0  TEST TRAPS FOR CALLING SEQUENCE ERRORS
 PROVOKE 11 ERROR REPORTS FOR DIMENSIONS AND INVALID ARGUMENTS
0**ERROR** SOME DIMENSIONS ARE LESS THAN ONE IN PTST
        MA=    0 N=   10 NX=   10 M=   10 NC=    0





0**ERROR** SOME DIMENSIONS ARE LESS THAN TWO IN GINVSE
          M =   10 MA =    0 N =   10 NA =   10





0**ERROR** SOME DIMENSIONS ARE LESS THAN ONE IN PTST
        MA=   11 N=   11 NX=    0 M=   11 NC=   11





0**ERROR** SOME DIMENSIONS ARE LESS THAN TWO IN GINVSE
          M =   11 MA =   11 N =   11 NA =    0





0**ERROR** SOME DIMENSIONS ARE LESS THAN ONE IN PTST
        MA=   12 N=   12 NX=   12 M=    0 NC=   12





0**ERROR** SOME DIMENSIONS ARE LESS THAN TWO IN GINVSE
          M =    0 MA =   12 N =   12 NA =   12





0**ERROR** SOME DIMENSIONS ARE LESS THAN ONE IN PTST
        MA=   13 N=    0 NX=   13 M=   13 NC=   13





0**ERROR** SOME DIMENSIONS ARE LESS THAN TWO IN GINVSE
          M =   13 MA =   13 N =    0 NA =   13





0**ERROR**     6 EXCEEDS ALLOWABLE VALUE FOR M IN GINVSE   MA=     5





0**ERROR**     7 EXCEEDS ALLOWABLE VALUE FOR N IN GINVSE   NA=     5





0
0**ERROR** MA =   3 AND NA =   3 FORBIDS OPTION  2 IN ZIELKE





0  END OF CALLING SEQUENCE ERROR TESTS
0TEST PTST WITH 3 BY 2 MATRICES
 TO VERIFY MATRIX MULTIPLICATIONS

           A                            X

         1.    2.                0.1   0.2  -0.2
         2.   -3.                0.3  -0.3   0.9
         0.5   0.
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    4.27200174E+00
  INVERSE MATRIX NORM=  1.03923047E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.89166671E+00       0.23000002E+01
                   NORMALIZED         0.20872340E+00       0.53838933E+00
0 XAX=TEST=X  ...     ACTUAL          0.18750001E+00       0.42000005E+00
                   NORMALIZED         0.18042198E+00       0.40414524E+00
0 (AX)T=TEST=AX  ...  ACTUAL          0.16833334E+01       0.32000000E+01
                   NORMALIZED         0.37916380E+00       0.72078657E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.54999995E+00       0.54999995E+00
                   NORMALIZED         0.12388518E+00       0.12388518E+00





0SAME TEST WITH A AND X EXCHANGED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    1.03923047E+00
  INVERSE MATRIX NORM=  4.27200174E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.18750001E+00       0.42000005E+00
                   NORMALIZED         0.18042198E+00       0.40414524E+00
0 XAX=TEST=X  ...     ACTUAL          0.89166671E+00       0.23000002E+01
                   NORMALIZED         0.20872340E+00       0.53838933E+00
0 (AX)T=TEST=AX  ...  ACTUAL          0.54999995E+00       0.54999995E+00
                   NORMALIZED         0.12388518E+00       0.12388518E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.16833334E+01       0.32000000E+01
                   NORMALIZED         0.37916380E+00       0.72078657E+00





0TEST PTST WITH ROW AND COLUMN VECTORS
           A                        X
          3.0                  0.12     0.16
          4.0
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    5.00000000E+00
  INVERSE MATRIX NORM=  1.99999988E-01
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.78231096E-07       0.89406967E-07
                   NORMALIZED         0.15646219E-07       0.17881394E-07
0 XAX=TEST=X  ...     ACTUAL          0.31292438E-08       0.35762786E-08
                   NORMALIZED         0.15646220E-07       0.17881394E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00





0SAME TEST WITH A AND X EXCHANGED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    1.99999988E-01
  INVERSE MATRIX NORM=  5.00000000E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.31292438E-08       0.35762786E-08
                   NORMALIZED         0.15646220E-07       0.17881394E-07
0 XAX=TEST=X  ...     ACTUAL          0.78231096E-07       0.89406967E-07
                   NORMALIZED         0.15646219E-07       0.17881394E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00





0TEST WITH TRIVIAL 1 BY 1 MATRIX A = 2.
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    5.00000000E-01
  INVERSE MATRIX NORM=  2.00000000E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 XAX=TEST=X  ...     ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 (AX)T=TEST=AX  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00





0  DATA VERIFICATION
 TESTING INVALID OPTION A9+                             
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     0    0    0   -9         0   2.00000


0
0**ERROR** OPTION   -9 IS NOT AVAILABLE FOR ZIELKE





0  DATA VERIFICATION
 TESTING ISEED.LT.0 IN GMATX                            
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     3    3    2    0        -1   0.20000


0**WARNING**        -1 WAS AN IMPROPER CHOICE FOR ISEED, WHICH WAS SET TO ONE IN GMATX
0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    3 BY    3
   PSEUDO-RANDOM NUMBER SEED=         1
 ROW   1
   9.82697785E-01 -9.85067412E-02 -8.54356289E-02
 ROW   2
  -9.85067412E-02  2.15517735E+00 -2.46614599E+00
 ROW   3
  -8.54356289E-02 -2.46614575E+00  2.86212492E+00
 SWEEP =   1     3 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     2 JACOBI ROTATIONS PERFORMED
 SWEEP =   3     1 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     1 JACOBI ROTATIONS PERFORMED
 SWEEP =   5     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    5.09901953E+00
  INVERSE MATRIX NORM=  1.01980400E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.39784936E-04       0.13824619E-03
                   NORMALIZED         0.78024677E-05       0.27112308E-04
0 XAX=TEST=X  ...     ACTUAL          0.79570436E-05       0.27648601E-04
                   NORMALIZED         0.78025223E-05       0.27111681E-04
0 (AX)T=TEST=AX  ...  ACTUAL          0.17053855E-07       0.22687528E-07
                   NORMALIZED         0.32795873E-08       0.43629860E-08
0 (XA)T=TEST=XA  ...  ACTUAL          0.90334070E-04       0.13271917E-03
                   NORMALIZED         0.17371936E-04       0.25522917E-04





0  DATA VERIFICATION
 TESTING M.LT.1 IN GMATX                                
                        
0    M    N    K  MOPT    ISEED    ALPHA 
    -1    1    1    0        34   0.10000


0**ERROR** DIMENSIONS OF A CANNOT BE LESS THAN 1, MA =    30 M =    -1 N =     1





0  DATA VERIFICATION
 TESTING ALPHA.LT.0.0 IN GMATX                          
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     4    4    4    0        56  -1.80000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    4 BY    4
   PSEUDO-RANDOM NUMBER SEED=        56
0**WARNING**  -1.80000 IS NOT ALLOWABLE FOR ALPHA AND WILL BE SET TO ONE IN GMATX
 ROW   1
   1.00000000E+00  3.55410670E-08  1.99718340E-08 -5.17700371E-09
 ROW   2
   3.55410670E-08  1.00000000E+00  2.61608317E-08 -7.09392323E-09
 ROW   3
   1.99718340E-08  2.61608317E-08  1.00000000E+00 -5.96046448E-08
 ROW   4
  -5.17700371E-09 -7.09392323E-09 -5.96046448E-08  1.00000000E+00
 SWEEP =   1     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    2.00000000E+00
  INVERSE MATRIX NORM=  2.00000000E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.38387327E-07       0.11920929E-06
                   NORMALIZED         0.19193664E-07       0.59604645E-07
0 XAX=TEST=X  ...     ACTUAL          0.38387327E-07       0.11920929E-06
                   NORMALIZED         0.19193664E-07       0.59604645E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00
0 (XA)T=TEST=XA  ...  ACTUAL          0.00000000E+00       0.00000000E+00
                   NORMALIZED         0.00000000E+00       0.00000000E+00





0  DATA VERIFICATION
 TESTING K.LT.0 IN GMATX                                
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5   -1    0        98   0.09000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    5 BY    5
   PSEUDO-RANDOM NUMBER SEED=        98
0**ERROR**   -1 IS AN INVALID VALUE FOR K ,THIS FORBIDS USE OF GMATX





0  DATA VERIFICATION
 TESTING K.GT.MIN0(M,N) IN GMATX                        
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    3    8    0         1   1.00000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    5 BY    3
   PSEUDO-RANDOM NUMBER SEED=         1
0**WARNING**    8 EXCEEDS ALLOWABLE VALUE FOR K (THE RANK).  K WILL BE SET TO     3
 INITIAL DIAGONAL ELEMENTS ARE   1.00000**(I-1)  FOR I=1 TO   3
 ROW   1
   5.82068205E-01  0.00000000E+00  0.00000000E+00
 ROW   2
  -1.79397076E-01  9.74653661E-01  0.00000000E+00
 ROW   3
  -5.65870285E-01 -1.40265986E-01  5.38849473E-01
 ROW   4
  -7.51459077E-02  5.74421510E-03 -7.07515240E-01
 ROW   5
   5.50597012E-01  1.74191490E-01  4.57234681E-01
 SWEEP =   1     3 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    1.73205078E+00
  INVERSE MATRIX NORM=  1.73205090E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.18762181E-07       0.47284953E-07
                   NORMALIZED         0.10832350E-07       0.27299981E-07
0 XAX=TEST=X  ...     ACTUAL          0.18377651E-07       0.48213955E-07
                   NORMALIZED         0.10610341E-07       0.27836339E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.49855209E-08       0.14164328E-07
                   NORMALIZED         0.16618403E-08       0.47214428E-08
0 (XA)T=TEST=XA  ...  ACTUAL          0.40772457E-08       0.61697571E-08
                   NORMALIZED         0.13590818E-08       0.20565858E-08





0  DATA VERIFICATION
 TESTING N.GT.M IN GMATX, GINVSE NOT CALLED             
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     3    4    1    0         0   1.00000


0**WARNING**         0 WAS AN IMPROPER CHOICE FOR ISEED, WHICH WAS SET TO ONE IN GMATX
0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    3 BY    4
   PSEUDO-RANDOM NUMBER SEED=         1
 ROW   1
   6.43693745E-01 -4.46213633E-01 -2.43667245E-01 -5.56664944E-01
 ROW   2
  -3.91788259E-02  2.71590725E-02  1.48309618E-02  3.38817611E-02
 ROW   3
  -7.58963749E-02  5.26119731E-02  2.87302211E-02  6.56350181E-02
0  DATA VERIFICATION
 TEST NO ERROR DATA SET WHICH GENERATES IDENTITY MATRIX 
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     4    4    4    0       453   1.00000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    4 BY    4
   PSEUDO-RANDOM NUMBER SEED=       453
 ROW   1
   9.99999881E-01  5.14190113E-08  3.82892260E-08  5.80972648E-09
 ROW   2
   5.14190113E-08  9.99999881E-01 -2.55898343E-08  3.52584451E-08
 ROW   3
   3.82892260E-08 -3.72141873E-09  9.99999821E-01  0.00000000E+00
 ROW   4
   5.80972648E-09  7.14337201E-10  1.49011612E-08  9.99999881E-01
 SWEEP =   1     1 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    1.99999976E+00
  INVERSE MATRIX NORM=  2.00000024E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.37627931E-07       0.10283802E-06
                   NORMALIZED         0.18813967E-07       0.51419018E-07
0 XAX=TEST=X  ...     ACTUAL          0.37627942E-07       0.10283804E-06
                   NORMALIZED         0.18813969E-07       0.51419015E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.12125383E-14       0.32939347E-14
                   NORMALIZED         0.30313456E-15       0.82348368E-15
0 (XA)T=TEST=XA  ...  ACTUAL          0.28196651E-14       0.10399361E-13
                   NORMALIZED         0.70491628E-15       0.25998402E-14





0  DATA VERIFICATION
 TEST 1 BY 5 ROW VECTOR                                 
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     1    5    1    0     12345   0.50000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    1 BY    5
   PSEUDO-RANDOM NUMBER SEED=     12345
 ROW   1
   1.75164267E-01 -9.01414752E-02 -3.05367947E-01  7.70313382E-01  5.23984492E-01
0  DATA VERIFICATION
 TEST 5 BY 1 COLUMN VECTOR                              
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    1    1    0     12345   0.50000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    5 BY    1
   PSEUDO-RANDOM NUMBER SEED=     12345
 ROW   1
   1.75164267E-01
 ROW   2
  -9.01414752E-02
 ROW   3
  -3.05367947E-01
 ROW   4
   7.70313382E-01
 ROW   5
   5.23984492E-01
0  DATA VERIFICATION
 TEST 1 BY 1 TRIVIAL CASE                               
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     1    1    1    0     12345   0.50000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    1 BY    1
   PSEUDO-RANDOM NUMBER SEED=     12345
 ROW   1
   1.00000000E+00
0  DATA VERIFICATION
 TEST 10 BY 5 MATRIX WITH POWER OF 2 SINGULAR VALUES    
                        
0    M    N    K  MOPT    ISEED    ALPHA 
    10    5    5    0     12345   0.50000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=   10 BY    5
   PSEUDO-RANDOM NUMBER SEED=     12345
 ROW   1
   1.58610678E+00  1.84216902E-01  6.93679601E-02  1.08681388E-01 -2.45845750E-01
 ROW   2
  -6.83281946E+00 -6.13709867E-01 -2.56829053E-01 -2.34877571E-01  1.19534147E+00
 ROW   3
  -2.39498925E+00 -8.01820934E-01  3.10373783E-01 -3.84789556E-01  2.73198456E-01
 ROW   4
  -9.47872877E-01  3.13393623E-02 -1.06013680E+00  9.74708557E-01 -2.59836763E-01
 ROW   5
  -4.91713852E-01  2.90693164E-01 -2.14555711E-01 -8.47951174E-01  1.72991961E-01
 ROW   6
   1.15783978E+00  1.25948381E+00  1.23817325E+00  6.81356955E+00  1.69166669E-01
 ROW   7
  -1.09057236E+00 -9.08142805E-01 -1.13941717E+00 -2.14476085E+00  3.41179729E-01
 ROW   8
  -4.20822948E-01  2.44918013E+00  4.09662151E+00  1.04122629E+01  6.53391075E+00
 ROW   9
  -2.71984905E-01 -1.55979490E+00  3.86429995E-01 -2.19994473E+00 -1.55811751E+00
 ROW  10
   2.00180009E-01  5.89401245E-01  7.85519361E-01  5.91283751E+00  4.60879505E-02
 SWEEP =   1    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   2    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   3    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    1.84661865E+01
  INVERSE MATRIX NORM=  1.15413678E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.28473185E-04       0.12006478E-03
                   NORMALIZED         0.15419093E-05       0.65018721E-05
0 XAX=TEST=X  ...     ACTUAL          0.53553367E-06       0.29808045E-05
                   NORMALIZED         0.46401232E-06       0.25827135E-05
0 (AX)T=TEST=AX  ...  ACTUAL          0.53874903E-07       0.36248102E-06
                   NORMALIZED         0.25278539E-08       0.17007903E-07
0 (XA)T=TEST=XA  ...  ACTUAL          0.10095247E-04       0.29475972E-04
                   NORMALIZED         0.47367718E-06       0.13830364E-05





0  DATA VERIFICATION
 TEST 10 BY 5 GENERATED MATRIX WITH RANK 2              
                        
0    M    N    K  MOPT    ISEED    ALPHA 
    10    5    2    0     54321   0.50000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=   10 BY    5
   PSEUDO-RANDOM NUMBER SEED=     54321
 ROW   1
   5.57762980E-01  2.96252146E-02 -3.36496353E-01 -1.17544852E-01  4.52737920E-02
 ROW   2
  -3.98572683E-01  1.49090169E-02  2.18915060E-01  8.27120170E-02 -2.64295749E-02
 ROW   3
  -2.66926795E-01 -8.51257503E-01  6.60847127E-01  8.60558152E-02 -1.59081444E-01
 ROW   4
   2.21661478E-01  5.80413342E-01 -4.73256201E-01 -6.69591278E-02  1.11340187E-01
 ROW   5
   1.97909802E-01  4.27410960E-01 -3.68324131E-01 -5.65511473E-02  8.45024884E-02
 ROW   6
   1.99439839E-01  6.75927997E-01 -5.17585516E-01 -6.57187030E-02  1.25409886E-01
 ROW   7
  -1.50022164E-01 -3.51832926E-01  2.95825660E-01  4.38588522E-02 -6.86261132E-02
 ROW   8
  -4.37328279E-01  1.60696000E-01  1.54019222E-01  8.56157392E-02 -5.30505739E-03
 ROW   9
   5.65774202E-01 -1.55830756E-02 -3.14081967E-01 -1.17608428E-01  3.84328440E-02
 ROW  10
   1.21352375E-02 -5.24707317E-01  3.06360662E-01  1.61468163E-02 -8.52566361E-02
 SWEEP =   1    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     6 JACOBI ROTATIONS PERFORMED
 SWEEP =   3     3 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    2.23606801E+00
  INVERSE MATRIX NORM=  1.11803412E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.27934886E-07       0.96261886E-07
                   NORMALIZED         0.12492861E-07       0.43049624E-07
0 XAX=TEST=X  ...     ACTUAL          0.17418840E-07       0.76437381E-07
                   NORMALIZED         0.15579882E-07       0.68367662E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.19653033E-07       0.77712556E-07
                   NORMALIZED         0.78612121E-08       0.31085019E-07
0 (XA)T=TEST=XA  ...  ACTUAL          0.26339574E-07       0.83826272E-07
                   NORMALIZED         0.10535828E-07       0.33530505E-07





0  DATA VERIFICATION
 TEST 5 BY 10 GENERATED MATRIX -- POWER OF 0.1, RANK 3  
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5   10    3    0     34521   0.10000


0GENERATING MATRIX BY PSEUDO-RANDOM JACOBI ROTATIONS
 ORDER=    5 BY   10
   PSEUDO-RANDOM NUMBER SEED=     34521
 ROW   1
   4.49530888E+00 -4.26735153E+01 -7.46518183E+00  1.78908100E+01  3.01770554E+01
 -1.44551630E+01  1.92071533E+01 -3.49878273E+01 -1.00336246E+01 -3.44462013E+01
 ROW   2
  -3.11685860E-01  3.05008316E+00 -6.28586471E-01 -6.29336119E-01 -2.10151529E+00
  1.36234999E-01 -7.89159060E-01  3.07052755E+00  5.33375978E-01  3.25299406E+00
 ROW   3
   2.71773152E-02 -5.25383949E-01  3.50976872E+00 -1.90635884E+00  7.56053686E-01
  2.82527494E+00 -1.45509934E+00 -2.55015302E+00  2.56916106E-01 -3.07083321E+00
 ROW   4
  -2.99376559E+00  2.85915375E+01  2.18777275E+00 -1.00540705E+01 -2.18428307E+01
  6.80677748E+00 -1.18264523E+01  2.59393978E+01  6.87538052E+00  2.56122303E+01
 ROW   5
   1.65184975E+00 -1.54564753E+01 -5.63087225E+00  8.15635777E+00  1.08712521E+01
 -7.57446098E+00  8.38503933E+00 -1.11115141E+01 -4.02958393E+00 -1.04147024E+01
0  DATA VERIFICATION
 TEST ZIELKE A1                                         
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5    1         0   0.10000


0
 ZIELKE MATRIX A1
 ROW   1
   1.00000001E-01  1.00000001E-01 -8.99999976E-01  1.00000001E-01
 ROW   2
   1.10000002E+00  1.00000001E-01  1.00000001E-01  1.00000001E-01
 ROW   3
   1.00000001E-01  1.00000001E-01 -8.99999976E-01  1.00000001E-01
 ROW   4
   1.10000002E+00  1.00000001E-01  1.00000001E-01  1.00000001E-01
 ROW   5
   1.10000002E+00  1.10000002E+00  1.00000001E-01  1.10000002E+00
 SWEEP =   1     6 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     6 JACOBI ROTATIONS PERFORMED
 SWEEP =   3     5 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    2.79284811E+00
  INVERSE MATRIX NORM=  1.37113082E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.46402224E-07       0.12993813E-06
                   NORMALIZED         0.16614662E-07       0.46525312E-07
0 XAX=TEST=X  ...     ACTUAL          0.20161272E-07       0.60051676E-07
                   NORMALIZED         0.14704120E-07       0.43797190E-07
0 (AX)T=TEST=AX  ...  ACTUAL          0.14454126E-07       0.27567149E-07
                   NORMALIZED         0.37745536E-08       0.71988913E-08
0 (XA)T=TEST=XA  ...  ACTUAL          0.84688260E-07       0.19222499E-06
                   NORMALIZED         0.22115511E-07       0.50197677E-07





0  DATA VERIFICATION
 TEST ZIELKE A2                                         
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5    2         0   0.10000


0
 ZIELKE MATRIX A2
 ROW   1
   1.10000002E+00  1.00000001E-01  1.00000001E-01  1.10000002E+00
 ROW   2
   2.09999990E+00  1.10000002E+00  1.10000002E+00  2.09999990E+00
 ROW   3
   3.09999990E+00  2.09999990E+00  2.09999990E+00  3.09999990E+00
 ROW   4
   1.10000002E+00  1.10000002E+00  1.00000001E-01  2.09999990E+00
 ROW   5
   1.00000024E-01  1.00000024E-01 -8.99999976E-01  1.09999990E+00
 SWEEP =   1     6 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     5 JACOBI ROTATIONS PERFORMED
 SWEEP =   3     4 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     2 JACOBI ROTATIONS PERFORMED
 SWEEP =   5     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    7.11336756E+00
  INVERSE MATRIX NORM=  1.64032507E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.29105999E-03       0.82397694E-03
                   NORMALIZED         0.40917326E-04       0.11583500E-03
0 XAX=TEST=X  ...     ACTUAL          0.53988897E-04       0.24107660E-03
                   NORMALIZED         0.32913536E-04       0.14696880E-03
0 (AX)T=TEST=AX  ...  ACTUAL          0.25887704E-06       0.52315028E-06
                   NORMALIZED         0.22186478E-07       0.44835424E-07
0 (XA)T=TEST=XA  ...  ACTUAL          0.88756246E-03       0.17348236E-02
                   NORMALIZED         0.76066557E-04       0.14867917E-03





0  DATA VERIFICATION
 TEST ZIELKE A3                                         
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5    3         0   0.10000


0
 ZIELKE MATRIX A3
 ROW   1
   1.00000001E-01  1.10000002E+00  2.09999990E+00  3.09999990E+00  1.00000001E-01
 ROW   2
   1.00000001E-01  2.09999990E+00  3.09999990E+00  5.09999990E+00  1.10000002E+00
 ROW   3
   1.10000002E+00  2.09999990E+00  3.09999990E+00  4.09999990E+00  2.09999990E+00
 ROW   4
   2.09999990E+00  3.09999990E+00  4.09999990E+00  5.09999990E+00  3.09999990E+00
 ROW   5
   3.09999990E+00  4.09999990E+00  5.09999990E+00  6.09999990E+00  5.09999990E+00
 ROW   6
   5.09999990E+00  5.09999990E+00  6.09999990E+00  6.09999990E+00  7.09999990E+00
 SWEEP =   1    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   2    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   3    10 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     5 JACOBI ROTATIONS PERFORMED
 SWEEP =   5     2 JACOBI ROTATIONS PERFORMED
 SWEEP =   6     0 JACOBI ROTATIONS PERFORMED
 SWEEP LIMIT REACHED 
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    2.12579384E+01
  INVERSE MATRIX NORM=  6.31148911E+00
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.60063775E-03       0.26103228E-02
                   NORMALIZED         0.28254752E-04       0.12279284E-03
0 XAX=TEST=X  ...     ACTUAL          0.40194418E-03       0.15135380E-02
                   NORMALIZED         0.63684522E-04       0.23980679E-03
0 (AX)T=TEST=AX  ...  ACTUAL          0.67217894E-06       0.13148360E-05
                   NORMALIZED         0.50099329E-08       0.97998312E-08
0 (XA)T=TEST=XA  ...  ACTUAL          0.65944181E-02       0.15707819E-01
                   NORMALIZED         0.49149996E-04       0.11707465E-03





0  DATA VERIFICATION
 TEST ZIELKE / RUTISHAUSER A4                           
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5    4         0   0.10000


0
 ZIELKE/RUTISHAUSER MATRIX A4
 ROW   1
   1.10000002E+00  2.09999990E+00  3.09999990E+00
 ROW   2
   2.09999990E+00  3.09999990E+00  4.09999990E+00
 ROW   3
   3.09999990E+00  4.09999990E+00  5.09999990E+00
 ROW   4
   4.09999990E+00  5.09999990E+00  6.09999990E+00
 ROW   5
   5.09999990E+00  6.09999990E+00  7.09999990E+00
 ROW   6
   6.09999990E+00  7.09999990E+00  8.10000038E+00
 ROW   7
   7.09999990E+00  8.10000038E+00  9.10000038E+00
 SWEEP =   1     3 JACOBI ROTATIONS PERFORMED
 SWEEP =   2     3 JACOBI ROTATIONS PERFORMED
 SWEEP =   3     2 JACOBI ROTATIONS PERFORMED
 SWEEP =   4     1 JACOBI ROTATIONS PERFORMED
 SWEEP =   5     0 JACOBI ROTATIONS PERFORMED
0 TEST PENROSE CONDITIONS

   A  IS THE INPUT MATRIX,  X  IS  THE INVERSE OF A
0 INPUT MATRIX NORM=    2.53812923E+01
  INVERSE MATRIX NORM=  7.40133405E-01
                                    AVERAGE DEVIATION    MAXIMUM DEVIATION
0 AXA=TEST=A  ...     ACTUAL          0.60323317E-04       0.14686305E-03
                   NORMALIZED         0.23766843E-05       0.57862717E-05
0 XAX=TEST=X  ...     ACTUAL          0.16724678E-05       0.41595081E-05
                   NORMALIZED         0.22596842E-05       0.56199437E-05
0 (AX)T=TEST=AX  ...  ACTUAL          0.11058319E-06       0.34618171E-06
                   NORMALIZED         0.58866116E-08       0.18428093E-07
0 (XA)T=TEST=XA  ...  ACTUAL          0.13104087E-03       0.19656237E-03
                   NORMALIZED         0.69756238E-05       0.10463492E-04





0  DATA VERIFICATION
 TEST ZIELKE INVERSE A1                                 
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5   -1         0   0.10000


0
 ZIELKE MATRIX A1+
 ROW   1
   5.00000007E-02  5.00000000E-01  5.00000007E-02  5.00000000E-01 -1.00000001E-01
 ROW   2
   0.00000000E+00 -2.50000000E-01  0.00000000E+00 -2.50000000E-01  5.00000000E-01
 ROW   3
  -5.50000012E-01  0.00000000E+00 -5.50000012E-01  0.00000000E+00  1.00000001E-01
 ROW   4
   0.00000000E+00 -2.50000000E-01  0.00000000E+00 -2.50000000E-01  5.00000000E-01
0  DATA VERIFICATION
 TEST ZIELKE INVERSE A2                                 
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5   -2         0   0.10000


0
 ZIELKE MATRIX A2+
 ROW   1
   7.53333330E-01  3.33333343E-01 -8.66666660E-02 -4.60000008E-01 -4.00000028E-02
 ROW   2
  -9.53333318E-01 -3.33333343E-01  2.86666662E-01  5.60000002E-01 -5.99999987E-02
 ROW   3
  -2.19999969E-01  0.00000000E+00  2.19999999E-01 -1.39999986E-01 -3.60000014E-01
 ROW   4
   1.99999996E-02  0.00000000E+00 -1.99999996E-02  2.39999980E-01  2.60000020E-01
0  DATA VERIFICATION
 TEST ZIELKE INVERSE A3                                 
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5   -3         0   0.10000


0
 ZIELKE MATRIX A3+
 ROW   1
   5.00000000E-01 -1.25000000E-01 -1.00000000E+00  8.75000000E-01 -6.25000000E-01
  3.75000000E-01
 ROW   2
  -1.00000000E+00  1.64999998E+00 -3.59999990E+00  2.20000005E+00 -4.00000006E-01
  1.50000006E-01
 ROW   3
   1.25000000E+00 -1.39999998E+00  2.34999990E+00 -1.20000005E+00 -9.99999940E-02
  9.99999940E-02
 ROW   4
  -2.50000000E-01  3.75000000E-01 -2.50000000E-01  1.25000000E-01  1.25000000E-01
 -1.25000000E-01
 ROW   5
  -5.00000000E-01 -2.50000000E-01  1.50000000E+00 -1.25000000E+00  7.50000000E-01
 -2.50000000E-01
0  DATA VERIFICATION
 TEST ZIELKE / RUTISHAUSER A4 INVERSE                   
                        
0    M    N    K  MOPT    ISEED    ALPHA 
     5    5    5   -4         0   0.10000


0
 ZIELKE/RUTISHAUSER MATRIX A4+
 ROW   1
  -3.80357146E-01  2.70238101E-01  1.70833334E-01 -7.14285746E-02  3.15476209E-02
  1.34523809E-01  2.37500012E-01
 ROW   2
  -3.57142873E-02 -2.38095243E-02 -1.19047621E-02  0.00000000E+00  1.19047621E-02
  2.38095243E-02  3.57142873E-02
 ROW   3
   3.08928579E-01  2.29761899E-01  1.50595233E-01  7.14285746E-02 -7.73809478E-03
 -8.69047642E-02 -1.66071430E-01
0  DATA VERIFICATION
 END OF TEST DATA SET - BLANK CARD IMAGE                
                        





 END OF DATA HAS BEEN REACHED (ALL INPUT VALUES ARE CONSIDERED TO BE ZERO)





