def r8poly_dif_test():
#*****************************************************************************80
#
## R8POLY_DIF_TEST tests R8POLY_DIF.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
test_num = 2
print ''
print 'R8POLY_DIF_TEST'
print ' R8POLY_DIF computes derivatives of an R8POLY.'
#
# 1: Differentiate X^3 + 2*X^2 - 5*X - 6 once.
# 2: Differentiate X^4 + 3*X^3 + 2*X^2 - 2 3 times.
#
for test in range(0, 2):
if (test == 0):
na = 3
d = 1
a = np.array([-6.0, -5.0, 2.0, 1.0])
elif (test == 1):
na = 4
d = 3
a = np.array([-2.0, 5.0, 2.0, 3.0, 1.0])
r8poly_print(na, a, ' The polynomial A:')
print ''
print ' Differentiate A %d times.' % (d)
b = r8poly_dif(na, a, d)
r8poly_print(na - d, b, ' The derivative, B:')
#
# Terminate.
#
print ''
print 'R8POLY_DIF_TEST:'
print ' Normal end of execution.'
return
def r8poly_degree_test ( ): #*****************************************************************************80 # ## R8POLY_DEGREE_TEST tests R8POLY_DEGREE. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 05 January 2015 # # Author: # # John Burkardt # import numpy as np from r8poly_print import r8poly_print c1 = np.array ( [ 1.0, 2.0, 3.0, 4.0 ] ) c2 = np.array ( [ 1.0, 2.0, 3.0, 0.0 ] ) c3 = np.array ( [ 1.0, 2.0, 0.0, 4.0 ] ) c4 = np.array ( [ 1.0, 0.0, 0.0, 0.0 ] ) c5 = np.array ( [ 0.0, 0.0, 0.0, 0.0 ] ) print '' print 'R8POLY_DEGREE_TEST' print ' R8POLY_DEGREE determines the degree of an R8POLY.' m = 3 r8poly_print ( m, c1, ' The R8POLY:' ) d = r8poly_degree ( m, c1 ) print ' Dimensioned degree = %d, Actual degree = %d' % ( m, d ) r8poly_print ( m, c2, ' The R8POLY:' ) d = r8poly_degree ( m, c2 ) print ' Dimensioned degree = %d, Actual degree = %d' % ( m, d ) r8poly_print ( m, c3, ' The R8POLY:' ) d = r8poly_degree ( m, c3 ) print ' Dimensioned degree = %d, Actual degree = %d' % ( m, d ) r8poly_print ( m, c4, ' The R8POLY:' ) d = r8poly_degree ( m, c4 ) print ' Dimensioned degree = %d, Actual degree = %d' % ( m, d ) r8poly_print ( m, c5, ' The R8POLY:' ) d = r8poly_degree ( m, c5 ) print ' Dimensioned degree = %d, Actual degree = %d' % ( m, d ) print '' print 'R8POLY_DEGREE_TEST:' print ' Normal end of execution.' return
def r8poly_degree_test():
#*****************************************************************************80
#
## R8POLY_DEGREE_TEST tests R8POLY_DEGREE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 January 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
c1 = np.array([1.0, 2.0, 3.0, 4.0])
c2 = np.array([1.0, 2.0, 3.0, 0.0])
c3 = np.array([1.0, 2.0, 0.0, 4.0])
c4 = np.array([1.0, 0.0, 0.0, 0.0])
c5 = np.array([0.0, 0.0, 0.0, 0.0])
print ''
print 'R8POLY_DEGREE_TEST'
print ' R8POLY_DEGREE determines the degree of an R8POLY.'
m = 3
r8poly_print(m, c1, ' The R8POLY:')
d = r8poly_degree(m, c1)
print ' Dimensioned degree = %d, Actual degree = %d' % (m, d)
r8poly_print(m, c2, ' The R8POLY:')
d = r8poly_degree(m, c2)
print ' Dimensioned degree = %d, Actual degree = %d' % (m, d)
r8poly_print(m, c3, ' The R8POLY:')
d = r8poly_degree(m, c3)
print ' Dimensioned degree = %d, Actual degree = %d' % (m, d)
r8poly_print(m, c4, ' The R8POLY:')
d = r8poly_degree(m, c4)
print ' Dimensioned degree = %d, Actual degree = %d' % (m, d)
r8poly_print(m, c5, ' The R8POLY:')
d = r8poly_degree(m, c5)
print ' Dimensioned degree = %d, Actual degree = %d' % (m, d)
print ''
print 'R8POLY_DEGREE_TEST:'
print ' Normal end of execution.'
return
def r8poly_dif_test ( ):
#*****************************************************************************80
#
## R8POLY_DIF_TEST tests R8POLY_DIF.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
test_num = 2
print ''
print 'R8POLY_DIF_TEST'
print ' R8POLY_DIF computes derivatives of an R8POLY.'
#
# 1: Differentiate X^3 + 2*X^2 - 5*X - 6 once.
# 2: Differentiate X^4 + 3*X^3 + 2*X^2 - 2 3 times.
#
for test in range ( 0, 2 ):
if ( test == 0 ):
na = 3
d = 1
a = np.array ( [ -6.0, -5.0, 2.0, 1.0 ] )
elif ( test == 1 ):
na = 4
d = 3
a = np.array ( [ -2.0, 5.0, 2.0, 3.0, 1.0 ] )
r8poly_print ( na, a, ' The polynomial A:' )
print ''
print ' Differentiate A %d times.' % ( d )
b = r8poly_dif ( na, a, d )
r8poly_print ( na - d, b, ' The derivative, B:' )
#
# Terminate.
#
print ''
print 'R8POLY_DIF_TEST:'
print ' Normal end of execution.'
return
def r8poly_value_horner_test():
#*****************************************************************************80
#
## R8POLY_VALUE_HORNER_TEST tests R8POLY_VALUE_HORNER.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 04 March 2016
#
# Author:
#
# John Burkardt
#
import numpy as np
import platform
from r8poly_print import r8poly_print
m = 4
n = 16
c = np.array([24.0, -50.0, +35.0, -10.0, 1.0])
print('')
print('R8POLY_VALUE_HORNER_TEST')
print(' Python version: %s' % (platform.python_version()))
print(' R8POLY_VALUE_HORNER evaluates a polynomial at a point')
print(' using Horners method.')
r8poly_print(m, c, ' The polynomial coefficients:')
x_lo = 0.0
x_hi = 5.0
x = np.linspace(x_lo, x_hi, n)
print('')
print(' I X P(X)')
print('')
for i in range(0, n):
p = r8poly_value_horner(m, c, x[i])
print(' %2d %8.4f %14.6g' % (i, x[i], p))
#
# Terminate.
#
print('')
print('R8POLY_VALUE_HORNER_TEST:')
print(' Normal end of execution.')
return
def r8poly_value_horner_test():
# *****************************************************************************80
#
## R8POLY_VALUE_HORNER_TEST tests R8POLY_VALUE_HORNER.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 January 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
from r8vec_linspace import r8vec_linspace
m = 4
n = 16
c = np.array([24.0, -50.0, +35.0, -10.0, 1.0])
print ""
print "R8POLY_VALUE_HORNER_TEST"
print " R8POLY_VALUE_HORNER evaluates a polynomial at a point"
print " using Horners method."
r8poly_print(m, c, " The polynomial coefficients:")
x_lo = 0.0
x_hi = 5.0
x = r8vec_linspace(n, x_lo, x_hi)
print ""
print " I X P(X)"
print ""
for i in range(0, n):
p = r8poly_value_horner(m, c, x[i])
print " %2d %8.4f %14.6g" % (i, x[i], p)
print ""
print "R8POLY_VALUE_HORNER_TEST:"
print " Normal end of execution."
return
def r8poly_value_horner_test():
#*****************************************************************************80
#
## R8POLY_VALUE_HORNER_TEST tests R8POLY_VALUE_HORNER.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 January 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
from r8vec_linspace import r8vec_linspace
m = 4
n = 16
c = np.array([24.0, -50.0, +35.0, -10.0, 1.0])
print ''
print 'R8POLY_VALUE_HORNER_TEST'
print ' R8POLY_VALUE_HORNER evaluates a polynomial at a point'
print ' using Horners method.'
r8poly_print(m, c, ' The polynomial coefficients:')
x_lo = 0.0
x_hi = 5.0
x = r8vec_linspace(n, x_lo, x_hi)
print ''
print ' I X P(X)'
print ''
for i in range(0, n):
p = r8poly_value_horner(m, c, x[i])
print ' %2d %8.4f %14.6g' % (i, x[i], p)
print ''
print 'R8POLY_VALUE_HORNER_TEST:'
print ' Normal end of execution.'
return
def roots_to_r8poly_test():
#*****************************************************************************80
#
## ROOTS_TO_R8POLY_TEST tests ROOTS_TO_R8POLY.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 11 March 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
from r8vec_print import r8vec_print
n = 5
x = np.array ( [ \
[ 1.0 ], \
[ -4.0 ], \
[ 3.0 ], \
[ 0.0 ], \
[ 3.0 ] ] )
print ''
print 'ROOTS_TO_R8POLY_TEST'
print ' ROOTS_TO_R8POLY is given N real roots,'
print ' and constructs the coefficient vector'
print ' of the corresponding polynomial.'
r8vec_print(n, x, ' N real roots:')
c = roots_to_r8poly(n, x)
r8poly_print(n, c, ' The polynomial:')
print ''
print 'ROOTS_TO_R8POLY_TEST:'
print ' Normal end of execution.'
return
def roots_to_r8poly_test():
# *****************************************************************************80
#
## ROOTS_TO_R8POLY_TEST tests ROOTS_TO_R8POLY.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 11 March 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
from r8vec_print import r8vec_print
n = 5
x = np.array([[1.0], [-4.0], [3.0], [0.0], [3.0]])
print ""
print "ROOTS_TO_R8POLY_TEST"
print " ROOTS_TO_R8POLY is given N real roots,"
print " and constructs the coefficient vector"
print " of the corresponding polynomial."
r8vec_print(n, x, " N real roots:")
c = roots_to_r8poly(n, x)
r8poly_print(n, c, " The polynomial:")
print ""
print "ROOTS_TO_R8POLY_TEST:"
print " Normal end of execution."
return
def r8poly_degree_test ( ): #*****************************************************************************80 # ## R8POLY_DEGREE_TEST tests R8POLY_DEGREE. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 26 May 2015 # # Author: # # John Burkardt # import numpy as np from r8poly_print import r8poly_print print '' print 'R8POLY_DEGREE_TEST' print ' R8POLY_DEGREE returns the degree of an R8POLY.' n = 10 a = np.array ( [ 0.0, 1.1, 0.0, 3.3, 4.4, 0.0, 6.6, 7.7, 0.0, 0.0, 0.0 ] ) r8poly_print ( n, a, ' The polynomial:' ) degree = r8poly_degree ( n, a ) print '' print ' The polynomial degree is %d' % ( degree ) # # Terminate. # print '' print 'R8POLY_DEGREE_TEST:' print ' Normal end of execution.' return
def r8poly_degree_test():
#*****************************************************************************80
#
## R8POLY_DEGREE_TEST tests R8POLY_DEGREE.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
print ''
print 'R8POLY_DEGREE_TEST'
print ' R8POLY_DEGREE returns the degree of an R8POLY.'
n = 10
a = np.array([0.0, 1.1, 0.0, 3.3, 4.4, 0.0, 6.6, 7.7, 0.0, 0.0, 0.0])
r8poly_print(n, a, ' The polynomial:')
degree = r8poly_degree(n, a)
print ''
print ' The polynomial degree is %d' % (degree)
#
# Terminate.
#
print ''
print 'R8POLY_DEGREE_TEST:'
print ' Normal end of execution.'
return
def r8poly_mul_test():
#*****************************************************************************80
#
## R8POLY_MUL_TEST tests R8POLY_MUL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 29 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
ntest = 2
print ''
print 'R8POLY_MUL_TEST'
print ' R8POLY_MUL multiplies two polynomials.'
#
# 1: Multiply (1+X) times (1-X). Answer is 1-X^2.
# 2: Multiply (1+2*X+3*X^2) by (1-2*X). Answer is 1 + 0*X - X^2 - 6*X^3
#
for itest in range(0, ntest):
if (itest == 0):
na = 1
a = np.array([1.0, 1.0])
nb = 1
b = np.array([1.0, -1.0])
elif (itest == 1):
na = 2
a = np.array([1.0, 2.0, 3.0])
nb = 1
b = np.array([1.0, -2.0])
c = r8poly_mul(na, a, nb, b)
r8poly_print(na, a, ' The factor A:')
r8poly_print(nb, b, ' The factor B:')
r8poly_print(na + nb, c, ' The product C = A*B:')
#
# Terminate.
#
print ''
print 'R8POLY_MUL_TEST:'
print ' Normal end of execution.'
return
def r8poly_mul_test ( ):
#*****************************************************************************80
#
## R8POLY_MUL_TEST tests R8POLY_MUL.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 29 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
ntest = 2
print ''
print 'R8POLY_MUL_TEST'
print ' R8POLY_MUL multiplies two polynomials.'
#
# 1: Multiply (1+X) times (1-X). Answer is 1-X^2.
# 2: Multiply (1+2*X+3*X^2) by (1-2*X). Answer is 1 + 0*X - X^2 - 6*X^3
#
for itest in range ( 0, ntest ):
if ( itest == 0 ):
na = 1
a = np.array ( [ 1.0, 1.0 ] )
nb = 1
b = np.array ( [ 1.0, -1.0 ] )
elif ( itest == 1 ):
na = 2
a = np.array ( [ 1.0, 2.0, 3.0 ] )
nb = 1
b = np.array ( [ 1.0, -2.0 ] )
c = r8poly_mul ( na, a, nb, b )
r8poly_print ( na, a, ' The factor A:' )
r8poly_print ( nb, b, ' The factor B:' )
r8poly_print ( na+nb, c, ' The product C = A*B:' )
#
# Terminate.
#
print ''
print 'R8POLY_MUL_TEST:'
print ' Normal end of execution.'
return
def zernike_poly_coef_test ( ):
#*****************************************************************************80
#
## ZERNIKE_POLY_COEF_TEST tests ZERNIKE_POLY_COEF.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 27 February 2015
#
# Author:
#
# John Burkardt
#
from r8poly_print import r8poly_print
n = 5
print ''
print 'ZERNIKE_POLY_COEF_TEST'
print ' ZERNIKE_POLY_COEF determines the Zernike'
print ' polynomial coefficients.'
for m in range ( 0, n + 1 ):
c = zernike_poly_coef ( m, n )
r8poly_print ( n, c, ' Zernike polynomial:' )
print ''
print 'ZERNIKE_POLY_COEF_TEST'
print ' Normal end of execution.'
return
def r8poly_add_test():
#*****************************************************************************80
#
## R8POLY_ADD_TEST tests R8POLY_ADD.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 28 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_degree import r8poly_degree
from r8poly_print import r8poly_print
print ''
print 'R8POLY_ADD_TEST'
print ' R8POLY_ADD adds two R8POLY\'s.'
na = 5
a = np.array([0.0, 1.1, 2.2, 3.3, 4.4, 5.5])
nb = 5
b = np.array([1.0, -2.1, 7.2, 8.3, 0.0, -5.5])
c = r8poly_add(na, a, nb, b)
r8poly_print(na, a, ' Polynomial A:')
r8poly_print(nb, b, ' Polynomial B:')
nc = max(na, nb)
nc2 = r8poly_degree(nc, c)
r8poly_print(nc2, c, ' Polynomial C = A+B:')
#
# Terminate.
#
print ''
print 'R8POLY_ADD_TEST:'
print ' Normal end of execution.'
return
def r8poly_add_test():
# *****************************************************************************80
#
## R8POLY_ADD_TEST tests R8POLY_ADD.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 28 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_degree import r8poly_degree
from r8poly_print import r8poly_print
print ""
print "R8POLY_ADD_TEST"
print " R8POLY_ADD adds two R8POLY's."
na = 5
a = np.array([0.0, 1.1, 2.2, 3.3, 4.4, 5.5])
nb = 5
b = np.array([1.0, -2.1, 7.2, 8.3, 0.0, -5.5])
c = r8poly_add(na, a, nb, b)
r8poly_print(na, a, " Polynomial A:")
r8poly_print(nb, b, " Polynomial B:")
nc = max(na, nb)
nc2 = r8poly_degree(nc, c)
r8poly_print(nc2, c, " Polynomial C = A+B:")
#
# Terminate.
#
print ""
print "R8POLY_ADD_TEST:"
print " Normal end of execution."
return
def r8poly_div_test():
#*****************************************************************************80
#
## R8POLY_DIV_TEST tests R8POLY_DIV.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
print ''
print 'R8POLY_DIV_TEST'
print ' R8POLY_DIV computes the quotient and'
print ' remainder for polynomial division.'
#
# 1: Divide X^3 + 2*X^2 - 5*X - 6 by X-2.
# Quotient is 3+4*X+X^2, remainder is 0.
#
# 2: Divide X^4 + 3*X^3 + 2*X^2 - 2 by X^2 + X - 3.
# Quotient is X^2 + 2*X + 3, remainder 8*X + 7.
#
ntest = 2
for test in range(0, ntest):
if (test == 0):
na = 3
a = np.array([-6.0, -5.0, 2.0, 1.0])
nb = 1
b = np.array([-2.0, 1.0])
elif (test == 1):
na = 4
a = np.array([-2.0, 5.0, 2.0, 3.0, 1.0])
nb = 2
b = np.array([-3.0, 1.0, 1.0])
r8poly_print(na, a, ' The polynomial to be divided, A:')
r8poly_print(nb, b, ' The divisor polynomial, B:')
nq, q, nr, r = r8poly_div(na, a, nb, b)
r8poly_print(nq, q, ' The quotient polynomial, Q:')
r8poly_print(nr, r, ' The remainder polynomial, R:')
#
# Terminate.
#
print ''
print 'R8POLY_DIV_TEST:'
print ' Normal end of execution.'
return
def r8poly_div_test ( ):
#*****************************************************************************80
#
## R8POLY_DIV_TEST tests R8POLY_DIV.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8poly_print import r8poly_print
print ''
print 'R8POLY_DIV_TEST'
print ' R8POLY_DIV computes the quotient and'
print ' remainder for polynomial division.'
#
# 1: Divide X^3 + 2*X^2 - 5*X - 6 by X-2.
# Quotient is 3+4*X+X^2, remainder is 0.
#
# 2: Divide X^4 + 3*X^3 + 2*X^2 - 2 by X^2 + X - 3.
# Quotient is X^2 + 2*X + 3, remainder 8*X + 7.
#
ntest = 2
for test in range ( 0, ntest ):
if ( test == 0 ):
na = 3
a = np.array ( [ -6.0, -5.0, 2.0, 1.0 ] )
nb = 1
b = np.array ( [ -2.0, 1.0 ] )
elif ( test == 1 ):
na = 4
a = np.array ( [ -2.0, 5.0, 2.0, 3.0, 1.0 ] )
nb = 2
b = np.array ( [ -3.0, 1.0, 1.0 ] )
r8poly_print ( na, a, ' The polynomial to be divided, A:' )
r8poly_print ( nb, b, ' The divisor polynomial, B:' )
nq, q, nr, r = r8poly_div ( na, a, nb, b )
r8poly_print ( nq, q, ' The quotient polynomial, Q:' )
r8poly_print ( nr, r, ' The remainder polynomial, R:' )
#
# Terminate.
#
print ''
print 'R8POLY_DIV_TEST:'
print ' Normal end of execution.'
return