alahd.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 730 行 · 第 1/2 页

         WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
         WRITE( IOUNIT, FMT = 9940 )1
         WRITE( IOUNIT, FMT = 9939 )2
         WRITE( IOUNIT, FMT = 9938 )3
         WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
      ELSE IF( LSAMEN( 2, P2, 'TZ' ) ) THEN
*
*        TZ:  Trapezoidal
*
         WRITE( IOUNIT, FMT = 9985 )PATH
         WRITE( IOUNIT, FMT = 9968 )
         WRITE( IOUNIT, FMT = 9929 )C1, C1
         WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
         WRITE( IOUNIT, FMT = 9940 )1
         WRITE( IOUNIT, FMT = 9937 )2
         WRITE( IOUNIT, FMT = 9938 )3
         WRITE( IOUNIT, FMT = 9940 )4
         WRITE( IOUNIT, FMT = 9937 )5
         WRITE( IOUNIT, FMT = 9938 )6
         WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
      ELSE IF( LSAMEN( 2, P2, 'LS' ) ) THEN
*
*        LS:  Least Squares driver routines for
*             LS, LSD, LSS, LSX and LSY.
*
         WRITE( IOUNIT, FMT = 9984 )PATH
         WRITE( IOUNIT, FMT = 9967 )
         WRITE( IOUNIT, FMT = 9921 )C1, C1, C1, C1, C1
         WRITE( IOUNIT, FMT = 9935 )1
         WRITE( IOUNIT, FMT = 9931 )2
         WRITE( IOUNIT, FMT = 9933 )3
         WRITE( IOUNIT, FMT = 9935 )4
         WRITE( IOUNIT, FMT = 9934 )5
         WRITE( IOUNIT, FMT = 9932 )6
         WRITE( IOUNIT, FMT = 9920 )
         WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
      ELSE IF( LSAMEN( 2, P2, 'LU' ) ) THEN
*
*        LU factorization variants
*
         WRITE( IOUNIT, FMT = 9983 )PATH
         WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
         WRITE( IOUNIT, FMT = 9979 )
         WRITE( IOUNIT, FMT = '( '' Test ratio:'' )' )
         WRITE( IOUNIT, FMT = 9962 )1
         WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
      ELSE IF( LSAMEN( 2, P2, 'CH' ) ) THEN
*
*        Cholesky factorization variants
*
         WRITE( IOUNIT, FMT = 9982 )PATH
         WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
         WRITE( IOUNIT, FMT = 9974 )
         WRITE( IOUNIT, FMT = '( '' Test ratio:'' )' )
         WRITE( IOUNIT, FMT = 9954 )1
         WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
      ELSE IF( LSAMEN( 2, P2, 'QS' ) ) THEN
*
*        QR factorization variants
*
         WRITE( IOUNIT, FMT = 9981 )PATH
         WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
         WRITE( IOUNIT, FMT = 9970 )
         WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
*
      ELSE
*
*        Print error message if no header is available.
*
         WRITE( IOUNIT, FMT = 9980 )PATH
      END IF
*
*     First line of header
*
 9999 FORMAT( / 1X, A3, ':  General dense matrices' )
 9998 FORMAT( / 1X, A3, ':  General band matrices' )
 9997 FORMAT( / 1X, A3, ':  General tridiagonal' )
 9996 FORMAT( / 1X, A3, ':  ', A9, ' positive definite matrices' )
 9995 FORMAT( / 1X, A3, ':  ', A9, ' positive definite packed matrices'
     $       )
 9994 FORMAT( / 1X, A3, ':  ', A9, ' positive definite band matrices' )
 9993 FORMAT( / 1X, A3, ':  ', A9, ' positive definite tridiagonal' )
 9992 FORMAT( / 1X, A3, ':  ', A9, ' indefinite matrices' )
 9991 FORMAT( / 1X, A3, ':  ', A9, ' indefinite packed matrices' )
 9990 FORMAT( / 1X, A3, ':  Triangular matrices' )
 9989 FORMAT( / 1X, A3, ':  Triangular packed matrices' )
 9988 FORMAT( / 1X, A3, ':  Triangular band matrices' )
 9987 FORMAT( / 1X, A3, ':  ', A2, ' factorization of general matrices'
     $       )
 9986 FORMAT( / 1X, A3, ':  QR factorization with column pivoting' )
 9985 FORMAT( / 1X, A3, ':  RQ factorization of trapezoidal matrix' )
 9984 FORMAT( / 1X, A3, ':  Least squares driver routines' )
 9983 FORMAT( / 1X, A3, ':  LU factorization variants' )
 9982 FORMAT( / 1X, A3, ':  Cholesky factorization variants' )
 9981 FORMAT( / 1X, A3, ':  QR factorization variants' )
 9980 FORMAT( / 1X, A3, ':  No header available' )
*
*     GE matrix types
*
 9979 FORMAT( 4X, '1. Diagonal', 24X, '7. Last n/2 columns zero', / 4X,
     $      '2. Upper triangular', 16X,
     $      '8. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '3. Lower triangular', 16X, '9. Random, CNDNUM = 0.1/EPS',
     $      / 4X, '4. Random, CNDNUM = 2', 13X,
     $      '10. Scaled near underflow', / 4X, '5. First column zero',
     $      14X, '11. Scaled near overflow', / 4X,
     $      '6. Last column zero' )
*
*     GB matrix types
*
 9978 FORMAT( 4X, '1. Random, CNDNUM = 2', 14X,
     $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '2. First column zero', 15X, '6. Random, CNDNUM = .01/EPS',
     $      / 4X, '3. Last column zero', 16X,
     $      '7. Scaled near underflow', / 4X,
     $      '4. Last n/2 columns zero', 11X, '8. Scaled near overflow' )
*
*     GT matrix types
*
 9977 FORMAT( ' Matrix types (1-6 have specified condition numbers):',
     $      / 4X, '1. Diagonal', 24X, '7. Random, unspecified CNDNUM',
     $      / 4X, '2. Random, CNDNUM = 2', 14X, '8. First column zero',
     $      / 4X, '3. Random, CNDNUM = sqrt(0.1/EPS)', 2X,
     $      '9. Last column zero', / 4X, '4. Random, CNDNUM = 0.1/EPS',
     $      7X, '10. Last n/2 columns zero', / 4X,
     $      '5. Scaled near underflow', 10X,
     $      '11. Scaled near underflow', / 4X,
     $      '6. Scaled near overflow', 11X, '12. Scaled near overflow' )
*
*     PT matrix types
*
 9976 FORMAT( ' Matrix types (1-6 have specified condition numbers):',
     $      / 4X, '1. Diagonal', 24X, '7. Random, unspecified CNDNUM',
     $      / 4X, '2. Random, CNDNUM = 2', 14X,
     $      '8. First row and column zero', / 4X,
     $      '3. Random, CNDNUM = sqrt(0.1/EPS)', 2X,
     $      '9. Last row and column zero', / 4X,
     $      '4. Random, CNDNUM = 0.1/EPS', 7X,
     $      '10. Middle row and column zero', / 4X,
     $      '5. Scaled near underflow', 10X,
     $      '11. Scaled near underflow', / 4X,
     $      '6. Scaled near overflow', 11X, '12. Scaled near overflow' )
*
*     PO, PP matrix types
*
 9975 FORMAT( 4X, '1. Diagonal', 24X,
     $      '6. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '2. Random, CNDNUM = 2', 14X, '7. Random, CNDNUM = 0.1/EPS',
     $      / 3X, '*3. First row and column zero', 7X,
     $      '8. Scaled near underflow', / 3X,
     $      '*4. Last row and column zero', 8X,
     $      '9. Scaled near overflow', / 3X,
     $      '*5. Middle row and column zero', / 3X,
     $      '(* - tests error exits from ', A3,
     $      'TRF, no test ratios are computed)' )
*
*     CH matrix types
*
 9974 FORMAT( 4X, '1. Diagonal', 24X,
     $      '6. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '2. Random, CNDNUM = 2', 14X, '7. Random, CNDNUM = 0.1/EPS',
     $      / 3X, '*3. First row and column zero', 7X,
     $      '8. Scaled near underflow', / 3X,
     $      '*4. Last row and column zero', 8X,
     $      '9. Scaled near overflow', / 3X,
     $      '*5. Middle row and column zero', / 3X,
     $      '(* - tests error exits, no test ratios are computed)' )
*
*     PB matrix types
*
 9973 FORMAT( 4X, '1. Random, CNDNUM = 2', 14X,
     $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 3X,
     $      '*2. First row and column zero', 7X,
     $      '6. Random, CNDNUM = 0.1/EPS', / 3X,
     $      '*3. Last row and column zero', 8X,
     $      '7. Scaled near underflow', / 3X,
     $      '*4. Middle row and column zero', 6X,
     $      '8. Scaled near overflow', / 3X,
     $      '(* - tests error exits from ', A3,
     $      'TRF, no test ratios are computed)' )
*
*     SSY, SSP, CHE, CHP matrix types
*
 9972 FORMAT( 4X, '1. Diagonal', 24X,
     $      '6. Last n/2 rows and columns zero', / 4X,
     $      '2. Random, CNDNUM = 2', 14X,
     $      '7. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '3. First row and column zero', 7X,
     $      '8. Random, CNDNUM = 0.1/EPS', / 4X,
     $      '4. Last row and column zero', 8X,
     $      '9. Scaled near underflow', / 4X,
     $      '5. Middle row and column zero', 5X,
     $      '10. Scaled near overflow' )
*
*     CSY, CSP matrix types
*
 9971 FORMAT( 4X, '1. Diagonal', 24X,
     $      '7. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '2. Random, CNDNUM = 2', 14X, '8. Random, CNDNUM = 0.1/EPS',
     $      / 4X, '3. First row and column zero', 7X,
     $      '9. Scaled near underflow', / 4X,
     $      '4. Last row and column zero', 7X,
     $      '10. Scaled near overflow', / 4X,
     $      '5. Middle row and column zero', 5X,
     $      '11. Block diagonal matrix', / 4X,
     $      '6. Last n/2 rows and columns zero' )
*
*     QR matrix types
*
 9970 FORMAT( 4X, '1. Diagonal', 24X,
     $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '2. Upper triangular', 16X, '6. Random, CNDNUM = 0.1/EPS',
     $      / 4X, '3. Lower triangular', 16X,
     $      '7. Scaled near underflow', / 4X, '4. Random, CNDNUM = 2',
     $      14X, '8. Scaled near overflow' )
*
*     QP matrix types
*
 9969 FORMAT( ' Matrix types (2-6 have condition 1/EPS):', / 4X,
     $      '1. Zero matrix', 21X, '4. First n/2 columns fixed', / 4X,
     $      '2. One small eigenvalue', 12X, '5. Last n/2 columns fixed',
     $      / 4X, '3. Geometric distribution', 10X,
     $      '6. Every second column fixed' )
*
*     TZ matrix types
*
 9968 FORMAT( ' Matrix types (2-3 have condition 1/EPS):', / 4X,
     $      '1. Zero matrix', / 4X, '2. One small eigenvalue', / 4X,
     $      '3. Geometric distribution' )
*
*     LS matrix types
*
 9967 FORMAT( ' Matrix types (1-3: full rank, 4-6: rank deficient):',
     $      / 4X, '1 and 4. Normal scaling', / 4X,
     $      '2 and 5. Scaled near overflow', / 4X,
     $      '3 and 6. Scaled near underflow' )
*
*     TR, TP matrix types
*
 9966 FORMAT( ' Matrix types for ', A3, ' routines:', / 4X,
     $      '1. Diagonal', 24X, '6. Scaled near overflow', / 4X,
     $      '2. Random, CNDNUM = 2', 14X, '7. Identity', / 4X,
     $      '3. Random, CNDNUM = sqrt(0.1/EPS)  ',
     $      '8. Unit triangular, CNDNUM = 2', / 4X,
     $      '4. Random, CNDNUM = 0.1/EPS', 8X,
     $      '9. Unit, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '5. Scaled near underflow', 10X,
     $      '10. Unit, CNDNUM = 0.1/EPS' )
 9965 FORMAT( ' Special types for testing ', A6, ':', / 3X,
     $      '11. Matrix elements are O(1), large right hand side', / 3X,
     $      '12. First diagonal causes overflow,',
     $      ' offdiagonal column norms < 1', / 3X,
     $      '13. First diagonal causes overflow,',
     $      ' offdiagonal column norms > 1', / 3X,
     $      '14. Growth factor underflows, solution does not overflow',
     $      / 3X, '15. Small diagonal causes gradual overflow', / 3X,
     $      '16. One zero diagonal element', / 3X,
     $      '17. Large offdiagonals cause overflow when adding a column'
     $      , / 3X, '18. Unit triangular with large right hand side' )
*
*     TB matrix types
*
 9964 FORMAT( ' Matrix types for ', A3, ' routines:', / 4X,
     $      '1. Random, CNDNUM = 2', 14X, '6. Identity', / 4X,
     $      '2. Random, CNDNUM = sqrt(0.1/EPS)  ',
     $      '7. Unit triangular, CNDNUM = 2', / 4X,
     $      '3. Random, CNDNUM = 0.1/EPS', 8X,
     $      '8. Unit, CNDNUM = sqrt(0.1/EPS)', / 4X,
     $      '4. Scaled near underflow', 11X,
     $      '9. Unit, CNDNUM = 0.1/EPS', / 4X,
     $      '5. Scaled near overflow' )
 9963 FORMAT( ' Special types for testing ', A6, ':', / 3X,
     $      '10. Matrix elements are O(1), large right hand side', / 3X,
     $      '11. First diagonal causes overflow,',
     $      ' offdiagonal column norms < 1', / 3X,
     $      '12. First diagonal causes overflow,',
     $      ' offdiagonal column norms > 1', / 3X,
     $      '13. Growth factor underflows, solution does not overflow',
     $      / 3X, '14. Small diagonal causes gradual overflow', / 3X,
     $      '15. One zero diagonal element', / 3X,
     $      '16. Large offdiagonals cause overflow when adding a column'
     $      , / 3X, '17. Unit triangular with large right hand side' )
*
*     Test ratios
*
 9962 FORMAT( 3X, I2, ': norm( L * U - A )  / ( N * norm(A) * EPS )' )
 9961 FORMAT( 3X, I2, ': norm( I - A*AINV ) / ',
     $      '( N * norm(A) * norm(AINV) * EPS )' )
 9960 FORMAT( 3X, I2, ': norm( B - A * X )  / ',
     $      '( norm(A) * norm(X) * EPS )' )
 9959 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
     $      '( norm(XACT) * CNDNUM * EPS )' )
 9958 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
     $      '( norm(XACT) * CNDNUM * EPS ), refined' )
 9957 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
     $      '( norm(XACT) * (error bound) )' )
 9956 FORMAT( 3X, I2, ': (backward error)   / EPS' )
 9955 FORMAT( 3X, I2, ': RCOND * CNDNUM - 1.0' )
 9954 FORMAT( 3X, I2, ': norm( U'' * U - A ) / ( N * norm(A) * EPS )',
     $      ', or', / 7X, 'norm( L * L'' - A ) / ( N * norm(A) * EPS )'
     $       )
 9953 FORMAT( 3X, I2, ': norm( U*D*U'' - A ) / ( N * norm(A) * EPS )',
     $      ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )'
     $       )
 9952 FORMAT( 3X, I2, ': norm( U''*D*U - A ) / ( N * norm(A) * EPS )',
     $      ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )'
     $       )
 9951 FORMAT( ' Test ratio for ', A6, ':', / 3X, I2,
     $      ': norm( s*b - A*x )  / ( norm(A) * norm(x) * EPS )' )
 9950 FORMAT( 3X, I2, ': norm( R - Q'' * A ) / ( M * norm(A) * EPS )' )
 9949 FORMAT( 3X, I2, ': norm( L - A * Q'' ) / ( N * norm(A) * EPS )' )
 9948 FORMAT( 3X, I2, ': norm( L - Q'' * A ) / ( M * norm(A) * EPS )' )
 9947 FORMAT( 3X, I2, ': norm( R - A * Q'' ) / ( N * norm(A) * EPS )' )
 9946 FORMAT( 3X, I2, ': norm( I - Q''*Q )   / ( M * EPS )' )
 9945 FORMAT( 3X, I2, ': norm( I - Q*Q'' )   / ( N * EPS )' )
 9944 FORMAT( 3X, I2, ': norm( Q*C - Q*C )  / ', '( ', A1,
     $      ' * norm(C) * EPS )' )
 9943 FORMAT( 3X, I2, ': norm( C*Q - C*Q )  / ', '( ', A1,
     $      ' * norm(C) * EPS )' )
 9942 FORMAT( 3X, I2, ': norm( Q''*C - Q''*C )/ ', '( ', A1,
     $      ' * norm(C) * EPS )' )
 9941 FORMAT( 3X, I2, ': norm( C*Q'' - C*Q'' )/ ', '( ', A1,
     $      ' * norm(C) * EPS )' )
 9940 FORMAT( 3X, I2, ': norm(svd(A) - svd(R)) / ',
     $      '( M * norm(svd(R)) * EPS )' )
 9939 FORMAT( 3X, I2, ': norm( A*P - Q*R )     / ( M * norm(A) * EPS )'
     $       )
 9938 FORMAT( 3X, I2, ': norm( I - Q''*Q )      / ( M * EPS )' )
 9937 FORMAT( 3X, I2, ': norm( A - R*Q )       / ( M * norm(A) * EPS )'
     $       )
 9936 FORMAT( ' Test ratios (1-2: ', A1, 'GELS, 3-6: ', A1,
     $      'GELSS, 7-10: ', A1, 'GELSX):' )
 9935 FORMAT( 3X, I2, ': norm( B - A * X )   / ',
     $      '( max(M,N) * norm(A) * norm(X) * EPS )' )
 9934 FORMAT( 3X, I2, ': norm( (A*X-B)'' *A ) / ',
     $      '( max(M,N,NRHS) * norm(A) * norm(B) * EPS )' )
 9933 FORMAT( 3X, I2, ': norm(svd(A)-svd(R)) / ',
     $      '( min(M,N) * norm(svd(R)) * EPS )' )
 9932 FORMAT( 3X, I2, ': Check if X is in the row space of A or A''' )
 9931 FORMAT( 3X, I2, ': norm( (A*X-B)'' *A ) / ',
     $      '( max(M,N,NRHS) * norm(A) * norm(B) * EPS )', / 7X,
     $      'if TRANS=''N'' and M.GE.N or TRANS=''T'' and M.LT.N, ',
     $      'otherwise', / 7X,
     $      'check if X is in the row space of A or A'' ',
     $      '(overdetermined case)' )
 9930 FORMAT( 3X, ' 7-10: same as 3-6' )
 9929 FORMAT( ' Test ratios (1-3: ', A1, 'TZRQF, 4-6: ', A1,
     $      'TZRZF):' )
 9920 FORMAT( 3X, ' 7-10: same as 3-6', 3X, ' 11-14: same as 3-6',
     $      3X, ' 15-18: same as 3-6' )
 9921 FORMAT( ' Test ratios:', / '    (1-2: ', A1, 'GELS, 3-6: ', A1,
     $      'GELSX, 7-10: ', A1, 'GELSY, 11-14: ', A1, 'GELSS, 15-18: ',
     $      A1, 'GELSD)' )
*
      RETURN
*
*     End of ALAHD
*
      END