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SmallMatrix< numberOfRows, numberOfColumns > Class Template Reference

Data type for small dense matrix. More...

#include <SmallMatrix.h>

Public Member Functions

 SmallMatrix ()
 Constructs a matrix of size n-rows by m-columns. More...
 
 SmallMatrix (const SmallVector< numberOfRows > &other)
 
 SmallMatrix (const Mdouble &c)
 Constructs a matrix of size n-rows by m-columns and initialises all entry to a constant. More...
 
 SmallMatrix (const std::initializer_list< SmallVector< numberOfRows >> &entries)
 
 SmallMatrix (const SmallMatrix &other)
 Construct and copy Matrix from another Matrix i.e. B(A) where B and A are both matrices. More...
 
 SmallMatrix (std::array< SmallVector< numberOfRows >, numberOfColumns > entries)
 Glues one or more vectors with the same number of rows together. More...
 
 SmallMatrix (SmallMatrix &&other)
 Move Matrix from another Matrix. More...
 
Mdouble & operator() (unsigned int n, unsigned int m)
 defines the operator(n,m) to access the element on row n and column m More...
 
const Mdouble & operator() (unsigned int n, unsigned int m) const
 defines the operator(n,m) to access the element on row n and column m More...
 
Mdouble & operator[] (const unsigned int n)
 Access the n linear element in the matrix. More...
 
const Mdouble & operator[] (const unsigned int n) const
 
SmallVector< numberOfRows > operator* (SmallVector< numberOfColumns > &right)
 Defines Matrix A times vector B and return vector C i.e. C_,j= A_ij B_,j. More...
 
SmallVector< numberOfRows > operator* (SmallVector< numberOfColumns > &right) const
 
SmallMatrix operator* (const Mdouble &right) const
 Does matrix A_ij=scalar*B_ij. More...
 
template<unsigned int K>
SmallMatrix< numberOfRows, K > operator* (const SmallMatrix< numberOfColumns, K > &other)
 Does matrix A_ij = B_ik * C_kj. More...
 
template<unsigned int K>
SmallMatrix< numberOfRows, K > operator* (const SmallMatrix< numberOfColumns, K > &other) const
 
SmallMatrix & operator+= (const SmallMatrix &other)
 
SmallMatrix & operator-= (const SmallMatrix &other)
 
SmallMatrix operator+ (const SmallMatrix &other) const
 
SmallMatrix operator- (const SmallMatrix &other) const
 
SmallMatrix operator- () const
 
SmallMatrix & operator*= (const Mdouble &scalar)
 Does matrix A_ij=scalar*A_ij. More...
 
SmallMatrix & operator*= (const SmallMatrix< numberOfColumns, numberOfColumns > &other)
 Does matrix A_ij = A_ik * B_kj note that other must be square because this is a fixed-size matrix. More...
 
SmallMatrix & operator/= (const Mdouble &scalar)
 Does matrix A_ij=scalar*A_ij. More...
 
SmallMatrix operator/ (const Mdouble &scalar) const
 this does element by divided by a scalar More...
 
SmallMatrix & operator= (const SmallMatrix &right)
 Assigns one matrix to another. More...
 
SmallMatrix & operator= (SmallMatrix &&right)
 Assigns one matrix to another. More...
 
SmallVector< numberOfRows > computeWedgeStuffVector () const
 computeWedgeStuffVector. More...
 
void axpy (Mdouble a, const SmallMatrix &x)
 Applies the matrix y=ax + y, where x is another matrix and a is a scalar. More...
 
unsigned int size () const
 Get total number of Matrix entries. More...
 
unsigned int getNumberOfRows () const
 Get the number of rows. More...
 
unsigned int getNRows () const
 
unsigned int getNumberOfColumns () const
 Get the number of columns. More...
 
unsigned int getNCols () const
 
SmallVector< numberOfRows > getColumn (unsigned int j) const
 get the j^th column More...
 
SmallVector< numberOfColumns > getRow (unsigned int i) const
 get the i^th row More...
 
SmallMatrix LUfactorisation () const
 Return the LUfactorisation of the matrix. More...
 
Mdouble determinant () const
 
SmallMatrix inverse () const
 return the inverse in the vector result. The size of result matches the matrix. More...
 
SmallMatrix< numberOfColumns,
numberOfRows > 		transpose () const
 
template<unsigned int numberOfRightHandSideColumns>
void solve (SmallMatrix< numberOfRows, numberOfRightHandSideColumns > &B) const
 solves Ax=B where A is the current matrix and B is passed in. The result is returned in B. More...
 
void solve (SmallVector< numberOfRows > &b) const
 solves Ax=b where A is the current matrix and NumericalVector b is the input parameter. More...
 
Mdouble * data ()
 
const Mdouble * data () const
 

Private Attributes

std::array< Mdouble,
numberOfRows *numberOfColumns > 		data_
 The actually data of the matrix class. More...
 

Detailed Description

template<unsigned int numberOfRows, unsigned int numberOfColumns>
class SmallMatrix< numberOfRows, numberOfColumns >

Data type for small dense matrix.

Stores small dense matrix efficiently. It only store Mdoubles as this is the main type linear algebra is done on in hpGEM It stores the matrix in fortran style (column-major) to give quicker access to extern BLAS libraries. For example, the order they are stored in a 2x2 matrix is 0 2 1 3

Definition at line 67 of file SmallMatrix.h.

Constructor & Destructor Documentation

template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( )
inline

Constructs a matrix of size n-rows by m-columns.

Definition at line 72 of file SmallMatrix.h.

73  : data_()
74  {
75  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( const SmallVector< numberOfRows > &  other)
inline

Definition at line 77 of file SmallMatrix.h.

References SmallVector< numberOfRows >::data(), SmallMatrix< numberOfRows, numberOfColumns >::data_, and logger.

78  : data_()
79  {
80  logger.assert(numberOfColumns == 1, "Trying to construct a matrix with more than 1 columns from a vector");
81  std::copy(other.data(), other.data() + numberOfRows, data_.begin());
82  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
SmallVector::data
const Mdouble * data() const
Definition: SmallVector.h:238
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( const Mdouble &  c)
inline

Constructs a matrix of size n-rows by m-columns and initialises all entry to a constant.

Definition at line 85 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

86  : data_()
87  {
88  data_.fill(c);
89  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( const std::initializer_list< SmallVector< numberOfRows >> &  entries)
inline

Definition at line 91 of file SmallMatrix.h.

References constants::i, and logger.

92  : data_()
93  {
94  logger.assert(entries.size() == numberOfColumns, "expected a matrix with % "
95  "columns, but got a matrix with % columns", numberOfColumns,
96  entries.size());
97  unsigned int column = 0;
98  for (const SmallVector<numberOfRows>& entry : entries)
99  {
100  for (unsigned int i = 0; i < numberOfRows; ++i)
101  {
102  (*this)(i, column) = entry[i];
103  }
104  ++column;
105  }
106  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( const SmallMatrix< numberOfRows, numberOfColumns > &  other)
inline

Construct and copy Matrix from another Matrix i.e. B(A) where B and A are both matrices.

Definition at line 109 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

110  : data_()
111  {
112  std::copy(other.data_.begin(), other.data_.end(), data_.begin());
113  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( std::array< SmallVector< numberOfRows >, numberOfColumns >  entries)
inline

Glues one or more vectors with the same number of rows together.

Definition at line 116 of file SmallMatrix.h.

References constants::i.

117  : data_()
118  {
119  for (unsigned int i = 0; i < numberOfRows; ++i)
120  {
121  for (unsigned int j = 0; j < numberOfColumns; ++j)
122  {
123  (*this)(i, j) = entries[j][i];
124  }
125  }
126  }
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix ( SmallMatrix< numberOfRows, numberOfColumns > &&  other)
inline

Move Matrix from another Matrix.

Definition at line 129 of file SmallMatrix.h.

130  : data_(std::move(other.data_))
131  {
132  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363

Member Function Documentation

template<unsigned int numberOfRows, unsigned int numberOfColumns>
void SmallMatrix< numberOfRows, numberOfColumns >::axpy ( Mdouble  a,
const SmallMatrix< numberOfRows, numberOfColumns > &  x 
)
inline

Applies the matrix y=ax + y, where x is another matrix and a is a scalar.

Definition at line 266 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_, and constants::i.

267  {
268  for (unsigned int i = 0; i < numberOfRows * numberOfColumns; ++i)
269  {
270  data_[i] += a * x[i];
271  }
272  }
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector< numberOfRows > SmallMatrix< numberOfRows, numberOfColumns >::computeWedgeStuffVector ( ) const

computeWedgeStuffVector.

Definition at line 201 of file SmallMatrix_impl.h.

References ERROR, and logger.

202 {
203  //copied from MiddleSizeMatrix to prevent constructing a temporary MiddleSizeMatrix
204  logger.assert(numberOfColumns == numberOfRows - 1,
205  "Matrix has wrong dimensions to construct the wedge stuff vector");
206  SmallVector<numberOfRows> result;
207 
208  switch (numberOfRows)
209  {
210  case 2:
211  result[0] = -(*this)(1, 0);
212  result[1] = +(*this)(0, 0);
213  break;
214  case 3:
215  result[0] = (*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1);
216  result[1] = (*this)(0, 1) * (*this)(2, 0) - (*this)(0, 0) * (*this)(2, 1); // includes minus sign already!
217  result[2] = (*this)(0, 0) * (*this)(1, 1) - (*this)(1, 0) * (*this)(0, 1);
218  break;
219  case 4:
220  result[0] = (*this)(1, 0) * (-(*this)(2, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(2, 2)) +
221  (*this)(2, 0) * ((*this)(1, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(1, 2)) +
222  (*this)(3, 0) * (-(*this)(1, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 2));
223 
224  result[1] = (*this)(0, 0) * ((*this)(2, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(2, 2)) +
225  (*this)(2, 0) * (-(*this)(0, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(0, 2)) +
226  (*this)(3, 0) * ((*this)(0, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 2));
227  result[2] = (*this)(0, 0) * (-(*this)(1, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(1, 2)) +
228  (*this)(1, 0) * ((*this)(0, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(0, 2)) +
229  (*this)(3, 0) * (-(*this)(0, 1) * (*this)(1, 2) + (*this)(1, 1) * (*this)(0, 2));
230  result[3] = (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(1, 2)) +
231  (*this)(1, 0) * (-(*this)(0, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(0, 2)) +
232  (*this)(2, 0) * ((*this)(0, 1) * (*this)(1, 2) - (*this)(1, 1) * (*this)(0, 2));
233  break;
234  default:
235  logger(ERROR, "Wedge product not implemented for this dimension");
236  } //end switch
237 
238  return (result);
239 }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
template<unsigned int numberOfRows, unsigned int numberOfColumns>
Mdouble* SmallMatrix< numberOfRows, numberOfColumns >::data ( )
inline

Definition at line 351 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

Referenced by SmallMatrix< numberOfRows, numberOfColumns >::getColumn(), SmallMatrix< numberOfRows, numberOfColumns >::inverse(), SmallMatrix< numberOfRows, numberOfColumns >::LUfactorisation(), SmallMatrix< numberOfRows, numberOfColumns >::operator*(), operator*(), and SmallMatrix< numberOfRows, numberOfColumns >::solve().

352  {
353  return data_.data();
354  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
const Mdouble* SmallMatrix< numberOfRows, numberOfColumns >::data ( ) const
inline

Definition at line 356 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

357  {
358  return data_.data();
359  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
Mdouble SmallMatrix< numberOfRows, numberOfColumns >::determinant ( ) const

Definition at line 261 of file SmallMatrix_impl.h.

References ERROR, and logger.

262 {
263  logger.assert(numberOfRows == numberOfColumns, "Matrix should be square to have a determinant!");
264 
265  switch (numberOfRows)
266  {
267  case 0:
268  return 1;
269  case 1:
270  return (*this)(0, 0);
271  case 2:
272  return (*this)(0, 0) * (*this)(1, 1) - (*this)(0, 1) * (*this)(1, 0);
273 
274  case 3:
275  return (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(1, 2) * (*this)(2, 1)) -
276  (*this)(0, 1) * ((*this)(1, 0) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 2)) +
277  (*this)(0, 2) * ((*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1));
278 
279  case 4:
280  return ((*this)(3, 0) * (*this)(2, 1) * (*this)(0, 3) - (*this)(2, 0) * (*this)(3, 1) * (*this)(0, 3)) *
281  (*this)(1, 2) +
282  (-(*this)(3, 0) * (*this)(0, 3) * (*this)(2, 2) + (*this)(2, 0) * (*this)(0, 3) * (*this)(3, 2)) *
283  (*this)(1, 1) +
284  ((*this)(3, 1) * (*this)(0, 3) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 3) * (*this)(3, 2)) *
285  (*this)(1, 0) +
286  (-(*this)(3, 0) * (*this)(2, 1) * (*this)(1, 3) + (*this)(2, 0) * (*this)(3, 1) * (*this)(1, 3) +
287  (-(*this)(2, 0) * (*this)(3, 3) + (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 1) +
288  ((*this)(2, 1) * (*this)(3, 3) - (*this)(3, 1) * (*this)(2, 3)) * (*this)(1, 0)) * (*this)(0, 2) +
289  ((*this)(3, 0) * (*this)(1, 3) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 3) * (*this)(3, 2) +
290  ((*this)(2, 0) * (*this)(3, 3) - (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 2) +
291  (-(*this)(2, 2) * (*this)(3, 3) + (*this)(2, 3) * (*this)(3, 2)) * (*this)(1, 0)) * (*this)(0, 1) +
292  (-(*this)(3, 1) * (*this)(1, 3) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 3) * (*this)(3, 2) +
293  ((*this)(3, 1) * (*this)(2, 3) - (*this)(2, 1) * (*this)(3, 3)) * (*this)(1, 2) +
294  (*this)(1, 1) * ((*this)(2, 2) * (*this)(3, 3) - (*this)(2, 3) * (*this)(3, 2))) * (*this)(0, 0);
295  // ... says Maple; this can possibly be done more efficiently,
296  // maybe even with LU (with pivoting, though...)
297  default:
298  logger(ERROR, "Computing the Determinant for size % is not implemented", numberOfRows);
299  break;
300  }
301  return 0;
302 }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfRows> SmallMatrix< numberOfRows, numberOfColumns >::getColumn ( unsigned int  j) const
inline

get the j^th column

Definition at line 304 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), and logger.

305  {
306  logger.assert(j < numberOfColumns, "Asked for column %, but there are only % columns", j, numberOfColumns);
307  return SmallVector<numberOfRows>(data() + j * numberOfRows);
308  }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
template<unsigned int numberOfRows, unsigned int numberOfColumns>
unsigned int SmallMatrix< numberOfRows, numberOfColumns >::getNCols ( ) const
inline

Definition at line 298 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::getNumberOfColumns().

299  {
300  return getNumberOfColumns();
301  }
SmallMatrix::getNumberOfColumns
unsigned int getNumberOfColumns() const
Get the number of columns.
Definition: SmallMatrix.h:293
template<unsigned int numberOfRows, unsigned int numberOfColumns>
unsigned int SmallMatrix< numberOfRows, numberOfColumns >::getNRows ( ) const
inline
Deprecated:
Does not conform naming convention, please use getNumberOfRows instead.

Definition at line 287 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::getNumberOfRows().

288  {
289  return getNumberOfRows();
290  }
SmallMatrix::getNumberOfRows
unsigned int getNumberOfRows() const
Get the number of rows.
Definition: SmallMatrix.h:281
template<unsigned int numberOfRows, unsigned int numberOfColumns>
unsigned int SmallMatrix< numberOfRows, numberOfColumns >::getNumberOfColumns ( ) const
inline

Get the number of columns.

Definition at line 293 of file SmallMatrix.h.

Referenced by SmallMatrix< numberOfRows, numberOfColumns >::getNCols().

294  {
295  return numberOfColumns;
296  }
template<unsigned int numberOfRows, unsigned int numberOfColumns>
unsigned int SmallMatrix< numberOfRows, numberOfColumns >::getNumberOfRows ( ) const
inline

Get the number of rows.

Definition at line 281 of file SmallMatrix.h.

Referenced by SmallMatrix< numberOfRows, numberOfColumns >::getNRows().

282  {
283  return numberOfRows;
284  }
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfColumns> SmallMatrix< numberOfRows, numberOfColumns >::getRow ( unsigned int  i) const
inline

get the i^th row

Definition at line 311 of file SmallMatrix.h.

References constants::i, and logger.

312  {
313  logger.assert(i < numberOfRows, "Asked for row %, but there are only % rows", i, numberOfRows);
314  SmallVector<numberOfColumns> result;
315  for (unsigned int j = 0; j < numberOfColumns; ++j)
316  {
317  result[j] = (*this)(i, j);
318  }
319  return result;
320  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns > SmallMatrix< numberOfRows, numberOfColumns >::inverse ( ) const

return the inverse in the vector result. The size of result matches the matrix.

Definition at line 305 of file SmallMatrix_impl.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), dgetrf_(), dgetri_(), and logger.

306 {
307  logger.assert(numberOfRows == numberOfColumns, "Cannot invert a non-square matrix");
308  SmallMatrix<numberOfRows, numberOfColumns> result = (*this);
309 
310  int nr = numberOfRows;
311  int nc = numberOfColumns;
312 
313  int nPivot = numberOfRows;
314  int iPivot[nPivot];
315 
316  int info = 0;
317 
318  dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
319 
320  int lwork = numberOfRows * numberOfColumns;
321  SmallMatrix work;
322  dgetri_(&nc, result.data(), &nc, iPivot, work.data(), &lwork, &info);
323 
324  return result;
325 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
dgetri_
void dgetri_(int *N, double *A, int *lda, int *IPIV, double *WORK, int *lwork, int *INFO)
This is the inverse calulation also from LAPACK. Calculates inverse if you pass it the LU factorisati...
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
dgetrf_
void dgetrf_(int *M, int *N, double *A, int *lda, int *IPIV, int *INFO)
This is LU factorisation of the matrix A. This has been taken from LAPACK.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns > SmallMatrix< numberOfRows, numberOfColumns >::LUfactorisation ( ) const

Return the LUfactorisation of the matrix.

Definition at line 242 of file SmallMatrix_impl.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), and dgetrf_().

243 {
244  int nr = numberOfRows;
245  int nc = numberOfColumns;
246  int nPivot = std::min(numberOfRows, numberOfColumns);
247  int iPivot[nPivot];
248 
249  SmallMatrix result(*this);
250 
251  int info;
252 
253  dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
254 
255  return result;
256 }
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
dgetrf_
void dgetrf_(int *M, int *N, double *A, int *lda, int *IPIV, int *INFO)
This is LU factorisation of the matrix A. This has been taken from LAPACK.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
Mdouble& SmallMatrix< numberOfRows, numberOfColumns >::operator() ( unsigned int  n,
unsigned int  m 
)
inline

defines the operator(n,m) to access the element on row n and column m

Definition at line 135 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_, and logger.

136  {
137  logger.assert(n < numberOfRows, "Requested row number % for a matrix with only % rows", n, numberOfRows);
138  logger.assert(m < numberOfColumns, "Requested column number % for a matrix with only % columns", m,
139  numberOfColumns);
140  return data_[n + m * numberOfRows];
141  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
const Mdouble& SmallMatrix< numberOfRows, numberOfColumns >::operator() ( unsigned int  n,
unsigned int  m 
) const
inline

defines the operator(n,m) to access the element on row n and column m

Definition at line 144 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_, and logger.

145  {
146  logger.assert(n < numberOfRows, "Requested row number % for a matrix with only % rows", n, numberOfRows);
147  logger.assert(m < numberOfColumns, "Requested column number % for a matrix with only % columns", m,
148  numberOfColumns);
149  return data_[n + m * numberOfRows];
150  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector< numberOfRows > SmallMatrix< numberOfRows, numberOfColumns >::operator* ( SmallVector< numberOfColumns > &  right)

Defines Matrix A times vector B and return vector C i.e. C_,j= A_ij B_,j.

Definition at line 81 of file SmallMatrix_impl.h.

References SmallVector< numberOfRows >::data(), DEBUG, dgemv_(), logger, SmallVector< numberOfRows >::size(), and WARN.

82 {
83  if (numberOfRows == 0)
84  {
85  logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
86  return SmallVector<numberOfRows>();
87  }
88  if (numberOfColumns == 0)
89  {
90  logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
91  return SmallVector<numberOfRows>();
92  }
93  int nr = numberOfRows;
94  int nc = numberOfColumns;
95 
96  int i_one = 1;
97  double d_one = 1.0;
98  double d_zero = 0.0;
99 
100  SmallVector<numberOfRows> result;
101 
102  logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
103 
104  dgemv_("N", &nr, &nc, &d_one, this->data(), &nr, right.data(), &i_one, &d_zero, result.data(), &i_one);
105  return result;
106 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
SmallVector::data
const Mdouble * data() const
Definition: SmallVector.h:238
SmallVector::size
unsigned int size() const
Definition: SmallVector.h:233
dgemv_
void dgemv_(const char *trans, int *m, int *n, double *alpha, double *A, int *LDA, double *x, int *incx, double *beta, double *y, int *incy)
This does matrix times vector and is from blas level 2.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector< numberOfRows > SmallMatrix< numberOfRows, numberOfColumns >::operator* ( SmallVector< numberOfColumns > &  right) const

Definition at line 110 of file SmallMatrix_impl.h.

References SmallVector< numberOfRows >::data(), DEBUG, dgemv_(), logger, SmallVector< numberOfRows >::size(), and WARN.

111 {
112  if (numberOfRows == 0)
113  {
114  logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
115  return SmallVector<numberOfRows>();
116  }
117  if (numberOfColumns == 0)
118  {
119  logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
120  return SmallVector<numberOfRows>();
121  }
122  int nr = numberOfRows;
123  int nc = numberOfColumns;
124 
125  int i_one = 1;
126  double d_one = 1.0;
127  double d_zero = 0.0;
128 
129  SmallVector<numberOfRows> result;
130 
131  logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
132 
133  dgemv_("N", &nr, &nc, &d_one, (const_cast<double*>(this->data())), &nr, right.data(), &i_one, &d_zero,
134  result.data(), &i_one);
135  return result;
136 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallVector
Implementation of a 3D vector (by Vitaliy).
Definition: SmallVector.h:61
SmallVector::data
const Mdouble * data() const
Definition: SmallVector.h:238
SmallVector::size
unsigned int size() const
Definition: SmallVector.h:233
dgemv_
void dgemv_(const char *trans, int *m, int *n, double *alpha, double *A, int *LDA, double *x, int *incx, double *beta, double *y, int *incy)
This does matrix times vector and is from blas level 2.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator* ( const Mdouble &  right) const
inline

Does matrix A_ij=scalar*B_ij.

Definition at line 173 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

174  {
175  SmallMatrix result;
176  std::transform(data_.begin(), data_.end(), result.data_.begin(),
177  std::bind(std::multiplies<Mdouble>(), std::placeholders::_1, right));
178  return result;
179  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int K>
SmallMatrix< numberOfRows, K > SmallMatrix< numberOfRows, numberOfColumns >::operator* ( const SmallMatrix< numberOfColumns, K > &  other)

Does matrix A_ij = B_ik * C_kj.

Definition at line 141 of file SmallMatrix_impl.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), dgemm_(), constants::i, logger, and WARN.

142 {
143  int i = numberOfRows;
144  int j = numberOfColumns;
145  int k = K;
146 
147  if (numberOfColumns == 0)
148  {
149  logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
150  return SmallMatrix<numberOfRows, K>();
151  }
152  //The result of the matrix is left.numberOfRows, right.numberOfColumns()
153  SmallMatrix<numberOfRows, K> C;
154 
155  double d_one = 1.0;
156  double d_zero = 0.0;
157 
158  //Let the actual multiplication be done by Fortran
159  dgemm_("N", "N", &i, &k, &j, &d_one, this->data(), &i, const_cast<double*>(other.data()), &j, &d_zero, C.data(),
160  &i);
161 
162  return C;
163 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
dgemm_
int dgemm_(const char *transA, const char *transB, int *M, int *N, int *k, double *alpha, double *A, int *LDA, double *B, int *LDB, double *beta, double *C, int *LDC)
This is the gernal matrix multiplication from blas level 3.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int K>
SmallMatrix< numberOfRows, K > SmallMatrix< numberOfRows, numberOfColumns >::operator* ( const SmallMatrix< numberOfColumns, K > &  other) const

Definition at line 168 of file SmallMatrix_impl.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), dgemm_(), constants::i, logger, and WARN.

169 {
170  int i = numberOfRows;
171  int j = numberOfColumns;
172  int k = K;
173 
174  if (numberOfColumns == 0)
175  {
176  logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
177  return SmallMatrix<numberOfRows, K>();
178  }
179  //The result of the matrix is left.Nrows, right.NCols()
180  SmallMatrix<numberOfRows, K> C;
181 
182  double d_one = 1.0;
183  double d_zero = 0.0;
184 
185  //Let the actual multiplication be done by Fortran
186  dgemm_("N", "N", &i, &k, &j, &d_one, const_cast<double*>(this->data()), &i, const_cast<double*>(other.data()), &j,
187  &d_zero, C.data(), &i);
188 
189  return C;
190 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
dgemm_
int dgemm_(const char *transA, const char *transB, int *M, int *N, int *k, double *alpha, double *A, int *LDA, double *B, int *LDB, double *beta, double *C, int *LDC)
This is the gernal matrix multiplication from blas level 3.
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator*= ( const Mdouble &  scalar)
inline

Does matrix A_ij=scalar*A_ij.

Definition at line 220 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

221  {
222  std::transform(data_.begin(), data_.end(), data_.begin(),
223  std::bind(std::multiplies<Mdouble>(), std::placeholders::_1, scalar));
224  return *this;
225  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix< numberOfRows, numberOfColumns > & SmallMatrix< numberOfRows, numberOfColumns >::operator*= ( const SmallMatrix< numberOfColumns, numberOfColumns > &  other)

Does matrix A_ij = A_ik * B_kj note that other must be square because this is a fixed-size matrix.

Definition at line 194 of file SmallMatrix_impl.h.

195 {
196  //blas does not support in-place multiply
197  return (*this) = (*this) * other;
198 }
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator+ ( const SmallMatrix< numberOfRows, numberOfColumns > &  other) const
inline

Definition at line 200 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

201  {
202  SmallMatrix result;
203  std::transform(data_.begin(), data_.end(), other.data_.begin(), result.data_.begin(), std::plus<Mdouble>());
204  return result;
205  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator+= ( const SmallMatrix< numberOfRows, numberOfColumns > &  other)
inline

Definition at line 188 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

189  {
190  std::transform(data_.begin(), data_.end(), other.data_.begin(), data_.begin(), std::plus<Mdouble>());
191  return *this;
192  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator- ( const SmallMatrix< numberOfRows, numberOfColumns > &  other) const
inline

Definition at line 207 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

208  {
209  SmallMatrix result;
210  std::transform(data_.begin(), data_.end(), other.data_.begin(), result.data_.begin(), std::minus<Mdouble>());
211  return result;
212  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator- ( ) const
inline

Definition at line 214 of file SmallMatrix.h.

215  {
216  return *this * -1.;
217  }
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator-= ( const SmallMatrix< numberOfRows, numberOfColumns > &  other)
inline

Definition at line 194 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

195  {
196  std::transform(data_.begin(), data_.end(), other.data_.begin(), data_.begin(), std::minus<Mdouble>());
197  return *this;
198  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator/ ( const Mdouble &  scalar) const
inline

this does element by divided by a scalar

Definition at line 240 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

241  {
242  SmallMatrix result;
243  std::transform(data_.begin(), data_.end(), result.data_.begin(),
244  std::bind(std::divides<Mdouble>(), std::placeholders::_1, scalar));
245  return result;
246  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator/= ( const Mdouble &  scalar)
inline

Does matrix A_ij=scalar*A_ij.

Definition at line 232 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

233  {
234  std::transform(data_.begin(), data_.end(), data_.begin(),
235  std::bind(std::divides<Mdouble>(), std::placeholders::_1, scalar));
236  return *this;
237  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator= ( const SmallMatrix< numberOfRows, numberOfColumns > &  right)
inline

Assigns one matrix to another.

Definition at line 249 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

250  {
251  std::copy(right.data_.begin(), right.data_.end(), data_.begin());
252  return *this;
253  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix& SmallMatrix< numberOfRows, numberOfColumns >::operator= ( SmallMatrix< numberOfRows, numberOfColumns > &&  right)
inline

Assigns one matrix to another.

Definition at line 256 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_.

257  {
258  std::move(right.data_.begin(), right.data_.end(), data_.begin());
259  return *this;
260  }
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
Mdouble& SmallMatrix< numberOfRows, numberOfColumns >::operator[] ( const unsigned int  n)
inline

Access the n linear element in the matrix.

Definition at line 153 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_, and logger.

154  {
155  logger.assert(n < numberOfRows * numberOfColumns, "Requested entry % for a matrix with only % entries", n,
156  numberOfRows * numberOfColumns);
157  return data_[n];
158  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
const Mdouble& SmallMatrix< numberOfRows, numberOfColumns >::operator[] ( const unsigned int  n) const
inline

Definition at line 160 of file SmallMatrix.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data_, and logger.

161  {
162  logger.assert(n < numberOfRows * numberOfColumns, "Requested entry % for a matrix with only % entries", n,
163  numberOfRows * numberOfColumns);
164  return data_[n];
165  }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
SmallMatrix::data_
std::array< Mdouble, numberOfRows *numberOfColumns > data_
The actually data of the matrix class.
Definition: SmallMatrix.h:363
template<unsigned int numberOfRows, unsigned int numberOfColumns>
unsigned int SmallMatrix< numberOfRows, numberOfColumns >::size ( ) const
inline

Get total number of Matrix entries.

Definition at line 275 of file SmallMatrix.h.

276  {
277  return numberOfRows * numberOfColumns;
278  }
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int numberOfRightHandSideColumns>
void SmallMatrix< numberOfRows, numberOfColumns >::solve ( SmallMatrix< numberOfRows, numberOfRightHandSideColumns > &  B) const

solves Ax=B where A is the current matrix and B is passed in. The result is returned in B.

Definition at line 329 of file SmallMatrix_impl.h.

References SmallMatrix< numberOfRows, numberOfColumns >::data(), dgesv_(), and logger.

Referenced by SuperQuadricParticle::computeContactPoint().

330 {
331  logger.assert(numberOfRows == numberOfColumns, "can only solve for square matrixes");
332 
333  int n = numberOfRows;
334  int nrhs = numberOfRightHandSideColumns;
335  int info;
336 
337  int IPIV[numberOfRows];
338  SmallMatrix<numberOfRows, numberOfColumns> matThis = *this;
339  dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, B.data(), &n, &info);
340 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
dgesv_
void dgesv_(int *N, int *NRHS, double *A, int *lda, int *IPIV, double *B, int *LDB, int *INFO)
This is used for solve Ax=B for x. Again this is from LAPACK.
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
void SmallMatrix< numberOfRows, numberOfColumns >::solve ( SmallVector< numberOfRows > &  b) const

solves Ax=b where A is the current matrix and NumericalVector b is the input parameter.

The result is returned in b.

Definition at line 343 of file SmallMatrix_impl.h.

References SmallVector< numberOfRows >::data(), SmallMatrix< numberOfRows, numberOfColumns >::data(), dgesv_(), and logger.

344 {
345  logger.assert(numberOfRows == numberOfColumns, "can only solve for square matrixes");
346 
347  int n = numberOfRows;
348  int nrhs = 1;
349  int info;
350 
351  int IPIV[numberOfRows];
352  SmallMatrix matThis = *this;
353  dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, b.data(), &n, &info);
354 }
SmallMatrix::data
Mdouble * data()
Definition: SmallMatrix.h:351
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
dgesv_
void dgesv_(int *N, int *NRHS, double *A, int *lda, int *IPIV, double *B, int *LDB, int *INFO)
This is used for solve Ax=B for x. Again this is from LAPACK.
SmallVector::data
const Mdouble * data() const
Definition: SmallVector.h:238
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix<numberOfColumns, numberOfRows> SmallMatrix< numberOfRows, numberOfColumns >::transpose ( ) const
inline

Definition at line 330 of file SmallMatrix.h.

References constants::i.

Referenced by SuperQuadricParticle::computeHessianLabFixed(), SuperQuadricParticle::getCurvature(), and Quaternion::rotateTensor().

331  {
332  SmallMatrix<numberOfColumns, numberOfRows> result;
333  for (unsigned int i = 0; i < numberOfRows; ++i)
334  {
335  for (unsigned int j = 0; j < numberOfColumns; ++j)
336  {
337  result(j, i) = (*this)(i, j);
338  }
339  }
340  return result;
341  }
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67

Member Data Documentation

template<unsigned int numberOfRows, unsigned int numberOfColumns>
std::array<Mdouble, numberOfRows * numberOfColumns> SmallMatrix< numberOfRows, numberOfColumns >::data_
private

The actually data of the matrix class.

Definition at line 363 of file SmallMatrix.h.

Referenced by SmallMatrix< numberOfRows, numberOfColumns >::axpy(), SmallMatrix< numberOfRows, numberOfColumns >::data(), SmallMatrix< numberOfRows, numberOfColumns >::operator()(), SmallMatrix< numberOfRows, numberOfColumns >::operator*(), SmallMatrix< numberOfRows, numberOfColumns >::operator*=(), SmallMatrix< numberOfRows, numberOfColumns >::operator+(), SmallMatrix< numberOfRows, numberOfColumns >::operator+=(), SmallMatrix< numberOfRows, numberOfColumns >::operator-(), SmallMatrix< numberOfRows, numberOfColumns >::operator-=(), SmallMatrix< numberOfRows, numberOfColumns >::operator/(), SmallMatrix< numberOfRows, numberOfColumns >::operator/=(), SmallMatrix< numberOfRows, numberOfColumns >::operator=(), SmallMatrix< numberOfRows, numberOfColumns >::operator[](), and SmallMatrix< numberOfRows, numberOfColumns >::SmallMatrix().

The documentation for this class was generated from the following files: