This is very much like the HepMatrix, except of course it is
restricted to Symmetric Matrix. All the operations for HepMatrix
can also be done here (except for the +=, -=, *= that don't
yield a symmetric matrix. e.g. +=(const Matrix &) is not defined)
The matrix is stored as a lower triangular matrix.
In addition to the (row, col) method of finding element,
fast(row, col) returns an element with checking to see if
row and col need to be interchanged so that
row >= col.
Author
Mike Smyth
See also
HepGenMatrix,
HepMatrix,
HepDiagMatrix,
HepVector,
HepPile,
Declaration
#include "CLHEP/Matrix/SymMatrix.h"
class HepSymMatrix : public HepGenMatrix
Public Member Classes
- HepSymMatrix_row
- Helper class to implement m[i][j]
- Declaration
- class HepSymMatrix_row
- Constructor
- inline HepSymMatrix_row(HepSymMatrix&, int)
- []
- inline HepDouble & operator[](int)
- HepSymMatrix_row_const
- Helper class to implement m[i][j]
- Declaration
- class HepSymMatrix_row_const
- Constructor
- inline HepSymMatrix_row_const(const HepSymMatrix&, int)
- []
- inline const HepDouble & operator[](int) const
Public Member Functions
- Constructor
- inline HepSymMatrix()
- Default constructor. Gives 0 x 0 symmetric matrix.
Another HepSymMatrix can be assigned to it.
- Constructor
- HepSymMatrix(int p)
- HepSymMatrix(int p, int)
- Gives p x p symmetric matrix.
With a second argument, the matrix is initialized.
0 means a zero matrix, 1 means the identity matrix.
- Constructor
- #ifdef HEP_USE_RANDOM
- HepSymMatrix(int p, HepRandom &r)
- #endif
- Constructor with a Random object.
- Constructor
- HepSymMatrix(const HepDiagMatrix &m1)
- Constructor from HepDiagMatrix.
- Copy constructor
- HepSymMatrix(const HepSymMatrix &m1)
- Destructor
- virtual ~HepSymMatrix()
- =
- HepSymMatrix & operator = (const HepSymMatrix &m2)
- HepSymMatrix & operator = (const HepDiagMatrix &m2)
- Assignment operators. Notice that there is no
HepSymMatrix = HepMatrix.
- +=
- HepSymMatrix & operator += (const HepSymMatrix &m2)
- HepSymMatrix & operator += (const HepDiagMatrix &m2)
- Add a HepSymMatrix.
- -
- HepSymMatrix operator - () const
- Unary minus, i.e. flip the sign of each element.
- -=
- HepSymMatrix & operator -= (const HepSymMatrix &m2)
- HepSymMatrix & operator -= (const HepDiagMatrix &m2)
- Subtract a HepSymMatrix.
- *=
- HepSymMatrix & operator *= (HepDouble t)
- Multiply a HepSymMatrix by a floating number.
- /=
- HepSymMatrix & operator /= (HepDouble t)
- Divide a HepSymMatrix by a floating number.
- ()
- const HepDouble & operator()(int row, int col) const
- HepDouble & operator()(int row, int col)
- Read and write a HepSymMatrix element.
** Note that indexing starts from (1,1) **
- []
- inline HepSymMatrix_row operator[] (int)
- inline HepSymMatrix_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
- HepSymMatrix apply(HepDouble (*f)(HepDouble, int, int)) const
- Apply a function to all elements of the matrix.
- assign
- void assign(const HepMatrix &m2)
- Assigns m2 to s, assuming m2 is a
symmetric matrix.
- void assign(const HepSymMatrix &)
- Another form of assignment. For consistency.
- determinant
- HepDouble determinant() const
- Calculate the determinant of the matrix.
- fast
- const HepDouble & fast(int row, int col) const
- HepDouble & fast(int row, int col)
- Fast element access. Must be row >= col.
** Note that indexing starts from (1,1) **
- inverse
- inline HepSymMatrix inverse(int &ifail) const
- Invert a HepSymMatrix. The matrix is not changed.
Returns 0 when successful, otherwise non-zero.
This inverse function has been taken from dsinv
of CERNLIB. This function works with symmetric positive
definit matrix only. If the the matrix is NOT positive definit,
the inverse returns ifail of non-zero.
Be sure to check this.
- invert
- void invert(int &ifail)
- Invert a HepSymMatrix.
N.B. the contents of the matrix are replaced by the inverse.
Returns ifail = 0 (zero) when successful,
otherwise non-zero.
This method has less overhead then inverse().
This invert function has been taken from dsinv
of CERNLIB. This function works with symmetric positive
definit matrix only. If the the matrix is NOT positive definit,
the invert returns ifail of non-zero.
Be sure to check this.
- num_col
- inline int num_col() const
- Returns number of columns.
- num_row
- inline int num_row() const
- Returns number of rows.
- similarity
- HepSymMatrix similarity(const HepMatrix &m1) const
- HepSymMatrix similarity(const HepSymMatrix &m1) const
- Returns m1*s*m1.T()
- HepDouble similarity(const HepVector &v) const
- Returns v.T()*s*v (This is a scaler).
- similarityT
- HepSymMatrix similarityT(const HepMatrix &m1) const
- Temporary. Test of new similarity.
Returns m1.T()*s*m1
- sub
- HepSymMatrix sub(int min_row, int max_row) const
- Returns a sub matrix of a HepSymMatrix.
- void sub(int row, const HepSymMatrix &m1)
- Sub matrix of this HepSymMatrix is replaced with m1.
- #ifdef HEP_CC_NEED_SUB_WITHOUT_CONST
- HepSymMatrix sub(int min_row, int max_row)
- #endif
- SGI CC bug. I have to have both with/without const.
I should not need one without const.
- T
- HepSymMatrix T() const
- Returns the transpose of a HepSymMatrix (which is itself).
- trace
- HepDouble trace() const
- Calculate the trace of the matrix (sum of diagonal elements).
Non-Member Functions
- +
- HepMatrix operator + (const HepMatrix &m1,
const HepSymMatrix &s2)
- HepMatrix operator + (const HepSymMatrix &s1,
const HepMatrix &m2)
- HepSymMatrix operator + (const HepSymMatrix &s1,
const HepSymMatrix &s2)
- Addition operators.
- -
- HepMatrix operator - (const HepMatrix &m1,
const HepSymMatrix &s2)
- HepMatrix operator - (const HepSymMatrix &s1,
const HepMatrix &m2)
- HepSymMatrix operator - (const HepSymMatrix &s1,
const HepSymMatrix &s2)
- Subtraction operators.
- *
- HepMatrix operator * (const HepMatrix &m1,
const HepSymMatrix &m2)
- HepMatrix operator * (const HepSymMatrix &m1,
const HepMatrix &m2)
- HepMatrix operator * (const HepSymMatrix &m1,
const HepSymMatrix &m2)
- HepVector operator * (const HepSymMatrix &m1,
const HepVector &m2)
- Multiplication operators.
Note that m *= m1 is always faster than m = m * m1
- HepSymMatrix operator * (HepDouble t,
const HepSymMatrix &s1)
- HepSymMatrix operator * (const HepSymMatrix &s1,
HepDouble t)
- Multiplication with a number.
- /
- HepSymMatrix operator / (const HepSymMatrix &s1,
HepDouble t)
- Division with a number.
Note that s /= t is faster if you can use it.
- <<
- HepStd::ostream & operator << (HepStd::ostream &s,
const HepSymMatrix &q)
- Output to a stream.
- condition
- HepDouble condition(const HepSymMatrix &m)
- Find the condition number of a symmetric matrix.
- diagonalize
- HepMatrix diagonalize(HepSymMatrix *s)
- Diagonalize a symmetric matrix.
- It returns the matrix U so that
s_old = U * s_diag * U.T()
- diag_step
- void diag_step(HepSymMatrix *t, int begin, int end)
- void diag_step(HepSymMatrix *t, HepMatrix *u, int begin,
int end)
- Implicit symmetric QR step with Wilkinson Shift.
- dsum
- HepSymMatrix dsum(const HepSymMatrix &s1,
const HepSymMatrix &s2)
- Direct sum of two symmetric matrices.
- house
- HepVector house(const HepSymMatrix &a, int row=1,
int col=1)
- Returns a Householder vector to zero elements.
- house_with_update2
- void house_with_update2(HepSymMatrix *a, HepMatrix *v, int row=1,
int col=1)
- Finds and does Householder reflection on matrix.
- tridiagonal
- void tridiagonal(HepSymMatrix *a, HepMatrix *hsm)
- HepMatrix tridiagonal(HepSymMatrix *a)
- Does a Householder tridiagonalization of a symmetric matrix.
- vT_times_v
- HepSymMatrix vT_times_v(const HepVector &v)
Example
CLHEP/test/testMatrix.cc
19 June 2001
EVC