#! /usr/bin/env python # def r4vec_covariance ( n, x, y ): #*****************************************************************************80 # ## R4VEC_COVARIANCE computes the covariance of two vectors. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 03 September 2018 # # Author: # # John Burkardt. # # Parameters: # # Input, integer N, the dimension of the two vectors. # # Input, real X(N), Y(N), the two vectors. # # Output, real VALUE, the covariance of the two vectors. # import numpy as np x_average = np.mean ( x[0:n] ) y_average = np.mean ( y[0:n] ) value = 0.0 for i in range ( 0, n ): value = value + ( x[i] - x_average ) * ( y[i] - y_average ) value = value / float ( n - 1 ) return value def r4vec_covariance_test ( ): #*****************************************************************************80 # ## R4VEC_COVARIANCE_TEST tests R4VEC_COVARIANCE. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 03 September 2018 # # Author: # # John Burkardt # import numpy as np from r4_uni_01 import r4_uni_01 print ( '' ) print ( 'R4VEC_COVARIANCE_TEST:' ) print ( ' R4VEC_COVARIANCE computes the covariance of two R4VECs.' ) n = 2 v1 = np.array ( [ 1.0, 0.0 ] ) print ( '' ) print ( ' Vector V1:' ), for i in range ( 0, n ): print ( '%g' % ( v1[i] ) ), print ( '' ) for i in range ( 0, 12 ): angle = float ( 2 * i ) * np.pi / 12.0 r = r4_uni_01 ( ) v2 = r * np.array ( [ np.cos(angle), np.sin(angle) ] ) print ( '' ) print ( ' Vector V2:' ), for i in range ( 0, n ): print ( '%g' % ( v2[i] ) ), print ( '' ) value = r4vec_covariance ( n, v1, v2 ) print ( ' Covariance(V1,V2) = %g' % ( value ) ) # # Terminate. # print ( '' ) print ( 'R4VEC_COVARIANCE_TEST' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) r4vec_covariance_test ( ) timestamp ( )