def dif2_condition_test():
#*****************************************************************************80
#
## DIF2_CONDITION_TEST tests DIF2_CONDITION.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 February 2015
#
# Author:
#
# John Burkardt
#
from dif2 import dif2
from r8mat_print import r8mat_print
print ''
print 'DIF2_CONDITION_TEST'
print ' DIF2_CONDITION computes the DIF2 condition.'
m = 5
n = m
a = dif2(m, n)
r8mat_print(m, n, a, ' DIF2 matrix:')
value = dif2_condition(n)
print ''
print ' Value = %g' % (value)
print ''
print 'DIF2_CONDITION_TEST'
print ' Normal end of execution.'
return
def dif2_determinant_test():
#*****************************************************************************80
#
## DIF2_DETERMINANT_TEST tests DIF2_DETERMINANT.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 21 January 2015
#
# Author:
#
# John Burkardt
#
from dif2 import dif2
from r8mat_print import r8mat_print
print ''
print 'DIF2_DETERMINANT_TEST'
print ' DIF2_DETERMINANT computes the DIF2 determinant.'
m = 5
n = m
a = dif2(m, n)
r8mat_print(m, n, a, ' DIF2 matrix:')
value = dif2_determinant(n)
print ''
print ' Value = %g' % (value)
print ''
print 'DIF2_DETERMINANT_TEST'
print ' Normal end of execution.'
return
def dif2_determinant_test ( ): #*****************************************************************************80 # ## DIF2_DETERMINANT_TEST tests DIF2_DETERMINANT. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 21 January 2015 # # Author: # # John Burkardt # from dif2 import dif2 from r8mat_print import r8mat_print print '' print 'DIF2_DETERMINANT_TEST' print ' DIF2_DETERMINANT computes the DIF2 determinant.' m = 5 n = m a = dif2 ( m, n ) r8mat_print ( m, n, a, ' DIF2 matrix:' ) value = dif2_determinant ( n ) print '' print ' Value = %g' % ( value ) print '' print 'DIF2_DETERMINANT_TEST' print ' Normal end of execution.' return
def dif2_condition_test ( ): #*****************************************************************************80 # ## DIF2_CONDITION_TEST tests DIF2_CONDITION. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 07 February 2015 # # Author: # # John Burkardt # from dif2 import dif2 from r8mat_print import r8mat_print print '' print 'DIF2_CONDITION_TEST' print ' DIF2_CONDITION computes the DIF2 condition.' m = 5 n = m a = dif2 ( m, n ) r8mat_print ( m, n, a, ' DIF2 matrix:' ) value = dif2_condition ( n ) print '' print ' Value = %g' % ( value ) print '' print 'DIF2_CONDITION_TEST' print ' Normal end of execution.' return
def dif2_test():
#*****************************************************************************80
#
## DIF2_TEST tests DIF2.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 21 January 2015
#
# Author:
#
# John Burkardt
#
from r8mat_print import r8mat_print
print ''
print 'DIF2_TEST'
print ' DIF2 computes the DIF2 matrix.'
m = 5
n = m
a = dif2(m, n)
r8mat_print(m, n, a, ' DIF2 matrix:')
print ''
print 'DIF2_TEST'
print ' Normal end of execution.'
return
def dif2_test ( ): #*****************************************************************************80 # ## DIF2_TEST tests DIF2. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 21 January 2015 # # Author: # # John Burkardt # from r8mat_print import r8mat_print print '' print 'DIF2_TEST' print ' DIF2 computes the DIF2 matrix.' m = 5 n = m a = dif2 ( m, n ) r8mat_print ( m, n, a, ' DIF2 matrix:' ) print '' print 'DIF2_TEST' print ' Normal end of execution.' return
def test_plu():
#*****************************************************************************80
#
## TEST_PLU tests the PLU factors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 April 2014
#
# Author:
#
# John Burkardt
#
import numpy as np
from bodewig import bodewig
from bodewig import bodewig_plu
from borderband import borderband
from borderband import borderband_plu
from dif2 import dif2
from dif2 import dif2_plu
from gfpp import gfpp
from gfpp import gfpp_plu
from givens import givens
from givens import givens_plu
from i4_uniform_ab import i4_uniform_ab
from kms import kms
from kms import kms_plu
from lehmer import lehmer
from lehmer import lehmer_plu
from maxij import maxij
from maxij import maxij_plu
from minij import minij
from minij import minij_plu
from moler1 import moler1
from moler1 import moler1_plu
from moler3 import moler3
from moler3 import moler3_plu
from oto import oto
from oto import oto_plu
from pascal2 import pascal2
from pascal2 import pascal2_plu
from plu import plu
from plu import plu_plu
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_plu import r8mat_is_plu
from r8mat_norm_fro import r8mat_norm_fro
from r8vec_uniform_ab import r8vec_uniform_ab
from vand2 import vand2
from vand2 import vand2_plu
from wilson import wilson
from wilson import wilson_plu
print ''
print 'TEST_PLU'
print ' A = a test matrix of order M by N'
print ' P, L, U are the PLU factors.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||A-PLU|| = Frobenius norm of A-P*L*U.'
print ''
print ' Title M N ',
print '||A|| ||A-PLU||'
print ''
#
# BODEWIG
#
title = 'BODEWIG'
m = 4
n = 4
a = bodewig()
p, l, u = bodewig_plu()
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# BORDERBAND
#
title = 'BORDERBAND'
m = 5
n = 5
a = borderband(n)
p, l, u = borderband_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# DIF2
#
title = 'DIF2'
m = 5
n = 5
a = dif2(m, n)
p, l, u = dif2_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# GFPP
#
title = 'GFPP'
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 = gfpp(n, alpha)
p, l, u = gfpp_plu(n, alpha)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# GIVENS
#
title = 'GIVENS'
m = 5
n = 5
a = givens(m, n)
p, l, u = givens_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# KMS
#
title = 'KMS'
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 = kms(alpha, m, n)
p, l, u = kms_plu(alpha, n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# LEHMER
#
title = 'LEHMER'
m = 5
n = 5
a = lehmer(m, n)
p, l, u = lehmer_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MAXIJ
#
title = 'MAXIJ'
m = 5
n = 5
a = maxij(m, n)
p, l, u = maxij_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MINIJ
#
title = 'MINIJ'
m = 5
n = 5
a = minij(n, n)
p, l, u = minij_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER1
#
title = 'MOLER1'
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 = moler1(alpha, n, n)
p, l, u = moler1_plu(alpha, n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER3
#
title = 'MOLER3'
m = 5
n = 5
a = moler3(m, n)
p, l, u = moler3_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# OTO
#
title = 'OTO'
m = 5
n = 5
a = oto(m, n)
p, l, u = oto_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# PASCAL2
#
title = 'PASCAL2'
m = 5
n = 5
a = pascal2(n)
p, l, u = pascal2_plu(n)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# PLU
#
title = 'PLU'
m = 5
n = 5
pivot = np.zeros(n)
seed = 123456789
for i in range(0, n):
i4_lo = i
i4_hi = n - 1
pivot[i], seed = i4_uniform_ab(i4_lo, i4_hi, seed)
a = plu(n, pivot)
p, l, u = plu_plu(n, pivot)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# VAND2
#
title = 'VAND2'
m = 4
n = 4
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
x, seed = r8vec_uniform_ab(m, r8_lo, r8_hi, seed)
a = vand2(m, x)
p, l, u = vand2_plu(m, x)
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# WILSON
#
title = 'WILSON'
m = 4
n = 4
a = wilson()
p, l, u = wilson_plu()
error_frobenius = r8mat_is_plu(m, n, a, p, l, u)
norm_a_frobenius = r8mat_norm_fro(m, n, a)
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# Terminate.
#
print ''
print 'TEST_PLU:'
print ' Normal end of execution.'
return
def test_plu ( ):
#*****************************************************************************80
#
## TEST_PLU tests the PLU factors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 07 April 2014
#
# Author:
#
# John Burkardt
#
import numpy as np
from bodewig import bodewig
from bodewig import bodewig_plu
from borderband import borderband
from borderband import borderband_plu
from dif2 import dif2
from dif2 import dif2_plu
from gfpp import gfpp
from gfpp import gfpp_plu
from givens import givens
from givens import givens_plu
from i4_uniform_ab import i4_uniform_ab
from kms import kms
from kms import kms_plu
from lehmer import lehmer
from lehmer import lehmer_plu
from maxij import maxij
from maxij import maxij_plu
from minij import minij
from minij import minij_plu
from moler1 import moler1
from moler1 import moler1_plu
from moler3 import moler3
from moler3 import moler3_plu
from oto import oto
from oto import oto_plu
from pascal2 import pascal2
from pascal2 import pascal2_plu
from plu import plu
from plu import plu_plu
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_plu import r8mat_is_plu
from r8mat_norm_fro import r8mat_norm_fro
from r8vec_uniform_ab import r8vec_uniform_ab
from vand2 import vand2
from vand2 import vand2_plu
from wilson import wilson
from wilson import wilson_plu
print ''
print 'TEST_PLU'
print ' A = a test matrix of order M by N'
print ' P, L, U are the PLU factors.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||A-PLU|| = Frobenius norm of A-P*L*U.'
print ''
print ' Title M N ',
print '||A|| ||A-PLU||'
print ''
#
# BODEWIG
#
title = 'BODEWIG'
m = 4
n = 4
a = bodewig ( )
p, l, u = bodewig_plu ( )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# BORDERBAND
#
title = 'BORDERBAND'
m = 5
n = 5
a = borderband ( n )
p, l, u = borderband_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# DIF2
#
title = 'DIF2'
m = 5
n = 5
a = dif2 ( m, n )
p, l, u = dif2_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# GFPP
#
title = 'GFPP'
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 = gfpp ( n, alpha )
p, l, u = gfpp_plu ( n, alpha )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# GIVENS
#
title = 'GIVENS'
m = 5
n = 5
a = givens ( m, n )
p, l, u = givens_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# KMS
#
title = 'KMS'
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 = kms ( alpha, m, n )
p, l, u = kms_plu ( alpha, n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# LEHMER
#
title = 'LEHMER'
m = 5
n = 5
a = lehmer ( m, n )
p, l, u = lehmer_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MAXIJ
#
title = 'MAXIJ'
m = 5
n = 5
a = maxij ( m, n )
p, l, u = maxij_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MINIJ
#
title = 'MINIJ'
m = 5
n = 5
a = minij ( n, n )
p, l, u = minij_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER1
#
title = 'MOLER1'
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 = moler1 ( alpha, n, n )
p, l, u = moler1_plu ( alpha, n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER3
#
title = 'MOLER3'
m = 5
n = 5
a = moler3 ( m, n )
p, l, u = moler3_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# OTO
#
title = 'OTO'
m = 5
n = 5
a = oto ( m, n )
p, l, u = oto_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# PASCAL2
#
title = 'PASCAL2'
m = 5
n = 5
a = pascal2 ( n )
p, l, u = pascal2_plu ( n )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# PLU
#
title = 'PLU'
m = 5
n = 5
pivot = np.zeros ( n )
seed = 123456789
for i in range ( 0, n ):
i4_lo = i
i4_hi = n - 1
pivot[i], seed = i4_uniform_ab ( i4_lo, i4_hi, seed )
a = plu ( n, pivot )
p, l, u = plu_plu ( n, pivot )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# VAND2
#
title = 'VAND2'
m = 4
n = 4
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
x, seed = r8vec_uniform_ab ( m, r8_lo, r8_hi, seed )
a = vand2 ( m, x )
p, l, u = vand2_plu ( m, x )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# WILSON
#
title = 'WILSON'
m = 4
n = 4
a = wilson ( )
p, l, u = wilson_plu ( )
error_frobenius = r8mat_is_plu ( m, n, a, p, l, u )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# Terminate.
#
print ''
print 'TEST_PLU:'
print ' Normal end of execution.'
return
def test_condition ( ): #*****************************************************************************80 # ## TEST_CONDITION tests the L1 condition number computations. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 11 April 2015 # # Author: # # John Burkardt # from aegerter import aegerter from aegerter import aegerter_condition from aegerter import aegerter_inverse from bab import bab from bab import bab_condition from bab import bab_inverse from bauer import bauer from bauer import bauer_condition from bauer import bauer_inverse from bis import bis from bis import bis_condition from bis import bis_inverse from biw import biw from biw import biw_condition from biw import biw_inverse from bodewig import bodewig from bodewig import bodewig_condition from bodewig import bodewig_inverse from boothroyd import boothroyd from boothroyd import boothroyd_condition from boothroyd import boothroyd_inverse from combin import combin from combin import combin_condition from combin import combin_inverse from companion import companion from companion import companion_condition from companion import companion_inverse from conex1 import conex1 from conex1 import conex1_condition from conex1 import conex1_inverse from conex2 import conex2 from conex2 import conex2_condition from conex2 import conex2_inverse from conex3 import conex3 from conex3 import conex3_condition from conex3 import conex3_inverse from conex4 import conex4 from conex4 import conex4_condition from conex4 import conex4_inverse from daub2 import daub2 from daub2 import daub2_condition from daub2 import daub2_inverse from daub4 import daub4 from daub4 import daub4_condition from daub4 import daub4_inverse from daub6 import daub6 from daub6 import daub6_condition from daub6 import daub6_inverse from daub8 import daub8 from daub8 import daub8_condition from daub8 import daub8_inverse from daub10 import daub10 from daub10 import daub10_condition from daub10 import daub10_inverse from daub12 import daub12 from daub12 import daub12_condition from daub12 import daub12_inverse from diagonal import diagonal from diagonal import diagonal_condition from diagonal import diagonal_inverse from dif2 import dif2 from dif2 import dif2_condition from dif2 import dif2_inverse from downshift import downshift from downshift import downshift_condition from downshift import downshift_inverse from exchange import exchange from exchange import exchange_condition from exchange import exchange_inverse from fibonacci2 import fibonacci2 from fibonacci2 import fibonacci2_condition from fibonacci2 import fibonacci2_inverse from gfpp import gfpp from gfpp import gfpp_condition from gfpp import gfpp_inverse from givens import givens from givens import givens_condition from givens import givens_inverse from hankel_n import hankel_n from hankel_n import hankel_n_condition from hankel_n import hankel_n_inverse from harman import harman from harman import harman_condition from harman import harman_inverse from hartley import hartley from hartley import hartley_condition from hartley import hartley_inverse from identity import identity from identity import identity_condition from identity import identity_inverse from ill3 import ill3 from ill3 import ill3_condition from ill3 import ill3_inverse from jordan import jordan from jordan import jordan_condition from jordan import jordan_inverse from kershaw import kershaw from kershaw import kershaw_condition from kershaw import kershaw_inverse from lietzke import lietzke from lietzke import lietzke_condition from lietzke import lietzke_inverse from maxij import maxij from maxij import maxij_condition from maxij import maxij_inverse from minij import minij from minij import minij_condition from minij import minij_inverse from orth_symm import orth_symm from orth_symm import orth_symm_condition from orth_symm import orth_symm_inverse from oto import oto from oto import oto_condition from oto import oto_inverse from pascal1 import pascal1 from pascal1 import pascal1_condition from pascal1 import pascal1_inverse from pascal3 import pascal3 from pascal3 import pascal3_condition from pascal3 import pascal3_inverse from pei import pei from pei import pei_condition from pei import pei_inverse from r8_uniform_ab import r8_uniform_ab from r8mat_norm_l1 import r8mat_norm_l1 from r8vec_uniform_ab import r8vec_uniform_ab from rodman import rodman from rodman import rodman_condition from rodman import rodman_inverse from rutis1 import rutis1 from rutis1 import rutis1_condition from rutis1 import rutis1_inverse from rutis2 import rutis2 from rutis2 import rutis2_condition from rutis2 import rutis2_inverse from rutis3 import rutis3 from rutis3 import rutis3_condition from rutis3 import rutis3_inverse from rutis5 import rutis5 from rutis5 import rutis5_condition from rutis5 import rutis5_inverse from summation import summation from summation import summation_condition from summation import summation_inverse from sweet1 import sweet1 from sweet1 import sweet1_condition from sweet1 import sweet1_inverse from sweet2 import sweet2 from sweet2 import sweet2_condition from sweet2 import sweet2_inverse from sweet3 import sweet3 from sweet3 import sweet3_condition from sweet3 import sweet3_inverse from sweet4 import sweet4 from sweet4 import sweet4_condition from sweet4 import sweet4_inverse from tri_upper import tri_upper from tri_upper import tri_upper_condition from tri_upper import tri_upper_inverse from upshift import upshift from upshift import upshift_condition from upshift import upshift_inverse from wilk03 import wilk03 from wilk03 import wilk03_condition from wilk03 import wilk03_inverse from wilk04 import wilk04 from wilk04 import wilk04_condition from wilk04 import wilk04_inverse from wilk05 import wilk05 from wilk05 import wilk05_condition from wilk05 import wilk05_inverse from wilson import wilson from wilson import wilson_condition from wilson import wilson_inverse print '' print 'TEST_CONDITION' print ' Compute the L1 condition number of an example of each' print ' test matrix' print '' print ' Title N COND COND' print '' # # AEGERTER # title = 'AEGERTER' n = 5 cond1 = aegerter_condition ( n ) a = aegerter ( n ) b = aegerter_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BAB # title = 'BAB' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) beta, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = bab_condition ( n, alpha, beta ) a = bab ( n, alpha, beta ) b = bab_inverse ( n, alpha, beta ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BAUER # title = 'BAUER' n = 6 cond1 = bauer_condition ( ) a = bauer ( ) b = bauer_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BIS # title = 'BIS' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) beta, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = bis_condition ( alpha, beta, n ) a = bis ( alpha, beta, n, n ) b = bis_inverse ( alpha, beta, n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BIW # title = 'BIW' n = 5 cond1 = biw_condition ( n ) a = biw ( n ) b = biw_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BODEWIG # title = 'BODEWIG' n = 4 cond1 = bodewig_condition ( ) a = bodewig ( ) b = bodewig_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # BOOTHROYD # title = 'BOOTHROYD' n = 5 cond1 = boothroyd_condition ( n ) a = boothroyd ( n ) b = boothroyd_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # COMBIN # title = 'COMBIN' n = 3 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) beta, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = combin_condition ( alpha, beta, n ) a = combin ( alpha, beta, n ) b = combin_inverse ( alpha, beta, n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # COMPANION # title = 'COMPANION' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 x, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed ) cond1 = companion_condition ( n, x ) a = companion ( n, x ) b = companion_inverse ( n, x ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # CONEX1 # title = 'CONEX1' n = 4 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = conex1_condition ( alpha ) a = conex1 ( alpha ) b = conex1_inverse ( alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # CONEX2 # title = 'CONEX2' n = 3 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = conex2_condition ( alpha ) a = conex2 ( alpha ) b = conex2_inverse ( alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # CONEX3 # title = 'CONEX3' n = 5 cond1 = conex3_condition ( n ) a = conex3 ( n ) b = conex3_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # CONEX4 # title = 'CONEX4' n = 4 cond1 = conex4_condition ( ) a = conex4 ( ) b = conex4_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB2 # title = 'DAUB2' n = 4 cond1 = daub2_condition ( n ) a = daub2 ( n ) b = daub2_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB4 # title = 'DAUB4' n = 8 cond1 = daub4_condition ( n ) a = daub4 ( n ) b = daub4_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB6 # title = 'DAUB6' n = 12 cond1 = daub6_condition ( n ) a = daub6 ( n ) b = daub6_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB8 # title = 'DAUB8' n = 16 cond1 = daub8_condition ( n ) a = daub8 ( n ) b = daub8_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB10 # title = 'DAUB10' n = 20 cond1 = daub10_condition ( n ) a = daub10 ( n ) b = daub10_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DAUB12 # title = 'DAUB12' n = 24 cond1 = daub12_condition ( n ) a = daub12 ( n ) b = daub12_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DIAGONAL # title = 'DIAGONAL' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 x, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed ) cond1 = diagonal_condition ( n, x ) a = diagonal ( n, n, x ) b = diagonal_inverse ( n, x ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DIF2 # title = 'DIF2' n = 5 cond1 = dif2_condition ( n ) a = dif2 ( n, n ) b = dif2_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # DOWNSHIFT # title = 'DOWNSHIFT' n = 5 cond1 = downshift_condition ( n ) a = downshift ( n ) b = downshift_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # EXCHANGE # title = 'EXCHANGE' n = 5 cond1 = exchange_condition ( n ) a = exchange ( n, n ) b = exchange_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # FIBONACCI2 # title = 'FIBONACCI2' n = 5 cond1 = fibonacci2_condition ( n ) a = fibonacci2 ( n ) b = fibonacci2_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # GFPP # title = 'GFPP' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = gfpp_condition ( n, alpha ) a = gfpp ( n, alpha ) b = gfpp_inverse ( n, alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # GIVENS # title = 'GIVENS' n = 5 cond1 = givens_condition ( n ) a = givens ( n, n ) b = givens_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # HANKEL_N # title = 'HANKEL_N' n = 5 cond1 = hankel_n_condition ( n ) a = hankel_n ( n ) b = hankel_n_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # HARMAN # title = 'HARMAN' n = 8 cond1 = harman_condition ( ) a = harman ( ) b = harman_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # HARTLEY # title = 'HARTLEY' n = 5 cond1 = hartley_condition ( n ) a = hartley ( n ) b = hartley_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # IDENTITY # title = 'IDENTITY' n = 5 cond1 = identity_condition ( n ) a = identity ( n, n ) b = identity_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # ILL3 # title = 'ILL3' n = 3 cond1 = ill3_condition ( ) a = ill3 ( ) b = ill3_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # JORDAN # title = 'JORDAN' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = jordan_condition ( n, alpha ) a = jordan ( n, n, alpha ) b = jordan_inverse ( n, alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # KERSHAW # title = 'KERSHAW' n = 4 cond1 = kershaw_condition ( ) a = kershaw ( ) b = kershaw_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # LIETZKE # title = 'LIETZKE' n = 5 cond1 = lietzke_condition ( n ) a = lietzke ( n ) b = lietzke_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # MAXIJ # title = 'MAXIJ' n = 5 cond1 = maxij_condition ( n ) a = maxij ( n, n ) b = maxij_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # MINIJ # title = 'MINIJ' n = 5 cond1 = minij_condition ( n ) a = minij ( n, n ) b = minij_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # ORTH_SYMM # title = 'ORTH_SYMM' n = 5 cond1 = orth_symm_condition ( n ) a = orth_symm ( n ) b = orth_symm_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # OTO # title = 'OTO' n = 5 cond1 = oto_condition ( n ) a = oto ( n, n ) b = oto_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # PASCAL1 # title = 'PASCAL1' n = 5 cond1 = pascal1_condition ( n ) a = pascal1 ( n ) b = pascal1_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # PASCAL3 # title = 'PASCAL3' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = pascal3_condition ( n, alpha ) a = pascal3 ( n, alpha ) b = pascal3_inverse ( n, alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # PEI # title = 'PEI' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = pei_condition ( alpha, n ) a = pei ( alpha, n ) b = pei_inverse ( alpha, n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # RODMAN # title = 'RODMAN' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = rodman_condition ( n, alpha ) a = rodman ( n, n, alpha ) b = rodman_inverse ( n, alpha ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # RUTIS1 # title = 'RUTIS1' n = 4 cond1 = rutis1_condition ( ) a = rutis1 ( ) b = rutis1_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # RUTIS2 # title = 'RUTIS2' n = 4 cond1 = rutis2_condition ( ) a = rutis2 ( ) b = rutis2_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # RUTIS3 # title = 'RUTIS3' n = 4 cond1 = rutis3_condition ( ) a = rutis3 ( ) b = rutis3_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # RUTIS5 # title = 'RUTIS5' n = 4 cond1 = rutis5_condition ( ) a = rutis5 ( ) b = rutis5_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # SUMMATION # title = 'SUMMATION' n = 5 cond1 = summation_condition ( n ) a = summation ( n, n ) b = summation_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # SWEET1 # title = 'SWEET1' n = 6 cond1 = sweet1_condition ( ) a = sweet1 ( ) b = sweet1_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # SWEET2 # title = 'SWEET2' n = 6 cond1 = sweet2_condition ( ) a = sweet2 ( ) b = sweet2_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # SWEET3 # title = 'SWEET3' n = 6 cond1 = sweet3_condition ( ) a = sweet3 ( ) b = sweet3_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # SWEET4 # title = 'SWEET4' n = 13 cond1 = sweet4_condition ( ) a = sweet4 ( ) b = sweet4_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # TRI_UPPER # title = 'TRI_UPPER' n = 5 r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) cond1 = tri_upper_condition ( alpha, n ) a = tri_upper ( alpha, n ) b = tri_upper_inverse ( alpha, n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # UPSHIFT # title = 'UPSHIFT' n = 5 cond1 = upshift_condition ( n ) a = upshift ( n ) b = upshift_inverse ( n ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # WILK03 # title = 'WILK03' n = 3 cond1 = wilk03_condition ( ) a = wilk03 ( ) b = wilk03_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # WILK04 # title = 'WILK04' n = 4 cond1 = wilk04_condition ( ) a = wilk04 ( ) b = wilk04_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # WILK05 # title = 'WILK05' n = 5 cond1 = wilk05_condition ( ) a = wilk05 ( ) b = wilk05_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # WILSON # title = 'WILSON' n = 4 cond1 = wilson_condition ( ) a = wilson ( ) b = wilson_inverse ( ) a_norm = r8mat_norm_l1 ( n, n, a ) b_norm = r8mat_norm_l1 ( n, n, b ) cond2 = a_norm * b_norm print ' %-20s %4d %14.6g %14.6g' % ( title, n, cond1, cond2 ) # # Terminate. # print '' print 'TEST_CONDITION' print ' Normal end of execution.' return
def test_condition():
#*****************************************************************************80
#
## TEST_CONDITION tests the L1 condition number computations.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 11 April 2015
#
# Author:
#
# John Burkardt
#
from aegerter import aegerter
from aegerter import aegerter_condition
from aegerter import aegerter_inverse
from bab import bab
from bab import bab_condition
from bab import bab_inverse
from bauer import bauer
from bauer import bauer_condition
from bauer import bauer_inverse
from bis import bis
from bis import bis_condition
from bis import bis_inverse
from biw import biw
from biw import biw_condition
from biw import biw_inverse
from bodewig import bodewig
from bodewig import bodewig_condition
from bodewig import bodewig_inverse
from boothroyd import boothroyd
from boothroyd import boothroyd_condition
from boothroyd import boothroyd_inverse
from combin import combin
from combin import combin_condition
from combin import combin_inverse
from companion import companion
from companion import companion_condition
from companion import companion_inverse
from conex1 import conex1
from conex1 import conex1_condition
from conex1 import conex1_inverse
from conex2 import conex2
from conex2 import conex2_condition
from conex2 import conex2_inverse
from conex3 import conex3
from conex3 import conex3_condition
from conex3 import conex3_inverse
from conex4 import conex4
from conex4 import conex4_condition
from conex4 import conex4_inverse
from daub2 import daub2
from daub2 import daub2_condition
from daub2 import daub2_inverse
from daub4 import daub4
from daub4 import daub4_condition
from daub4 import daub4_inverse
from daub6 import daub6
from daub6 import daub6_condition
from daub6 import daub6_inverse
from daub8 import daub8
from daub8 import daub8_condition
from daub8 import daub8_inverse
from daub10 import daub10
from daub10 import daub10_condition
from daub10 import daub10_inverse
from daub12 import daub12
from daub12 import daub12_condition
from daub12 import daub12_inverse
from diagonal import diagonal
from diagonal import diagonal_condition
from diagonal import diagonal_inverse
from dif2 import dif2
from dif2 import dif2_condition
from dif2 import dif2_inverse
from downshift import downshift
from downshift import downshift_condition
from downshift import downshift_inverse
from exchange import exchange
from exchange import exchange_condition
from exchange import exchange_inverse
from fibonacci2 import fibonacci2
from fibonacci2 import fibonacci2_condition
from fibonacci2 import fibonacci2_inverse
from gfpp import gfpp
from gfpp import gfpp_condition
from gfpp import gfpp_inverse
from givens import givens
from givens import givens_condition
from givens import givens_inverse
from hankel_n import hankel_n
from hankel_n import hankel_n_condition
from hankel_n import hankel_n_inverse
from harman import harman
from harman import harman_condition
from harman import harman_inverse
from hartley import hartley
from hartley import hartley_condition
from hartley import hartley_inverse
from identity import identity
from identity import identity_condition
from identity import identity_inverse
from ill3 import ill3
from ill3 import ill3_condition
from ill3 import ill3_inverse
from jordan import jordan
from jordan import jordan_condition
from jordan import jordan_inverse
from kershaw import kershaw
from kershaw import kershaw_condition
from kershaw import kershaw_inverse
from lietzke import lietzke
from lietzke import lietzke_condition
from lietzke import lietzke_inverse
from maxij import maxij
from maxij import maxij_condition
from maxij import maxij_inverse
from minij import minij
from minij import minij_condition
from minij import minij_inverse
from orth_symm import orth_symm
from orth_symm import orth_symm_condition
from orth_symm import orth_symm_inverse
from oto import oto
from oto import oto_condition
from oto import oto_inverse
from pascal1 import pascal1
from pascal1 import pascal1_condition
from pascal1 import pascal1_inverse
from pascal3 import pascal3
from pascal3 import pascal3_condition
from pascal3 import pascal3_inverse
from pei import pei
from pei import pei_condition
from pei import pei_inverse
from r8_uniform_ab import r8_uniform_ab
from r8mat_norm_l1 import r8mat_norm_l1
from r8vec_uniform_ab import r8vec_uniform_ab
from rodman import rodman
from rodman import rodman_condition
from rodman import rodman_inverse
from rutis1 import rutis1
from rutis1 import rutis1_condition
from rutis1 import rutis1_inverse
from rutis2 import rutis2
from rutis2 import rutis2_condition
from rutis2 import rutis2_inverse
from rutis3 import rutis3
from rutis3 import rutis3_condition
from rutis3 import rutis3_inverse
from rutis5 import rutis5
from rutis5 import rutis5_condition
from rutis5 import rutis5_inverse
from summation import summation
from summation import summation_condition
from summation import summation_inverse
from sweet1 import sweet1
from sweet1 import sweet1_condition
from sweet1 import sweet1_inverse
from sweet2 import sweet2
from sweet2 import sweet2_condition
from sweet2 import sweet2_inverse
from sweet3 import sweet3
from sweet3 import sweet3_condition
from sweet3 import sweet3_inverse
from sweet4 import sweet4
from sweet4 import sweet4_condition
from sweet4 import sweet4_inverse
from tri_upper import tri_upper
from tri_upper import tri_upper_condition
from tri_upper import tri_upper_inverse
from upshift import upshift
from upshift import upshift_condition
from upshift import upshift_inverse
from wilk03 import wilk03
from wilk03 import wilk03_condition
from wilk03 import wilk03_inverse
from wilk04 import wilk04
from wilk04 import wilk04_condition
from wilk04 import wilk04_inverse
from wilk05 import wilk05
from wilk05 import wilk05_condition
from wilk05 import wilk05_inverse
from wilson import wilson
from wilson import wilson_condition
from wilson import wilson_inverse
print ''
print 'TEST_CONDITION'
print ' Compute the L1 condition number of an example of each'
print ' test matrix'
print ''
print ' Title N COND COND'
print ''
#
# AEGERTER
#
title = 'AEGERTER'
n = 5
cond1 = aegerter_condition(n)
a = aegerter(n)
b = aegerter_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BAB
#
title = 'BAB'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
beta, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = bab_condition(n, alpha, beta)
a = bab(n, alpha, beta)
b = bab_inverse(n, alpha, beta)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BAUER
#
title = 'BAUER'
n = 6
cond1 = bauer_condition()
a = bauer()
b = bauer_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BIS
#
title = 'BIS'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
beta, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = bis_condition(alpha, beta, n)
a = bis(alpha, beta, n, n)
b = bis_inverse(alpha, beta, n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BIW
#
title = 'BIW'
n = 5
cond1 = biw_condition(n)
a = biw(n)
b = biw_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BODEWIG
#
title = 'BODEWIG'
n = 4
cond1 = bodewig_condition()
a = bodewig()
b = bodewig_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# BOOTHROYD
#
title = 'BOOTHROYD'
n = 5
cond1 = boothroyd_condition(n)
a = boothroyd(n)
b = boothroyd_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# COMBIN
#
title = 'COMBIN'
n = 3
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
beta, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = combin_condition(alpha, beta, n)
a = combin(alpha, beta, n)
b = combin_inverse(alpha, beta, n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# COMPANION
#
title = 'COMPANION'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
x, seed = r8vec_uniform_ab(n, r8_lo, r8_hi, seed)
cond1 = companion_condition(n, x)
a = companion(n, x)
b = companion_inverse(n, x)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# CONEX1
#
title = 'CONEX1'
n = 4
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = conex1_condition(alpha)
a = conex1(alpha)
b = conex1_inverse(alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# CONEX2
#
title = 'CONEX2'
n = 3
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = conex2_condition(alpha)
a = conex2(alpha)
b = conex2_inverse(alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# CONEX3
#
title = 'CONEX3'
n = 5
cond1 = conex3_condition(n)
a = conex3(n)
b = conex3_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# CONEX4
#
title = 'CONEX4'
n = 4
cond1 = conex4_condition()
a = conex4()
b = conex4_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB2
#
title = 'DAUB2'
n = 4
cond1 = daub2_condition(n)
a = daub2(n)
b = daub2_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB4
#
title = 'DAUB4'
n = 8
cond1 = daub4_condition(n)
a = daub4(n)
b = daub4_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB6
#
title = 'DAUB6'
n = 12
cond1 = daub6_condition(n)
a = daub6(n)
b = daub6_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB8
#
title = 'DAUB8'
n = 16
cond1 = daub8_condition(n)
a = daub8(n)
b = daub8_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB10
#
title = 'DAUB10'
n = 20
cond1 = daub10_condition(n)
a = daub10(n)
b = daub10_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DAUB12
#
title = 'DAUB12'
n = 24
cond1 = daub12_condition(n)
a = daub12(n)
b = daub12_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DIAGONAL
#
title = 'DIAGONAL'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
x, seed = r8vec_uniform_ab(n, r8_lo, r8_hi, seed)
cond1 = diagonal_condition(n, x)
a = diagonal(n, n, x)
b = diagonal_inverse(n, x)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DIF2
#
title = 'DIF2'
n = 5
cond1 = dif2_condition(n)
a = dif2(n, n)
b = dif2_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# DOWNSHIFT
#
title = 'DOWNSHIFT'
n = 5
cond1 = downshift_condition(n)
a = downshift(n)
b = downshift_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# EXCHANGE
#
title = 'EXCHANGE'
n = 5
cond1 = exchange_condition(n)
a = exchange(n, n)
b = exchange_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# FIBONACCI2
#
title = 'FIBONACCI2'
n = 5
cond1 = fibonacci2_condition(n)
a = fibonacci2(n)
b = fibonacci2_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# GFPP
#
title = 'GFPP'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = gfpp_condition(n, alpha)
a = gfpp(n, alpha)
b = gfpp_inverse(n, alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# GIVENS
#
title = 'GIVENS'
n = 5
cond1 = givens_condition(n)
a = givens(n, n)
b = givens_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# HANKEL_N
#
title = 'HANKEL_N'
n = 5
cond1 = hankel_n_condition(n)
a = hankel_n(n)
b = hankel_n_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# HARMAN
#
title = 'HARMAN'
n = 8
cond1 = harman_condition()
a = harman()
b = harman_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# HARTLEY
#
title = 'HARTLEY'
n = 5
cond1 = hartley_condition(n)
a = hartley(n)
b = hartley_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# IDENTITY
#
title = 'IDENTITY'
n = 5
cond1 = identity_condition(n)
a = identity(n, n)
b = identity_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# ILL3
#
title = 'ILL3'
n = 3
cond1 = ill3_condition()
a = ill3()
b = ill3_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# JORDAN
#
title = 'JORDAN'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = jordan_condition(n, alpha)
a = jordan(n, n, alpha)
b = jordan_inverse(n, alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# KERSHAW
#
title = 'KERSHAW'
n = 4
cond1 = kershaw_condition()
a = kershaw()
b = kershaw_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# LIETZKE
#
title = 'LIETZKE'
n = 5
cond1 = lietzke_condition(n)
a = lietzke(n)
b = lietzke_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# MAXIJ
#
title = 'MAXIJ'
n = 5
cond1 = maxij_condition(n)
a = maxij(n, n)
b = maxij_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# MINIJ
#
title = 'MINIJ'
n = 5
cond1 = minij_condition(n)
a = minij(n, n)
b = minij_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# ORTH_SYMM
#
title = 'ORTH_SYMM'
n = 5
cond1 = orth_symm_condition(n)
a = orth_symm(n)
b = orth_symm_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# OTO
#
title = 'OTO'
n = 5
cond1 = oto_condition(n)
a = oto(n, n)
b = oto_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# PASCAL1
#
title = 'PASCAL1'
n = 5
cond1 = pascal1_condition(n)
a = pascal1(n)
b = pascal1_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# PASCAL3
#
title = 'PASCAL3'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = pascal3_condition(n, alpha)
a = pascal3(n, alpha)
b = pascal3_inverse(n, alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# PEI
#
title = 'PEI'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = pei_condition(alpha, n)
a = pei(alpha, n)
b = pei_inverse(alpha, n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# RODMAN
#
title = 'RODMAN'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = rodman_condition(n, alpha)
a = rodman(n, n, alpha)
b = rodman_inverse(n, alpha)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# RUTIS1
#
title = 'RUTIS1'
n = 4
cond1 = rutis1_condition()
a = rutis1()
b = rutis1_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# RUTIS2
#
title = 'RUTIS2'
n = 4
cond1 = rutis2_condition()
a = rutis2()
b = rutis2_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# RUTIS3
#
title = 'RUTIS3'
n = 4
cond1 = rutis3_condition()
a = rutis3()
b = rutis3_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# RUTIS5
#
title = 'RUTIS5'
n = 4
cond1 = rutis5_condition()
a = rutis5()
b = rutis5_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# SUMMATION
#
title = 'SUMMATION'
n = 5
cond1 = summation_condition(n)
a = summation(n, n)
b = summation_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# SWEET1
#
title = 'SWEET1'
n = 6
cond1 = sweet1_condition()
a = sweet1()
b = sweet1_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# SWEET2
#
title = 'SWEET2'
n = 6
cond1 = sweet2_condition()
a = sweet2()
b = sweet2_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# SWEET3
#
title = 'SWEET3'
n = 6
cond1 = sweet3_condition()
a = sweet3()
b = sweet3_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# SWEET4
#
title = 'SWEET4'
n = 13
cond1 = sweet4_condition()
a = sweet4()
b = sweet4_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# TRI_UPPER
#
title = 'TRI_UPPER'
n = 5
r8_lo = -5.0
r8_hi = +5.0
seed = 123456789
alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed)
cond1 = tri_upper_condition(alpha, n)
a = tri_upper(alpha, n)
b = tri_upper_inverse(alpha, n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# UPSHIFT
#
title = 'UPSHIFT'
n = 5
cond1 = upshift_condition(n)
a = upshift(n)
b = upshift_inverse(n)
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# WILK03
#
title = 'WILK03'
n = 3
cond1 = wilk03_condition()
a = wilk03()
b = wilk03_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# WILK04
#
title = 'WILK04'
n = 4
cond1 = wilk04_condition()
a = wilk04()
b = wilk04_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# WILK05
#
title = 'WILK05'
n = 5
cond1 = wilk05_condition()
a = wilk05()
b = wilk05_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# WILSON
#
title = 'WILSON'
n = 4
cond1 = wilson_condition()
a = wilson()
b = wilson_inverse()
a_norm = r8mat_norm_l1(n, n, a)
b_norm = r8mat_norm_l1(n, n, b)
cond2 = a_norm * b_norm
print ' %-20s %4d %14.6g %14.6g' % (title, n, cond1, cond2)
#
# Terminate.
#
print ''
print 'TEST_CONDITION'
print ' Normal end of execution.'
return
def test_solution ( ):
#*****************************************************************************80
#
## TEST_SOLUTION tests the linear solution computations.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 March 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from a123 import a123
from a123 import a123_rhs
from a123 import a123_solution
from bodewig import bodewig
from bodewig import bodewig_rhs
from bodewig import bodewig_solution
from dif2 import dif2
from dif2 import dif2_rhs
from dif2 import dif2_solution
from frank import frank
from frank import frank_rhs
from frank import frank_solution
from poisson import poisson
from poisson import poisson_rhs
from poisson import poisson_solution
from r8mat_is_solution import r8mat_is_solution
from r8mat_norm_fro import r8mat_norm_fro
from wilk03 import wilk03
from wilk03 import wilk03_rhs
from wilk03 import wilk03_solution
from wilk04 import wilk04
from wilk04 import wilk04_rhs
from wilk04 import wilk04_solution
from wilson import wilson
from wilson import wilson_rhs
from wilson import wilson_solution
print ''
print 'TEST_SOLUTION'
print ' Compute the Frobenius norm of the solution error:'
print ' A * X - B'
print ' given MxN matrix A, NxK solution X, MxK right hand side B.'
print ''
print ' Title M N K ||A||',
print ' ||A*X-B||'
print ''
#
# A123 matrix.
#
title = 'A123'
m = 3
n = 3
k = 1
a = a123 ( )
b = a123_rhs ( )
x = a123_solution ( )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# BODEWIG matrix.
#
title = 'BODEWIG'
m = 4
n = 4
k = 1
a = bodewig ( )
b = bodewig_rhs ( )
x = bodewig_solution ( )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# DIF2 matrix.
#
title = 'DIF2'
m = 10
n = 10
k = 2
a = dif2 ( m, n )
b = dif2_rhs ( m, k )
x = dif2_solution ( n, k )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# FRANK matrix.
#
title = 'FRANK'
m = 10
n = 10
k = 2
a = frank ( n )
b = frank_rhs ( m, k )
x = frank_solution ( n, k )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# POISSON matrix.
#
title = 'POISSON'
nrow = 4
ncol = 5
m = nrow * ncol
n = nrow * ncol
k = 1
a = poisson ( nrow, ncol )
b = poisson_rhs ( nrow, ncol, k )
x = poisson_solution ( nrow, ncol, k )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# WILK03 matrix.
#
title = 'WILK03'
m = 3
n = 3
k = 1
a = wilk03 ( )
b = wilk03_rhs ( )
x = wilk03_solution ( )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# WILK04 matrix.
#
title = 'WILK04'
m = 4
n = 4
k = 1
a = wilk04 ( )
b = wilk04_rhs ( )
x = wilk04_solution ( )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# WILSON matrix.
#
title = 'WILSON'
m = 4
n = 4
k = 1
a = wilson ( )
b = wilson_rhs ( )
x = wilson_solution ( )
error_frobenius = r8mat_is_solution ( m, n, k, a, x, b )
norm_frobenius = r8mat_norm_fro ( n, n, a )
print ' %-20s %4d %4d %4d %14g %14g' \
% ( title, m, n, k, norm_frobenius, error_frobenius )
#
# Terminate.
#
print ''
print 'TEST_SOLUTION'
print ' Normal end of execution.'
return
def test_llt ( ):
#*****************************************************************************80
#
#% TEST_LLT tests LLT factors.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 April 2015
#
# Author:
#
# John Burkardt
#
from dif2 import dif2
from dif2 import dif2_llt
from givens import givens
from givens import givens_llt
from kershaw import kershaw
from kershaw import kershaw_llt
from lehmer import lehmer
from lehmer import lehmer_llt
from minij import minij
from minij import minij_llt
from moler1 import moler1
from moler1 import moler1_llt
from moler3 import moler3
from moler3 import moler3_llt
from oto import oto
from oto import oto_llt
from pascal2 import pascal2
from pascal2 import pascal2_llt
from wilson import wilson
from wilson import wilson_llt
from r8_uniform_ab import r8_uniform_ab
from r8mat_is_llt import r8mat_is_llt
from r8mat_norm_fro import r8mat_norm_fro
print ''
print 'TEST_LLT'
print ' A = a test matrix of order M by M'
print ' L is an M by N lower triangular Cholesky factor.'
print ''
print ' ||A|| = Frobenius norm of A.'
print ' ||A-LLT|| = Frobenius norm of A-L*L\'.'
print ''
print ' Title M N ',
print '||A|| ||A-LLT||'
print ''
#
# DIF2
#
title = 'DIF2'
m = 5
n = 5
a = dif2 ( m, n )
l = dif2_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# GIVENS
#
title = 'GIVENS'
m = 5
n = 5
a = givens ( m, n )
l = givens_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# KERSHAW
#
title = 'KERSHAW'
m = 4
n = 4
a = kershaw ( )
l = kershaw_llt ( )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# LEHMER
#
title = 'LEHMER'
m = 5
n = 5
a = lehmer ( n, n )
l = lehmer_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MINIJ
#
title = 'MINIJ'
m = 5
n = 5
a = minij ( n, n )
l = minij_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER1
#
title = 'MOLER1'
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 = moler1 ( alpha, m, n )
l = moler1_llt ( alpha, n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# MOLER3
#
title = 'MOLER3'
m = 5
n = 5
a = moler3 ( m, n )
l = moler3_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# OTO
#
title = 'OTO'
m = 5
n = 5
a = oto ( m, n )
l = oto_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# PASCAL2
#
title = 'PASCAL2'
m = 5
n = 5
a = pascal2 ( n )
l = pascal2_llt ( n )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# WILSON
#
title = 'WILSON'
m = 4
n = 4
a = wilson ( )
l = wilson_llt ( )
error_frobenius = r8mat_is_llt ( m, n, a, l )
norm_a_frobenius = r8mat_norm_fro ( m, n, a )
print ' %-20s %4d %4d %14g %14g' \
% ( title, m, n, norm_a_frobenius, error_frobenius )
#
# Terminate.
#
print ''
print 'TEST_LLT:'
print ' Normal end of execution.'
return