def i4vec_descends_test():
#*****************************************************************************80
#
## I4VEC_DESCENDS_TEST tests I4VEC_DESCENDS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n = 4
test_num = 6
x_test = np.array ( [ \
[ 1, 3, 2, 4 ], \
[ 2, 2, 2, 2 ], \
[ 1, 2, 2, 4 ], \
[ 1, 2, 3, 4 ], \
[ 4, 4, 3, 1 ], \
[ 9, 7, 3, 0 ] ] )
print ''
print 'I4VEC_DESCENDS_TEST'
print ' I4VEC_DESCENDS determines if an I4VEC descends.'
for i in range(0, test_num):
x = np.zeros(n)
for j in range(0, n):
x[j] = x_test[i, j]
i4vec_transpose_print(n, x, ' Test vector:')
value = i4vec_descends(n, x)
print ' I4VEC_DESCENDS = %s' % (value)
#
# Terminate.
#
print ''
print 'I4VEC_DESCENDS_TEST'
print ' Normal end of execution.'
return
def catalan_row_next_test():
#*****************************************************************************80
#
## CATALAN_ROW_NEXT_TEST tests CATALAN_ROW_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 08 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'CATALAN_ROW_NEXT_TEST'
print ' CATALAN_ROW_NEXT computes a row of Catalan\'s triangle.'
print ''
print ' First, compute row 7 from scratch.'
ido = 0
i = 7
c = np.zeros(0)
c = catalan_row_next(ido, i, c)
i4vec_transpose_print(i + 1, c, ' Row 7:')
print ''
print ' Now compute rows one at a time:'
print ''
n = 10
ido = 0
c = np.zeros(0)
for i in range(0, n + 1):
c = catalan_row_next(ido, i, c)
i4vec_transpose_print(i + 1, c, '')
ido = 1
#
# Terminate.
#
print ''
print 'CATALAN_ROW_NEXT_TEST'
print ' Normal end of execution.'
return
def i4vec_descends_test ( ):
#*****************************************************************************80
#
## I4VEC_DESCENDS_TEST tests I4VEC_DESCENDS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n = 4
test_num = 6
x_test = np.array ( [ \
[ 1, 3, 2, 4 ], \
[ 2, 2, 2, 2 ], \
[ 1, 2, 2, 4 ], \
[ 1, 2, 3, 4 ], \
[ 4, 4, 3, 1 ], \
[ 9, 7, 3, 0 ] ] )
print ''
print 'I4VEC_DESCENDS_TEST'
print ' I4VEC_DESCENDS determines if an I4VEC descends.'
for i in range ( 0, test_num ):
x = np.zeros ( n )
for j in range ( 0, n ):
x[j] = x_test[i,j]
i4vec_transpose_print ( n, x, ' Test vector:' )
value = i4vec_descends ( n, x )
print ' I4VEC_DESCENDS = %s' % ( value )
#
# Terminate.
#
print ''
print 'I4VEC_DESCENDS_TEST'
print ' Normal end of execution.'
return
def catalan_row_next_test ( ):
#*****************************************************************************80
#
## CATALAN_ROW_NEXT_TEST tests CATALAN_ROW_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 08 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'CATALAN_ROW_NEXT_TEST'
print ' CATALAN_ROW_NEXT computes a row of Catalan\'s triangle.'
print ''
print ' First, compute row 7 from scratch.'
ido = 0
i = 7
c = np.zeros ( 0 )
c = catalan_row_next ( ido, i, c )
i4vec_transpose_print ( i + 1, c, ' Row 7:' )
print ''
print ' Now compute rows one at a time:'
print ''
n = 10
ido = 0
c = np.zeros ( 0 )
for i in range ( 0, n + 1 ):
c = catalan_row_next ( ido, i, c )
i4vec_transpose_print ( i + 1, c, '' )
ido = 1
#
# Terminate.
#
print ''
print 'CATALAN_ROW_NEXT_TEST'
print ' Normal end of execution.'
return
def vec_lex_next_test():
#*****************************************************************************80
#
## VEC_LEX_NEXT_TEST tests VEC_LEX_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 19 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'VEC_LEX_NEXT_TEST'
print ' VEC_LEX_NEXT generates all DIM_NUM-vectors'
print ' in lex order in a given base BASE.'
dim_num = 3
base = 3
a = np.zeros(dim_num)
more = False
print ''
print ' The spatial dimension DIM_NUM = %d' % (dim_num)
print ' The base BASE = %d' % (base)
print ''
while (True):
a, more = vec_lex_next(dim_num, base, a, more)
if (not more):
break
i4vec_transpose_print(dim_num, a, '')
#
# Terminate.
#
print ''
print 'VEC_LEX_NEXT_TEST:'
print ' Normal end of execution.'
return
def comb_next_test ( ):
#*****************************************************************************80
#
## COMB_NEXT_TEST tests COMB_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 08 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n = 5
print ''
print 'COMB_NEXT_TEST'
print ' COMB_NEXT produces combinations.'
print ' We are selecting from a set of size %d' % ( n )
for k in range ( 1, n + 1 ):
print ''
print ' Combinations of size %d:' % ( k )
print ''
a = np.zeros ( k )
done = True
while ( True ):
a, done = comb_next ( n, k, a, done )
if ( done ):
break
i4vec_transpose_print ( k, a, '' )
#
# Terminate.
#
print ''
print 'COMB_NEXT_TEST'
print ' Normal end of execution.'
return
def vec_lex_next_test ( ):
#*****************************************************************************80
#
## VEC_LEX_NEXT_TEST tests VEC_LEX_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 19 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'VEC_LEX_NEXT_TEST'
print ' VEC_LEX_NEXT generates all DIM_NUM-vectors'
print ' in lex order in a given base BASE.'
dim_num = 3
base = 3
a = np.zeros ( dim_num )
more = False
print ''
print ' The spatial dimension DIM_NUM = %d' % ( dim_num )
print ' The base BASE = %d' % ( base )
print ''
while ( True ):
a, more = vec_lex_next ( dim_num, base, a, more )
if ( not more ):
break
i4vec_transpose_print ( dim_num, a, '' )
#
# Terminate.
#
print ''
print 'VEC_LEX_NEXT_TEST:'
print ' Normal end of execution.'
return
def thue_ternary_next_test():
#*****************************************************************************80
#
## THUE_TERNARY_NEXT_TEST tests THUE_TERNARY_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'THUE_TERNARY_NEXT_TEST'
print ' THUE_TERNARY_NEXT returns the next'
print ' Thue ternary sequence.'
print ''
thue = np.zeros(1)
n = 1
thue[0] = 1
i4vec_transpose_print(n, thue, str(0))
for i in range(1, 6):
[n, thue] = thue_ternary_next(n, thue)
i4vec_transpose_print(n, thue, str(i))
#
# Terminate.
#
print ''
print 'THUE_TERNARY_NEXT_TEST:'
print ' Normal end of execution.'
return
def i4vec_sort_bubble_a_test ( ): #*****************************************************************************80 # ## I4VEC_SORT_BUBBLE_A_TEST tests I4VEC_SORT_BUBBLE_A. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 07 May 2015 # # Author: # # John Burkardt # from i4vec_transpose_print import i4vec_transpose_print from i4vec_uniform_ab import i4vec_uniform_ab print '' print 'I4VEC_SORT_BUBBLE_A_TEST' print ' I4VEC_SORT_BUBBLE_A ascending sorts an I4VEC.' n = 20 i4_lo = 0 i4_hi = 3 * n seed = 123456789 a, seed = i4vec_uniform_ab ( n, i4_lo, i4_hi, seed ) i4vec_transpose_print ( n, a, ' Unsorted:' ) a = i4vec_sort_bubble_a ( n, a ) i4vec_transpose_print ( n, a, ' Ascending sorted:' ) # # Terminate. # print '' print 'I4VEC_SORT_BUBBLE_A_TEST:' print ' Normal end of execution.' return
def i4vec_sort_bubble_a_test():
#*****************************************************************************80
#
## I4VEC_SORT_BUBBLE_A_TEST tests I4VEC_SORT_BUBBLE_A.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 May 2015
#
# Author:
#
# John Burkardt
#
from i4vec_transpose_print import i4vec_transpose_print
from i4vec_uniform_ab import i4vec_uniform_ab
print ''
print 'I4VEC_SORT_BUBBLE_A_TEST'
print ' I4VEC_SORT_BUBBLE_A ascending sorts an I4VEC.'
n = 20
i4_lo = 0
i4_hi = 3 * n
seed = 123456789
a, seed = i4vec_uniform_ab(n, i4_lo, i4_hi, seed)
i4vec_transpose_print(n, a, ' Unsorted:')
a = i4vec_sort_bubble_a(n, a)
i4vec_transpose_print(n, a, ' Ascending sorted:')
#
# Terminate.
#
print ''
print 'I4VEC_SORT_BUBBLE_A_TEST:'
print ' Normal end of execution.'
return
def thue_ternary_next_test ( ):
#*****************************************************************************80
#
## THUE_TERNARY_NEXT_TEST tests THUE_TERNARY_NEXT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
print ''
print 'THUE_TERNARY_NEXT_TEST'
print ' THUE_TERNARY_NEXT returns the next'
print ' Thue ternary sequence.'
print ''
thue = np.zeros ( 1 )
n = 1
thue[0] = 1
i4vec_transpose_print ( n, thue, str ( 0 ) )
for i in range ( 1, 6 ):
[ n, thue ] = thue_ternary_next ( n, thue )
i4vec_transpose_print ( n, thue, str ( i ) )
#
# Terminate.
#
print ''
print 'THUE_TERNARY_NEXT_TEST:'
print ' Normal end of execution.'
return
def perm0_check_test ( ): #*****************************************************************************80 # ## PERM0_CHECK_TEST tests PERM0_CHECK. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 24 May 2015 # # Author: # # John Burkardt # import numpy as np from i4vec_transpose_print import i4vec_transpose_print n = 5 p1 = np.array ( [ 5, 2, 3, 4, 1 ] ) p2 = np.array ( [ 4, 1, 3, 0, 2 ] ) p3 = np.array ( [ 0, 2, 1, 3, 2 ] ) print '' print 'PERM0_CHECK_TEST' print ' PERM0_CHECK checks a permutation of 0,...,N-1.' i4vec_transpose_print ( n, p1, ' Permutation 1:' ) check = perm0_check ( n, p1 ) i4vec_transpose_print ( n, p2, ' Permutation 2:' ) check = perm0_check ( n, p2 ) i4vec_transpose_print ( n, p3, ' Permutation 3:' ) check = perm0_check ( n, p3 ) # # Terminate. # print '' print 'PERM0_CHECK_TEST:' print ' Normal end of execution.' return
def vector_constrained_next3_test():
#*****************************************************************************80
#
## VECTOR_CONSTRAINED_NEXT3_TEST tests VECTOR_CONSTRAINED_NEXT3.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n_max = 3
print ''
print 'VECTOR_CONSTRAINED_NEXT3_TEST'
print ' VECTOR_CONSTRAINED_NEXT3:'
print ' Consider vectors:'
print ' X_MIN(1:N) <= X(1:N) <= X_MAX(1:N),'
print ' Set'
print ' CONSTRAINT = sum ( X(1:N) / X_MAX(1:N) )'
print ' Accept only vectors for which:'
print ' CONSTRAINT <= 1'
x_min = np.array([1, 1, 1])
x_max = np.array([5, 6, 4])
for n in range(2, n_max + 1):
more = False
i4vec_transpose_print(n, x_min, ' XMIN:')
i4vec_transpose_print(n, x_max, ' XMAX:')
i = 0
x_prod = np.prod(x_max)
print ''
print ' Maximum allowed CONSTRAINT = P = %d' % (x_prod)
print ''
x = np.zeros(n)
while (True):
x, constraint, more = vector_constrained_next3 ( n, x_min, x_max, x, \
more )
if (not more):
break
i = i + 1
print ' %8d' % (i),
for j in range(0, n):
print ' %8d' % (x[j]),
print ' %12g' % (constraint)
#
# Terminate.
#
print ''
print 'VECTOR_CONSTRAINED_NEXT3_TEST'
print ' Normal end of execution.'
return
def monomial_value_test():
#*****************************************************************************80
#
## MONOMIAL_VALUE_TEST tests MONOMIAL_VALUE on sets of data in various dimensions.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 April 2015
#
# Author:
#
# John Burkardt
#
from i4vec_transpose_print import i4vec_transpose_print
from i4vec_uniform_ab import i4vec_uniform_ab
from monomial_value import monomial_value
from r8mat_nint import r8mat_nint
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'MONOMIAL_VALUE_TEST'
print ' Use monomial_value() to evaluate some monomials'
print ' in dimensions 1 through 3.'
e_min = -3
e_max = 6
n = 5
seed = 123456789
x_min = -2.0
x_max = +10.0
for m in range(1, 4):
print ''
print ' Spatial dimension M = %d' % (m)
e, seed = i4vec_uniform_ab(m, e_min, e_max, seed)
i4vec_transpose_print(m, e, ' Exponents:')
x, seed = r8mat_uniform_ab(m, n, x_min, x_max, seed)
#
# To make checking easier, make the X values integers.
#
x = r8mat_nint(m, n, x)
v = monomial_value(m, n, e, x)
print ''
print ' V(X) ',
for i in range(0, m):
print ' X(%d)' % (i),
print ''
print ''
for j in range(0, n):
print '%14.6g ' % (v[j]),
for i in range(0, m):
print '%10.4f' % (x[i, j]),
print ''
print ''
print 'MONOMIAL_VALUE_TEST'
print ' Normal end of execution.'
return
def vector_constrained_next_test ( ):
#*****************************************************************************80
#
## VECTOR_CONSTRAINED_NEXT_TEST tests VECTOR_CONSTRAINED_NEXT
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 29 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n = 3
print ''
print 'VECTOR_CONSTRAINED_NEXT_TEST'
print ' VECTOR_CONSTRAINED_NEXT:'
print ' Consider vectors:'
print ' X_MIN(1:N) <= X(1:N) <= X_MAX(1:N),'
print ' Set'
print ' P = Product X_MAX(1:N)'
print ' Accept only vectors for which:'
print ' sum ( (X(1:N)-1) * P / X_MAX(1:N) ) <= P'
more = False
x_min = np.array ( [ 2, 2, 1 ] )
x_max = np.array ( [ 4, 5, 3 ] )
i4vec_transpose_print ( n, x_min, ' XMIN:' )
i4vec_transpose_print ( n, x_max, ' XMAX:' )
i = 0
x_prod = np.prod ( x_max )
print ''
print ' Maximum allowed CONSTRAINT = P = %d' % ( x_prod )
print ''
x = np.zeros ( n )
while ( True ):
x, constraint, more = vector_constrained_next ( n, x_min, x_max, x, more )
if ( not more ):
break
i = i + 1
print ' %8d: %8d %8d %8d %12d' % ( i, x[0], x[1], x[2], constraint )
#
# Terminate.
#
print ''
print 'VECTOR_CONSTRAINED_NEXT_TEST'
print ' Normal end of execution.'
return
def vector_constrained_next_test():
#*****************************************************************************80
#
## VECTOR_CONSTRAINED_NEXT_TEST tests VECTOR_CONSTRAINED_NEXT
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 29 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n = 3
print ''
print 'VECTOR_CONSTRAINED_NEXT_TEST'
print ' VECTOR_CONSTRAINED_NEXT:'
print ' Consider vectors:'
print ' X_MIN(1:N) <= X(1:N) <= X_MAX(1:N),'
print ' Set'
print ' P = Product X_MAX(1:N)'
print ' Accept only vectors for which:'
print ' sum ( (X(1:N)-1) * P / X_MAX(1:N) ) <= P'
more = False
x_min = np.array([2, 2, 1])
x_max = np.array([4, 5, 3])
i4vec_transpose_print(n, x_min, ' XMIN:')
i4vec_transpose_print(n, x_max, ' XMAX:')
i = 0
x_prod = np.prod(x_max)
print ''
print ' Maximum allowed CONSTRAINT = P = %d' % (x_prod)
print ''
x = np.zeros(n)
while (True):
x, constraint, more = vector_constrained_next(n, x_min, x_max, x, more)
if (not more):
break
i = i + 1
print ' %8d: %8d %8d %8d %12d' % (i, x[0], x[1], x[2], constraint)
#
# Terminate.
#
print ''
print 'VECTOR_CONSTRAINED_NEXT_TEST'
print ' Normal end of execution.'
return
def vector_constrained_next3_test ( ):
#*****************************************************************************80
#
## VECTOR_CONSTRAINED_NEXT3_TEST tests VECTOR_CONSTRAINED_NEXT3.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from i4vec_transpose_print import i4vec_transpose_print
n_max = 3
print ''
print 'VECTOR_CONSTRAINED_NEXT3_TEST'
print ' VECTOR_CONSTRAINED_NEXT3:'
print ' Consider vectors:'
print ' X_MIN(1:N) <= X(1:N) <= X_MAX(1:N),'
print ' Set'
print ' CONSTRAINT = sum ( X(1:N) / X_MAX(1:N) )'
print ' Accept only vectors for which:'
print ' CONSTRAINT <= 1'
x_min = np.array ( [ 1, 1, 1 ] )
x_max = np.array ( [ 5, 6, 4 ] )
for n in range ( 2, n_max + 1 ):
more = False
i4vec_transpose_print ( n, x_min, ' XMIN:' )
i4vec_transpose_print ( n, x_max, ' XMAX:' )
i = 0
x_prod = np.prod ( x_max )
print ''
print ' Maximum allowed CONSTRAINT = P = %d' % ( x_prod )
print ''
x = np.zeros ( n )
while ( True ):
x, constraint, more = vector_constrained_next3 ( n, x_min, x_max, x, \
more )
if ( not more ):
break
i = i + 1
print ' %8d' % ( i ),
for j in range ( 0, n ):
print ' %8d' % ( x[j] ),
print ' %12g' % ( constraint )
#
# Terminate.
#
print ''
print 'VECTOR_CONSTRAINED_NEXT3_TEST'
print ' Normal end of execution.'
return
def monomial_value_test ( ):
#*****************************************************************************80
#
## MONOMIAL_VALUE_TEST tests MONOMIAL_VALUE on sets of data in various dimensions.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 April 2015
#
# Author:
#
# John Burkardt
#
from i4vec_transpose_print import i4vec_transpose_print
from i4vec_uniform_ab import i4vec_uniform_ab
from monomial_value import monomial_value
from r8mat_nint import r8mat_nint
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'MONOMIAL_VALUE_TEST'
print ' Use monomial_value() to evaluate some monomials'
print ' in dimensions 1 through 3.'
e_min = -3
e_max = 6
n = 5
seed = 123456789
x_min = -2.0
x_max = +10.0
for m in range ( 1, 4 ):
print ''
print ' Spatial dimension M = %d' % ( m )
e, seed = i4vec_uniform_ab ( m, e_min, e_max, seed )
i4vec_transpose_print ( m, e, ' Exponents:' )
x, seed = r8mat_uniform_ab ( m, n, x_min, x_max, seed )
#
# To make checking easier, make the X values integers.
#
x = r8mat_nint ( m, n, x )
v = monomial_value ( m, n, e, x )
print ''
print ' V(X) ',
for i in range ( 0, m ):
print ' X(%d)' % ( i ),
print ''
print ''
for j in range ( 0, n ):
print '%14.6g ' % ( v[j] ),
for i in range ( 0, m ):
print '%10.4f' % ( x[i,j] ),
print ''
print ''
print 'MONOMIAL_VALUE_TEST'
print ' Normal end of execution.'
return
