def lpp_to_polynomial_test():
#*****************************************************************************80
#
## LPP_TO_POLYNOMIAL_TEST tests LPP_TO_POLYNOMIAL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from polynomial_print import polynomial_print
import numpy as np
m = 2
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' LPP_TO_POLYNOMIAL is given a Legendre product polynomial'
print ' and determines its polynomial representation.'
print ''
print ' Using spatial dimension M = %d' % (m)
for rank in range(1, 12):
l = comp_unrank_grlex(m, rank)
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
c = np.zeros(o_max, dtype=np.float64)
e = np.zeros(o_max, dtype=np.int32)
o, c, e = lpp_to_polynomial(m, l, o_max)
label = ' LPP #' + repr ( rank ) + ' = L(' + repr ( l[0] ) \
+ ',X)*L(' + repr ( l[1] ) + ',Y) = '
print ''
polynomial_print(m, o, c, e, label)
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' Normal end of execution.'
return
def lpp_to_polynomial_test ( ):
#*****************************************************************************80
#
## LPP_TO_POLYNOMIAL_TEST tests LPP_TO_POLYNOMIAL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 October 2014
#
# Author:
#
# John Burkardt
#
from comp_unrank_grlex import comp_unrank_grlex
from polynomial_print import polynomial_print
import numpy as np
m = 2
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' LPP_TO_POLYNOMIAL is given a Legendre product polynomial'
print ' and determines its polynomial representation.'
print ''
print ' Using spatial dimension M = %d' % ( m )
for rank in range ( 1, 12 ):
l = comp_unrank_grlex ( m, rank )
o_max = 1
for i in range ( 0, m ):
o_max = o_max * ( l[i] + 2 ) // 2
c = np.zeros ( o_max, dtype = np.float64 )
e = np.zeros ( o_max, dtype = np.int32 )
o, c, e = lpp_to_polynomial ( m, l, o_max )
label = ' LPP #' + repr ( rank ) + ' = L(' + repr ( l[0] ) \
+ ',X)*L(' + repr ( l[1] ) + ',Y) = '
print ''
polynomial_print ( m, o, c, e, label )
print ''
print 'LPP_TO_POLYNOMIAL_TEST:'
print ' Normal end of execution.'
return
def polynomial_value_test():
#*****************************************************************************80
#
## POLYNOMIAL_VALUE_TEST tests POLYNOMIAL_VALUE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 27 October 2014
#
# Author:
#
# John Burkardt
#
from polynomial_print import polynomial_print
import numpy as np
m = 3
o = 6
c = np.array([7.0, -5.0, 9.0, 11.0, 0.0, -13.0], dtype=np.float64)
e = np.array([1, 2, 4, 5, 12, 33], dtype=np.int32)
nx = 2
x = np.array ( [ 1.0, 2.0, 3.0, \
-2.0, 4.0, 1.0 ], dtype = np.float64 )
print ''
print 'POLYNOMIAL_VALUE_TEST'
print ' POLYNOMIAL_VALUE evaluates a polynomial.'
print ''
title = ' P(X) = '
polynomial_print(m, o, c, e, title)
p = polynomial_value(m, o, c, e, nx, x)
print ''
for j in range(0, nx):
print ' P(%f,%f,%f) = %g' % (x[0 + j * m], x[1 + j * m], x[2 + j * m],
p[j])
print ''
print 'POLYNOMIAL_VALUE_TEST:'
print ' Normal end of execution.'
return
def polynomial_value_test ( ):
#*****************************************************************************80
#
## POLYNOMIAL_VALUE_TEST tests POLYNOMIAL_VALUE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 27 October 2014
#
# Author:
#
# John Burkardt
#
from polynomial_print import polynomial_print
import numpy as np
m = 3
o = 6
c = np.array ( [ 7.0, - 5.0, 9.0, 11.0, 0.0, - 13.0 ], dtype = np.float64 )
e = np.array ( [ 1, 2, 4, 5, 12, 33 ], dtype = np.int32 )
nx = 2
x = np.array ( [ 1.0, 2.0, 3.0, \
-2.0, 4.0, 1.0 ], dtype = np.float64 );
print ''
print 'POLYNOMIAL_VALUE_TEST'
print ' POLYNOMIAL_VALUE evaluates a polynomial.'
print ''
title = ' P(X) = '
polynomial_print ( m, o, c, e, title )
p = polynomial_value ( m, o, c, e, nx, x )
print ''
for j in range ( 0, nx ):
print ' P(%f,%f,%f) = %g' % ( x[0+j*m], x[1+j*m], x[2+j*m], p[j] )
print ''
print 'POLYNOMIAL_VALUE_TEST:'
print ' Normal end of execution.'
return
def lp_coefficients_test ( ):
#*****************************************************************************80
#
## LP_COEFFICIENTS_TEST tests LP_COEFFICIENTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 October 2014
#
# Author:
#
# John Burkardt
#
from polynomial_print import polynomial_print
import numpy as np
m = 1
n_max = 10
print ''
print 'LP_COEFFICIENTS_TEST'
print ' LP_COEFFICIENTS: coefficients of Legendre polynomial P(n,x).'
print ''
for n in range ( 0, n_max + 1 ):
o, c, f = lp_coefficients ( n )
e = np.zeros ( o, dtype = np.int32 )
for i in range ( 0, o ):
e[i] = f[i] + 1
label = ' P(' + repr ( n ) + ',x) = '
polynomial_print ( m, o, c, e, label )
print ''
print 'LP_COEFFICIENTS_TEST:'
print ' Normal end of execution.'
return
def polynomial_sort_test():
#*****************************************************************************80
#
## POLYNOMIAL_SORT_TEST tests POLYNOMIAL_SORT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 27 October 2014
#
# Author:
#
# John Burkardt
#
from polynomial_print import polynomial_print
import numpy as np
m = 3
o = 6
c = np.array([0.0, 9.0, -5.0, -13.0, 7.0, 11.0], dtype=np.float64)
e = np.array([12, 4, 2, 33, 1, 5], dtype=np.int32)
print ''
print 'POLYNOMIAL_SORT_TEST'
print ' POLYNOMIAL_SORT sorts a polynomial by exponent index.'
print ''
title = ' Unsorted polynomial:'
polynomial_print(m, o, c, e, title)
c, e = polynomial_sort(o, c, e)
print ''
title = ' Sorted polynomial:'
polynomial_print(m, o, c, e, title)
print ''
print 'POLYNOMIAL_SORT_TEST:'
print ' Normal end of execution.'
return
def polynomial_sort_test ( ): #*****************************************************************************80 # ## POLYNOMIAL_SORT_TEST tests POLYNOMIAL_SORT. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 27 October 2014 # # Author: # # John Burkardt # from polynomial_print import polynomial_print import numpy as np m = 3 o = 6 c = np.array ( [ 0.0, 9.0, -5.0, - 13.0, 7.0, 11.0 ], dtype = np.float64 ) e = np.array ( [ 12, 4, 2, 33, 1, 5 ], dtype = np.int32 ) print '' print 'POLYNOMIAL_SORT_TEST' print ' POLYNOMIAL_SORT sorts a polynomial by exponent index.' print '' title = ' Unsorted polynomial:' polynomial_print ( m, o, c, e, title ) c, e = polynomial_sort ( o, c, e ) print '' title = ' Sorted polynomial:' polynomial_print ( m, o, c, e, title ) print '' print 'POLYNOMIAL_SORT_TEST:' print ' Normal end of execution.' return
def polynomial_compress_test ( ):
#*****************************************************************************80
#
## POLYNOMIAL_COMPRESS_TEST tests POLYNOMIAL_COMPRESS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 27 October 2014
#
# Author:
#
# John Burkardt
#
from polynomial_print import polynomial_print
import numpy as np
print ''
print 'POLYNOMIAL_COMPRESS_TEST'
print ' POLYNOMIAL_COMPRESS compresses a polynomial.'
m = 3
o = 10
c = np.array ( [ 7.0, - 5.0, 5.0, 9.0, 11.0, 3.0, 6.0, 0.0, - 13.0, 1.0E-20 ], \
dtype = np.float64 )
e = np.array ( [ 1, 2, 2, 4, 5, 5, 5, 12, 33, 35 ], dtype = np.int32 )
print ''
title = ' Uncompressed polynomial ='
polynomial_print ( m, o, c, e, title )
o2, c2, e2 = polynomial_compress ( o, c, e )
print ''
title = ' Compressed polynomial ='
polynomial_print ( m, o2, c2, e2, title )
print ''
print 'POLYNOMIAL_COMPRESS_TEST:'
print ' Normal end of execution.'
return
