#! /usr/bin/env python3
#
def complex_numbers_test ( ):

#*****************************************************************************80
#
## complex_numbers_test() demonstrates the use of complex numbers.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    10 December 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'complex_numbers_test():' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test complex number usage.' )
#
#  Single precision complex numbers: "complex64".
#
  complex_numbers_test01 ( )
  complex_numbers_test02 ( )
  complex_numbers_test03 ( )
#
#  Double precision complex numbers: "complex128".
#
  complex_numbers_test04 ( )
  complex_numbers_test05 ( )
  complex_numbers_test06 ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'complex_numbers_test():' )
  print ( '  Normal end of execution.' )
  return

def complex_numbers_test01 ( ):

#*****************************************************************************80
#
## complex_numbers_test01() demonstrates declaration and assignment.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 December 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
#
#  Declare a complex number A.
#  Declare a complex vector B.
#  Declare a complex array C.
#
  print ( '' )
  print ( 'complex_numbers_test01():' )
  print ( '  Declare single precision complex variables.' )
  print ( '  Assign value with an = statement.' )
#
#  Assign values to A, B, and C.
#
  a = np.complex64 ( 1.0 + 2.0j )
  print ( '' )
  print ( '  Scalar a:' )
  print ( '    (%+g%+gj)' % ( a.real, a.imag ) )

  b = np.zeros ( 3, dtype = np.complex64 )
  b[0] =   1.0 - 2.0j
  b[1] = - 3.0 + 4.0j
  b[2] = - 5.0 - 6.0j
  print ( '' )
  print ( '  Vector b:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( b[i].real, b[i].imag ) )

  c = np.zeros ( [ 2, 2 ], dtype = np.complex64 )
  c[0,0] = 1.0 + 0.1j
  c[0,1] = 1.0 + 0.2j
  c[1,0] = 2.0 + 0.1j
  c[1,1] = 2.0 + 0.2j
  print ( '' )
  print ( '  Matrix c:' )
  for i in range ( 0, 2 ):
    for j in range ( 0, 2 ):
      print ( '  (%+g%+gj)' % ( c[i,j].real, c[i,j].imag ), end = '' )
    print ( '' )

  return

def complex_numbers_test02 ( ):

#*****************************************************************************80
#
## complex_numbers_test02() demonstrate declaration and initialization for complex variables.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    09 May 2017
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  print ( '' )
  print ( 'complex_numbers_test02' )
  print ( '  Declare single precision complex variables.' )
  print ( '  Initialize value as part of the declaration.' )

  a = np.complex64 ( 1.0 + 2.0j )
  print ( '' )
  print ( '  Scalar a:' )
  print ( '    (%+g%+gj)' % ( a.real, a.imag ) )

  b = np.array ( [ 1.0 + 2.0j, 3.0 + 4.0j, 5.0 + 6.0j ], dtype = np.complex64 )
  print ( '' )
  print ( '  Vector b:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( b[i].real, b[i].imag ) )

  c = np.array ( [ [ 1.0 + 0.1j, 1.0 + 0.2j ], \
                   [ 2.0 + 0.1j, 2.0 + 0.2j ] ], dtype = np.complex64 )
  print ( '' )
  print ( '  Matrix c:' )
  for i in range ( 0, 2 ):
    for j in range ( 0, 2 ):
      print ( '  (%+g%+gj)' % ( c[i,j].real, c[i,j].imag ), end = '' )
    print ( '' )
#
#  Stupidly, Python won't let you say d = complex ( dr, di )...
#
  dr = np.array ( [ 1.0, 2.0, 3.0 ], dtype = np.float32 )
  di = np.array ( [ 4.0, 5.0, 6.0 ], dtype = np.float32 )
  d = dr + di * 1j
  print ( '' )
  print ( '  Vector d = dr + di * 1j:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( d[i].real, d[i].imag ) )

  return

def complex_numbers_test03 ( ):

#*****************************************************************************80
#
## complex_numbers_test03(): intrinsic functions for complex variables.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 December 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  a = np.complex64 ( 1.0 + 2.0j )

  print ( '' )
  print ( 'complex_numbers_test03' )
  print ( '  Apply intrinsic functions to single precision complex variables' )
  print ( '' )
  print ( '  1j =                 (%+g%+g)' % ( 1j.real, 1j.imag ) )
  print ( '  a =                  (%+g%+g)' % ( a.real, a.imag ) )
  print ( '  - a =                (%+g%+g)' % ( - a.real, -a.imag ) )
  print ( '  a + 3 =              (%+g%+g)' % ( ( a + 3 ).real, ( a + 3 ).imag ) )
  print ( '  a + 5j =             (%+g%+g)' % ( ( a + 5j ).real, ( a + 5j ).imag ) )
  print ( '  4 * a =              (%+g%+g)' % ( ( 4 * a ).real, ( 4 * a ).imag ) )
  print ( '  a / 8 =              (%+g%+g)' % ( ( a / 8 ).real, ( a / 8 ).imag ) )
  print ( '  a * a =              (%+g%+g)' % ( ( a * a ).real, ( a * a ).imag ) )
  print ( '  a ** 2 =             (%+g%+g)' % ( ( a ** 2 ).real, ( a ** 2 ).imag ) )
  print ( '  2 ** a =             (%+g%+g)' % ( ( 2 ** a ).real, ( 2 ** a ).imag ) )
  print ( '  a ** a =             (%+g%+g)' % ( ( a ** a ).real, ( a ** a ).imag ) )
  print ( '  1/a =                (%+g%+g)' % ( ( 1.0 / a ).real, ( 1.0 / a ).imag ) )
  print ( '' )
  print ( '  abs(a) =             (%+g)'    % ( abs ( a ) ) )
  print ( '  arccos(a) =          (%+g%+g)' % ( ( np.arccos ( a ) ).real, ( np.arccos ( a ) ).imag ) )
  print ( '  arccosh(a) =         (%+g%+g)' %  ( ( np.arccosh ( a ) ).real, ( np.arccosh ( a ) ).imag ) )
  print ( '  angle(a) =           %+g'     % np.angle ( a ) )
  print ( '  arcsin(a) =          (%+g%+g)' % ( ( np.arcsin ( a ) ).real, ( np.arcsin ( a ) ).imag ) )
  print ( '  arcsinh(a) =         (%+g%+g)' %  ( ( np.arcsinh ( a ) ).real, ( np.arcsinh ( a ) ).imag ) )
  print ( '  arctan(a) =          (%+g%+g)' % ( ( np.arctan ( a ) ).real, ( np.arctan ( a ) ).imag ) )
  print ( '  arctanh(a) =         (%+g%+g)' %  ( ( np.arctanh ( a ) ).real, ( np.arctanh ( a ) ).imag ) )
  print ( '  complex(1) =         (%+g%+g)' % ( ( complex ( 1 ) ).real, ( complex ( 1 ) ).imag ) )
  print ( '  conjugate(a) =       (%+g%+g)' % ( np.conjugate ( a ).real, np.conjugate ( a ).imag ) )
  print ( '  cos(a) =             (%+g%+g)' %  ( ( np.cos ( a ) ).real, ( np.cos ( a ) ).imag ) )
  print ( '  cosh(a) =            (%+g%+g)' %  ( ( np.cosh ( a ) ).real, ( np.cosh ( a ) ).imag ) )
  print ( '  exp(a) =             (%+g%+g)' % ( ( np.exp ( a ) ).real, ( np.exp ( a ) ).imag ) )
  print ( '  a.imag =              %+g'     %  ( a.imag ) )
  print ( '  isinf(a) =            %+s'     % ( np.isinf(a) ) )
  print ( '  isnan(a) =            %+s'     % ( np.isnan(a) ) )
  print ( '  log(a) =             (%+g%+g)' % ( ( np.log ( a ) ).real, ( np.log ( a ) ).imag ) )
  print ( '  log10(a) =           (%+g%+g)' % ( ( np.log10 ( a ) ).real, ( np.log10 ( a ) ).imag ) )
  print ( '  a.real =              %+g'     %  ( a.real ) )
  print ( '  sin(a) =             (%+g%+g)' %  ( ( np.sin ( a ) ).real, ( np.sin ( a ) ).imag ) )
  print ( '  sinh(a) =            (%+g%+g)' %  ( ( np.sinh ( a ) ).real, ( np.sinh ( a ) ).imag ) )
  print ( '  sqrt(a) =            (%+g%+g)' %  ( ( np.sqrt ( a ) ).real, ( np.sqrt ( a ) ).imag ) )
  print ( '  tan(a) =             (%+g%+g)' %  ( ( np.tan ( a ) ).real, ( np.tan ( a ) ).imag ) )
  print ( '  tanh(a) =            (%+24.16g%+24.16g)' %  ( ( np.tanh ( a ) ).real, ( np.tanh ( a ) ).imag ) )

  return

def complex_numbers_test04 ( ):

#*****************************************************************************80
#
## complex_numbers_test04() demonstrates declaration and assignment.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 December 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
#
#  Declare a complex number A.
#  Declare a complex vector B.
#  Declare a complex array C.
#
  print ( '' )
  print ( 'complex_numbers_test04' )
  print ( '  Declare double precision complex variables.' )
  print ( '  Assign value with an = statement.' )
#
#  Assign values to A, B, and C.
#
  a = np.complex128 ( 1.0 + 2.0j )
  print ( '' )
  print ( '  Scalar a:' )
  print ( '    (%+g%+gj)' % ( a.real, a.imag ) )

  b = np.zeros ( 3, dtype = np.complex128 )
  b[0] =   1.0 - 2.0j
  b[1] = - 3.0 + 4.0j
  b[2] = - 5.0 - 6.0j
  print ( '' )
  print ( '  Vector b:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( b[i].real, b[i].imag ) )

  c = np.zeros ( [ 2, 2 ], dtype = np.complex128 )
  c[0,0] = 1.0 + 0.1j
  c[0,1] = 1.0 + 0.2j
  c[1,0] = 2.0 + 0.1j
  c[1,1] = 2.0 + 0.2j
  print ( '' )
  print ( '  Matrix c:' )
  for i in range ( 0, 2 ):
    for j in range ( 0, 2 ):
      print ( '  (%+g%+gj)' % ( c[i,j].real, c[i,j].imag ), end = '' )
    print ( '' )

  return

def complex_numbers_test05 ( ):

#*****************************************************************************80
#
## complex_numbers_test05() demonstrate declaration and initialization for complex variables.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    09 May 2017
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  print ( '' )
  print ( 'complex_numbers_test05' )
  print ( '  Declare a double precision complex variable.' )
  print ( '  Initialize value as part of the declaration.' )

  a = np.complex128 ( 1.0 + 2.0j )
  print ( '' )
  print ( '  Scalar a:' )
  print ( '    (%+g%+gj)' % ( a.real, a.imag ) )

  b = np.array ( [ 1.0 + 2.0j, 3.0 + 4.0j, 5.0 + 6.0j ], dtype = np.complex128 )
  print ( '' )
  print ( '  Vector b:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( b[i].real, b[i].imag ) )

  c = np.array ( [ [ 1.0 + 0.1j, 1.0 + 0.2j ], \
                   [ 2.0 + 0.1j, 2.0 + 0.2j ] ], dtype = np.complex128 )
  print ( '' )
  print ( '  Matrix c:' )
  for i in range ( 0, 2 ):
    for j in range ( 0, 2 ):
      print ( '  (%+g%+gj)' % ( c[i,j].real, c[i,j].imag ), end = '' )
    print ( '' )
#
#  Stupidly, Python won't let you say d = complex ( dr, di )...
#
  dr = np.array ( [ 1.0, 2.0, 3.0 ], dtype = np.float64 )
  di = np.array ( [ 4.0, 5.0, 6.0 ], dtype = np.float64 )
  d = dr + di * 1j
  print ( '' )
  print ( '  Vector d = dr + di * 1j:' )
  for i in range ( 0, 3 ):
    print ( '    (%+g%+gj)' % ( d[i].real, d[i].imag ) )

  return

def complex_numbers_test06 ( ):

#*****************************************************************************80
#
## complex_numbers_test06(): intrinsic functions for complex variables.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 December 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  a = np.complex128 ( 1.0 + 2.0j )

  print ( '' )
  print ( 'complex_numbers_test06' )
  print ( '  Apply intrinsic functions to double precision complex variables' )
  print ( '' )
  print ( '  1j =                 (%+g%+g)' % ( 1j.real, 1j.imag ) )
  print ( '  a =                  (%+g%+g)' % ( a.real, a.imag ) )
  print ( '  - a =                (%+g%+g)' % ( - a.real, -a.imag ) )
  print ( '  a + 3 =              (%+g%+g)' % ( ( a + 3 ).real, ( a + 3 ).imag ) )
  print ( '  a + 5j =             (%+g%+g)' % ( ( a + 5j ).real, ( a + 5j ).imag ) )
  print ( '  4 * a =              (%+g%+g)' % ( ( 4 * a ).real, ( 4 * a ).imag ) )
  print ( '  a / 8 =              (%+g%+g)' % ( ( a / 8 ).real, ( a / 8 ).imag ) )
  print ( '  a * a =              (%+g%+g)' % ( ( a * a ).real, ( a * a ).imag ) )
  print ( '  a ** 2 =             (%+g%+g)' % ( ( a ** 2 ).real, ( a ** 2 ).imag ) )
  print ( '  2 ** a =             (%+g%+g)' % ( ( 2 ** a ).real, ( 2 ** a ).imag ) )
  print ( '  a ** a =             (%+g%+g)' % ( ( a ** a ).real, ( a ** a ).imag ) )
  print ( '  1/a =                (%+g%+g)' % ( ( 1.0 / a ).real, ( 1.0 / a ).imag ) )
  print ( '' )
  print ( '  abs(a) =             (%+g)'    % ( abs ( a ) ) )
  print ( '  arccos(a) =          (%+g%+g)' % ( ( np.arccos ( a ) ).real, ( np.arccos ( a ) ).imag ) )
  print ( '  arccosh(a) =         (%+g%+g)' % ( ( np.arccosh ( a ) ).real, ( np.arccosh ( a ) ).imag ) )
  print ( '  angle(a) =           %+g'     % np.angle ( a ) )
  print ( '  arcsin(a) =          (%+g%+g)' % ( ( np.arcsin ( a ) ).real, ( np.arcsin ( a ) ).imag ) )
  print ( '  arcsinh(a) =         (%+g%+g)' %  ( ( np.arcsinh ( a ) ).real, ( np.arcsinh ( a ) ).imag ) )
  print ( '  arctan(a) =          (%+g%+g)' % ( ( np.arctan ( a ) ).real, ( np.arctan ( a ) ).imag ) )
  print ( '  arctanh(a) =         (%+g%+g)' %  ( ( np.arctanh ( a ) ).real, ( np.arctanh ( a ) ).imag ) )
  print ( '  complex(1) =         (%+g%+g)' % ( ( complex ( 1 ) ).real, ( complex ( 1 ) ).imag ) )
  print ( '  conjugate(a) =       (%+g%+g)' % ( np.conjugate ( a ).real, np.conjugate ( a ).imag ) )
  print ( '  cos(a) =             (%+g%+g)' %  ( ( np.cos ( a ) ).real, ( np.cos ( a ) ).imag ) )
  print ( '  cosh(a) =            (%+g%+g)' %  ( ( np.cosh ( a ) ).real, ( np.cosh ( a ) ).imag ) )
  print ( '  exp(a) =             (%+g%+g)' % ( ( np.exp ( a ) ).real, ( np.exp ( a ) ).imag ) )
  print ( '  a.imag =              %+g'     %  ( a.imag ) )
  print ( '  isinf(a) =            %+s'     % ( np.isinf(a) ) )
  print ( '  isnan(a) =            %+s'     % ( np.isnan(a) ) )
  print ( '  log(a) =             (%+g%+g)' % ( ( np.log ( a ) ).real, ( np.log ( a ) ).imag ) )
  print ( '  log10(a) =           (%+g%+g)' % ( ( np.log10 ( a ) ).real, ( np.log10 ( a ) ).imag ) )
  print ( '  a.real =              %+g'     %  ( a.real ) )
  print ( '  sin(a) =             (%+g%+g)' %  ( ( np.sin ( a ) ).real, ( np.sin ( a ) ).imag ) )
  print ( '  sinh(a) =            (%+g%+g)' %  ( ( np.sinh ( a ) ).real, ( np.sinh ( a ) ).imag ) )
  print ( '  sqrt(a) =            (%+g%+g)' %  ( ( np.sqrt ( a ) ).real, ( np.sqrt ( a ) ).imag ) )
  print ( '  tan(a) =             (%+g%+g)' %  ( ( np.tan ( a ) ).real, ( np.tan ( a ) ).imag ) )
  print ( '  tanh(a) =            (%+g%+g)' %  ( ( np.tanh ( a ) ).real, ( np.tanh ( a ) ).imag ) )

  return

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    06 April 2013
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return None

if ( __name__ == '__main__' ):
  timestamp ( )
  complex_numbers_test ( )
  timestamp ( )