def normal_01_cdf_inverse(p):
#*****************************************************************************80
#
## NORMAL_01_CDF_INVERSE inverts the standard normal CDF.
#
# Discussion:
#
# The result is accurate to about 1 part in 10^16.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 15 February 2015
#
# Author:
#
# Original FORTRAN77 version by Michael Wichura.
# Python version by John Burkardt.
#
# Reference:
#
# Michael Wichura,
# The Percentage Points of the Normal Distribution,
# Algorithm AS 241,
# Applied Statistics,
# Volume 37, Number 3, pages 477-484, 1988.
#
# Parameters:
#
# Input, real P, the value of the cumulative probability
# densitity function. 0 < P < 1. If P is not in this range, an "infinite"
# result is returned.
#
# Output, real VALUE, the normal deviate value with the
# property that the probability of a standard normal deviate being
# less than or equal to the value is P.
#
import numpy as np
from r8_huge import r8_huge
from r8poly_value_horner import r8poly_value_horner
a = np.array ( (\
3.3871328727963666080, 1.3314166789178437745e+2, \
1.9715909503065514427e+3, 1.3731693765509461125e+4, \
4.5921953931549871457e+4, 6.7265770927008700853e+4, \
3.3430575583588128105e+4, 2.5090809287301226727e+3 ))
b = np.array ( (\
1.0, 4.2313330701600911252e+1, \
6.8718700749205790830e+2, 5.3941960214247511077e+3, \
2.1213794301586595867e+4, 3.9307895800092710610e+4, \
2.8729085735721942674e+4, 5.2264952788528545610e+3 ))
c = np.array ( (\
1.42343711074968357734, 4.63033784615654529590, \
5.76949722146069140550, 3.64784832476320460504, \
1.27045825245236838258, 2.41780725177450611770e-1, \
2.27238449892691845833e-2, 7.74545014278341407640e-4 ))
const1 = 0.180625
const2 = 1.6
d = np.array ( (\
1.0, 2.05319162663775882187, \
1.67638483018380384940, 6.89767334985100004550e-1, \
1.48103976427480074590e-1, 1.51986665636164571966e-2, \
5.47593808499534494600e-4, 1.05075007164441684324e-9 ))
e = np.array ( (\
6.65790464350110377720, 5.46378491116411436990, \
1.78482653991729133580, 2.96560571828504891230e-1, \
2.65321895265761230930e-2, 1.24266094738807843860e-3, \
2.71155556874348757815e-5, 2.01033439929228813265e-7 ))
f = np.array ( (\
1.0, 5.99832206555887937690e-1, \
1.36929880922735805310e-1, 1.48753612908506148525e-2, \
7.86869131145613259100e-4, 1.84631831751005468180e-5, \
1.42151175831644588870e-7, 2.04426310338993978564e-15 ))
split1 = 0.425
split2 = 5.0
if (p <= 0.0):
value = -r8_huge()
return value
if (1.0 <= p):
value = r8_huge()
return value
q = p - 0.5
if (abs(q) <= split1):
r = const1 - q * q
value = q * r8poly_value_horner ( 7, a, r ) \
/ r8poly_value_horner ( 7, b, r )
else:
if (q < 0.0):
r = p
else:
r = 1.0 - p
if (r <= 0.0):
value = r8_huge()
else:
r = np.sqrt(-np.log(r))
if (r <= split2):
r = r - const2
value = r8poly_value_horner ( 7, c, r ) \
/ r8poly_value_horner ( 7, d, r )
else:
r = r - split2
value = r8poly_value_horner ( 7, e, r ) \
/ r8poly_value_horner ( 7, f, r )
if (q < 0.0):
value = -value
return value
def normal_01_cdf_inverse ( p ):
#*****************************************************************************80
#
## NORMAL_01_CDF_INVERSE inverts the standard normal CDF.
#
# Discussion:
#
# The result is accurate to about 1 part in 10^16.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 15 February 2015
#
# Author:
#
# Original FORTRAN77 version by Michael Wichura.
# Python version by John Burkardt.
#
# Reference:
#
# Michael Wichura,
# The Percentage Points of the Normal Distribution,
# Algorithm AS 241,
# Applied Statistics,
# Volume 37, Number 3, pages 477-484, 1988.
#
# Parameters:
#
# Input, real P, the value of the cumulative probability
# densitity function. 0 < P < 1. If P is not in this range, an "infinite"
# result is returned.
#
# Output, real VALUE, the normal deviate value with the
# property that the probability of a standard normal deviate being
# less than or equal to the value is P.
#
import numpy as np
from r8_huge import r8_huge
from r8poly_value_horner import r8poly_value_horner
a = np.array ( (\
3.3871328727963666080, 1.3314166789178437745e+2, \
1.9715909503065514427e+3, 1.3731693765509461125e+4, \
4.5921953931549871457e+4, 6.7265770927008700853e+4, \
3.3430575583588128105e+4, 2.5090809287301226727e+3 ))
b = np.array ( (\
1.0, 4.2313330701600911252e+1, \
6.8718700749205790830e+2, 5.3941960214247511077e+3, \
2.1213794301586595867e+4, 3.9307895800092710610e+4, \
2.8729085735721942674e+4, 5.2264952788528545610e+3 ))
c = np.array ( (\
1.42343711074968357734, 4.63033784615654529590, \
5.76949722146069140550, 3.64784832476320460504, \
1.27045825245236838258, 2.41780725177450611770e-1, \
2.27238449892691845833e-2, 7.74545014278341407640e-4 ))
const1 = 0.180625
const2 = 1.6
d = np.array ( (\
1.0, 2.05319162663775882187, \
1.67638483018380384940, 6.89767334985100004550e-1, \
1.48103976427480074590e-1, 1.51986665636164571966e-2, \
5.47593808499534494600e-4, 1.05075007164441684324e-9 ))
e = np.array ( (\
6.65790464350110377720, 5.46378491116411436990, \
1.78482653991729133580, 2.96560571828504891230e-1, \
2.65321895265761230930e-2, 1.24266094738807843860e-3, \
2.71155556874348757815e-5, 2.01033439929228813265e-7 ))
f = np.array ( (\
1.0, 5.99832206555887937690e-1, \
1.36929880922735805310e-1, 1.48753612908506148525e-2, \
7.86869131145613259100e-4, 1.84631831751005468180e-5, \
1.42151175831644588870e-7, 2.04426310338993978564e-15 ))
split1 = 0.425
split2 = 5.0
if ( p <= 0.0 ):
value = - r8_huge ( )
return value
if ( 1.0 <= p ):
value = r8_huge ( )
return value
q = p - 0.5
if ( abs ( q ) <= split1 ):
r = const1 - q * q
value = q * r8poly_value_horner ( 7, a, r ) \
/ r8poly_value_horner ( 7, b, r )
else:
if ( q < 0.0 ):
r = p
else:
r = 1.0 - p
if ( r <= 0.0 ):
value = r8_huge ( )
else:
r = np.sqrt ( - np.log ( r ) )
if ( r <= split2 ):
r = r - const2
value = r8poly_value_horner ( 7, c, r ) \
/ r8poly_value_horner ( 7, d, r )
else:
r = r - split2
value = r8poly_value_horner ( 7, e, r ) \
/ r8poly_value_horner ( 7, f, r )
if ( q < 0.0 ):
value = - value
return value
def truncated_normal_rule ( *args ):
#*****************************************************************************80
#
## MAIN is the main program for TRUNCATED_NORMAL_RULE.
#
# Discussion:
#
# This program computes a truncated normal quadrature rule
# and writes it to a file.
#
# The user specifies:
# * option: 0/1/2/3 for none, lower, upper, double truncation.
# * N, the number of points in the rule
# * MU, the mean of the original normal distribution
# * SIGMA, the standard deviation of the original normal distribution,
# * A, the left endpoint (for options 1 or 3)
# * B, the right endpoint (for options 2 or 3)
# * HEADER, the root name of the output files.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 23 March 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from moment_method import moment_method
from normal_ms_moment import normal_ms_moments
from r8_huge import r8_huge
from rule_write import rule_write
from sys import exit
from truncated_normal_a_moment import truncated_normal_a_moments
from truncated_normal_ab_moment import truncated_normal_ab_moments
from truncated_normal_b_moment import truncated_normal_b_moments
print ''
print 'TRUNCATED_NORMAL_RULE'
print ' Python version'
print ''
print ' For the (truncated) Gaussian probability density function'
print ' pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi )'
print ' compute an N-point quadrature rule for approximating'
print ' Integral ( A <= x <= B ) f(x) pdf(x) dx'
print ''
print ' The value of OPTION determines the truncation interval [A,B]:'
print ' 0: (-oo,+oo)'
print ' 1: [A,+oo)'
print ' 2: (-oo,B]'
print ' 3: [A,B]'
print ''
print ' The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME.'
print ''
print ' HEADER is used to generate 3 files:'
print ''
print ' header_w.txt - the weight file'
print ' header_x.txt - the abscissa file.'
print ' header_r.txt - the region file, listing A and B.'
argument_count = ( len ( args ) )
iarg = 0
#
# Get OPTION.
#
if ( argument_count < iarg + 1 ):
option = eval ( input ( ' Enter OPTION, 0/1/2/3: ' ) )
else:
option = args[iarg]
iarg = iarg + 1
if ( option < 0 or 3 < option ):
print ''
print 'TRUNCATED_NORMAL_RULE - Fatal error!'
print ' 0 <= OPTION <= 3 was required.'
exit ( 'TRUNCATED_NORMAL_RULE - Fatal error!' )
#
# Get N.
#
if ( argument_count < iarg + 1 ):
n = eval ( input ( ' Enter the rule order N: ' ) )
else:
n = args[iarg]
iarg = iarg + 1
#
# Get MU.
#
if ( argument_count < iarg + 1 ):
mu = eval ( input ( ' Enter MU, the mean value of the normal distribution: ' ) )
else:
mu = args[iarg]
iarg = iarg + 1
#
# Get SIGMA.
#
if ( argument_count < iarg + 1 ):
sigma = eval ( input ( ' Enter SIGMA, the standard deviation: ' ) )
else:
sigma = args[iarg]
iarg = iarg + 1
#
# Get A.
#
if ( option == 1 or option == 3 ):
if ( argument_count < iarg + 1 ):
a = eval ( input ( ' Enter the left endpoint A: ' ) )
else:
a = args[iarg]
iarg = iarg + 1
else:
a = - r8_huge ( )
#
# Get B.
#
if ( option == 2 or option == 3 ):
if ( argument_count < iarg + 1 ):
b = eval ( input ( ' Enter the right endpoint B: ' ) )
else:
b = args[iarg]
iarg = iarg + 1
else:
b = r8_huge ( )
#
# Get HEADER.
#
if ( argument_count < iarg + 1 ):
print ''
print ' HEADER is the "root name" of the quadrature files.'
header = input ( ' Enter HEADER as a quoted string: ' )
else:
header = args[iarg]
iarg = iarg + 1
#
# Input summary.
#
print ''
print ' OPTION = %d' % ( option )
print ' N = %d' % ( n )
print ' MU = %g' % ( mu )
print ' SIGMA = %g' % ( sigma )
if ( option == 1 or option == 3 ):
print ' A = %g' % ( a )
else:
print ' A = -oo'
if ( option == 2 or option == 3 ):
print ' B = %g' % ( b )
else:
print ' B = +oo'
print ' HEADER = "%s"' % ( header )
#
# Compute the moments.
#
if ( option == 0 ):
moment = normal_ms_moments ( 2 * n + 1, mu, sigma )
elif ( option == 1 ):
moment = truncated_normal_a_moments ( 2 * n + 1, mu, sigma, a )
elif ( option == 2 ):
moment = truncated_normal_b_moments ( 2 * n + 1, mu, sigma, b )
elif ( option == 3 ):
moment = truncated_normal_ab_moments ( 2 * n + 1, mu, sigma, a, b )
#
# Compute the rule.
#
x, w = moment_method ( n, moment )
r = np.array ( [ [ a ], [ b ] ] )
#
# Write the rule.
#
rule_write ( n, header, x, w, r )
#
# Terminate.
#
print ''
print 'TRUNCATED_NORMAL_RULE:'
print ' Normal end of execution.'
return
