HepMatrix


The HepMatrix class does all the obvious things, in all the obvious ways.

Authors

Nobu Katayama and Mike Smyth

See also

HepGenMatrix, HepSymMatrix, HepDiagMatrix, HepVector, HepPile,

Declaration

#include "CLHEP/Matrix/Matrix.h"

class HepMatrix : public HepGenMatrix

Public Member Classes

HepMatrix_row
Helper class to implement m[i][j]
Declaration
class HepMatrix_row
Constructor
inline HepMatrix_row(HepMatrix&, int)
[]
HepDouble & operator[](int)

HepMatrix_row_const
Helper class to implement m[i][j]
Declaration
class HepMatrix_row_const
Constructor
inline HepMatrix_row_const(const HepMatrix&, int)
[]
const HepDouble & operator[](int) const

Public Member Functions

Constructor
inline HepMatrix()
Default constructor. Gives 0 x 0 matrix. Another Matrix can be assigned to it.
Constructor
HepMatrix(int p, int q)
Gives an unitialized p x q matrix.
Constructor
HepMatrix(int p, int q, int i)
Gives an initialized p x q matrix.
If i=0, it is initialized to all 0. If i=1, the diagonal elements are set to 1.
Constructor
#ifdef HEP_USE_RANDOM
HepMatrix(int p, int q, HepRandom &r)
#endif
Constructor with a Random object.
Constructor
HepMatrix(const HepSymMatrix &m1)
Constructor from HepSymMatrix.
Constructor
HepMatrix(const HepDiagMatrix &m1)
Constructor from HepDiagMatrix.
Constructor
HepMatrix(const HepVector &m1)
Constructor from HepVector.
Copy constructor
HepMatrix(const HepMatrix &m1)
Destructor
virtual ~HepMatrix()
=
HepMatrix & operator = (const HepMatrix &m2)
HepMatrix & operator = (const HepSymMatrix &m2)
HepMatrix & operator = (const HepDiagMatrix &m2)
HepMatrix & operator = (const HepVector &m2)
HepMatrix & operator = (const HepRotation &m2)
Assignment operators.
+=
HepMatrix & operator += (const HepMatrix &m2)
HepMatrix & operator += (const HepSymMatrix &m2)
HepMatrix & operator += (const HepDiagMatrix &m2)
HepMatrix & operator += (const HepVector &m2)
Add a Matrix.
When adding Vector, Matrix must have num_col of one.
-
HepMatrix operator - () const
Unary minus, i.e. flip the sign of each element.
-=
HepMatrix & operator -= (const HepMatrix &m2)
HepMatrix & operator -= (const HepSymMatrix &m2)
HepMatrix & operator -= (const HepDiagMatrix &m2)
HepMatrix & operator -= (const HepVector &m2)
Subtract a Matrix.
When subtracting Vector, Matrix must have num_col of one.
*=
HepMatrix & operator *= (HepDouble t)
Multiply a Matrix by a floating number.
/=
HepMatrix & operator /= (HepDouble t)
Divide a Matrix by a floating number.
()
inline virtual const HepDouble & operator()(int row, int col) const
inline virtual HepDouble & operator()(int row, int col)
Read or write a matrix element.
** Note that the indexing starts from (1,1) **
[]
inline HepMatrix_row operator[] (int)
inline const HepMatrix_row_const operator[] (int) const
Read or write a matrix element.
While it may not look like it, you simply do m[i][j] to get an element.
** Note that the indexing starts from [0][0] **
apply
HepMatrix apply(HepDouble (*f)(HepDouble, int, int)) const
Apply a function to all elements of the matrix.
determinant
HepDouble determinant() const
Calculate the determinant of the matrix.
inverse
inline HepMatrix inverse(int& ierr) const
Invert a Matrix. Matrix must be square and is not changed.
Returns ierr = 0 (zero) when successful, otherwise non-zero.
invert
virtual void invert(int& ierr)
Invert a Matrix. Matrix must be square.
N.B. the contents of the matrix are replaced by the inverse.
Returns ierr = 0 (zero) when successful, otherwise non-zero.
This method has less overhead then inverse().
num_col
inline virtual int num_col() const
Returns the number of columns.
num_row
inline virtual int num_row() const
Returns the number of rows.
sub
HepMatrix sub(int min_row, int max_row, int min_col, int max_col) const
Returns a sub matrix of a Matrix.
WARNING: rows and columns are numbered from 1.

void sub(int row, int col, const HepMatrix &m1)
Sub matrix of this Matrix is replaced with m1.
WARNING: rows and columns are numbered from 1.
T
HepMatrix T() const
Returns the transpose of a Matrix.
trace
HepDouble trace() const
Calculate the trace of the matrix (sum of diagonal elements).

Non-Member Functions

+
HepMatrix operator + (const HepMatrix &m1, const HepMatrix &m2)
Adds two matrices.
Note that m += m1 is always faster than m = m + m1.
-
HepMatrix operator - (const HepMatrix &m1, const HepMatrix &m2)
Subtracts two matrices.
Note that m -= m1 is always faster than m = m - m1.
*
HepMatrix operator * (const HepMatrix &m1, const HepMatrix &m2)
HepMatrix operator * (const HepMatrix &m1, const HepSymMatrix &m2)
HepMatrix operator * (const HepMatrix &m1, const HepDiagMatrix &m2)
HepMatrix operator * (const HepSymMatrix &m1, const HepMatrix &m2)
HepMatrix operator * (const HepDiagMatrix &m1, const HepMatrix &m2)
HepMatrix operator * (const HepVector &m1, const HepMatrix &m2)
HepVector operator * (const HepMatrix &m1, const HepVector &m2)
HepMatrix operator * (const HepSymMatrix &m1, const HepSymMatrix &m2)
Multiply a Matrix by a Matrix or Vector.
Note that m *= m1 is always faster than m = m * m1.

HepMatrix operator * (HepDouble t, const HepMatrix &m1)
HepMatrix operator * (const HepMatrix &m1, HepDouble t)
Multiplication with a number.
/
HepMatrix operator / (const HepMatrix &m1, HepDouble t)
Division with a number.
Note that m /= t is faster if you can use it.
<<
ostream & operator << (ostream &s, const HepMatrix &q)
Output to a stream.
back_solve
void back_solve(const HepMatrix &R, HepVector *b)
void back_solve(const HepMatrix &R, HepMatrix *b)
Solves R*x = b where R is upper triangular.
Also has a variation that solves a number of equations of this form in one step, where b is a matrix with each column a different vector.
See also solve.
col_givens
void col_givens(HepMatrix *A, HepDouble c, HepDouble s, int k1, int k2, int row_min=1, int row_max=0)
Does a column Givens update.
col_house
void col_house(HepMatrix *a, const HepMatrix &v, HepDouble vnormsq, int row, int col, int row_start, int col_start)
void col_house(HepMatrix *a, const HepMatrix &v, int row, int col, int row_start, int col_start)
Does a column Householder update.
dsum
HepMatrix dsum(const HepMatrix &, const HepMatrix &)
Direct sum of two matrices.
The direct sum of A and B is the matrix:
          A 0
          0 B
givens
void givens(HepDouble a, HepDouble b, HepDouble *c, HepDouble *s)
Agorithm 5.1.5 in Golub and Van Loan
house
HepVector house(const HepMatrix &a, int row=1, int col=1)
Returns a Householder vector to zero elements.
house_with_update
void house_with_update(HepMatrix *a, int row=1, int col=1)
void house_with_update(HepMatrix *a, HepMatrix *v, int row=1, int col=1)
Finds and does Householder reflection on matrix.
qr_decomp
void qr_decomp(HepMatrix *A, HepMatrix *hsm)
HepMatrix qr_decomp(HepMatrix *A)
Does a QR decomposition of a matrix.
qr_inverse
HepMatrix qr_inverse(const HepMatrix &A)
HepMatrix qr_inverse(HepMatrix *A)
Finds the inverse of a matrix using QR decomposition.
Note, often what you really want is solve or back_solve, they can be much quicker than inverse in many calculations.
qr_solve
HepVector qr_solve(const HepMatrix &A, const HepVector &b)
HepVector qr_solve(HepMatrix *A, const HepVector &b)
HepMatrix qr_solve(const HepMatrix &A, const HepMatrix &b)
HepMatrix qr_solve(HepMatrix *A, const HepMatrix &b)
Works like back_solve, except matrix does not need to be upper triangular. For nonsquare matrix, it solves in the least square sense.
row_givens
void row_givens(HepMatrix *A, HepDouble c, HepDouble s, int k1, int k2, int col_min=1, int col_max=0)
Does a row Givens update.
row_house
void row_house(HepMatrix *a, const HepVector &v, HepDouble vnormsq, int row=1, int col=1)
void row_house(HepMatrix *a, const HepMatrix &v, HepDouble vnormsq, int row, int col, int row_start, int col_start)
void row_house(HepMatrix *a, const HepMatrix &v, int row, int col, int row_start, int col_start)
Does a row Householder update.
solve
HepVector solve(const HepMatrix &, const HepVector &)
Solve the system of linear equations using LU decomposition.
swap
inline void swap(HepMatrix &m1, HepMatrix &m2)
Swap m1 with m2.

Example

CLHEP/test/testMatrix.cc


6 October 1997
EVC