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.

            : data_()
    {
    }

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.

            : data_()
    {
        logger.assert_debug(numberOfColumns == 1, "Trying to construct a matrix with more than 1 columns from a vector");
        std::copy(other.data(), other.data() + numberOfRows, data_.begin());
    }

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_.

            : data_()
    {
        data_.fill(c);
    }

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.

            : data_()
    {
        logger.assert_debug(entries.size() == numberOfColumns, "expected a matrix with % "
                                                         "columns, but got a matrix with % columns", numberOfColumns,
                      entries.size());
        unsigned int column = 0;
        for (const SmallVector<numberOfRows>& entry : entries)
        {
            for (unsigned int i = 0; i < numberOfRows; ++i)
            {
                (*this)(i, column) = entry[i];
            }
            ++column;
        }
    }

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_.

            : data_()
    {
        std::copy(other.data_.begin(), other.data_.end(), data_.begin());
    }

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.

            : data_()
    {
        for (unsigned int i = 0; i < numberOfRows; ++i)
        {
            for (unsigned int j = 0; j < numberOfColumns; ++j)
            {
                (*this)(i, j) = entries[j][i];
            }
        }
    }

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.

            : data_(std::move(other.data_))
    {
    }

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.

    {
        for (unsigned int i = 0; i < numberOfRows * numberOfColumns; ++i)
        {
            data_[i] += a * x[i];
        }
    }

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.

{
    //copied from MiddleSizeMatrix to prevent constructing a temporary MiddleSizeMatrix
    logger.assert_debug(numberOfColumns == numberOfRows - 1,
                  "Matrix has wrong dimensions to construct the wedge stuff vector");
    SmallVector<numberOfRows> result;
    
    switch (numberOfRows)
    {
        case 2:
            result[0] = -(*this)(1, 0);
            result[1] = +(*this)(0, 0);
            break;
        case 3:
            result[0] = (*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1);
            result[1] = (*this)(0, 1) * (*this)(2, 0) - (*this)(0, 0) * (*this)(2, 1); // includes minus sign already!
            result[2] = (*this)(0, 0) * (*this)(1, 1) - (*this)(1, 0) * (*this)(0, 1);
            break;
        case 4:
            result[0] = (*this)(1, 0) * (-(*this)(2, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(2, 2)) +
                        (*this)(2, 0) * ((*this)(1, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(1, 2)) +
                        (*this)(3, 0) * (-(*this)(1, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 2));
            
            result[1] = (*this)(0, 0) * ((*this)(2, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(2, 2)) +
                        (*this)(2, 0) * (-(*this)(0, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(0, 2)) +
                        (*this)(3, 0) * ((*this)(0, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 2));
            result[2] = (*this)(0, 0) * (-(*this)(1, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(1, 2)) +
                        (*this)(1, 0) * ((*this)(0, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(0, 2)) +
                        (*this)(3, 0) * (-(*this)(0, 1) * (*this)(1, 2) + (*this)(1, 1) * (*this)(0, 2));
            result[3] = (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(1, 2)) +
                        (*this)(1, 0) * (-(*this)(0, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(0, 2)) +
                        (*this)(2, 0) * ((*this)(0, 1) * (*this)(1, 2) - (*this)(1, 1) * (*this)(0, 2));
            break;
        default:
            logger(ERROR, "Wedge product not implemented for this dimension");
    } //end switch
    
    return (result);
}

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().

    {
        return data_.data();
    }

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_.

    {
        return data_.data();
    }

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.

{
    logger.assert_debug(numberOfRows == numberOfColumns, "Matrix should be square to have a determinant!");
    
    switch (numberOfRows)
    {
        case 0:
            return 1;
        case 1:
            return (*this)(0, 0);
        case 2:
            return (*this)(0, 0) * (*this)(1, 1) - (*this)(0, 1) * (*this)(1, 0);
        
        case 3:
            return (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(1, 2) * (*this)(2, 1)) -
                   (*this)(0, 1) * ((*this)(1, 0) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 2)) +
                   (*this)(0, 2) * ((*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1));
        
        case 4:
            return ((*this)(3, 0) * (*this)(2, 1) * (*this)(0, 3) - (*this)(2, 0) * (*this)(3, 1) * (*this)(0, 3)) *
                   (*this)(1, 2) +
                   (-(*this)(3, 0) * (*this)(0, 3) * (*this)(2, 2) + (*this)(2, 0) * (*this)(0, 3) * (*this)(3, 2)) *
                   (*this)(1, 1) +
                   ((*this)(3, 1) * (*this)(0, 3) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 3) * (*this)(3, 2)) *
                   (*this)(1, 0) +
                   (-(*this)(3, 0) * (*this)(2, 1) * (*this)(1, 3) + (*this)(2, 0) * (*this)(3, 1) * (*this)(1, 3) +
                    (-(*this)(2, 0) * (*this)(3, 3) + (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 1) +
                    ((*this)(2, 1) * (*this)(3, 3) - (*this)(3, 1) * (*this)(2, 3)) * (*this)(1, 0)) * (*this)(0, 2) +
                   ((*this)(3, 0) * (*this)(1, 3) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 3) * (*this)(3, 2) +
                    ((*this)(2, 0) * (*this)(3, 3) - (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 2) +
                    (-(*this)(2, 2) * (*this)(3, 3) + (*this)(2, 3) * (*this)(3, 2)) * (*this)(1, 0)) * (*this)(0, 1) +
                   (-(*this)(3, 1) * (*this)(1, 3) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 3) * (*this)(3, 2) +
                    ((*this)(3, 1) * (*this)(2, 3) - (*this)(2, 1) * (*this)(3, 3)) * (*this)(1, 2) +
                    (*this)(1, 1) * ((*this)(2, 2) * (*this)(3, 3) - (*this)(2, 3) * (*this)(3, 2))) * (*this)(0, 0);
            // ... says Maple; this can possibly be done more efficiently,
            // maybe even with LU (with pivoting, though...)
        default:
            logger(ERROR, "Computing the Determinant for size % is not implemented", numberOfRows);
            break;
    }
    return 0;
}

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.

    {
        logger.assert_debug(j < numberOfColumns, "Asked for column %, but there are only % columns", j, numberOfColumns);
        return SmallVector<numberOfRows>(data() + j * numberOfRows);
    }

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().

    {
        return getNumberOfColumns();
    }

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().

    {
        return getNumberOfRows();
    }

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().

    {
        return numberOfColumns;
    }

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().

    {
        return numberOfRows;
    }

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.

    {
        logger.assert_debug(i < numberOfRows, "Asked for row %, but there are only % rows", i, numberOfRows);
        SmallVector<numberOfColumns> result;
        for (unsigned int j = 0; j < numberOfColumns; ++j)
        {
            result[j] = (*this)(i, j);
        }
        return result;
    }

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.

{
    logger.assert_debug(numberOfRows == numberOfColumns, "Cannot invert a non-square matrix");
    SmallMatrix<numberOfRows, numberOfColumns> result = (*this);
    
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int nPivot = numberOfRows;
    int iPivot[nPivot];
    
    int info = 0;
    
    dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
    
    int lwork = numberOfRows * numberOfColumns;
    SmallMatrix work;
    dgetri_(&nc, result.data(), &nc, iPivot, work.data(), &lwork, &info);
    
    return result;
}

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_().

{
    int nr = numberOfRows;
    int nc = numberOfColumns;
    int nPivot = std::min(numberOfRows, numberOfColumns);
    int iPivot[nPivot];
    
    SmallMatrix result(*this);
    
    int info;
    
    dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
    
    return result;
}

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.

    {
        logger.assert_debug(n < numberOfRows, "Requested row number % for a matrix with only % rows", n, numberOfRows);
        logger.assert_debug(m < numberOfColumns, "Requested column number % for a matrix with only % columns", m,
                      numberOfColumns);
        return data_[n + m * numberOfRows];
    }

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.

    {
        logger.assert_debug(n < numberOfRows, "Requested row number % for a matrix with only % rows", n, numberOfRows);
        logger.assert_debug(m < numberOfColumns, "Requested column number % for a matrix with only % columns", m,
                      numberOfColumns);
        return data_[n + m * numberOfRows];
    }

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.

{
    if (numberOfRows == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
        return SmallVector<numberOfRows>();
    }
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
        return SmallVector<numberOfRows>();
    }
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int i_one = 1;
    double d_one = 1.0;
    double d_zero = 0.0;
    
    SmallVector<numberOfRows> result;
    
    logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
    
    dgemv_("N", &nr, &nc, &d_one, this->data(), &nr, right.data(), &i_one, &d_zero, result.data(), &i_one);
    return result;
}

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.

{
    if (numberOfRows == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
        return SmallVector<numberOfRows>();
    }
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
        return SmallVector<numberOfRows>();
    }
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int i_one = 1;
    double d_one = 1.0;
    double d_zero = 0.0;
    
    SmallVector<numberOfRows> result;
    
    logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
    
    dgemv_("N", &nr, &nc, &d_one, (const_cast<double*>(this->data())), &nr, right.data(), &i_one, &d_zero,
           result.data(), &i_one);
    return result;
}

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_.

    {
        SmallMatrix result;
        std::transform(data_.begin(), data_.end(), result.data_.begin(),
                       std::bind(std::multiplies<Mdouble>(), std::placeholders::_1, right));
        return result;
    }

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.

{
    int i = numberOfRows;
    int j = numberOfColumns;
    int k = K;
    
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
        return SmallMatrix<numberOfRows, K>();
    }
    //The result of the matrix is left.numberOfRows, right.numberOfColumns()
    SmallMatrix<numberOfRows, K> C;
    
    double d_one = 1.0;
    double d_zero = 0.0;
    
    //Let the actual multiplication be done by Fortran
    dgemm_("N", "N", &i, &k, &j, &d_one, this->data(), &i, const_cast<double*>(other.data()), &j, &d_zero, C.data(),
           &i);
    
    return C;
}

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.

{
    int i = numberOfRows;
    int j = numberOfColumns;
    int k = K;
    
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
        return SmallMatrix<numberOfRows, K>();
    }
    //The result of the matrix is left.Nrows, right.NCols()
    SmallMatrix<numberOfRows, K> C;
    
    double d_one = 1.0;
    double d_zero = 0.0;
    
    //Let the actual multiplication be done by Fortran
    dgemm_("N", "N", &i, &k, &j, &d_one, const_cast<double*>(this->data()), &i, const_cast<double*>(other.data()), &j,
           &d_zero, C.data(), &i);
    
    return C;
}

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_.

    {
        std::transform(data_.begin(), data_.end(), data_.begin(),
                       std::bind(std::multiplies<Mdouble>(), std::placeholders::_1, scalar));
        return *this;
    }

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.

{
    //blas does not support in-place multiply
    return (*this) = (*this) * other;
}

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_.

    {
        SmallMatrix result;
        std::transform(data_.begin(), data_.end(), other.data_.begin(), result.data_.begin(), std::plus<Mdouble>());
        return result;
    }

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_.

    {
        std::transform(data_.begin(), data_.end(), other.data_.begin(), data_.begin(), std::plus<Mdouble>());
        return *this;
    }

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_.

    {
        SmallMatrix result;
        std::transform(data_.begin(), data_.end(), other.data_.begin(), result.data_.begin(), std::minus<Mdouble>());
        return result;
    }

template<unsigned int numberOfRows, unsigned int numberOfColumns>

SmallMatrix SmallMatrix< numberOfRows, numberOfColumns >::operator- ( ) const

inline

Definition at line 214 of file SmallMatrix.h.

    {
        return *this * -1.;
    }

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_.

    {
        std::transform(data_.begin(), data_.end(), other.data_.begin(), data_.begin(), std::minus<Mdouble>());
        return *this;
    }

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_.

    {
        SmallMatrix result;
        std::transform(data_.begin(), data_.end(), result.data_.begin(),
                       std::bind(std::divides<Mdouble>(), std::placeholders::_1, scalar));
        return result;
    }

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_.

    {
        std::transform(data_.begin(), data_.end(), data_.begin(),
                       std::bind(std::divides<Mdouble>(), std::placeholders::_1, scalar));
        return *this;
    }

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_.

    {
        std::copy(right.data_.begin(), right.data_.end(), data_.begin());
        return *this;
    }

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_.

    {
        std::move(right.data_.begin(), right.data_.end(), data_.begin());
        return *this;
    }

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.

    {
        logger.assert_debug(n < numberOfRows * numberOfColumns, "Requested entry % for a matrix with only % entries", n,
                      numberOfRows * numberOfColumns);
        return data_[n];
    }

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.

    {
        logger.assert_debug(n < numberOfRows * numberOfColumns, "Requested entry % for a matrix with only % entries", n,
                      numberOfRows * numberOfColumns);
        return data_[n];
    }

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.

    {
        return numberOfRows * numberOfColumns;
    }

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().

{
    logger.assert_debug(numberOfRows == numberOfColumns, "can only solve for square matrixes");
    
    int n = numberOfRows;
    int nrhs = numberOfRightHandSideColumns;
    int info;
    
    int IPIV[numberOfRows];
    SmallMatrix<numberOfRows, numberOfColumns> matThis = *this;
    dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, B.data(), &n, &info);
}

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.

{
    logger.assert_debug(numberOfRows == numberOfColumns, "can only solve for square matrixes");
    
    int n = numberOfRows;
    int nrhs = 1;
    int info;
    
    int IPIV[numberOfRows];
    SmallMatrix matThis = *this;
    dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, b.data(), &n, &info);
}

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().

    {
        SmallMatrix<numberOfColumns, numberOfRows> result;
        for (unsigned int i = 0; i < numberOfRows; ++i)
        {
            for (unsigned int j = 0; j < numberOfColumns; ++j)
            {
                result(j, i) = (*this)(i, j);
            }
        }
        return result;
    }

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().

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

• Math/SmallMatrix.h
• Math/SmallMatrix_impl.h