

 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    2    1.00E-08 )

 Condition no. =  6.2500E+02     Residual function =  3.162277660E+01
 --------------------------------------------------------------------


 Enter acheck.     Test of aprod for LSQR and CRAIG
 aprod seems OK.   Relative error =   7.0E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 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
                                                                                    phi    dknorm   dxk  alfa_opt
     0  0.000000000E+00  1.250758627E+03  1.00E+00  6.62E-04

     1 -1.569523708E+01  4.508643183E+02  3.60E-01  7.04E-01  8.88E-01  1.00E+00  1.2E+03 1.1E+00 1.3E+03 5.5E-01
     2  2.895287270E+00  2.381656023E+02  1.90E-01  4.38E-01  1.18E+00  2.12E+00 -3.8E+02 1.4E+00 5.4E+02 2.9E-01
     3  6.914168784E+00  1.496722377E+02  1.20E-01  3.16E-01  1.39E+00  3.40E+00  1.9E+02 1.7E+00 3.1E+02 1.9E-01
     4  1.929180742E+00  1.044696696E+02  8.35E-02  2.43E-01  1.56E+00  4.82E+00 -1.1E+02 1.9E+00 2.0E+02 1.4E-01
     5 -4.030073311E+00  7.854670980E+01  6.28E-02  1.91E-01  1.70E+00  6.39E+00  6.9E+01 2.1E+00 1.5E+02 1.1E-01
     6 -8.170857369E+00  6.260650712E+01  5.01E-02  1.52E-01  1.83E+00  8.09E+00 -4.7E+01 2.4E+00 1.1E+02 9.0E-02
     7 -1.028185061E+01  5.237781045E+01  4.19E-02  1.20E-01  1.93E+00  9.92E+00  3.4E+01 2.6E+00 9.0E+01 7.6E-02
     8 -1.086059048E+01  4.564076779E+01  3.65E-02  9.39E-02  2.02E+00  1.19E+01 -2.6E+01 2.9E+00 7.4E+01 6.6E-02
     9 -1.044238556E+01  4.113093676E+01  3.29E-02  7.27E-02  2.09E+00  1.40E+01  2.0E+01 3.2E+00 6.3E+01 5.9E-02
    10 -9.437438588E+00  3.807969510E+01  3.04E-02  5.55E-02  2.15E+00  1.63E+01 -1.6E+01 3.5E+00 5.5E+01 5.3E-02

    20  8.976385404E-01  3.171296389E+01  2.54E-02  1.58E-03  2.55E+00  6.46E+01 -2.3E+00 1.4E+01 3.2E+01 2.6E-02

    30  9.266202721E-01  3.162326291E+01  2.53E-02  1.61E-04  3.15E+00  2.80E+02 -4.5E-01 6.8E+01 3.1E+01 1.4E-02

    40  4.463025060E-01  3.162278316E+01  2.53E-02  1.44E-06  3.66E+00  6.60E+02 -6.4E-04 1.9E+01 1.2E-02 9.8E-03

    50  1.000001656E-01  3.162277660E+01  2.53E-02  4.82E-09  4.14E+00  2.69E+03 -2.6E-06 1.9E+00 4.9E-06 5.2E-03

    60  9.999999981E-02  3.162277660E+01  2.53E-02  2.23E-12  4.50E+00  2.93E+03 -2.3E-09 1.5E+01 3.5E-08 5.2E-03

    66  9.999999998E-02  3.162277660E+01  2.53E-02  1.06E-15  4.71E+00  3.07E+03 -3.6E-12 2.5E+00 8.9E-12 5.2E-03
    70  9.999999998E-02  3.162277660E+01  2.53E-02  1.88E-15  4.86E+00  3.17E+03 -2.9E-12 1.9E+01 5.6E-11 5.2E-03

    71  9.999999998E-02  3.162277660E+01  2.53E-02  1.25E-15  4.91E+00  3.20E+03  4.2E-13 3.2E+00 1.3E-12 5.2E-03
    72  9.999999998E-02  3.162277660E+01  2.53E-02  1.51E-17  4.94E+00  3.22E+03 -6.9E-13 6.2E+00 4.3E-12 5.2E-03

 Exit  LSQR.       istop  = 3               itn    =      72
 Exit  LSQR.       anorm  = 4.94062E+00     acond  = 3.22385E+03
 Exit  LSQR.       bnorm  = 1.25076E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 2.35170E-15
 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)         = 3.16227766E+01 = rho1
    norm(A'r)       = 7.623E-13      = sigma1

    norm(s)         = 3.162E+09
    norm(x,s)       = 3.162E+09
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 7.905E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 3.077E-03 (Ax = b)
    test2           = 4.879E-15 (least-squares)
    test3           = 5.060E-15 (damped least-squares)


 Solution  x:
     1  0.100000E+00     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  =  9.37E-14


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    3    1.00E-09 )

 Condition no. =  1.5625E+04     Residual function =  3.162277660E+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-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
                                                                                    phi    dknorm   dxk  alfa_opt
     0  0.000000000E+00  1.124758738E+03  1.00E+00  7.28E-04

     1 -2.024780599E+01  4.445459391E+02  3.95E-01  6.73E-01  8.91E-01  1.00E+00  1.0E+03 1.1E+00 1.2E+03 5.8E-01
     2 -4.437078376E+00  2.497498983E+02  2.22E-01  4.11E-01  1.18E+00  2.15E+00 -3.7E+02 1.4E+00 5.3E+02 3.1E-01
     3  7.016884706E+00  1.633307620E+02  1.45E-01  2.93E-01  1.38E+00  3.47E+00  1.9E+02 1.7E+00 3.3E+02 2.1E-01
     4  1.026274765E+01  1.165741020E+02  1.04E-01  2.22E-01  1.54E+00  4.95E+00 -1.1E+02 2.0E+00 2.3E+02 1.5E-01
     5  8.511358718E+00  8.827921379E+01  7.85E-02  1.73E-01  1.66E+00  6.61E+00  7.6E+01 2.3E+00 1.8E+02 1.2E-01
     6  4.564132190E+00  6.995558376E+01  6.22E-02  1.35E-01  1.76E+00  8.45E+00 -5.4E+01 2.7E+00 1.5E+02 9.3E-02
     7  6.893647511E-02  5.760137809E+01  5.12E-02  1.05E-01  1.83E+00  1.05E+01  4.0E+01 3.1E+00 1.2E+02 7.7E-02
     8 -4.112941580E+00  4.909607612E+01  4.37E-02  8.05E-02  1.89E+00  1.28E+01 -3.0E+01 3.6E+00 1.1E+02 6.5E-02
     9 -7.562719628E+00  4.320398305E+01  3.84E-02  5.99E-02  1.93E+00  1.54E+01  2.3E+01 4.2E+00 9.7E+01 5.6E-02
    10 -1.009825707E+01  3.914274191E+01  3.48E-02  4.32E-02  1.96E+00  1.83E+01 -1.8E+01 4.9E+00 9.0E+01 4.9E-02

    20 -5.040230267E+00  3.174137352E+01  2.82E-02  9.61E-04  2.54E+00  9.50E+01 -3.9E-01 3.4E+00 1.3E+00 2.2E-02

    30  8.265763387E-01  3.162623208E+01  2.81E-02  2.19E-03  2.98E+00  3.77E+02 -2.9E-01 7.5E+01 2.2E+01 1.2E-02

    40  1.472516426E+00  3.162289257E+01  2.81E-02  2.01E-06  3.51E+00  1.03E+03 -1.7E-03 8.7E+00 1.5E-02 7.7E-03

    50  1.062876863E+00  3.162278139E+01  2.81E-02  2.61E-07  3.92E+00  2.55E+03 -3.8E-04 4.1E+01 1.6E-02 5.2E-03

    60  4.710610499E-01  3.162277661E+01  2.81E-02  2.56E-07  4.24E+00  8.74E+03 -3.0E-04 3.6E+01 1.1E-02 2.9E-03

    70  4.704179285E-01  3.162277661E+01  2.81E-02  3.79E-08  4.58E+00  9.89E+03 -2.1E-05 3.7E+02 7.5E-03 2.8E-03

    80  1.000449459E-01  3.162277660E+01  2.81E-02  2.65E-08  4.89E+00  7.70E+04 -2.5E-05 4.5E+02 1.1E-02 1.0E-03

    90  1.000000204E-01  3.162277660E+01  2.81E-02  5.48E-12  5.17E+00  8.15E+04 -2.0E-09 1.6E+01 3.2E-08 1.0E-03

   100  1.000000134E-01  3.162277660E+01  2.81E-02  1.36E-14  5.48E+00  8.64E+04 -6.8E-12 3.4E+00 2.4E-11 1.0E-03

   105  1.000000130E-01  3.162277660E+01  2.81E-02  2.93E-16  5.69E+00  8.96E+04  1.5E-12 1.5E+00 2.2E-12 1.0E-03

 Exit  LSQR.       istop  = 3               itn    =     105
 Exit  LSQR.       anorm  = 5.68664E+00     acond  = 8.96364E+04
 Exit  LSQR.       bnorm  = 1.12476E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 5.26981E-14
 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)         = 3.16227766E+01 = rho1
    norm(A'r)       = 6.823E-13      = sigma1

    norm(s)         = 3.162E+10
    norm(x,s)       = 3.162E+10
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 6.819E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.746E-03 (Ax = b)
    test2           = 3.794E-15 (least-squares)
    test3           = 3.792E-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  =  4.06E-11


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    4    1.00E-10 )

 Condition no. =  3.9062E+05     Residual function =  3.162277660E+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-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
                                                                                    phi    dknorm   dxk  alfa_opt
     0  0.000000000E+00  1.036803633E+03  1.00E+00  7.88E-04

     1 -2.290522293E+01  4.288179200E+02  4.14E-01  6.51E-01  8.98E-01  1.00E+00  9.4E+02 1.1E+00 1.1E+03 6.1E-01
     2 -1.229519129E+01  2.473115009E+02  2.39E-01  3.92E-01  1.18E+00  2.16E+00 -3.5E+02 1.5E+00 5.1E+02 3.2E-01
     3  2.912832494E-01  1.637962341E+02  1.58E-01  2.74E-01  1.37E+00  3.52E+00  1.9E+02 1.8E+00 3.3E+02 2.1E-01
     4  8.372079751E+00  1.171216132E+02  1.13E-01  2.03E-01  1.51E+00  5.07E+00 -1.1E+02 2.2E+00 2.5E+02 1.5E-01
     5  1.186968037E+01  8.809237204E+01  8.50E-02  1.54E-01  1.61E+00  6.84E+00  7.7E+01 2.6E+00 2.0E+02 1.2E-01
     6  1.189447236E+01  6.891427148E+01  6.65E-02  1.16E-01  1.68E+00  8.87E+00 -5.5E+01 3.1E+00 1.7E+02 9.0E-02
     7  9.555842886E+00  5.587265850E+01  5.39E-02  8.60E-02  1.73E+00  1.12E+01  4.0E+01 3.8E+00 1.5E+02 7.3E-02
     8  5.773292099E+00  4.696743386E+01  4.53E-02  6.16E-02  1.76E+00  1.40E+01 -3.0E+01 4.6E+00 1.4E+02 6.0E-02
     9  1.300148876E+00  4.098569994E+01  3.95E-02  4.20E-02  1.79E+00  1.75E+01  2.3E+01 5.7E+00 1.3E+02 5.0E-02
    10 -3.232558656E+00  3.709579579E+01  3.58E-02  2.71E-02  1.80E+00  2.18E+01 -1.7E+01 7.1E+00 1.2E+02 4.2E-02

    20 -1.047331587E+01  3.168657934E+01  3.06E-02  3.88E-04  2.42E+00  1.47E+02 -2.0E-01 3.7E+00 7.3E-01 1.7E-02

    30 -2.132582570E+00  3.162440981E+01  3.05E-02  2.37E-05  2.95E+00  6.28E+02 -1.0E-02 3.3E+00 3.3E-02 9.0E-03

    40  1.968519814E-01  3.162303561E+01  3.05E-02  4.40E-05  3.36E+00  1.50E+03 -3.7E-02 1.8E+02 6.7E+00 6.2E-03

    50  1.512203568E+00  3.162278175E+01  3.05E-02  4.93E-05  3.76E+00  6.13E+03 -2.3E-02 7.6E+02 1.7E+01 3.3E-03

    60  1.506677286E+00  3.162277863E+01  3.05E-02  8.39E-07  4.11E+00  8.59E+03 -7.3E-04 3.0E+02 2.2E-01 2.9E-03

    70  1.107467137E+00  3.162277664E+01  3.05E-02  1.32E-09  4.42E+00  2.26E+04 -3.9E-07 2.2E+00 8.6E-07 1.8E-03

    80  1.093040654E+00  3.162277664E+01  3.05E-02  2.76E-08  4.72E+00  2.99E+04 -1.9E-05 3.1E+02 5.8E-03 1.7E-03

    90  4.760857630E-01  3.162277660E+01  3.05E-02  1.49E-09  5.02E+00  1.25E+05 -1.7E-05 2.9E+02 4.9E-03 8.3E-04

   100  4.760755607E-01  3.162277660E+01  3.05E-02  4.86E-11  5.27E+00  1.31E+05 -2.8E-08 6.4E+01 1.8E-06 8.3E-04

   110  4.363931561E-01  3.162277660E+01  3.05E-02  1.69E-08  5.52E+00  7.14E+05 -1.1E-05 1.3E+05 1.5E+00 3.7E-04

   120  2.855415358E-01  3.162277660E+01  3.05E-02  8.20E-10  5.78E+00  1.61E+06 -5.4E-07 6.0E+03 3.2E-03 2.5E-04

   130  9.999278444E-02  3.162277660E+01  3.05E-02  3.05E-12  6.04E+00  2.36E+06 -2.6E-09 2.9E+01 7.3E-08 2.1E-04

   140  9.999244459E-02  3.162277660E+01  3.05E-02  1.18E-12  6.26E+00  2.45E+06 -8.9E-10 8.5E+01 7.6E-08 2.1E-04

   150  9.999227011E-02  3.162277660E+01  3.05E-02  7.52E-14  6.46E+00  2.53E+06 -4.8E-11 1.0E+01 4.9E-10 2.1E-04

   153  9.999226680E-02  3.162277660E+01  3.05E-02  4.79E-16  6.51E+00  2.55E+06  5.9E-11 1.4E+01 8.2E-10 2.1E-04
   154  9.999226680E-02  3.162277660E+01  3.05E-02  3.93E-17  6.59E+00  2.58E+06 -9.9E-14 1.0E+00 1.0E-13 2.1E-04

 Exit  LSQR.       istop  = 3               itn    =     154
 Exit  LSQR.       anorm  = 6.58996E+00     acond  = 2.57947E+06
 Exit  LSQR.       bnorm  = 1.03680E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 8.19002E-15
 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)         = 3.16227766E+01 = rho1
    norm(A'r)       = 4.957E-13      = sigma1

    norm(s)         = 3.162E+11
    norm(x,s)       = 3.162E+11
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 4.957E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.418E-03 (Ax = b)
    test2           = 2.379E-15 (least-squares)
    test3           = 2.379E-15 (damped least-squares)


 Solution  x:
     1  0.999923E-01     2  0.199994         3  0.299992         4  0.399996    
     5  0.499990         6  0.599994         7  0.699992         8  0.799990    

 LSQR  appears to be successful.     Relative error in  x  =  2.69E-08


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    5    1.00E-11 )

 Condition no. =  9.7656E+06     Residual function =  3.162277660E+01
 --------------------------------------------------------------------


 Enter acheck.     Test of aprod for LSQR and CRAIG
 aprod seems OK.   Relative error =   3.4E-16


 Enter LSQR.       Least-squares solution of  Ax = b
 The matrix  A  has   2000 rows   and   1000 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
                                                                                    phi    dknorm   dxk  alfa_opt
     0  0.000000000E+00  9.715494276E+02  1.00E+00  8.45E-04

     1 -2.412106256E+01  4.116661440E+02  4.24E-01  6.34E-01  9.06E-01  1.00E+00  8.8E+02 1.1E+00 9.7E+02 6.2E-01
     2 -1.824596476E+01  2.396665255E+02  2.47E-01  3.74E-01  1.18E+00  2.18E+00 -3.3E+02 1.5E+00 4.9E+02 3.3E-01
     3 -7.118201010E+00  1.585407904E+02  1.63E-01  2.56E-01  1.36E+00  3.57E+00  1.8E+02 1.9E+00 3.4E+02 2.1E-01
     4  2.622411370E+00  1.122939257E+02  1.16E-01  1.84E-01  1.47E+00  5.19E+00 -1.1E+02 2.3E+00 2.6E+02 1.5E-01
     5  9.349109039E+00  8.319677884E+01  8.56E-02  1.34E-01  1.55E+00  7.12E+00  7.5E+01 2.9E+00 2.2E+02 1.1E-01
     6  1.286861549E+01  6.400704762E+01  6.59E-02  9.65E-02  1.60E+00  9.44E+00 -5.3E+01 3.7E+00 2.0E+02 8.4E-02
     7  1.344322975E+01  5.123459726E+01  5.27E-02  6.67E-02  1.63E+00  1.23E+01  3.8E+01 4.7E+00 1.8E+02 6.5E-02
     8  1.153767000E+01  4.292240575E+01  4.42E-02  4.35E-02  1.65E+00  1.60E+01 -2.8E+01 6.1E+00 1.7E+02 5.2E-02
     9  7.760937412E+00  3.776481275E+01  3.89E-02  2.63E-02  1.66E+00  2.08E+01  2.0E+01 8.0E+00 1.6E+02 4.3E-02
    10  2.839816142E+00  3.476091919E+01  3.58E-02  1.47E-02  1.67E+00  2.74E+01 -1.5E+01 1.1E+01 1.6E+02 3.5E-02

    20 -1.336969948E+01  3.166075481E+01  3.26E-02  3.64E-04  2.29E+00  2.00E+02 -7.4E-02 5.1E+00 3.8E-01 1.4E-02

    30 -6.083030011E+00  3.162348609E+01  3.25E-02  3.92E-05  2.77E+00  1.04E+03 -1.7E-01 1.3E+02 2.2E+01 6.8E-03

    40 -2.662235686E+00  3.162289174E+01  3.25E-02  2.07E-04  3.22E+00  2.50E+03 -2.2E-02 3.4E+02 7.4E+00 4.7E-03

    50 -2.732264356E-01  3.162279151E+01  3.25E-02  1.99E-05  3.62E+00  5.31E+03 -2.4E-03 2.5E+02 5.9E-01 3.4E-03

    60  1.201613436E+00  3.162277770E+01  3.25E-02  5.67E-07  4.02E+00  1.40E+04 -3.6E-04 4.2E+02 1.5E-01 2.2E-03

    70  1.561188758E+00  3.162277664E+01  3.25E-02  1.08E-08  4.34E+00  4.41E+04 -7.4E-05 1.3E+02 9.5E-03 1.3E-03

    80  1.560424732E+00  3.162277664E+01  3.25E-02  1.90E-08  4.61E+00  4.75E+04 -6.0E-05 1.6E+03 9.6E-02 1.3E-03

    90  1.132677258E+00  3.162277660E+01  3.25E-02  5.43E-09  4.89E+00  2.01E+05 -3.0E-05 8.0E+02 2.4E-02 6.5E-04

   100  1.124357793E+00  3.162277660E+01  3.25E-02  5.21E-11  5.15E+00  2.14E+05 -5.0E-08 9.2E+01 4.6E-06 6.5E-04

   110  1.124338681E+00  3.162277660E+01  3.25E-02  1.11E-09  5.40E+00  2.24E+05 -6.9E-07 1.7E+03 1.2E-03 6.5E-04

   120  7.263829581E-01  3.162277660E+01  3.25E-02  5.94E-08  5.65E+00  1.37E+06 -2.1E-05 5.1E+04 1.0E+00 2.7E-04

   130  4.772327335E-01  3.162277660E+01  3.25E-02  5.49E-11  5.93E+00  1.83E+06 -3.8E-06 9.6E+03 3.7E-02 2.4E-04

   140  4.772313748E-01  3.162277660E+01  3.25E-02  1.12E-14  6.15E+00  1.89E+06 -4.7E-11 1.6E+01 7.6E-10 2.4E-04

   150  4.772313728E-01  3.162277660E+01  3.25E-02  1.22E-12  6.33E+00  1.95E+06 -3.8E-10 2.5E+02 9.5E-08 2.4E-04

   157  4.772310992E-01  3.162277660E+01  3.25E-02  1.48E-15  6.52E+00  2.01E+06  4.6E-11 3.1E+01 1.4E-09 2.4E-04
   158  4.772310992E-01  3.162277660E+01  3.25E-02  1.56E-15  6.53E+00  2.01E+06 -1.4E-12 4.5E+00 6.2E-12 2.4E-04
   159  4.772310992E-01  3.162277660E+01  3.25E-02  2.75E-15  6.53E+00  2.01E+06  1.1E-11 5.1E+01 5.7E-10 2.4E-04
   160  4.772310992E-01  3.162277660E+01  3.25E-02  1.39E-15  6.56E+00  2.02E+06 -9.8E-13 4.8E+00 4.7E-12 2.4E-04

   161  4.772310992E-01  3.162277660E+01  3.25E-02  2.64E-15  6.57E+00  2.02E+06  1.5E-12 9.0E+00 1.3E-11 2.4E-04
   164  4.772310992E-01  3.162277660E+01  3.25E-02  1.77E-15  6.66E+00  2.05E+06 -2.2E-12 1.4E+01 3.0E-11 2.4E-04
   170  4.771614020E-01  3.162277660E+01  3.25E-02  6.04E-11  6.73E+00  2.25E+06 -1.9E-08 1.3E+05 2.5E-03 2.3E-04

   180  4.718174168E-01  3.162277660E+01  3.25E-02  5.01E-10  6.92E+00  8.25E+06 -1.1E-07 7.8E+05 8.7E-02 1.2E-04

   190  4.151011102E-01  3.162277660E+01  3.25E-02  4.60E-11  7.18E+00  2.81E+07 -6.9E-08 4.8E+05 3.3E-02 6.6E-05

   200  1.137866609E-01  3.162277660E+01  3.25E-02  3.78E-11  7.35E+00  6.94E+07 -6.7E-07 4.6E+06 3.1E+00 4.3E-05

   210  8.860577850E-02  3.162277660E+01  3.25E-02  4.89E-15  7.53E+00  7.36E+07 -1.2E-10 8.4E+02 1.0E-07 4.2E-05

   220  8.860567896E-02  3.162277660E+01  3.25E-02  7.69E-14  7.69E+00  7.52E+07 -5.1E-10 3.7E+03 1.9E-06 4.2E-05

   224  8.860567650E-02  3.162277660E+01  3.25E-02  5.59E-17  7.78E+00  7.60E+07 -1.3E-12 9.1E+00 1.1E-11 4.2E-05

 Exit  LSQR.       istop  = 3               itn    =     224
 Exit  LSQR.       anorm  = 7.77584E+00     acond  = 7.59737E+07
 Exit  LSQR.       bnorm  = 9.71549E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 1.37365E-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-11
    norm(x)         = 1.827E+03
    norm(r)         = 3.16227766E+01 = rho1
    norm(A'r)       = 9.817E-13      = sigma1

    norm(s)         = 3.162E+12
    norm(x,s)       = 3.162E+12
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 9.817E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.083E-03 (Ax = b)
    test2           = 3.992E-15 (least-squares)
    test3           = 3.992E-15 (damped least-squares)


 Solution  x:
     1  0.886057E-01     2  0.188282         3  0.288714         4  0.388858    
     5  0.487640         6  0.587637         7  0.689307         8  0.787809    

 LSQR  appears to be successful.     Relative error in  x  =  4.22E-05


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    6    1.00E-12 )

 Condition no. =  2.4414E+08     Residual function =  3.162277660E+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-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
                                                                                    phi    dknorm   dxk  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  8.3E+02 1.1E+00 9.1E+02 6.3E-01
     2 -2.224414133E+01  2.299330660E+02  2.50E-01  3.58E-01  1.18E+00  2.19E+00 -3.2E+02 1.5E+00 4.8E+02 3.3E-01
     3 -1.321097804E+01  1.506103812E+02  1.64E-01  2.38E-01  1.34E+00  3.62E+00  1.7E+02 2.0E+00 3.4E+02 2.1E-01
     4 -3.367416062E+00  1.049231607E+02  1.14E-01  1.66E-01  1.44E+00  5.35E+00 -1.1E+02 2.6E+00 2.8E+02 1.4E-01
     5  5.036316961E+00  7.625044968E+01  8.28E-02  1.15E-01  1.50E+00  7.50E+00  7.2E+01 3.3E+00 2.4E+02 1.0E-01
     6  1.099397591E+01  5.775402438E+01  6.27E-02  7.77E-02  1.53E+00  1.02E+01 -5.0E+01 4.4E+00 2.2E+02 7.6E-02
     7  1.404999112E+01  4.603739639E+01  5.00E-02  4.91E-02  1.55E+00  1.39E+01  3.5E+01 5.9E+00 2.1E+02 5.8E-02
     8  1.413848446E+01  3.901907185E+01  4.24E-02  2.85E-02  1.56E+00  1.88E+01 -2.4E+01 8.1E+00 2.0E+02 4.5E-02
     9  1.156137863E+01  3.514014542E+01  3.82E-02  1.50E-02  1.57E+00  2.59E+01  1.7E+01 1.1E+01 1.9E+02 3.6E-02
    10  6.963640872E+00  3.317616216E+01  3.60E-02  7.17E-03  1.57E+00  3.61E+01 -1.2E+01 1.6E+01 1.9E+02 2.9E-02

    20 -1.261939645E+01  3.164984153E+01  3.44E-02  1.28E-03  2.19E+00  2.47E+02 -9.0E-02 1.2E+01 1.0E+00 1.3E-02

    30 -1.025547906E+01  3.162318472E+01  3.43E-02  2.41E-05  2.85E+00  1.60E+03 -1.6E-01 2.4E+02 3.9E+01 5.6E-03

    40 -6.772318199E+00  3.162284325E+01  3.43E-02  1.49E-05  3.21E+00  3.54E+03 -2.4E-03 8.2E+01 1.9E-01 4.0E-03

    50 -3.176427368E+00  3.162278464E+01  3.43E-02  1.20E-06  3.64E+00  9.27E+03 -1.7E-03 4.0E+02 6.7E-01 2.6E-03

    60 -4.553109570E-01  3.162277728E+01  3.43E-02  1.64E-07  3.95E+00  2.27E+04 -1.5E-04 7.0E+01 1.0E-02 1.7E-03

    70  9.732699748E-01  3.162277671E+01  3.43E-02  1.60E-07  4.32E+00  6.79E+04 -3.6E-05 8.8E+01 3.2E-03 1.1E-03

    80  1.171485938E+00  3.162277663E+01  3.43E-02  4.16E-10  4.62E+00  7.71E+04 -1.4E-05 5.5E+02 7.6E-03 1.0E-03

    90  1.572724174E+00  3.162277660E+01  3.43E-02  1.59E-09  4.87E+00  3.01E+05 -1.4E-06 5.9E+01 8.0E-05 5.3E-04

   100  1.574463231E+00  3.162277660E+01  3.43E-02  8.74E-11  5.10E+00  3.16E+05 -2.4E-07 1.9E+01 4.7E-06 5.3E-04

   110  1.574284185E+00  3.162277660E+01  3.43E-02  6.30E-11  5.38E+00  3.36E+05 -2.0E-08 3.6E+01 7.1E-07 5.3E-04

   120  1.141246616E+00  3.162277660E+01  3.43E-02  5.95E-09  5.60E+00  1.89E+06 -3.9E-05 7.1E+04 2.8E+00 2.3E-04

   130  1.131290044E+00  3.162277660E+01  3.43E-02  1.59E-11  5.81E+00  1.98E+06 -6.3E-07 1.5E+03 9.7E-04 2.3E-04

   140  1.131298916E+00  3.162277660E+01  3.43E-02  1.55E-11  6.01E+00  2.05E+06 -1.1E-08 8.1E+01 8.7E-07 2.3E-04

   150  1.131195479E+00  3.162277660E+01  3.43E-02  4.42E-13  6.31E+00  2.17E+06 -2.0E-10 7.5E+01 1.5E-08 2.2E-04

   160  1.131187165E+00  3.162277660E+01  3.43E-02  4.29E-13  6.50E+00  2.23E+06 -5.7E-10 2.2E+02 1.3E-07 2.2E-04

   170  4.775640236E-01  3.162277660E+01  3.43E-02  2.84E-11  6.68E+00  2.56E+07 -4.2E-07 1.6E+05 7.0E-02 6.7E-05

   180  4.775468272E-01  3.162277660E+01  3.43E-02  2.05E-12  6.86E+00  2.63E+07 -4.4E-09 1.7E+03 7.5E-06 6.7E-05

   190  4.775273137E-01  3.162277660E+01  3.43E-02  3.65E-13  7.02E+00  2.69E+07 -2.1E-09 8.1E+02 1.7E-06 6.7E-05

   200  4.772488504E-01  3.162277660E+01  3.43E-02  3.48E-14  7.26E+00  2.78E+07 -1.6E-10 6.3E+01 1.0E-08 6.7E-05

   203  4.772488503E-01  3.162277660E+01  3.43E-02  6.47E-16  7.26E+00  2.78E+07  4.4E-11 2.6E+01 1.1E-09 6.7E-05
   204  4.772488503E-01  3.162277660E+01  3.43E-02  1.29E-15  7.27E+00  2.78E+07 -4.7E-13 3.1E+00 1.5E-12 6.7E-05
   205  4.772488503E-01  3.162277660E+01  3.43E-02  1.44E-15  7.31E+00  2.80E+07  9.3E-13 7.0E+00 6.5E-12 6.7E-05
   206  4.772488503E-01  3.162277660E+01  3.43E-02  9.00E-16  7.31E+00  2.80E+07 -1.7E-11 1.4E+02 2.3E-09 6.7E-05
   207  4.772488503E-01  3.162277660E+01  3.43E-02  1.17E-15  7.33E+00  2.81E+07  5.2E-13 4.9E+00 2.5E-12 6.7E-05
   208  4.772488503E-01  3.162277660E+01  3.43E-02  1.74E-15  7.36E+00  2.82E+07 -5.6E-13 5.6E+00 3.1E-12 6.7E-05
   209  4.772488503E-01  3.162277660E+01  3.43E-02  6.46E-17  7.41E+00  2.84E+07  9.4E-13 9.8E+00 9.3E-12 6.7E-05

 Exit  LSQR.       istop  = 3               itn    =     209
 Exit  LSQR.       anorm  = 7.40911E+00     acond  = 2.83762E+07
 Exit  LSQR.       bnorm  = 9.21079E+02     xnorm  = 1.82706E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 1.51381E-14
 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)         = 3.16227766E+01 = rho1
    norm(A'r)       = 5.216E-13      = sigma1

    norm(s)         = 3.162E+13
    norm(x,s)       = 3.162E+13
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 5.216E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.187E-03 (Ax = b)
    test2           = 2.226E-15 (least-squares)
    test3           = 2.226E-15 (damped least-squares)


 Solution  x:
     1  0.477249         2  0.476897         3  0.476662         4  0.476500    
     5  0.476299         6  0.475971         7  0.475399         8  0.475041    

 LSQR  appears to have failed.       Relative error in  x  =  7.58E-03


 --------------------------------------------------------------------
 Least-Squares Test Problem      P( 2000 1000   40    7    1.00E-13 )

 Condition no. =  6.1035E+09     Residual function =  3.162277660E+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-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
                                                                                    phi    dknorm   dxk  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  7.9E+02 1.1E+00 8.6E+02 6.4E-01
     2 -2.477913716E+01  2.193708762E+02  2.49E-01  3.41E-01  1.18E+00  2.20E+00 -3.1E+02 1.5E+00 4.7E+02 3.3E-01
     3 -1.776850890E+01  1.414330764E+02  1.61E-01  2.21E-01  1.32E+00  3.69E+00  1.7E+02 2.1E+00 3.5E+02 2.0E-01
     4 -8.448828545E+00  9.648095038E+01  1.10E-01  1.48E-01  1.40E+00  5.56E+00 -1.0E+02 2.8E+00 2.9E+02 1.4E-01
     5  7.462713431E-01  6.872328235E+01  7.80E-02  9.74E-02  1.44E+00  7.99E+00  6.8E+01 3.9E+00 2.6E+02 9.4E-02
     6  8.324225295E+00  5.155052189E+01  5.85E-02  6.06E-02  1.47E+00  1.13E+01 -4.5E+01 5.4E+00 2.4E+02 6.7E-02
     7  1.328456787E+01  4.146406784E+01  4.71E-02  3.44E-02  1.48E+00  1.60E+01  3.1E+01 7.6E+00 2.3E+02 5.0E-02
     8  1.508697417E+01  3.605910765E+01  4.09E-02  1.73E-02  1.48E+00  2.29E+01 -2.0E+01 1.1E+01 2.2E+02 3.9E-02
     9  1.370782345E+01  3.345655265E+01  3.80E-02  7.84E-03  1.49E+00  3.32E+01  1.3E+01 1.6E+01 2.2E+02 3.0E-02
    10  9.665346503E+00  3.233251419E+01  3.67E-02  1.69E-02  1.49E+00  4.92E+01 -8.6E+00 2.4E+01 2.1E+02 2.4E-02

    20 -1.212740117E+01  3.162905855E+01  3.59E-02  2.68E-05  2.31E+00  5.05E+02 -1.0E+00 1.8E+02 1.8E+02 9.1E-03

    30 -1.326350752E+01  3.162306611E+01  3.59E-02  1.13E-06  2.83E+00  2.08E+03 -8.2E-04 2.3E+00 1.9E-03 4.9E-03

    40 -9.869217608E+00  3.162281306E+01  3.59E-02  2.68E-05  3.19E+00  6.71E+03 -2.6E-02 1.5E+03 3.8E+01 2.9E-03

    50 -7.146126839E+00  3.162278240E+01  3.59E-02  8.50E-06  3.63E+00  1.25E+04 -2.4E-03 9.7E+02 2.3E+00 2.3E-03

    60 -3.516757348E+00  3.162277713E+01  3.59E-02  1.61E-08  3.92E+00  3.19E+04 -4.6E-05 1.8E+02 8.1E-03 1.5E-03

    70 -5.570194059E-01  3.162277663E+01  3.59E-02  7.58E-10  4.19E+00  9.78E+04 -5.8E-05 2.3E+02 1.3E-02 8.6E-04

    80 -5.569093646E-01  3.162277663E+01  3.59E-02  5.50E-08  4.55E+00  1.06E+05 -1.1E-05 6.3E+02 6.7E-03 8.6E-04

    90  1.153934307E+00  3.162277660E+01  3.59E-02  1.41E-08  4.84E+00  3.94E+05 -1.5E-05 9.0E+02 1.3E-02 4.6E-04

   100  1.155186839E+00  3.162277660E+01  3.59E-02  4.72E-12  5.06E+00  4.13E+05 -4.6E-08 4.4E+01 2.0E-06 4.6E-04

   110  1.158936896E+00  3.162277660E+01  3.59E-02  2.56E-10  5.27E+00  4.65E+05 -9.9E-06 1.6E+04 1.6E-01 4.4E-04

   120  1.581511370E+00  3.162277660E+01  3.59E-02  1.21E-11  5.56E+00  2.12E+06 -8.6E-09 1.5E+01 1.3E-07 2.1E-04

   130  1.581431264E+00  3.162277660E+01  3.59E-02  1.08E-10  5.75E+00  2.19E+06 -2.0E-06 4.1E+03 8.2E-03 2.1E-04

   140  1.581420279E+00  3.162277660E+01  3.59E-02  9.41E-12  5.94E+00  2.26E+06 -3.1E-09 3.9E+02 1.2E-06 2.1E-04

   150  1.554231297E+00  3.162277660E+01  3.59E-02  1.60E-11  6.23E+00  4.96E+06 -2.5E-07 3.2E+04 8.1E-03 1.5E-04

   160  1.550659861E+00  3.162277660E+01  3.59E-02  5.65E-11  6.38E+00  5.33E+06 -3.0E-08 3.7E+03 1.1E-04 1.4E-04

   170  1.134189463E+00  3.162277660E+01  3.59E-02  9.65E-13  6.57E+00  1.85E+07 -4.9E-10 6.2E+01 3.0E-08 7.8E-05

   180  1.134189222E+00  3.162277660E+01  3.59E-02  9.73E-12  6.78E+00  1.91E+07 -4.0E-09 6.2E+02 2.5E-06 7.8E-05

   188  1.134189158E+00  3.162277660E+01  3.59E-02  1.32E-15  6.94E+00  1.95E+07 -1.4E-10 4.2E+01 5.8E-09 7.8E-05
   190  1.134188757E+00  3.162277660E+01  3.59E-02  4.46E-12  6.94E+00  1.95E+07 -2.1E-09 7.6E+03 1.6E-05 7.8E-05

   196  1.134185903E+00  3.162277660E+01  3.59E-02  9.84E-16  7.09E+00  2.00E+07 -4.4E-12 1.6E+01 7.0E-11 7.8E-05
   197  1.134185903E+00  3.162277660E+01  3.59E-02  6.84E-16  7.09E+00  2.00E+07  2.0E-12 1.2E+01 2.3E-11 7.8E-05
   198  1.134185903E+00  3.162277660E+01  3.59E-02  1.54E-16  7.10E+00  2.00E+07 -8.3E-13 7.2E+00 6.0E-12 7.8E-05

 Exit  LSQR.       istop  = 3               itn    =     198
 Exit  LSQR.       anorm  = 7.09548E+00     acond  = 1.99869E+07
 Exit  LSQR.       bnorm  = 8.80846E+02     xnorm  = 1.82666E+03
 Exit  LSQR.       rnorm  = 3.16228E+01     arnorm = 3.45841E-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-13
    norm(x)         = 1.827E+03
    norm(r)         = 3.16227766E+01 = rho1
    norm(A'r)       = 9.556E-13      = sigma1

    norm(s)         = 3.162E+14
    norm(x,s)       = 3.162E+14
    norm(rbar)      = 3.16227766E+01 = rho2
    norm(Abar'rbar) = 9.556E-13      = sigma2

    inform          = 2
    tol             = 1.490E-08
    test1           = 2.285E-03 (Ax = b)
    test2           = 4.259E-15 (least-squares)
    test3           = 4.259E-15 (damped least-squares)


 Solution  x:
     1   1.13419         2   1.13396         3   1.13343         4   1.13296    
     5   1.13206         6   1.13106         7   1.12995         8   1.12863    

 LSQR  appears to have failed.       Relative error in  x  =  2.21E-02


 --------------------------------------------------------------------
 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 =   1.9E-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
                                                                                    phi    dknorm   dxk  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  1.2E+03 1.1E+00 1.3E+03 5.5E-01
     2  2.895287270E+00  2.360568875E+02  1.89E-01  4.42E-01  1.18E+00  2.12E+00 -3.8E+02 1.4E+00 5.4E+02 2.9E-01
     3  6.914168784E+00  1.462934678E+02  1.17E-01  3.24E-01  1.39E+00  3.40E+00  1.9E+02 1.7E+00 3.1E+02 1.9E-01
     4  1.929180742E+00  9.956862892E+01  7.96E-02  2.55E-01  1.56E+00  4.82E+00 -1.1E+02 1.9E+00 2.0E+02 1.4E-01
     5 -4.030073311E+00  7.189983046E+01  5.75E-02  2.09E-01  1.70E+00  6.39E+00  6.9E+01 2.1E+00 1.5E+02 1.1E-01
     6 -8.170857369E+00  5.403308925E+01  4.32E-02  1.76E-01  1.83E+00  8.09E+00 -4.7E+01 2.4E+00 1.1E+02 8.3E-02
     7 -1.028185061E+01  4.175446117E+01  3.34E-02  1.50E-01  1.93E+00  9.92E+00  3.4E+01 2.6E+00 9.0E+01 6.8E-02
     8 -1.086059048E+01  3.291017600E+01  2.63E-02  1.30E-01  2.02E+00  1.19E+01 -2.6E+01 2.9E+00 7.4E+01 5.6E-02
     9 -1.044238556E+01  2.630121592E+01  2.10E-02  1.14E-01  2.09E+00  1.40E+01  2.0E+01 3.2E+00 6.3E+01 4.7E-02
    10 -9.437438588E+00  2.121469253E+01  1.70E-02  9.96E-02  2.15E+00  1.63E+01 -1.6E+01 3.5E+00 5.5E+01 3.9E-02

    20  8.989311751E-01  2.389468663E+00  1.91E-03  1.96E-02  2.55E+00  6.46E+01 -2.3E+00 1.4E+01 3.2E+01 7.2E-03

    30  9.281365546E-01  1.820896376E-01  1.46E-04  4.94E-02  3.15E+00  2.79E+02 -4.1E-01 6.1E+01 2.5E+01 1.1E-03

    40  4.463434198E-01  2.037357388E-02  1.63E-05  2.00E-03  3.66E+00  6.59E+02 -5.6E-04 1.7E+01 9.3E-03 2.5E-04

    50  9.999971485E-02  1.890550349E-05  1.51E-08  3.08E-02  4.10E+00  2.67E+03 -5.3E-06 4.6E+00 2.5E-05 4.0E-06

    60  9.999999994E-02  1.827111108E-05  1.46E-08  3.45E-07  4.50E+00  2.93E+03 -2.1E-09 1.5E+01 3.3E-08 3.9E-06

    70  1.000000000E-01  1.827111108E-05  1.46E-08  1.02E-09  4.83E+00  3.15E+03 -6.0E-13 4.1E+00 2.5E-12 3.9E-06

    80  1.000000000E-01  1.827111108E-05  1.46E-08  1.80E-12  5.14E+00  3.38E+03 -2.9E-16 5.2E+00 1.5E-15 3.9E-06

    90  1.000000000E-01  1.827111108E-05  1.46E-08  1.05E-14  5.45E+00  3.68E+03 -3.5E-18 1.5E+01 5.3E-17 3.8E-06

   100  1.000000000E-01  1.827111108E-05  1.46E-08  4.63E-15  5.79E+00  5.33E+03 -1.0E-18 5.5E+00 5.7E-18 3.3E-06

   102  1.000000000E-01  1.827111108E-05  1.46E-08  3.09E-16  5.84E+00  5.37E+03 -3.8E-18 2.3E+01 8.6E-17 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 = 3.29871E-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)         = 1.52310042E-12 = rho1
    norm(A'r)       = 6.624E-13      = sigma1

    norm(s)         = 1.523E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-05 = rho2
    norm(Abar'rbar) = 5.612E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 1.278E-16 (Ax = b)
    test2           = 7.451E-02 (least-squares)
    test3           = 5.262E-09 (damped least-squares)


 Solution  x:
     1  0.100000E+00     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  =  1.04E-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
                                                                                    phi    dknorm   dxk  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  1.0E+03 1.1E+00 1.2E+03 5.8E-01
     2 -4.437078376E+00  2.477398064E+02  2.20E-01  4.15E-01  1.18E+00  2.15E+00 -3.7E+02 1.4E+00 5.3E+02 3.1E-01
     3  7.016884706E+00  1.602402503E+02  1.43E-01  2.99E-01  1.38E+00  3.47E+00  1.9E+02 1.7E+00 3.3E+02 2.0E-01
     4  1.026274765E+01  1.122030359E+02  9.98E-02  2.31E-01  1.54E+00  4.95E+00 -1.1E+02 2.0E+00 2.3E+02 1.5E-01
     5  8.511358718E+00  8.242098997E+01  7.33E-02  1.85E-01  1.66E+00  6.61E+00  7.6E+01 2.3E+00 1.8E+02 1.1E-01
     6  4.564132190E+00  6.240018990E+01  5.55E-02  1.52E-01  1.76E+00  8.45E+00 -5.4E+01 2.7E+00 1.5E+02 8.8E-02
     7  6.893647511E-02  4.814476875E+01  4.28E-02  1.26E-01  1.83E+00  1.05E+01  4.0E+01 3.1E+00 1.2E+02 7.0E-02
     8 -4.112941580E+00  3.755562129E+01  3.34E-02  1.05E-01  1.89E+00  1.28E+01 -3.0E+01 3.6E+00 1.1E+02 5.7E-02
     9 -7.562719628E+00  2.943780141E+01  2.62E-02  8.79E-02  1.93E+00  1.54E+01  2.3E+01 4.2E+00 9.7E+01 4.6E-02
    10 -1.009825707E+01  2.306846861E+01  2.05E-02  7.32E-02  1.96E+00  1.83E+01 -1.8E+01 4.9E+00 9.0E+01 3.8E-02

    20 -5.038748544E+00  2.740631534E+00  2.44E-03  1.32E-02  2.51E+00  9.39E+01 -2.1E-01 2.3E+00 4.6E-01 6.4E-03

    30  5.931390405E-01  5.390813542E-01  4.79E-04  3.82E-02  3.02E+00  3.19E+02 -8.4E-02 2.2E+01 1.8E+00 1.7E-03

    40  1.472496136E+00  8.564508202E-02  7.62E-05  4.96E-04  3.51E+00  1.03E+03 -1.8E-03 2.9E+00 5.0E-03 4.0E-04

    50  1.062480523E+00  1.740424505E-02  1.55E-05  7.54E-04  3.92E+00  2.56E+03 -5.9E-04 6.5E+01 3.8E-02 1.2E-04

    60  4.710576356E-01  8.738037104E-04  7.77E-07  6.29E-03  4.20E+00  8.64E+03 -3.4E-05 5.0E+00 1.7E-04 1.5E-05

    70  4.602569834E-01  8.588606556E-04  7.64E-07  1.43E-03  4.58E+00  1.55E+04 -4.7E-05 8.4E+02 3.9E-02 1.2E-05

    80  1.000120257E-01  5.102106555E-06  4.54E-09  2.19E-02  4.89E+00  7.70E+04 -8.4E-07 2.0E+01 1.7E-05 4.2E-07

    90  1.000000044E-01  1.827144408E-06  1.63E-09  8.31E-05  5.17E+00  8.14E+04 -1.1E-08 1.3E+01 1.5E-07 2.5E-07

   100  1.000000007E-01  1.827111458E-06  1.63E-09  3.69E-05  5.44E+00  8.57E+04 -5.9E-10 6.9E+01 4.1E-08 2.5E-07

   110  9.999999999E-02  1.827111108E-06  1.63E-09  1.66E-10  5.74E+00  9.05E+04 -1.7E-14 2.8E+00 4.8E-14 2.5E-07

   120  1.000000000E-01  1.827111108E-06  1.63E-09  4.98E-10  6.03E+00  9.51E+04 -1.7E-13 1.1E+02 1.9E-11 2.5E-07

   130  1.000000000E-01  1.827111108E-06  1.63E-09  4.91E-11  6.28E+00  9.94E+04 -1.6E-15 8.1E+02 1.3E-12 2.5E-07

   140  1.000000000E-01  1.827111108E-06  1.63E-09  1.21E-13  6.47E+00  1.03E+05 -5.0E-17 3.2E+01 1.6E-15 2.5E-07

   143  1.000000000E-01  1.827111108E-06  1.63E-09  1.32E-15  6.58E+00  1.05E+05  2.5E-19 5.9E+00 1.5E-18 2.5E-07
   145  1.000000000E-01  1.827111108E-06  1.63E-09  1.09E-15  6.60E+00  1.05E+05  1.3E-19 8.7E+00 1.1E-18 2.5E-07
   146  1.000000000E-01  1.827111108E-06  1.63E-09  1.33E-15  6.60E+00  1.05E+05 -6.8E-20 7.0E+00 4.8E-19 2.5E-07
   147  1.000000000E-01  1.827111108E-06  1.63E-09  1.96E-15  6.61E+00  1.05E+05  5.0E-20 6.0E+00 3.0E-19 2.5E-07
   149  1.000000000E-01  1.827111108E-06  1.63E-09  2.77E-15  6.70E+00  1.07E+05  1.6E-18 2.0E+02 3.1E-16 2.5E-07
   150  1.000000000E-01  1.827111108E-06  1.63E-09  1.18E-15  6.71E+00  1.07E+05 -9.9E-20 1.3E+01 1.3E-18 2.5E-07

   160  1.000000000E-01  1.827111108E-06  1.63E-09  5.56E-15  6.95E+00  1.54E+05 -2.2E-18 3.3E+02 7.2E-16 2.1E-07

   170  1.000000000E-01  1.827111108E-06  1.63E-09  1.62E-14  7.13E+00  1.59E+05 -1.2E-18 1.8E+02 2.1E-16 2.1E-07

   174  1.000000000E-01  1.827111108E-06  1.63E-09  1.26E-18  7.23E+00  1.61E+05 -4.3E-19 6.4E+01 2.7E-17 2.1E-07

 Exit  LSQR.       istop  = 3               itn    =     174
 Exit  LSQR.       anorm  = 7.22692E+00     acond  = 1.61087E+05
 Exit  LSQR.       bnorm  = 1.12431E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-06     arnorm = 1.66113E-23
 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)         = 8.40213541E-13 = rho1
    norm(A'r)       = 6.255E-13      = sigma1

    norm(s)         = 8.402E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-06 = rho2
    norm(Abar'rbar) = 6.251E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 5.864E-17 (Ax = b)
    test2           = 1.030E-01 (least-squares)
    test3           = 4.734E-08 (damped least-squares)


 Solution  x:
     1  0.100000E+00     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  =  1.08E-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 =   2.0E-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
                                                                                    phi    dknorm   dxk  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  9.4E+02 1.1E+00 1.1E+03 6.0E-01
     2 -1.229519129E+01  2.452814271E+02  2.37E-01  3.95E-01  1.18E+00  2.16E+00 -3.5E+02 1.5E+00 5.1E+02 3.2E-01
     3  2.912832494E-01  1.607146736E+02  1.55E-01  2.79E-01  1.37E+00  3.52E+00  1.9E+02 1.8E+00 3.3E+02 2.1E-01
     4  8.372079751E+00  1.127717708E+02  1.09E-01  2.11E-01  1.51E+00  5.07E+00 -1.1E+02 2.2E+00 2.5E+02 1.5E-01
     5  1.186968037E+01  8.222083684E+01  7.93E-02  1.65E-01  1.61E+00  6.84E+00  7.7E+01 2.6E+00 2.0E+02 1.1E-01
     6  1.189447236E+01  6.123052191E+01  5.91E-02  1.31E-01  1.68E+00  8.87E+00 -5.5E+01 3.1E+00 1.7E+02 8.5E-02
     7  9.555842886E+00  4.606250067E+01  4.44E-02  1.04E-01  1.73E+00  1.12E+01  4.0E+01 3.8E+00 1.5E+02 6.6E-02
     8  5.773292099E+00  3.472664457E+01  3.35E-02  8.33E-02  1.76E+00  1.40E+01 -3.0E+01 4.6E+00 1.4E+02 5.1E-02
     9  1.300148876E+00  2.607350378E+01  2.52E-02  6.60E-02  1.79E+00  1.75E+01  2.3E+01 5.7E+00 1.3E+02 4.0E-02
    10 -3.232558662E+00  1.939324792E+01  1.87E-02  5.18E-02  1.80E+00  2.18E+01 -1.7E+01 7.1E+00 1.2E+02 3.1E-02

    20 -1.047254331E+01  2.009590105E+00  1.94E-03  7.06E-03  2.41E+00  1.46E+02 -1.0E-01 2.7E+00 2.8E-01 4.3E-03

    30 -2.137245974E+00  3.221402721E-01  3.11E-04  1.18E-02  2.89E+00  6.15E+02 -2.2E-02 7.3E+00 1.6E-01 9.1E-04

    40  8.995872471E-01  8.300854984E-02  8.01E-05  2.04E-02  3.36E+00  2.19E+03 -1.1E-01 5.2E+02 5.5E+01 2.6E-04

    50  1.530312732E+00  1.305086448E-02  1.26E-05  2.53E-02  3.76E+00  6.32E+03 -3.2E-02 1.1E+03 3.5E+01 6.5E-05

    60  1.486107173E+00  1.103914376E-02  1.07E-05  1.31E-02  4.06E+00  9.50E+03 -1.4E-03 5.7E+02 7.9E-01 5.1E-05

    70  1.107467995E+00  1.492425368E-03  1.44E-06  2.95E-05  4.40E+00  2.25E+04 -1.2E-05 1.3E+01 1.6E-04 1.3E-05

    80  1.099603724E+00  1.483272895E-03  1.43E-06  9.85E-03  4.70E+00  2.72E+04 -1.4E-04 2.3E+03 3.2E-01 1.2E-05

    90  4.760838699E-01  3.567067302E-05  3.44E-08  1.38E-02  4.97E+00  1.24E+05 -1.5E-05 2.6E+02 4.0E-03 8.8E-07

   100  4.760759988E-01  3.534403253E-05  3.41E-08  1.13E-05  5.25E+00  1.31E+05 -7.7E-09 6.3E+01 4.9E-07 8.8E-07

   110  4.696160834E-01  3.504089573E-05  3.38E-08  5.14E-04  5.52E+00  3.14E+05 -4.1E-06 4.5E+04 1.8E-01 5.8E-07

   120  4.666640910E-01  3.490144062E-05  3.37E-08  6.09E-04  5.78E+00  3.84E+05 -1.3E-06 1.4E+04 1.7E-02 5.4E-07

   130  1.000056352E-01  2.344254038E-07  2.26E-10  2.35E-02  6.03E+00  2.36E+06 -5.4E-07 6.0E+03 3.3E-03 1.8E-08

   140  1.000000249E-01  1.829710650E-07  1.77E-10  2.44E-04  6.25E+00  2.45E+06 -1.2E-09 2.1E+01 2.5E-08 1.6E-08

   150  9.999999903E-02  1.827204515E-07  1.76E-10  5.25E-04  6.40E+00  2.51E+06 -7.9E-10 5.3E+01 4.2E-08 1.6E-08

   160  9.999999832E-02  1.827111443E-07  1.76E-10  3.34E-05  6.64E+00  2.60E+06 -7.6E-11 1.6E+03 1.2E-07 1.6E-08

   170  1.000000001E-01  1.827111108E-07  1.76E-10  1.02E-09  6.86E+00  2.69E+06 -2.4E-12 5.1E+01 1.2E-10 1.6E-08

   180  1.000000001E-01  1.827111108E-07  1.76E-10  2.23E-09  7.06E+00  2.76E+06 -1.2E-14 5.7E+01 7.0E-13 1.6E-08

   190  1.000000001E-01  1.827111108E-07  1.76E-10  2.49E-11  7.25E+00  2.84E+06 -1.8E-15 8.0E+02 1.5E-12 1.6E-08

   200  1.000000001E-01  1.827111108E-07  1.76E-10  8.77E-10  7.45E+00  2.92E+06 -2.6E-15 1.8E+03 4.7E-12 1.6E-08

   210  1.000000001E-01  1.827111108E-07  1.76E-10  4.78E-11  7.64E+00  3.00E+06 -4.2E-16 2.9E+02 1.2E-13 1.6E-08

   217  1.000000001E-01  1.827111108E-07  1.76E-10  2.04E-15  7.79E+00  3.06E+06  6.9E-20 3.3E+00 2.3E-19 1.6E-08
   220  1.000000001E-01  1.827111108E-07  1.76E-10  5.87E-13  7.81E+00  3.06E+06 -1.3E-18 4.4E+02 5.7E-16 1.6E-08

   225  1.000000001E-01  1.827111108E-07  1.76E-10  2.72E-15  7.94E+00  3.11E+06  2.9E-20 1.2E+01 3.5E-19 1.6E-08
   227  1.000000001E-01  1.827111108E-07  1.76E-10  2.41E-15  7.95E+00  3.12E+06  1.0E-19 4.9E+01 4.9E-18 1.6E-08
   229  1.000000001E-01  1.827111108E-07  1.76E-10  5.93E-16  7.99E+00  3.14E+06  5.1E-20 2.9E+01 1.5E-18 1.6E-08
   230  1.000000001E-01  1.827111108E-07  1.76E-10  1.54E-14  7.99E+00  3.14E+06 -7.4E-20 9.5E+01 7.0E-18 1.6E-08

   231  1.000000001E-01  1.827111108E-07  1.76E-10  1.39E-15  8.06E+00  3.16E+06  2.4E-20 3.1E+01 7.3E-19 1.6E-08
   232  1.000000001E-01  1.827111108E-07  1.76E-10  1.43E-16  8.06E+00  3.16E+06 -1.2E-20 1.7E+01 2.1E-19 1.6E-08

 Exit  LSQR.       istop  = 3               itn    =     232
 Exit  LSQR.       anorm  = 8.05840E+00     acond  = 3.16065E+06
 Exit  LSQR.       bnorm  = 1.03632E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-07     arnorm = 2.11090E-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)         = 9.98544262E-13 = rho1
    norm(A'r)       = 6.655E-13      = sigma1

    norm(s)         = 9.985E-03
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-07 = rho2
    norm(Abar'rbar) = 6.655E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 6.336E-17 (Ax = b)
    test2           = 8.271E-02 (least-squares)
    test3           = 4.520E-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  =  4.53E-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 =   7.4E-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
                                                                                    phi    dknorm   dxk  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  8.8E+02 1.1E+00 9.7E+02 6.2E-01
     2 -1.824596476E+01  2.375711335E+02  2.45E-01  3.77E-01  1.18E+00  2.18E+00 -3.3E+02 1.5E+00 4.9E+02 3.3E-01
     3 -7.118201010E+00  1.553550200E+02  1.60E-01  2.61E-01  1.36E+00  3.57E+00  1.8E+02 1.9E+00 3.4E+02 2.1E-01
     4  2.622411370E+00  1.077493654E+02  1.11E-01  1.92E-01  1.47E+00  5.19E+00 -1.1E+02 2.3E+00 2.6E+02 1.5E-01
     5  9.349109039E+00  7.695260886E+01  7.92E-02  1.45E-01  1.55E+00  7.12E+00  7.5E+01 2.9E+00 2.2E+02 1.1E-01
     6  1.286861549E+01  5.564981711E+01  5.73E-02  1.11E-01  1.60E+00  9.44E+00 -5.3E+01 3.7E+00 2.0E+02 7.8E-02
     7  1.344322975E+01  4.031108974E+01  4.15E-02  8.47E-02  1.63E+00  1.23E+01  3.8E+01 4.7E+00 1.8E+02 5.8E-02
     8  1.153767000E+01  2.902297219E+01  2.99E-02  6.43E-02  1.65E+00  1.60E+01 -2.8E+01 6.1E+00 1.7E+02 4.3E-02
     9  7.760937414E+00  2.064415371E+01  2.13E-02  4.82E-02  1.66E+00  2.08E+01  2.0E+01 8.0E+00 1.6E+02 3.2E-02
    10  2.839815951E+00  1.443334690E+01  1.49E-02  3.55E-02  1.67E+00  2.74E+01 -1.5E+01 1.1E+01 1.6E+02 2.3E-02

    20 -1.333427223E+01  1.535116353E+00  1.58E-03  2.65E-02  2.28E+00  2.03E+02 -2.3E-01 1.8E+01 4.1E+00 3.1E-03

    30 -6.117633997E+00  2.153414214E-01  2.22E-04  9.94E-03  2.81E+00  1.05E+03 -3.4E-02 2.6E+01 8.9E-01 5.6E-04

    40 -2.647629456E+00  8.505970382E-02  8.76E-05  7.26E-02  3.22E+00  2.52E+03 -2.3E-02 3.5E+02 8.1E+00 2.4E-04

    50  6.926024354E-01  1.926556044E-02  1.98E-05  6.70E-02  3.69E+00  1.08E+04 -2.4E-02 2.5E+03 6.1E+01 6.0E-05

    60  1.201266702E+00  8.316821714E-03  8.56E-06  2.15E-04  4.02E+00  1.40E+04 -4.2E-04 4.8E+02 2.0E-01 3.6E-05

    70  1.561190524E+00  1.489119365E-03  1.53E-06  3.84E-04  4.34E+00  4.41E+04 -6.6E-05 9.8E+01 6.4E-03 9.0E-06

    80  1.561057687E+00  1.487867213E-03  1.53E-06  5.68E-05  4.64E+00  4.72E+04 -1.1E-05 2.8E+02 3.0E-03 8.9E-06

    90  1.124590798E+00  1.246657515E-04  1.28E-07  2.22E-03  4.89E+00  2.03E+05 -8.7E-06 2.6E+02 2.2E-03 1.3E-06

   100  1.124359741E+00  1.225146450E-04  1.26E-07  3.95E-06  5.15E+00  2.14E+05 -1.4E-07 3.5E+02 5.1E-05 1.3E-06

   110  1.123120171E+00  1.223946965E-04  1.26E-07  2.84E-04  5.40E+00  2.36E+05 -4.8E-06 1.2E+04 5.6E-02 1.2E-06

   120  4.787162251E-01  5.744401707E-06  5.92E-09  3.43E-04  5.65E+00  1.74E+06 -1.8E-05 4.4E+04 7.8E-01 1.0E-07

   130  4.772645319E-01  1.581210657E-06  1.63E-09  1.95E-02  5.86E+00  1.81E+06 -5.4E-07 1.3E+03 7.2E-04 5.3E-08

   140  4.772415312E-01  1.418238709E-06  1.46E-09  3.66E-07  6.13E+00  1.89E+06 -1.7E-11 1.4E+01 2.3E-10 5.0E-08

   150  4.772413741E-01  1.418235681E-06  1.46E-09  1.46E-07  6.33E+00  1.95E+06 -9.0E-11 9.7E+01 8.7E-09 5.0E-08

   160  4.772413684E-01  1.418235626E-06  1.46E-09  1.67E-06  6.53E+00  2.01E+06 -5.3E-11 3.6E+02 1.9E-08 5.0E-08

   170  4.738193339E-01  1.411776919E-06  1.45E-09  1.75E-06  6.73E+00  6.60E+06 -1.3E-09 9.3E+03 1.2E-05 2.8E-08

   180  4.735931374E-01  1.411350196E-06  1.45E-09  4.79E-04  6.93E+00  7.00E+06 -3.4E-08 2.3E+05 7.8E-03 2.8E-08

   190  4.714672842E-01  1.407331610E-06  1.45E-09  3.26E-04  7.12E+00  8.88E+06 -2.6E-08 1.8E+05 4.5E-03 2.5E-08

   200  9.999997523E-02  1.830313587E-08  1.88E-11  3.77E-04  7.28E+00  7.11E+07 -5.5E-10 3.8E+03 2.1E-06 1.0E-09

   210  9.999986526E-02  1.828931338E-08  1.88E-11  3.99E-05  7.46E+00  7.29E+07 -3.5E-10 2.5E+03 8.9E-07 1.0E-09

   220  9.999986468E-02  1.828925745E-08  1.88E-11  4.40E-06  7.64E+00  7.46E+07 -1.2E-11 1.2E+02 1.4E-09 1.0E-09

   230  9.999999995E-02  1.827111981E-08  1.88E-11  3.37E-06  7.87E+00  7.69E+07 -2.7E-12 1.3E+02 3.6E-10 1.0E-09

   240  1.000000000E-01  1.827111112E-08  1.88E-11  2.14E-08  8.01E+00  7.83E+07 -2.7E-13 1.2E+02 3.2E-11 1.0E-09

   250  1.000000000E-01  1.827111108E-08  1.88E-11  3.22E-10  8.17E+00  7.99E+07 -1.5E-14 3.7E+01 5.6E-13 1.0E-09

   260  1.000000000E-01  1.827111108E-08  1.88E-11  1.16E-11  8.33E+00  8.14E+07 -3.9E-17 1.0E+01 4.1E-16 1.0E-09

   270  1.000000000E-01  1.827111108E-08  1.88E-11  2.55E-10  8.48E+00  8.28E+07 -5.2E-16 6.3E+02 3.3E-13 1.0E-09

   280  9.999999911E-02  1.827111108E-08  1.88E-11  1.79E-09  8.63E+00  8.44E+07 -2.2E-13 2.7E+05 5.8E-08 1.0E-09

   290  9.999999911E-02  1.827111108E-08  1.88E-11  1.59E-10  8.79E+00  8.59E+07 -1.3E-15 1.7E+03 2.2E-12 1.0E-09

   300  9.999999911E-02  1.827111108E-08  1.88E-11  2.26E-09  8.93E+00  8.73E+07 -9.1E-16 1.2E+03 1.1E-12 1.0E-09

   310  9.999999910E-02  1.827111108E-08  1.88E-11  1.18E-08  9.09E+00  8.88E+07 -2.8E-15 3.6E+03 1.0E-11 1.0E-09

   317  9.999999910E-02  1.827111108E-08  1.88E-11  1.33E-15  9.19E+00  8.98E+07  5.5E-18 7.2E+00 4.0E-17 1.0E-09
   318  9.999999910E-02  1.827111108E-08  1.88E-11  2.93E-16  9.24E+00  9.03E+07 -2.3E-22 1.0E+00 2.4E-22 1.0E-09

 Exit  LSQR.       istop  = 3               itn    =     318
 Exit  LSQR.       anorm  = 9.23868E+00     acond  = 9.03112E+07
 Exit  LSQR.       bnorm  = 9.71035E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-08     arnorm = 4.94552E-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)         = 1.15247812E-12 = rho1
    norm(A'r)       = 9.563E-13      = sigma1

    norm(s)         = 1.152E-01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-08 = rho2
    norm(Abar'rbar) = 9.563E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 6.456E-17 (Ax = b)
    test2           = 8.981E-02 (least-squares)
    test3           = 5.665E-06 (damped least-squares)


 Solution  x:
     1  0.100000E+00     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  =  3.91E-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
                                                                                    phi    dknorm   dxk  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  8.3E+02 1.1E+00 9.1E+02 6.3E-01
     2 -2.224414133E+01  2.277481391E+02  2.47E-01  3.61E-01  1.18E+00  2.19E+00 -3.2E+02 1.5E+00 4.8E+02 3.3E-01
     3 -1.321097804E+01  1.472531389E+02  1.60E-01  2.44E-01  1.34E+00  3.62E+00  1.7E+02 2.0E+00 3.4E+02 2.1E-01
     4 -3.367416062E+00  1.000443384E+02  1.09E-01  1.74E-01  1.44E+00  5.35E+00 -1.1E+02 2.6E+00 2.8E+02 1.4E-01
     5  5.036316961E+00  6.938393962E+01  7.54E-02  1.27E-01  1.50E+00  7.50E+00  7.2E+01 3.3E+00 2.4E+02 9.8E-02
     6  1.099397591E+01  4.832729386E+01  5.25E-02  9.29E-02  1.53E+00  1.02E+01 -5.0E+01 4.4E+00 2.2E+02 6.9E-02
     7  1.404999112E+01  3.345806131E+01  3.63E-02  6.76E-02  1.55E+00  1.39E+01  3.5E+01 5.9E+00 2.1E+02 4.9E-02
     8  1.413848446E+01  2.285799571E+01  2.48E-02  4.86E-02  1.56E+00  1.88E+01 -2.4E+01 8.1E+00 2.0E+02 3.4E-02
     9  1.156137856E+01  1.532415806E+01  1.66E-02  3.43E-02  1.57E+00  2.59E+01  1.7E+01 1.1E+01 1.9E+02 2.4E-02
    10  6.963653189E+00  1.003283279E+01  1.09E-02  2.37E-02  1.57E+00  3.61E+01 -1.2E+01 1.6E+01 1.9E+02 1.6E-02

    20 -1.268926403E+01  1.278052398E+00  1.39E-03  1.02E-01  2.19E+00  2.60E+02 -2.9E-01 3.8E+01 1.1E+01 2.5E-03

    30 -1.033564289E+01  1.688305957E-01  1.83E-04  1.19E-02  2.84E+00  1.58E+03 -4.3E-02 6.6E+01 2.8E+00 4.1E-04

    40 -6.758424214E+00  6.481367050E-02  7.04E-05  5.31E-03  3.21E+00  3.56E+03 -4.4E-03 1.5E+02 6.5E-01 1.8E-04

    50 -2.054898790E+00  1.786580010E-02  1.94E-05  7.28E-03  3.56E+00  1.48E+04 -1.1E-02 2.7E+03 3.0E+01 4.9E-05

    60 -4.552999018E-01  6.568122413E-03  7.14E-06  2.54E-05  3.89E+00  2.24E+04 -6.8E-05 1.3E+02 8.7E-03 2.5E-05

    70  1.171427491E+00  1.396930583E-03  1.52E-06  2.12E-04  4.29E+00  7.15E+04 -3.5E-05 8.5E+01 3.0E-03 6.8E-06

    80  1.171619843E+00  1.396563671E-03  1.52E-06  2.53E-05  4.56E+00  7.62E+04 -2.5E-06 1.1E+02 2.8E-04 6.8E-06

    90  1.570884640E+00  2.196095763E-04  2.39E-07  8.22E-03  4.83E+00  2.98E+05 -2.5E-05 1.1E+03 2.6E-02 1.4E-06

   100  1.574464742E+00  1.837749121E-04  2.00E-07  7.26E-07  5.08E+00  3.15E+05 -5.2E-09 5.4E+00 2.8E-08 1.3E-06

   110  1.573516406E+00  1.836011879E-04  1.99E-07  1.15E-04  5.30E+00  3.37E+05 -3.0E-07 5.5E+02 1.7E-04 1.3E-06

   120  1.131489483E+00  1.024359056E-05  1.11E-08  8.64E-04  5.57E+00  1.90E+06 -9.9E-08 1.8E+02 1.8E-05 1.3E-07

   130  1.131317194E+00  9.933742066E-06  1.08E-08  5.09E-05  5.81E+00  1.98E+06 -3.1E-07 6.2E+02 1.9E-04 1.3E-07

   140  1.131300291E+00  9.905114295E-06  1.08E-08  1.81E-06  6.01E+00  2.05E+06 -9.6E-10 6.7E+01 6.4E-08 1.3E-07

   150  1.131293238E+00  9.905011054E-06  1.08E-08  1.84E-06  6.21E+00  2.12E+06 -1.7E-09 6.3E+02 1.1E-06 1.3E-07

   160  1.131292438E+00  9.905001184E-06  1.08E-08  4.69E-07  6.39E+00  2.18E+06 -1.0E-09 3.8E+02 3.8E-07 1.3E-07

   170  4.836999456E-01  9.460476488E-07  1.03E-09  3.90E-04  6.58E+00  2.51E+07 -9.4E-09 3.6E+03 3.4E-05 1.2E-08

   180  4.836281158E-01  9.403706753E-07  1.02E-09  2.86E-04  6.76E+00  2.58E+07 -3.8E-08 1.5E+04 5.5E-04 1.2E-08

   190  4.826798068E-01  8.644981577E-07  9.39E-10  2.38E-02  6.99E+00  2.67E+07 -3.5E-07 1.4E+05 4.8E-02 1.1E-08

   200  4.775241452E-01  5.679669775E-08  6.17E-11  6.68E-06  7.16E+00  2.74E+07 -4.5E-11 1.8E+01 8.1E-10 2.8E-09

   210  4.775241440E-01  5.679667084E-08  6.17E-11  1.41E-07  7.32E+00  2.80E+07 -7.6E-12 4.7E+02 3.6E-09 2.8E-09

   220  4.775241437E-01  5.679666861E-08  6.17E-11  5.48E-09  7.48E+00  2.86E+07 -1.6E-14 1.5E+01 2.4E-13 2.8E-09

   230  4.775241247E-01  5.679665663E-08  6.17E-11  2.51E-06  7.64E+00  2.92E+07 -3.6E-11 4.2E+04 1.5E-06 2.8E-09

   240  4.775241039E-01  5.679664356E-08  6.17E-11  6.20E-10  7.85E+00  3.01E+07 -8.4E-16 1.5E+00 1.3E-15 2.8E-09

   250  4.775240929E-01  5.679664263E-08  6.17E-11  5.82E-08  8.00E+00  3.07E+07 -5.9E-13 2.5E+03 1.5E-09 2.8E-09

   260  4.775240913E-01  5.679664251E-08  6.17E-11  2.15E-08  8.15E+00  3.12E+07 -2.3E-13 1.0E+03 2.4E-10 2.8E-09

   270  4.775144156E-01  5.679591539E-08  6.17E-11  8.26E-05  8.28E+00  3.33E+07 -1.8E-10 7.7E+05 1.4E-04 2.8E-09

   280  1.216323776E-01  1.370644216E-08  1.49E-11  6.11E-05  8.43E+00  2.00E+09 -1.0E-11 4.4E+04 4.4E-07 1.8E-10

   290  1.216292871E-01  1.370548078E-08  1.49E-11  3.12E-04  8.61E+00  2.04E+09 -1.4E-10 5.9E+05 8.1E-05 1.8E-10

   300  1.214237268E-01  1.364140739E-08  1.48E-11  1.05E-04  8.74E+00  2.07E+09 -6.7E-11 2.9E+05 1.9E-05 1.8E-10

   310  1.212727432E-01  1.359413447E-08  1.48E-11  7.08E-07  8.88E+00  2.11E+09 -1.0E-09 4.4E+06 4.5E-03 1.8E-10

   320  1.001522736E-01  2.153580371E-09  2.34E-12  5.23E-03  9.01E+00  2.20E+09 -1.6E-09 7.1E+06 1.2E-02 6.9E-11

   330  1.000071690E-01  1.843978348E-09  2.00E-12  1.45E-03  9.15E+00  2.23E+09 -2.8E-11 1.2E+05 3.3E-06 6.4E-11

   340  9.999991135E-02  1.827115926E-09  1.98E-12  1.12E-06  9.32E+00  2.28E+09 -1.0E-12 4.4E+03 4.4E-09 6.4E-11

   350  9.999990934E-02  1.827111218E-09  1.98E-12  6.37E-08  9.45E+00  2.31E+09 -2.6E-14 2.0E+02 5.1E-12 6.4E-11

   360  9.999990937E-02  1.827111116E-09  1.98E-12  3.65E-09  9.59E+00  2.34E+09 -3.2E-16 3.3E+00 1.1E-15 6.4E-11

   370  9.999990937E-02  1.827111116E-09  1.98E-12  6.86E-10  9.69E+00  2.37E+09 -1.6E-17 2.0E+02 3.1E-15 6.4E-11

   380  9.999990937E-02  1.827111116E-09  1.98E-12  2.80E-09  9.89E+00  2.41E+09 -1.5E-16 2.0E+03 3.0E-13 6.4E-11

   390  9.999990937E-02  1.827111116E-09  1.98E-12  2.76E-11  9.98E+00  2.44E+09 -6.5E-19 1.2E+01 7.7E-18 6.4E-11

   400  9.999990937E-02  1.827111116E-09  1.98E-12  4.51E-11  1.01E+01  2.47E+09 -2.1E-18 4.6E+01 9.7E-17 6.4E-11

   410  9.999990937E-02  1.827111116E-09  1.98E-12  1.21E-10  1.02E+01  2.50E+09 -2.4E-17 5.5E+02 1.3E-14 6.4E-11

   420  9.999991077E-02  1.827111114E-09  1.98E-12  7.37E-09  1.04E+01  2.53E+09 -1.7E-14 3.9E+05 6.7E-09 6.4E-11

   430  9.999991502E-02  1.827111108E-09  1.98E-12  2.49E-07  1.05E+01  2.56E+09 -1.8E-14 4.1E+05 7.4E-09 6.4E-11

   440  9.999991506E-02  1.827111108E-09  1.98E-12  1.06E-12  1.06E+01  2.59E+09 -1.4E-18 3.3E+01 4.6E-17 6.4E-11

   450  9.999991506E-02  1.827111108E-09  1.98E-12  2.32E-10  1.07E+01  2.62E+09 -9.7E-18 2.5E+03 2.5E-14 6.4E-11

   460  9.999991506E-02  1.827111108E-09  1.98E-12  8.09E-14  1.08E+01  2.64E+09 -3.8E-21 3.0E+01 1.1E-19 6.4E-11

   465  9.999991506E-02  1.827111108E-09  1.98E-12  2.85E-15  1.09E+01  2.66E+09  2.0E-22 3.4E+00 6.9E-22 6.4E-11
   466  9.999991506E-02  1.827111108E-09  1.98E-12  2.85E-15  1.09E+01  2.66E+09 -4.4E-22 1.1E+01 4.7E-21 6.4E-11
   469  9.999991506E-02  1.827111108E-09  1.98E-12  2.74E-15  1.09E+01  2.67E+09  2.8E-21 9.6E+01 2.7E-19 6.4E-11
   470  9.999991506E-02  1.827111108E-09  1.98E-12  1.57E-13  1.09E+01  2.67E+09 -5.6E-20 2.1E+03 1.2E-16 6.4E-11

   473  9.999991506E-02  1.827111108E-09  1.98E-12  1.83E-15  1.10E+01  2.69E+09  7.3E-22 2.8E+01 2.1E-20 6.4E-11
   474  9.999991506E-02  1.827111108E-09  1.98E-12  6.88E-16  1.10E+01  2.69E+09 -4.1E-22 1.9E+01 8.0E-21 6.4E-11
   475  9.999991506E-02  1.827111108E-09  1.98E-12  8.06E-16  1.10E+01  2.69E+09  2.6E-22 2.3E+01 6.0E-21 6.4E-11
   476  9.999991506E-02  1.827111108E-09  1.98E-12  1.26E-15  1.10E+01  2.69E+09 -3.9E-23 4.1E+00 1.6E-22 6.4E-11
   480  9.999991506E-02  1.827111108E-09  1.98E-12  3.05E-14  1.11E+01  2.70E+09 -6.7E-22 7.6E+01 5.1E-20 6.4E-11

   482  9.999991506E-02  1.827111108E-09  1.98E-12  6.39E-16  1.11E+01  2.71E+09 -1.2E-20 1.4E+03 1.7E-17 6.4E-11
   490  9.999991506E-02  1.827111108E-09  1.98E-12  2.24E-12  1.12E+01  2.73E+09 -2.2E-18 3.0E+05 6.5E-13 6.4E-11

   497  9.999991506E-02  1.827111108E-09  1.98E-12  7.45E-16  1.13E+01  2.76E+09  7.3E-23 1.0E+01 7.4E-22 6.4E-11
   498  9.999991506E-02  1.827111108E-09  1.98E-12  1.28E-16  1.13E+01  2.76E+09 -2.2E-22 3.4E+01 7.5E-21 6.4E-11

 Exit  LSQR.       istop  = 3               itn    =     498
 Exit  LSQR.       anorm  = 1.12949E+01     acond  = 2.75822E+09
 Exit  LSQR.       bnorm  = 9.20536E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-09     arnorm = 2.63909E-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)         = 7.22742574E-13 = rho1
    norm(A'r)       = 5.802E-13      = sigma1

    norm(s)         = 7.227E-01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711125E-09 = rho2
    norm(Abar'rbar) = 5.802E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.353E-17 (Ax = b)
    test2           = 7.107E-02 (least-squares)
    test3           = 2.811E-05 (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  =  3.61E-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 =   3.4E-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
                                                                                    phi    dknorm   dxk  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  7.9E+02 1.1E+00 8.6E+02 6.4E-01
     2 -2.477913716E+01  2.170796658E+02  2.47E-01  3.45E-01  1.18E+00  2.20E+00 -3.1E+02 1.5E+00 4.7E+02 3.3E-01
     3 -1.776850890E+01  1.378525121E+02  1.57E-01  2.27E-01  1.32E+00  3.69E+00  1.7E+02 2.1E+00 3.5E+02 2.0E-01
     4 -8.448828545E+00  9.115137842E+01  1.04E-01  1.57E-01  1.40E+00  5.56E+00 -1.0E+02 2.8E+00 2.9E+02 1.3E-01
     5  7.462713431E-01  6.101548604E+01  6.93E-02  1.10E-01  1.44E+00  7.99E+00  6.8E+01 3.9E+00 2.6E+02 8.9E-02
     6  8.324225295E+00  4.071186937E+01  4.62E-02  7.68E-02  1.47E+00  1.13E+01 -4.5E+01 5.4E+00 2.4E+02 6.0E-02
     7  1.328456787E+01  2.681918944E+01  3.05E-02  5.31E-02  1.48E+00  1.60E+01  3.1E+01 7.6E+00 2.3E+02 4.0E-02
     8  1.508697430E+01  1.732799020E+01  1.97E-02  3.61E-02  1.48E+00  2.29E+01 -2.0E+01 1.1E+01 2.2E+02 2.7E-02
     9  1.370779512E+01  1.092432664E+01  1.24E-02  2.40E-02  1.49E+00  3.32E+01  1.3E+01 1.6E+01 2.2E+02 1.7E-02
    10  9.647108004E+00  6.693642326E+00  7.60E-03  2.88E-02  1.49E+00  4.93E+01 -8.6E+00 2.4E+01 2.1E+02 1.1E-02

    20 -1.212654421E+01  6.303875300E-01  7.16E-04  1.59E-03  2.31E+00  5.05E+02 -8.2E-01 1.4E+02 1.1E+02 1.3E-03

    30 -1.326307032E+01  1.353049398E-01  1.54E-04  2.97E-03  2.73E+00  2.01E+03 -2.2E-03 1.7E+01 3.8E-02 3.2E-04

    40 -8.964045637E+00  4.053212964E-02  4.60E-05  1.51E-02  3.19E+00  8.20E+03 -9.1E-03 5.2E+02 4.7E+00 9.4E-05

    50 -3.637252841E+00  6.656900962E-03  7.56E-06  2.86E-02  3.63E+00  2.91E+04 -4.2E-03 1.7E+03 7.0E+00 2.1E-05

    60 -3.516875743E+00  5.772963427E-03  6.56E-06  5.17E-05  3.92E+00  3.19E+04 -2.7E-05 1.0E+02 2.8E-03 2.0E-05

    70 -5.572608044E-01  1.366434075E-03  1.55E-06  1.65E-05  4.19E+00  9.77E+04 -1.2E-06 5.9E+00 7.0E-06 5.7E-06

    80 -3.621706042E-01  1.288355816E-03  1.46E-06  6.76E-02  4.44E+00  1.56E+05 -4.5E-04 2.6E+04 1.2E+01 4.5E-06

    90  1.155156444E+00  2.297480913E-04  2.61E-07  4.47E-05  4.78E+00  3.90E+05 -5.0E-05 2.9E+03 1.4E-01 1.2E-06

   100  1.155276704E+00  2.296600994E-04  2.61E-07  1.05E-04  5.00E+00  4.10E+05 -4.2E-06 6.7E+03 2.8E-02 1.2E-06

   110  1.155877550E+00  2.294909099E-04  2.61E-07  1.55E-03  5.22E+00  4.34E+05 -2.6E-06 4.2E+03 1.1E-02 1.2E-06

   120  1.581471542E+00  2.241927995E-05  2.55E-08  1.18E-03  5.47E+00  2.09E+06 -2.2E-07 3.7E+02 8.3E-05 1.8E-07

   130  1.581421256E+00  2.238632168E-05  2.54E-08  5.51E-05  5.74E+00  2.19E+06 -4.4E-08 1.4E+02 6.1E-06 1.8E-07

   140  1.581414973E+00  2.238604527E-05  2.54E-08  9.29E-06  5.92E+00  2.26E+06 -3.3E-08 4.2E+03 1.4E-04 1.8E-07

   150  1.580349197E+00  2.235399982E-05  2.54E-08  9.94E-06  6.10E+00  2.50E+06 -5.6E-09 7.0E+02 3.9E-06 1.7E-07

   160  1.144307814E+00  3.457107322E-06  3.93E-09  1.02E-02  6.35E+00  1.77E+07 -2.0E-05 2.5E+06 4.9E+01 2.6E-08

   170  1.134216006E+00  8.141761493E-07  9.25E-10  6.97E-04  6.52E+00  1.84E+07 -5.7E-08 7.1E+03 4.0E-04 1.3E-08

   180  1.134208456E+00  8.080405896E-07  9.18E-10  1.70E-06  6.73E+00  1.90E+07 -4.5E-10 6.2E+01 2.8E-08 1.3E-08

   190  1.134261271E+00  7.959773936E-07  9.04E-10  1.68E-07  6.89E+00  1.94E+07 -4.6E-10 9.1E+01 4.2E-08 1.2E-08

   200  1.134261271E+00  7.959773798E-07  9.04E-10  3.63E-08  7.11E+00  2.00E+07 -1.8E-12 6.2E+01 1.1E-10 1.2E-08

   210  1.134261176E+00  7.959773261E-07  9.04E-10  8.75E-07  7.26E+00  2.04E+07 -1.1E-11 6.5E+02 7.2E-09 1.2E-08

   220  1.134250214E+00  7.959708137E-07  9.04E-10  1.97E-06  7.42E+00  2.09E+07 -4.2E-11 2.5E+03 1.1E-07 1.2E-08

   230  1.130638005E+00  7.938205594E-07  9.02E-10  2.63E-06  7.61E+00  3.42E+07 -2.5E-11 1.5E+03 3.8E-08 9.8E-09

   240  1.129326320E+00  7.930225991E-07  9.01E-10  1.96E-03  7.78E+00  3.87E+07 -2.0E-08 1.2E+06 2.3E-02 9.3E-09

   250  9.602159023E-01  6.823933510E-07  7.75E-10  1.48E-02  7.92E+00  1.96E+08 -2.0E-07 1.2E+07 2.3E+00 3.9E-09

   260  5.089455495E-01  1.739366791E-07  1.98E-10  2.04E-04  8.08E+00  3.77E+08 -2.0E-09 1.2E+05 2.5E-04 1.4E-09

   270  4.776028593E-01  3.774470096E-09  4.29E-12  5.26E-04  8.26E+00  3.95E+08 -2.9E-10 1.8E+04 5.1E-06 2.1E-10

   280  4.775935123E-01  2.289243058E-09  2.60E-12  1.58E-07  8.39E+00  4.01E+08 -2.1E-14 2.5E+01 5.3E-13 1.6E-10

   290  4.775935098E-01  2.289044002E-09  2.60E-12  1.88E-05  8.52E+00  4.07E+08 -6.0E-12 9.7E+03 5.8E-08 1.6E-10

   300  4.775935083E-01  2.288815448E-09  2.60E-12  2.00E-04  8.70E+00  4.16E+08 -2.4E-11 3.9E+04 9.2E-07 1.6E-10

   310  4.775935699E-01  2.286949460E-09  2.60E-12  3.32E-06  8.86E+00  4.23E+08 -3.0E-12 5.1E+03 1.5E-08 1.6E-10

   320  4.775938770E-01  2.278845913E-09  2.59E-12  6.82E-06  8.98E+00  4.29E+08 -6.5E-11 1.1E+05 7.1E-06 1.6E-10

   330  4.775938912E-01  2.278470218E-09  2.59E-12  1.23E-05  9.10E+00  4.35E+08 -1.4E-12 2.3E+03 3.2E-09 1.6E-10

   340  4.775938914E-01  2.278465822E-09  2.59E-12  1.39E-10  9.26E+00  4.42E+08 -7.2E-18 1.8E+01 1.3E-16 1.6E-10

   350  4.775938914E-01  2.278465822E-09  2.59E-12  7.15E-11  9.38E+00  4.48E+08 -6.6E-17 1.7E+02 1.2E-14 1.6E-10

   360  4.775938195E-01  2.278465606E-09  2.59E-12  5.99E-06  9.51E+00  4.55E+08 -2.1E-13 5.8E+05 1.2E-07 1.6E-10

   370  4.775920665E-01  2.278460346E-09  2.59E-12  2.58E-08  9.69E+00  4.81E+08 -3.0E-13 8.0E+05 2.4E-07 1.6E-10

   380  4.775920647E-01  2.278460341E-09  2.59E-12  8.37E-08  9.80E+00  4.86E+08 -1.6E-14 4.2E+04 6.5E-10 1.6E-10

   390  4.775920529E-01  2.278460305E-09  2.59E-12  1.49E-08  9.91E+00  4.92E+08 -2.4E-13 6.5E+05 1.6E-07 1.6E-10

   400  4.775882988E-01  2.278449075E-09  2.59E-12  2.38E-05  1.01E+01  5.36E+08 -1.9E-12 5.2E+06 1.0E-05 1.5E-10

   410  4.760067314E-01  2.273712680E-09  2.58E-12  9.95E-08  1.02E+01  4.05E+09 -1.6E-14 4.3E+04 7.0E-10 5.6E-11

   420  4.760066398E-01  2.273712406E-09  2.58E-12  1.39E-05  1.03E+01  4.09E+09 -7.3E-13 2.0E+06 1.4E-06 5.6E-11

   430  4.760063307E-01  2.273711481E-09  2.58E-12  2.36E-08  1.04E+01  4.15E+09 -7.0E-16 1.9E+03 1.3E-12 5.6E-11

   440  4.760058394E-01  2.273710005E-09  2.58E-12  8.24E-07  1.06E+01  4.20E+09 -1.9E-12 5.1E+06 9.7E-06 5.6E-11

   450  3.774595014E-01  1.955398490E-09  2.22E-12  6.46E-04  1.07E+01  3.35E+10 -4.6E-11 1.2E+08 5.6E-03 1.8E-11

   460  2.943235837E-01  1.639487850E-09  1.86E-12  1.43E-05  1.08E+01  4.59E+10 -4.4E-13 1.2E+06 5.2E-07 1.5E-11

   470  1.039701073E-01  2.960354017E-10  3.36E-13  3.27E-05  1.09E+01  6.62E+10 -3.7E-10 9.9E+08 3.7E-01 5.2E-12

   480  1.000363025E-01  1.841191999E-10  2.09E-13  6.44E-04  1.10E+01  6.72E+10 -3.8E-11 1.0E+08 3.9E-03 4.1E-12

   490  9.999880937E-02  1.827230458E-10  2.08E-13  1.14E-07  1.11E+01  6.78E+10 -3.7E-16 9.9E+02 3.7E-13 4.0E-12

   500  9.999880886E-02  1.827230273E-10  2.08E-13  1.07E-06  1.13E+01  6.87E+10 -8.9E-15 2.4E+04 2.1E-10 4.0E-12

   510  9.999854705E-02  1.827133635E-10  2.08E-13  7.69E-08  1.14E+01  6.93E+10 -1.7E-15 4.5E+03 7.5E-12 4.0E-12

   520  9.999854705E-02  1.827133635E-10  2.08E-13  1.26E-07  1.14E+01  6.99E+10 -3.9E-16 1.2E+03 4.7E-13 4.0E-12

   530  9.999854705E-02  1.827133635E-10  2.08E-13  1.32E-10  1.16E+01  7.07E+10 -3.8E-18 1.2E+01 4.4E-17 4.0E-12

   540  9.999854704E-02  1.827133625E-10  2.08E-13  2.74E-09  1.17E+01  7.13E+10 -4.7E-17 2.8E+02 1.3E-14 4.0E-12

   550  9.999854704E-02  1.827133624E-10  2.08E-13  1.65E-08  1.18E+01  7.18E+10 -6.4E-17 3.9E+02 2.5E-14 4.0E-12

   560  9.999854704E-02  1.827133624E-10  2.08E-13  3.21E-09  1.19E+01  7.27E+10 -7.2E-16 4.4E+03 3.2E-12 4.0E-12

   570  9.999854704E-02  1.827133624E-10  2.08E-13  1.03E-11  1.20E+01  7.34E+10 -1.8E-18 2.7E+01 4.7E-17 4.0E-12

   580  9.999854704E-02  1.827133624E-10  2.08E-13  6.65E-11  1.21E+01  7.39E+10 -1.1E-18 5.0E+01 5.3E-17 4.0E-12

   590  9.999854704E-02  1.827133623E-10  2.08E-13  2.38E-08  1.22E+01  7.46E+10 -1.3E-16 6.6E+03 8.3E-13 4.0E-12

   600  9.999864596E-02  1.827118720E-10  2.08E-13  5.57E-05  1.23E+01  7.52E+10 -7.2E-13 3.8E+07 2.7E-05 4.0E-12

   610  9.999869649E-02  1.827111109E-10  2.08E-13  9.49E-10  1.24E+01  7.57E+10 -4.8E-17 2.5E+03 1.2E-13 4.0E-12

   620  9.999869649E-02  1.827111109E-10  2.08E-13  6.99E-12  1.25E+01  7.65E+10 -2.1E-19 1.4E+01 2.9E-18 4.0E-12

   630  9.999869649E-02  1.827111109E-10  2.08E-13  1.09E-12  1.26E+01  7.71E+10 -3.5E-21 4.7E+01 1.7E-19 4.0E-12

   640  9.999869649E-02  1.827111109E-10  2.08E-13  1.47E-14  1.27E+01  7.77E+10 -1.6E-22 9.5E+00 1.6E-21 4.0E-12

   650  9.999869649E-02  1.827111109E-10  2.08E-13  2.03E-13  1.28E+01  7.84E+10 -2.0E-21 1.3E+02 2.6E-19 4.0E-12

   660  9.999869649E-02  1.827111109E-10  2.08E-13  7.78E-12  1.29E+01  7.90E+10 -1.9E-18 1.2E+05 2.4E-13 4.0E-12

   670  9.999869649E-02  1.827111109E-10  2.08E-13  7.70E-12  1.30E+01  7.95E+10 -8.9E-20 5.8E+03 5.1E-16 4.0E-12

   680  9.999869649E-02  1.827111109E-10  2.08E-13  6.26E-11  1.31E+01  7.99E+10 -1.7E-19 1.1E+04 1.9E-15 4.0E-12

   690  9.999869649E-02  1.827111109E-10  2.08E-13  6.49E-12  1.32E+01  8.08E+10 -6.3E-20 4.1E+03 2.6E-16 4.0E-12

   700  9.999869649E-02  1.827111109E-10  2.08E-13  2.63E-11  1.33E+01  8.13E+10 -1.2E-18 7.7E+04 9.0E-14 4.0E-12

   708  9.999869649E-02  1.827111109E-10  2.08E-13  1.49E-15  1.34E+01  8.18E+10 -7.7E-23 5.6E+00 4.3E-22 4.0E-12
   710  9.999869649E-02  1.827111109E-10  2.08E-13  2.32E-13  1.34E+01  8.18E+10 -1.2E-21 3.4E+02 4.2E-19 4.0E-12

   712  9.999869649E-02  1.827111109E-10  2.08E-13  2.40E-15  1.34E+01  8.20E+10 -1.9E-22 5.6E+01 1.1E-20 4.0E-12
   713  9.999869649E-02  1.827111109E-10  2.08E-13  1.72E-15  1.34E+01  8.20E+10  3.2E-23 1.1E+01 3.4E-22 4.0E-12
   714  9.999869649E-02  1.827111109E-10  2.08E-13  2.63E-15  1.34E+01  8.20E+10 -1.6E-23 6.6E+00 1.1E-22 4.0E-12
   720  9.999869649E-02  1.827111109E-10  2.08E-13  5.57E-14  1.35E+01  8.24E+10 -2.4E-22 1.1E+02 2.6E-20 4.0E-12

   730  9.999869649E-02  1.827111109E-10  2.08E-13  1.03E-11  1.36E+01  8.30E+10 -2.1E-19 9.7E+04 2.0E-14 4.0E-12

   740  9.999869649E-02  1.827111109E-10  2.08E-13  1.29E-13  1.37E+01  8.35E+10 -7.2E-22 3.4E+02 2.4E-19 4.0E-12

   750  9.999869649E-02  1.827111109E-10  2.08E-13  4.25E-13  1.38E+01  8.42E+10 -5.3E-21 2.5E+03 1.3E-17 4.0E-12

   753  9.999869649E-02  1.827111109E-10  2.08E-13  1.12E-16  1.38E+01  8.43E+10  4.8E-22 2.2E+02 1.1E-19 4.0E-12

 Exit  LSQR.       istop  = 3               itn    =     753
 Exit  LSQR.       anorm  = 1.38114E+01     acond  = 8.43030E+10
 Exit  LSQR.       bnorm  = 8.80278E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-10     arnorm = 2.82782E-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)         = 9.44510781E-13 = rho1
    norm(A'r)       = 7.439E-13      = sigma1

    norm(s)         = 9.445E+00
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82713552E-10 = rho2
    norm(Abar'rbar) = 7.439E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.617E-17 (Ax = b)
    test2           = 5.703E-02 (least-squares)
    test3           = 2.948E-04 (damped least-squares)


 Solution  x:
     1  0.999987E-01     2  0.200000         3  0.300000         4  0.400000    
     5  0.500002         6  0.600004         7  0.700005         8  0.800006    

 LSQR  appears to be successful.     Relative error in  x  =  6.54E-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 =   1.4E-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
                                                                                    phi    dknorm   dxk  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  1.2E+03 1.1E+00 1.3E+03 5.5E-01
     2 -2.022218888E+01  2.366648551E+02  1.89E-01  4.41E-01  1.18E+00  2.12E+00 -3.8E+02 1.4E+00 5.4E+02 2.9E-01
     3 -1.368214317E+01  1.468584013E+02  1.18E-01  3.23E-01  1.39E+00  3.40E+00  1.9E+02 1.7E+00 3.1E+02 1.9E-01
     4 -8.500660046E+00  9.996107126E+01  8.00E-02  2.55E-01  1.56E+00  4.83E+00 -1.1E+02 1.9E+00 2.0E+02 1.4E-01
     5 -4.843832613E+00  7.213638259E+01  5.77E-02  2.09E-01  1.70E+00  6.39E+00  6.9E+01 2.1E+00 1.5E+02 1.1E-01
     6 -2.325528667E+00  5.415595941E+01  4.33E-02  1.76E-01  1.82E+00  8.09E+00 -4.8E+01 2.4E+00 1.1E+02 8.3E-02
     7 -5.967528345E-01  4.180081114E+01  3.35E-02  1.51E-01  1.93E+00  9.93E+00  3.4E+01 2.6E+00 9.0E+01 6.8E-02
     8  5.892115846E-01  3.290744559E+01  2.63E-02  1.31E-01  2.02E+00  1.19E+01 -2.6E+01 2.9E+00 7.4E+01 5.6E-02
     9  1.397830815E+00  2.626856207E+01  2.10E-02  1.14E-01  2.09E+00  1.40E+01  2.0E+01 3.2E+00 6.3E+01 4.7E-02
    10  1.939370290E+00  2.116522153E+01  1.69E-02  9.99E-02  2.15E+00  1.63E+01 -1.6E+01 3.5E+00 5.5E+01 3.9E-02

    20  1.826807178E+00  2.365776501E+00  1.89E-03  2.09E-02  2.55E+00  6.46E+01 -2.3E+00 1.4E+01 3.2E+01 7.2E-03

    30  5.429335248E-01  1.875758189E-01  1.50E-04  6.38E-02  3.15E+00  2.78E+02 -4.5E-01 6.7E+01 3.0E+01 1.1E-03

    40  2.252560241E-01  2.029787414E-02  1.62E-05  2.64E-03  3.65E+00  6.58E+02 -4.9E-04 1.5E+01 7.2E-03 2.5E-04

    50  4.150697621E-05  1.969927445E-05  1.58E-08  1.23E-02  4.15E+00  2.70E+03 -5.0E-06 1.5E+00 7.4E-06 4.1E-06

    60  4.192213140E-05  1.827111106E-05  1.46E-08  1.11E-06  4.50E+00  2.93E+03 -1.6E-09 1.6E+01 2.5E-08 3.9E-06

    70  4.192211663E-05  1.827111106E-05  1.46E-08  6.20E-10  4.85E+00  3.16E+03 -1.7E-13 1.7E+01 2.9E-12 3.9E-06

    80  4.192211662E-05  1.827111106E-05  1.46E-08  3.07E-13  5.19E+00  3.40E+03 -2.9E-15 8.4E+00 2.4E-14 3.9E-06

    90  4.192211663E-05  1.827111106E-05  1.46E-08  2.00E-15  5.50E+00  3.71E+03 -3.8E-18 1.0E+01 3.9E-17 3.8E-06

    92  4.192211663E-05  1.827111106E-05  1.46E-08  2.11E-15  5.58E+00  3.76E+03 -6.2E-19 3.8E+00 2.4E-18 3.8E-06
   100  4.192211664E-05  1.827111106E-05  1.46E-08  4.17E-15  5.77E+00  5.30E+03 -3.3E-18 2.6E+01 8.6E-17 3.3E-06

   101  4.192211664E-05  1.827111106E-05  1.46E-08  2.66E-15  5.77E+00  5.31E+03  6.1E-18 5.1E+01 3.1E-16 3.3E-06
   102  4.192211664E-05  1.827111106E-05  1.46E-08  5.63E-17  5.84E+00  5.37E+03 -3.3E-19 3.0E+00 1.0E-18 3.3E-06

 Exit  LSQR.       istop  = 3               itn    =     102
 Exit  LSQR.       anorm  = 5.83659E+00     acond  = 5.36973E+03
 Exit  LSQR.       bnorm  = 1.24934E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-05     arnorm = 6.00127E-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)         = 1.59350291E-12 = rho1
    norm(A'r)       = 7.494E-13      = sigma1

    norm(s)         = 1.594E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-05 = rho2
    norm(Abar'rbar) = 6.345E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 1.338E-16 (Ax = b)
    test2           = 8.058E-02 (least-squares)
    test3           = 5.950E-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  =  4.73E-15


 --------------------------------------------------------------------
 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 =   1.4E-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
                                                                                    phi    dknorm   dxk  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  1.0E+03 1.1E+00 1.2E+03 5.8E-01
     2 -2.536537104E+01  2.478419375E+02  2.21E-01  4.14E-01  1.18E+00  2.15E+00 -3.7E+02 1.4E+00 5.3E+02 3.1E-01
     3 -2.234334321E+01  1.605741928E+02  1.43E-01  2.98E-01  1.38E+00  3.47E+00  1.9E+02 1.7E+00 3.3E+02 2.1E-01
     4 -1.850838596E+01  1.125867821E+02  1.00E-01  2.30E-01  1.54E+00  4.96E+00 -1.1E+02 2.0E+00 2.3E+02 1.5E-01
     5 -1.486363650E+01  8.277614326E+01  7.37E-02  1.85E-01  1.66E+00  6.62E+00  7.6E+01 2.3E+00 1.8E+02 1.1E-01
     6 -1.164113584E+01  6.269864588E+01  5.58E-02  1.52E-01  1.76E+00  8.46E+00 -5.4E+01 2.7E+00 1.5E+02 8.8E-02
     7 -8.856664513E+00  4.838096211E+01  4.31E-02  1.26E-01  1.83E+00  1.05E+01  4.0E+01 3.1E+00 1.2E+02 7.1E-02
     8 -6.469341196E+00  3.773364443E+01  3.36E-02  1.05E-01  1.89E+00  1.28E+01 -3.0E+01 3.6E+00 1.1E+02 5.7E-02
     9 -4.430203839E+00  2.956546508E+01  2.63E-02  8.81E-02  1.93E+00  1.54E+01  2.3E+01 4.2E+00 9.8E+01 4.6E-02
    10 -2.696584122E+00  2.315451278E+01  2.06E-02  7.34E-02  1.96E+00  1.84E+01 -1.8E+01 4.9E+00 9.0E+01 3.8E-02

    20  2.749763454E+00  2.723170269E+00  2.42E-03  1.09E-02  2.54E+00  9.51E+01 -5.5E-01 4.5E+00 2.5E+00 6.3E-03

    30  2.121950894E+00  5.420599081E-01  4.83E-04  3.02E-02  2.98E+00  3.06E+02 -5.6E-02 1.4E+01 8.1E-01 1.7E-03

    40  1.134411834E+00  8.478369333E-02  7.55E-05  5.57E-04  3.51E+00  1.03E+03 -2.1E-03 6.5E+00 1.4E-02 4.0E-04

    50  6.282812447E-01  1.728571150E-02  1.54E-05  3.45E-04  3.92E+00  2.55E+03 -3.0E-04 3.1E+01 9.2E-03 1.2E-04

    60  2.413214821E-01  8.690280874E-04  7.74E-07  9.26E-04  4.31E+00  8.88E+03 -6.2E-06 3.1E+00 1.9E-05 1.5E-05

    70  2.412372816E-01  8.683885206E-04  7.73E-07  5.88E-04  4.64E+00  9.63E+03 -5.4E-06 9.8E+01 5.3E-04 1.5E-05

    80  1.157860651E-04  1.507496556E-05  1.34E-08  1.60E-02  4.89E+00  7.71E+04 -1.2E-06 2.3E+01 2.7E-05 7.2E-07

    90  4.186692721E-05  1.829907537E-06  1.63E-09  3.06E-03  5.17E+00  8.14E+04 -3.1E-08 3.4E+01 1.1E-06 2.5E-07

   100  4.192228537E-05  1.827111138E-06  1.63E-09  1.64E-06  5.49E+00  8.65E+04 -4.6E-10 6.5E+01 3.0E-08 2.5E-07

   110  4.192210659E-05  1.827111106E-06  1.63E-09  2.11E-09  5.73E+00  9.03E+04 -3.7E-14 5.3E+00 2.0E-13 2.5E-07

   120  4.192212427E-05  1.827111106E-06  1.63E-09  8.58E-10  6.03E+00  9.50E+04 -1.1E-13 4.4E+01 5.0E-12 2.5E-07

   130  4.192212427E-05  1.827111106E-06  1.63E-09  3.53E-13  6.29E+00  9.92E+04 -1.0E-17 1.4E+00 1.4E-17 2.5E-07

   140  4.192212414E-05  1.827111106E-06  1.63E-09  5.53E-13  6.48E+00  1.03E+05 -8.1E-18 8.4E+00 6.8E-17 2.5E-07

   143  4.192212414E-05  1.827111106E-06  1.63E-09  2.59E-15  6.59E+00  1.05E+05  2.6E-19 2.0E+00 5.4E-19 2.5E-07
   145  4.192212414E-05  1.827111106E-06  1.63E-09  1.43E-15  6.67E+00  1.06E+05  5.3E-20 2.2E+00 1.2E-19 2.5E-07
   149  4.192212414E-05  1.827111106E-06  1.63E-09  2.51E-15  6.71E+00  1.07E+05  3.5E-19 2.5E+01 8.8E-18 2.5E-07
   150  4.192212414E-05  1.827111106E-06  1.63E-09  1.57E-15  6.72E+00  1.07E+05 -3.6E-19 2.9E+01 1.0E-17 2.5E-07

   151  4.192212414E-05  1.827111106E-06  1.63E-09  2.43E-16  6.76E+00  1.07E+05  2.5E-20 2.4E+00 5.9E-20 2.5E-07

 Exit  LSQR.       istop  = 3               itn    =     151
 Exit  LSQR.       anorm  = 6.75962E+00     acond  = 1.07441E+05
 Exit  LSQR.       bnorm  = 1.12336E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-06     arnorm = 2.99870E-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)         = 8.65850491E-13 = rho1
    norm(A'r)       = 5.006E-13      = sigma1

    norm(s)         = 8.659E-04
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-06 = rho2
    norm(Abar'rbar) = 5.007E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 6.426E-17 (Ax = b)
    test2           = 8.554E-02 (least-squares)
    test3           = 4.054E-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  =  4.33E-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 =   7.0E-17


 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
                                                                                    phi    dknorm   dxk  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  9.4E+02 1.1E+00 1.1E+03 6.0E-01
     2 -2.645951529E+01  2.450483281E+02  2.37E-01  3.94E-01  1.18E+00  2.16E+00 -3.5E+02 1.5E+00 5.1E+02 3.2E-01
     3 -2.607148844E+01  1.607382862E+02  1.55E-01  2.79E-01  1.37E+00  3.52E+00  1.8E+02 1.8E+00 3.3E+02 2.1E-01
     4 -2.401574568E+01  1.129290043E+02  1.09E-01  2.11E-01  1.51E+00  5.07E+00 -1.1E+02 2.2E+00 2.5E+02 1.5E-01
     5 -2.135943597E+01  8.243448020E+01  7.96E-02  1.64E-01  1.61E+00  6.84E+00  7.7E+01 2.6E+00 2.0E+02 1.1E-01
     6 -1.851085751E+01  6.145549031E+01  5.93E-02  1.30E-01  1.68E+00  8.87E+00 -5.5E+01 3.1E+00 1.7E+02 8.5E-02
     7 -1.564469118E+01  4.627345613E+01  4.47E-02  1.04E-01  1.73E+00  1.12E+01  4.0E+01 3.8E+00 1.5E+02 6.6E-02
     8 -1.284656410E+01  3.491021125E+01  3.37E-02  8.32E-02  1.76E+00  1.41E+01 -3.0E+01 4.6E+00 1.4E+02 5.1E-02
     9 -1.016820875E+01  2.622363730E+01  2.53E-02  6.60E-02  1.79E+00  1.75E+01  2.3E+01 5.7E+00 1.3E+02 4.0E-02
    10 -7.649778767E+00  1.950853237E+01  1.88E-02  5.19E-02  1.80E+00  2.18E+01 -1.8E+01 7.1E+00 1.3E+02 3.1E-02

    20  2.137798634E+00  2.004766023E+00  1.94E-03  5.88E-03  2.43E+00  1.47E+02 -1.2E+00 2.0E+01 2.4E+01 4.3E-03

    30  2.713136967E+00  3.187164333E-01  3.08E-04  5.17E-03  2.95E+00  6.28E+02 -3.3E-02 1.0E+01 3.4E-01 9.1E-04

    40  1.839327338E+00  4.969376211E-02  4.80E-05  9.42E-03  3.36E+00  2.45E+03 -8.8E-02 4.3E+02 3.8E+01 1.9E-04

    50  1.353896728E+00  2.398774165E-02  2.32E-05  4.38E-02  3.76E+00  5.79E+03 -3.5E-02 1.2E+03 4.2E+01 9.2E-05

    60  1.206168167E+00  1.135670688E-02  1.10E-05  2.92E-03  4.12E+00  8.02E+03 -3.0E-04 1.3E+02 3.9E-02 5.7E-05

    70  6.583646624E-01  1.481591073E-03  1.43E-06  2.89E-04  4.39E+00  2.24E+04 -6.0E-06 2.1E+01 1.3E-04 1.3E-05

    80  6.481347306E-01  1.463281492E-03  1.41E-06  8.14E-03  4.70E+00  3.00E+04 -1.1E-04 1.9E+03 2.1E-01 1.1E-05

    90  2.445899548E-01  3.542710640E-05  3.42E-08  2.10E-03  5.02E+00  1.25E+05 -1.4E-05 2.7E+02 3.7E-03 8.8E-07

   100  2.445858329E-01  3.521012278E-05  3.40E-08  2.33E-05  5.27E+00  1.31E+05 -1.1E-08 3.6E+01 4.0E-07 8.8E-07

   110  2.443786485E-01  3.519507961E-05  3.40E-08  1.49E-03  5.54E+00  1.52E+05 -3.3E-07 3.7E+03 1.2E-03 8.4E-07

   120  2.414461207E-01  3.498239986E-05  3.38E-08  1.98E-04  5.79E+00  2.94E+05 -2.9E-07 3.2E+03 9.2E-04 6.1E-07

   130  1.146422168E-04  6.543528194E-07  6.32E-10  1.84E-03  6.04E+00  2.36E+06 -1.0E-07 1.1E+03 1.1E-04 3.0E-08

   140  6.966792712E-05  4.464172305E-07  4.31E-10  1.79E-03  6.25E+00  2.45E+06 -9.8E-09 1.1E+02 1.1E-06 2.5E-08

   150  4.189962477E-05  1.827118589E-07  1.76E-10  3.48E-06  6.49E+00  2.54E+06 -1.1E-11 6.7E+00 7.3E-11 1.6E-08

   160  4.191457340E-05  1.827113092E-07  1.76E-10  1.41E-04  6.68E+00  2.62E+06 -2.3E-10 2.4E+03 5.7E-07 1.6E-08

   170  4.192219841E-05  1.827111119E-07  1.76E-10  6.14E-08  6.91E+00  2.71E+06 -6.6E-13 7.3E+00 4.8E-12 1.6E-08

   180  4.192223911E-05  1.827111106E-07  1.76E-10  8.70E-10  7.12E+00  2.79E+06 -1.1E-14 3.1E+01 3.4E-13 1.6E-08

   190  4.192223911E-05  1.827111106E-07  1.76E-10  8.01E-10  7.31E+00  2.86E+06 -1.3E-15 3.6E+02 4.7E-13 1.6E-08

   200  4.192223910E-05  1.827111106E-07  1.76E-10  3.08E-10  7.46E+00  2.92E+06 -7.8E-16 5.1E+02 4.0E-13 1.6E-08

   210  4.192223231E-05  1.827111106E-07  1.76E-10  1.50E-12  7.70E+00  3.02E+06 -4.8E-18 5.5E+00 2.6E-17 1.6E-08

   220  4.192223231E-05  1.827111106E-07  1.76E-10  2.07E-13  7.83E+00  3.07E+06 -4.5E-19 1.0E+01 4.5E-18 1.6E-08

   228  4.192223231E-05  1.827111106E-07  1.76E-10  2.62E-15  7.99E+00  3.13E+06 -2.1E-20 2.9E+00 6.1E-20 1.6E-08
   229  4.192223231E-05  1.827111106E-07  1.76E-10  2.53E-15  8.02E+00  3.15E+06  5.5E-21 1.6E+00 9.0E-21 1.6E-08
   230  4.192223231E-05  1.827111106E-07  1.76E-10  2.97E-15  8.06E+00  3.16E+06 -1.3E-20 5.2E+00 6.6E-20 1.6E-08

   235  4.192223231E-05  1.827111106E-07  1.76E-10  2.46E-16  8.14E+00  3.19E+06  7.8E-20 3.7E+01 2.9E-18 1.6E-08

 Exit  LSQR.       istop  = 3               itn    =     235
 Exit  LSQR.       anorm  = 8.13520E+00     acond  = 3.19077E+06
 Exit  LSQR.       bnorm  = 1.03550E+03     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-07     arnorm = 3.65295E-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)         = 9.86552725E-13 = rho1
    norm(A'r)       = 6.659E-13      = sigma1

    norm(s)         = 9.866E-03
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-07 = rho2
    norm(Abar'rbar) = 6.659E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 6.205E-17 (Ax = b)
    test2           = 8.297E-02 (least-squares)
    test3           = 4.480E-07 (damped least-squares)


 Solution  x:
     1  0.419222E-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  =  1.05E-11


 --------------------------------------------------------------------
 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 =   2.8E-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
                                                                                    phi    dknorm   dxk  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  8.8E+02 1.1E+00 9.7E+02 6.2E-01
     2 -2.596081160E+01  2.371904556E+02  2.44E-01  3.77E-01  1.18E+00  2.17E+00 -3.3E+02 1.5E+00 4.9E+02 3.3E-01
     3 -2.724993460E+01  1.551916987E+02  1.60E-01  2.61E-01  1.36E+00  3.56E+00  1.8E+02 1.9E+00 3.4E+02 2.1E-01
     4 -2.658801144E+01  1.077314213E+02  1.11E-01  1.92E-01  1.47E+00  5.19E+00 -1.1E+02 2.3E+00 2.6E+02 1.5E-01
     5 -2.492214847E+01  7.702278580E+01  7.94E-02  1.45E-01  1.55E+00  7.12E+00  7.5E+01 2.9E+00 2.2E+02 1.1E-01
     6 -2.267029833E+01  5.576674457E+01  5.75E-02  1.11E-01  1.60E+00  9.45E+00 -5.3E+01 3.7E+00 2.0E+02 7.8E-02
     7 -2.005231567E+01  4.044553417E+01  4.17E-02  8.46E-02  1.63E+00  1.23E+01  3.8E+01 4.7E+00 1.8E+02 5.8E-02
     8 -1.720991793E+01  2.915470492E+01  3.00E-02  6.42E-02  1.65E+00  1.60E+01 -2.8E+01 6.1E+00 1.7E+02 4.3E-02
     9 -1.425515843E+01  2.075998677E+01  2.14E-02  4.81E-02  1.66E+00  2.09E+01  2.0E+01 8.0E+00 1.6E+02 3.2E-02
    10 -1.129010604E+01  1.452597689E+01  1.50E-02  3.55E-02  1.67E+00  2.74E+01 -1.5E+01 1.1E+01 1.6E+02 2.3E-02

    20  4.825087145E-01  1.545313849E+00  1.59E-03  1.94E-02  2.28E+00  2.01E+02 -1.7E-01 1.3E+01 2.2E+00 3.1E-03

    30  2.832643839E+00  2.141614020E-01  2.21E-04  3.07E-02  2.82E+00  1.06E+03 -5.8E-02 4.5E+01 2.6E+00 5.6E-04

    40  2.807111357E+00  8.721204267E-02  8.99E-05  5.91E-04  3.34E+00  2.33E+03 -3.5E-04 5.1E+00 1.8E-03 2.6E-04

    50  2.453721081E+00  3.016164389E-02  3.11E-05  5.69E-03  3.69E+00  5.57E+03 -4.1E-03 4.4E+02 1.8E+00 1.0E-04

    60  1.911627020E+00  8.229728410E-03  8.48E-06  3.42E-05  4.02E+00  1.39E+04 -1.0E-04 8.1E+01 8.4E-03 3.6E-05

    70  1.269352223E+00  1.491775242E-03  1.54E-06  4.82E-03  4.34E+00  4.41E+04 -1.5E-03 1.7E+03 2.5E+00 9.0E-06

    80  1.268578257E+00  1.472776766E-03  1.52E-06  2.68E-05  4.64E+00  4.72E+04 -3.6E-06 9.6E+01 3.4E-04 8.9E-06

    90  6.697060394E-01  1.228821569E-04  1.27E-07  2.28E-03  4.90E+00  2.03E+05 -2.5E-06 6.9E+01 1.7E-04 1.3E-06

   100  6.696027229E-01  1.216247391E-04  1.25E-07  1.05E-05  5.24E+00  2.17E+05 -3.3E-08 5.6E+00 1.8E-07 1.3E-06

   110  6.695957921E-01  1.216234060E-04  1.25E-07  2.91E-06  5.49E+00  2.28E+05 -7.1E-09 1.7E+01 1.2E-07 1.3E-06

   120  4.459927976E-01  8.365637303E-05  8.62E-08  6.63E-02  5.70E+00  1.29E+06 -7.0E-05 1.8E+05 1.2E+01 4.5E-07

   130  2.457654616E-01  4.093501695E-06  4.22E-09  4.10E-02  5.91E+00  1.82E+06 -2.6E-06 6.5E+03 1.7E-02 8.5E-08

   140  2.453436558E-01  1.412862624E-06  1.46E-09  9.62E-07  6.14E+00  1.89E+06 -2.8E-11 1.8E+00 5.0E-11 5.0E-08

   150  2.453436320E-01  1.412861721E-06  1.46E-09  6.92E-08  6.33E+00  1.95E+06 -1.6E-09 3.3E+03 5.2E-06 5.0E-08

   160  2.453436317E-01  1.412861712E-06  1.46E-09  1.04E-07  6.53E+00  2.01E+06 -2.4E-12 1.4E+01 3.4E-11 5.0E-08

   170  2.444995544E-01  1.410432042E-06  1.45E-09  8.05E-03  6.73E+00  4.38E+06 -8.0E-08 5.5E+05 4.5E-02 3.4E-08

   180  2.272988293E-01  1.359974031E-06  1.40E-09  1.58E-02  6.91E+00  1.84E+07 -2.8E-07 1.9E+06 5.3E-01 1.7E-08

   190  2.159991483E-01  1.325775783E-06  1.37E-09  2.05E-04  7.17E+00  2.43E+07 -2.7E-08 1.9E+05 5.1E-03 1.5E-08

   200  4.336254305E-02  5.940067963E-07  6.12E-10  7.42E-03  7.35E+00  6.51E+07 -2.6E-07 1.8E+06 4.8E-01 6.1E-09

   210  4.748959598E-05  1.915702073E-08  1.97E-11  3.91E-04  7.53E+00  7.36E+07 -3.4E-10 2.4E+03 8.2E-07 1.0E-09

   220  4.513145939E-05  1.864781068E-08  1.92E-11  5.33E-06  7.68E+00  7.50E+07 -1.2E-12 1.4E+01 1.7E-11 1.0E-09

   230  4.323434378E-05  1.842614170E-08  1.90E-11  6.70E-03  7.85E+00  7.67E+07 -2.4E-09 3.1E+04 7.4E-05 1.0E-09

   240  4.192153856E-05  1.827111107E-08  1.88E-11  1.65E-08  8.00E+00  7.82E+07 -4.4E-15 2.8E+00 1.2E-14 1.0E-09

   250  4.192153802E-05  1.827111106E-08  1.88E-11  5.13E-07  8.16E+00  7.97E+07 -2.3E-13 2.5E+02 5.7E-11 1.0E-09

   260  4.192153612E-05  1.827111106E-08  1.88E-11  2.24E-07  8.35E+00  8.16E+07 -5.9E-14 8.6E+02 5.1E-11 1.0E-09

   270  4.192153521E-05  1.827111106E-08  1.88E-11  7.07E-11  8.51E+00  8.32E+07 -1.7E-17 1.2E+01 2.1E-16 1.0E-09

   280  4.192272319E-05  1.827111106E-08  1.88E-11  3.78E-07  8.65E+00  8.46E+07 -3.6E-13 2.8E+05 1.0E-07 1.0E-09

   290  4.192287776E-05  1.827111106E-08  1.88E-11  9.65E-09  8.83E+00  8.63E+07 -2.3E-14 1.8E+04 4.0E-10 1.0E-09

   300  4.192287783E-05  1.827111106E-08  1.88E-11  4.19E-11  8.96E+00  8.76E+07 -1.4E-17 2.2E+01 3.0E-16 1.0E-09

   310  4.192287783E-05  1.827111106E-08  1.88E-11  2.21E-11  9.09E+00  8.88E+07 -5.0E-18 1.8E+01 9.2E-17 1.0E-09

   320  4.192287774E-05  1.827111106E-08  1.88E-11  1.81E-12  9.27E+00  9.07E+07 -6.6E-19 2.8E+00 1.9E-18 1.0E-09

   329  4.192287774E-05  1.827111106E-08  1.88E-11  1.03E-15  9.40E+00  9.19E+07  1.1E-20 4.1E+00 4.6E-20 1.0E-09
   330  4.192287774E-05  1.827111106E-08  1.88E-11  1.62E-16  9.43E+00  9.22E+07 -2.7E-22 1.5E+00 4.2E-22 1.0E-09


 Exit  LSQR.       istop  = 3               itn    =     330
 Exit  LSQR.       anorm  = 9.42730E+00     acond  = 9.21551E+07
 Exit  LSQR.       bnorm  = 9.70353E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-08     arnorm = 2.79529E-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)         = 7.35003635E-13 = rho1
    norm(A'r)       = 5.605E-13      = sigma1

    norm(s)         = 7.350E-02
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711111E-08 = rho2
    norm(Abar'rbar) = 5.605E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 4.040E-17 (Ax = b)
    test2           = 8.089E-02 (least-squares)
    test3           = 3.254E-06 (damped least-squares)


 Solution  x:
     1  0.419229E-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  =  1.04E-10


 --------------------------------------------------------------------
 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 =   2.8E-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
                                                                                    phi    dknorm   dxk  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  8.3E+02 1.1E+00 9.1E+02 6.3E-01
     2 -2.491620749E+01  2.273238818E+02  2.47E-01  3.61E-01  1.18E+00  2.19E+00 -3.2E+02 1.5E+00 4.8E+02 3.3E-01
     3 -2.727058314E+01  1.470028524E+02  1.60E-01  2.44E-01  1.34E+00  3.62E+00  1.7E+02 2.0E+00 3.4E+02 2.1E-01
     4 -2.762338174E+01  9.992899974E+01  1.09E-01  1.74E-01  1.44E+00  5.35E+00 -1.1E+02 2.6E+00 2.8E+02 1.4E-01
     5 -2.677116869E+01  6.936381708E+01  7.54E-02  1.27E-01  1.50E+00  7.50E+00  7.2E+01 3.3E+00 2.4E+02 9.8E-02
     6 -2.508690921E+01  4.836804697E+01  5.26E-02  9.27E-02  1.53E+00  1.02E+01 -5.0E+01 4.4E+00 2.2E+02 6.9E-02
     7 -2.278857494E+01  3.353135997E+01  3.64E-02  6.75E-02  1.55E+00  1.39E+01  3.5E+01 5.9E+00 2.1E+02 4.9E-02
     8 -2.003892020E+01  2.294165156E+01  2.49E-02  4.85E-02  1.56E+00  1.89E+01 -2.4E+01 8.1E+00 2.0E+02 3.5E-02
     9 -1.698519447E+01  1.540241771E+01  1.67E-02  3.43E-02  1.57E+00  2.59E+01  1.7E+01 1.1E+01 1.9E+02 2.4E-02
    10 -1.377297980E+01  1.009643339E+01  1.10E-02  2.37E-02  1.57E+00  3.61E+01 -1.2E+01 1.6E+01 1.9E+02 1.6E-02

    20 -2.135485253E+00  1.316785647E+00  1.43E-03  1.81E-02  2.20E+00  2.48E+02 -5.4E-02 6.9E+00 3.8E-01 2.6E-03

    30  2.333332119E+00  1.640337892E-01  1.78E-04  8.87E-03  2.85E+00  1.59E+03 -2.7E-01 4.1E+02 1.1E+02 4.0E-04

    40  2.828610750E+00  6.446670910E-02  7.01E-05  2.01E-03  3.21E+00  3.54E+03 -9.6E-04 3.3E+01 3.2E-02 1.8E-04

    50  2.779678925E+00  2.037157348E-02  2.21E-05  1.43E-02  3.56E+00  1.20E+04 -5.8E-03 1.4E+03 8.2E+00 5.8E-05

    60  2.521428790E+00  6.491961554E-03  7.06E-06  2.16E-05  3.88E+00  2.24E+04 -2.6E-06 4.2E+00 1.1E-05 2.5E-05

    70  1.953108098E+00  1.381093408E-03  1.50E-06  6.29E-04  4.29E+00  7.15E+04 -2.9E-04 7.1E+02 2.1E-01 6.7E-06

    80  1.953012744E+00  1.380519390E-03  1.50E-06  2.76E-05  4.56E+00  7.60E+04 -7.5E-07 3.2E+01 2.4E-05 6.7E-06

    90  1.289137021E+00  1.859765758E-04  2.02E-07  9.48E-04  4.82E+00  2.98E+05 -1.2E-06 5.2E+01 6.0E-05 1.3E-06

   100  1.288486088E+00  1.819049060E-04  1.98E-07  4.25E-05  5.08E+00  3.15E+05 -7.9E-08 6.7E+00 5.3E-07 1.3E-06

   110  1.279702638E+00  1.805925995E-04  1.96E-07  3.66E-05  5.32E+00  3.93E+05 -6.0E-07 1.1E+03 6.7E-04 1.2E-06

   120  6.742196216E-01  9.924853647E-06  1.08E-08  1.97E-02  5.54E+00  1.89E+06 -1.0E-04 1.9E+05 2.0E+01 1.3E-07

   130  6.741940742E-01  9.856894475E-06  1.07E-08  2.02E-03  5.81E+00  1.98E+06 -2.5E-07 8.2E+02 2.0E-04 1.3E-07

   140  6.741839476E-01  9.833232602E-06  1.07E-08  2.01E-04  6.00E+00  2.05E+06 -2.3E-08 8.2E+01 1.9E-06 1.3E-07

   150  6.740995582E-01  9.832151580E-06  1.07E-08  2.01E-06  6.23E+00  2.15E+06 -3.6E-09 1.4E+03 5.1E-06 1.2E-07

   160  6.740877328E-01  9.832013855E-06  1.07E-08  7.06E-06  6.39E+00  2.21E+06 -1.2E-09 4.8E+02 5.9E-07 1.2E-07

   170  2.606950461E-01  1.852007786E-06  2.01E-09  1.03E-02  6.61E+00  2.49E+07 -2.0E-07 7.7E+04 1.5E-02 1.6E-08

   180  2.459261463E-01  3.145282207E-07  3.42E-10  1.95E-05  6.81E+00  2.61E+07 -9.6E-10 3.7E+02 3.6E-07 6.7E-09

   190  2.457539734E-01  2.400929019E-07  2.61E-10  6.59E-03  7.01E+00  2.68E+07 -1.9E-07 7.4E+04 1.4E-02 5.9E-09

   200  2.455274566E-01  5.658812554E-08  6.15E-11  2.89E-04  7.15E+00  2.74E+07 -2.2E-09 8.7E+02 1.9E-06 2.8E-09

   210  2.455274534E-01  5.658167114E-08  6.15E-11  8.66E-08  7.36E+00  2.82E+07 -2.9E-13 1.3E+02 3.7E-11 2.8E-09

   220  2.455274535E-01  5.658167058E-08  6.15E-11  1.27E-06  7.52E+00  2.88E+07 -6.0E-12 3.1E+03 1.9E-08 2.8E-09

   230  2.455274539E-01  5.658166953E-08  6.15E-11  4.82E-07  7.74E+00  2.96E+07 -1.7E-12 9.8E+02 1.6E-09 2.8E-09

   240  2.455274870E-01  5.658157855E-08  6.15E-11  2.08E-08  7.89E+00  3.02E+07 -8.5E-14 1.7E+02 1.4E-11 2.8E-09

   250  2.455274855E-01  5.658157837E-08  6.15E-11  3.03E-07  8.03E+00  3.07E+07 -3.2E-12 1.4E+04 4.3E-08 2.8E-09

   260  2.455273446E-01  5.658156219E-08  6.15E-11  9.21E-06  8.17E+00  3.13E+07 -1.2E-11 5.3E+04 6.5E-07 2.8E-09

   270  2.455273017E-01  5.658155726E-08  6.15E-11  3.84E-07  8.37E+00  3.21E+07 -1.5E-12 6.7E+03 1.0E-08 2.8E-09

   280  1.841722070E-01  4.900771300E-08  5.33E-11  1.58E-04  8.52E+00  1.04E+09 -2.1E-09 9.2E+06 2.0E-02 4.7E-10

   290  7.157441428E-02  3.056353245E-08  3.32E-11  5.73E-06  8.66E+00  1.78E+09 -2.3E-11 1.0E+05 2.3E-06 2.9E-10

   300  7.156795403E-02  3.056215693E-08  3.32E-11  7.37E-06  8.79E+00  1.81E+09 -2.2E-11 9.6E+04 2.1E-06 2.9E-10

   310  6.574478283E-02  2.929612014E-08  3.18E-11  5.94E-05  8.95E+00  1.87E+09 -3.2E-11 1.4E+05 4.3E-06 2.8E-10

   320  6.512618603E-02  2.915840211E-08  3.17E-11  1.10E-04  9.11E+00  1.91E+09 -4.6E-11 2.0E+05 8.9E-06 2.8E-10

   330  1.053068980E-04  2.040316790E-09  2.22E-12  4.82E-04  9.25E+00  2.26E+09 -3.7E-11 1.6E+05 6.0E-06 6.8E-11

   340  4.196879779E-05  1.827222627E-09  1.99E-12  5.26E-06  9.39E+00  2.29E+09 -2.1E-12 9.2E+03 2.0E-08 6.4E-11

   350  4.193745175E-05  1.827111128E-09  1.99E-12  2.72E-08  9.55E+00  2.33E+09 -2.8E-15 1.2E+01 3.4E-14 6.4E-11

   360  4.193745168E-05  1.827111128E-09  1.99E-12  2.13E-09  9.67E+00  2.36E+09 -8.1E-16 2.0E+01 1.6E-14 6.4E-11

   370  4.193745207E-05  1.827111124E-09  1.99E-12  2.10E-10  9.79E+00  2.39E+09 -1.4E-17 4.5E+00 6.3E-17 6.4E-11

   380  4.193744101E-05  1.827111124E-09  1.99E-12  1.70E-10  9.91E+00  2.42E+09 -3.1E-16 6.6E+02 2.1E-13 6.4E-11

   390  4.193744101E-05  1.827111124E-09  1.99E-12  5.66E-11  1.00E+01  2.45E+09 -3.5E-18 7.8E+00 2.7E-17 6.4E-11

   400  4.193744125E-05  1.827111124E-09  1.99E-12  3.84E-10  1.02E+01  2.49E+09 -3.9E-17 5.8E+02 2.3E-14 6.4E-11

   410  4.193744162E-05  1.827111124E-09  1.99E-12  9.15E-10  1.03E+01  2.52E+09 -2.8E-17 4.2E+02 1.2E-14 6.4E-11

   420  4.193744180E-05  1.827111124E-09  1.99E-12  1.60E-10  1.04E+01  2.55E+09 -8.0E-17 1.2E+03 9.5E-14 6.4E-11

   430  4.194778690E-05  1.827111106E-09  1.99E-12  2.89E-10  1.06E+01  2.58E+09 -6.8E-17 1.0E+03 6.9E-14 6.4E-11

   440  4.194778694E-05  1.827111106E-09  1.99E-12  1.43E-09  1.07E+01  2.62E+09 -1.0E-16 1.6E+03 1.6E-13 6.4E-11

   450  4.194779324E-05  1.827111106E-09  1.99E-12  3.28E-12  1.08E+01  2.64E+09 -7.1E-19 1.1E+01 7.9E-18 6.4E-11

   460  4.194779324E-05  1.827111106E-09  1.99E-12  1.62E-13  1.09E+01  2.67E+09 -1.9E-20 3.0E+01 5.7E-19 6.4E-11

   470  4.194779324E-05  1.827111106E-09  1.99E-12  5.68E-13  1.10E+01  2.70E+09 -2.5E-19 5.4E+02 1.3E-16 6.4E-11

   472  4.194779324E-05  1.827111106E-09  1.99E-12  2.42E-15  1.11E+01  2.71E+09 -5.9E-21 1.3E+01 7.6E-20 6.4E-11
   474  4.194779324E-05  1.827111106E-09  1.99E-12  1.84E-15  1.11E+01  2.72E+09 -2.5E-22 5.7E+00 1.4E-21 6.4E-11
   480  4.194779324E-05  1.827111106E-09  1.99E-12  4.81E-13  1.11E+01  2.72E+09 -1.9E-20 6.6E+02 1.3E-17 6.4E-11

   490  4.194779324E-05  1.827111106E-09  1.99E-12  1.78E-12  1.13E+01  2.76E+09 -2.4E-19 8.7E+03 2.1E-15 6.4E-11

   500  4.194779326E-05  1.827111106E-09  1.99E-12  4.63E-14  1.14E+01  2.78E+09 -6.6E-21 2.5E+02 1.6E-18 6.4E-11

   508  4.194779326E-05  1.827111106E-09  1.99E-12  2.32E-15  1.15E+01  2.81E+09 -4.0E-20 1.5E+03 6.0E-17 6.4E-11
   510  4.194779326E-05  1.827111106E-09  1.99E-12  1.03E-14  1.15E+01  2.81E+09 -6.0E-22 2.6E+01 1.5E-20 6.4E-11

   512  4.194779326E-05  1.827111106E-09  1.99E-12  6.73E-18  1.15E+01  2.82E+09 -1.2E-21 5.3E+01 6.5E-20 6.4E-11

 Exit  LSQR.       istop  = 3               itn    =     512
 Exit  LSQR.       anorm  = 1.15326E+01     acond  = 2.81628E+09
 Exit  LSQR.       bnorm  = 9.19970E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-09     arnorm = 1.41815E-25
 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)         = 8.24226726E-13 = rho1
    norm(A'r)       = 5.927E-13      = sigma1

    norm(s)         = 8.242E-01
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82711129E-09 = rho2
    norm(Abar'rbar) = 5.927E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.748E-17 (Ax = b)
    test2           = 6.235E-02 (least-squares)
    test3           = 2.813E-05 (damped least-squares)


 Solution  x:
     1  0.419478E-04     2  0.100048         3  0.200058         4  0.300071    
     5  0.400089         6  0.500111         7  0.600137         8  0.700166    

 LSQR  appears to be successful.     Relative error in  x  =  2.25E-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 =   7.1E-17


 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
                                                                                    phi    dknorm   dxk  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  7.9E+02 1.1E+00 8.6E+02 6.4E-01
     2 -2.375095537E+01  2.166607925E+02  2.46E-01  3.45E-01  1.18E+00  2.20E+00 -3.1E+02 1.5E+00 4.7E+02 3.3E-01
     3 -2.680778713E+01  1.375730438E+02  1.56E-01  2.27E-01  1.32E+00  3.69E+00  1.7E+02 2.1E+00 3.5E+02 2.0E-01
     4 -2.790545888E+01  9.099234087E+01  1.03E-01  1.56E-01  1.40E+00  5.56E+00 -1.0E+02 2.8E+00 2.9E+02 1.3E-01
     5 -2.769789733E+01  6.094925399E+01  6.93E-02  1.10E-01  1.44E+00  7.99E+00  6.8E+01 3.9E+00 2.6E+02 8.9E-02
     6 -2.649845769E+01  4.070971620E+01  4.63E-02  7.67E-02  1.47E+00  1.13E+01 -4.5E+01 5.4E+00 2.4E+02 6.0E-02
     7 -2.450619289E+01  2.685449180E+01  3.05E-02  5.30E-02  1.48E+00  1.60E+01  3.1E+01 7.6E+00 2.3E+02 4.0E-02
     8 -2.188969497E+01  1.737868266E+01  1.98E-02  3.61E-02  1.48E+00  2.29E+01 -2.0E+01 1.1E+01 2.2E+02 2.7E-02
     9 -1.881797962E+01  1.097464397E+01  1.25E-02  2.40E-02  1.49E+00  3.32E+01  1.3E+01 1.6E+01 2.2E+02 1.7E-02
    10 -1.553346711E+01  6.816215309E+00  7.75E-03  1.07E-01  1.49E+00  4.91E+01 -8.6E+00 2.4E+01 2.1E+02 1.1E-02

    20 -2.794108319E+00  6.342842859E-01  7.21E-04  3.70E-03  2.31E+00  5.05E+02 -9.5E-01 1.6E+02 1.5E+02 1.3E-03

    30  1.150029064E+00  1.352776762E-01  1.54E-04  2.87E-03  2.73E+00  2.01E+03 -1.8E-03 1.4E+01 2.6E-02 3.2E-04

    40  2.444248675E+00  4.536980001E-02  5.16E-05  5.91E-03  3.19E+00  7.27E+03 -2.9E-02 1.6E+03 4.7E+01 1.1E-04

    50  2.817206405E+00  1.911950381E-02  2.17E-05  6.35E-03  3.63E+00  1.21E+04 -1.3E-03 5.4E+02 7.2E-01 5.6E-05

    60  2.879171018E+00  5.714945139E-03  6.50E-06  1.09E-04  3.92E+00  3.19E+04 -5.5E-05 2.1E+02 1.2E-02 2.0E-05

    70  2.553741665E+00  1.350911372E-03  1.54E-06  2.54E-05  4.19E+00  9.78E+04 -7.4E-05 2.9E+02 2.2E-02 5.6E-06

    80  2.553761373E+00  1.350162670E-03  1.53E-06  4.61E-05  4.55E+00  1.06E+05 -1.2E-05 7.0E+02 8.5E-03 5.6E-06

    90  1.976097957E+00  2.273250637E-04  2.58E-07  7.97E-03  4.78E+00  3.90E+05 -4.4E-05 2.6E+03 1.1E-01 1.2E-06

   100  1.976053941E+00  2.270096485E-04  2.58E-07  6.11E-07  5.06E+00  4.13E+05 -4.8E-09 3.8E+00 1.8E-08 1.2E-06

   110  1.975699829E+00  2.269567250E-04  2.58E-07  1.09E-05  5.27E+00  4.32E+05 -2.3E-07 3.7E+02 8.5E-05 1.2E-06

   120  1.298680439E+00  2.228119891E-05  2.53E-08  5.88E-05  5.56E+00  2.12E+06 -7.9E-07 1.3E+03 1.0E-03 1.8E-07

   130  1.298593335E+00  2.215857473E-05  2.52E-08  2.29E-04  5.75E+00  2.19E+06 -6.4E-07 3.1E+03 2.0E-03 1.8E-07

   140  1.298592886E+00  2.215831564E-05  2.52E-08  5.34E-06  5.94E+00  2.26E+06 -9.1E-09 1.1E+03 1.0E-05 1.8E-07

   150  1.285014912E+00  2.191552102E-05  2.49E-08  4.03E-04  6.20E+00  3.48E+06 -2.6E-06 3.3E+05 8.6E-01 1.5E-07

   160  1.090286846E+00  1.808177461E-05  2.06E-08  1.46E-05  6.40E+00  1.06E+07 -2.3E-08 2.9E+03 6.6E-05 7.7E-08

   170  6.761870208E-01  8.179071783E-07  9.30E-10  2.33E-04  6.57E+00  1.85E+07 -1.8E-07 2.2E+04 3.9E-03 1.3E-08

   180  6.761308199E-01  7.902218943E-07  8.98E-10  1.15E-05  6.81E+00  1.92E+07 -3.5E-10 4.5E+01 1.6E-08 1.2E-08

   190  6.761308141E-01  7.902197424E-07  8.98E-10  8.71E-08  6.96E+00  1.96E+07 -4.1E-12 1.1E+01 4.6E-11 1.2E-08

   200  6.761309767E-01  7.901941660E-07  8.98E-10  1.39E-07  7.12E+00  2.00E+07 -1.4E-12 8.4E+01 1.2E-10 1.2E-08

   210  6.761309732E-01  7.901941631E-07  8.98E-10  5.87E-08  7.28E+00  2.05E+07 -3.7E-13 2.2E+01 8.0E-12 1.2E-08

   220  6.761303645E-01  7.901936074E-07  8.98E-10  1.53E-06  7.48E+00  2.11E+07 -1.8E-10 1.1E+04 1.9E-06 1.2E-08

   230  5.602324972E-01  6.756274728E-07  7.68E-10  1.37E-02  7.66E+00  1.91E+08 -4.1E-07 2.5E+07 1.0E+01 3.9E-09

   240  4.921013443E-01  5.981236822E-07  6.80E-10  3.21E-05  7.80E+00  2.44E+08 -1.7E-09 1.0E+05 1.7E-04 3.2E-09

   250  4.547297850E-01  5.509266961E-07  6.26E-10  4.50E-04  7.99E+00  2.74E+08 -7.5E-08 4.5E+06 3.4E-01 3.0E-09

   260  2.458678815E-01  2.087922275E-08  2.37E-11  2.47E-05  8.13E+00  3.88E+08 -3.6E-08 2.2E+06 7.7E-02 4.9E-10

   270  2.456290882E-01  9.469530748E-09  1.08E-11  2.27E-02  8.26E+00  3.95E+08 -3.2E-09 1.9E+05 6.2E-04 3.3E-10

   280  2.455711718E-01  2.371287527E-09  2.70E-12  2.21E-04  8.47E+00  4.05E+08 -1.1E-11 6.4E+02 6.9E-09 1.6E-10

   290  2.455711716E-01  2.371215980E-09  2.70E-12  8.90E-07  8.61E+00  4.11E+08 -3.0E-13 6.9E+01 2.1E-11 1.6E-10

   300  2.455721099E-01  2.316010547E-09  2.63E-12  1.76E-05  8.73E+00  4.17E+08 -1.6E-12 8.7E+02 1.4E-09 1.6E-10

   310  2.455728762E-01  2.269876768E-09  2.58E-12  6.12E-07  8.90E+00  4.25E+08 -7.8E-14 4.4E+01 3.5E-12 1.6E-10

   320  2.455728762E-01  2.269876748E-09  2.58E-12  4.49E-06  9.03E+00  4.31E+08 -2.4E-13 1.1E+03 2.6E-10 1.6E-10

   330  2.455728762E-01  2.269876680E-09  2.58E-12  1.37E-06  9.16E+00  4.38E+08 -1.9E-13 1.4E+03 2.6E-10 1.6E-10

   340  2.455728761E-01  2.269874903E-09  2.58E-12  1.17E-07  9.29E+00  4.44E+08 -3.5E-15 3.0E+01 1.1E-13 1.6E-10

   350  2.455728761E-01  2.269874897E-09  2.58E-12  4.38E-11  9.46E+00  4.52E+08 -6.6E-18 1.6E+01 1.1E-16 1.6E-10

   360  2.455728482E-01  2.269874766E-09  2.58E-12  9.87E-09  9.59E+00  4.58E+08 -5.2E-15 1.4E+04 7.3E-11 1.6E-10

   370  2.455728447E-01  2.269874749E-09  2.58E-12  3.05E-06  9.69E+00  4.64E+08 -1.6E-13 4.4E+05 7.3E-08 1.6E-10

   380  2.455555723E-01  2.269793153E-09  2.58E-12  8.87E-07  9.85E+00  6.95E+08 -1.1E-13 2.9E+05 3.2E-08 1.3E-10

   390  2.455553433E-01  2.269792072E-09  2.58E-12  1.69E-07  9.96E+00  7.05E+08 -5.2E-15 1.4E+04 7.4E-11 1.3E-10

   400  2.455553414E-01  2.269792063E-09  2.58E-12  4.53E-09  1.01E+01  7.15E+08 -3.2E-15 8.7E+03 2.8E-11 1.3E-10

   410  2.455553413E-01  2.269792063E-09  2.58E-12  5.95E-07  1.02E+01  7.23E+08 -1.5E-14 4.0E+04 5.9E-10 1.3E-10

   420  2.455552591E-01  2.269791675E-09  2.58E-12  2.01E-09  1.04E+01  7.34E+08 -1.2E-15 3.2E+03 3.7E-12 1.3E-10

   430  2.455552499E-01  2.269791633E-09  2.58E-12  5.42E-06  1.05E+01  7.42E+08 -4.4E-13 1.2E+06 5.1E-07 1.3E-10

   440  1.583024643E-01  1.825613633E-09  2.08E-12  4.08E-03  1.06E+01  3.85E+10 -7.9E-11 2.1E+08 1.7E-02 1.7E-11

   450  4.363636050E-02  9.706951303E-10  1.10E-12  1.37E-04  1.07E+01  5.93E+10 -1.1E-09 3.1E+09 3.5E+00 9.8E-12

   460  1.765687145E-03  2.632646651E-10  2.99E-13  2.36E-04  1.08E+01  6.58E+10 -1.1E-12 3.0E+06 3.4E-06 4.9E-12

   470  2.366288367E-04  1.934676180E-10  2.20E-13  2.71E-05  1.09E+01  6.67E+10 -1.1E-11 3.1E+07 3.6E-04 4.2E-12

   480  1.425178805E-04  1.883285822E-10  2.14E-13  7.34E-04  1.11E+01  6.76E+10 -4.0E-11 1.1E+08 4.4E-03 4.1E-12

   490  1.187559012E-04  1.870087118E-10  2.13E-13  8.09E-05  1.12E+01  6.82E+10 -1.9E-11 5.1E+07 9.5E-04 4.1E-12

   500  1.175581346E-04  1.869420292E-10  2.12E-13  2.27E-03  1.13E+01  6.88E+10 -4.9E-12 1.3E+07 6.4E-05 4.1E-12

   510  4.248549028E-05  1.827143356E-10  2.08E-13  3.69E-06  1.14E+01  6.96E+10 -5.2E-12 1.4E+07 7.4E-05 4.0E-12

   520  4.248397656E-05  1.827142493E-10  2.08E-13  3.22E-08  1.15E+01  7.02E+10 -9.6E-15 2.6E+04 2.5E-10 4.0E-12

   530  4.248396267E-05  1.827142486E-10  2.08E-13  1.87E-11  1.16E+01  7.09E+10 -5.0E-19 2.0E+00 9.9E-19 4.0E-12

   540  4.248396267E-05  1.827142486E-10  2.08E-13  4.36E-10  1.17E+01  7.15E+10 -9.4E-19 4.2E+01 3.9E-17 4.0E-12

   550  4.248383733E-05  1.827142479E-10  2.08E-13  2.44E-08  1.18E+01  7.23E+10 -1.4E-16 6.4E+03 9.2E-13 4.0E-12

   560  4.248372147E-05  1.827142473E-10  2.08E-13  5.63E-09  1.19E+01  7.28E+10 -2.1E-16 9.1E+03 1.9E-12 4.0E-12

   570  4.248372119E-05  1.827142473E-10  2.08E-13  2.90E-08  1.21E+01  7.36E+10 -2.8E-16 1.3E+04 3.5E-12 4.0E-12

   580  4.246369204E-05  1.827141402E-10  2.08E-13  3.08E-06  1.22E+01  7.42E+10 -3.4E-14 1.5E+06 5.0E-08 4.0E-12

   590  4.242114647E-05  1.827139129E-10  2.08E-13  1.30E-05  1.22E+01  7.47E+10 -2.8E-13 1.3E+07 3.6E-06 4.0E-12

   600  4.242003862E-05  1.827139070E-10  2.08E-13  2.09E-07  1.24E+01  7.55E+10 -5.6E-16 2.5E+04 1.4E-11 4.0E-12

   610  4.191445204E-05  1.827112045E-10  2.08E-13  7.72E-06  1.25E+01  7.62E+10 -1.4E-13 6.1E+06 8.4E-07 4.0E-12

   620  4.189688981E-05  1.827111107E-10  2.08E-13  7.78E-08  1.26E+01  7.67E+10 -1.4E-15 6.4E+04 9.2E-11 4.0E-12

   630  4.189687653E-05  1.827111106E-10  2.08E-13  3.26E-12  1.27E+01  7.74E+10 -1.2E-20 4.4E+01 5.2E-19 4.0E-12

   640  4.189687653E-05  1.827111106E-10  2.08E-13  3.34E-12  1.28E+01  7.80E+10 -1.3E-19 4.8E+02 6.2E-17 4.0E-12

   650  4.189687653E-05  1.827111106E-10  2.08E-13  1.24E-12  1.29E+01  7.85E+10 -7.7E-21 3.9E+01 3.0E-19 4.0E-12

   660  4.189687617E-05  1.827111106E-10  2.08E-13  4.38E-12  1.30E+01  7.93E+10 -3.9E-20 2.0E+02 7.9E-18 4.0E-12

   670  4.189687617E-05  1.827111106E-10  2.08E-13  6.52E-12  1.31E+01  7.98E+10 -3.9E-20 2.2E+02 8.8E-18 4.0E-12

   680  4.189687617E-05  1.827111106E-10  2.08E-13  7.95E-11  1.32E+01  8.03E+10 -1.2E-18 6.9E+03 8.4E-15 4.0E-12

   690  4.189687640E-05  1.827111106E-10  2.08E-13  4.76E-10  1.33E+01  8.09E+10 -1.8E-18 1.0E+04 1.8E-14 4.0E-12

   700  4.189687659E-05  1.827111106E-10  2.08E-13  1.66E-11  1.34E+01  8.16E+10 -9.0E-20 5.1E+02 4.6E-17 4.0E-12

   710  4.189687659E-05  1.827111106E-10  2.08E-13  2.57E-13  1.35E+01  8.21E+10 -4.4E-21 7.1E+01 3.1E-19 4.0E-12

   720  4.189687659E-05  1.827111106E-10  2.08E-13  3.68E-12  1.35E+01  8.26E+10 -1.2E-18 2.0E+04 2.5E-14 4.0E-12

   730  4.189687659E-05  1.827111106E-10  2.08E-13  4.78E-14  1.36E+01  8.32E+10 -1.3E-22 3.4E+00 4.5E-22 4.0E-12

   740  4.189687659E-05  1.827111106E-10  2.08E-13  1.51E-14  1.37E+01  8.38E+10 -8.6E-22 8.4E+01 7.3E-20 4.0E-12

   750  4.189687659E-05  1.827111106E-10  2.08E-13  3.87E-15  1.38E+01  8.43E+10 -3.2E-22 3.3E+01 1.1E-20 4.0E-12

   756  4.189687659E-05  1.827111106E-10  2.08E-13  4.25E-16  1.39E+01  8.47E+10 -6.9E-22 1.0E+02 7.0E-20 4.0E-12
   757  4.189687659E-05  1.827111106E-10  2.08E-13  3.25E-16  1.39E+01  8.48E+10  3.4E-24 3.1E+00 1.1E-23 4.0E-12
   758  4.189687659E-05  1.827111106E-10  2.08E-13  1.74E-16  1.39E+01  8.48E+10 -8.9E-24 1.4E+01 1.2E-22 4.0E-12

 Exit  LSQR.       istop  = 3               itn    =     758
 Exit  LSQR.       anorm  = 1.38884E+01     acond  = 8.47732E+10
 Exit  LSQR.       bnorm  = 8.79805E+02     xnorm  = 1.82711E+03
 Exit  LSQR.       rnorm  = 1.82711E-10     arnorm = 4.41016E-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)         = 8.03955988E-13 = rho1
    norm(A'r)       = 5.970E-13      = sigma1

    norm(s)         = 8.040E+00
    norm(x,s)       = 1.827E+03
    norm(rbar)      = 1.82712879E-10 = rho2
    norm(Abar'rbar) = 5.970E-13      = sigma2

    inform          = 1
    tol             = 1.490E-08
    test1           = 3.062E-17 (Ax = b)
    test2           = 5.346E-02 (least-squares)
    test3           = 2.353E-04 (damped least-squares)


 Solution  x:
     1  0.418969E-04     2  0.100049         3  0.200058         4  0.300071    
     5  0.400091         6  0.500111         7  0.600140         8  0.700166    

 LSQR  appears to be successful.     Relative error in  x  =  2.67E-08
