def mono_between_random(m, n1, n2, seed):
#*****************************************************************************80
#
## MONO_BETWEEN_RANDOM: random monomial with total degree between N1 and N2.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N1, N2, the minimum and maximum degrees.
# 0 <= N1 <= N2.
#
# Input, integer SEED, the random number seed.
#
# Output integer X[M], the random monomial.
#
# Output integer RANK, the rank of the monomial.
#
# Output, integer SEED, the updated random number seed.
#
from i4_uniform_ab import i4_uniform_ab
from mono_unrank_grlex import mono_unrank_grlex
from mono_upto_enum import mono_upto_enum
n1_copy = max(n1, 0)
rank_min = mono_upto_enum(m, n1_copy - 1) + 1
rank_max = mono_upto_enum(m, n2)
rank, seed = i4_uniform_ab(rank_min, rank_max, seed)
x = mono_unrank_grlex(m, rank)
return x, rank, seed
def mono_total_random(m, n, seed):
#*****************************************************************************80
#
## MONO_TOTAL_RANDOM: random monomial with total degree equal to N.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 21 November 2013
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N, the degree.
# 0 <= N.
#
# Input, integer SEED, the random number seed.
#
# Output, integer X[M], the random monomial.
#
# Output, integer RANK, the rank of the monomial.
#
# Output, integer SEED, the random number seed.
#
from i4_uniform_ab import i4_uniform_ab
from mono_unrank_grlex import mono_unrank_grlex
from mono_upto_enum import mono_upto_enum
rank_min = mono_upto_enum(m, n - 1) + 1
rank_max = mono_upto_enum(m, n)
rank, seed = i4_uniform_ab(rank_min, rank_max, seed)
x = mono_unrank_grlex(m, rank)
return x, rank, seed
def mono_total_random ( m, n, seed ): #*****************************************************************************80 # ## MONO_TOTAL_RANDOM: random monomial with total degree equal to N. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 21 November 2013 # # Author: # # John Burkardt # # Parameters: # # Input, integer M, the spatial dimension. # # Input, integer N, the degree. # 0 <= N. # # Input, integer SEED, the random number seed. # # Output, integer X[M], the random monomial. # # Output, integer RANK, the rank of the monomial. # # Output, integer SEED, the random number seed. # from i4_uniform_ab import i4_uniform_ab from mono_unrank_grlex import mono_unrank_grlex from mono_upto_enum import mono_upto_enum rank_min = mono_upto_enum ( m, n - 1 ) + 1 rank_max = mono_upto_enum ( m, n ) rank, seed = i4_uniform_ab ( rank_min, rank_max, seed ) x = mono_unrank_grlex ( m, rank ) return x, rank, seed
def mono_unrank_grlex_test():
#******************************************************************************/
#
## MONO_UNRANK_GRLEX_TEST tests MONO_UNRANK_GRLEX.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 October 2014
#
# Author:
#
# John Burkardt
#
from i4_uniform_ab import i4_uniform_ab
from mono_upto_enum import mono_upto_enum
from mono_upto_next_grlex import mono_upto_next_grlex
import numpy as np
m = 3
print ''
print 'MONO_UNRANK_GRLEX'
print ' MONO_UNRANK_GRLEX is given a rank, and returns the corresponding'
print ' monomial in the sequence of all monomials in M dimensions'
print ' in grlex order.'
print ''
print ' For reference, print a monomial sequence with ranks.'
n = 4
rank_max = mono_upto_enum(m, n)
print ''
print ' Let M = %d' % (m)
print ' N = %d' % (n)
print ''
x = np.zeros(m, dtype=np.int32)
i = 1
while (True):
print ' %2d ' % (i),
for j in range(0, m):
print '%2d' % (x[j]),
print ''
if (x[0] == n):
break
mono_upto_next_grlex(m, n, x)
i = i + 1
print ''
print ' Now choose random ranks between 1 and %d' % (rank_max)
print ''
seed = 123456789
test_num = 5
for test in range(0, test_num):
rank, seed = i4_uniform_ab(1, rank_max, seed)
x = mono_unrank_grlex(m, rank)
print ' %2d ' % (rank),
for j in range(0, m):
print '%2d' % (x[j]),
print ''
print ''
print 'MONO_UNRANK_GRLEX_TEST'
print ' Normal end of execution.'
return
def mono_unrank_grlex_test ( ):
#******************************************************************************/
#
## MONO_UNRANK_GRLEX_TEST tests MONO_UNRANK_GRLEX.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 October 2014
#
# Author:
#
# John Burkardt
#
from i4_uniform_ab import i4_uniform_ab
from mono_upto_enum import mono_upto_enum
from mono_upto_next_grlex import mono_upto_next_grlex
import numpy as np
m = 3
print ''
print 'MONO_UNRANK_GRLEX'
print ' MONO_UNRANK_GRLEX is given a rank, and returns the corresponding'
print ' monomial in the sequence of all monomials in M dimensions'
print ' in grlex order.'
print ''
print ' For reference, print a monomial sequence with ranks.'
n = 4
rank_max = mono_upto_enum ( m, n )
print ''
print ' Let M = %d' % ( m )
print ' N = %d' % ( n )
print ''
x = np.zeros ( m, dtype = np.int32 )
i = 1
while ( True ):
print ' %2d ' % ( i ),
for j in range ( 0, m ):
print '%2d' % ( x[j] ),
print ''
if ( x[0] == n ):
break
mono_upto_next_grlex ( m, n, x )
i = i + 1
print ''
print ' Now choose random ranks between 1 and %d' % ( rank_max )
print ''
seed = 123456789
test_num = 5
for test in range ( 0, test_num ):
rank, seed = i4_uniform_ab ( 1, rank_max, seed )
x = mono_unrank_grlex ( m, rank )
print ' %2d ' % ( rank ),
for j in range ( 0, m ):
print '%2d' % ( x[j] ),
print ''
print ''
print 'MONO_UNRANK_GRLEX_TEST'
print ' Normal end of execution.'
return
