Linear Algebra

Classes
class	kjb::Index_range
class	kjb::Int_matrix
	This class implements matrices, in the linear-algebra sense, restricted to integer-valued elements. More...
class	kjb::Int_vector
	This class implements vectors, in the linear-algebra sense, restricted to integer-valued elements. More...
struct	kjb::Matrix_traits< value_type >
struct	kjb::Matrix_traits< int >
struct	kjb::Matrix_traits< double >
class	kjb::Generic_matrix_view< Matrix_type >
struct	kjb::Generic_const_matrix_view< Matrix_type >
class	kjb::Matrix
	This class implements matrices, in the linear-algebra sense, with real-valued elements. More...
class	kjb::Matrix_d< M, N, Transposed >
class	kjb::Matrix_stream_io
	static functions to read and write matrix classes with iostream. More...
class	kjb::Generic_vector_view< Vector_type >
struct	kjb::Generic_const_vector_view< Vector_type >
class	kjb::Vector
	This class implements vectors, in the linear-algebra sense, with real-valued elements. More...
class	kjb::Vector_d< D >
class	kjb::Vector_stream_io
	functions to read and write vector classes with streams. More...

Typedefs
typedef boost::multi_array_ref < double, 2 >	kjb::Matrix_stl_view
typedef Generic_matrix_view < Matrix >	kjb::Matrix_view
typedef const Generic_matrix_view< const Matrix >	kjb::Const_matrix_view
typedef Generic_vector_view < Matrix >	kjb::Matrix_vector_view
typedef const Generic_vector_view< const Matrix >	kjb::Const_matrix_vector_view
typedef Vector_d< 2 >	kjb::Vector2
typedef Vector_d< 3 >	kjb::Vector3
typedef Vector_d< 4 >	kjb::Vector4

Functions
template<class Indexable >
Indexable	kjb::ew_multiply (const Indexable &I, const Indexable &J)
	Multiply the elements of two Indexable things. Must be indexed via operator() and assignable. More...
template<class Indexable >
void	kjb::ew_abs_ow (Indexable &I)
	Element-wise abosulte value. More...
template<class Indexable >
void	kjb::ew_square_ow (Indexable &I)
	Square the elements of an indexable class in place. I must be indexed via operator(). More...
template<class Indexable >
Indexable	kjb::ew_square (const Indexable &I)
	Square the elements of an indexable class; the result is returned. I must be indexed via operator(). More...
template<class Indexable >
void	kjb::ew_sqrt_ow (Indexable &I)
	Take the square root of the elements of an indexable class in place. I must be indexed via operator(). More...
template<class Indexable >
Indexable	kjb::ew_sqrt (const Indexable &I)
	Take the square root the elements of an indexable class; the result is returned. I must be indexed via operator(). More...
void	kjb::swap (Index_range &r1, Index_range &r2)
std::istream &	kjb::operator>> (std::istream &ist, Index_range &ir)
Int_matrix	kjb::create_row_matrix (const Int_matrix::Vec_type &)
	Construct a one-row matrix by deep-copying a vector. More...
Int_matrix	kjb::create_diagonal_matrix (const Int_matrix::Vec_type &diagnoal)
	Construct a one-row matrix by deep-copying a vector. More...
Int_matrix	kjb::create_column_matrix (const Int_matrix::Vec_type &)
	Construct a one-column matrix by deep-copying a vector. More...
bool	kjb::operator== (const Int_matrix &op1, const Int_matrix::Impl_type &op2)
	Test for exact equality between two matrices. More...
std::ostream &	kjb::operator<< (std::ostream &out, const Int_matrix &m)
	Display matrix contents in an ASCII format. More...
Int_matrix	kjb::create_identity_int_matrix (int rank)
	Construct an identity matrix of specified rank. More...
Int_matrix	kjb::create_zero_int_matrix (int rows, int columns)
	Construct a zero matrix of specified size. More...
Int_matrix	kjb::create_zero_int_matrix (int rows)
	Construct a square zero matrix of specified size. More...
Int_matrix	kjb::operator* (const Int_matrix &op1, const Int_matrix &op2)
	Compute product of this matrix (on the left) and another. More...
Int_matrix	kjb::operator* (const Int_matrix &op1, Int_matrix::Value_type op2)
	Compute the product of this matrix and a scalar, yielding a new matrix. More...
Int_matrix	kjb::operator* (Int_matrix::Value_type op1, const Int_matrix &op2)
	Compute product of scalar and matrix, returning a new matrix. More...
Int_matrix	kjb::operator/ (const Int_matrix &op1, Int_matrix::Value_type op2)
	Compute new matrix equal to lefthand matrix with each entry divided by a scalar value. More...
Int_matrix	kjb::operator+ (const Int_matrix &op1, const Int_matrix &op2)
	Compute matrix addition, returning a new matrix. More...
Int_matrix	kjb::operator- (const Int_matrix &op1, const Int_matrix &op2)
	Compute matrix difference, returning a new matrix. More...
Int_matrix	kjb::operator- (const Int_matrix &op1)
	Return the additive inverse of this matrix. More...
bool	kjb::operator== (const Int_matrix &op1, const Int_matrix &op2)
	Test for exact equality between two matrices. More...
bool	kjb::operator!= (const Int_matrix &op1, const Int_matrix::Impl_type &op2)
	Test for any difference between two matrices. More...
bool	kjb::operator!= (const Int_matrix &op1, const Int_matrix &op2)
	Test for any difference between two matrices. More...
bool	kjb::operator== (const Int_matrix::Impl_type &op1, const Int_matrix &op2)
	Test for exact equality between two matrices. More...
bool	kjb::operator!= (const Int_matrix::Impl_type &op1, const Int_matrix &op2)
	Test for any difference between two matrices. More...
Int_matrix	kjb::matrix_transpose (const Int_matrix &op1)
	Test for any difference between two matrices. More...
Int_matrix	kjb::abs (const Int_matrix &mat)
	Compute the elementwise absolute value of a matrix. More...
Int_matrix::Value_type	kjb::max_abs_difference (const Int_matrix &op1, const Int_matrix &op2)
	Find the largest difference between two matrices. More...
Int_matrix::Value_type	kjb::min (const Int_matrix &mat)
	Return the minimum value in this matrix. More...
Int_matrix::Value_type	kjb::max (const Int_matrix &mat)
	Return the maximum value in this matrix. More...
Int_vector	kjb::operator* (const Int_vector &op1, const Int_matrix &op2)
	Return product of this (as a row-vec) times matrix on the right. More...
Int_vector	kjb::operator* (const Int_matrix &op1, const Int_vector &op2)
	Compute product of this matrix (on the left) and a column vector (on the right). More...
bool	kjb::operator== (const Int_vector &op1, const Int_vector::Impl_type &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator< (const Int_vector &op1, const Int_vector &op2)
	Test weak lexicographic ordering between vectors. More...
Int_vector	kjb::cross (const Int_vector &op1, const Int_vector &op2)
	Compute cross product of op1 and op2. More...
std::ostream &	kjb::operator<< (std::ostream &out, const Int_vector &m)
	Display vector contents in an ASCII format. More...
Int_vector	kjb::create_random_int_vector (int length)
	Construct a vector with random contents. More...
Int_vector	kjb::create_vector_from_vector_section (const Int_vector &iv, int begin, int length)
	Construct a vector by deep-copying a section of another vector. More...
Int_vector	kjb::operator* (const Int_vector &op1, Int_vector::Value_type op2)
	Scalar multiply, resulting in a new vector, e.g., v * 6. More...
Int_vector	kjb::operator* (Int_vector::Value_type op1, const Int_vector &op2)
	Scalar multiplication of a vector. More...
Int_vector	kjb::operator/ (const Int_vector &op1, Int_vector::Value_type op2)
	Scalar integer division, yielding a new vector. More...
Int_vector	kjb::operator+ (const Int_vector &op1, const Int_vector &op2)
	Add two vectors, creating a new vector, e.g., v + w. More...
Int_vector	kjb::operator- (const Int_vector &op1, const Int_vector &op2)
	Subtract one vector from another, resulting in a new vector, e.g., v - w. More...
Int_vector	kjb::operator- (const Int_vector &op1)
	Return the negation of a vector, as in (-v), resulting in a new vector. More...
bool	kjb::operator== (const Int_vector::Impl_type &op1, const Int_vector &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator!= (const Int_vector &op1, const Int_vector::Impl_type &op2)
	Test for (any) inequality between vectors. More...
bool	kjb::operator!= (const Int_vector::Impl_type &op1, const Int_vector &op2)
	Test for inequality between vectors. More...
bool	kjb::operator== (const Int_vector &op1, const Int_vector &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator!= (const Int_vector &op1, const Int_vector &op2)
	Test for (any) inequality between vectors. More...
bool	kjb::operator<= (const Int_vector &op1, const Int_vector &op2)
	Test lexicographic ordering between vectors. More...
bool	kjb::operator> (const Int_vector &op1, const Int_vector &op2)
	Test lexicographic ordering between vectors. More...
bool	kjb::operator>= (const Int_vector &op1, const Int_vector &op2)
	Test lexicographic ordering between vectors. More...
Int_vector::Value_type	kjb::max_abs_difference (const Int_vector &op1, const Int_vector &op2)
	Return the maximum of the absolute values of the elementwise difference between two vectors, provided they have the same length. More...
long int	kjb::dot (const Int_vector &op1, const Int_vector &op2)
	Returns dot product of this and op2. More...
double	kjb::norm2 (const Int_vector &op1)
	Compute l2-norm of vector. More...
double	kjb::vector_distance (const Int_vector &op1, const Int_vector &op2)
	Compute the Euclidian distance between two vectors. More...
double	kjb::vector_distance_squared (const Int_vector &op1, const Int_vector &op2)
	Compute the square of the Euclidian distance between two vectors. More...
template<class Iterator >
Matrix_traits< typename std::iterator_traits< Iterator > ::value_type::value_type > ::Matrix_type	kjb::create_matrix_from_rows (Iterator begin, Iterator end)
	Build a matrix from a container of row vectors. More...
template<class Iterator >
Matrix_traits< typename std::iterator_traits< Iterator > ::value_type::value_type > ::Matrix_type	kjb::create_matrix_from_columns (const Iterator &begin, const Iterator &end)
	Build a matrix from a container of column vectors. More...
template<class Container_ >
Matrix_traits< typename Container_::value_type::value_type > ::Matrix_type	kjb::create_matrix_from_columns (const Container_ &cols)
	Build a matrix from a container of column vectors. More...
template<class Container_ >
Matrix_traits< typename Container_::value_type::value_type > ::Matrix_type	kjb::create_matrix_from_rows (const Container_ &rows)
	Build a matrix from a container of row vectors. More...
Matrix_stl_view	kjb::get_matrix_stl_view (kjb::Matrix &mat)
Matrix	kjb::create_identity_matrix (int rank)
	Construct an identity matrix of specified rank. More...
Matrix	kjb::create_identity_matrix (int num_rows, int num_cols)
	Construct a rank-deficient identity matrix with the specified number of rows and columns. More...
Matrix	kjb::create_zero_matrix (int rows, int columns)
	Construct a zero matrix of specified size. More...
Matrix	kjb::create_zero_matrix (int size)
	Construct a square zero matrix of specified size. More...
Matrix	kjb::create_random_matrix (int num_rows, int num_cols)
Matrix	kjb::create_gauss_random_matrix (int num_rows, int num_cols)
Matrix	kjb::create_diagonal_matrix (const Matrix::Vec_type &diagonal)
	Construct a diagonal matrix from the specified vector. More...
Matrix	kjb::create_diagonal_matrix (const Matrix::Vec_type &diagonal, size_t n)
	Construct a "repeating" diagonal matrix from the specified vector. More...
Matrix	kjb::create_diagonal_matrix (int size, Matrix::Value_type a)
	Construct a diagonal matrix of the specified size, where the diagonal elements are set to the given value. More...
Matrix	kjb::create_row_matrix (const Vector &)
	Construct a one-row matrix by deep-copying a vector. More...
Matrix	kjb::create_column_matrix (const Vector &)
	Construct a one-column matrix by deep-copying a vector. More...
Matrix	kjb::operator* (const Matrix &op1, const Matrix &op2)
	Compute product of this matrix (on the left) and another. More...
Matrix	kjb::operator* (const Matrix &op1, Matrix::Value_type op2)
	Compute the product of this matrix and a scalar, yielding a new matrix. More...
Matrix	kjb::operator* (Matrix::Value_type op1, const Matrix &op2)
	Compute product of scalar and matrix, returning a new matrix. More...
Matrix	kjb::operator/ (const Matrix &op1, Matrix::Value_type op2)
	Compute new matrix equal to lefthand matrix with each entry divided by a scalar value. More...
Matrix	kjb::operator+ (const Matrix &op1, const Matrix &op2)
	Compute matrix addition, returning a new matrix. More...
Matrix	kjb::operator+ (const Matrix &op1, double op2)
	Compute matrix addition, returning a new matrix. More...
Matrix	kjb::operator- (const Matrix &op1, const Matrix &op2)
	Compute matrix difference, returning a new matrix. More...
Matrix	kjb::shift_rows_by (const Matrix &op1, const Vector &op2)
	Add the same vector to each row, return a new Matrix. More...
Matrix	kjb::shift_columns_by (const Matrix &op1, const Vector &op2)
	Add the same vector to each column, return a new Matrix. More...
Matrix	kjb::ew_multiply_rows_by (const Matrix &op1, const Vector &op2)
	Elementwise multiply each row of op1 by a op2, return a new Matrix. More...
Matrix	kjb::ew_multiply (const Matrix &op1, const Matrix &op2)
	Elementwise product of two matrices. More...
Matrix	kjb::operator- (const Matrix &op1, double op2)
	Compute matrix difference, returning a new matrix. More...
Matrix	kjb::operator- (const Matrix &op1)
	Return the additive inverse of this matrix. More...
bool	kjb::operator== (const Matrix &op1, const Matrix::Impl_type &op2)
	Test for exact equality between two matrices. More...
bool	kjb::operator== (const Matrix &op1, const Matrix &op2)
	Test for exact equality between two matrices. More...
bool	kjb::operator!= (const Matrix &op1, const Matrix::Impl_type &op2)
	Test for any difference between two matrices. More...
bool	kjb::operator!= (const Matrix &op1, const Matrix &op2)
	Test for any difference between two matrices. More...
bool	kjb::operator== (const Matrix::Impl_type &op1, const Matrix &op2)
	Test for exact equality between two matrices. More...
bool	kjb::operator!= (const Matrix::Impl_type &op1, const Matrix &op2)
	Test for any difference between two matrices. More...
bool	kjb::operator< (const Matrix &op1, const Matrix &op2)
	Returns true if a is lexicographically less-than b. More...
Matrix	kjb::matrix_inverse (const Matrix &op1)
	Invert this matrix. More...
Matrix	kjb::matrix_transpose (const Matrix &op1)
	Transpose this matrix. More...
Matrix	kjb::abs (const Matrix &mat)
	Compute the elementwise absolute value of a matrix. More...
double	kjb::sum_squared_elements (const Matrix &mat)
	Compute the sum of squared elements. More...
Matrix::Value_type	kjb::max_abs_difference (const Matrix &op1, const Matrix &op2)
	Find the largest difference between two matrices. More...
Matrix::Value_type	kjb::min (const Matrix &mat)
	Return the minimum value in this matrix. More...
Matrix::Value_type	kjb::max (const Matrix &mat)
	Return the maximum value in this matrix. More...
std::ostream &	kjb::operator<< (std::ostream &out, const Matrix &m)
	Display matrix contents in an ASCII format. More...
double	kjb::det (const Matrix &mat)
Matrix	kjb::outer_product (const Vector &v1, const Vector &v2)
Matrix::Vec_type	kjb::sum_matrix_cols (const Matrix &)
	Compute the matrix's sum across columns (a.k.a. row-wise sum) More...
Matrix::Vec_type	kjb::sum_matrix_rows (const Matrix &)
	Compute the matrix's sum down (a.k.a. columnar sum), like MATLAB. More...
Int_matrix	kjb::create_int_matrix_from_matrix_floor (const Matrix &)
	Construct an Int_matrix with elements equal to the floor() of a given floating-point Matrix. More...
Int_matrix	kjb::floor (const Matrix &m)
Int_matrix	kjb::create_int_matrix_from_matrix_ceil (const Matrix &)
	Construct a matrix with elements equal to the ceiling, ceil() of a given floating-point Matrix. More...
Matrix	kjb::logical_or (Matrix a, Matrix b)
	returns a matrix with 1s and 0s. 1 if either has a non zero value in that position, 0 otherwise More...
Matrix	kjb::logical_and (Matrix a, Matrix b)
	returns a matrix with 1s and 0s. 1 if both matricies have a non zero value in that position, 0 otherwise More...
Matrix	kjb::logical_not (Matrix a)
	returns a matrix with 1s and 0s. 1 if the value is 0, and 0 otherwise. More...
Matrix	kjb::tile_matrix (Matrix trixy, unsigned m, unsigned n)
	Construct a tiling of the given matrix. More...
Matrix	kjb::tile_matrix (int tehnum, unsigned m, unsigned n)
	Construct a tiling of the given matrix, in this case, a matrix of the given number with the specified size. More...
Vector	kjb::create_random_vector (int length)
	Construct a vector with values drawn from a uniform distribution over [0,1]. More...
Vector	kjb::create_gauss_random_vector (int length)
	Construct a vector with values drawn from a standard Gaussian distribution (mean 0, variance 1);. More...
Vector	kjb::create_zero_vector (int length)
	Construct a vector containing zeroes. More...
Vector	kjb::create_vector_from_vector_section (const Vector &iv, int begin, int length)
	Construct a vector by deep-copying a section of another vector. More...
Vector	kjb::operator* (const Vector &op1, const Matrix &op2)
	Return product of op1 (as a row-vec) times matrix on the right. More...
Vector	kjb::operator* (const Matrix &op1, const Vector &op2)
	Compute product of this matrix (on the left) and a column vector (on the right). More...
Vector	kjb::operator* (const Vector &op1, Vector::Value_type op2)
	Scalar multiply, resulting in a new vector, e.g., v * 6. More...
Vector	kjb::operator* (Vector::Value_type op1, const Vector &op2)
	Scalar multiplication of a vector. More...
Vector	kjb::operator/ (const Vector &op1, Vector::Value_type op2)
	Scalar division, yielding a new vector. More...
Vector	kjb::operator+ (const Vector &op1, const Vector &op2)
	Add two vectors, creating a new vector, e.g., v + w. More...
Vector	kjb::operator- (const Vector &op1, const Vector &op2)
	Subtract one vector from another, resulting in a new vector, e.g., v - w. More...
Vector	kjb::operator- (const Vector &op1)
	Return the negation of a vector, as in (-v), resulting in a new vector. More...
bool	kjb::operator== (const Vector &op1, const Vector::Impl_type &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator== (const Vector::Impl_type &op1, const Vector &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator!= (const Vector &op1, const Vector::Impl_type &op2)
	Test for (any) inequality between vectors. More...
bool	kjb::operator!= (const Vector::Impl_type &op1, const Vector &op2)
	Test for inequality between vectors. More...
bool	kjb::operator== (const Vector &op1, const Vector &op2)
	Test for exact equality between vectors. More...
bool	kjb::operator!= (const Vector &op1, const Vector &op2)
	Test for (any) inequality between vectors. More...
bool	kjb::operator< (const Vector &op1, const Vector &op2)
	Test weak lexicographic ordering between vectors. More...
bool	kjb::operator<= (const Vector &op1, const Vector &op2)
	Test lexicographic ordering between vectors. More...
bool	kjb::operator> (const Vector &op1, const Vector &op2)
	Test lexicographic ordering between vectors. More...
bool	kjb::operator>= (const Vector &op1, const Vector &op2)
	Test lexicographic ordering between vectors. More...
std::ostream &	kjb::operator<< (std::ostream &out, const Vector &m)
	Display vector contents in an ASCII format. More...
std::ostream &	kjb::stream_write_vector (std::ostream &ost, const Vector &m)
	Write vector to an output stream so it can be read with read_vector. More...
std::istream &	kjb::stream_read_vector (std::istream &ist, Vector &m)
	Read vector from an input stream. More...
Vector::Value_type	kjb::max_abs_difference (const Vector &op1, const Vector &op2)
	Return the maximum of the absolute values of the elementwise difference between two vectors, provided they have the same length. More...
Vector::Value_type	kjb::dot (const Vector &op1, const Vector &op2)
	Returns dot product of op1 and op2. More...
Vector	kjb::cross (const Vector &op1, const Vector &op2)
	Compute cross product of op1 and op2. More...
double	kjb::norm1 (const Vector &op)
	Compute L1-norm of vector. More...
double	kjb::norm2 (const Vector &op1)
	Compute L2-norm of vector. More...
double	kjb::vector_distance (const Vector &op1, const Vector &op2)
	Compute the Euclidian distance between two vectors. More...
double	kjb::vector_distance_squared (const Vector &op1, const Vector &op2)
	Compute the square of the Euclidian distance between two vectors. More...
Vector::Value_type	kjb::max (const Vector &vec)
	Return the maximum element in the vector. More...
Vector::Value_type	kjb::min (const Vector &vec)
	Return the minimum element in the vector. More...
Vector	kjb::cat_vectors (const Vector &first, const Vector &second)
	Concatenate two vectors. More...
template<class InputIterator >
Vector	kjb::cat_vectors (InputIterator first, InputIterator last)
	Concatenate the vectors in the given sequence of vectors. More...
template<class OutputIterator >
OutputIterator	kjb::separate_vector (const Vector &vec, int sz, OutputIterator result)
	Separate the given vector into vectors of the give size; the vectors will be output into the output iterator. More...
std::vector< Vector >	kjb::get_transpose (const std::vector< Vector > &m)
	Treat a std::vector of kjb::Vectors as a matrix and get its 'transpose'. More...
Int_vector	kjb::floor (const Vector &realv)
	Build an Int_vector that is the element-wise floor of a real Vector. More...
kjb::Vector	kjb::create_uniformly_spaced_vector (double a, double b, unsigned n)
template<std::size_t D>
Vector	kjb::operator* (const Matrix &m, const Vector_d< D > v)
	multiply by static vector More...
Vector	kjb::multiply_matrix_and_vector_d_dispatch_ (const Matrix &m, const double *v, size_t size)
	dispatch for operator*(Matrix, Vector_d). This deals with a circular dependency between matrix.h and vector_d.h by moving template code into a cpp file. DO NOT CALL DIRECTLY! More...
template<std::size_t D>
Vector_d< D >	kjb::operator- (const Vector_d< D > &first, const Vector_d< D > &second)
template<std::size_t D>
Vector_d< D >	kjb::operator- (const Vector_d< D > &first, double second)
template<std::size_t D>
Vector_d< D >	kjb::operator- (double first, const Vector_d< D > &second)
template<std::size_t D>
Vector_d< D >	kjb::operator- (const Vector_d< D > &first)
template<std::size_t D>
Vector_d< D >	kjb::operator+ (const Vector_d< D > &first, const Vector_d< D > &second)
template<std::size_t D>
Vector_d< D >	kjb::operator+ (const Vector_d< D > &first, double second)
template<std::size_t D>
Vector_d< D >	kjb::operator+ (double first, const Vector_d< D > &second)
template<std::size_t D>
Vector_d< D >	kjb::operator* (const Vector_d< D > &v, double s)
template<std::size_t D>
Vector_d< D >	kjb::operator* (double s, const Vector_d< D > &v)
template<std::size_t D>
Vector_d< D >	kjb::operator/ (const Vector_d< D > &v, double s)
template<std::size_t N>
void	kjb::swap (Vector_d< N > &first, Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator== (const Vector_d< N > &first, const Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator!= (const Vector_d< N > &first, const Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator< (const Vector_d< N > &first, const Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator> (const Vector_d< N > &first, const Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator<= (const Vector_d< N > &first, const Vector_d< N > &second)
template<std::size_t N>
bool	kjb::operator>= (const Vector_d< N > &first, const Vector_d< N > &second)
template<size_t D>
double	kjb::norm1 (const kjb::Vector_d< D > &v)
template<size_t D>
double	kjb::norm2 (const kjb::Vector_d< D > &v)
template<size_t D>
Vector_d< D >	kjb::create_random_vector ()
template<size_t D>
Vector_d< D >	kjb::create_gauss_random_vector ()
Vector2	kjb::create_random_vector2 ()
Vector3	kjb::create_random_vector3 ()
Vector4	kjb::create_random_vector4 ()
template<size_t D>
Vector_d< D >	kjb::create_unit_vector (size_t d)
Vector2	kjb::make_vector2 (const Vector &v)
Vector3	kjb::make_vector3 (const Vector &v)
Vector4	kjb::make_vector4 (const Vector &v)
template<std::size_t D>
std::ostream &	kjb::operator<< (std::ostream &out, const Vector_d< D > &v)
template<std::size_t D>
std::istream &	kjb::operator>> (std::istream &ist, Vector_d< D > &v)
template<std::size_t D>
double	kjb::dot (const Vector_d< D > &op1, const Vector_d< D > &op2)
template<std::size_t D>
double	kjb::vector_distance (const Vector_d< D > &op1, const Vector_d< D > &op2)
	Compute the Euclidian distance between two vectors. More...
template<std::size_t D>
double	kjb::vector_distance_squared (const Vector_d< D > &op1, const Vector_d< D > &op2)
	Compute the Euclidian distance between two vectors. More...
Vector3	kjb::cross (const Vector3 &op1, const Vector3 &op2)
	kjb::Int_matrix::Int_matrix (int rows, int cols, const Value_type *data)
	Ctor builds a matrix and initializes entries from an array. More...
	kjb::Int_matrix::Int_matrix (const std::string &file_name)
	Read matrix from file. More...
Int_matrix &	kjb::Int_matrix::resize (int new_rows, int new_cols, Value_type pad=Value_type(0))
	Resize this matrix, retaining previous values. More...
Vec_type	kjb::Int_matrix::get_row (int row) const
	Return a specified row of this matrix, in the form of an Int_vector. More...
Vec_type	kjb::Int_matrix::get_col (int col) const
	Return a specified column of this matrix, in the form of an Int_vector. More...
Int_matrix &	kjb::Int_matrix::operator/= (Int_matrix::Value_type op2)
	Perform integer division on each entry in the matrix by a scalar value. More...
Mat_type &	kjb::Int_matrix::mapcar (Mapper)
	Transform the elements of a matrix. More...
template<class Generic_vector >
void	kjb::Int_matrix::set_row (int row, const Generic_vector &v)
	Replace a row of the matrix with the given vector. More...
template<class Iterator >
void	kjb::Int_matrix::set_row (int row, Iterator begin, Iterator end)
	Dispatch for set_row. Don't call directly. More...
template<class Generic_vector >
void	kjb::Int_matrix::set_col (int col, const Generic_vector &v)
	Replace a column of the matrix with the given vector. "vector" can be any collection of values convertible to int. More...
template<class Iterator >
void	kjb::Int_matrix::set_col (int col, Iterator begin, Iterator end)
	Dispatch for set_col. Don't call directly. More...
	kjb::Int_vector::Int_vector (const Mat_type &src)
	Ctor builds from a one-row or one-column Int_matrix (making a deep copy). More...
	kjb::Int_vector::Int_vector (const std::string &file_name)
	Construct a vector by reading contents from a named file. More...
Int_vector &	kjb::Int_vector::resize (int new_length, Value_type pad=Value_type(0))
	Resize vector, retaining previous values. More...
Int_vector &	kjb::Int_vector::randomize (int length)
	Clobber current vector; resize and fill with random values. More...
Int_vector &	kjb::Int_vector::operator/= (Value_type op2)
	Scalar integer division of self, in-place. More...
Vec_type &	kjb::Int_vector::mapcar (Mapper)
	Transform the elements of a vector. More...
kjb::Int_matrix	kjb::Int_vector::hat () const
	Construct an "equivalent" skew-symmetric matrix from 3-vector. More...
Int_vector &	kjb::Int_vector::cross_with (const Int_vector &op2)
	Compute (in place) cross product of this vector and op2. More...
template<typename InputIterator >
void	kjb::Int_vector::insert (iterator position, InputIterator begin_, InputIterator end_)
	Insert range [begin, end) before position. More...
template<typename OutputIterator >
OutputIterator	kjb::Matrix::get_all_rows (OutputIterator result) const
	Return all rows of this matrix into the provided iterator. More...
template<typename OutputIterator >
OutputIterator	kjb::Matrix::get_all_cols (OutputIterator result) const
	Return all columns of this matrix into the provided iterator. More...
template<class Generic_vector >
void	kjb::Matrix::set_row (int row, const Generic_vector &v)
	Replace a row of the matrix with the given vector. More...
template<class Iterator >
void	kjb::Matrix::set_row (int row, Iterator begin, Iterator end)
	Dispatch for set_row. Don't call directly. More...
template<class Generic_vector >
void	kjb::Matrix::set_col (int col, const Generic_vector &v)
	Replace a column of the matrix with the given vector. "vector" can be any collection of values convertible to double. More...
template<class Iterator >
void	kjb::Matrix::set_col (int col, Iterator begin, Iterator end)
	Dispatch for set_col. Don't call directly. More...
template<typename InputIterator >
void	kjb::Vector::insert (iterator position, InputIterator begin_, InputIterator end_)
	Insert range [begin, end) before position. More...
template<typename InputIterator >
void	kjb::Vector::assign (InputIterator begin_, InputIterator end_)
	Assign this vector to the values in sequence (begin_, and_) More...

Detailed Description

This group tries to gather all the general-purpose matrix- and vector-related functions and classes, including basic math and basic utilities and manipulations.

Typedef Documentation

typedef const Generic_vector_view<const Matrix> kjb::Const_matrix_vector_view

typedef const Generic_matrix_view<const Matrix> kjb::Const_matrix_view

typedef boost::multi_array_ref<double, 2> kjb::Matrix_stl_view

typedef Generic_vector_view<Matrix> kjb::Matrix_vector_view

typedef Generic_matrix_view<Matrix> kjb::Matrix_view

typedef Vector_d< 2 > kjb::Vector2

typedef Vector_d< 3 > kjb::Vector3

typedef Vector_d< 4 > kjb::Vector4

Function Documentation

Int_matrix kjb::abs ( const Int_matrix &  mat )

inline

Compute the elementwise absolute value of a matrix.

Matrix kjb::abs ( const Matrix &  mat )

inline

Compute the elementwise absolute value of a matrix.

template<typename InputIterator >

void kjb::Vector::assign	(	InputIterator	begin_,
		InputIterator	end_
	)

Assign this vector to the values in sequence (begin_, and_)

Vector kjb::cat_vectors ( const Vector &  first, const Vector &  second  )

inline

Concatenate two vectors.

template<class InputIterator >

Vector kjb::cat_vectors	(	InputIterator	first,
		InputIterator	last
	)

Concatenate the vectors in the given sequence of vectors.

Int_matrix kjb::create_column_matrix

(

const Int_matrix::Vec_type &

vec

)

Construct a one-column matrix by deep-copying a vector.

Matrix kjb::create_column_matrix

(

const Matrix::Vec_type &

vec

)

Construct a one-column matrix by deep-copying a vector.

Int_matrix kjb::create_diagonal_matrix

(

const Int_matrix::Vec_type &

diagonal

)

Construct a one-row matrix by deep-copying a vector.

Matrix kjb::create_diagonal_matrix

(

const Matrix::Vec_type &

diagonal

)

Construct a diagonal matrix from the specified vector.

Matrix kjb::create_diagonal_matrix	(	const Matrix::Vec_type &	diagonal,
		size_t	n
	)

Construct a "repeating" diagonal matrix from the specified vector.

Matrix kjb::create_diagonal_matrix ( int  size, Matrix::Value_type  a  )

inline

Construct a diagonal matrix of the specified size, where the diagonal elements are set to the given value.

Matrix kjb::create_gauss_random_matrix	(	int	num_rows,
		int	num_cols
	)

Construct a matrix with gaussian random values. Numbers are generated from kjb_rand(), which is seeded by kjb_seed_rand().

See Also

gauss_rand, kjb_seed_rand

template<size_t D>

Vector_d< D > kjb::create_gauss_random_vector

(

)

Vector kjb::create_gauss_random_vector

(

int

length

)

Construct a vector with values drawn from a standard Gaussian distribution (mean 0, variance 1);.

Int_matrix kjb::create_identity_int_matrix ( int  rank )

inline

Construct an identity matrix of specified rank.

Matrix kjb::create_identity_matrix ( int  rank )

inline

Construct an identity matrix of specified rank.

Matrix kjb::create_identity_matrix ( int  num_rows, int  num_cols  )

inline

Construct a rank-deficient identity matrix with the specified number of rows and columns.

Int_matrix kjb::create_int_matrix_from_matrix_ceil

(

const Matrix &

)

Construct a matrix with elements equal to the ceiling, ceil() of a given floating-point Matrix.

Warning

If you ought to check for overflow you must do it yourself.

Note

This was moved from l_int_matrix.h to avoid a circular dependency.

Int_matrix kjb::create_int_matrix_from_matrix_floor

(

const Matrix &

)

Construct an Int_matrix with elements equal to the floor() of a given floating-point Matrix.

Warning

If you ought to check for overflow you must do it yourself.

Note

This was moved from l_int_matrix.h to avoid a circular dependency.

template<class Iterator >

Matrix_traits<typename std::iterator_traits<Iterator>::value_type::value_type>::Matrix_type kjb::create_matrix_from_columns	(	const Iterator &	begin,
		const Iterator &	end
	)

Build a matrix from a container of column vectors.

template<class Container_ >

Matrix_traits<typename Container_::value_type::value_type>::Matrix_type kjb::create_matrix_from_columns ( const Container_ &  cols )

inline

Build a matrix from a container of column vectors.

template<class Iterator >

Matrix_traits<typename std::iterator_traits<Iterator>::value_type::value_type>::Matrix_type kjb::create_matrix_from_rows	(	Iterator	begin,
		Iterator	end
	)

Build a matrix from a container of row vectors.

template<class Container_ >

Matrix_traits<typename Container_::value_type::value_type>::Matrix_type kjb::create_matrix_from_rows ( const Container_ &  rows )

inline

Build a matrix from a container of row vectors.

Int_vector kjb::create_random_int_vector ( int  length )

inline

Construct a vector with random contents.

Matrix kjb::create_random_matrix ( int  num_rows, int  num_cols  )

inline

Construct a matrix with uniform random values in [0,1]. Numbers are generated from kjb_rand(), which is seeded by kjb_seed_rand().

See Also

kjb_rand, kjb_seed_rand

template<size_t D>

Vector_d< D > kjb::create_random_vector

(

)

Vector kjb::create_random_vector ( int  length )

inline

Construct a vector with values drawn from a uniform distribution over [0,1].

Vector2 kjb::create_random_vector2 ( )

inline

Vector3 kjb::create_random_vector3 ( )

inline

Vector4 kjb::create_random_vector4 ( )

inline

Int_matrix kjb::create_row_matrix

(

const Int_matrix::Vec_type &

vec

)

Construct a one-row matrix by deep-copying a vector.

Matrix kjb::create_row_matrix

(

const Matrix::Vec_type &

vec

)

Construct a one-row matrix by deep-copying a vector.

kjb::Vector kjb::create_uniformly_spaced_vector	(	double	a,
		double	b,
		unsigned	n
	)

template<size_t D>

Vector_d< D > kjb::create_unit_vector

(

size_t

d

)

Int_vector kjb::create_vector_from_vector_section ( const Int_vector &  iv, int  begin, int  length  )

inline

Construct a vector by deep-copying a section of another vector.

See Also

kjb_c::copy_int_vector_section()

Vector kjb::create_vector_from_vector_section ( const Vector &  iv, int  begin, int  length  )

inline

Construct a vector by deep-copying a section of another vector.

See Also

kjb_c::copy_vector_segment()

Note

The stl-style "fill" constructor is a more generic alternative to this: Vector v(v2.begin()+start, v2.begin()+start+length)

Int_matrix kjb::create_zero_int_matrix ( int  rows, int  columns  )

inline

Construct a zero matrix of specified size.

Int_matrix kjb::create_zero_int_matrix ( int  rows )

inline

Construct a square zero matrix of specified size.

Matrix kjb::create_zero_matrix ( int  rows, int  columns  )

inline

Construct a zero matrix of specified size.

Matrix kjb::create_zero_matrix ( int  size )

inline

Construct a square zero matrix of specified size.

Vector kjb::create_zero_vector ( int  length )

inline

Construct a vector containing zeroes.

Deprecated:

Better to use Vector(length, 0.0) instead.

Int_vector kjb::cross	(	const Int_vector &	op1,
		const Int_vector &	op2
	)

Compute cross product of op1 and op2.

Store result in this vector. Only defined for dimension = 3.

Vector3 kjb::cross ( const Vector3 &  op1, const Vector3 &  op2  )

inline

Compute cross product between two 3-vectors

Vector kjb::cross	(	const Vector &	op1,
		const Vector &	op2
	)

Compute cross product of op1 and op2.

Store result in this vector. Only defined for dimension = 3.

Int_vector & kjb::Int_vector::cross_with

(

const Int_vector &

op2

)

Compute (in place) cross product of this vector and op2.

Store result in this vector. Only defined for dimension = 3.

double kjb::det

(

const Matrix &

mat

)

Compute the matrix determinant.

Note

This is not implemented for matrices larger than 3x3. Even if it was, it would probably be slow. Prefer Matrix::abs_of_determinant() over this if you don't care about the sign of the determinant

template<std::size_t D>

double kjb::dot	(	const Vector_d< D > &	op1,
		const Vector_d< D > &	op2
	)

long int kjb::dot ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Returns dot product of this and op2.

Vector::Value_type kjb::dot ( const Vector &  op1, const Vector &  op2  )

inline

Returns dot product of op1 and op2.

template<class Indexable >

void kjb::ew_abs_ow

(

Indexable &

I

)

Element-wise abosulte value.

template<class Indexable >

Indexable kjb::ew_multiply	(	const Indexable &	I,
		const Indexable &	J
	)

Multiply the elements of two Indexable things. Must be indexed via operator() and assignable.

Matrix kjb::ew_multiply ( const Matrix &  op1, const Matrix &  op2  )

inline

Elementwise product of two matrices.

Author

Colin Dawson

Matrix kjb::ew_multiply_rows_by ( const Matrix &  op1, const Vector &  op2  )

inline

Elementwise multiply each row of op1 by a op2, return a new Matrix.

Author

Colin Dawson

template<class Indexable >

Indexable kjb::ew_sqrt

(

const Indexable &

I

)

Take the square root the elements of an indexable class; the result is returned. I must be indexed via operator().

template<class Indexable >

void kjb::ew_sqrt_ow

(

Indexable &

I

)

Take the square root of the elements of an indexable class in place. I must be indexed via operator().

template<class Indexable >

Indexable kjb::ew_square

(

const Indexable &

I

)

Square the elements of an indexable class; the result is returned. I must be indexed via operator().

template<class Indexable >

void kjb::ew_square_ow

(

Indexable &

I

)

Square the elements of an indexable class in place. I must be indexed via operator().

Int_vector kjb::floor

(

const Vector &

realv

)

Build an Int_vector that is the element-wise floor of a real Vector.

Int_matrix kjb::floor

(

const Matrix &

m

)

alias for create_int_matrix_from_matrix_floor()

template<typename OutputIterator >

OutputIterator kjb::Matrix::get_all_cols

(

OutputIterator

result

)

const

Return all columns of this matrix into the provided iterator.

template<typename OutputIterator >

OutputIterator kjb::Matrix::get_all_rows

(

OutputIterator

result

)

const

Return all rows of this matrix into the provided iterator.

Int_matrix::Vec_type kjb::Int_matrix::get_col

(

int

col

)

const

Return a specified column of this matrix, in the form of an Int_vector.

Matrix_stl_view kjb::get_matrix_stl_view

(

kjb::Matrix &

mat

)

Get view of the matrix that has a similar interface to an stl-style std::vector<std::vector<double> >. When subscripting, inidices are specified using subscript operators, not the parentheses operator; i.e. you can index using m[1][2] instead of m(1,2); This is a lightweight operation: no copy is made, only metadata is allocated; Naturally, caller is responsible for ensuring that the returned view is outlived by this Matrix.

Int_matrix::Vec_type kjb::Int_matrix::get_row

(

int

row

)

const

Return a specified row of this matrix, in the form of an Int_vector.

std::vector< Vector > kjb::get_transpose

(

const std::vector< Vector > &

m

)

Treat a std::vector of kjb::Vectors as a matrix and get its 'transpose'.

Int_matrix kjb::Int_vector::hat

(

)

const

Construct an "equivalent" skew-symmetric matrix from 3-vector.

The result is useful for computing a cross product. Only implemented for dimension = 3. The formula is as follows:

                     (  0 -c  b )
 Hat of (a b c)' :=  (  c  0 -a )
                     ( -b  a  0 ).

template<typename InputIterator >

void kjb::Int_vector::insert	(	iterator	position,
		InputIterator	begin_,
		InputIterator	end_
	)

Insert range [begin, end) before position.

template<typename InputIterator >

void kjb::Vector::insert	(	iterator	position,
		InputIterator	begin_,
		InputIterator	end_
	)

Insert range [begin, end) before position.

kjb::Int_matrix::Int_matrix	(	int	rows,
		int	cols,
		const Value_type *	data
	)

Ctor builds a matrix and initializes entries from an array.

The data array must be of length at least (rows x cols). The matrix is filled in row-major order.

kjb::Int_matrix::Int_matrix

(

const std::string &

file_name

)

Read matrix from file.

See Also

kjb_c::read_matrix

kjb::Int_vector::Int_vector ( const Mat_type &  src )

explicit

Ctor builds from a one-row or one-column Int_matrix (making a deep copy).

kjb::Int_vector::Int_vector

(

const std::string &

file_name

)

Construct a vector by reading contents from a named file.

Matrix kjb::logical_and	(	Matrix	a,
		Matrix	b
	)

returns a matrix with 1s and 0s. 1 if both matricies have a non zero value in that position, 0 otherwise

Matrix kjb::logical_not

(

Matrix

a

)

returns a matrix with 1s and 0s. 1 if the value is 0, and 0 otherwise.

Matrix kjb::logical_or	(	Matrix	a,
		Matrix	b
	)

returns a matrix with 1s and 0s. 1 if either has a non zero value in that position, 0 otherwise

Vector2 kjb::make_vector2

(

const Vector &

v

)

Precondition

v.size() == 2

Vector3 kjb::make_vector3

(

const Vector &

v

)

Precondition

v.size() == 3

Vector4 kjb::make_vector4

(

const Vector &

v

)

Precondition

v.size() == 4

Int_matrix & kjb::Int_matrix::mapcar

(

Mapper

fun

)

Transform the elements of a matrix.

Apply a transformation fun to each element of the matrix, in place, and return an lvalue of the modified matrix.

Int_vector & kjb::Int_vector::mapcar

(

Mapper

fun

)

Transform the elements of a vector.

Apply a transformation fun to each element of the vector, in place, and return an lvalue of the modified vector.

Matrix kjb::matrix_inverse

(

const Matrix &

op1

)

Invert this matrix.

Int_matrix kjb::matrix_transpose ( const Int_matrix &  op1 )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

Matrix kjb::matrix_transpose ( const Matrix &  op1 )

inline

Transpose this matrix.

Int_matrix::Value_type kjb::max ( const Int_matrix &  mat )

inline

Return the maximum value in this matrix.

Vector::Value_type kjb::max ( const Vector &  vec )

inline

Return the maximum element in the vector.

Matrix::Value_type kjb::max ( const Matrix &  mat )

inline

Return the maximum value in this matrix.

Int_matrix::Value_type kjb::max_abs_difference ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Find the largest difference between two matrices.

That is, this method compares two matrices of the same size, computes the absolute values of the differences of corresponding elements, and returns the maximum.

Exceptions

Dimension_mismatch

if they differ in sizes

Int_vector::Value_type kjb::max_abs_difference ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Return the maximum of the absolute values of the elementwise difference between two vectors, provided they have the same length.

Exceptions

Dimension_mismatch,if

the lengths differ.

Matrix::Value_type kjb::max_abs_difference	(	const Matrix &	op1,
		const Matrix &	op2
	)

Find the largest difference between two matrices.

That is, this method compares two matrices of the same size, computes the absolute values of the differences of corresponding elements, and returns the maximum.

Exceptions

Dimension_mismatch

if they differ in sizes

Vector::Value_type kjb::max_abs_difference ( const Vector &  op1, const Vector &  op2  )

inline

Return the maximum of the absolute values of the elementwise difference between two vectors, provided they have the same length.

Exceptions

Dimension_mismatch,if

the lengths differ.

Int_matrix::Value_type kjb::min ( const Int_matrix &  mat )

inline

Return the minimum value in this matrix.

Vector::Value_type kjb::min ( const Vector &  vec )

inline

Return the minimum element in the vector.

Matrix::Value_type kjb::min ( const Matrix &  mat )

inline

Return the minimum value in this matrix.

Vector kjb::multiply_matrix_and_vector_d_dispatch_	(	const Matrix &	m,
		const double *	v,
		size_t	size
	)

dispatch for operator*(Matrix, Vector_d). This deals with a circular dependency between matrix.h and vector_d.h by moving template code into a cpp file. DO NOT CALL DIRECTLY!

template<size_t D>

double kjb::norm1

(

const kjb::Vector_d< D > &

v

)

double kjb::norm1 ( const Vector &  op )

inline

Compute L1-norm of vector.

This function is required for some KJB algorithms, and is required to adhere to the ModelParameters concept.

template<size_t D>

double kjb::norm2

(

const kjb::Vector_d< D > &

v

)

double kjb::norm2 ( const Int_vector &  op1 )

inline

Compute l2-norm of vector.

This function is required for some KJB algorithms, and is required to adhere to the ModelParameters concept.

double kjb::norm2 ( const Vector &  op1 )

inline

Compute L2-norm of vector.

This function is required for some KJB algorithms, and is required to adhere to the ModelParameters concept.

template<std::size_t N>

bool kjb::operator!=	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator!= ( const Int_matrix &  op1, const Int_matrix::Impl_type &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator!= ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator!= ( const Int_matrix::Impl_type &  op1, const Int_matrix &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator!= ( const Int_vector &  op1, const Int_vector::Impl_type &  op2  )

inline

Test for (any) inequality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator!= ( const Int_vector::Impl_type &  op1, const Int_vector &  op2  )

inline

Test for inequality between vectors.

This is an inline to allow the KJB C struct appear on the left side of the ==.

bool kjb::operator!= ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Test for (any) inequality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator!= ( const Vector &  op1, const Vector::Impl_type &  op2  )

inline

Test for (any) inequality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator!= ( const Vector::Impl_type &  op1, const Vector &  op2  )

inline

Test for inequality between vectors.

This is an inline to allow the KJB C struct appear on the left side of the ==.

bool kjb::operator!= ( const Vector &  op1, const Vector &  op2  )

inline

Test for (any) inequality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator!= ( const Matrix &  op1, const Matrix::Impl_type &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator!= ( const Matrix &  op1, const Matrix &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator!= ( const Matrix::Impl_type &  op1, const Matrix &  op2  )

inline

Test for any difference between two matrices.

Warning

Using floating point exact equality can be perilous.

Int_vector kjb::operator*	(	const Int_vector &	op1,
		const Int_matrix &	op2
	)

Return product of this (as a row-vec) times matrix on the right.

Semantics could be expressed as vT * M, where vT is this vector, as a row, and M is a matrix with the same number of rows as the length of vT.

Note

Prior to 1 Feb. 2010, this method was badly flawed.

template<std::size_t D>

Vector kjb::operator*	(	const Matrix &	m,
		const Vector_d< D >	v
	)

multiply by static vector

Int_vector kjb::operator*	(	const Int_matrix &	op1,
		const Int_vector &	op2
	)

Compute product of this matrix (on the left) and a column vector (on the right).

Exceptions

Dimension_mismatch

if the number of columns of this matrix does not equal the length of right factor op2.

template<std::size_t D>

Vector_d< D > kjb::operator*	(	const Vector_d< D > &	v,
		double	s
	)

template<std::size_t D>

Vector_d< D > kjb::operator*	(	double	s,
		const Vector_d< D > &	v
	)

Vector kjb::operator*	(	const Vector &	op1,
		const Matrix &	op2
	)

Return product of op1 (as a row-vec) times matrix on the right.

Semantics could be expressed as op1^T * M, where M is a matrix with the same number of rows as the length of op1^T.

Vector kjb::operator*	(	const Matrix &	op1,
		const Vector &	op2
	)

Compute product of this matrix (on the left) and a column vector (on the right).

Exceptions

Dimension_mismatch

if the number of columns of this matrix does not equal the length of right factor op2.

Int_matrix kjb::operator* ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Compute product of this matrix (on the left) and another.

Exceptions

Dimension_mismatch

if the number of columns of this matrix does not equal the number of rows of right factor op2.

Int_matrix kjb::operator* ( const Int_matrix &  op1, Int_matrix::Value_type  op2  )

inline

Compute the product of this matrix and a scalar, yielding a new matrix.

Int_matrix kjb::operator* ( Int_matrix::Value_type  op1, const Int_matrix &  op2  )

inline

Compute product of scalar and matrix, returning a new matrix.

Int_vector kjb::operator* ( const Int_vector &  op1, Int_vector::Value_type  op2  )

inline

Scalar multiply, resulting in a new vector, e.g., v * 6.

Int_vector kjb::operator* ( Int_vector::Value_type  op1, const Int_vector &  op2  )

inline

Scalar multiplication of a vector.

This is an inline to allow the scalar to appear on the left side of the operator.

Vector kjb::operator* ( const Vector &  op1, Vector::Value_type  op2  )

inline

Scalar multiply, resulting in a new vector, e.g., v * 6.

Vector kjb::operator* ( Vector::Value_type  op1, const Vector &  op2  )

inline

Scalar multiplication of a vector.

This is an inline to allow the scalar to appear on the left side of the operator.

Matrix kjb::operator* ( const Matrix &  op1, const Matrix &  op2  )

inline

Compute product of this matrix (on the left) and another.

Exceptions

Dimension_mismatch

if the number of columns of this matrix does not equal the number of rows of right factor op2.

Matrix kjb::operator* ( const Matrix &  op1, Matrix::Value_type  op2  )

inline

Compute the product of this matrix and a scalar, yielding a new matrix.

Matrix kjb::operator* ( Matrix::Value_type  op1, const Matrix &  op2  )

inline

Compute product of scalar and matrix, returning a new matrix.

template<std::size_t D>

Vector_d< D > kjb::operator+	(	const Vector_d< D > &	first,
		const Vector_d< D > &	second
	)

template<std::size_t D>

Vector_d< D > kjb::operator+	(	const Vector_d< D > &	first,
		double	second
	)

template<std::size_t D>

Vector_d< D > kjb::operator+	(	double	first,
		const Vector_d< D > &	second
	)

Int_matrix kjb::operator+ ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Compute matrix addition, returning a new matrix.

Int_vector kjb::operator+ ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Add two vectors, creating a new vector, e.g., v + w.

Vector kjb::operator+ ( const Vector &  op1, const Vector &  op2  )

inline

Add two vectors, creating a new vector, e.g., v + w.

Matrix kjb::operator+ ( const Matrix &  op1, const Matrix &  op2  )

inline

Compute matrix addition, returning a new matrix.

Matrix kjb::operator+ ( const Matrix &  op1, double  op2  )

inline

Compute matrix addition, returning a new matrix.

template<std::size_t D>

Vector_d< D > kjb::operator-	(	const Vector_d< D > &	first,
		const Vector_d< D > &	second
	)

template<std::size_t D>

Vector_d< D > kjb::operator-	(	const Vector_d< D > &	first,
		double	second
	)

template<std::size_t D>

Vector_d< D > kjb::operator-	(	double	first,
		const Vector_d< D > &	second
	)

template<std::size_t D>

Vector_d< D > kjb::operator-

(

const Vector_d< D > &

first

)

Int_matrix kjb::operator- ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Compute matrix difference, returning a new matrix.

Int_matrix kjb::operator- ( const Int_matrix &  op1 )

inline

Return the additive inverse of this matrix.

Int_vector kjb::operator- ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Subtract one vector from another, resulting in a new vector, e.g., v - w.

Int_vector kjb::operator- ( const Int_vector &  op1 )

inline

Return the negation of a vector, as in (-v), resulting in a new vector.

Vector kjb::operator- ( const Vector &  op1, const Vector &  op2  )

inline

Subtract one vector from another, resulting in a new vector, e.g., v - w.

Vector kjb::operator- ( const Vector &  op1 )

inline

Return the negation of a vector, as in (-v), resulting in a new vector.

Matrix kjb::operator- ( const Matrix &  op1, const Matrix &  op2  )

inline

Compute matrix difference, returning a new matrix.

Matrix kjb::operator- ( const Matrix &  op1, double  op2  )

inline

Compute matrix difference, returning a new matrix.

Matrix kjb::operator- ( const Matrix &  op1 )

inline

Return the additive inverse of this matrix.

template<std::size_t D>

Vector_d< D > kjb::operator/	(	const Vector_d< D > &	v,
		double	s
	)

Int_matrix kjb::operator/ ( const Int_matrix &  op1, Int_matrix::Value_type  op2  )

inline

Compute new matrix equal to lefthand matrix with each entry divided by a scalar value.

Exceptions

Divide_by_zero

if the given value is zero.

Warning

This uses integer division, truncating fractions toward zero.

Int_vector kjb::operator/ ( const Int_vector &  op1, Int_vector::Value_type  op2  )

inline

Scalar integer division, yielding a new vector.

Vector kjb::operator/ ( const Vector &  op1, Vector::Value_type  op2  )

inline

Scalar division, yielding a new vector.

Matrix kjb::operator/ ( const Matrix &  op1, Matrix::Value_type  op2  )

inline

Compute new matrix equal to lefthand matrix with each entry divided by a scalar value.

Exceptions

Divide_by_zero

if the given value is zero.

Int_matrix & kjb::Int_matrix::operator/=

(

Int_matrix::Value_type

op2

)

Perform integer division on each entry in the matrix by a scalar value.

Returns

an lvalue to this matrix

Warning

This uses integer division, truncating fractions toward zero.

Exceptions

Divide_by_zero

if the scalar value is zero.

Int_vector & kjb::Int_vector::operator/=

(

Value_type

op2

)

Scalar integer division of self, in-place.

bool kjb::operator<	(	const Int_vector &	op1,
		const Int_vector &	op2
	)

Test weak lexicographic ordering between vectors.

template<std::size_t N>

bool kjb::operator<	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator<	(	const Vector &	op1,
		const Vector &	op2
	)

Test weak lexicographic ordering between vectors.

bool kjb::operator< ( const Matrix &  op1, const Matrix &  op2  )

inline

Returns true if a is lexicographically less-than b.

template<std::size_t D>

std::ostream & kjb::operator<<	(	std::ostream &	out,
		const Vector_d< D > &	v
	)

std::ostream & kjb::operator<<	(	std::ostream &	out,
		const Int_matrix &	m
	)

Display matrix contents in an ASCII format.

This routine is mostly for debugging; consider one of the many KJB output routines for more output in a more standardized form.

std::ostream & kjb::operator<<	(	std::ostream &	out,
		const Int_vector &	m
	)

Display vector contents in an ASCII format.

This routine is mostly for debugging; consider one of the many KJB output routines for more output in a more standardized form.

std::ostream & kjb::operator<<	(	std::ostream &	out,
		const Vector &	m
	)

Display vector contents in an ASCII format.

This routine is mostly for debugging; consider one of the many KJB output routines for more output in a more standardized form.

std::ostream & kjb::operator<<	(	std::ostream &	out,
		const Matrix &	m
	)

Display matrix contents in an ASCII format.

This routine is mostly for debugging; consider one of the many KJB output routines for more output in a more standardized form.

template<std::size_t N>

bool kjb::operator<=	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator<= ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Test lexicographic ordering between vectors.

bool kjb::operator<= ( const Vector &  op1, const Vector &  op2  )

inline

Test lexicographic ordering between vectors.

bool kjb::operator==	(	const Int_matrix &	op1,
		const Int_matrix::Impl_type &	op2
	)

Test for exact equality between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator==	(	const Int_vector &	op1,
		const Int_vector::Impl_type &	op2
	)

Test for exact equality between vectors.

Warning

Exact comparison of floating-point values is perilous.

template<std::size_t N>

bool kjb::operator==	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator==	(	const Vector &	op1,
		const Vector::Impl_type &	op2
	)

Test for exact equality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator==	(	const Matrix &	op1,
		const Matrix::Impl_type &	op2
	)

Test for exact equality between two matrices.

Kludge:

Should have a separate function for approximate equality with a threshold. Consult w/Luca, as it's his change. –Kyle CVPR 2010

Warning

Using floating point exact equality can be perilous.

bool kjb::operator== ( const Int_matrix &  op1, const Int_matrix &  op2  )

inline

Test for exact equality between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator== ( const Int_matrix::Impl_type &  op1, const Int_matrix &  op2  )

inline

Test for exact equality between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator== ( const Int_vector::Impl_type &  op1, const Int_vector &  op2  )

inline

Test for exact equality between vectors.

This is an inline to allow the KJB C struct appear on the left side of the ==.

bool kjb::operator== ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Test for exact equality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator== ( const Vector::Impl_type &  op1, const Vector &  op2  )

inline

Test for exact equality between vectors.

This is an inline to allow the KJB C struct appear on the left side of the ==.

bool kjb::operator== ( const Vector &  op1, const Vector &  op2  )

inline

Test for exact equality between vectors.

Warning

Exact comparison of floating-point values is perilous.

bool kjb::operator== ( const Matrix &  op1, const Matrix &  op2  )

inline

Test for exact equality between two matrices.

Warning

Using floating point exact equality can be perilous.

bool kjb::operator== ( const Matrix::Impl_type &  op1, const Matrix &  op2  )

inline

Test for exact equality between two matrices.

Warning

Using floating point exact equality can be perilous.

template<std::size_t N>

bool kjb::operator>	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator> ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Test lexicographic ordering between vectors.

bool kjb::operator> ( const Vector &  op1, const Vector &  op2  )

inline

Test lexicographic ordering between vectors.

template<std::size_t N>

bool kjb::operator>=	(	const Vector_d< N > &	first,
		const Vector_d< N > &	second
	)

bool kjb::operator>= ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Test lexicographic ordering between vectors.

bool kjb::operator>= ( const Vector &  op1, const Vector &  op2  )

inline

Test lexicographic ordering between vectors.

template<std::size_t D>

std::istream & kjb::operator>>	(	std::istream &	ist,
		Vector_d< D > &	v
	)

std::istream& kjb::operator>> ( std::istream &  ist, Index_range &  ir  )

inline

Read Index range from a text stream. Assumes string has no whitespace

Matrix kjb::outer_product ( const Vector &  v1, const Vector &  v2  )

inline

Compute the outer-product (dyadic product) of two vectors.

Int_vector & kjb::Int_vector::randomize

(

int

length

)

Clobber current vector; resize and fill with random values.

Returns

an lvalue to this object

See Also

rand(3)

Random values are uniformly distributed between 0 and RAND_MAX.

Int_matrix & kjb::Int_matrix::resize	(	int	new_rows,
		int	new_cols,
		Value_type	pad = Value_type(0)
	)

Resize this matrix, retaining previous values.

Int_vector & kjb::Int_vector::resize	(	int	new_length,
		Value_type	pad = Value_type(0)
	)

Resize vector, retaining previous values.

template<class OutputIterator >

OutputIterator kjb::separate_vector	(	const Vector &	vec,
		int	sz,
		OutputIterator	result
	)

Separate the given vector into vectors of the give size; the vectors will be output into the output iterator.

template<class Generic_vector >

void kjb::Int_matrix::set_col	(	int	col,
		const Generic_vector &	v
	)

Replace a column of the matrix with the given vector. "vector" can be any collection of values convertible to int.

template<class Iterator >

void kjb::Int_matrix::set_col	(	int	col,
		Iterator	begin,
		Iterator	end
	)

Dispatch for set_col. Don't call directly.

template<class Generic_vector >

void kjb::Matrix::set_col	(	int	col,
		const Generic_vector &	v
	)

Replace a column of the matrix with the given vector. "vector" can be any collection of values convertible to double.

template<class Iterator >

void kjb::Matrix::set_col	(	int	col,
		Iterator	begin,
		Iterator	end
	)

Dispatch for set_col. Don't call directly.

template<class Generic_vector >

void kjb::Int_matrix::set_row	(	int	row,
		const Generic_vector &	v
	)

Replace a row of the matrix with the given vector.

template<class Iterator >

void kjb::Int_matrix::set_row	(	int	row,
		Iterator	begin,
		Iterator	end
	)

Dispatch for set_row. Don't call directly.

template<class Generic_vector >

void kjb::Matrix::set_row	(	int	row,
		const Generic_vector &	v
	)

Replace a row of the matrix with the given vector.

template<class Iterator >

void kjb::Matrix::set_row	(	int	row,
		Iterator	begin,
		Iterator	end
	)

Dispatch for set_row. Don't call directly.

Matrix kjb::shift_columns_by ( const Matrix &  op1, const Vector &  op2  )

inline

Add the same vector to each column, return a new Matrix.

Author

Colin Dawson

Matrix kjb::shift_rows_by ( const Matrix &  op1, const Vector &  op2  )

inline

Add the same vector to each row, return a new Matrix.

Author

Colin Dawson

std::istream & kjb::stream_read_vector	(	std::istream &	ist,
		Vector &	m
	)

Read vector from an input stream.

Vector is assumed to have been written using stream_write_vector().

If you aren't using boost serialization, this is the preferred way to de-serialize a vector.

std::ostream & kjb::stream_write_vector	(	std::ostream &	ost,
		const Vector &	m
	)

Write vector to an output stream so it can be read with read_vector.

If you aren't using boost serialization, this is the preferred way to serialize a vector for later reading with stream_read_vector.

Warning

In general, using operator<< is NOT recommended for serialization, because the vector length is not written

Matrix::Vec_type kjb::sum_matrix_cols

(

const Matrix &

)

Compute the matrix's sum across columns (a.k.a. row-wise sum)

Returns

A vector of length m.get_num_rows() whose ith element is m(i,0) + m(i,1) + ...

This is a thin wrapper around kjb_c::sum_matrix_cols.

Matrix::Vec_type kjb::sum_matrix_rows

(

const Matrix &

)

Compute the matrix's sum down (a.k.a. columnar sum), like MATLAB.

Returns

A vector of length m.get_num_cols() whose ith element is m(0,i) + m(1,i) + ...

This is a thin wrapper around kjb_c::sum_matrix_rows.

double kjb::sum_squared_elements ( const Matrix &  mat )

inline

Compute the sum of squared elements.

template<std::size_t N>

void kjb::swap	(	Vector_d< N > &	first,
		Vector_d< N > &	second
	)

void kjb::swap ( Index_range &  r1, Index_range &  r2  )

inline

Matrix kjb::tile_matrix	(	Matrix	trixy,
		unsigned	m,
		unsigned	n
	)

Construct a tiling of the given matrix.

Author

Josh Bowdish

Note

should be roughly the same as matlab's repmat()

Matrix kjb::tile_matrix	(	int	tehnum,
		unsigned	m,
		unsigned	n
	)

Construct a tiling of the given matrix, in this case, a matrix of the given number with the specified size.

Author

Josh Bowdish

Note

should be roughly the same as matlab's repmat()

Deprecated:

Warning

do not use this, just use a constructor instead.

Deprecated on 17 July 2013. Remove in 6 months (after 16 January 2014).

template<std::size_t D>

double kjb::vector_distance	(	const Vector_d< D > &	op1,
		const Vector_d< D > &	op2
	)

Compute the Euclidian distance between two vectors.

A routine that computes the distance between two vectors

double kjb::vector_distance ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Compute the Euclidian distance between two vectors.

A routine that computes the distance between two vectors

double kjb::vector_distance ( const Vector &  op1, const Vector &  op2  )

inline

Compute the Euclidian distance between two vectors.

A routine that computes the distance between two vectors

template<std::size_t D>

double kjb::vector_distance_squared	(	const Vector_d< D > &	op1,
		const Vector_d< D > &	op2
	)

Compute the Euclidian distance between two vectors.

A routine that computes the distance between two vectors

double kjb::vector_distance_squared ( const Int_vector &  op1, const Int_vector &  op2  )

inline

Compute the square of the Euclidian distance between two vectors.

A routine that computes the square of the distance between two vectors

double kjb::vector_distance_squared ( const Vector &  op1, const Vector &  op2  )

inline

Compute the square of the Euclidian distance between two vectors.

A routine that computes the square of the distance between two vectors