def tri_upper_determinant_test ( ): #*****************************************************************************80 # ## TRI_UPPER_DETERMINANT_TEST tests TRI_UPPER_DETERMINANT. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 25 February 2015 # # Author: # # John Burkardt # from tri_upper import tri_upper from r8_uniform_ab import r8_uniform_ab from r8mat_print import r8mat_print print '' print 'TRI_UPPER_DETERMINANT_TEST' print ' TRI_UPPER_DETERMINANT computes the determinant of the TRI_UPPER matrix.' print '' m = 5 n = m r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab ( r8_lo, r8_hi, seed ) a = tri_upper ( alpha, n ) r8mat_print ( n, n, a, ' TRI_UPPER matrix:' ) value = tri_upper_determinant ( alpha, n ) print '' print ' Value = %g' % ( value ) print '' print 'TRI_UPPER_DETERMINANT_TEST' print ' Normal end of execution.' return
def tri_upper_determinant_test(): #*****************************************************************************80 # ## TRI_UPPER_DETERMINANT_TEST tests TRI_UPPER_DETERMINANT. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 25 February 2015 # # Author: # # John Burkardt # from tri_upper import tri_upper from r8_uniform_ab import r8_uniform_ab from r8mat_print import r8mat_print print '' print 'TRI_UPPER_DETERMINANT_TEST' print ' TRI_UPPER_DETERMINANT computes the determinant of the TRI_UPPER matrix.' print '' m = 5 n = m r8_lo = -5.0 r8_hi = +5.0 seed = 123456789 alpha, seed = r8_uniform_ab(r8_lo, r8_hi, seed) a = tri_upper(alpha, n) r8mat_print(n, n, a, ' TRI_UPPER matrix:') value = tri_upper_determinant(alpha, n) print '' print ' Value = %g' % (value) print '' print 'TRI_UPPER_DETERMINANT_TEST' print ' Normal end of execution.' return
def tri_upper_test ( ): #*****************************************************************************80 # ## TRI_UPPER_TEST tests TRI_UPPER. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 17 December 2014 # # Author: # # John Burkardt # from r8_uniform_01 import r8_uniform_01 from r8mat_print import r8mat_print print '' print 'TRI_UPPER_TEST' print ' TRI_UPPER computes the TRI_UPPER matrix.' seed = 123456789 n = 5 alpha, seed = r8_uniform_01 ( seed ) a = tri_upper ( alpha, n ) r8mat_print ( n, n, a, ' TRI_UPPER matrix:' ) print '' print 'TRI_UPPER_TEST' print ' Normal end of execution.' return
def tri_upper_test(): #*****************************************************************************80 # ## TRI_UPPER_TEST tests TRI_UPPER. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 17 December 2014 # # Author: # # John Burkardt # from r8_uniform_01 import r8_uniform_01 from r8mat_print import r8mat_print print '' print 'TRI_UPPER_TEST' print ' TRI_UPPER computes the TRI_UPPER matrix.' seed = 123456789 n = 5 alpha, seed = r8_uniform_01(seed) a = tri_upper(alpha, n) r8mat_print(n, n, a, ' TRI_UPPER matrix:') print '' print 'TRI_UPPER_TEST' 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