiagSCMatrixdouble
Definition: matrix.h:507
sc::RefSymmSCMatrix::nblock
int nblock() const
If this matrix is blocked return the number of blocks.
sc::RefDiagSCMatrix::block
RefDiagSCMatrix block(int i) const
If this matrix is blocked return block i.
sc::Ref< SCVector >::operator*
SCVector & operator*() const
Returns a C++ reference to the reference counted object.
Definition: ref.h:390
sc::RefSymmSCMatrix::eigvecs
RefSCMatrix eigvecs() const
Returns the eigenvectors of the reference matrix.
sc::RefDiagSCMatrix
The RefDiagSCMatrix class is a smart pointer to an DiagSCMatrix specialization.
Definition: matrix.h:380
sc::RefSymmSCMatrix::clone
RefSymmSCMatrix clone() const
These call the SCMatrix members of the same name after checking for references to 0.
sc::DiagSCMatrix
The SymmSCMatrix class is the abstract base class for diagonal double valued matrices.
Definition: abstract.h:503
sc::RefSCMatrix::solve_lin
double solve_lin(const RefSCVector &v) const
Solves this x = v.
sc::RefSCVector::RefSCVector
RefSCVector()
Initializes the vector pointer to 0.
sc::RefSymmSCMatrix::solve_lin
double solve_lin(const RefSCVector &) const
Solves this x = v.
sc::RefSCVector::operator=
RefSCVector & operator=(SCVector *v)
Make this refer to v.
sc::StateIn
Restores objects that derive from SavableState.
Definition: statein.h:70
sc::RefSCDimension
The RefSCDimension class is a smart pointer to an SCDimension specialization.
Definition: dim.h:156
sc::RefSCMatrix::operator()
SCMatrixdouble operator()(int i, int j) const
Assign and examine matrix elements.
sc::RefSymmSCMatrix::eigvals
RefDiagSCMatrix eigvals() const
Returns the eigenvalues of the reference matrix.
sc::RefSymmSCMatrix::block
RefSymmSCMatrix block(int i) const
If this matrix is blocked return block i.
sc::SCVectordouble
Definition: matrix.h:457
sc::RefDiagSCMatrix::restore
void restore(StateIn &)
Restores the matrix from StateIn object. The matrix must have been initialized already.
sc::RefSCMatrix::operator-
RefSCMatrix operator-(const RefSCMatrix &) const
Matrix subtraction.
sc::RefSymmSCMatrix::operator=
RefSymmSCMatrix & operator=(SymmSCMatrix *m)
Make this refer to m.
sc::RefSCMatrix::restore
void restore(StateIn &)
Restores the matrix from StateIn object. The matrix must have been initialized already.
sc::RefDiagSCMatrix::RefDiagSCMatrix
RefDiagSCMatrix()
Initializes the matrix pointer to 0.
sc::RefDiagSCMatrix::operator+
RefDiagSCMatrix operator+(const RefDiagSCMatrix &) const
Matrix addition and subtraction.
sc::RefSCMatrix::RefSCMatrix
RefSCMatrix()
Initializes the matrix pointer to 0.
sc::RefSCMatrix::svd
void svd(const RefSCMatrix &U, const RefDiagSCMatrix &sigma, const RefSCMatrix &V)
Compute the singular value decomposition, this = U sigma V.t().
sc::RefDiagSCMatrix::nblock
int nblock() const
If this matrix is blocked return the number of blocks.
sc::RefSCVector::operator()
SCVectordouble operator()(int) const
Return an l-value that can be used to assign or retrieve an element.
sc::RefDiagSCMatrix::gi
RefDiagSCMatrix gi() const
Return the generalized inverse of this.
sc::RefSymmSCMatrix::accumulate_transform
void accumulate_transform(const RefSCMatrix &a, const RefSymmSCMatrix &b, SCMatrix::Transform=SCMatrix::NormalTransform) const
Add a * b * a.t() to this.
sc::RefSCVector
The RefSCVector class is a smart pointer to an SCVector specialization.
Definition: matrix.h:55
sc::RefSCVector::symmetric_outer_product
RefSymmSCMatrix symmetric_outer_product() const
The outer product of this with itself is a symmetric matrix.
sc::StateOut
Serializes objects that derive from SavableState.
Definition: stateout.h:61
sc::RefSCMatrix::operator=
RefSCMatrix & operator=(SCMatrix *m)
Make this refer to m.
sc::RefSCMatrix::t
RefSCMatrix t() const
Return the transpose of this.
sc::SCMatrixdouble
Definition: matrix.h:473
sc::SymmSCMatrix
The SymmSCMatrix class is the abstract base class for symmetric double valued matrices.
Definition: abstract.h:364
sc::RefDiagSCMatrix::operator()
DiagSCMatrixdouble operator()(int i) const
Assign and examine matrix elements.
sc::RefSCVector::operator[]
SCVectordouble operator[](int) const
Return an l-value that can be used to assign or retrieve an element.
sc::ExEnv::out0
static std::ostream & out0()
Return an ostream that writes from node 0.
sc::RefSCMatrix::gi
RefSCMatrix gi() const
Return the generalized inverse of this.
sc::RefSCMatrix::determ
double determ() const
Returns the determinant of the referenced matrix.
sc::SCMatrix
The SCMatrix class is the abstract base class for general double valued n by m matrices.
Definition: abstract.h:195
sc::RefSymmSCMatrix::operator()
SymmSCMatrixdouble operator()(int i, int j) const
Assign and examine matrix elements.
sc::RefSCVector::outer_product
RefSCMatrix outer_product(const RefSCVector &v) const
Return the outer product between this and v.
sc::RefDiagSCMatrix::operator=
RefDiagSCMatrix & operator=(DiagSCMatrix *m)
Make this refer to m.
sc::RefSCVector::operator+
RefSCVector operator+(const RefSCVector &a) const
Add two vectors.
sc::RefDiagSCMatrix::determ
double determ() const
Returns the determinant of the referenced matrix.
sc::RefSCMatrix::block
RefSCMatrix block(int i) const
If this matrix is blocked return block i.
sc::RefSCVector::restore
void restore(StateIn &)
Restores the matrix from StateIn object. The vector must have been initialized already.
sc::RefSymmSCMatrix::RefSymmSCMatrix
RefSymmSCMatrix()
Initializes the matrix pointer to 0.
sc::RefSymmSCMatrix::gi
RefSymmSCMatrix gi() const
Return the generalized inverse of this.
sc::RefSCVector::operator-
RefSCVector operator-(const RefSCVector &a) const
Subtract two vectors.
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