def rosser1_test():
#*****************************************************************************80
#
## ROSSER1_TEST tests ROSSER1.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 February 2015
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
print ''
print 'ROSSER1_TEST'
print ' ROSSER1 computes the ROSSER1 matrix.'
n = 8
a = rosser1()
r8mat_print(n, n, a, ' ROSSER1 matrix:')
print ''
print 'ROSSER1_TEST'
print ' Normal end of execution.'
return
def rosser1_test ( ): #*****************************************************************************80 # ## ROSSER1_TEST tests ROSSER1. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 10 February 2015 # # Author: # # John Burkardt # from r8mat_print import r8mat_print print '' print 'ROSSER1_TEST' print ' ROSSER1 computes the ROSSER1 matrix.' n = 8 a = rosser1 ( ) r8mat_print ( n, n, a, ' ROSSER1 matrix:' ) print '' print 'ROSSER1_TEST' print ' Normal end of execution.' return
def rosser1_determinant_test ( ): #*****************************************************************************80 # ## ROSSER1_DETERMINANT_TEST tests ROSSER1_DETERMINANT. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 23 February 2015 # # Author: # # John Burkardt # from rosser1 import rosser1 from r8mat_print import r8mat_print print '' print 'ROSSER1_DETERMINANT_TEST' print ' ROSSER1_DETERMINANT computes the ROSSER1 determinant.' seed = 123456789 m = 8 n = m a = rosser1 ( ) r8mat_print ( n, n, a, ' ROSSER1 matrix:' ) value = rosser1_determinant ( ) print ' Value = %g' % ( value ) print '' print 'ROSSER1_DETERMINANT_TEST' print ' Normal end of execution.' return
def rosser1_determinant_test():
#*****************************************************************************80
#
## ROSSER1_DETERMINANT_TEST tests ROSSER1_DETERMINANT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 23 February 2015
#
# Author:
#
# John Burkardt
#
from rosser1 import rosser1
from r8mat_print import r8mat_print
print ''
print 'ROSSER1_DETERMINANT_TEST'
print ' ROSSER1_DETERMINANT computes the ROSSER1 determinant.'
seed = 123456789
m = 8
n = m
a = rosser1()
r8mat_print(n, n, a, ' ROSSER1 matrix:')
value = rosser1_determinant()
print ' Value = %g' % (value)
print ''
print 'ROSSER1_DETERMINANT_TEST'
print ' Normal end of execution.'
return
def test_null_right():
#*****************************************************************************80
#
## TEST_NULL_RIGHT tests right null vectors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 12 March 2015
#
# Author:
#
# John Burkardt
#
from a123 import a123
from a123 import a123_null_right
from archimedes import archimedes
from archimedes import archimedes_null_right
from cheby_diff1 import cheby_diff1
from cheby_diff1 import cheby_diff1_null_right
from creation import creation
from creation import creation_null_right
from dif1 import dif1
from dif1 import dif1_null_right
from dif1cyclic import dif1cyclic
from dif1cyclic import dif1cyclic_null_right
from dif2cyclic import dif2cyclic
from dif2cyclic import dif2cyclic_null_right
from fibonacci1 import fibonacci1
from fibonacci1 import fibonacci1_null_right
from hamming import hamming
from hamming import hamming_null_right
from line_adj import line_adj
from line_adj import line_adj_null_right
from moler2 import moler2
from moler2 import moler2_null_right
from neumann import neumann
from neumann import neumann_null_right
from one import one
from one import one_null_right
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_null_right import r8mat_is_null_right
from r8mat_norm_fro import r8mat_norm_fro
from r8vec_norm_l2 import r8vec_norm_l2
from ring_adj import ring_adj
from ring_adj import ring_adj_null_right
from rosser1 import rosser1
from rosser1 import rosser1_null_right
from zero import zero
from zero import zero_null_right
print ''
print 'TEST_NULL_RIGHT'
print ' A = a test matrix of order M by N'
print ' x = an N vector, candidate for a right null vector.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||x|| = L2 norm of x.'
print ' ||A*x||/||x|| = L2 norm of A*x over L2 norm of x.'
print ''
print ' Title M N ',
print '||A|| ||x|| ||A*x||/||x||'
print ''
#
# A123
#
title = 'A123'
m = 3
n = 3
a = a123()
x = a123_null_right()
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ARCHIMEDES
#
title = 'ARCHIMEDES'
m = 7
n = 8
a = archimedes()
x = archimedes_null_right()
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CHEBY_DIFF1
#
title = 'CHEBY_DIFF1'
m = 5
n = m
a = cheby_diff1(n)
x = cheby_diff1_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CREATION
#
title = 'CREATION'
m = 5
n = m
a = creation(m, n)
x = creation_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1
# Only has null vectors for N odd.
#
title = 'DIF1'
m = 5
n = m
a = dif1(m, n)
x = dif1_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1CYCLIC
#
title = 'DIF1CYCLIC'
m = 5
n = m
a = dif1cyclic(n)
x = dif1cyclic_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF2CYCLIC
#
title = 'DIF2CYCLIC'
m = 5
n = m
a = dif2cyclic(n)
x = dif2cyclic_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# FIBONACCI1
#
title = 'FIBONACCI1'
m = 5
n = m
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
f1, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
f2, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
a = fibonacci1(n, f1, f2)
x = fibonacci1_null_right(m, n, f1, f2)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# HAMMING
#
title = 'HAMMING'
m = 5
n = (2**m) - 1
a = hamming(m, n)
x = hamming_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# LINE_ADJ
#
title = 'LINE_ADJ'
m = 7
n = m
a = line_adj(n)
x = line_adj_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# MOLER2
#
title = 'MOLER2'
m = 5
n = 5
a = moler2()
x = moler2_null_right()
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# NEUMANN
#
title = 'NEUMANN'
row_num = 5
col_num = 5
m = row_num * col_num
n = row_num * col_num
a = neumann(row_num, col_num)
x = neumann_null_right(row_num, col_num)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ONE
#
title = 'ONE'
m = 5
n = 5
a = one(m, n)
x = one_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# RING_ADJ
# N must be a multiple of 4 for there to be a null vector.
#
title = 'RING_ADJ'
m = 12
n = 12
a = ring_adj(m, n)
x = ring_adj_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ROSSER1
#
title = 'ROSSER1'
m = 8
n = 8
a = rosser1()
x = rosser1_null_right()
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ZERO
#
title = 'ZERO'
m = 5
n = 5
a = zero(m, n)
x = zero_null_right(m, n)
error_l2 = r8mat_is_null_right(m, n, a, x)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
norm_x_l2 = r8vec_norm_l2(n, x)
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# Terminate.
#
print ''
print 'TEST_NULL_RIGHT:'
print ' Normal end of execution.'
return
def test_null_right ( ):
#*****************************************************************************80
#
## TEST_NULL_RIGHT tests right null vectors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 12 March 2015
#
# Author:
#
# John Burkardt
#
from a123 import a123
from a123 import a123_null_right
from archimedes import archimedes
from archimedes import archimedes_null_right
from cheby_diff1 import cheby_diff1
from cheby_diff1 import cheby_diff1_null_right
from creation import creation
from creation import creation_null_right
from dif1 import dif1
from dif1 import dif1_null_right
from dif1cyclic import dif1cyclic
from dif1cyclic import dif1cyclic_null_right
from dif2cyclic import dif2cyclic
from dif2cyclic import dif2cyclic_null_right
from fibonacci1 import fibonacci1
from fibonacci1 import fibonacci1_null_right
from hamming import hamming
from hamming import hamming_null_right
from line_adj import line_adj
from line_adj import line_adj_null_right
from moler2 import moler2
from moler2 import moler2_null_right
from neumann import neumann
from neumann import neumann_null_right
from one import one
from one import one_null_right
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_null_right import r8mat_is_null_right
from r8mat_norm_fro import r8mat_norm_fro
from r8vec_norm_l2 import r8vec_norm_l2
from ring_adj import ring_adj
from ring_adj import ring_adj_null_right
from rosser1 import rosser1
from rosser1 import rosser1_null_right
from zero import zero
from zero import zero_null_right
print ''
print 'TEST_NULL_RIGHT'
print ' A = a test matrix of order M by N'
print ' x = an N vector, candidate for a right null vector.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||x|| = L2 norm of x.'
print ' ||A*x||/||x|| = L2 norm of A*x over L2 norm of x.'
print ''
print ' Title M N ',
print '||A|| ||x|| ||A*x||/||x||'
print ''
#
# A123
#
title = 'A123'
m = 3
n = 3
a = a123 ( )
x = a123_null_right ( )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ARCHIMEDES
#
title = 'ARCHIMEDES'
m = 7
n = 8
a = archimedes ( )
x = archimedes_null_right ( )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CHEBY_DIFF1
#
title = 'CHEBY_DIFF1'
m = 5
n = m
a = cheby_diff1 ( n )
x = cheby_diff1_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CREATION
#
title = 'CREATION'
m = 5
n = m
a = creation ( m, n )
x = creation_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1
# Only has null vectors for N odd.
#
title = 'DIF1'
m = 5
n = m
a = dif1 ( m, n )
x = dif1_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1CYCLIC
#
title = 'DIF1CYCLIC'
m = 5
n = m
a = dif1cyclic ( n )
x = dif1cyclic_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF2CYCLIC
#
title = 'DIF2CYCLIC'
m = 5
n = m
a = dif2cyclic ( n )
x = dif2cyclic_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# FIBONACCI1
#
title = 'FIBONACCI1'
m = 5
n = m
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
f1, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
f2, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
a = fibonacci1 ( n, f1, f2 )
x = fibonacci1_null_right ( m, n, f1, f2 )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# HAMMING
#
title = 'HAMMING'
m = 5
n = ( 2 ** m ) - 1
a = hamming ( m, n )
x = hamming_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# LINE_ADJ
#
title = 'LINE_ADJ'
m = 7
n = m
a = line_adj ( n )
x = line_adj_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# MOLER2
#
title = 'MOLER2'
m = 5
n = 5
a = moler2 ( )
x = moler2_null_right ( )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# NEUMANN
#
title = 'NEUMANN'
row_num = 5
col_num = 5
m = row_num * col_num
n = row_num * col_num
a = neumann ( row_num, col_num )
x = neumann_null_right ( row_num, col_num )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ONE
#
title = 'ONE'
m = 5
n = 5
a = one ( m, n )
x = one_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# RING_ADJ
# N must be a multiple of 4 for there to be a null vector.
#
title = 'RING_ADJ'
m = 12
n = 12
a = ring_adj ( m, n )
x = ring_adj_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ROSSER1
#
title = 'ROSSER1'
m = 8
n = 8
a = rosser1 ( )
x = rosser1_null_right ( )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ZERO
#
title = 'ZERO'
m = 5
n = 5
a = zero ( m, n )
x = zero_null_right ( m, n )
error_l2 = r8mat_is_null_right ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( n, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# Terminate.
#
print ''
print 'TEST_NULL_RIGHT:'
print ' Normal end of execution.'
return
def test_null_left ( ):
#*****************************************************************************80
#
## TEST_NULL_LEFT tests left null vectors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 17 March 2015
#
# Author:
#
# John Burkardt
#
from a123 import a123
from a123 import a123_null_left
from cheby_diff1 import cheby_diff1
from cheby_diff1 import cheby_diff1_null_left
from creation import creation
from creation import creation_null_left
from dif1 import dif1
from dif1 import dif1_null_left
from dif1cyclic import dif1cyclic
from dif1cyclic import dif1cyclic_null_left
from dif2cyclic import dif2cyclic
from dif2cyclic import dif2cyclic_null_left
from eberlein import eberlein
from eberlein import eberlein_null_left
from fibonacci1 import fibonacci1
from fibonacci1 import fibonacci1_null_left
from lauchli import lauchli
from lauchli import lauchli_null_left
from line_adj import line_adj
from line_adj import line_adj_null_left
from moler2 import moler2
from moler2 import moler2_null_left
from one import one
from one import one_null_left
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_null_left import r8mat_is_null_left
from r8mat_norm_fro import r8mat_norm_fro
from r8vec_norm_l2 import r8vec_norm_l2
from ring_adj import ring_adj
from ring_adj import ring_adj_null_left
from rosser1 import rosser1
from rosser1 import rosser1_null_left
from zero import zero
from zero import zero_null_left
print ''
print 'TEST_NULL_LEFT'
print ' A = a test matrix of order M by N'
print ' x = an M vector, candidate for a left null vector.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||x|| = L2 norm of x.'
print ' ||A''*x||/||x|| = L2 norm of A\'*x over L2 norm of x.'
print ''
print ' Title M N ',
print '||A|| ||x|| ||A\'*x||/||x||'
print ''
#
# A123
#
title = 'A123'
m = 3
n = 3
a = a123 ( )
x = a123_null_left ( )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CHEBY_DIFF1
#
title = 'CHEBY_DIFF1'
m = 5
n = m
a = cheby_diff1 ( n )
x = cheby_diff1_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# CREATION
#
title = 'CREATION'
m = 5
n = m
a = creation ( m, n )
x = creation_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1
#
title = 'DIF1'
m = 5
n = 5
a = dif1 ( m, n )
x = dif1_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF1CYCLIC
#
title = 'DIF1CYCLIC'
m = 5
n = m
a = dif1cyclic ( n )
x = dif1cyclic_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# DIF2CYCLIC
#
title = 'DIF2CYCLIC'
m = 5
n = 5
a = dif2cyclic ( n )
x = dif2cyclic_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# EBERLEIN
#
title = 'EBERLEIN'
m = 5
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
a = eberlein ( alpha, n )
x = eberlein_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# FIBONACCI1
#
title = 'FIBONACCI1'
m = 5
n = m
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
f1, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
f2, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
a = fibonacci1 ( n, f1, f2 )
x = fibonacci1_null_left ( m, n, f1, f2 )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# LAUCHLI
#
title = 'LAUCHLI'
m = 6
n = m - 1
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
a = lauchli ( alpha, m, n )
x = lauchli_null_left ( alpha, m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# LINE_ADJ
#
title = 'LINE_ADJ'
m = 7
n = m
a = line_adj ( n )
x = line_adj_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# MOLER2
#
title = 'MOLER2'
m = 5
n = m
a = moler2 ( )
x = moler2_null_left ( )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ONE
#
title = 'ONE'
m = 5
n = 5
a = one ( m, n )
x = one_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# RING_ADJ
# N must be a multiple of 4 for there to be a null vector.
#
title = 'RING_ADJ'
m = 12
n = 12
a = ring_adj ( m, n )
x = ring_adj_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ROSSER1
#
title = 'ROSSER1'
m = 8
n = 8
a = rosser1 ( )
x = rosser1_null_left ( )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# ZERO
#
title = 'ZERO'
m = 5
n = 5
a = zero ( m, n )
x = zero_null_left ( m, n )
error_l2 = r8mat_is_null_left ( m, n, a, x )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
norm_x_l2 = r8vec_norm_l2 ( m, x )
print ' %-20s %4d %4d %14g %14g %10.2g' \
% ( title, m, n, norm_a_frobenius, norm_x_l2, error_l2 )
#
# Terminate.
#
print ''
print 'TEST_NULL_LEFT:'
print ' Normal end of execution.'
return