

 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    2    1.00E-02 )
 Condition no. =  9.8749E+01     Residual function =  3.165162796E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   7.6E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-02   wantse =         F
 atol   =  3.18E-16               conlim =  9.87E+04
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.251026233E+03  1.00E+00  6.62E-04
     1 -1.569382661E+01  4.513015121E+02  3.61E-01  7.04E-01  8.88E-01  1.00E+00  5.5E-01
     2  2.897013496E+00  2.389170081E+02  1.91E-01  4.36E-01  1.18E+00  2.12E+00  2.9E-01
     3  6.912476123E+00  1.508301251E+02  1.21E-01  3.14E-01  1.39E+00  3.40E+00  1.9E-01
     4  1.925468458E+00  1.061006594E+02  8.48E-02  2.39E-01  1.56E+00  4.82E+00  1.4E-01
     5 -4.031144634E+00  8.068847228E+01  6.45E-02  1.86E-01  1.70E+00  6.39E+00  1.1E-01
     6 -8.164502129E+00  6.526230465E+01  5.22E-02  1.45E-01  1.83E+00  8.09E+00  9.2E-02
     7 -1.026456074E+01  5.551640158E+01  4.44E-02  1.13E-01  1.93E+00  9.92E+00  7.8E-02
     8 -1.083036972E+01  4.920410096E+01  3.93E-02  8.72E-02  2.02E+00  1.19E+01  6.8E-02
     9 -1.039855535E+01  4.504692088E+01  3.60E-02  6.64E-02  2.09E+00  1.40E+01  6.1E-02
    10 -9.380373468E+00  4.227482078E+01  3.38E-02  5.00E-02  2.15E+00  1.63E+01  5.6E-02
    20  8.956177896E-01  3.662630556E+01  2.93E-02  1.58E-03  2.55E+00  6.45E+01  2.8E-02
    30  4.676353374E-01  3.654706202E+01  2.92E-02  4.86E-05  3.15E+00  2.51E+02  1.6E-02
    40  1.003079085E-01  3.654666958E+01  2.92E-02  3.77E-06  3.66E+00  5.51E+02  1.2E-02
    50  9.999999951E-02  3.654666951E+01  2.92E-02  1.52E-11  4.14E+00  6.26E+02  1.1E-02
    59  1.000000000E-01  3.654666951E+01  2.92E-02  7.71E-16  4.50E+00  6.86E+02  1.1E-02
    60  1.000000000E-01  3.654666951E+01  2.92E-02  1.60E-15  4.50E+00  6.90E+02  1.1E-02
    61  1.000000000E-01  3.654666951E+01  2.92E-02  3.54E-16  4.55E+00  6.99E+02  1.1E-02
    62  1.000000000E-01  3.654666951E+01  2.92E-02  1.08E-16  4.57E+00  7.01E+02  1.1E-02

 Exit  LSQR.       istop  = 3               itn    =      62
 Exit  LSQR.       Anorm  = 4.56805E+00     Acond  = 7.01224E+02
 Exit  LSQR.       bnorm  = 1.25103E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.65467E+01     Arnorm = 1.80399E-14
 Exit  LSQR.       max dx = 1.3E+03 occurred at itn        1
 Exit  LSQR.              = 7.2E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-02
    norm(x)         = 1.827E+03
    norm(r)         = 3.16516280E+01 = rho1
    norm(A'r)       = 1.827E-01      = sigma1

    norm(s)         = 3.165E+03
    norm(x,s)       = 3.655E+03
    norm(rbar)      = 3.65466695E+01 = rho2
    norm(Abar'rbar) = 5.685E-13      = sigma2

    inform          = 3
    tol             = 1.490E-08
    test1           = 3.298E-03 (Ax = b)
    test2           = 1.264E-03 (least-squares)
    test3           = 3.405E-15 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  5.77E-15


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    3    1.00E-03 )
 Condition no. =  9.9796E+02     Residual function =  3.162364242E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.6E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-03   wantse =         F
 atol   =  3.18E-16               conlim =  9.98E+05
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.124761730E+03  1.00E+00  7.28E-04
     1 -2.024778976E+01  4.445508835E+02  3.95E-01  6.73E-01  8.91E-01  1.00E+00  5.8E-01
     2 -4.437036642E+00  2.497578091E+02  2.22E-01  4.11E-01  1.18E+00  2.15E+00  3.1E-01
     3  7.016901406E+00  1.633423201E+02  1.45E-01  2.93E-01  1.38E+00  3.47E+00  2.1E-01
     4  1.026269712E+01  1.165898904E+02  1.04E-01  2.22E-01  1.54E+00  4.95E+00  1.5E-01
     5  8.511232527E+00  8.829972244E+01  7.85E-02  1.73E-01  1.66E+00  6.61E+00  1.2E-01
     6  4.563956177E+00  6.998116189E+01  6.22E-02  1.35E-01  1.76E+00  8.45E+00  9.3E-02
     7  6.876673714E-02  5.763216488E+01  5.12E-02  1.05E-01  1.83E+00  1.05E+01  7.7E-02
     8 -4.113020748E+00  4.913193846E+01  4.37E-02  8.04E-02  1.89E+00  1.28E+01  6.5E-02
     9 -7.562594838E+00  4.324449567E+01  3.84E-02  5.99E-02  1.93E+00  1.54E+01  5.6E-02
    10 -1.009778237E+01  3.918723449E+01  3.48E-02  4.31E-02  1.96E+00  1.83E+01  4.9E-02
    20 -5.028362208E+00  3.179504338E+01  2.83E-02  1.16E-03  2.50E+00  9.38E+01  2.2E-02
    30  6.225162344E-01  3.168093575E+01  2.82E-02  1.29E-03  2.98E+00  3.23E+02  1.3E-02
    40  1.363094331E+00  3.167653023E+01  2.82E-02  1.93E-06  3.50E+00  1.01E+03  7.7E-03
    50  7.373757826E-01  3.167639280E+01  2.82E-02  1.69E-06  3.84E+00  2.26E+03  5.4E-03
    60  1.405348541E-01  3.167638076E+01  2.82E-02  8.50E-08  4.23E+00  4.54E+03  4.0E-03
    70  9.999935981E-02  3.167638071E+01  2.82E-02  1.13E-09  4.55E+00  6.62E+03  3.4E-03
    80  9.999999378E-02  3.167638071E+01  2.82E-02  3.45E-12  4.89E+00  7.13E+03  3.4E-03
    90  9.999999986E-02  3.167638071E+01  2.82E-02  2.45E-13  5.17E+00  7.56E+03  3.4E-03
    93  9.999999998E-02  3.167638071E+01  2.82E-02  4.61E-17  5.27E+00  7.72E+03  3.4E-03

 Exit  LSQR.       istop  = 3               itn    =      93
 Exit  LSQR.       Anorm  = 5.26803E+00     Acond  = 7.71629E+03
 Exit  LSQR.       bnorm  = 1.12476E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16764E+01     Arnorm = 7.68724E-15
 Exit  LSQR.       max dx = 1.2E+03 occurred at itn        1
 Exit  LSQR.              = 6.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-03
    norm(x)         = 1.827E+03
    norm(r)         = 3.16236424E+01 = rho1
    norm(A'r)       = 1.827E-03      = sigma1

    norm(s)         = 3.162E+04
    norm(x,s)       = 3.168E+04
    norm(rbar)      = 3.16763807E+01 = rho2
    norm(Abar'rbar) = 8.718E-13      = sigma2

    inform          = 3
    tol             = 1.490E-08
    test1           = 2.942E-03 (Ax = b)
    test2           = 1.097E-05 (least-squares)
    test3           = 5.225E-15 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.72E-13


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    4    1.00E-04 )
 Condition no. =  9.9967E+03     Residual function =  3.162282452E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   1.3E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-04   wantse =         F
 atol   =  3.18E-16               conlim =  1.00E+07
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.036803666E+03  1.00E+00  7.88E-04
     1 -2.290522276E+01  4.288179779E+02  4.14E-01  6.51E-01  8.98E-01  1.00E+00  6.1E-01
     2 -1.229519069E+01  2.473115919E+02  2.39E-01  3.92E-01  1.18E+00  2.16E+00  3.2E-01
     3  2.912839266E-01  1.637963649E+02  1.58E-01  2.74E-01  1.37E+00  3.52E+00  2.1E-01
     4  8.372079894E+00  1.171217907E+02  1.13E-01  2.03E-01  1.51E+00  5.07E+00  1.5E-01
     5  1.186967936E+01  8.809260300E+01  8.50E-02  1.54E-01  1.61E+00  6.84E+00  1.2E-01
     6  1.189446970E+01  6.891456184E+01  6.65E-02  1.16E-01  1.68E+00  8.87E+00  9.0E-02
     7  9.555838382E+00  5.587301182E+01  5.39E-02  8.60E-02  1.73E+00  1.12E+01  7.3E-02
     8  5.773286086E+00  4.696784938E+01  4.53E-02  6.16E-02  1.76E+00  1.40E+01  6.0E-02
     9  1.300142613E+00  4.098617139E+01  3.95E-02  4.20E-02  1.79E+00  1.75E+01  5.0E-02
    10 -3.232562301E+00  3.709631214E+01  3.58E-02  2.71E-02  1.80E+00  2.18E+01  4.2E-02
    20 -1.047338372E+01  3.168716491E+01  3.06E-02  3.77E-04  2.43E+00  1.47E+02  1.7E-02
    30 -2.131856168E+00  3.162499006E+01  3.05E-02  3.92E-05  2.92E+00  6.22E+02  9.0E-03
    40  8.750540925E-01  3.162347281E+01  3.05E-02  5.62E-05  3.36E+00  2.15E+03  5.2E-03
    50  1.482699147E+00  3.162335684E+01  3.05E-02  2.11E-05  3.76E+00  6.18E+03  3.2E-03
    60  1.462228123E+00  3.162335497E+01  3.05E-02  7.67E-07  4.07E+00  8.00E+03  3.0E-03
    70  8.833865648E-01  3.162335253E+01  3.05E-02  6.61E-09  4.39E+00  2.06E+04  1.9E-03
    80  1.462338138E-01  3.162335236E+01  3.05E-02  1.21E-06  4.70E+00  4.86E+04  1.3E-03
    90  1.319365245E-01  3.162335236E+01  3.05E-02  6.04E-09  4.98E+00  5.20E+04  1.3E-03
   100  1.002811364E-01  3.162335236E+01  3.05E-02  2.25E-08  5.27E+00  7.56E+04  1.1E-03
   110  9.999998219E-02  3.162335236E+01  3.05E-02  1.20E-10  5.54E+00  7.98E+04  1.1E-03
   120  9.999997810E-02  3.162335236E+01  3.05E-02  1.64E-13  5.78E+00  8.33E+04  1.1E-03
   130  9.999999965E-02  3.162335236E+01  3.05E-02  4.45E-15  6.04E+00  8.71E+04  1.1E-03
   132  9.999999972E-02  3.162335236E+01  3.05E-02  1.62E-15  6.12E+00  8.83E+04  1.1E-03
   133  9.999999972E-02  3.162335236E+01  3.05E-02  2.02E-16  6.13E+00  8.83E+04  1.1E-03

 Exit  LSQR.       istop  = 3               itn    =     133
 Exit  LSQR.       Anorm  = 6.12613E+00     Acond  = 8.83042E+04
 Exit  LSQR.       bnorm  = 1.03680E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16234E+01     Arnorm = 3.90657E-14
 Exit  LSQR.       max dx = 1.1E+03 occurred at itn        1
 Exit  LSQR.              = 5.8E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-04
    norm(x)         = 1.827E+03
    norm(r)         = 3.16228245E+01 = rho1
    norm(A'r)       = 1.827E-05      = sigma1

    norm(s)         = 3.162E+05
    norm(x,s)       = 3.162E+05
    norm(rbar)      = 3.16233524E+01 = rho2
    norm(Abar'rbar) = 6.106E-13      = sigma2

    inform          = 3
    tol             = 1.490E-08
    test1           = 2.586E-03 (Ax = b)
    test2           = 9.431E-08 (least-squares)
    test3           = 3.152E-15 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  5.26E-12


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    5    1.00E-05 )
 Condition no. =  9.9995E+04     Residual function =  3.162277952E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.1E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-05   wantse =         F
 atol   =  3.18E-16               conlim =  1.00E+08
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.715494280E+02  1.00E+00  8.45E-04
     1 -2.412106255E+01  4.116661449E+02  4.24E-01  6.34E-01  9.06E-01  1.00E+00  6.2E-01
     2 -1.824596475E+01  2.396665268E+02  2.47E-01  3.74E-01  1.18E+00  2.18E+00  3.3E-01
     3 -7.118200999E+00  1.585407923E+02  1.63E-01  2.56E-01  1.36E+00  3.57E+00  2.1E-01
     4  2.622411380E+00  1.122939283E+02  1.16E-01  1.84E-01  1.47E+00  5.19E+00  1.5E-01
     5  9.349109039E+00  8.319678233E+01  8.56E-02  1.34E-01  1.55E+00  7.12E+00  1.1E-01
     6  1.286861547E+01  6.400705208E+01  6.59E-02  9.65E-02  1.60E+00  9.44E+00  8.4E-02
     7  1.344322969E+01  5.123460276E+01  5.27E-02  6.67E-02  1.63E+00  1.23E+01  6.5E-02
     8  1.153766988E+01  4.292241224E+01  4.42E-02  4.35E-02  1.65E+00  1.60E+01  5.2E-02
     9  7.760937243E+00  3.776482006E+01  3.89E-02  2.63E-02  1.66E+00  2.08E+01  4.3E-02
    10  2.839815541E+00  3.476092705E+01  3.58E-02  1.47E-02  1.67E+00  2.74E+01  3.5E-02
    20 -1.336581893E+01  3.166056236E+01  3.26E-02  7.45E-04  2.28E+00  2.01E+02  1.4E-02
    30 -6.132881595E+00  3.162353433E+01  3.25E-02  1.01E-04  2.88E+00  1.07E+03  6.8E-03
    40 -2.843186170E+00  3.162290761E+01  3.25E-02  6.41E-07  3.37E+00  2.35E+03  5.0E-03
    50 -2.829155842E-01  3.162279982E+01  3.25E-02  7.47E-07  3.69E+00  5.34E+03  3.5E-03
    60  1.199589697E+00  3.162278591E+01  3.25E-02  2.80E-07  4.02E+00  1.39E+04  2.2E-03
    70  1.546444780E+00  3.162278484E+01  3.25E-02  6.34E-08  4.34E+00  4.39E+04  1.3E-03
    80  1.546393831E+00  3.162278484E+01  3.25E-02  8.66E-09  4.61E+00  4.67E+04  1.3E-03
    90  9.678250921E-01  3.162278480E+01  3.25E-02  7.64E-10  4.89E+00  1.90E+05  6.7E-04
   100  9.677892749E-01  3.162278480E+01  3.25E-02  5.79E-10  5.15E+00  2.00E+05  6.7E-04
   110  9.540917752E-01  3.162278480E+01  3.25E-02  2.34E-08  5.49E+00  2.23E+05  6.5E-04
   120  1.229254088E-01  3.162278480E+01  3.25E-02  9.36E-09  5.71E+00  5.88E+05  4.1E-04
   130  1.228633290E-01  3.162278480E+01  3.25E-02  2.18E-11  5.93E+00  6.11E+05  4.1E-04
   140  1.228584680E-01  3.162278480E+01  3.25E-02  8.59E-11  6.15E+00  6.33E+05  4.1E-04
   150  1.000087339E-01  3.162278480E+01  3.25E-02  1.06E-10  6.37E+00  9.12E+05  3.5E-04
   160  1.000010912E-01  3.162278480E+01  3.25E-02  9.94E-12  6.57E+00  9.41E+05  3.5E-04
   170  9.999993804E-02  3.162278480E+01  3.25E-02  4.39E-13  6.76E+00  9.69E+05  3.5E-04
   173  9.999993804E-02  3.162278480E+01  3.25E-02  2.38E-16  6.85E+00  9.82E+05  3.5E-04

 Exit  LSQR.       istop  = 3               itn    =     173
 Exit  LSQR.       Anorm  = 6.84982E+00     Acond  = 9.81551E+05
 Exit  LSQR.       bnorm  = 9.71549E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     Arnorm = 5.15827E-14
 Exit  LSQR.       max dx = 9.7E+02 occurred at itn        1
 Exit  LSQR.              = 5.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-05
    norm(x)         = 1.827E+03
    norm(r)         = 3.16227795E+01 = rho1
    norm(A'r)       = 1.827E-07      = sigma1

    norm(s)         = 3.162E+06
    norm(x,s)       = 3.162E+06
    norm(rbar)      = 3.16227848E+01 = rho2
    norm(Abar'rbar) = 7.212E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.345E-03 (Ax = b)
    test2           = 8.435E-10 (least-squares)
    test3           = 3.329E-15 (damped least-squares)


 Solution  x:
     1  0.999999E-01     2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.26E-09


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    6    1.00E-06 )
 Condition no. =  9.9999E+05     Residual function =  3.162277678E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   7.5E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-06   wantse =         F
 atol   =  3.18E-16               conlim =  1.00E+09
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.210791621E+02  1.00E+00  8.97E-04
     1 -2.443055276E+01  3.951289622E+02  4.29E-01  6.18E-01  9.14E-01  1.00E+00  6.3E-01
     2 -2.224414133E+01  2.299330661E+02  2.50E-01  3.58E-01  1.18E+00  2.19E+00  3.3E-01
     3 -1.321097804E+01  1.506103813E+02  1.64E-01  2.38E-01  1.34E+00  3.62E+00  2.1E-01
     4 -3.367416061E+00  1.049231608E+02  1.14E-01  1.66E-01  1.44E+00  5.35E+00  1.4E-01
     5  5.036316961E+00  7.625044979E+01  8.28E-02  1.15E-01  1.50E+00  7.50E+00  1.0E-01
     6  1.099397591E+01  5.775402451E+01  6.27E-02  7.77E-02  1.53E+00  1.02E+01  7.6E-02
     7  1.404999112E+01  4.603739656E+01  5.00E-02  4.91E-02  1.55E+00  1.39E+01  5.8E-02
     8  1.413848446E+01  3.901907204E+01  4.24E-02  2.85E-02  1.56E+00  1.88E+01  4.5E-02
     9  1.156137776E+01  3.514014564E+01  3.82E-02  1.50E-02  1.57E+00  2.59E+01  3.6E-02
    10  6.963810705E+00  3.317616264E+01  3.60E-02  7.17E-03  1.57E+00  3.61E+01  2.9E-02
    20 -1.262942115E+01  3.164961571E+01  3.44E-02  1.91E-03  2.20E+00  2.50E+02  1.3E-02
    30 -1.024518441E+01  3.162317765E+01  3.43E-02  4.92E-06  2.85E+00  1.60E+03  5.6E-03
    40 -6.777780822E+00  3.162284358E+01  3.43E-02  2.11E-06  3.21E+00  3.53E+03  4.0E-03
    50 -3.250362707E+00  3.162278508E+01  3.43E-02  3.66E-07  3.57E+00  8.53E+03  2.7E-03
    60 -4.552765447E-01  3.162277752E+01  3.43E-02  1.52E-07  3.98E+00  2.29E+04  1.7E-03
    70  1.137756881E+00  3.162277688E+01  3.43E-02  3.71E-06  4.29E+00  7.08E+04  1.0E-03
    80  1.171195877E+00  3.162277687E+01  3.43E-02  2.00E-09  4.60E+00  7.67E+04  1.0E-03
    90  1.567813277E+00  3.162277684E+01  3.43E-02  1.16E-09  4.88E+00  3.01E+05  5.3E-04
   100  1.568889007E+00  3.162277684E+01  3.43E-02  1.17E-10  5.18E+00  3.20E+05  5.3E-04
   110  1.568273996E+00  3.162277684E+01  3.43E-02  1.76E-09  5.41E+00  3.38E+05  5.3E-04
   120  1.096480257E+00  3.162277684E+01  3.43E-02  8.60E-09  5.63E+00  1.70E+06  2.4E-04
   130  1.021497918E+00  3.162277684E+01  3.43E-02  3.87E-10  5.81E+00  1.88E+06  2.3E-04
   140  1.021342806E+00  3.162277684E+01  3.43E-02  1.63E-12  6.09E+00  1.97E+06  2.3E-04
   150  4.670017401E-01  3.162277684E+01  3.43E-02  2.41E-10  6.31E+00  5.21E+06  1.4E-04
   160  3.521633464E-01  3.162277684E+01  3.43E-02  1.25E-09  6.45E+00  5.78E+06  1.4E-04
   170  1.155926470E-01  3.162277684E+01  3.43E-02  1.71E-10  6.70E+00  6.85E+06  1.3E-04
   180  1.155906913E-01  3.162277684E+01  3.43E-02  1.75E-12  6.88E+00  7.04E+06  1.3E-04
   190  1.155905699E-01  3.162277684E+01  3.43E-02  2.59E-14  7.08E+00  7.24E+06  1.3E-04
   200  1.155782202E-01  3.162277684E+01  3.43E-02  1.89E-14  7.26E+00  7.43E+06  1.3E-04
   210  1.155782144E-01  3.162277684E+01  3.43E-02  5.03E-14  7.41E+00  7.58E+06  1.3E-04
   220  1.030994471E-01  3.162277684E+01  3.43E-02  2.91E-12  7.63E+00  1.04E+07  1.1E-04
   230  1.000000240E-01  3.162277684E+01  3.43E-02  3.71E-12  7.79E+00  1.11E+07  1.1E-04
   239  9.999794679E-02  3.162277684E+01  3.43E-02  2.51E-15  7.94E+00  1.13E+07  1.1E-04
   240  9.999794679E-02  3.162277684E+01  3.43E-02  5.11E-16  7.94E+00  1.13E+07  1.1E-04
   241  9.999794679E-02  3.162277684E+01  3.43E-02  1.51E-17  7.94E+00  1.13E+07  1.1E-04

 Exit  LSQR.       istop  = 3               itn    =     241
 Exit  LSQR.       Anorm  = 7.94322E+00     Acond  = 1.13469E+07
 Exit  LSQR.       bnorm  = 9.21079E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     Arnorm = 3.80535E-15
 Exit  LSQR.       max dx = 9.1E+02 occurred at itn        1
 Exit  LSQR.              = 5.0E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-06
    norm(x)         = 1.827E+03
    norm(r)         = 3.16227768E+01 = rho1
    norm(A'r)       = 1.827E-09      = sigma1

    norm(s)         = 3.162E+07
    norm(x,s)       = 3.162E+07
    norm(rbar)      = 3.16227768E+01 = rho2
    norm(Abar'rbar) = 7.747E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.049E-03 (Ax = b)
    test2           = 7.273E-12 (least-squares)
    test3           = 3.084E-15 (damped least-squares)


 Solution  x:
     1  0.999979E-01     2  0.199995         3  0.299994         4  0.399991    
     5  0.499991         6  0.600000         7  0.700001         8  0.799985    


 LSQR  appears to be successful.
 Relative error in  x  =  7.32E-08


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    7    1.00E-07 )
 Condition no. =  1.0000E+07     Residual function =  3.162277661E+01
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   8.3E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 columns
 damp   =  1.00000000000000E-07   wantse =         F
 atol   =  3.18E-16               conlim =  1.00E+10
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  8.808458173E+02  1.00E+00  9.45E-04
     1 -2.422195397E+01  3.796781520E+02  4.31E-01  6.03E-01  9.23E-01  1.00E+00  6.4E-01
     2 -2.477913716E+01  2.193708762E+02  2.49E-01  3.41E-01  1.18E+00  2.20E+00  3.3E-01
     3 -1.776850890E+01  1.414330764E+02  1.61E-01  2.21E-01  1.32E+00  3.69E+00  2.0E-01
     4 -8.448828545E+00  9.648095039E+01  1.10E-01  1.48E-01  1.40E+00  5.56E+00  1.4E-01
     5  7.462713431E-01  6.872328235E+01  7.80E-02  9.74E-02  1.44E+00  7.99E+00  9.4E-02
     6  8.324225295E+00  5.155052190E+01  5.85E-02  6.06E-02  1.47E+00  1.13E+01  6.7E-02
     7  1.328456786E+01  4.146406785E+01  4.71E-02  3.44E-02  1.48E+00  1.60E+01  5.0E-02
     8  1.508697446E+01  3.605910766E+01  4.09E-02  1.73E-02  1.48E+00  2.29E+01  3.9E-02
     9  1.370776303E+01  3.345655263E+01  3.80E-02  7.84E-03  1.49E+00  3.32E+01  3.0E-02
    10  9.669404920E+00  3.232530691E+01  3.67E-02  9.36E-03  1.49E+00  4.93E+01  2.4E-02
    20 -1.212587523E+01  3.162906029E+01  3.59E-02  3.93E-05  2.31E+00  5.05E+02  9.1E-03
    30 -1.326379497E+01  3.162306620E+01  3.59E-02  1.10E-05  2.74E+00  2.01E+03  4.9E-03
    40 -9.569977066E+00  3.162280973E+01  3.59E-02  2.34E-05  3.19E+00  7.22E+03  2.8E-03
    50 -6.205881384E+00  3.162278105E+01  3.59E-02  1.34E-05  3.57E+00  1.81E+04  1.9E-03
    60 -3.516189567E+00  3.162277714E+01  3.59E-02  3.14E-08  3.92E+00  3.20E+04  1.5E-03
    70 -5.571805067E-01  3.162277664E+01  3.59E-02  7.95E-10  4.19E+00  9.78E+04  8.6E-04
    80 -5.562457015E-01  3.162277664E+01  3.59E-02  1.90E-08  4.54E+00  1.06E+05  8.6E-04
    90  1.154552315E+00  3.162277661E+01  3.59E-02  6.98E-10  4.78E+00  3.90E+05  4.6E-04
   100  1.155178149E+00  3.162277661E+01  3.59E-02  1.01E-08  5.00E+00  4.09E+05  4.6E-04
   110  1.155909078E+00  3.162277661E+01  3.59E-02  4.67E-09  5.27E+00  4.37E+05  4.6E-04
   120  1.579373051E+00  3.162277661E+01  3.59E-02  4.12E-11  5.55E+00  2.11E+06  2.1E-04
   130  1.579280548E+00  3.162277661E+01  3.59E-02  1.57E-10  5.74E+00  2.19E+06  2.1E-04
   140  1.579264864E+00  3.162277661E+01  3.59E-02  4.91E-10  5.93E+00  2.26E+06  2.1E-04
   150  1.576149841E+00  3.162277661E+01  3.59E-02  6.85E-12  6.18E+00  2.66E+06  2.0E-04
   160  1.575634079E+00  3.162277661E+01  3.59E-02  1.70E-10  6.36E+00  2.78E+06  2.0E-04
   170  1.056933998E+00  3.162277661E+01  3.59E-02  3.68E-13  6.57E+00  1.79E+07  8.0E-05
   180  1.056933787E+00  3.162277661E+01  3.59E-02  7.46E-13  6.80E+00  1.85E+07  8.0E-05
   190  1.056933152E+00  3.162277661E+01  3.59E-02  1.47E-11  6.95E+00  1.89E+07  8.0E-05
   197  1.056891898E+00  3.162277661E+01  3.59E-02  2.01E-15  7.10E+00  1.93E+07  8.0E-05
   200  1.056891894E+00  3.162277661E+01  3.59E-02  1.43E-14  7.11E+00  1.93E+07  8.0E-05
   210  1.055783542E+00  3.162277661E+01  3.59E-02  6.14E-13  7.32E+00  2.01E+07  8.0E-05
   220  1.038458046E+00  3.162277661E+01  3.59E-02  7.65E-11  7.47E+00  2.27E+07  7.5E-05
   230  1.096247569E-01  3.162277661E+01  3.59E-02  1.81E-14  7.65E+00  7.78E+07  4.1E-05
   240  1.096247523E-01  3.162277661E+01  3.59E-02  4.11E-14  7.79E+00  7.93E+07  4.1E-05
   250  1.092330280E-01  3.162277661E+01  3.59E-02  3.20E-14  7.99E+00  8.13E+07  4.1E-05
   260  1.092242657E-01  3.162277661E+01  3.59E-02  4.21E-14  8.12E+00  8.27E+07  4.1E-05
   265  1.091385334E-01  3.162277661E+01  3.59E-02  2.52E-16  8.24E+00  8.39E+07  4.1E-05

 Exit  LSQR.       istop  = 3               itn    =     265
 Exit  LSQR.       Anorm  = 8.24247E+00     Acond  = 8.38980E+07
 Exit  LSQR.       bnorm  = 8.80846E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     Arnorm = 6.56943E-14
 Exit  LSQR.       max dx = 8.6E+02 occurred at itn        1
 Exit  LSQR.              = 4.7E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-07
    norm(x)         = 1.827E+03
    norm(r)         = 3.16227766E+01 = rho1
    norm(A'r)       = 1.834E-11      = sigma1

    norm(s)         = 3.162E+08
    norm(x,s)       = 3.162E+08
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 5.557E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 1.984E-03 (Ax = b)
    test2           = 7.038E-14 (least-squares)
    test3           = 2.132E-15 (damped least-squares)


 Solution  x:
     1  0.109139         2  0.205252         3  0.303031         4  0.398222    
     5  0.496653         6  0.590571         7  0.687856         8  0.784782    


 LSQR  appears to be successful.
 Relative error in  x  =  2.81E-04


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    2    1.00E-08 )
 Condition no. =  6.2500E+02     Residual function =  1.351130091E-12
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   1.3E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-08   wantse =         F
 atol   =  3.18E-16               conlim =  6.25E+05
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.250358806E+03  1.00E+00  6.63E-04
     1 -1.569523708E+01  4.497539700E+02  3.60E-01  7.06E-01  8.88E-01  1.00E+00  5.5E-01
     2  2.895287270E+00  2.360568875E+02  1.89E-01  4.42E-01  1.18E+00  2.12E+00  2.9E-01
     3  6.914168784E+00  1.462934678E+02  1.17E-01  3.24E-01  1.39E+00  3.40E+00  1.9E-01
     4  1.929180742E+00  9.956862892E+01  7.96E-02  2.55E-01  1.56E+00  4.82E+00  1.4E-01
     5 -4.030073311E+00  7.189983046E+01  5.75E-02  2.09E-01  1.70E+00  6.39E+00  1.1E-01
     6 -8.170857369E+00  5.403308925E+01  4.32E-02  1.76E-01  1.83E+00  8.09E+00  8.3E-02
     7 -1.028185061E+01  4.175446117E+01  3.34E-02  1.50E-01  1.93E+00  9.92E+00  6.8E-02
     8 -1.086059048E+01  3.291017600E+01  2.63E-02  1.30E-01  2.02E+00  1.19E+01  5.6E-02
     9 -1.044238556E+01  2.630121592E+01  2.10E-02  1.14E-01  2.09E+00  1.40E+01  4.7E-02
    10 -9.437438588E+00  2.121469253E+01  1.70E-02  9.96E-02  2.15E+00  1.63E+01  3.9E-02
    20  8.996819441E-01  2.390187891E+00  1.91E-03  2.15E-02  2.55E+00  6.46E+01  7.2E-03
    30  9.270667113E-01  1.748092040E-01  1.40E-04  1.86E-02  3.15E+00  2.80E+02  1.0E-03
    40  4.459333261E-01  2.036524001E-02  1.63E-05  2.88E-03  3.66E+00  6.62E+02  2.5E-04
    50  9.999947191E-02  1.989769250E-05  1.59E-08  2.11E-02  4.11E+00  2.67E+03  4.1E-06
    60  9.999999997E-02  1.827111108E-05  1.46E-08  7.34E-07  4.50E+00  2.93E+03  3.9E-06
    70  1.000000000E-01  1.827111108E-05  1.46E-08  9.13E-10  4.83E+00  3.15E+03  3.9E-06
    80  1.000000000E-01  1.827111108E-05  1.46E-08  3.88E-13  5.15E+00  3.38E+03  3.9E-06
    90  1.000000000E-01  1.827111108E-05  1.46E-08  8.00E-15  5.45E+00  3.68E+03  3.8E-06
   100  1.000000000E-01  1.827111108E-05  1.46E-08  1.29E-14  5.76E+00  5.30E+03  3.3E-06
   102  1.000000000E-01  1.827111108E-05  1.46E-08  9.99E-17  5.84E+00  5.37E+03  3.3E-06

 Exit  LSQR.       istop  = 3               itn    =     102
 Exit  LSQR.       Anorm  = 5.83666E+00     Acond  = 5.36980E+03
 Exit  LSQR.       bnorm  = 1.25036E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-05     Arnorm = 1.06485E-20
 Exit  LSQR.       max dx = 1.3E+03 occurred at itn        1
 Exit  LSQR.              = 7.2E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-08
    norm(x)         = 1.827E+03
    norm(r)         = 1.52211584E-12 = rho1
    norm(A'r)       = 6.651E-13      = sigma1

    norm(s)         = 1.522E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-05 = rho2
    norm(Abar'rbar) = 5.511E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 1.278E-16 (Ax = b)
    test2           = 7.487E-02 (least-squares)
    test3           = 5.167E-09 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.78E-14


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    3    1.00E-09 )
 Condition no. =  1.5625E+04     Residual function =  2.340076968E-13
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   6.5E-17


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-09   wantse =         F
 atol   =  3.18E-16               conlim =  1.56E+07
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.124314110E+03  1.00E+00  7.28E-04
     1 -2.024780599E+01  4.434197695E+02  3.94E-01  6.75E-01  8.91E-01  1.00E+00  5.8E-01
     2 -4.437078376E+00  2.477398064E+02  2.20E-01  4.15E-01  1.18E+00  2.15E+00  3.1E-01
     3  7.016884706E+00  1.602402503E+02  1.43E-01  2.99E-01  1.38E+00  3.47E+00  2.0E-01
     4  1.026274765E+01  1.122030359E+02  9.98E-02  2.31E-01  1.54E+00  4.95E+00  1.5E-01
     5  8.511358718E+00  8.242098997E+01  7.33E-02  1.85E-01  1.66E+00  6.61E+00  1.1E-01
     6  4.564132190E+00  6.240018990E+01  5.55E-02  1.52E-01  1.76E+00  8.45E+00  8.8E-02
     7  6.893647511E-02  4.814476875E+01  4.28E-02  1.26E-01  1.83E+00  1.05E+01  7.0E-02
     8 -4.112941580E+00  3.755562129E+01  3.34E-02  1.05E-01  1.89E+00  1.28E+01  5.7E-02
     9 -7.562719628E+00  2.943780141E+01  2.62E-02  8.79E-02  1.93E+00  1.54E+01  4.6E-02
    10 -1.009825707E+01  2.306846861E+01  2.05E-02  7.32E-02  1.96E+00  1.83E+01  3.8E-02
    20 -5.035831628E+00  2.739433197E+00  2.44E-03  1.63E-02  2.48E+00  9.29E+01  6.4E-03
    30  1.124013950E+00  3.601797047E-01  3.20E-04  1.75E-01  2.98E+00  4.41E+02  1.2E-03
    40  1.472402234E+00  8.564454273E-02  7.62E-05  5.45E-04  3.51E+00  1.03E+03  4.0E-04
    50  1.063043900E+00  1.741376789E-02  1.55E-05  2.00E-04  3.90E+00  2.53E+03  1.2E-04
    60  4.710591702E-01  8.739956333E-04  7.77E-07  1.05E-02  4.18E+00  8.60E+03  1.5E-05
    70  4.295795277E-01  8.220208040E-04  7.31E-07  1.35E-02  4.55E+00  2.55E+04  9.0E-06
    80  1.000186679E-01  7.568286506E-06  6.73E-09  6.35E-02  4.89E+00  7.70E+04  5.1E-07
    90  1.000000003E-01  1.827149957E-06  1.63E-09  2.34E-04  5.16E+00  8.14E+04  2.5E-07
   100  1.000000012E-01  1.827111576E-06  1.63E-09  5.21E-05  5.43E+00  8.57E+04  2.5E-07
   110  9.999999998E-02  1.827111108E-06  1.63E-09  1.06E-09  5.74E+00  9.05E+04  2.5E-07
   120  1.000000000E-01  1.827111108E-06  1.63E-09  3.96E-11  6.01E+00  9.48E+04  2.5E-07
   130  9.999999999E-02  1.827111108E-06  1.63E-09  6.33E-10  6.22E+00  9.88E+04  2.5E-07
   140  9.999999999E-02  1.827111108E-06  1.63E-09  7.82E-14  6.44E+00  1.02E+05  2.5E-07
   146  9.999999999E-02  1.827111108E-06  1.63E-09  1.14E-15  6.60E+00  1.05E+05  2.5E-07
   147  9.999999999E-02  1.827111108E-06  1.63E-09  9.66E-16  6.61E+00  1.05E+05  2.5E-07
   148  9.999999999E-02  1.827111108E-06  1.63E-09  2.32E-15  6.61E+00  1.05E+05  2.5E-07
   150  9.999999999E-02  1.827111108E-06  1.63E-09  1.65E-13  6.64E+00  1.06E+05  2.5E-07
   160  1.000000000E-01  1.827111108E-06  1.63E-09  6.98E-15  6.89E+00  1.53E+05  2.1E-07
   161  1.000000000E-01  1.827111108E-06  1.63E-09  1.84E-15  6.90E+00  1.54E+05  2.1E-07
   162  1.000000000E-01  1.827111108E-06  1.63E-09  1.53E-15  6.94E+00  1.55E+05  2.1E-07
   168  1.000000000E-01  1.827111108E-06  1.63E-09  5.30E-16  7.10E+00  1.58E+05  2.1E-07
   169  1.000000000E-01  1.827111108E-06  1.63E-09  6.26E-16  7.11E+00  1.58E+05  2.1E-07
   170  1.000000000E-01  1.827111108E-06  1.63E-09  3.29E-16  7.14E+00  1.59E+05  2.1E-07
   171  1.000000000E-01  1.827111108E-06  1.63E-09  9.55E-16  7.14E+00  1.59E+05  2.1E-07
   172  1.000000000E-01  1.827111108E-06  1.63E-09  1.54E-16  7.14E+00  1.59E+05  2.1E-07

 Exit  LSQR.       istop  = 3               itn    =     172
 Exit  LSQR.       Anorm  = 7.14393E+00     Acond  = 1.59237E+05
 Exit  LSQR.       bnorm  = 1.12431E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-06     Arnorm = 2.00628E-21
 Exit  LSQR.       max dx = 1.2E+03 occurred at itn        1
 Exit  LSQR.              = 6.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-09
    norm(x)         = 1.827E+03
    norm(r)         = 6.75040148E-13 = rho1
    norm(A'r)       = 5.141E-13      = sigma1

    norm(s)         = 6.750E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-06 = rho2
    norm(Abar'rbar) = 5.145E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.761E-17 (Ax = b)
    test2           = 1.066E-01 (least-squares)
    test3           = 3.941E-08 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.47E-13


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    4    1.00E-10 )
 Condition no. =  3.9062E+05     Residual function =  5.505354820E-14
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   1.3E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-10   wantse =         F
 atol   =  3.18E-16               conlim =  3.91E+08
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.036321269E+03  1.00E+00  7.89E-04
     1 -2.290522293E+01  4.276503344E+02  4.13E-01  6.53E-01  8.98E-01  1.00E+00  6.0E-01
     2 -1.229519129E+01  2.452814271E+02  2.37E-01  3.95E-01  1.18E+00  2.16E+00  3.2E-01
     3  2.912832494E-01  1.607146736E+02  1.55E-01  2.79E-01  1.37E+00  3.52E+00  2.1E-01
     4  8.372079751E+00  1.127717708E+02  1.09E-01  2.11E-01  1.51E+00  5.07E+00  1.5E-01
     5  1.186968037E+01  8.222083684E+01  7.93E-02  1.65E-01  1.61E+00  6.84E+00  1.1E-01
     6  1.189447236E+01  6.123052191E+01  5.91E-02  1.31E-01  1.68E+00  8.87E+00  8.5E-02
     7  9.555842886E+00  4.606250067E+01  4.44E-02  1.04E-01  1.73E+00  1.12E+01  6.6E-02
     8  5.773292099E+00  3.472664457E+01  3.35E-02  8.33E-02  1.76E+00  1.40E+01  5.1E-02
     9  1.300148876E+00  2.607350378E+01  2.52E-02  6.60E-02  1.79E+00  1.75E+01  4.0E-02
    10 -3.232558669E+00  1.939324792E+01  1.87E-02  5.18E-02  1.80E+00  2.18E+01  3.1E-02
    20 -1.047231653E+01  2.009566353E+00  1.94E-03  7.17E-03  2.40E+00  1.46E+02  4.3E-03
    30 -2.134966879E+00  3.220999881E-01  3.11E-04  6.22E-03  2.93E+00  6.24E+02  9.1E-04
    40  5.387315818E-01  1.083027649E-01  1.05E-04  1.77E-02  3.36E+00  1.87E+03  3.3E-04
    50  1.491068356E+00  2.189241802E-02  2.11E-05  4.13E-02  3.76E+00  5.93E+03  8.7E-05
    60  1.329628283E+00  8.515005934E-03  8.22E-06  6.78E-03  4.12E+00  1.54E+04  3.5E-05
    70  1.107467931E+00  1.492425153E-03  1.44E-06  5.33E-05  4.38E+00  2.24E+04  1.3E-05
    80  8.599660800E-01  1.163792248E-03  1.12E-06  6.21E-02  4.70E+00  7.58E+04  6.3E-06
    90  4.763538974E-01  4.534520291E-05  4.38E-08  4.87E-03  5.02E+00  1.25E+05  1.0E-06
   100  4.760759205E-01  3.534402254E-05  3.41E-08  4.02E-06  5.27E+00  1.32E+05  8.8E-07
   110  4.575445334E-01  3.445936533E-05  3.33E-08  4.77E-03  5.52E+00  4.99E+05  4.6E-07
   120  2.149322613E-01  1.953702888E-05  1.89E-08  2.44E-02  5.78E+00  1.89E+06  1.8E-07
   130  1.005061144E-01  1.312014930E-06  1.27E-09  4.41E-02  6.01E+00  2.35E+06  4.3E-08
   140  1.000000177E-01  1.827420739E-07  1.76E-10  7.38E-05  6.26E+00  2.45E+06  1.6E-08
   150  9.999999967E-02  1.827111280E-07  1.76E-10  4.97E-05  6.43E+00  2.52E+06  1.6E-08
   160  9.999999966E-02  1.827111116E-07  1.76E-10  1.25E-07  6.66E+00  2.61E+06  1.6E-08
   170  9.999999999E-02  1.827111108E-07  1.76E-10  1.19E-08  6.84E+00  2.68E+06  1.6E-08
   180  1.000000000E-01  1.827111108E-07  1.76E-10  8.78E-12  7.04E+00  2.76E+06  1.6E-08
   190  1.000000000E-01  1.827111108E-07  1.76E-10  8.98E-10  7.25E+00  2.84E+06  1.6E-08
   200  1.000000000E-01  1.827111108E-07  1.76E-10  1.94E-09  7.46E+00  2.92E+06  1.6E-08
   210  1.000000000E-01  1.827111108E-07  1.76E-10  1.82E-12  7.64E+00  3.00E+06  1.6E-08
   216  1.000000000E-01  1.827111108E-07  1.76E-10  2.97E-15  7.74E+00  3.04E+06  1.6E-08
   217  1.000000000E-01  1.827111108E-07  1.76E-10  1.11E-15  7.75E+00  3.04E+06  1.6E-08
   218  1.000000000E-01  1.827111108E-07  1.76E-10  2.94E-16  7.79E+00  3.05E+06  1.6E-08

 Exit  LSQR.       istop  = 3               itn    =     218
 Exit  LSQR.       Anorm  = 7.78844E+00     Acond  = 3.05475E+06
 Exit  LSQR.       bnorm  = 1.03632E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-07     Arnorm = 4.19012E-22
 Exit  LSQR.       max dx = 1.1E+03 occurred at itn        1
 Exit  LSQR.              = 5.8E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-10
    norm(x)         = 1.827E+03
    norm(r)         = 7.90044355E-13 = rho1
    norm(A'r)       = 6.403E-13      = sigma1

    norm(s)         = 7.900E-03
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-07 = rho2
    norm(Abar'rbar) = 6.403E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 5.175E-17 (Ax = b)
    test2           = 1.041E-01 (least-squares)
    test3           = 4.500E-07 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.52E-12


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    5    1.00E-11 )
 Condition no. =  9.7656E+06     Residual function =  1.359023811E-14
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.7E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-11   wantse =         F
 atol   =  3.18E-16               conlim =  9.77E+09
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.710346493E+02  1.00E+00  8.45E-04
     1 -2.412106256E+01  4.104497706E+02  4.23E-01  6.36E-01  9.06E-01  1.00E+00  6.2E-01
     2 -1.824596476E+01  2.375711335E+02  2.45E-01  3.77E-01  1.18E+00  2.18E+00  3.3E-01
     3 -7.118201010E+00  1.553550200E+02  1.60E-01  2.61E-01  1.36E+00  3.57E+00  2.1E-01
     4  2.622411370E+00  1.077493654E+02  1.11E-01  1.92E-01  1.47E+00  5.19E+00  1.5E-01
     5  9.349109039E+00  7.695260886E+01  7.92E-02  1.45E-01  1.55E+00  7.12E+00  1.1E-01
     6  1.286861549E+01  5.564981711E+01  5.73E-02  1.11E-01  1.60E+00  9.44E+00  7.8E-02
     7  1.344322975E+01  4.031108974E+01  4.15E-02  8.47E-02  1.63E+00  1.23E+01  5.8E-02
     8  1.153767000E+01  2.902297219E+01  2.99E-02  6.43E-02  1.65E+00  1.60E+01  4.3E-02
     9  7.760937429E+00  2.064415371E+01  2.13E-02  4.82E-02  1.66E+00  2.08E+01  3.2E-02
    10  2.839814774E+00  1.443334690E+01  1.49E-02  3.55E-02  1.67E+00  2.74E+01  2.3E-02
    20 -1.337282972E+01  1.551066928E+00  1.60E-03  4.62E-03  2.30E+00  2.02E+02  3.2E-03
    30 -6.107927383E+00  2.143050643E-01  2.21E-04  1.34E-02  2.83E+00  1.06E+03  5.6E-04
    40 -2.843352165E+00  8.811598200E-02  9.07E-05  7.21E-04  3.31E+00  2.31E+03  2.6E-04
    50  8.763593882E-01  1.628310573E-02  1.68E-05  1.03E-01  3.69E+00  1.15E+04  5.4E-05
    60  1.204414332E+00  8.290757129E-03  8.54E-06  5.15E-04  4.02E+00  1.43E+04  3.6E-05
    70  1.561179786E+00  1.488426091E-03  1.53E-06  2.14E-04  4.34E+00  4.41E+04  9.0E-06
    80  1.557919355E+00  1.482552221E-03  1.53E-06  2.43E-03  4.61E+00  4.95E+04  8.7E-06
    90  1.126165007E+00  1.474203082E-04  1.52E-07  4.84E-04  4.89E+00  2.03E+05  1.4E-06
   100  1.124359697E+00  1.225147551E-04  1.26E-07  3.32E-06  5.19E+00  2.15E+05  1.3E-06
   110  1.124341926E+00  1.225118504E-04  1.26E-07  1.35E-04  5.49E+00  2.28E+05  1.3E-06
   120  4.885035761E-01  1.591113876E-05  1.64E-08  3.42E-02  5.70E+00  1.74E+06  1.7E-07
   130  4.772550558E-01  1.524660556E-06  1.57E-09  1.69E-02  5.91E+00  1.82E+06  5.2E-08
   140  4.772408735E-01  1.418278540E-06  1.46E-09  5.53E-06  6.12E+00  1.89E+06  5.0E-08
   150  4.772413763E-01  1.418235947E-06  1.46E-09  3.73E-07  6.33E+00  1.95E+06  5.0E-08
   160  4.772413742E-01  1.418235611E-06  1.46E-09  2.56E-06  6.54E+00  2.02E+06  5.0E-08
   170  4.754554192E-01  1.414871820E-06  1.46E-09  9.97E-04  6.80E+00  5.03E+06  3.2E-08
   180  4.634786689E-01  1.392100977E-06  1.43E-09  6.79E-04  6.99E+00  1.32E+07  2.0E-08
   190  4.453658616E-01  1.356977886E-06  1.40E-09  1.48E-03  7.17E+00  2.05E+07  1.6E-08
   200  1.000027155E-01  1.865230402E-08  1.92E-11  5.75E-04  7.32E+00  7.15E+07  1.0E-09
   210  9.999998038E-02  1.827228994E-08  1.88E-11  1.17E-05  7.50E+00  7.33E+07  1.0E-09
   220  9.999997662E-02  1.827186009E-08  1.88E-11  5.85E-07  7.67E+00  7.50E+07  1.0E-09
   230  1.000000009E-01  1.827111513E-08  1.88E-11  3.17E-05  7.90E+00  7.72E+07  1.0E-09
   240  1.000000010E-01  1.827111209E-08  1.88E-11  1.79E-07  8.07E+00  7.88E+07  1.0E-09
   250  1.000000012E-01  1.827111134E-08  1.88E-11  3.06E-08  8.22E+00  8.03E+07  1.0E-09
   260  1.000000013E-01  1.827111108E-08  1.88E-11  2.70E-11  8.38E+00  8.19E+07  1.0E-09
   270  1.000000013E-01  1.827111108E-08  1.88E-11  9.09E-11  8.53E+00  8.33E+07  1.0E-09
   280  1.000000014E-01  1.827111108E-08  1.88E-11  1.52E-08  8.66E+00  8.47E+07  1.0E-09
   290  1.000000014E-01  1.827111108E-08  1.88E-11  1.73E-09  8.82E+00  8.62E+07  1.0E-09
   300  1.000000014E-01  1.827111108E-08  1.88E-11  1.27E-10  9.00E+00  8.80E+07  1.0E-09
   310  1.000000014E-01  1.827111108E-08  1.88E-11  9.47E-11  9.15E+00  8.94E+07  1.0E-09
   320  1.000000014E-01  1.827111108E-08  1.88E-11  4.76E-14  9.30E+00  9.09E+07  1.0E-09
   322  1.000000014E-01  1.827111108E-08  1.88E-11  1.30E-15  9.31E+00  9.10E+07  1.0E-09
   324  1.000000014E-01  1.827111108E-08  1.88E-11  5.30E-17  9.35E+00  9.14E+07  1.0E-09

 Exit  LSQR.       istop  = 3               itn    =     324
 Exit  LSQR.       Anorm  = 9.34839E+00     Acond  = 9.13837E+07
 Exit  LSQR.       bnorm  = 9.71035E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-08     Arnorm = 9.05576E-24
 Exit  LSQR.       max dx = 9.7E+02 occurred at itn        1
 Exit  LSQR.              = 5.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-11
    norm(x)         = 1.827E+03
    norm(r)         = 9.31998493E-13 = rho1
    norm(A'r)       = 7.480E-13      = sigma1

    norm(s)         = 9.320E-02
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-08 = rho2
    norm(Abar'rbar) = 7.480E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 5.163E-17 (Ax = b)
    test2           = 8.586E-02 (least-squares)
    test3           = 4.380E-06 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  7.27E-11


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    6    1.00E-12 )
 Condition no. =  2.4414E+08     Residual function =  3.387612114E-15
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.1E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-12   wantse =         F
 atol   =  3.18E-16               conlim =  2.44E+11
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.205361605E+02  1.00E+00  8.98E-04
     1 -2.443055276E+01  3.938615198E+02  4.28E-01  6.20E-01  9.14E-01  1.00E+00  6.3E-01
     2 -2.224414133E+01  2.277481391E+02  2.47E-01  3.61E-01  1.18E+00  2.19E+00  3.3E-01
     3 -1.321097804E+01  1.472531389E+02  1.60E-01  2.44E-01  1.34E+00  3.62E+00  2.1E-01
     4 -3.367416062E+00  1.000443384E+02  1.09E-01  1.74E-01  1.44E+00  5.35E+00  1.4E-01
     5  5.036316961E+00  6.938393962E+01  7.54E-02  1.27E-01  1.50E+00  7.50E+00  9.8E-02
     6  1.099397591E+01  4.832729386E+01  5.25E-02  9.29E-02  1.53E+00  1.02E+01  6.9E-02
     7  1.404999112E+01  3.345806131E+01  3.63E-02  6.76E-02  1.55E+00  1.39E+01  4.9E-02
     8  1.413848446E+01  2.285799571E+01  2.48E-02  4.86E-02  1.56E+00  1.88E+01  3.4E-02
     9  1.156137830E+01  1.532415806E+01  1.66E-02  3.43E-02  1.57E+00  2.59E+01  2.4E-02
    10  6.963704534E+00  1.003283262E+01  1.09E-02  2.37E-02  1.57E+00  3.61E+01  1.6E-02
    20 -1.367783570E+01  7.441206870E-01  8.08E-04  1.45E-01  2.19E+00  3.92E+02  1.5E-03
    30 -1.024542645E+01  1.591939739E-01  1.73E-04  8.04E-04  2.85E+00  1.60E+03  4.0E-04
    40 -6.485088123E+00  6.255582473E-02  6.80E-05  1.64E-02  3.21E+00  4.03E+03  1.7E-04
    50 -3.048693404E+00  2.204365586E-02  2.39E-05  1.62E-03  3.57E+00  9.93E+03  6.6E-05
    60 -4.549421868E-01  6.567702172E-03  7.13E-06  4.38E-05  3.89E+00  2.24E+04  2.5E-05
    70  1.171426557E+00  1.396948576E-03  1.52E-06  4.21E-05  4.23E+00  7.06E+04  6.8E-06
    80  1.171443702E+00  1.396881461E-03  1.52E-06  1.02E-04  4.45E+00  7.43E+04  6.8E-06
    90  1.568854229E+00  2.387824150E-04  2.59E-07  1.28E-02  4.80E+00  2.95E+05  1.5E-06
   100  1.574464644E+00  1.837749096E-04  2.00E-07  2.58E-06  5.06E+00  3.14E+05  1.3E-06
   110  1.571847882E+00  1.832715931E-04  1.99E-07  1.30E-03  5.29E+00  3.53E+05  1.2E-06
   120  1.131334993E+00  1.006954920E-05  1.09E-08  5.29E-03  5.52E+00  1.88E+06  1.3E-07
   130  1.131297078E+00  9.922704281E-06  1.08E-08  8.57E-04  5.73E+00  1.95E+06  1.3E-07
   140  1.131300719E+00  9.905113401E-06  1.08E-08  2.42E-06  6.00E+00  2.04E+06  1.3E-07
   150  1.131244601E+00  9.904643321E-06  1.08E-08  1.17E-05  6.21E+00  2.13E+06  1.3E-07
   160  1.131124500E+00  9.903649108E-06  1.08E-08  1.89E-05  6.38E+00  2.21E+06  1.3E-07
   170  4.777844616E-01  1.893260420E-07  2.06E-10  4.37E-04  6.56E+00  2.51E+07  5.2E-09
   180  4.777830043E-01  1.887415422E-07  2.05E-10  1.85E-04  6.74E+00  2.58E+07  5.2E-09
   190  4.777797851E-01  1.874107616E-07  2.04E-10  2.04E-05  6.96E+00  2.66E+07  5.2E-09
   200  4.775241976E-01  5.679709291E-08  6.17E-11  2.82E-06  7.15E+00  2.74E+07  2.8E-09
   210  4.775241976E-01  5.679708557E-08  6.17E-11  2.40E-06  7.32E+00  2.80E+07  2.8E-09
   220  4.775241972E-01  5.679707759E-08  6.17E-11  1.85E-07  7.48E+00  2.86E+07  2.8E-09
   230  4.775241139E-01  5.679662212E-08  6.17E-11  8.62E-07  7.63E+00  2.92E+07  2.8E-09
   240  4.775241079E-01  5.679661139E-08  6.17E-11  2.02E-06  7.84E+00  3.00E+07  2.8E-09
   250  4.775108727E-01  5.679561860E-08  6.17E-11  1.79E-05  8.00E+00  3.27E+07  2.8E-09
   260  4.775002093E-01  5.679481848E-08  6.17E-11  1.81E-06  8.14E+00  3.50E+07  2.7E-09
   270  4.208790381E-01  5.236700969E-08  5.69E-11  1.64E-03  8.29E+00  7.85E+08  5.5E-10
   280  1.158174720E-01  1.175348453E-08  1.28E-11  1.12E-04  8.46E+00  2.02E+09  1.6E-10
   290  1.158111819E-01  1.175120008E-08  1.28E-11  1.38E-05  8.62E+00  2.06E+09  1.6E-10
   300  1.157561020E-01  1.173121291E-08  1.27E-11  2.85E-03  8.76E+00  2.09E+09  1.6E-10
   310  1.105457946E-01  9.655295655E-09  1.05E-11  9.99E-05  8.92E+00  2.15E+09  1.5E-10
   320  1.000015981E-01  1.830608100E-09  1.99E-12  4.99E-05  9.05E+00  2.21E+09  6.4E-11
   330  1.000002170E-01  1.827394178E-09  1.99E-12  7.85E-06  9.18E+00  2.24E+09  6.4E-11
   340  1.000001058E-01  1.827135001E-09  1.98E-12  6.47E-06  9.34E+00  2.28E+09  6.4E-11
   350  1.000000957E-01  1.827111503E-09  1.98E-12  1.57E-09  9.47E+00  2.31E+09  6.4E-11
   360  1.000000957E-01  1.827111502E-09  1.98E-12  4.84E-08  9.59E+00  2.34E+09  6.4E-11
   370  1.000000957E-01  1.827111494E-09  1.98E-12  9.30E-09  9.72E+00  2.37E+09  6.4E-11
   380  1.000000957E-01  1.827111494E-09  1.98E-12  4.49E-10  9.89E+00  2.41E+09  6.4E-11
   390  1.000000957E-01  1.827111494E-09  1.98E-12  4.16E-09  1.00E+01  2.44E+09  6.4E-11
   400  1.000000955E-01  1.827111493E-09  1.98E-12  3.51E-08  1.01E+01  2.47E+09  6.4E-11
   410  1.000000315E-01  1.827111128E-09  1.98E-12  1.12E-06  1.02E+01  2.50E+09  6.4E-11
   420  1.000000279E-01  1.827111108E-09  1.98E-12  9.58E-11  1.04E+01  2.54E+09  6.4E-11
   430  1.000000279E-01  1.827111108E-09  1.98E-12  6.65E-12  1.05E+01  2.57E+09  6.4E-11
   440  1.000000279E-01  1.827111108E-09  1.98E-12  2.03E-12  1.06E+01  2.59E+09  6.4E-11
   446  1.000000279E-01  1.827111108E-09  1.98E-12  2.04E-15  1.07E+01  2.62E+09  6.4E-11
   447  1.000000279E-01  1.827111108E-09  1.98E-12  1.73E-15  1.07E+01  2.62E+09  6.4E-11
   450  1.000000279E-01  1.827111108E-09  1.98E-12  1.76E-13  1.07E+01  2.62E+09  6.4E-11
   460  1.000000279E-01  1.827111108E-09  1.98E-12  2.38E-13  1.08E+01  2.65E+09  6.4E-11
   465  1.000000279E-01  1.827111108E-09  1.98E-12  1.75E-16  1.09E+01  2.67E+09  6.4E-11

 Exit  LSQR.       istop  = 3               itn    =     465
 Exit  LSQR.       Anorm  = 1.09390E+01     Acond  = 2.67131E+09
 Exit  LSQR.       bnorm  = 9.20536E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-09     Arnorm = 3.50479E-24
 Exit  LSQR.       max dx = 9.1E+02 occurred at itn        1
 Exit  LSQR.              = 5.0E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-12
    norm(x)         = 1.827E+03
    norm(r)         = 8.25665942E-13 = rho1
    norm(A'r)       = 6.491E-13      = sigma1

    norm(s)         = 8.257E-01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711129E-09 = rho2
    norm(Abar'rbar) = 6.491E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.949E-17 (Ax = b)
    test2           = 7.186E-02 (least-squares)
    test3           = 3.247E-05 (damped least-squares)


 Solution  x:
     1  0.100000         2  0.200000         3  0.300000         4  0.400000    
     5  0.500000         6  0.600000         7  0.700000         8  0.800000    


 LSQR  appears to be successful.
 Relative error in  x  =  1.02E-09


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 1000   40    7    1.00E-13 )
 Condition no. =  6.1035E+09     Residual function =  8.463025879E-16
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.8E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   1000 columns
 damp   =  1.00000000000000E-13   wantse =         F
 atol   =  3.18E-16               conlim =  6.10E+12
 btol   =  3.18E-16               itnlim =      8200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  8.802779981E+02  1.00E+00  9.46E-04
     1 -2.422195397E+01  3.783589553E+02  4.30E-01  6.05E-01  9.23E-01  1.00E+00  6.4E-01
     2 -2.477913716E+01  2.170796658E+02  2.47E-01  3.45E-01  1.18E+00  2.20E+00  3.3E-01
     3 -1.776850890E+01  1.378525121E+02  1.57E-01  2.27E-01  1.32E+00  3.69E+00  2.0E-01
     4 -8.448828545E+00  9.115137842E+01  1.04E-01  1.57E-01  1.40E+00  5.56E+00  1.3E-01
     5  7.462713431E-01  6.101548604E+01  6.93E-02  1.10E-01  1.44E+00  7.99E+00  8.9E-02
     6  8.324225295E+00  4.071186937E+01  4.62E-02  7.68E-02  1.47E+00  1.13E+01  6.0E-02
     7  1.328456787E+01  2.681918944E+01  3.05E-02  5.31E-02  1.48E+00  1.60E+01  4.0E-02
     8  1.508697435E+01  1.732799020E+01  1.97E-02  3.61E-02  1.48E+00  2.29E+01  2.7E-02
     9  1.370778590E+01  1.092432663E+01  1.24E-02  2.40E-02  1.49E+00  3.32E+01  1.7E-02
    10  9.648835708E+00  6.689826212E+00  7.60E-03  1.78E-02  1.49E+00  4.93E+01  1.1E-02
    20 -1.212824859E+01  6.304636182E-01  7.16E-04  2.12E-03  2.31E+00  5.05E+02  1.3E-03
    30 -1.324951967E+01  1.349693628E-01  1.53E-04  8.76E-03  2.73E+00  2.02E+03  3.2E-04
    40 -7.972289743E+00  3.034724694E-02  3.45E-05  2.64E-02  3.17E+00  9.50E+03  7.5E-05
    50 -3.760582449E+00  7.471160118E-03  8.49E-06  1.44E-01  3.50E+00  2.77E+04  2.3E-05
    60 -3.516869244E+00  5.772948771E-03  6.56E-06  5.77E-05  3.92E+00  3.19E+04  2.0E-05
    70 -5.570579103E-01  1.366150384E-03  1.55E-06  3.55E-06  4.19E+00  9.77E+04  5.7E-06
    80 -2.351225472E-01  1.235080581E-03  1.40E-06  5.97E-03  4.44E+00  1.83E+05  4.1E-06
    90  1.155130277E+00  2.298013456E-04  2.61E-07  5.88E-05  4.78E+00  3.90E+05  1.2E-06
   100  1.155188322E+00  2.296980456E-04  2.61E-07  3.09E-05  5.00E+00  4.08E+05  1.2E-06
   110  1.195102232E+00  2.188279056E-04  2.49E-07  1.46E-02  5.21E+00  7.30E+05  9.3E-07
   120  1.581337623E+00  2.242424742E-05  2.55E-08  3.14E-05  5.45E+00  2.08E+06  1.8E-07
   130  1.581421764E+00  2.238624925E-05  2.54E-08  1.09E-05  5.74E+00  2.19E+06  1.8E-07
   140  1.581421505E+00  2.238622182E-05  2.54E-08  9.24E-06  5.93E+00  2.26E+06  1.8E-07
   150  1.529094130E+00  2.103866096E-05  2.39E-08  5.31E-04  6.11E+00  6.27E+06  1.1E-07
   160  1.473983854E+00  1.951748521E-05  2.22E-08  8.32E-03  6.29E+00  8.93E+06  8.7E-08
   170  1.134264711E+00  7.964140066E-07  9.05E-10  2.30E-05  6.52E+00  1.84E+07  1.2E-08
   180  1.134264723E+00  7.964053359E-07  9.05E-10  1.45E-06  6.69E+00  1.88E+07  1.2E-08
   190  1.134261248E+00  7.959773875E-07  9.04E-10  6.48E-06  6.85E+00  1.93E+07  1.2E-08
   200  1.134261015E+00  7.959772113E-07  9.04E-10  3.48E-06  7.08E+00  1.99E+07  1.2E-08
   210  1.134260117E+00  7.959766870E-07  9.04E-10  1.35E-06  7.25E+00  2.04E+07  1.2E-08
   220  1.117831697E+00  7.860260040E-07  8.93E-10  3.95E-05  7.41E+00  5.95E+07  7.3E-09
   230  1.117807695E+00  7.860113715E-07  8.93E-10  1.65E-05  7.61E+00  6.11E+07  7.3E-09
   240  5.873307528E-01  3.254190657E-07  3.70E-10  2.84E-03  7.75E+00  3.38E+08  2.0E-09
   250  4.790469911E-01  3.745770068E-08  4.26E-11  9.59E-03  7.89E+00  3.76E+08  6.6E-10
   260  4.775942228E-01  2.326428255E-09  2.64E-12  2.53E-03  8.09E+00  3.86E+08  1.6E-10
   270  4.775939951E-01  2.278945208E-09  2.59E-12  4.89E-07  8.22E+00  3.93E+08  1.6E-10
   280  4.775939951E-01  2.278944830E-09  2.59E-12  3.33E-07  8.38E+00  4.00E+08  1.6E-10
   290  4.775939949E-01  2.278943427E-09  2.59E-12  5.85E-05  8.51E+00  4.07E+08  1.6E-10
   300  4.775939419E-01  2.278532802E-09  2.59E-12  4.29E-08  8.70E+00  4.15E+08  1.6E-10
   310  4.775939238E-01  2.278455786E-09  2.59E-12  4.36E-05  8.81E+00  4.21E+08  1.6E-10
   320  4.775939236E-01  2.278455067E-09  2.59E-12  3.09E-07  8.95E+00  4.28E+08  1.6E-10
   330  4.775939236E-01  2.278455064E-09  2.59E-12  4.72E-09  9.11E+00  4.35E+08  1.6E-10
   340  4.775939236E-01  2.278455064E-09  2.59E-12  1.32E-10  9.24E+00  4.41E+08  1.6E-10
   350  4.775938894E-01  2.278454963E-09  2.59E-12  8.09E-08  9.36E+00  4.47E+08  1.6E-10
   360  4.775906183E-01  2.278445339E-09  2.59E-12  7.79E-05  9.49E+00  4.84E+08  1.6E-10
   370  4.775900584E-01  2.278443691E-09  2.59E-12  3.10E-07  9.66E+00  4.97E+08  1.6E-10
   380  4.775900563E-01  2.278443685E-09  2.59E-12  7.64E-09  9.78E+00  5.03E+08  1.6E-10
   390  4.775894205E-01  2.278441809E-09  2.59E-12  1.17E-05  9.88E+00  5.14E+08  1.5E-10
   400  4.775893873E-01  2.278441711E-09  2.59E-12  2.78E-08  1.00E+01  5.23E+08  1.5E-10
   410  4.775893853E-01  2.278441705E-09  2.59E-12  6.18E-10  1.01E+01  5.28E+08  1.5E-10
   420  4.738247766E-01  2.267128787E-09  2.58E-12  2.58E-05  1.03E+01  6.27E+09  4.5E-11
   430  4.737554939E-01  2.266920057E-09  2.58E-12  3.81E-05  1.04E+01  6.42E+09  4.5E-11
   440  3.006921773E-01  1.665792869E-09  1.89E-12  1.11E-03  1.05E+01  4.39E+10  1.5E-11
   450  1.000150316E-01  1.832971163E-10  2.08E-13  8.54E-06  1.06E+01  6.49E+10  4.1E-12
   460  1.000102069E-01  1.831172599E-10  2.08E-13  6.98E-04  1.07E+01  6.55E+10  4.1E-12
   470  1.000040779E-01  1.828885385E-10  2.08E-13  1.34E-05  1.09E+01  6.64E+10  4.0E-12
   480  9.999935322E-02  1.827120292E-10  2.08E-13  1.07E-06  1.10E+01  6.70E+10  4.0E-12
   490  9.999935276E-02  1.827120120E-10  2.08E-13  6.43E-07  1.11E+01  6.76E+10  4.0E-12
   500  9.999933151E-02  1.827111813E-10  2.08E-13  1.10E-08  1.12E+01  6.85E+10  4.0E-12
   510  9.999933151E-02  1.827111813E-10  2.08E-13  2.40E-10  1.13E+01  6.91E+10  4.0E-12
   520  9.999933151E-02  1.827111813E-10  2.08E-13  3.45E-09  1.14E+01  6.96E+10  4.0E-12
   530  9.999933151E-02  1.827111813E-10  2.08E-13  2.00E-09  1.15E+01  7.04E+10  4.0E-12
   540  9.999933151E-02  1.827111813E-10  2.08E-13  2.70E-10  1.16E+01  7.10E+10  4.0E-12
   550  9.999933151E-02  1.827111813E-10  2.08E-13  2.55E-11  1.18E+01  7.18E+10  4.0E-12
   560  9.999933151E-02  1.827111813E-10  2.08E-13  2.55E-10  1.18E+01  7.23E+10  4.0E-12
   570  9.999933150E-02  1.827111813E-10  2.08E-13  7.79E-09  1.19E+01  7.29E+10  4.0E-12
   580  9.999933150E-02  1.827111813E-10  2.08E-13  1.05E-10  1.21E+01  7.37E+10  4.0E-12
   590  9.999933131E-02  1.827111812E-10  2.08E-13  4.53E-07  1.22E+01  7.42E+10  4.0E-12
   600  9.999920089E-02  1.827111108E-10  2.08E-13  6.55E-12  1.23E+01  7.50E+10  4.0E-12
   610  9.999920089E-02  1.827111108E-10  2.08E-13  1.98E-12  1.24E+01  7.55E+10  4.0E-12
   620  9.999920090E-02  1.827111108E-10  2.08E-13  2.29E-10  1.25E+01  7.62E+10  4.0E-12
   630  9.999920090E-02  1.827111108E-10  2.08E-13  1.76E-09  1.26E+01  7.67E+10  4.0E-12
   640  9.999920091E-02  1.827111108E-10  2.08E-13  5.31E-08  1.27E+01  7.75E+10  4.0E-12
   650  9.999920091E-02  1.827111108E-10  2.08E-13  5.82E-15  1.28E+01  7.80E+10  4.0E-12
   660  9.999920091E-02  1.827111108E-10  2.08E-13  2.15E-13  1.29E+01  7.85E+10  4.0E-12
   670  9.999920091E-02  1.827111108E-10  2.08E-13  6.57E-11  1.29E+01  7.90E+10  4.0E-12
   680  9.999920091E-02  1.827111108E-10  2.08E-13  1.05E-13  1.31E+01  7.98E+10  4.0E-12
   690  9.999920091E-02  1.827111108E-10  2.08E-13  7.40E-13  1.31E+01  8.02E+10  4.0E-12
   700  9.999920091E-02  1.827111108E-10  2.08E-13  8.44E-13  1.32E+01  8.07E+10  4.0E-12
   704  9.999920091E-02  1.827111108E-10  2.08E-13  2.95E-15  1.33E+01  8.12E+10  4.0E-12
   705  9.999920091E-02  1.827111108E-10  2.08E-13  1.08E-15  1.33E+01  8.12E+10  4.0E-12
   707  9.999920091E-02  1.827111108E-10  2.08E-13  5.49E-16  1.33E+01  8.12E+10  4.0E-12
   708  9.999920091E-02  1.827111108E-10  2.08E-13  1.27E-15  1.33E+01  8.12E+10  4.0E-12
   709  9.999920091E-02  1.827111108E-10  2.08E-13  1.31E-15  1.33E+01  8.14E+10  4.0E-12
   710  9.999920091E-02  1.827111108E-10  2.08E-13  9.31E-16  1.33E+01  8.15E+10  4.0E-12
   711  9.999920091E-02  1.827111108E-10  2.08E-13  1.31E-15  1.34E+01  8.15E+10  4.0E-12
   720  9.999920091E-02  1.827111108E-10  2.08E-13  1.04E-11  1.34E+01  8.21E+10  4.0E-12
   726  9.999920091E-02  1.827111108E-10  2.08E-13  2.51E-15  1.35E+01  8.24E+10  4.0E-12
   727  9.999920091E-02  1.827111108E-10  2.08E-13  6.83E-16  1.35E+01  8.24E+10  4.0E-12
   728  9.999920091E-02  1.827111108E-10  2.08E-13  1.25E-15  1.35E+01  8.25E+10  4.0E-12
   730  9.999920091E-02  1.827111108E-10  2.08E-13  2.31E-15  1.35E+01  8.26E+10  4.0E-12
   731  9.999920091E-02  1.827111108E-10  2.08E-13  2.01E-15  1.35E+01  8.26E+10  4.0E-12
   733  9.999920091E-02  1.827111108E-10  2.08E-13  4.60E-16  1.36E+01  8.29E+10  4.0E-12
   734  9.999920091E-02  1.827111108E-10  2.08E-13  6.81E-16  1.36E+01  8.29E+10  4.0E-12
   735  9.999920091E-02  1.827111108E-10  2.08E-13  5.87E-17  1.36E+01  8.29E+10  4.0E-12

 Exit  LSQR.       istop  = 3               itn    =     735
 Exit  LSQR.       Anorm  = 1.35788E+01     Acond  = 8.28834E+10
 Exit  LSQR.       bnorm  = 8.80278E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-10     Arnorm = 1.45752E-25
 Exit  LSQR.       max dx = 8.6E+02 occurred at itn        1
 Exit  LSQR.              = 4.7E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-13
    norm(x)         = 1.827E+03
    norm(r)         = 1.18832453E-12 = rho1
    norm(A'r)       = 9.921E-13      = sigma1

    norm(s)         = 1.188E+01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82714975E-10 = rho2
    norm(Abar'rbar) = 9.921E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.626E-17 (Ax = b)
    test2           = 6.148E-02 (least-squares)
    test3           = 3.999E-04 (damped least-squares)


 Solution  x:
     1  0.999992E-01     2  0.200000         3  0.300000         4  0.399999    
     5  0.500001         6  0.600002         7  0.700001         8  0.800001    


 LSQR  appears to be successful.
 Relative error in  x  =  3.04E-08


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    2    1.00E-08 )
 Condition no. =  6.2500E+02     Residual function =  1.343553250E-12
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.8E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-08   wantse =         F
 atol   =  3.18E-16               conlim =  6.25E+05
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.249337798E+03  1.00E+00  6.63E-04
     1 -2.402620751E+01  4.498264693E+02  3.60E-01  7.05E-01  8.88E-01  1.00E+00  5.5E-01
     2 -2.022218888E+01  2.366648551E+02  1.89E-01  4.41E-01  1.18E+00  2.12E+00  2.9E-01
     3 -1.368214317E+01  1.468584013E+02  1.18E-01  3.23E-01  1.39E+00  3.40E+00  1.9E-01
     4 -8.500660046E+00  9.996107126E+01  8.00E-02  2.55E-01  1.56E+00  4.83E+00  1.4E-01
     5 -4.843832613E+00  7.213638259E+01  5.77E-02  2.09E-01  1.70E+00  6.39E+00  1.1E-01
     6 -2.325528667E+00  5.415595941E+01  4.33E-02  1.76E-01  1.82E+00  8.09E+00  8.3E-02
     7 -5.967528345E-01  4.180081114E+01  3.35E-02  1.51E-01  1.93E+00  9.93E+00  6.8E-02
     8  5.892115846E-01  3.290744559E+01  2.63E-02  1.31E-01  2.02E+00  1.19E+01  5.6E-02
     9  1.397830815E+00  2.626856207E+01  2.10E-02  1.14E-01  2.09E+00  1.40E+01  4.7E-02
    10  1.939370290E+00  2.116522153E+01  1.69E-02  9.99E-02  2.15E+00  1.63E+01  3.9E-02
    20  1.825970980E+00  2.365313448E+00  1.89E-03  1.96E-02  2.55E+00  6.46E+01  7.2E-03
    30  5.353268996E-01  1.738888507E-01  1.39E-04  2.02E-02  3.15E+00  2.80E+02  1.0E-03
    40  2.252188737E-01  2.029764483E-02  1.62E-05  2.12E-03  3.66E+00  6.59E+02  2.5E-04
    50  4.180369377E-05  1.885384547E-05  1.51E-08  4.94E-02  4.05E+00  2.64E+03  4.0E-06
    60  4.192209490E-05  1.827111106E-05  1.46E-08  2.71E-06  4.50E+00  2.93E+03  3.9E-06
    70  4.192211714E-05  1.827111106E-05  1.46E-08  5.86E-09  4.83E+00  3.15E+03  3.9E-06
    80  4.192211728E-05  1.827111106E-05  1.46E-08  5.53E-13  5.19E+00  3.40E+03  3.9E-06
    90  4.192211727E-05  1.827111106E-05  1.46E-08  2.06E-14  5.48E+00  3.70E+03  3.8E-06
    99  4.192211725E-05  1.827111106E-05  1.46E-08  1.07E-15  5.77E+00  5.31E+03  3.3E-06
   100  4.192211725E-05  1.827111106E-05  1.46E-08  6.49E-16  5.81E+00  5.35E+03  3.3E-06
   101  4.192211725E-05  1.827111106E-05  1.46E-08  8.20E-17  5.84E+00  5.37E+03  3.3E-06

 Exit  LSQR.       istop  = 3               itn    =     101
 Exit  LSQR.       Anorm  = 5.83627E+00     Acond  = 5.36848E+03
 Exit  LSQR.       bnorm  = 1.24934E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-05     Arnorm = 8.74226E-21
 Exit  LSQR.       max dx = 1.3E+03 occurred at itn        1
 Exit  LSQR.              = 7.2E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-08
    norm(x)         = 1.827E+03
    norm(r)         = 1.62227530E-12 = rho1
    norm(A'r)       = 8.364E-13      = sigma1

    norm(s)         = 1.622E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-05 = rho2
    norm(Abar'rbar) = 7.301E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 1.362E-16 (Ax = b)
    test2           = 8.834E-02 (least-squares)
    test3           = 6.847E-09 (damped least-squares)


 Solution  x:
     1  0.419221E-04     2  0.100048         3  0.200058         4  0.300072    
     5  0.400089         6  0.500111         7  0.600137         8  0.700166    


 LSQR  appears to be successful.
 Relative error in  x  =  1.86E-14


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    3    1.00E-09 )
 Condition no. =  1.5625E+04     Residual function =  2.329778320E-13
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   6.9E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-09   wantse =         F
 atol   =  3.18E-16               conlim =  1.56E+07
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.123359829E+03  1.00E+00  7.29E-04
     1 -2.363600419E+01  4.429684871E+02  3.94E-01  6.74E-01  8.91E-01  1.00E+00  5.8E-01
     2 -2.536537104E+01  2.478419375E+02  2.21E-01  4.14E-01  1.18E+00  2.15E+00  3.1E-01
     3 -2.234334321E+01  1.605741928E+02  1.43E-01  2.98E-01  1.38E+00  3.47E+00  2.1E-01
     4 -1.850838596E+01  1.125867821E+02  1.00E-01  2.30E-01  1.54E+00  4.96E+00  1.5E-01
     5 -1.486363650E+01  8.277614326E+01  7.37E-02  1.85E-01  1.66E+00  6.62E+00  1.1E-01
     6 -1.164113584E+01  6.269864588E+01  5.58E-02  1.52E-01  1.76E+00  8.46E+00  8.8E-02
     7 -8.856664513E+00  4.838096211E+01  4.31E-02  1.26E-01  1.83E+00  1.05E+01  7.1E-02
     8 -6.469341196E+00  3.773364443E+01  3.36E-02  1.05E-01  1.89E+00  1.28E+01  5.7E-02
     9 -4.430203839E+00  2.956546508E+01  2.63E-02  8.81E-02  1.93E+00  1.54E+01  4.6E-02
    10 -2.696584122E+00  2.315451278E+01  2.06E-02  7.34E-02  1.96E+00  1.84E+01  3.8E-02
    20  2.749967457E+00  2.714396068E+00  2.42E-03  2.78E-02  2.44E+00  9.18E+01  6.3E-03
    30  2.058735657E+00  5.116450042E-01  4.55E-04  9.64E-02  2.98E+00  3.36E+02  1.6E-03
    40  1.134467661E+00  8.478454509E-02  7.55E-05  4.93E-04  3.51E+00  1.03E+03  4.0E-04
    50  6.283808430E-01  1.728745086E-02  1.54E-05  1.91E-04  3.91E+00  2.54E+03  1.2E-04
    60  2.413194176E-01  8.685459955E-04  7.73E-07  8.20E-04  4.24E+00  8.73E+03  1.5E-05
    70  2.372218646E-01  8.611348599E-04  7.67E-07  8.15E-04  4.58E+00  1.33E+04  1.3E-05
    80  2.690047281E-04  2.646434901E-05  2.36E-08  5.15E-02  4.88E+00  7.68E+04  9.6E-07
    90  4.194199468E-05  1.827705829E-06  1.63E-09  6.73E-04  5.17E+00  8.14E+04  2.5E-07
   100  4.192216742E-05  1.827111120E-06  1.63E-09  1.41E-06  5.49E+00  8.65E+04  2.5E-07
   110  4.192213151E-05  1.827111106E-06  1.63E-09  1.96E-10  5.74E+00  9.05E+04  2.5E-07
   120  4.192212710E-05  1.827111106E-06  1.63E-09  9.63E-10  6.03E+00  9.50E+04  2.5E-07
   130  4.192212576E-05  1.827111106E-06  1.63E-09  3.04E-10  6.24E+00  9.88E+04  2.5E-07
   140  4.192212496E-05  1.827111106E-06  1.63E-09  2.75E-14  6.47E+00  1.03E+05  2.5E-07
   143  4.192212496E-05  1.827111106E-06  1.63E-09  1.96E-15  6.58E+00  1.05E+05  2.5E-07
   149  4.192212496E-05  1.827111106E-06  1.63E-09  2.20E-15  6.72E+00  1.07E+05  2.5E-07
   150  4.192212496E-05  1.827111106E-06  1.63E-09  1.75E-15  6.72E+00  1.07E+05  2.5E-07
   160  4.192212532E-05  1.827111106E-06  1.63E-09  2.90E-14  6.95E+00  1.55E+05  2.1E-07
   170  4.192212532E-05  1.827111106E-06  1.63E-09  7.06E-14  7.17E+00  1.60E+05  2.1E-07
   174  4.192212532E-05  1.827111106E-06  1.63E-09  3.00E-19  7.23E+00  1.61E+05  2.1E-07

 Exit  LSQR.       istop  = 3               itn    =     174
 Exit  LSQR.       Anorm  = 7.22692E+00     Acond  = 1.61087E+05
 Exit  LSQR.       bnorm  = 1.12336E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-06     Arnorm = 3.95539E-24
 Exit  LSQR.       max dx = 1.2E+03 occurred at itn        1
 Exit  LSQR.              = 6.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-09
    norm(x)         = 1.827E+03
    norm(r)         = 9.38127173E-13 = rho1
    norm(A'r)       = 6.568E-13      = sigma1

    norm(s)         = 9.381E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-06 = rho2
    norm(Abar'rbar) = 6.562E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 6.548E-17 (Ax = b)
    test2           = 9.688E-02 (least-squares)
    test3           = 4.970E-08 (damped least-squares)


 Solution  x:
     1  0.419221E-04     2  0.100048         3  0.200058         4  0.300072    
     5  0.400089         6  0.500111         7  0.600137         8  0.700166    


 LSQR  appears to be successful.
 Relative error in  x  =  5.36E-13


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    4    1.00E-10 )
 Condition no. =  3.9062E+05     Residual function =  5.483800908E-14
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   5.6E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-10   wantse =         F
 atol   =  3.18E-16               conlim =  3.91E+08
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  1.035503865E+03  1.00E+00  7.90E-04
     1 -2.196079333E+01  4.270217666E+02  4.12E-01  6.53E-01  8.98E-01  1.00E+00  6.0E-01
     2 -2.645951529E+01  2.450483281E+02  2.37E-01  3.94E-01  1.18E+00  2.16E+00  3.2E-01
     3 -2.607148844E+01  1.607382862E+02  1.55E-01  2.79E-01  1.37E+00  3.52E+00  2.1E-01
     4 -2.401574568E+01  1.129290043E+02  1.09E-01  2.11E-01  1.51E+00  5.07E+00  1.5E-01
     5 -2.135943597E+01  8.243448020E+01  7.96E-02  1.64E-01  1.61E+00  6.84E+00  1.1E-01
     6 -1.851085751E+01  6.145549031E+01  5.93E-02  1.30E-01  1.68E+00  8.87E+00  8.5E-02
     7 -1.564469118E+01  4.627345613E+01  4.47E-02  1.04E-01  1.73E+00  1.12E+01  6.6E-02
     8 -1.284656410E+01  3.491021125E+01  3.37E-02  8.32E-02  1.76E+00  1.41E+01  5.1E-02
     9 -1.016820875E+01  2.622363730E+01  2.53E-02  6.60E-02  1.79E+00  1.75E+01  4.0E-02
    10 -7.649778744E+00  1.950853237E+01  1.88E-02  5.19E-02  1.80E+00  2.18E+01  3.1E-02
    20  2.137879416E+00  2.004762425E+00  1.94E-03  5.88E-03  2.43E+00  1.47E+02  4.3E-03
    30  2.714505527E+00  3.189186508E-01  3.08E-04  5.97E-03  2.95E+00  6.27E+02  9.1E-04
    40  2.034537362E+00  9.345052188E-02  9.02E-05  2.23E-02  3.36E+00  2.06E+03  2.9E-04
    50  1.271377621E+00  1.685590176E-02  1.63E-05  8.43E-02  3.76E+00  6.17E+03  7.5E-05
    60  1.122262028E+00  1.049135668E-02  1.01E-05  3.92E-03  4.07E+00  1.09E+04  4.6E-05
    70  6.583646996E-01  1.481584671E-03  1.43E-06  1.34E-05  4.42E+00  2.26E+04  1.3E-05
    80  6.573514875E-01  1.479808584E-03  1.43E-06  9.47E-04  4.71E+00  2.47E+04  1.2E-05
    90  2.445862034E-01  3.521515785E-05  3.40E-08  1.26E-04  5.02E+00  1.25E+05  8.8E-07
   100  2.445858018E-01  3.521008928E-05  3.40E-08  1.11E-05  5.28E+00  1.32E+05  8.8E-07
   110  2.440172123E-01  3.516903347E-05  3.40E-08  1.09E-03  5.55E+00  1.74E+05  7.8E-07
   120  2.244938451E-01  3.373056952E-05  3.26E-08  4.96E-03  5.78E+00  6.64E+05  4.0E-07
   130  4.204405259E-05  1.845604356E-07  1.78E-10  4.33E-03  6.03E+00  2.36E+06  1.6E-08
   140  4.199741860E-05  1.839181408E-07  1.78E-10  1.85E-03  6.27E+00  2.45E+06  1.6E-08
   150  4.192694418E-05  1.827123920E-07  1.76E-10  1.39E-04  6.48E+00  2.54E+06  1.6E-08
   160  4.192460094E-05  1.827111251E-07  1.76E-10  2.72E-05  6.67E+00  2.61E+06  1.6E-08
   170  4.192217149E-05  1.827111106E-07  1.76E-10  2.04E-07  6.86E+00  2.69E+06  1.6E-08
   180  4.192216104E-05  1.827111106E-07  1.76E-10  9.45E-10  7.06E+00  2.76E+06  1.6E-08
   190  4.192216047E-05  1.827111106E-07  1.76E-10  1.88E-10  7.28E+00  2.85E+06  1.6E-08
   200  4.192213676E-05  1.827111106E-07  1.76E-10  6.99E-09  7.47E+00  2.93E+06  1.6E-08
   210  4.192213585E-05  1.827111106E-07  1.76E-10  5.32E-12  7.65E+00  3.00E+06  1.6E-08
   220  4.192213585E-05  1.827111106E-07  1.76E-10  2.24E-16  7.85E+00  3.08E+06  1.6E-08

 Exit  LSQR.       istop  = 3               itn    =     220
 Exit  LSQR.       Anorm  = 7.85148E+00     Acond  = 3.07947E+06
 Exit  LSQR.       bnorm  = 1.03550E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-07     Arnorm = 3.21506E-22
 Exit  LSQR.       max dx = 1.1E+03 occurred at itn        1
 Exit  LSQR.              = 5.8E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-10
    norm(x)         = 1.827E+03
    norm(r)         = 7.13826562E-13 = rho1
    norm(A'r)       = 5.260E-13      = sigma1

    norm(s)         = 7.138E-03
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-07 = rho2
    norm(Abar'rbar) = 5.260E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.641E-17 (Ax = b)
    test2           = 9.385E-02 (least-squares)
    test3           = 3.666E-07 (damped least-squares)


 Solution  x:
     1  0.419221E-04     2  0.100048         3  0.200058         4  0.300072    
     5  0.400089         6  0.500111         7  0.600137         8  0.700166    


 LSQR  appears to be successful.
 Relative error in  x  =  1.53E-12


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    5    1.00E-11 )
 Condition no. =  9.7656E+06     Residual function =  1.353835357E-14
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   9.1E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-11   wantse =         F
 atol   =  3.18E-16               conlim =  9.77E+09
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.703527094E+02  1.00E+00  8.46E-04
     1 -2.012872225E+01  4.098051391E+02  4.22E-01  6.36E-01  9.06E-01  1.00E+00  6.2E-01
     2 -2.596081160E+01  2.371904556E+02  2.44E-01  3.77E-01  1.18E+00  2.17E+00  3.3E-01
     3 -2.724993460E+01  1.551916987E+02  1.60E-01  2.61E-01  1.36E+00  3.56E+00  2.1E-01
     4 -2.658801144E+01  1.077314213E+02  1.11E-01  1.92E-01  1.47E+00  5.19E+00  1.5E-01
     5 -2.492214847E+01  7.702278580E+01  7.94E-02  1.45E-01  1.55E+00  7.12E+00  1.1E-01
     6 -2.267029833E+01  5.576674457E+01  5.75E-02  1.11E-01  1.60E+00  9.45E+00  7.8E-02
     7 -2.005231567E+01  4.044553417E+01  4.17E-02  8.46E-02  1.63E+00  1.23E+01  5.8E-02
     8 -1.720991793E+01  2.915470492E+01  3.00E-02  6.42E-02  1.65E+00  1.60E+01  4.3E-02
     9 -1.425515842E+01  2.075998677E+01  2.14E-02  4.81E-02  1.66E+00  2.09E+01  3.2E-02
    10 -1.129010659E+01  1.452597689E+01  1.50E-02  3.55E-02  1.67E+00  2.74E+01  2.3E-02
    20  4.903628391E-01  1.540444195E+00  1.59E-03  2.41E-02  2.28E+00  2.03E+02  3.1E-03
    30  2.829036396E+00  2.209667705E-01  2.28E-04  7.93E-02  2.77E+00  1.03E+03  5.7E-04
    40  2.807089919E+00  8.721841336E-02  8.99E-05  1.60E-03  3.30E+00  2.31E+03  2.6E-04
    50  2.456930114E+00  3.024656612E-02  3.12E-05  4.61E-03  3.69E+00  5.50E+03  1.1E-04
    60  1.911456918E+00  8.227701716E-03  8.48E-06  1.66E-04  4.02E+00  1.39E+04  3.6E-05
    70  1.268824693E+00  1.475570223E-03  1.52E-06  8.05E-04  4.34E+00  4.41E+04  8.9E-06
    80  1.268520331E+00  1.472783795E-03  1.52E-06  1.86E-04  4.61E+00  4.69E+04  8.9E-06
    90  6.696363100E-01  1.219893098E-04  1.26E-07  7.30E-04  4.89E+00  2.03E+05  1.3E-06
   100  6.696027781E-01  1.216246870E-04  1.25E-07  4.66E-06  5.15E+00  2.14E+05  1.3E-06
   110  6.692732292E-01  1.215770772E-04  1.25E-07  1.51E-03  5.40E+00  2.29E+05  1.3E-06
   120  2.503139839E-01  1.325018410E-05  1.37E-08  9.55E-02  5.65E+00  1.73E+06  1.5E-07
   130  2.454425419E-01  2.369519229E-06  2.44E-09  7.84E-03  5.94E+00  1.83E+06  6.5E-08
   140  2.453435628E-01  1.412874820E-06  1.46E-09  3.86E-06  6.15E+00  1.89E+06  5.0E-08
   150  2.453436338E-01  1.412861736E-06  1.46E-09  5.54E-06  6.33E+00  1.95E+06  5.0E-08
   160  2.453436336E-01  1.412861729E-06  1.46E-09  2.04E-08  6.54E+00  2.02E+06  5.0E-08
   170  2.453418112E-01  1.412856476E-06  1.46E-09  1.60E-04  6.73E+00  2.08E+06  5.0E-08
   180  2.264019059E-01  1.357164385E-06  1.40E-09  7.55E-04  6.93E+00  1.89E+07  1.6E-08
   190  2.124277316E-01  1.314561802E-06  1.35E-09  8.17E-06  7.12E+00  2.56E+07  1.4E-08
   200  6.652697953E-05  2.315145483E-08  2.39E-11  3.73E-03  7.29E+00  7.12E+07  1.1E-09
   210  4.173892271E-05  1.828366657E-08  1.88E-11  6.68E-07  7.53E+00  7.36E+07  1.0E-09
   220  4.173755190E-05  1.828333511E-08  1.88E-11  8.48E-07  7.68E+00  7.50E+07  1.0E-09
   230  4.180949802E-05  1.827856374E-08  1.88E-11  4.44E-04  7.85E+00  7.67E+07  1.0E-09
   240  4.192198943E-05  1.827111142E-08  1.88E-11  4.47E-07  8.01E+00  7.82E+07  1.0E-09
   250  4.192200482E-05  1.827111108E-08  1.88E-11  2.43E-07  8.16E+00  7.97E+07  1.0E-09
   260  4.192201592E-05  1.827111106E-08  1.88E-11  1.21E-08  8.32E+00  8.13E+07  1.0E-09
   270  4.192201606E-05  1.827111106E-08  1.88E-11  1.23E-10  8.48E+00  8.29E+07  1.0E-09
   280  4.192263396E-05  1.827111106E-08  1.88E-11  2.68E-08  8.64E+00  8.45E+07  1.0E-09
   290  4.192283947E-05  1.827111106E-08  1.88E-11  2.43E-11  8.82E+00  8.63E+07  1.0E-09
   300  4.192283947E-05  1.827111106E-08  1.88E-11  1.30E-11  8.98E+00  8.78E+07  1.0E-09
   310  4.192283947E-05  1.827111106E-08  1.88E-11  1.45E-10  9.10E+00  8.90E+07  1.0E-09
   320  4.192283947E-05  1.827111106E-08  1.88E-11  2.79E-12  9.26E+00  9.05E+07  1.0E-09
   327  4.192283947E-05  1.827111106E-08  1.88E-11  1.95E-15  9.37E+00  9.16E+07  1.0E-09
   328  4.192283947E-05  1.827111106E-08  1.88E-11  1.25E-16  9.38E+00  9.17E+07  1.0E-09

 Exit  LSQR.       istop  = 3               itn    =     328
 Exit  LSQR.       Anorm  = 9.38346E+00     Acond  = 9.17265E+07
 Exit  LSQR.       bnorm  = 9.70353E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-08     Arnorm = 2.14855E-23
 Exit  LSQR.       max dx = 9.7E+02 occurred at itn        1
 Exit  LSQR.              = 5.3E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-11
    norm(x)         = 1.827E+03
    norm(r)         = 7.55500040E-13 = rho1
    norm(A'r)       = 5.989E-13      = sigma1

    norm(s)         = 7.555E-02
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-08 = rho2
    norm(Abar'rbar) = 5.989E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.171E-17 (Ax = b)
    test2           = 8.448E-02 (least-squares)
    test3           = 3.493E-06 (damped least-squares)


 Solution  x:
     1  0.419228E-04     2  0.100048         3  0.200058         4  0.300072    
     5  0.400089         6  0.500111         7  0.600137         8  0.700166    


 LSQR  appears to be successful.
 Relative error in  x  =  5.06E-11


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    6    1.00E-12 )
 Condition no. =  2.4414E+08     Residual function =  3.374751307E-15
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   9.9E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-12   wantse =         F
 atol   =  3.18E-16               conlim =  2.44E+11
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  9.199695526E+02  1.00E+00  8.99E-04
     1 -1.845383551E+01  3.932613424E+02  4.27E-01  6.20E-01  9.14E-01  1.00E+00  6.3E-01
     2 -2.491620749E+01  2.273238818E+02  2.47E-01  3.61E-01  1.18E+00  2.19E+00  3.3E-01
     3 -2.727058314E+01  1.470028524E+02  1.60E-01  2.44E-01  1.34E+00  3.62E+00  2.1E-01
     4 -2.762338174E+01  9.992899974E+01  1.09E-01  1.74E-01  1.44E+00  5.35E+00  1.4E-01
     5 -2.677116869E+01  6.936381708E+01  7.54E-02  1.27E-01  1.50E+00  7.50E+00  9.8E-02
     6 -2.508690921E+01  4.836804697E+01  5.26E-02  9.27E-02  1.53E+00  1.02E+01  6.9E-02
     7 -2.278857494E+01  3.353135997E+01  3.64E-02  6.75E-02  1.55E+00  1.39E+01  4.9E-02
     8 -2.003892021E+01  2.294165156E+01  2.49E-02  4.85E-02  1.56E+00  1.89E+01  3.5E-02
     9 -1.698519388E+01  1.540241771E+01  1.67E-02  3.43E-02  1.57E+00  2.59E+01  2.4E-02
    10 -1.377309471E+01  1.009643069E+01  1.10E-02  2.37E-02  1.57E+00  3.61E+01  1.6E-02
    20 -2.088877566E+00  1.306145470E+00  1.42E-03  5.91E-02  2.19E+00  2.51E+02  2.5E-03
    30  2.354273621E+00  1.585287476E-01  1.72E-04  6.98E-04  2.85E+00  1.60E+03  4.0E-04
    40  2.828130532E+00  6.449174364E-02  7.01E-05  3.75E-04  3.21E+00  3.53E+03  1.8E-04
    50  2.848799572E+00  2.255207981E-02  2.45E-05  1.19E-03  3.58E+00  8.65E+03  7.2E-05
    60  2.521429083E+00  6.492218197E-03  7.06E-06  1.59E-03  3.89E+00  2.24E+04  2.5E-05
    70  2.042935703E+00  2.865108504E-03  3.11E-06  1.43E-01  4.29E+00  6.64E+04  1.0E-05
    80  1.953030484E+00  1.380492929E-03  1.50E-06  1.27E-05  4.62E+00  7.71E+04  6.7E-06
    90  1.298510138E+00  2.447633979E-04  2.66E-07  2.61E-03  4.87E+00  2.99E+05  1.5E-06
   100  1.288486995E+00  1.819049994E-04  1.98E-07  1.77E-05  5.10E+00  3.16E+05  1.3E-06
   110  1.288455033E+00  1.819001508E-04  1.98E-07  5.23E-06  5.38E+00  3.33E+05  1.3E-06
   120  7.240379629E-01  5.265450228E-05  5.72E-08  5.53E-02  5.60E+00  1.83E+06  3.0E-07
   130  6.742086251E-01  9.895100602E-06  1.08E-08  4.25E-04  5.81E+00  1.98E+06  1.3E-07
   140  6.741842598E-01  9.833850712E-06  1.07E-08  3.47E-04  6.00E+00  2.04E+06  1.3E-07
   150  6.741809863E-01  9.833108541E-06  1.07E-08  8.31E-07  6.28E+00  2.14E+06  1.3E-07
   160  6.741774061E-01  9.833060458E-06  1.07E-08  1.92E-06  6.45E+00  2.20E+06  1.3E-07
   170  2.481517445E-01  7.702123188E-07  8.37E-10  2.46E-03  6.65E+00  2.54E+07  1.1E-08
   180  2.476933880E-01  6.998299679E-07  7.61E-10  6.69E-04  6.81E+00  2.60E+07  1.0E-08
   190  2.456261518E-01  1.514761109E-07  1.65E-10  4.87E-04  7.05E+00  2.70E+07  4.7E-09
   200  2.455313738E-01  6.316110627E-08  6.87E-11  6.82E-03  7.23E+00  2.77E+07  3.0E-09
   210  2.455274155E-01  5.658187046E-08  6.15E-11  7.45E-08  7.42E+00  2.84E+07  2.8E-09
   220  2.455274156E-01  5.658186782E-08  6.15E-11  4.38E-06  7.58E+00  2.90E+07  2.8E-09
   230  2.455274156E-01  5.658186575E-08  6.15E-11  2.23E-07  7.78E+00  2.98E+07  2.8E-09
   240  2.455274891E-01  5.658156292E-08  6.15E-11  1.18E-07  7.94E+00  3.04E+07  2.8E-09
   250  2.455274891E-01  5.658156292E-08  6.15E-11  2.51E-08  8.09E+00  3.10E+07  2.8E-09
   260  2.455274889E-01  5.658156290E-08  6.15E-11  6.70E-08  8.23E+00  3.15E+07  2.8E-09
   270  2.455274606E-01  5.658155965E-08  6.15E-11  1.80E-06  8.43E+00  3.23E+07  2.8E-09
   280  2.454732154E-01  5.657531489E-08  6.15E-11  1.18E-04  8.57E+00  4.52E+07  2.4E-09
   290  6.110818883E-03  9.097390910E-09  9.89E-12  1.28E-04  8.71E+00  2.10E+09  1.4E-10
   300  6.110283998E-03  9.097007992E-09  9.89E-12  1.54E-05  8.84E+00  2.13E+09  1.4E-10
   310  6.106537230E-03  9.094314034E-09  9.89E-12  4.90E-06  9.03E+00  2.18E+09  1.4E-10
   320  3.188915323E-03  6.672923576E-09  7.25E-12  2.55E-04  9.18E+00  2.23E+09  1.2E-10
   330  3.160526071E-03  6.645026402E-09  7.22E-12  2.95E-04  9.32E+00  2.26E+09  1.2E-10
   340  7.957486418E-04  3.633857353E-09  3.95E-12  3.76E-02  9.44E+00  2.30E+09  9.0E-11
   350  4.254833338E-05  1.829410120E-09  1.99E-12  1.28E-03  9.61E+00  2.35E+09  6.4E-11
   360  4.190619268E-05  1.827111606E-09  1.99E-12  4.14E-09  9.74E+00  2.38E+09  6.4E-11
   370  4.190619130E-05  1.827111593E-09  1.99E-12  1.37E-08  9.85E+00  2.41E+09  6.4E-11
   380  4.190619126E-05  1.827111593E-09  1.99E-12  7.15E-08  9.99E+00  2.44E+09  6.4E-11
   390  4.190615582E-05  1.827111590E-09  1.99E-12  2.23E-09  1.01E+01  2.48E+09  6.4E-11
   400  4.190615583E-05  1.827111590E-09  1.99E-12  2.94E-10  1.03E+01  2.50E+09  6.4E-11
   410  4.190615584E-05  1.827111590E-09  1.99E-12  2.53E-10  1.04E+01  2.53E+09  6.4E-11
   420  4.190615584E-05  1.827111590E-09  1.99E-12  1.23E-09  1.05E+01  2.57E+09  6.4E-11
   430  4.194413108E-05  1.827111258E-09  1.99E-12  1.72E-06  1.06E+01  2.59E+09  6.4E-11
   440  4.196158903E-05  1.827111105E-09  1.99E-12  4.94E-12  1.08E+01  2.63E+09  6.4E-11
   450  4.196158906E-05  1.827111105E-09  1.99E-12  2.66E-11  1.09E+01  2.65E+09  6.4E-11
   460  4.196158906E-05  1.827111105E-09  1.99E-12  4.74E-12  1.10E+01  2.69E+09  6.4E-11
   470  4.196158906E-05  1.827111105E-09  1.99E-12  1.81E-12  1.11E+01  2.72E+09  6.4E-11
   480  4.196158906E-05  1.827111105E-09  1.99E-12  2.95E-13  1.12E+01  2.74E+09  6.4E-11
   488  4.196158906E-05  1.827111105E-09  1.99E-12  6.44E-16  1.13E+01  2.77E+09  6.4E-11
   489  4.196158906E-05  1.827111105E-09  1.99E-12  7.59E-16  1.13E+01  2.77E+09  6.4E-11
   490  4.196158906E-05  1.827111105E-09  1.99E-12  3.24E-14  1.13E+01  2.77E+09  6.4E-11
   496  4.196158906E-05  1.827111105E-09  1.99E-12  1.73E-16  1.14E+01  2.79E+09  6.4E-11

 Exit  LSQR.       istop  = 3               itn    =     496
 Exit  LSQR.       Anorm  = 1.14298E+01     Acond  = 2.79118E+09
 Exit  LSQR.       bnorm  = 9.19970E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-09     Arnorm = 3.60793E-24
 Exit  LSQR.       max dx = 9.1E+02 occurred at itn        1
 Exit  LSQR.              = 5.0E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-12
    norm(x)         = 1.827E+03
    norm(r)         = 9.40246648E-13 = rho1
    norm(A'r)       = 7.407E-13      = sigma1

    norm(s)         = 9.402E-01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711135E-09 = rho2
    norm(Abar'rbar) = 7.407E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.312E-17 (Ax = b)
    test2           = 6.892E-02 (least-squares)
    test3           = 3.547E-05 (damped least-squares)


 Solution  x:
     1  0.419616E-04     2  0.100048         3  0.200058         4  0.300071    
     5  0.400089         6  0.500111         7  0.600136         8  0.700166    


 LSQR  appears to be successful.
 Relative error in  x  =  4.26E-09


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 1000 2000   40    7    1.00E-13 )
 Condition no. =  6.1035E+09     Residual function =  8.430939221E-16
 --------------------------------------------------------------------


 Enter Acheck.     Test of Aprod for LSQR and CRAIG
 Aprod seems OK.   Relative error =   4.3E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   1000 rows   and   2000 columns
 damp   =  1.00000000000000E-13   wantse =         F
 atol   =  3.18E-16               conlim =  6.10E+12
 btol   =  3.18E-16               itnlim =     12200


   Itn       x(1)           Function     Compatible   LS     Norm Abar Cond Abar alfa_opt
     0  0.000000000E+00  8.798048753E+02  1.00E+00  9.47E-04
     1 -1.700356276E+01  3.778204977E+02  4.29E-01  6.05E-01  9.23E-01  1.00E+00  6.4E-01
     2 -2.375095537E+01  2.166607925E+02  2.46E-01  3.45E-01  1.18E+00  2.20E+00  3.3E-01
     3 -2.680778713E+01  1.375730438E+02  1.56E-01  2.27E-01  1.32E+00  3.69E+00  2.0E-01
     4 -2.790545888E+01  9.099234087E+01  1.03E-01  1.56E-01  1.40E+00  5.56E+00  1.3E-01
     5 -2.769789733E+01  6.094925399E+01  6.93E-02  1.10E-01  1.44E+00  7.99E+00  8.9E-02
     6 -2.649845769E+01  4.070971620E+01  4.63E-02  7.67E-02  1.47E+00  1.13E+01  6.0E-02
     7 -2.450619289E+01  2.685449180E+01  3.05E-02  5.30E-02  1.48E+00  1.60E+01  4.0E-02
     8 -2.188969492E+01  1.737868266E+01  1.98E-02  3.61E-02  1.48E+00  2.29E+01  2.7E-02
     9 -1.881799087E+01  1.097464382E+01  1.25E-02  2.40E-02  1.49E+00  3.32E+01  1.7E-02
    10 -1.549490918E+01  6.761451411E+00  7.69E-03  6.62E-02  1.49E+00  4.92E+01  1.1E-02
    20 -2.792371857E+00  6.338200898E-01  7.20E-04  1.28E-03  2.31E+00  5.05E+02  1.3E-03
    30  1.149906592E+00  1.352806917E-01  1.54E-04  9.40E-04  2.73E+00  2.01E+03  3.2E-04
    40  2.379712584E+00  4.938499590E-02  5.61E-05  3.70E-03  3.19E+00  6.31E+03  1.2E-04
    50  2.870123723E+00  8.470766110E-03  9.63E-06  6.61E-02  3.63E+00  2.81E+04  2.5E-05
    60  2.877955860E+00  5.704332136E-03  6.48E-06  6.91E-04  3.92E+00  3.24E+04  2.0E-05
    70  2.553910797E+00  1.350339265E-03  1.53E-06  7.59E-06  4.19E+00  9.78E+04  5.6E-06
    80  2.553717647E+00  1.350125115E-03  1.53E-06  1.20E-03  4.44E+00  1.04E+05  5.6E-06
    90  1.976122718E+00  2.277185459E-04  2.59E-07  1.30E-04  4.78E+00  3.90E+05  1.2E-06
   100  1.976050638E+00  2.270092072E-04  2.58E-07  3.80E-05  5.00E+00  4.08E+05  1.2E-06
   110  1.968503508E+00  2.257676730E-04  2.57E-07  1.57E-03  5.22E+00  4.72E+05  1.2E-06
   120  1.298598844E+00  2.216197754E-05  2.52E-08  1.70E-05  5.51E+00  2.10E+06  1.8E-07
   130  1.298594433E+00  2.215914159E-05  2.52E-08  2.00E-05  5.74E+00  2.19E+06  1.8E-07
   140  1.298569795E+00  2.215790595E-05  2.52E-08  2.59E-04  5.92E+00  2.26E+06  1.8E-07
   150  1.215819277E+00  2.063525062E-05  2.35E-08  2.87E-04  6.18E+00  6.72E+06  1.0E-07
   160  7.600296016E-01  8.169700117E-06  9.29E-09  1.69E-04  6.36E+00  1.67E+07  4.1E-08
   170  6.761307937E-01  7.902386928E-07  8.98E-10  1.76E-05  6.53E+00  1.84E+07  1.2E-08
   180  6.761307821E-01  7.902365673E-07  8.98E-10  1.52E-06  6.73E+00  1.89E+07  1.2E-08
   190  6.761309267E-01  7.902019462E-07  8.98E-10  7.74E-05  6.96E+00  1.96E+07  1.2E-08
   200  6.761309713E-01  7.901941994E-07  8.98E-10  8.81E-08  7.12E+00  2.00E+07  1.2E-08
   210  6.761309066E-01  7.901941408E-07  8.98E-10  9.92E-06  7.27E+00  2.05E+07  1.2E-08
   220  6.761211587E-01  7.901851375E-07  8.98E-10  7.02E-06  7.47E+00  2.11E+07  1.2E-08
   230  6.385417313E-01  7.548230309E-07  8.58E-10  1.69E-05  7.62E+00  1.10E+08  5.4E-09
   240  6.385377306E-01  7.548191804E-07  8.58E-10  9.37E-06  7.82E+00  1.12E+08  5.4E-09
   250  3.374372311E-01  3.649616722E-07  4.15E-10  6.80E-02  7.96E+00  3.37E+08  2.2E-09
   260  2.455802295E-01  4.094455297E-09  4.65E-12  7.13E-05  8.13E+00  3.88E+08  2.2E-10
   270  2.455747125E-01  2.958638036E-09  3.36E-12  8.68E-03  8.26E+00  3.94E+08  1.8E-10
   280  2.455722735E-01  2.279757409E-09  2.59E-12  6.10E-06  8.44E+00  4.03E+08  1.6E-10
   290  2.455722735E-01  2.279755908E-09  2.59E-12  1.33E-07  8.57E+00  4.10E+08  1.6E-10
   300  2.455727101E-01  2.272371935E-09  2.58E-12  4.93E-05  8.76E+00  4.18E+08  1.6E-10
   310  2.455728572E-01  2.269899053E-09  2.58E-12  4.92E-05  8.87E+00  4.24E+08  1.6E-10
   320  2.455728576E-01  2.269887339E-09  2.58E-12  8.23E-06  9.03E+00  4.31E+08  1.6E-10
   330  2.455728576E-01  2.269886760E-09  2.58E-12  6.49E-07  9.19E+00  4.39E+08  1.6E-10
   340  2.455728576E-01  2.269886685E-09  2.58E-12  1.45E-08  9.31E+00  4.45E+08  1.6E-10
   350  2.455728576E-01  2.269886683E-09  2.58E-12  1.03E-10  9.43E+00  4.50E+08  1.6E-10
   360  2.455727854E-01  2.269886351E-09  2.58E-12  1.70E-05  9.55E+00  4.57E+08  1.6E-10
   370  2.455719137E-01  2.269882356E-09  2.58E-12  1.42E-06  9.70E+00  4.78E+08  1.6E-10
   380  2.454954669E-01  2.269531919E-09  2.58E-12  5.35E-07  9.82E+00  1.16E+09  1.0E-10
   390  2.454950402E-01  2.269529963E-09  2.58E-12  1.63E-06  9.95E+00  1.18E+09  1.0E-10
   400  2.454943977E-01  2.269527017E-09  2.58E-12  1.38E-07  1.01E+01  1.20E+09  1.0E-10
   410  2.453872051E-01  2.269035429E-09  2.58E-12  1.35E-06  1.02E+01  1.78E+09  8.4E-11
   420  2.451913664E-01  2.268137035E-09  2.58E-12  1.91E-06  1.03E+01  2.53E+09  7.1E-11
   430  2.451679822E-01  2.268029559E-09  2.58E-12  1.23E-05  1.05E+01  2.64E+09  7.0E-11
   440  2.426328898E-01  2.256347617E-09  2.56E-12  3.04E-05  1.06E+01  7.08E+09  4.3E-11
   450  1.866988580E-01  1.981148692E-09  2.25E-12  1.34E-04  1.07E+01  3.20E+10  1.9E-11
   460  1.653687158E-01  1.865541014E-09  2.12E-12  3.16E-04  1.08E+01  3.78E+10  1.7E-11
   470  4.236613823E-05  1.827437103E-10  2.08E-13  1.28E-06  1.09E+01  6.68E+10  4.0E-12
   480  4.229792485E-05  1.827398188E-10  2.08E-13  1.14E-04  1.10E+01  6.74E+10  4.0E-12
   490  4.211829128E-05  1.827295720E-10  2.08E-13  9.40E-06  1.12E+01  6.83E+10  4.0E-12
   500  4.193960364E-05  1.827193766E-10  2.08E-13  7.44E-09  1.13E+01  6.89E+10  4.0E-12
   510  4.193906627E-05  1.827193451E-10  2.08E-13  1.58E-06  1.14E+01  6.96E+10  4.0E-12
   520  4.188600210E-05  1.827162367E-10  2.08E-13  1.80E-06  1.15E+01  7.04E+10  4.0E-12
   530  4.188597921E-05  1.827162354E-10  2.08E-13  1.18E-10  1.16E+01  7.10E+10  4.0E-12
   540  4.188597691E-05  1.827162353E-10  2.08E-13  1.01E-08  1.17E+01  7.15E+10  4.0E-12
   550  4.188597668E-05  1.827162353E-10  2.08E-13  6.60E-09  1.18E+01  7.23E+10  4.0E-12
   560  4.188597660E-05  1.827162353E-10  2.08E-13  2.20E-07  1.19E+01  7.29E+10  4.0E-12
   570  4.188597514E-05  1.827162351E-10  2.08E-13  9.83E-09  1.20E+01  7.35E+10  4.0E-12
   580  4.188019935E-05  1.827154812E-10  2.08E-13  8.83E-06  1.22E+01  7.43E+10  4.0E-12
   590  4.188005973E-05  1.827154629E-10  2.08E-13  2.32E-06  1.23E+01  7.49E+10  4.0E-12
   600  4.187864720E-05  1.827152780E-10  2.08E-13  2.48E-06  1.24E+01  7.54E+10  4.0E-12
   610  4.184684742E-05  1.827111153E-10  2.08E-13  5.75E-06  1.25E+01  7.62E+10  4.0E-12
   620  4.184681212E-05  1.827111107E-10  2.08E-13  1.75E-09  1.26E+01  7.67E+10  4.0E-12
   630  4.184681212E-05  1.827111107E-10  2.08E-13  9.99E-12  1.27E+01  7.73E+10  4.0E-12
   640  4.184681212E-05  1.827111107E-10  2.08E-13  6.66E-14  1.28E+01  7.81E+10  4.0E-12
   650  4.184681212E-05  1.827111107E-10  2.08E-13  1.03E-10  1.29E+01  7.86E+10  4.0E-12
   660  4.184680432E-05  1.827111107E-10  2.08E-13  1.21E-09  1.30E+01  7.91E+10  4.0E-12
   670  4.184680390E-05  1.827111107E-10  2.08E-13  2.03E-14  1.31E+01  7.99E+10  4.0E-12
   680  4.184680390E-05  1.827111107E-10  2.08E-13  3.05E-11  1.32E+01  8.04E+10  4.0E-12
   690  4.184680390E-05  1.827111107E-10  2.08E-13  1.01E-13  1.33E+01  8.10E+10  4.0E-12
   700  4.184680390E-05  1.827111107E-10  2.08E-13  1.33E-11  1.34E+01  8.17E+10  4.0E-12
   710  4.184680390E-05  1.827111107E-10  2.08E-13  2.15E-13  1.35E+01  8.22E+10  4.0E-12
   717  4.184680390E-05  1.827111107E-10  2.08E-13  1.49E-15  1.35E+01  8.26E+10  4.0E-12
   720  4.184680390E-05  1.827111107E-10  2.08E-13  2.56E-12  1.35E+01  8.26E+10  4.0E-12
   730  4.184680390E-05  1.827111107E-10  2.08E-13  6.83E-15  1.36E+01  8.32E+10  4.0E-12
   740  4.184680390E-05  1.827111107E-10  2.08E-13  4.31E-14  1.37E+01  8.39E+10  4.0E-12
   750  4.184680390E-05  1.827111107E-10  2.08E-13  2.76E-14  1.38E+01  8.44E+10  4.0E-12
   756  4.184680390E-05  1.827111107E-10  2.08E-13  2.47E-15  1.39E+01  8.48E+10  4.0E-12
   757  4.184680390E-05  1.827111107E-10  2.08E-13  2.05E-15  1.39E+01  8.48E+10  4.0E-12
   758  4.184680390E-05  1.827111107E-10  2.08E-13  9.36E-16  1.39E+01  8.48E+10  4.0E-12
   760  4.184680390E-05  1.827111107E-10  2.08E-13  1.33E-15  1.39E+01  8.49E+10  4.0E-12
   761  4.184680390E-05  1.827111107E-10  2.08E-13  4.24E-16  1.39E+01  8.51E+10  4.0E-12
   762  4.184680390E-05  1.827111107E-10  2.08E-13  3.48E-16  1.40E+01  8.52E+10  4.0E-12
   763  4.184680390E-05  1.827111107E-10  2.08E-13  1.55E-16  1.40E+01  8.52E+10  4.0E-12

 Exit  LSQR.       istop  = 3               itn    =     763
 Exit  LSQR.       Anorm  = 1.39596E+01     Acond  = 8.52081E+10
 Exit  LSQR.       bnorm  = 8.79805E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-10     Arnorm = 3.96505E-25
 Exit  LSQR.       max dx = 8.6E+02 occurred at itn        1
 Exit  LSQR.              = 4.7E-01*xnorm
 Exit  LSQR.       A damped least-squares solution was found, given atol


 Enter xcheck.     Does x solve Ax = b, etc?
    damp            = 1.000E-13
    norm(x)         = 1.827E+03
    norm(r)         = 9.21801355E-13 = rho1
    norm(A'r)       = 7.524E-13      = sigma1

    norm(s)         = 9.218E+00
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82713436E-10 = rho2
    norm(Abar'rbar) = 7.524E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.494E-17 (Ax = b)
    test2           = 5.847E-02 (least-squares)
    test3           = 2.950E-04 (damped least-squares)


 Solution  x:
     1  0.418468E-04     2  0.100048         3  0.200058         4  0.300073    
     5  0.400092         6  0.500116         7  0.600141         8  0.700171    


 LSQR  appears to be successful.
 Relative error in  x  =  6.58E-08
