#! /usr/bin/env python3
#
def bmi_english ( weight_lb, height_in ):

#*****************************************************************************80
#
## bmi_english() computes the BMI (body mass index).
#  
#  Discussion: the BMI has a simple formula when the input is defined in metric units
#  This program accepts data in English units (pounds and inches) and applies the
#  correct unit conversions.  An "ideal" BMI is between 18.5 and 30.  Above 30 begins
#  to count as "obese" and below 18.5 is considered "underweight".
# 
#  Example: bmi_english ( 150, 60 ) returns the value 29.30
#  
#  Modified: 12 May 2022
#  
#  Author: John Burkardt
#  
#  Reference:  https://en.wikipedia.org/wiki/Body_mass_index
#  
#  Input: 
#    weight_lb, the weight in pounds.
#    height_in, the height in inches.
#    
#  Output:
#    value, the body mass index.
#
  value = ( weight_lb / 2.204 ) * ( 39.370 / height_in )**2
  return value

def bmi_english_test ( ):

#*****************************************************************************80
#
## bmi_english_test() tests bmi_english().
# 
  print ( '' )
  print ( 'value = bmi_english ( weight_lb, height_in ) demonstration:' )
  print ( '' )
  value = bmi_english ( 100, 50 )
  print ( '  bmi_english(100,50) = ', value )
  value = bmi_english ( 150, 60 )
  print ( '  bmi_english(150,60) = ', value )
  value = bmi_english ( 200, 70 )
  print ( '  bmi_english(200,70) = ', value )

def c_to_f ( c ):

#*****************************************************************************80
#
## c_to_f() converts Celsius to Fahrenheit temperature.
#
  f = ( 9 / 5 ) * c + 32
  return f

def c_to_k ( c ):

#*****************************************************************************80
#
## c_to_k() converts Celsius temperature to Kelvin.
#
  k = c + 273.15
  return k

def cosm_sinn ( m, n ):

#*****************************************************************************80
#
## cosm_sinn() evaluates integral(0 <= theta <= pi/2) cos^m(theta) sin^n(theta) dtheta
#
  from math import pi
  from my_library import double_factorial

# backslash lets us split the following long line

  value = double_factorial ( m - 1 ) * double_factorial ( n - 1 ) \
    / double_factorial ( m + n )
  
  if ( ( m % 2 == 0 ) and ( n % 2 == 0 ) ):
    value = value * pi / 2.0

  return value

def cosm_sinn_test ( ):

#*****************************************************************************80
#
## cosm_sinn_test() tests cosm_sinn().
#
  print ( '' )
  print ( 'cosm_sinn_test():' )
  print ( '  Test cosm_sinn()' )
  print ( '' )
  print ( 'm n integral value' )

  for m in range ( 2, 5 ):
    print ( '' )
    for n in range ( 2, 5 ):
      print ( m, n, cosm_sinn ( m, n ) )

  return

def double_factorial ( n ):

#*****************************************************************************80
#
## double_factorial() evaluates the double factorial function.
#
#  Discussion:
#
#    The double factorial function of n is represented by n!!
#
#    If n is even, n!! = 2 * 4 * ... * n-2 * n
#
#    If n is odd, n!! = 1 * 3 * ... * n-2 * n
#
#  Modified:
#
#    17 January 2023
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer n: the argument.
#
#  Output:
#
#    integer value: the value of n!!
#
  value = 1
  
  while ( 0 < n ):
    value = value * n
    n = n - 2

  return value

def double_factorial_test ( ):

#*****************************************************************************80
#
## double_factorial() evaluates the double factorial function.
#
  exact = [ 1, 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 125135, 645120 ]
  exact_num = len ( exact )

  print ( '' )
  print ( 'double_factorial_test():' )
  print ( '  Test double_factorial(n)' )
  print ( '' )

  for n in range ( 0, exact_num ):
    value = double_factorial ( n )
    print ( n, value, exact[n] )

  return

def f_to_c ( f ):

#*****************************************************************************80
#
## f_to_c() converts Fahrenheit temperatures to Celsius.
#
  c = ( 5 / 9 ) * ( f - 32 )
  return c

def f_to_k ( f ):

#*****************************************************************************80
#
## f_to_k() converts Fahrenheit temperatures to Kelvin.
#
  c = f_to_c ( f )
  k = c + 273.15
  return k

def k_to_c ( k ):

#*****************************************************************************80
#
## k_to_c() converts Kelvin temperatures to Celsius.
#
  c = k - 273.15
  return c

def k_to_f ( k ):

#*****************************************************************************80
#
## k_to_f() converts Kelvin temperatures to Fahrenheit.
#
  c = k_to_c ( k )
  f = c_to_f ( c )
  return f

if ( __name__ == "__main__" ):

  bmi_english_test ( )
  double_factorial_test ( )
  cosm_sinn_test ( )