gausselim< T > Class Template Reference

Gaussian Elimination state machine. More...

#include <gausselim.h>

Collaboration diagram for gausselim< T >:

List of all members.

Public Member Functions
	gausselim (T *mat_, uintc dim_)
	Supply matrix A and C for equation AX = C.
	~gausselim ()
	Memory cleanup.
boolc	eval ()
	Solve the system for a diagonal of ones.
void	columnC (T *C) const
	Gets column C.
void	rowget (uintc i)
	Writes the row to x.
void	rowput (uintc i)
	Writes x to the i'th row.
void	mult (T const alpha)
	alpha*x -> x.
void	swap (uintc i, uintc k)
	Swap the rows.
void	norm (uintc row, uintc col)
	Normalize by dividing the row by mat[row][col].
boolc	pivot (uintc k)
	Pivotes the row with the highest magitude in the k'th column of rows k,k+1,.
void	substitute (uintc i)
	Normalize i and substitue into all other equations.
	operator stringc () const
	Serialize this object by writing it out as a string.
Public Attributes
T *	mat
	Matrix {A,C} where AX=C.
T *	row
	Tempory row variable.
uintc	dim
	dim=N.

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Detailed Description

template<typename T>
class gausselim< T >

Gaussian Elimination state machine.

Features: partial pivoting. Reference: An Introduction to Numerical Analysis by K. Atkinson, 2nd edition, pages 515+ .

Example

    //x + 5y = 11
    //x + y + z = 0
    //2x + z = -1
    double e3[] = 
    {
      1.0, 5.0, 0.0, 11.0,
      1.0, 1.0, 1.0, 0.0,
      2.0, 0.0, 1.0, -1.0
    };
    gausselim<double> g(e3,3);
    g.eval();
    g.print();

Definition at line 34 of file gausselim.h.

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Constructor & Destructor Documentation

template<typename T>

gausselim< T >::gausselim	(	T *	mat_,
		uintc	dim_
	)			[inline]

Supply matrix A and C for equation AX = C.

Definition at line 47 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::row.

    : mat(mat_), dim(dim_)
    { row = new T[dim+1]; }

template<typename T>

gausselim< T >::~gausselim

(

)

[inline]

Memory cleanup.

Definition at line 51 of file gausselim.h.

References gausselim< T >::row.

    { delete[] row; }

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Member Function Documentation

template<typename T >

void gausselim< T >::columnC

(

T *

C

)

const [inline]

Gets column C.

After solving the equation, lets you extract the solution.

Definition at line 94 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::mat.

Referenced by tetrahedron< PT, PD >::circumcenter(), and gausselimtest::test02().

{
  for (uint i=0; i<dim; ++i)
    C[i] = mat[3+i*4];
}

template<typename T >

boolc gausselim< T >::eval

(

)

[inline]

Solve the system for a diagonal of ones.

The last column C is the solution to the system.

Definition at line 101 of file gausselim.h.

References gausselim< T >::dim, gausselim< T >::pivot(), and gausselim< T >::substitute().

Referenced by tetrahedron< PT, PD >::circumcenter(), gausselimtest::test01(), and gausselimtest::test02().

{
  for (uint i=0; i<dim; ++i)
  {
    if (pivot(i)==false)
      return false;

    substitute(i);
  }

  return true;
}

template<typename T >

void gausselim< T >::mult

(

T const

alpha

)

[inline]

alpha*x -> x.

Definition at line 194 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::row.

{
  for (uint i=0; i<dim+1; ++i)
    row[i] *= alpha;
}

template<typename T >

void gausselim< T >::norm	(	uintc	row,
		uintc	col
	)			[inline]

Normalize by dividing the row by mat[row][col].

Definition at line 201 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::mat.

Referenced by gausselim< T >::substitute().

{
  assert(row<dim);
  assert(col<dim);

  uint b = row*(dim+1);

  T alpha = mat[b+col];
  if (alpha==0)
    return;

  alpha = 1.0/alpha;

  for (uint i=0; i<dim+1; ++i)
    mat[b++] *= alpha;
}

template<typename T >

gausselim< T >::operator stringc

(

)

const [inline]

Serialize this object by writing it out as a string.

Definition at line 238 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::mat.

{
  stringstream ss;
  
  for (uint i=0; i<dim; ++i)
  {
    for (uint k=0; k<dim+1; ++k)
    {
      ss << mat[i*(dim+1)+k] << " ";
    }
    if (i!=dim-1)
      ss << "\n";
  }

  return ss.str();
}

template<typename T >

boolc gausselim< T >::pivot

(

uintc

k

)

[inline]

Pivotes the row with the highest magitude in the k'th column of rows k,k+1,.

.,N-1.

Definition at line 143 of file gausselim.h.

References gausselim< T >::dim, gausselim< T >::mat, and gausselim< T >::swap().

Referenced by gausselim< T >::eval().

{
  assert(k<dim);

  T lgnum = mat[ k*(dim+1) + k ];
  T lgnum2 = lgnum*lgnum;
  uint lgi = k;
  T x;
  T x2;
  for (uint i=k+1; i<dim; ++i)
  {
    x = mat[ i*(dim+1) + k ];
    x2 = x*x;
    if (x2>lgnum2)
    {
      lgnum2 = x2;
      lgnum = x;
      lgi = i;
    }
  }

  if (k!=lgi)
    swap(k,lgi);

  if (lgnum2 < zero<T>::val )
    return false;

  return true;
}

template<typename T >

void gausselim< T >::rowget

(

uintc

i

)

[inline]

Writes the row to x.

Definition at line 174 of file gausselim.h.

References gausselim< T >::dim, gausselim< T >::mat, and gausselim< T >::row.

Referenced by gausselim< T >::substitute().

{
  assert(i<dim);

  uint b = i*(dim+1);
  for (uint k=0; k<dim+1; ++k)
    row[k] = mat[b+k];
} 

template<typename T >

void gausselim< T >::rowput

(

uintc

i

)

[inline]

Writes x to the i'th row.

Definition at line 184 of file gausselim.h.

References gausselim< T >::dim, gausselim< T >::mat, and gausselim< T >::row.

{
  assert(i<dim);

  uint b = i*(dim+1);
  for (uint k=0; k<dim+1; ++k)
    mat[b+k] = row[k];
} 

template<typename T >

void gausselim< T >::substitute

(

uintc

i

)

[inline]

Normalize i and substitue into all other equations.

Definition at line 115 of file gausselim.h.

References gausselim< T >::dim, gausselim< T >::mat, gausselim< T >::norm(), r, gausselim< T >::row, and gausselim< T >::rowget().

Referenced by gausselim< T >::eval().

{
  norm(k,k);

  rowget(k);
  for (uint i=0; i<dim+1; ++i)
    row[i] *= -1;

  uint b=0;
  T r;

  for (uint i=0; i<dim; ++i)
  {
    if (i==k)
    {
      b += (dim+1);
      continue;
    }

    r = mat[b+k];

    for (uint m=0; m<dim+1; ++m)
      mat[b++] += row[m]*r;
  }

}

template<typename T >

void gausselim< T >::swap	(	uintc	i,
		uintc	k
	)			[inline]

Swap the rows.

Definition at line 219 of file gausselim.h.

References gausselim< T >::dim, and gausselim< T >::mat.

Referenced by gausselim< T >::pivot().

{
  assert(i<dim);
  assert(k<dim);

  T t;
  uint bi = i*(dim+1);
  uint bk = k*(dim+1);
  for (uint j=0; j<dim+1; ++j)
  {
    t = mat[bi];
    mat[bi] = mat[bk];
    mat[bk] = t;
    ++bi;
    ++bk;
  }
}

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Member Data Documentation

template<typename T>

uintc gausselim< T >::dim

dim=N.

Definition at line 44 of file gausselim.h.

Referenced by gausselim< T >::columnC(), gausselim< T >::eval(), gausselim< T >::gausselim(), gausselim< T >::mult(), gausselim< T >::norm(), gausselim< T >::operator stringc(), gausselim< T >::pivot(), gausselim< T >::rowget(), gausselim< T >::rowput(), gausselim< T >::substitute(), and gausselim< T >::swap().

template<typename T>

T* gausselim< T >::mat

Matrix {A,C} where AX=C.

Definition at line 40 of file gausselim.h.

Referenced by gausselim< T >::columnC(), gausselim< T >::norm(), gausselim< T >::operator stringc(), gausselim< T >::pivot(), gausselim< T >::rowget(), gausselim< T >::rowput(), gausselim< T >::substitute(), and gausselim< T >::swap().

template<typename T>

T* gausselim< T >::row

Tempory row variable.

Definition at line 42 of file gausselim.h.

Referenced by gausselim< T >::gausselim(), gausselim< T >::mult(), gausselim< T >::rowget(), gausselim< T >::rowput(), gausselim< T >::substitute(), and gausselim< T >::~gausselim().

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

• mathlib/gausselim.h