sdrvgg.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 890 行 · 第 1/3 页

   70             CONTINUE
                  CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
     $                         LDA, WORK( 2*N+1 ), IINFO )
                  IF( IINFO.NE.0 )
     $               GO TO 100
                  CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
     $                         A, LDA, WORK( 2*N+1 ), IINFO )
                  IF( IINFO.NE.0 )
     $               GO TO 100
                  CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
     $                         LDA, WORK( 2*N+1 ), IINFO )
                  IF( IINFO.NE.0 )
     $               GO TO 100
                  CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
     $                         B, LDA, WORK( 2*N+1 ), IINFO )
                  IF( IINFO.NE.0 )
     $               GO TO 100
               END IF
            ELSE
*
*              Random matrices
*
               DO 90 JC = 1, N
                  DO 80 JR = 1, N
                     A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
     $                             SLARND( 2, ISEED )
                     B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
     $                             SLARND( 2, ISEED )
   80             CONTINUE
   90          CONTINUE
            END IF
*
  100       CONTINUE
*
            IF( IINFO.NE.0 ) THEN
               WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
     $            IOLDSD
               INFO = ABS( IINFO )
               RETURN
            END IF
*
  110       CONTINUE
*
*           Call SGEGS to compute H, T, Q, Z, alpha, and beta.
*
            CALL SLACPY( ' ', N, N, A, LDA, S, LDA )
            CALL SLACPY( ' ', N, N, B, LDA, T, LDA )
            NTEST = 1
            RESULT( 1 ) = ULPINV
*
            CALL SGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHR1, ALPHI1,
     $                  BETA1, Q, LDQ, Z, LDQ, WORK, LWORK, IINFO )
            IF( IINFO.NE.0 ) THEN
               WRITE( NOUNIT, FMT = 9999 )'SGEGS', IINFO, N, JTYPE,
     $            IOLDSD
               INFO = ABS( IINFO )
               GO TO 140
            END IF
*
            NTEST = 4
*
*           Do tests 1--4
*
            CALL SGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK,
     $                   RESULT( 1 ) )
            CALL SGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK,
     $                   RESULT( 2 ) )
            CALL SGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
     $                   RESULT( 3 ) )
            CALL SGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
     $                   RESULT( 4 ) )
*
*           Do test 5: compare eigenvalues with diagonals.
*           Also check Schur form of A.
*
            TEMP1 = ZERO
*
            DO 120 J = 1, N
               ILABAD = .FALSE.
               IF( ALPHI1( J ).EQ.ZERO ) THEN
                  TEMP2 = ( ABS( ALPHR1( J )-S( J, J ) ) /
     $                    MAX( SAFMIN, ABS( ALPHR1( J ) ), ABS( S( J,
     $                    J ) ) )+ABS( BETA1( J )-T( J, J ) ) /
     $                    MAX( SAFMIN, ABS( BETA1( J ) ), ABS( T( J,
     $                    J ) ) ) ) / ULP
                  IF( J.LT.N ) THEN
                     IF( S( J+1, J ).NE.ZERO )
     $                  ILABAD = .TRUE.
                  END IF
                  IF( J.GT.1 ) THEN
                     IF( S( J, J-1 ).NE.ZERO )
     $                  ILABAD = .TRUE.
                  END IF
               ELSE
                  IF( ALPHI1( J ).GT.ZERO ) THEN
                     I1 = J
                  ELSE
                     I1 = J - 1
                  END IF
                  IF( I1.LE.0 .OR. I1.GE.N ) THEN
                     ILABAD = .TRUE.
                  ELSE IF( I1.LT.N-1 ) THEN
                     IF( S( I1+2, I1+1 ).NE.ZERO )
     $                  ILABAD = .TRUE.
                  ELSE IF( I1.GT.1 ) THEN
                     IF( S( I1, I1-1 ).NE.ZERO )
     $                  ILABAD = .TRUE.
                  END IF
                  IF( .NOT.ILABAD ) THEN
                     CALL SGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA,
     $                            BETA1( J ), ALPHR1( J ), ALPHI1( J ),
     $                            TEMP2, IINFO )
                     IF( IINFO.GE.3 ) THEN
                        WRITE( NOUNIT, FMT = 9997 )IINFO, J, N, JTYPE,
     $                     IOLDSD
                        INFO = ABS( IINFO )
                     END IF
                  ELSE
                     TEMP2 = ULPINV
                  END IF
               END IF
               TEMP1 = MAX( TEMP1, TEMP2 )
               IF( ILABAD ) THEN
                  WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD
               END IF
  120       CONTINUE
            RESULT( 5 ) = TEMP1
*
*           Call SGEGV to compute S2, T2, VL, and VR, do tests.
*
*           Eigenvalues and Eigenvectors
*
            CALL SLACPY( ' ', N, N, A, LDA, S2, LDA )
            CALL SLACPY( ' ', N, N, B, LDA, T2, LDA )
            NTEST = 6
            RESULT( 6 ) = ULPINV
*
            CALL SGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHR2, ALPHI2,
     $                  BETA2, VL, LDQ, VR, LDQ, WORK, LWORK, IINFO )
            IF( IINFO.NE.0 ) THEN
               WRITE( NOUNIT, FMT = 9999 )'SGEGV', IINFO, N, JTYPE,
     $            IOLDSD
               INFO = ABS( IINFO )
               GO TO 140
            END IF
*
            NTEST = 7
*
*           Do Tests 6 and 7
*
            CALL SGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHR2,
     $                   ALPHI2, BETA2, WORK, DUMMA( 1 ) )
            RESULT( 6 ) = DUMMA( 1 )
            IF( DUMMA( 2 ).GT.THRSHN ) THEN
               WRITE( NOUNIT, FMT = 9998 )'Left', 'SGEGV', DUMMA( 2 ),
     $            N, JTYPE, IOLDSD
            END IF
*
            CALL SGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHR2,
     $                   ALPHI2, BETA2, WORK, DUMMA( 1 ) )
            RESULT( 7 ) = DUMMA( 1 )
            IF( DUMMA( 2 ).GT.THRESH ) THEN
               WRITE( NOUNIT, FMT = 9998 )'Right', 'SGEGV', DUMMA( 2 ),
     $            N, JTYPE, IOLDSD
            END IF
*
*           Check form of Complex eigenvalues.
*
            DO 130 J = 1, N
               ILABAD = .FALSE.
               IF( ALPHI2( J ).GT.ZERO ) THEN
                  IF( J.EQ.N ) THEN
                     ILABAD = .TRUE.
                  ELSE IF( ALPHI2( J+1 ).GE.ZERO ) THEN
                     ILABAD = .TRUE.
                  END IF
               ELSE IF( ALPHI2( J ).LT.ZERO ) THEN
                  IF( J.EQ.1 ) THEN
                     ILABAD = .TRUE.
                  ELSE IF( ALPHI2( J-1 ).LE.ZERO ) THEN
                     ILABAD = .TRUE.
                  END IF
               END IF
               IF( ILABAD ) THEN
                  WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD
               END IF
  130       CONTINUE
*
*           End of Loop -- Check for RESULT(j) > THRESH
*
  140       CONTINUE
*
            NTESTT = NTESTT + NTEST
*
*           Print out tests which fail.
*
            DO 150 JR = 1, NTEST
               IF( RESULT( JR ).GE.THRESH ) THEN
*
*                 If this is the first test to fail,
*                 print a header to the data file.
*
                  IF( NERRS.EQ.0 ) THEN
                     WRITE( NOUNIT, FMT = 9995 )'SGG'
*
*                    Matrix types
*
                     WRITE( NOUNIT, FMT = 9994 )
                     WRITE( NOUNIT, FMT = 9993 )
                     WRITE( NOUNIT, FMT = 9992 )'Orthogonal'
*
*                    Tests performed
*
                     WRITE( NOUNIT, FMT = 9991 )'orthogonal', '''',
     $                  'transpose', ( '''', J = 1, 5 )
*
                  END IF
                  NERRS = NERRS + 1
                  IF( RESULT( JR ).LT.10000.0 ) THEN
                     WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR,
     $                  RESULT( JR )
                  ELSE
                     WRITE( NOUNIT, FMT = 9989 )N, JTYPE, IOLDSD, JR,
     $                  RESULT( JR )
                  END IF
               END IF
  150       CONTINUE
*
  160    CONTINUE
  170 CONTINUE
*
*     Summary
*
      CALL ALASVM( 'SGG', NOUNIT, NERRS, NTESTT, 0 )
      RETURN
*
 9999 FORMAT( ' SDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
     $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
 9998 FORMAT( ' SDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
     $      'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
     $      'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
     $      ')' )
*
 9997 FORMAT( ' SDRVGG: SGET53 returned INFO=', I1, ' for eigenvalue ',
     $      I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(',
     $      3( I5, ',' ), I5, ')' )
*
 9996 FORMAT( ' SDRVGG: S not in Schur form at eigenvalue ', I6, '.',
     $      / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
     $      I5, ')' )
*
 9995 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem driver'
     $       )
*
 9994 FORMAT( ' Matrix types (see SDRVGG for details): ' )
*
 9993 FORMAT( ' Special Matrices:', 23X,
     $      '(J''=transposed Jordan block)',
     $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
     $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
     $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
     $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
     $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
     $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
 9992 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
     $      / '  16=Transposed Jordan Blocks             19=geometric ',
     $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
     $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
     $      'alpha, beta=0,1            21=random alpha, beta=0,1',
     $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
     $      '23=(small,large)    24=(small,small)    25=(large,large)',
     $      / '  26=random O(1) matrices.' )
*
 9991 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
     $      'Q and Z are ', A, ',', / 20X,
     $      'l and r are the appropriate left and right', / 19X,
     $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
     $      ' means ', A, '.)', / ' 1 = | A - Q S Z', A,
     $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
     $      ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
     $      ' | / ( n ulp )             4 = | I - ZZ', A,
     $      ' | / ( n ulp )', /
     $      ' 5 = difference between (alpha,beta) and diagonals of',
     $      ' (S,T)', / ' 6 = max | ( b A - a B )', A,
     $      ' l | / const.   7 = max | ( b A - a B ) r | / const.',
     $      / 1X )
 9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
     $      4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 )
 9989 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
     $      4( I4, ',' ), ' result ', I3, ' is', 1P, E10.3 )
*
*     End of SDRVGG
*
      END