gm_rule.h File Reference

Go to the source code of this file.

Functions
void	comp_next (int n, int k, int a[], int *more, int *h, int *t)
void	gm_rule_set (int rule, int dim_num, int point_num, double w[], double x[])
int	gm_rule_size (int rule, int dim_num)
int	i4_choose (int n, int k)
int	i4_huge (void)
int	i4_max (int i1, int i2)
int	i4_min (int i1, int i2)
int	i4_power (int i, int j)
double *	monomial_value (int dim_num, int point_num, double x[], int expon[])
double	r8_abs (double x)
double	r8_factorial (int n)
double	r8vec_dot (int n, double a1[], double a2[])
double *	r8vec_uniform_01 (int n, int *seed)
double	simplex_unit_monomial_int (int dim_num, int expon[])
double	simplex_unit_monomial_quadrature (int dim_num, int expon[], int point_num, double x[], double w[])
double *	simplex_unit_sample (int dim_num, int n, int *seed)
double *	simplex_unit_to_general (int dim_num, int point_num, double t[], double ref[])
double	simplex_unit_volume (int dim_num)
void	timestamp (void)

Function Documentation

comp_next()

void comp_next	(	int	n,
		int	k,
		int	a[],
		int *	more,
		int *	h,
		int *	t
	)

Definition at line 10 of file gm_rule.c.

{
  int i;
 
  if ( !( *more ) )
  {
    *t = n;
    *h = 0;
    a[0] = n;
    for ( i = 1; i < k; i++ )
    {
       a[i] = 0;
    }
  }
  else
  {
    if ( 1 < *t )
    {
      *h = 0;
    }
    *h = *h + 1;
    *t = a[*h-1];
    a[*h-1] = 0;
    a[0] = *t - 1;
    a[*h] = a[*h] + 1;
  }
 
  *more = ( a[k-1] != n );
 
  return;
}

gm_rule_set()

void gm_rule_set	(	int	rule,
		int	dim_num,
		int	point_num,
		double	w[],
		double	x[]
	)

Definition at line 152 of file gm_rule.c.

{
  int *beta;
  int beta_sum;
  int d;
  int dim;
  int h;
  int i;
  int j;
  int j_hi;
  int k;
  int more;
  int n;
  double one_pm;
  int s;
  int t;
  double weight;
 
  s = rule;
  d = 2 * s + 1;
  k = 0;
  n = dim_num;
  one_pm = 1.0;
 
  beta = ( int * ) malloc ( ( dim_num + 1 ) * sizeof ( int ) );
 
  for ( i = 0; i <= s; i++ )
  {
    weight = ( double ) one_pm;
 
    j_hi = i4_max ( n, i4_max ( d, d + n - i ) );
 
    for ( j = 1; j <= j_hi; j++ )
    {
      if ( j <= n )
      {
        weight = weight * ( double ) ( j );
      }
      if ( j <= d )
      {
        weight = weight * ( double ) ( d + n - 2 * i );
      }
      if ( j <= 2 * s )
      {
        weight = weight / 2.0;
      }
      if ( j <= i )
      {
        weight = weight / ( double ) ( j );
      }
      if ( j <= d + n - i )
      {
        weight = weight / ( double ) ( j );
      }
    }
 
    one_pm = - one_pm;
 
    beta_sum = s - i;
    more = 0;
    h = 0;
    t = 0;
 
    for ( ; ; )
    {
      comp_next ( beta_sum, dim_num + 1, beta, &more, &h, &t );
 
      w[k] = weight;
      for ( dim = 0; dim < dim_num; dim++ )
      {
        x[dim+k*dim_num] = ( double ) ( 2 * beta[dim+1] + 1 )
                         / ( double ) ( d + n - 2 * i );
      }
      k = k + 1;
 
      if ( !more )
      {
        break;
      }
    }
  }
 
  free ( beta );
 
  return;
}

gm_rule_size()

int gm_rule_size	(	int	rule,
		int	dim_num
	)

Definition at line 294 of file gm_rule.c.

{
  int arg1;
  int point_num;
 
  arg1 = dim_num + rule + 1;
 
  point_num = i4_choose ( arg1, rule );
 
  return point_num;
}

i4_choose()

int i4_choose	(	int	n,
		int	k
	)

Definition at line 353 of file gm_rule.c.

{
  int i;
  int mn;
  int mx;
  int value;
 
  mn = i4_min ( k, n - k );
 
  if ( mn < 0 )
  {
    value = 0;
  }
  else if ( mn == 0 )
  {
    value = 1;
  }
  else
  {
    mx = i4_max ( k, n - k );
    value = mx + 1;
 
    for ( i = 2; i <= mn; i++ )
    {
      value = ( value * ( mx + i ) ) / i;
    }
  }
 
  return value;
}

i4_huge()

int i4_huge

(

void

)

Definition at line 428 of file gm_rule.c.

{
  static int value = 2147483647;
 
  return value;
}

i4_max()

int i4_max	(	int	i1,
		int	i2
	)

Definition at line 459 of file gm_rule.c.

{
  int value;
 
  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}

i4_min()

int i4_min	(	int	i1,
		int	i2
	)

Definition at line 500 of file gm_rule.c.

{
  int value;
 
  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}

i4_power()

int i4_power	(	int	i,
		int	j
	)

Definition at line 541 of file gm_rule.c.

{
  int k;
  int value;
 
  if ( j < 0 )
  {
    if ( i == 1 )
    {
      value = 1;
    }
    else if ( i == 0 )
    {
      fprintf ( stderr, "\n" );
      fprintf ( stderr, "I4_POWER - Fatal error!\n" );
      fprintf ( stderr, "  I^J requested, with I = 0 and J negative.\n" );
      exit ( 1 );
    }
    else
    {
      value = 0;
    }
  }
  else if ( j == 0 )
  {
    if ( i == 0 )
    {
      fprintf ( stderr, "\n" );
      fprintf ( stderr, "I4_POWER - Fatal error!\n" );
      fprintf ( stderr, "  I^J requested, with I = 0 and J = 0.\n" );
      exit ( 1 );
    }
    else
    {
      value = 1;
    }
  }
  else if ( j == 1 )
  {
    value = i;
  }
  else
  {
    value = 1;
    for ( k = 1; k <= j; k++ )
    {
      value = value * i;
    }
  }
  return value;
}

monomial_value()

double * monomial_value	(	int	dim_num,
		int	point_num,
		double	x[],
		int	expon[]
	)

Definition at line 619 of file gm_rule.c.

{
  int dim;
  int point;
  double *value;
 
  value = ( double * ) malloc ( point_num * sizeof ( double ) );
 
  for ( point = 0; point < point_num; point++ )
  {
    value[point] = 1.0;
  }
 
  for ( dim = 0; dim < dim_num; dim++ )
  {
    if ( 0 != expon[dim] )
    {
      for ( point = 0; point < point_num; point++ )
      {
        value[point] = value[point] * pow ( x[dim+point*dim_num], expon[dim] );
      }
    }
  }
 
  return value;
}

r8_abs()

double r8_abs

(

double

x

)

Definition at line 689 of file gm_rule.c.

{
  double value;
 
  if ( 0.0 <= x )
  {
    value = + x;
  }
  else
  {
    value = - x;
  }
  return value;
}

r8_factorial()

double r8_factorial

(

int

n

)

Definition at line 730 of file gm_rule.c.

{
  int i;
  double value;
 
  value = 1.0;
 
  for ( i = 1; i <= n; i++ )
  {
    value = value * ( double ) ( i );
  }
 
  return value;
}

r8vec_dot()

double r8vec_dot	(	int	n,
		double	a1[],
		double	a2[]
	)

r8vec_uniform_01()

double * r8vec_uniform_01	(	int	n,
		int *	seed
	)

simplex_unit_monomial_int()

double simplex_unit_monomial_int	(	int	dim_num,
		int	expon[]
	)

Definition at line 918 of file gm_rule.c.

{
  int dim;
  int i;
  int k;
  double value;
 
  value = 1.0;
 
  k = 0;
 
  for ( dim = 0; dim < dim_num; dim++ )
  {
    for ( i = 1; i <= expon[dim]; i++ )
    {
      k = k + 1;
      value = value * ( double ) ( i ) / ( double ) ( k );
    }
  }
 
  for ( dim = 0; dim < dim_num; dim++ )
  {
    k = k + 1;
    value = value / ( double ) ( k );
  }
 
  return value;
}

simplex_unit_monomial_quadrature()

double simplex_unit_monomial_quadrature	(	int	dim_num,
		int	expon[],
		int	point_num,
		double	x[],
		double	w[]
	)

Definition at line 986 of file gm_rule.c.

{
  double exact = 1.0;
  double quad;
  double quad_error;
  double scale;
  double *value;
  double volume;
/*
  Get the exact value of the integral of the unscaled monomial.
*/
  scale = simplex_unit_monomial_int ( dim_num, expon );
/*
  Evaluate the monomial at the quadrature points.
*/
  value = monomial_value ( dim_num, point_num, x, expon );
/*
  Compute the weighted sum and divide by the exact value.
*/
  volume = simplex_unit_volume ( dim_num );
  quad = volume * r8vec_dot_product ( point_num, w, value ) / scale;
 
  free ( value );
/*
  Error:
*/
  quad_error = r8_abs ( quad - exact );
 
  return quad_error;
}

simplex_unit_sample()

double * simplex_unit_sample	(	int	dim_num,
		int	n,
		int *	seed
	)

Definition at line 1052 of file gm_rule.c.

{
  double *e;
  int i;
  int j;
  double total;
  double *x;
/*
  The construction begins by sampling DIM_NUM+1 points from the
  exponential distribution with parameter 1.
*/
  x = ( double * ) malloc ( dim_num * n * sizeof ( double ) );
 
  for ( j = 0; j < n; j++ )
  {
    e = r8vec_uniform_01_new ( dim_num+1, seed );
 
    for ( i = 0; i <= dim_num; i++ )
    {
      e[i] = -log ( e[i] );
    }
 
    total = 0.0;
    for ( i = 0; i <= dim_num; i++ )
    {
      total = total + e[i];
    }
 
    for ( i = 0; i < dim_num; i++ )
    {
      x[i+dim_num*j] = e[i] / total;
    }
    free ( e );
  }
 
  return x;
}

simplex_unit_to_general()

double * simplex_unit_to_general	(	int	dim_num,
		int	point_num,
		double	t[],
		double	ref[]
	)

Definition at line 1137 of file gm_rule.c.

{
  int dim;
  double *phy;
  int point;
  int vertex;
 
  phy = ( double * ) malloc ( dim_num * point_num * sizeof ( double ) );
//
//  The image of each point is initially the image of the origin.
//
//  Insofar as the pre-image differs from the origin in a given vertex
//  direction, add that proportion of the difference between the images
//  of the origin and the vertex.
//
  for ( point = 0; point < point_num; point++ )
  {
    for ( dim = 0; dim < dim_num; dim++ )
    {
      phy[dim+point*dim_num] = t[dim+0*dim_num];
 
      for ( vertex = 1; vertex < dim_num + 1; vertex++ )
      {
        phy[dim+point*dim_num] = phy[dim+point*dim_num]
        + ( t[dim+vertex*dim_num] - t[dim+0*dim_num] ) * ref[vertex-1+point*dim_num];
      }
    }
  }
 
  return phy;
}

simplex_unit_volume()

double simplex_unit_volume

(

int

dim_num

)

Definition at line 1224 of file gm_rule.c.

{
  int i;
  double volume;
 
  volume = 1.0;
  for ( i = 1; i <= dim_num; i++ )
  {
    volume = volume / ( ( double ) i );
  }
 
  return volume;
}

timestamp()

void timestamp

(

void

)

Definition at line 1268 of file gm_rule.c.

{
# define TIME_SIZE 40
 
  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  size_t len;
  time_t now;
 
  (void)(len);
 
  now = time ( NULL );
  tm = localtime ( &now );
 
  len = strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );
 
  fprintf ( stdout, "%s\n", time_buffer );
 
  return;
# undef TIME_SIZE
}