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(na, a, nb, b):
#*****************************************************************************80
#
## R8POLY_DIV computes the quotient and remainder of two polynomials.
#
# Discussion:
#
# The polynomials are assumed to be stored in power sum form.
#
# The power sum form of a polynomial is:
#
# p(x) = a(0) + a(1) * x + ... + a(n-1) * x^(n-1) + a(n) * x^(n)
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer NA, the dimension of A.
#
# Input, real A(1:NA+1), the coefficients of the polynomial to be divided.
#
# Input, integer NB, the dimension of B.
#
# Input, real B(1:NB+1), the coefficients of the divisor polynomial.
#
# Output, integer NQ, the degree of Q.
# If the divisor polynomial is zero, NQ is returned as -1.
#
# Output, real Q(1:NA-NB+1), contains the quotient of A/B.
# If A and B have full degree, Q should be dimensioned Q(0:NA-NB).
# In any case, Q(0:NA) should be enough.
#
# Output, integer NR, the degree of R.
# If the divisor polynomial is zero, NR is returned as -1.
#
# Output, real R(1:NB), contains the remainder of A/B.
# If B has full degree, R should be dimensioned R(0:NB-1).
# Otherwise, R will actually require less space.
#
import numpy as np
from r8poly_degree import r8poly_degree
na2 = r8poly_degree(na, a)
nb2 = r8poly_degree(nb, b)
if (b[nb2] == 0.0):
nq = -1
nr = -1
return nq, q, nr, r
nq = na2 - nb2
q = np.zeros(nq + 1)
for i in range(nq, -1, -1):
q[i] = a[i + nb2] / b[nb2]
a[i + nb2] = 0.0
for j in range(0, nb2):
a[i + j] = a[i + j] - q[i] * b[j]
nr = nb2 - 1
r = np.zeros(nr + 1)
for i in range(0, nr + 1):
r[i] = a[i]
return nq, q, nr, r
def r8poly_div ( na, a, nb, b ):
#*****************************************************************************80
#
## R8POLY_DIV computes the quotient and remainder of two polynomials.
#
# Discussion:
#
# The polynomials are assumed to be stored in power sum form.
#
# The power sum form of a polynomial is:
#
# p(x) = a(0) + a(1) * x + ... + a(n-1) * x^(n-1) + a(n) * x^(n)
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 30 May 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer NA, the dimension of A.
#
# Input, real A(1:NA+1), the coefficients of the polynomial to be divided.
#
# Input, integer NB, the dimension of B.
#
# Input, real B(1:NB+1), the coefficients of the divisor polynomial.
#
# Output, integer NQ, the degree of Q.
# If the divisor polynomial is zero, NQ is returned as -1.
#
# Output, real Q(1:NA-NB+1), contains the quotient of A/B.
# If A and B have full degree, Q should be dimensioned Q(0:NA-NB).
# In any case, Q(0:NA) should be enough.
#
# Output, integer NR, the degree of R.
# If the divisor polynomial is zero, NR is returned as -1.
#
# Output, real R(1:NB), contains the remainder of A/B.
# If B has full degree, R should be dimensioned R(0:NB-1).
# Otherwise, R will actually require less space.
#
import numpy as np
from r8poly_degree import r8poly_degree
na2 = r8poly_degree ( na, a )
nb2 = r8poly_degree ( nb, b )
if ( b[nb2] == 0.0 ):
nq = -1
nr = -1
return nq, q, nr, r
nq = na2 - nb2
q = np.zeros ( nq + 1 )
for i in range ( nq, -1, -1 ):
q[i] = a[i+nb2] / b[nb2]
a[i+nb2] = 0.0
for j in range ( 0, nb2 ):
a[i+j] = a[i+j] - q[i] * b[j]
nr = nb2 - 1
r = np.zeros ( nr + 1 )
for i in range ( 0, nr + 1 ):
r[i] = a[i]
return nq, q, nr, r
def r8poly_print ( n, a, title ):
#*****************************************************************************80
#
## R8POLY_PRINT prints out a polynomial.
#
# Discussion:
#
# The power sum form is:
#
# p(x) = a(0) + a(1) * x + ... + a(n-1) * x^(n-1) + a(n) * x^(n)
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 28 May 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer N, the dimension of A.
#
# Input, real A[0:N], the polynomial coefficients.
# A(1) is the constant term and
# A(N+1) is the coefficient of X^N.
#
# Input, character TITLE(*), an optional title.
#
from r8poly_degree import r8poly_degree
if ( 0 < len ( title ) ):
print ''
print title
print ''
n = r8poly_degree ( n, a )
if ( a[n] < 0.0 ):
plus_minus = '-'
else:
plus_minus = ' '
mag = abs ( a[n] )
if ( 2 <= n ):
print ' p(x) = %c%14f * x^%d' % ( plus_minus, mag, n )
elif ( n == 1 ):
print ' p(x) = %c%14f * x' % ( plus_minus, mag )
elif ( n == 0 ):
print ' p(x) = %c%14f' % ( plus_minus, mag )
for i in range ( n - 1, -1, -1 ):
if ( a[i] < 0.0 ):
plus_minus = '-'
else:
plus_minus = '+'
mag = abs ( a[i] )
if ( mag != 0.0 ):
if ( 2 <= i ):
print ' %c%14f * x^%d' % ( plus_minus, mag, i )
elif ( i == 1 ):
print ' %c%14f * x' % ( plus_minus, mag )
elif ( i == 0 ):
print ' %c%14f' % ( plus_minus, mag )
return
def r8poly_print(m, a, title):
#*****************************************************************************80
#
## R8POLY_PRINT prints out a polynomial.
#
# Discussion:
#
# The power sum form is:
#
# p(x) = a(0) + a(1) * x + ... + a(m-1) * x^(m-1) + a(m) * x^(m)
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 January 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the nominal degree of the polynomial.
#
# Input, real A[0:M], the polynomial coefficients.
# A[0] is the constant term and
# A[M] is the coefficient of X^M.
#
# Input, string TITLE, a title.
#
from r8poly_degree import r8poly_degree
print ''
print title
print ''
m2 = r8poly_degree(m, a)
if (a[m2] < 0.0):
plus_minus = '-'
else:
plus_minus = ' '
mag = abs(a[m2])
if (2 <= m2):
print ' p(x) = %c %g * x^%d' % (plus_minus, mag, m2)
elif (m2 == 1):
print ' p(x) = %c %g * x' % (plus_minus, mag)
elif (m2 == 0):
print ' p(x) = %c %g' % (plus_minus, mag)
for i in range(m2 - 1, -1, -1):
if (a[i] < 0.0):
plus_minus = '-'
else:
plus_minus = '+'
mag = abs(a[i])
if (mag != 0.0):
if (2 <= i):
print ' %c %g * x^%d' % (plus_minus, mag, i)
elif (i == 1):
print ' %c %g * x' % (plus_minus, mag)
elif (i == 0):
print ' %c %g' % (plus_minus, mag)
def r8poly_print ( m, a, title ):
#*****************************************************************************80
#
## R8POLY_PRINT prints out a polynomial.
#
# Discussion:
#
# The power sum form is:
#
# p(x) = a(0) + a(1) * x + ... + a(m-1) * x^(m-1) + a(m) * x^(m)
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 January 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the nominal degree of the polynomial.
#
# Input, real A[0:M], the polynomial coefficients.
# A[0] is the constant term and
# A[M] is the coefficient of X^M.
#
# Input, string TITLE, a title.
#
from r8poly_degree import r8poly_degree
print ''
print title
print ''
m2 = r8poly_degree ( m, a )
if ( a[m2] < 0.0 ):
plus_minus = '-'
else:
plus_minus = ' '
mag = abs ( a[m2] )
if ( 2 <= m2 ):
print ' p(x) = %c %g * x^%d' % ( plus_minus, mag, m2 )
elif ( m2 == 1 ):
print ' p(x) = %c %g * x' % ( plus_minus, mag )
elif ( m2 == 0 ):
print ' p(x) = %c %g' % ( plus_minus, mag )
for i in range ( m2 - 1, -1, -1 ):
if ( a[i] < 0.0 ):
plus_minus = '-'
else:
plus_minus = '+'
mag = abs ( a[i] )
if ( mag != 0.0 ):
if ( 2 <= i ):
print ' %c %g * x^%d' % ( plus_minus, mag, i )
elif ( i == 1 ):
print ' %c %g * x' % ( plus_minus, mag )
elif ( i == 0 ):
print ' %c %g' % ( plus_minus, mag )