#! /usr/bin/env python # def arctan_values ( n_data ): #*****************************************************************************80 # ## ARCTAN_VALUES returns some values of the arc tangent function. # # Discussion: # # In Mathematica, the function can be evaluated by: # # ArcTan[x] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 23 December 2014 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz, Irene Stegun, # Handbook of Mathematical Functions, # National Bureau of Standards, 1964, # ISBN: 0-486-61272-4, # LC: QA47.A34. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Cambridge University Press, 1999, # ISBN: 0-521-64314-7, # LC: QA76.95.W65. # # 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 = 11 fx_vec = np.array ( ( \ 0.00000000000000000000, \ 0.24497866312686415417, \ 0.32175055439664219340, \ 0.46364760900080611621, \ 0.78539816339744830962, \ 1.1071487177940905030, \ 1.2490457723982544258, \ 1.3258176636680324651, \ 1.3734007669450158609, \ 1.4711276743037345919, \ 1.5208379310729538578 ) ) x_vec = np.array ( ( \ 0.00000000000000000000, \ 0.25000000000000000000, \ 0.33333333333333333333, \ 0.50000000000000000000, \ 1.0000000000000000000, \ 2.0000000000000000000, \ 3.0000000000000000000, \ 4.0000000000000000000, \ 5.0000000000000000000, \ 10.000000000000000000, \ 20.000000000000000000 ) ) 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 arctan_values_test ( ): #*****************************************************************************80 # ## ARCTAN_VALUES_TEST tests ARCTAN VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 23 December 2014 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'ARCTAN_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' ARCTAN_VALUES stores values of' ) print ( ' the arc tangent function.' ) print ( '' ) print ( ' X F(X)' ) print ( '' ) n_data = 0 while ( True ): n_data, x, fx = arctan_values ( n_data ) if ( n_data == 0 ): break print ( ' %12f %24.16g' % ( x, fx ) ) # # Terminate. # print ( '' ) print ( 'ARCTAN_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) arctan_values_test ( ) timestamp ( )