#! /usr/bin/env python # def psi_values ( n_data ): #*****************************************************************************80 # ## PSI_VALUES returns some values of the Psi or Digamma function. # # Discussion: # # In Mathematica, the function can be evaluated by: # # PolyGamma[x] # # or # # PolyGamma[0,x] # # PSI(X) = d ln ( Gamma ( X ) ) / d X = Gamma'(X) / Gamma(X) # # PSI(1) = -Euler's constant. # # PSI(X+1) = PSI(X) + 1 / X. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 20 February 2015 # # 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 F, the value of the function. # import numpy as np n_max = 20 f_vec = np.array ( ( \ -10.42375494041108E+00, \ -5.289039896592188E+00, \ -3.502524222200133E+00, \ -2.561384544585116E+00, \ -1.963510026021423E+00, \ -1.540619213893190E+00, \ -1.220023553697935E+00, \ -0.9650085667061385E+00, \ -0.7549269499470514E+00, \ -0.5772156649015329E+00, \ -0.4237549404110768E+00, \ -0.2890398965921883E+00, \ -0.1691908888667997E+00, \ -0.6138454458511615E-01, \ 0.3648997397857652E-01, \ 0.1260474527734763E+00, \ 0.2085478748734940E+00, \ 0.2849914332938615E+00, \ 0.3561841611640597E+00, \ 0.4227843350984671E+00 )) x_vec = np.array ( ( \ 0.1E+00, \ 0.2E+00, \ 0.3E+00, \ 0.4E+00, \ 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 f = 0.0 else: x = x_vec[n_data] f = f_vec[n_data] n_data = n_data + 1 return n_data, x, f def psi_values_test ( ): #*****************************************************************************80 # ## PSI_VALUES_TEST demonstrates the use of PSI_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 20 February 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'PSI_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' PSI_VALUES stores values of the PSI function.' ) print ( '' ) print ( ' X PSI(X)' ) print ( '' ) n_data = 0 while ( True ): n_data, x, f = psi_values ( n_data ) if ( n_data == 0 ): break print ( ' %12f %24.16f' % ( x, f ) ) # # Terminate. # print ( '' ) print ( 'PSI_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) psi_values_test ( ) timestamp ( )