#! /usr/bin/env python # def bessel_k1_values ( n_data ): #*****************************************************************************80 # ## BESSEL_K1_VALUES returns some values of the K1 Bessel function. # # Discussion: # # The modified Bessel functions In(Z) and Kn(Z) are solutions of # the differential equation # # Z^2 W'' + Z * W' - ( Z^2 + N^2 ) * W = 0. # # The modified Bessel function K1(Z) corresponds to N = 1. # # In Mathematica, the function can be evaluated by: # # BesselK[1,x] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 December 2014 # # 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 = 20 fx_vec = np.array ( ( \ 0.9853844780870606E+01, \ 0.4775972543220472E+01, \ 0.2184354424732687E+01, \ 0.1302834939763502E+01, \ 0.8617816344721803E+00, \ 0.6019072301972346E+00, \ 0.4345923910607150E+00, \ 0.3208359022298758E+00, \ 0.2406339113576119E+00, \ 0.1826230998017470E+00, \ 0.1398658818165224E+00, \ 0.7389081634774706E-01, \ 0.4015643112819418E-01, \ 0.2223939292592383E-01, \ 0.1248349888726843E-01, \ 0.7078094908968090E-02, \ 0.4044613445452164E-02, \ 0.1343919717735509E-02, \ 0.1553692118050011E-03, \ 0.1864877345382558E-04 ) ) x_vec = np.array ( ( \ 0.1E+00, \ 0.2E+00, \ 0.4E+00, \ 0.6E+00, \ 0.8E+00, \ 1.0E+00, \ 1.2E+00, \ 1.4E+00, \ 1.6E+00, \ 1.8E+00, \ 2.0E+00, \ 2.5E+00, \ 3.0E+00, \ 3.5E+00, \ 4.0E+00, \ 4.5E+00, \ 5.0E+00, \ 6.0E+00, \ 8.0E+00, \ 10.0E+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 bessel_k1_values_test ( ): #*****************************************************************************80 # ## BESSEL_K1_VALUES_TEST demonstrates the use of BESSEL_K1_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 December 2014 # # Author: # # John Burkardt # print ( '' ) print ( 'BESSEL_K1_VALUES_TEST:' ) print ( ' BESSEL_K1_VALUES stores values of the Bessel K function. of order 1.' ) print ( '' ) print ( ' X K(1,X)' ) print ( '' ) n_data = 0 while ( True ): n_data, x, fx = bessel_k1_values ( n_data ) if ( n_data == 0 ): break print ( ' %12f %24.16g' % ( x, fx ) ) # # Terminate. # print ( '' ) print ( 'BESSEL_K1_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) bessel_k1_values_test ( ) timestamp ( )