def r8_gamma_log_test():
#*****************************************************************************80
#
## R8_GAMMA_LOG_TEST tests R8_GAMMA_LOG.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 July 2014
#
# Author:
#
# John Burkardt
#
import platform
from gamma_log_values import gamma_log_values
from r8_gamma_log import r8_gamma_log
print('')
print('R8_GAMMA_LOG_TEST:')
print(' Python version: %s' % (platform.python_version()))
print(' R8_GAMMA_LOG evaluates the logarithm of the Gamma function.')
print('')
print(' X GAMMA_LOG(X) R8_GAMMA_LOG(X)')
print('')
n_data = 0
while (True):
n_data, x, fx1 = gamma_log_values(n_data)
if (n_data == 0):
break
fx2 = r8_gamma_log(x)
print(' %12g %24.16g %24.16g' % (x, fx1, fx2))
#
# Terminate.
#
print('')
print('R8_GAMMA_LOG_TEST')
print(' Normal end of execution.')
return
def r8_gamma_log_test():
# *****************************************************************************80
#
## R8_GAMMA_LOG_TEST tests R8_GAMMA_LOG.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 July 2014
#
# Author:
#
# John Burkardt
#
from gamma_log_values import gamma_log_values
from r8_gamma_log import r8_gamma_log
print ""
print "R8_GAMMA_LOG_TEST:"
print " R8_GAMMA_LOG evaluates the logarithm of the Gamma function."
print ""
print " X GAMMA_LOG(X) R8_GAMMA_LOG(X)"
print ""
n_data = 0
while True:
n_data, x, fx1 = gamma_log_values(n_data)
if n_data == 0:
break
fx2 = r8_gamma_log(x)
print " %12g %24.16g %24.16g" % (x, fx1, fx2)
#
# Terminate.
#
print ""
print "R8_GAMMA_LOG_TEST"
print " Normal end of execution."
return
def r8_gamma_log_test():
#*****************************************************************************80
#
## R8_GAMMA_LOG_TEST tests R8_GAMMA_LOG.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 July 2014
#
# Author:
#
# John Burkardt
#
from gamma_log_values import gamma_log_values
from r8_gamma_log import r8_gamma_log
print ''
print 'R8_GAMMA_LOG_TEST:'
print ' R8_GAMMA_LOG evaluates the logarithm of the Gamma function.'
print ''
print ' X GAMMA_LOG(X) R8_GAMMA_LOG(X)'
print ''
n_data = 0
while (True):
n_data, x, fx1 = gamma_log_values(n_data)
if (n_data == 0):
break
fx2 = r8_gamma_log(x)
print ' %12g %24.16g %24.16g' % (x, fx1, fx2)
print ''
print 'R8_GAMMA_LOG_TEST'
print ' Normal end of execution.'
return
def r8_gamma_log_test ( ):
#*****************************************************************************80
#
## R8_GAMMA_LOG_TEST tests R8_GAMMA_LOG.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 25 July 2014
#
# Author:
#
# John Burkardt
#
from gamma_log_values import gamma_log_values
from r8_gamma_log import r8_gamma_log
print ''
print 'R8_GAMMA_LOG_TEST:'
print ' R8_GAMMA_LOG evaluates the logarithm of the Gamma function.'
print ''
print ' X GAMMA_LOG(X) R8_GAMMA_LOG(X)'
print ''
n_data = 0
while ( True ):
n_data, x, fx1 = gamma_log_values ( n_data )
if ( n_data == 0 ):
break
fx2 = r8_gamma_log ( x )
print ' %12g %24.16g %24.16g' % ( x, fx1, fx2 )
print ''
print 'R8_GAMMA_LOG_TEST'
print ' Normal end of execution.'
return
def r8_factorial_log ( n ): #*****************************************************************************80 # ## R8_FACTORIAL_LOG computes the natural logarithm of the factorial N! # # Discussion: # # LOG ( FACTORIAL ( N ) ) # = LOG ( product ( 1 <= I <= N ) I ) # = sum ( ( 1 <= I <= N ) LOG ( I ) ) # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 13 February 2010 # # Author: # # John Burkardt # # Parameters: # # Input, integer N, the argument of the factorial function. # If N is less than 1, VALUE is returned as 0. # # Output, real VALUE, the logarithm of the factorial of N. # from r8_gamma_log import r8_gamma_log value = r8_gamma_log ( float ( n + 1 ) ) return value
def commul ( n, nfactor, iarray ):
#*****************************************************************************80
#
## COMMUL computes a multinomial combinatorial coefficient.
#
# Discussion:
#
# The multinomial coefficient is a generalization of the binomial
# coefficient. It may be interpreted as the number of combinations of
# N objects, where IARRAY(1) objects are indistinguishable of type 1,
# ... and IARRAY(K) are indistinguishable of type NFACT.
#
# The formula is
#
# NCOMB = N! / ( IARRAY(1)! IARRAY(2)! ... IARRAY(NFACT)! )
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 January 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer N, determines the numerator.
#
# Input, integer NFACTOR, the number of factors in the numerator.
#
# Input, integer IARRAY(NFACTOR).
# IARRAY contains the NFACT values used in the denominator.
# Note that the sum of these entries should be N,
# and that all entries should be nonnegative.
#
# Output, integer NCOMB, the value of the multinomial coefficient.
#
import numpy as np
from r8_gamma_log import r8_gamma_log
from sys import exit
for i in range ( 0, nfactor ):
if ( iarray[i] < 0 ):
print ''
print 'COMMUL - Fatal error!'
print ' Entry %d of IARRAY = %d' % ( i, iarray[i] )
print 1, ' But this value must be nonnegative.'
exit ( 'COMMUL - Fatal error!' )
isum = np.sum ( iarray )
if ( isum != n ):
print ''
print 'COMMUL - Fatal error!'
print ' The sum of the IARRAY entries is %d' % (isum )
print ' But it must equal N = %d' % ( n )
exit ( 'COMMUL - Fatal error!' )
facn = r8_gamma_log ( float ( n + 1 ) )
for i in range ( 0, nfactor ):
fack = r8_gamma_log ( float ( iarray[i] + 1 ) )
facn = facn - fack
ncomb = int ( np.round ( np.exp ( facn ) ) )
return ncomb
def commul(n, nfactor, iarray):
#*****************************************************************************80
#
## COMMUL computes a multinomial combinatorial coefficient.
#
# Discussion:
#
# The multinomial coefficient is a generalization of the binomial
# coefficient. It may be interpreted as the number of combinations of
# N objects, where IARRAY(1) objects are indistinguishable of type 1,
# ... and IARRAY(K) are indistinguishable of type NFACT.
#
# The formula is
#
# NCOMB = N! / ( IARRAY(1)! IARRAY(2)! ... IARRAY(NFACT)! )
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 January 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer N, determines the numerator.
#
# Input, integer NFACTOR, the number of factors in the numerator.
#
# Input, integer IARRAY(NFACTOR).
# IARRAY contains the NFACT values used in the denominator.
# Note that the sum of these entries should be N,
# and that all entries should be nonnegative.
#
# Output, integer NCOMB, the value of the multinomial coefficient.
#
import numpy as np
from r8_gamma_log import r8_gamma_log
from sys import exit
for i in range(0, nfactor):
if (iarray[i] < 0):
print ''
print 'COMMUL - Fatal error!'
print ' Entry %d of IARRAY = %d' % (i, iarray[i])
print 1, ' But this value must be nonnegative.'
exit('COMMUL - Fatal error!')
isum = np.sum(iarray)
if (isum != n):
print ''
print 'COMMUL - Fatal error!'
print ' The sum of the IARRAY entries is %d' % (isum)
print ' But it must equal N = %d' % (n)
exit('COMMUL - Fatal error!')
facn = r8_gamma_log(float(n + 1))
for i in range(0, nfactor):
fack = r8_gamma_log(float(iarray[i] + 1))
facn = facn - fack
ncomb = int(np.round(np.exp(facn)))
return ncomb
def r8_choose(n, k):
#*****************************************************************************80
#
## R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.
#
# Discussion:
#
# The value is calculated in such a way as to avoid overflow and
# roundoff. The calculation is done in R8 arithmetic.
#
# The formula used is:
#
# C(N,K) = N! / ( K! * (N-K)! )
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer N, K, are the values of N and K.
#
# Output, real VALUE, the number of combinations of N
# things taken K at a time.
#
import numpy as np
from r8_gamma_log import r8_gamma_log
if (n < 0):
value = 0.0
elif (k == 0):
value = 1.0
elif (k == 1):
value = float(n)
elif (1 < k and k < n - 1):
facn = r8_gamma_log(float(n + 1))
fack = r8_gamma_log(float(k + 1))
facnmk = r8_gamma_log(float(n - k + 1))
value = round(np.exp(facn - fack - facnmk))
elif (k == n - 1):
value = float(n)
elif (k == n):
value = 1.0
else:
value = 0.0
return value
