def r8mat_norm_li_test():
#*****************************************************************************80
#
## R8MAT_NORM_LI_TEST tests R8MAT_NORM_LI.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 16 February 2015
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
m = 5
n = 4
x1 = -5.0
x2 = +5.0
seed = 123456789
a, seed = r8mat_uniform_ab(m, n, x1, x2, seed)
for j in range(0, n):
for i in range(0, m):
a[i, j] = round(a[i, j])
print ''
print 'R8MAT_NORM_LI_TEST'
print ' R8MAT_NORM_LI computes the Loo norm of an R8MAT;'
t = r8mat_norm_li(m, n, a)
r8mat_print(m, n, a, ' A:')
print ''
print ' Computed Loo norm = %g' % (t)
print ''
print 'R8MAT_NORM_LI_TEST'
print ' Normal end of execution.'
return
def r8mat_norm_li_test():
# *****************************************************************************80
#
## R8MAT_NORM_LI_TEST tests R8MAT_NORM_LI.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 16 February 2015
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
m = 5
n = 4
x1 = -5.0
x2 = +5.0
seed = 123456789
a, seed = r8mat_uniform_ab(m, n, x1, x2, seed)
for j in range(0, n):
for i in range(0, m):
a[i, j] = round(a[i, j])
print ""
print "R8MAT_NORM_LI_TEST"
print " R8MAT_NORM_LI computes the Loo norm of an R8MAT;"
t = r8mat_norm_li(m, n, a)
r8mat_print(m, n, a, " A:")
print ""
print " Computed Loo norm = %g" % (t)
print ""
print "R8MAT_NORM_LI_TEST"
print " Normal end of execution."
return
def r8mat_nint_test():
# *****************************************************************************80
#
## R8MAT_NINT_TEST tests R8MAT_NINT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 December 2014
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
m = 5
n = 4
print ""
print "R8MAT_NINT_TEST"
print " R8MAT_NINT rounds an R8MAT."
x1 = -5.0
x2 = +5.0
seed = 123456789
a, seed = r8mat_uniform_ab(m, n, x1, x2, seed)
r8mat_print(m, n, a, " Matrix A:")
a = r8mat_nint(m, n, a)
r8mat_print(m, n, a, " Rounded matrix A:")
print ""
print "R8MAT_NINT_TEST"
print " Normal end of execution."
return
def r8mat_nint_test():
#*****************************************************************************80
#
## R8MAT_NINT_TEST tests R8MAT_NINT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 December 2014
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
m = 5
n = 4
print ''
print 'R8MAT_NINT_TEST'
print ' R8MAT_NINT rounds an R8MAT.'
x1 = -5.0
x2 = +5.0
seed = 123456789
a, seed = r8mat_uniform_ab(m, n, x1, x2, seed)
r8mat_print(m, n, a, ' Matrix A:')
a = r8mat_nint(m, n, a)
r8mat_print(m, n, a, ' Rounded matrix A:')
print ''
print 'R8MAT_NINT_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 lpp_value_test():
# *****************************************************************************80
#
## LPP_VALUE_TEST tests LPP_VALUE.
#
# 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 lpp_to_polynomial import lpp_to_polynomial
from polynomial_value import polynomial_value
from r8mat_uniform_ab import r8mat_uniform_ab
print ""
print "LPP_VALUE_TEST:"
print " LPP_VALUE evaluates a Legendre product polynomial."
m = 3
n = 1
xlo = -1.0
xhi = +1.0
seed = 123456789
x, seed = r8mat_uniform_ab(m, n, xlo, xhi, seed)
print ""
print " Evaluate at X = ",
for j in range(0, n):
for i in range(0, m):
print "%g " % (x[i][j]),
print ""
print ""
print " Rank I1 I2 I3: L(I1,X1)*L(I2,X2)*L(I3,X3) P(X1,X2,X3)"
print ""
for rank in range(1, 21):
l = comp_unrank_grlex(m, rank)
#
# Evaluate the LPP directly.
#
v1 = lpp_value(m, n, l, x)
#
# Convert the LPP to a polynomial.
#
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
o, c, e = lpp_to_polynomial(m, l, o_max)
#
# Evaluate the polynomial.
#
v2 = polynomial_value(m, o, c, e, n, x)
#
# Compare results.
#
print " %4d %2d %2d %2d %14.6g %14.6g" % (rank, l[0], l[1], l[2], v1[0], v2[0])
print ""
print "LPP_VALUE_TEST:"
print " Normal end of execution."
return
def r8vec_house_column_test ( ):
#*****************************************************************************80
#
## R8VEC_HOUSE_COLUMN_TEST tests R8VEC_HOUSE_COLUMN.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 14 February 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8mat_house_form import r8mat_house_form
from r8mat_mm import r8mat_mm
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'R8VEC_HOUSE_COLUMN_TEST'
print ' R8VEC_HOUSE_COLUMN returns the compact form of'
print ' a Householder matrix that "packs" a column'
print ' of a matrix.'
#
# Get a random matrix.
#
n = 4
r8_lo = 0.0
r8_hi = 5.0
seed = 123456789;
a, seed = r8mat_uniform_ab ( n, n, r8_lo, r8_hi, seed )
r8mat_print ( n, n, a, ' Matrix A:' )
a_col = np.zeros ( n )
for k in range ( 0, n - 1 ):
print ''
print ' Working on column K = %d' % ( k )
for i in range ( 0, n ):
a_col[i] = a[i,k]
v = r8vec_house_column ( n, a_col, k )
h = r8mat_house_form ( n, v )
r8mat_print ( n, n, h, ' Householder matrix H:' )
ha = r8mat_mm ( n, n, n, h, a )
r8mat_print ( n, n, ha, ' Product H*A:' )
#
# If we set A := HA, then we can successively convert A to upper
# triangular form.
#
a = ha
print ''
print 'R8VEC_HOUSE_COLUMN_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 r8mat_is_solution_test():
#*****************************************************************************80
#
## R8MAT_IS_SOLUTION_TEST tests R8MAT_IS_SOLUTION.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 02 March 2015
#
# Author:
#
# John Burkardt
#
from i4_uniform_ab import i4_uniform_ab
from r8mat_mm import r8mat_mm
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'R8MAT_IS_SOLUTION_TEST:'
print ' R8MAT_IS_SOLUTION tests whether X is the solution of'
print ' A*X=B by computing the Frobenius norm of the residual.'
#
# Get random shapes.
#
i4_lo = 1
i4_hi = 10
seed = 123456789
m, seed = i4_uniform_ab(i4_lo, i4_hi, seed)
n, seed = i4_uniform_ab(i4_lo, i4_hi, seed)
k, seed = i4_uniform_ab(i4_lo, i4_hi, seed)
#
# Get a random A.
#
r8_lo = -5.0
r8_hi = +5.0
a, seed = r8mat_uniform_ab(m, n, r8_lo, r8_hi, seed)
#
# Get a random X.
#
r8_lo = -5.0
r8_hi = +5.0
x, seed = r8mat_uniform_ab(n, k, r8_lo, r8_hi, seed)
#
# Compute B = A * X.
#
b = r8mat_mm(m, n, k, a, x)
#
# Compute || A*X-B||
#
enorm = r8mat_is_solution(m, n, k, a, x, b)
print ''
print ' A is %d by %d' % (m, n)
print ' X is %d by %d' % (n, k)
print ' B is %d by %d' % (m, k)
print ' Frobenius error in A*X-B is %g' % (enorm)
print ''
print 'R8MAT_IS_SOLUTION_TEST'
print ' Normal end of execution.'
return
def r8mat_is_solution_test ( ): #*****************************************************************************80 # ## R8MAT_IS_SOLUTION_TEST tests R8MAT_IS_SOLUTION. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 02 March 2015 # # Author: # # John Burkardt # from i4_uniform_ab import i4_uniform_ab from r8mat_mm import r8mat_mm from r8mat_uniform_ab import r8mat_uniform_ab print '' print 'R8MAT_IS_SOLUTION_TEST:' print ' R8MAT_IS_SOLUTION tests whether X is the solution of' print ' A*X=B by computing the Frobenius norm of the residual.' # # Get random shapes. # i4_lo = 1 i4_hi = 10 seed = 123456789 m, seed = i4_uniform_ab ( i4_lo, i4_hi, seed ) n, seed = i4_uniform_ab ( i4_lo, i4_hi, seed ) k, seed = i4_uniform_ab ( i4_lo, i4_hi, seed ) # # Get a random A. # r8_lo = -5.0 r8_hi = +5.0 a, seed = r8mat_uniform_ab ( m, n, r8_lo, r8_hi, seed ) # # Get a random X. # r8_lo = -5.0 r8_hi = +5.0 x, seed = r8mat_uniform_ab ( n, k, r8_lo, r8_hi, seed ) # # Compute B = A * X. # b = r8mat_mm ( m, n, k, a, x ) # # Compute || A*X-B|| # enorm = r8mat_is_solution ( m, n, k, a, x, b ) print '' print ' A is %d by %d' % ( m, n ) print ' X is %d by %d' % ( n, k ) print ' B is %d by %d' % ( m, k ) print ' Frobenius error in A*X-B is %g' % ( enorm ) print '' print 'R8MAT_IS_SOLUTION_TEST' print ' Normal end of execution.' return
def lpp_value_test():
#*****************************************************************************80
#
## LPP_VALUE_TEST tests LPP_VALUE.
#
# 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 lpp_to_polynomial import lpp_to_polynomial
from polynomial_value import polynomial_value
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'LPP_VALUE_TEST:'
print ' LPP_VALUE evaluates a Legendre product polynomial.'
m = 3
n = 1
xlo = -1.0
xhi = +1.0
seed = 123456789
x, seed = r8mat_uniform_ab(m, n, xlo, xhi, seed)
print ''
print ' Evaluate at X = ',
for j in range(0, n):
for i in range(0, m):
print '%g ' % (x[i][j]),
print ''
print ''
print ' Rank I1 I2 I3: L(I1,X1)*L(I2,X2)*L(I3,X3) P(X1,X2,X3)'
print ''
for rank in range(1, 21):
l = comp_unrank_grlex(m, rank)
#
# Evaluate the LPP directly.
#
v1 = lpp_value(m, n, l, x)
#
# Convert the LPP to a polynomial.
#
o_max = 1
for i in range(0, m):
o_max = o_max * (l[i] + 2) // 2
o, c, e = lpp_to_polynomial(m, l, o_max)
#
# Evaluate the polynomial.
#
v2 = polynomial_value(m, o, c, e, n, x)
#
# Compare results.
#
print ' %4d %2d %2d %2d %14.6g %14.6g' % \
( rank, l[0], l[1], l[2], v1[0], v2[0] )
print ''
print 'LPP_VALUE_TEST:'
print ' Normal end of execution.'
return
def r8vec_house_column_test ( ):
#*****************************************************************************80
#
## R8VEC_HOUSE_COLUMN_TEST tests R8VEC_HOUSE_COLUMN.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 14 February 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r8mat_house_form import r8mat_house_form
from r8mat_mm import r8mat_mm
from r8mat_print import r8mat_print
from r8mat_uniform_ab import r8mat_uniform_ab
print ''
print 'R8VEC_HOUSE_COLUMN_TEST'
print ' R8VEC_HOUSE_COLUMN returns the compact form of'
print ' a Householder matrix that "packs" a column'
print ' of a matrix.'
#
# Get a random matrix.
#
n = 4
r8_lo = 0.0
r8_hi = 5.0
seed = 123456789;
a, seed = r8mat_uniform_ab ( n, n, r8_lo, r8_hi, seed )
r8mat_print ( n, n, a, ' Matrix A:' )
a_col = np.zeros ( n )
for k in range ( 0, n - 1 ):
print ''
print ' Working on column K = %d' % ( k )
for i in range ( 0, n ):
a_col[i] = a[i,k]
v = r8vec_house_column ( n, a_col, k )
h = r8mat_house_form ( n, v )
r8mat_print ( n, n, h, ' Householder matrix H:' )
ha = r8mat_mm ( n, n, n, h, a )
r8mat_print ( n, n, ha, ' Product H*A:' )
#
# If we set A := HA, then we can successively convert A to upper
# triangular form.
#
a = ha
#
# Terminate.
#
print ''
print 'R8VEC_HOUSE_COLUMN_TEST'
print ' Normal end of execution.'
return
