#! /usr/bin/env python # def ei_values ( n_data ): #*****************************************************************************80 # ## EI_VALUES returns some values of the exponential integral function EI(X). # # Definition: # # The exponential integral EI(X) has the formula: # # EI(X) = - integral ( -X <= T <= Infinity ) exp ( -T ) / T dT # # In Mathematica, the function can be evaluated by: # # ExpIntegralEi[x] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 16 September 2004 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz and Irene Stegun, # Handbook of Mathematical Functions, # US Department of Commerce, 1964. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Wolfram Media / Cambridge University Press, 1999. # # Parameters: # # Input/output, integer N_DATA. The user sets N_DATA to 0 before the # first call. On each call, the routine increments N_DATA by 1, and # returns the corresponding data; when there is no more data, the # output value of N_DATA will be 0 again. # # Output, real X, the argument of the function. # # Output, real FX, the value of the function. # import numpy as np n_max = 16 fx_vec = np.array ( ( 0.4542199048631736E+00, \ 0.7698812899373594E+00, \ 0.1064907194624291E+01, \ 0.1347396548212326E+01, \ 0.1622811713696867E+01, \ 0.1895117816355937E+01, \ 0.2167378279563403E+01, \ 0.2442092285192652E+01, \ 0.2721398880232024E+01, \ 0.3007207464150646E+01, \ 0.3301285449129798E+01, \ 0.3605319949019469E+01, \ 0.3920963201354904E+01, \ 0.4249867557487934E+01, \ 0.4593713686953585E+01, \ 0.4954234356001890E+01 )) x_vec = np.array ( ( 0.5E+00, \ 0.6E+00, \ 0.7E+00, \ 0.8E+00, \ 0.9E+00, \ 1.0E+00, \ 1.1E+00, \ 1.2E+00, \ 1.3E+00, \ 1.4E+00, \ 1.5E+00, \ 1.6E+00, \ 1.7E+00, \ 1.8E+00, \ 1.9E+00, \ 2.0E+00 )) if ( n_data < 0 ): n_data = 0 if ( n_max <= n_data ): n_data = 0 x = 0.0 fx = 0.0 else: x = x_vec[n_data] fx = fx_vec[n_data] n_data = n_data + 1 return n_data, x, fx def ei_values_test ( ): #*****************************************************************************80 # ## EI_VALUES_TEST demonstrates the use of EI_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 03 February 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'EI_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' EI_VALUES stores values of the exponential integral.' ) print ( '' ) print ( ' X EI(X)' ) print ( '' ) n_data = 0 while ( True ): n_data, x, fx = ei_values ( n_data ) if ( n_data == 0 ): break print ( ' %12f %24.16f' % ( x, fx ) ) # # Terminate. # print ( '' ) print ( 'EI_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) ei_values_test ( ) timestamp ( )