def lpp_to_polynomial_test():
#*****************************************************************************80
#
## LPP_TO_POLYNOMIAL_TEST tests LPP_TO_POLYNOMIAL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from polynomial_print import polynomial_print
import numpy as np
m = 2
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' LPP_TO_POLYNOMIAL is given a Legendre product polynomial'
print ' and determines its polynomial representation.'
print ''
print ' Using spatial dimension M = %d' % (m)
for rank in range(1, 12):
l = comp_unrank_grlex(m, rank)
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
c = np.zeros(o_max, dtype=np.float64)
e = np.zeros(o_max, dtype=np.int32)
o, c, e = lpp_to_polynomial(m, l, o_max)
label = ' LPP #' + repr ( rank ) + ' = L(' + repr ( l[0] ) \
+ ',X)*L(' + repr ( l[1] ) + ',Y) = '
print ''
polynomial_print(m, o, c, e, label)
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' Normal end of execution.'
return
def lpp_to_polynomial_test ( ):
#*****************************************************************************80
#
## LPP_TO_POLYNOMIAL_TEST tests LPP_TO_POLYNOMIAL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from polynomial_print import polynomial_print
import numpy as np
m = 2
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' LPP_TO_POLYNOMIAL is given a Legendre product polynomial'
print ' and determines its polynomial representation.'
print ''
print ' Using spatial dimension M = %d' % ( m )
for rank in range ( 1, 12 ):
l = comp_unrank_grlex ( m, rank )
o_max = 1
for i in range ( 0, m ):
o_max = o_max * ( l[i] + 2 ) // 2
c = np.zeros ( o_max, dtype = np.float64 )
e = np.zeros ( o_max, dtype = np.int32 )
o, c, e = lpp_to_polynomial ( m, l, o_max )
label = ' LPP #' + repr ( rank ) + ' = L(' + repr ( l[0] ) \
+ ',X)*L(' + repr ( l[1] ) + ',Y) = '
print ''
polynomial_print ( m, o, c, e, label )
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' Normal end of execution.'
return
def comp_random_grlex ( kc, rank1, rank2, seed ):
#*****************************************************************************80
#
## COMP_RANDOM_GRLEX: random composition with degree less than or equal to NC.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 September 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, int KC, the number of parts in the composition.
#
# Input, int RANK1, RANK2, the minimum and maximum ranks.
# 1 <= RANK1 <= RANK2.
#
# Input, int SEED, the random number seed.
#
# Output, int X[KC], the random composition.
#
# Output, int RANK, the rank of the composition.
#
# Output, int SEED, the random number seed.
#
from comp_unrank_grlex import comp_unrank_grlex
from i4_uniform_ab import i4_uniform_ab
from sys import exit
#
# Ensure that 1 <= KC.
#
if ( kc < 1 ):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' KC < 1'
exit ( 'COMP_RANDOM_GRLEX - Fatal error!' );
#
# Ensure that 1 <= RANK1.
#
if ( rank1 < 1 ):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' RANK1 < 1'
exit ( 'COMP_RANDOM_GRLEX - Fatal error!' );
#
# Ensure that RANK1 <= RANK2.
#
if ( rank2 < rank1 ):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' RANK2 < RANK1'
exit ( 'COMP_RANDOM_GRLEX - Fatal error!' )
#
# Choose RANK between RANK1 and RANK2.
#
rank, seed = i4_uniform_ab ( rank1, rank2, seed )
#
# Recover the composition of given RANK.
#
xc = comp_unrank_grlex ( kc, rank )
return xc, rank, seed
def lpp_value_test():
# *****************************************************************************80
#
## LPP_VALUE_TEST tests LPP_VALUE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from lpp_to_polynomial import lpp_to_polynomial
from polynomial_value import polynomial_value
from r8mat_uniform_ab import r8mat_uniform_ab
print ""
print "LPP_VALUE_TEST:"
print " LPP_VALUE evaluates a Legendre product polynomial."
m = 3
n = 1
xlo = -1.0
xhi = +1.0
seed = 123456789
x, seed = r8mat_uniform_ab(m, n, xlo, xhi, seed)
print ""
print " Evaluate at X = ",
for j in range(0, n):
for i in range(0, m):
print "%g " % (x[i][j]),
print ""
print ""
print " Rank I1 I2 I3: L(I1,X1)*L(I2,X2)*L(I3,X3) P(X1,X2,X3)"
print ""
for rank in range(1, 21):
l = comp_unrank_grlex(m, rank)
#
# Evaluate the LPP directly.
#
v1 = lpp_value(m, n, l, x)
#
# Convert the LPP to a polynomial.
#
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
o, c, e = lpp_to_polynomial(m, l, o_max)
#
# Evaluate the polynomial.
#
v2 = polynomial_value(m, o, c, e, n, x)
#
# Compare results.
#
print " %4d %2d %2d %2d %14.6g %14.6g" % (rank, l[0], l[1], l[2], v1[0], v2[0])
print ""
print "LPP_VALUE_TEST:"
print " Normal end of execution."
return
def comp_random_grlex(kc, rank1, rank2, seed):
#*****************************************************************************80
#
## COMP_RANDOM_GRLEX: random composition with degree less than or equal to NC.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 September 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, int KC, the number of parts in the composition.
#
# Input, int RANK1, RANK2, the minimum and maximum ranks.
# 1 <= RANK1 <= RANK2.
#
# Input, int SEED, the random number seed.
#
# Output, int X[KC], the random composition.
#
# Output, int RANK, the rank of the composition.
#
# Output, int SEED, the random number seed.
#
from comp_unrank_grlex import comp_unrank_grlex
from i4_uniform_ab import i4_uniform_ab
from sys import exit
#
# Ensure that 1 <= KC.
#
if (kc < 1):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' KC < 1'
exit('COMP_RANDOM_GRLEX - Fatal error!')
#
# Ensure that 1 <= RANK1.
#
if (rank1 < 1):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' RANK1 < 1'
exit('COMP_RANDOM_GRLEX - Fatal error!')
#
# Ensure that RANK1 <= RANK2.
#
if (rank2 < rank1):
print ''
print 'COMP_RANDOM_GRLEX - Fatal error!'
print ' RANK2 < RANK1'
exit('COMP_RANDOM_GRLEX - Fatal error!')
#
# Choose RANK between RANK1 and RANK2.
#
rank, seed = i4_uniform_ab(rank1, rank2, seed)
#
# Recover the composition of given RANK.
#
xc = comp_unrank_grlex(kc, rank)
return xc, rank, seed
def lpp_value_test():
#*****************************************************************************80
#
## LPP_VALUE_TEST tests LPP_VALUE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from lpp_to_polynomial import lpp_to_polynomial
from polynomial_value import polynomial_value
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'LPP_VALUE_TEST:'
print ' LPP_VALUE evaluates a Legendre product polynomial.'
m = 3
n = 1
xlo = -1.0
xhi = +1.0
seed = 123456789
x, seed = r8mat_uniform_ab(m, n, xlo, xhi, seed)
print ''
print ' Evaluate at X = ',
for j in range(0, n):
for i in range(0, m):
print '%g ' % (x[i][j]),
print ''
print ''
print ' Rank I1 I2 I3: L(I1,X1)*L(I2,X2)*L(I3,X3) P(X1,X2,X3)'
print ''
for rank in range(1, 21):
l = comp_unrank_grlex(m, rank)
#
# Evaluate the LPP directly.
#
v1 = lpp_value(m, n, l, x)
#
# Convert the LPP to a polynomial.
#
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
o, c, e = lpp_to_polynomial(m, l, o_max)
#
# Evaluate the polynomial.
#
v2 = polynomial_value(m, o, c, e, n, x)
#
# Compare results.
#
print ' %4d %2d %2d %2d %14.6g %14.6g' % \
( rank, l[0], l[1], l[2], v1[0], v2[0] )
print ''
print 'LPP_VALUE_TEST:'
print ' Normal end of execution.'
return