#! /usr/bin/env python
#
def q8_multiply ( q1, q2 ):

#*****************************************************************************80
#
## Q8_MULTIPLY multiplies two quaternions.
#
#  Discussion:
#
#    A quaternion is a quadruplet (A,B,C,D) of real numbers, which
#    may be written as
#
#      Q = A + Bi + Cj + Dk.
#
#    To multiply two quaternions, use the relationships:
#
#      i * j = -j * i = k
#      j * k = -k * j = i
#      k * i = -i * k = j
#      i * i =  j * j = k * k = -1
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 August 2018
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real Q1[3], Q2[3], the two quaternions to be multiplied.
#
#    Output, real Q3[3], the product of the two quaternions.
#
  import numpy as np

  q3 = np.zeros ( 4 )

  q3[0] = q1[0] * q2[0] - q1[1] * q2[1] - q1[2] * q2[2] - q1[3] * q2[3]
  q3[1] = q1[0] * q2[1] + q1[1] * q2[0] + q1[2] * q2[3] - q1[3] * q2[2]
  q3[2] = q1[0] * q2[2] - q1[1] * q2[3] + q1[2] * q2[0] + q1[3] * q2[1]
  q3[3] = q1[0] * q2[3] + q1[1] * q2[2] - q1[2] * q2[1] + q1[3] * q2[0]

  return q3

def q8_multiply_test ( ):

#*****************************************************************************80
#
## Q8_MULTIPLY_TEST tests Q8_MULTIPLY.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 July 2018
#
#  Author:
#
#    John Burkardt
#
  import platform
  from q8_normal_01 import q8_normal_01
  from q8_transpose_print import q8_transpose_print

  seed = 123456789

  print ( '' )
  print ( 'Q8_MULTIPLY_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Q8_MULTIPLY multiplies two quaternions' )

  for i in range ( 0, 5 ):

    q1, seed = q8_normal_01 ( seed )
    q2, seed = q8_normal_01 ( seed )
    q3 = q8_multiply ( q1, q2 )

    print ( '' )
    q8_transpose_print ( q1, '  q1 = q8_normal_01 ( seed ) :' )
    q8_transpose_print ( q2, '  q2 = q8_normal_01 ( seed ) :' )
    q8_transpose_print ( q3, '  q3 = q8_multiply ( q1, q2 ):' )  
#
#  Terminate.
#
  print ( '' )
  print ( 'Q8_MULTIPLY_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  q8_multiply_test ( )
  timestamp ( )