#! /usr/bin/env python3 # def cosine_transform_data ( n, d ): #*****************************************************************************80 # ## cosine_transform_data() does a cosine transform on a vector of data. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 August 2015 # # Author: # # John Burkardt # # Input: # # integer N, the number of data points. # # real D(N), the vector of data. # # Output: # # real C(N), the cosine transform coefficients. # import numpy as np c = np.zeros ( n ) for i in range ( 0, n ): for j in range ( 0, n ): angle = np.pi * float ( 2 * j + 1 ) * float ( i ) / 2.0 / float ( n ) c[i] = c[i] + d[j] * np.cos ( angle ) c[i] = c[i] * np.sqrt ( 2.0 / float ( n ) ) return c def cosine_transform_inverse ( n, c ): #*****************************************************************************80 # ## cosine_transform_inverse() does an inverse cosine transform. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 August 2015 # # Author: # # John Burkardt # # Input: # # integer N, the number of data points. # # real C(N), the cosine transform coefficients. # # Output: # # real D(N), the vector of data. # import numpy as np d = np.zeros ( n ) for i in range ( 0, n ): d[i] = c[0] / 2.0 for j in range ( 1, n ): d[i] = d[i] + np.cos ( np.pi * float ( 2 * i + 1 ) \ * float ( j ) / 2.0 / float ( n ) ) * c[j] d[i] = d[i] * np.sqrt ( 2.0 / float ( n ) ) return d def cosine_transform_data_test ( ): #*****************************************************************************80 # ## cosine_transform_data_test() tests cosine_transform_data(). # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 August 2015 # # Author: # # John Burkardt # import numpy as np import platform n = 10 print ( '' ) print ( 'COSINE_TRANSFORM_DATA_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' COSINE_TRANSFORM_DATA does a cosine transform of data' ) print ( ' defined by a vector.' ) print ( '' ) print ( ' Apply the transform, then its inverse.' ) print ( ' Let R be a random N vector.' ) print ( ' Let S be the transform of D.' ) print ( ' Let T be the transform of E.' ) print ( ' Then R and T will be equal.' ) r = np.random.rand ( n ) s = cosine_transform_data ( n, r ) t = cosine_transform_inverse ( n, s ) print ( '' ) print ( ' I R(I) S(I) T(I)' ) print ( '' ) for i in range ( 0, n ): print ( ' %4d %10f %10f %10f' % ( i, r[i], s[i], t[i] ) ) # # Terminate. # print ( '' ) print ( 'COSINE_TRANSFORM_DATA_TEST' ) print ( ' Normal end of execution.' ) return def cosine_transform_test ( ): #*****************************************************************************80 # ## cosine_transform_test() tests cosine_transform(). # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 28 August 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'cosine_transform_test()' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' Test cosine_transform().' ) cosine_transform_data_test ( ) # # Terminate. # print ( '' ) print ( 'cosine_transform_test():' ) print ( ' Normal end of execution.' ) return def r8vec_print ( n, a, title ): #*****************************************************************************80 # ## r8vec_print() prints an R8VEC. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 31 August 2014 # # Author: # # John Burkardt # # Input: # # integer N, the dimension of the vector. # # real A(N), the vector to be printed. # # string TITLE, a title. # print ( '' ) print ( title ) print ( '' ) for i in range ( 0, n ): print ( '%6d: %12g' % ( i, a[i] ) ) return def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 06 April 2013 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return None if ( __name__ == '__main__' ): timestamp ( ) cosine_transform_test ( ) timestamp ( )