numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/aladhd.f | 18693B | -rw-r--r-- |
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*> \brief \b ALADHD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ALADHD( IOUNIT, PATH ) * * .. Scalar Arguments .. * CHARACTER*3 PATH * INTEGER IOUNIT * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ALADHD prints header information for the driver routines test paths. *> \endverbatim * * Arguments: * ========== * *> \param[in] IOUNIT *> \verbatim *> IOUNIT is INTEGER *> The unit number to which the header information should be *> printed. *> \endverbatim *> *> \param[in] PATH *> \verbatim *> PATH is CHARACTER*3 *> The name of the path for which the header information is to *> be printed. Current paths are *> _GE: General matrices *> _GB: General band *> _GT: General Tridiagonal *> _PO: Symmetric or Hermitian positive definite *> _PS: Symmetric or Hermitian positive semi-definite *> _PP: Symmetric or Hermitian positive definite packed *> _PB: Symmetric or Hermitian positive definite band *> _PT: Symmetric or Hermitian positive definite tridiagonal *> _SY: Symmetric indefinite, *> with partial (Bunch-Kaufman) pivoting *> _SR: Symmetric indefinite, *> with rook (bounded Bunch-Kaufman) pivoting *> _SK: Symmetric indefinite, *> with rook (bounded Bunch-Kaufman) pivoting *> ( new storage format for factors: *> L and diagonal of D is stored in A, *> subdiagonal of D is stored in E ) *> _SP: Symmetric indefinite packed, *> with partial (Bunch-Kaufman) pivoting *> _HA: (complex) Hermitian , *> Assen Algorithm *> _HE: (complex) Hermitian indefinite, *> with partial (Bunch-Kaufman) pivoting *> _HR: (complex) Hermitian indefinite, *> with rook (bounded Bunch-Kaufman) pivoting *> _HK: (complex) Hermitian indefinite, *> with rook (bounded Bunch-Kaufman) pivoting *> ( new storage format for factors: *> L and diagonal of D is stored in A, *> subdiagonal of D is stored in E ) *> _HP: (complex) Hermitian indefinite packed, *> with partial (Bunch-Kaufman) pivoting *> The first character must be one of S, D, C, or Z (C or Z only *> if complex). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup aux_lin * * ===================================================================== SUBROUTINE ALADHD( IOUNIT, PATH ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER*3 PATH INTEGER IOUNIT * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL CORZ, SORD CHARACTER C1, C3 CHARACTER*2 P2 CHARACTER*9 SYM * .. * .. External Functions .. LOGICAL LSAME, LSAMEN EXTERNAL LSAME, LSAMEN * .. * .. Executable Statements .. * IF( IOUNIT.LE.0 ) $ RETURN C1 = PATH( 1: 1 ) C3 = PATH( 3: 3 ) P2 = PATH( 2: 3 ) SORD = LSAME( C1, 'S' ) .OR. LSAME( C1, 'D' ) CORZ = LSAME( C1, 'C' ) .OR. LSAME( C1, 'Z' ) IF( .NOT.( SORD .OR. CORZ ) ) $ RETURN * IF( LSAMEN( 2, P2, 'GE' ) ) THEN * * GE: General dense * WRITE( IOUNIT, FMT = 9999 )PATH WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9989 ) WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9981 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = 9972 )7 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'GB' ) ) THEN * * GB: General band * WRITE( IOUNIT, FMT = 9998 )PATH WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9988 ) WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9981 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = 9972 )7 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'GT' ) ) THEN * * GT: General tridiagonal * WRITE( IOUNIT, FMT = 9997 )PATH WRITE( IOUNIT, FMT = 9987 ) WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9981 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'PO' ) .OR. LSAMEN( 2, P2, 'PP' ) $ .OR. LSAMEN( 2, P2, 'PS' ) ) THEN * * PO: Positive definite full * PS: Positive definite full * PP: Positive definite packed * IF( SORD ) THEN SYM = 'Symmetric' ELSE SYM = 'Hermitian' END IF IF( LSAME( C3, 'O' ) ) THEN WRITE( IOUNIT, FMT = 9996 )PATH, SYM ELSE WRITE( IOUNIT, FMT = 9995 )PATH, SYM END IF WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9985 )PATH WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9975 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'PB' ) ) THEN * * PB: Positive definite band * IF( SORD ) THEN WRITE( IOUNIT, FMT = 9994 )PATH, 'Symmetric' ELSE WRITE( IOUNIT, FMT = 9994 )PATH, 'Hermitian' END IF WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9984 )PATH WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9975 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'PT' ) ) THEN * * PT: Positive definite tridiagonal * IF( SORD ) THEN WRITE( IOUNIT, FMT = 9993 )PATH, 'Symmetric' ELSE WRITE( IOUNIT, FMT = 9993 )PATH, 'Hermitian' END IF WRITE( IOUNIT, FMT = 9986 ) WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9973 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9978 )4 WRITE( IOUNIT, FMT = 9977 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'SY' ) .OR. LSAMEN( 2, P2, 'SP' ) ) THEN * * SY: Symmetric indefinite full * with partial (Bunch-Kaufman) pivoting algorithm * SP: Symmetric indefinite packed * with partial (Bunch-Kaufman) pivoting algorithm * IF( LSAME( C3, 'Y' ) ) THEN WRITE( IOUNIT, FMT = 9992 )PATH, 'Symmetric' ELSE WRITE( IOUNIT, FMT = 9991 )PATH, 'Symmetric' END IF WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) IF( SORD ) THEN WRITE( IOUNIT, FMT = 9983 ) ELSE WRITE( IOUNIT, FMT = 9982 ) END IF WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9974 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9977 )4 WRITE( IOUNIT, FMT = 9978 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'SR' ) .OR. LSAMEN( 2, P2, 'SK') ) THEN * * SR: Symmetric indefinite full, * with rook (bounded Bunch-Kaufman) pivoting algorithm * * SK: Symmetric indefinite full, * with rook (bounded Bunch-Kaufman) pivoting algorithm, * ( new storage format for factors: * L and diagonal of D is stored in A, * subdiagonal of D is stored in E ) * WRITE( IOUNIT, FMT = 9992 )PATH, 'Symmetric' * WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) IF( SORD ) THEN WRITE( IOUNIT, FMT = 9983 ) ELSE WRITE( IOUNIT, FMT = 9982 ) END IF * WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9974 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'HA' ) ) THEN * * HA: Hermitian * Aasen algorithm WRITE( IOUNIT, FMT = 9971 )PATH, 'Hermitian' * WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9983 ) * WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9974 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9977 )4 WRITE( IOUNIT, FMT = 9978 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) ELSE IF( LSAMEN( 2, P2, 'HE' ) .OR. $ LSAMEN( 2, P2, 'HP' ) ) THEN * * HE: Hermitian indefinite full * with partial (Bunch-Kaufman) pivoting algorithm * HP: Hermitian indefinite packed * with partial (Bunch-Kaufman) pivoting algorithm * IF( LSAME( C3, 'E' ) ) THEN WRITE( IOUNIT, FMT = 9992 )PATH, 'Hermitian' ELSE WRITE( IOUNIT, FMT = 9991 )PATH, 'Hermitian' END IF * WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9983 ) * WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9974 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = 9977 )4 WRITE( IOUNIT, FMT = 9978 )5 WRITE( IOUNIT, FMT = 9976 )6 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE IF( LSAMEN( 2, P2, 'HR' ) .OR. LSAMEN( 2, P2, 'HK' ) ) THEN * * HR: Hermitian indefinite full, * with rook (bounded Bunch-Kaufman) pivoting algorithm * * HK: Hermitian indefinite full, * with rook (bounded Bunch-Kaufman) pivoting algorithm, * ( new storage format for factors: * L and diagonal of D is stored in A, * subdiagonal of D is stored in E ) * WRITE( IOUNIT, FMT = 9992 )PATH, 'Hermitian' * WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' ) WRITE( IOUNIT, FMT = 9983 ) * WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' ) WRITE( IOUNIT, FMT = 9974 )1 WRITE( IOUNIT, FMT = 9980 )2 WRITE( IOUNIT, FMT = 9979 )3 WRITE( IOUNIT, FMT = '( '' Messages:'' )' ) * ELSE * * Print error message if no header is available. * WRITE( IOUNIT, FMT = 9990 )PATH END IF * * First line of header * 9999 FORMAT( / 1X, A3, ' drivers: General dense matrices' ) 9998 FORMAT( / 1X, A3, ' drivers: General band matrices' ) 9997 FORMAT( / 1X, A3, ' drivers: General tridiagonal' ) 9996 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' positive definite matrices' ) 9995 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' positive definite packed matrices' ) 9994 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' positive definite band matrices' ) 9993 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' positive definite tridiagonal' ) 9971 FORMAT( / 1X, A3, ' drivers: ', A9, ' indefinite matrices', $ ', "Aasen" Algorithm' ) 9992 FORMAT( / 1X, A3, ' drivers: ', A9, ' indefinite matrices', $ ', "rook" (bounded Bunch-Kaufman) pivoting' ) 9991 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' indefinite packed matrices', $ ', partial (Bunch-Kaufman) pivoting' ) 9891 FORMAT( / 1X, A3, ' drivers: ', A9, $ ' indefinite packed matrices', $ ', "rook" (bounded Bunch-Kaufman) pivoting' ) 9990 FORMAT( / 1X, A3, ': No header available' ) * * GE matrix types * 9989 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 * 9988 FORMAT( 4X, '1. Random, CNDNUM = 2', 14X, $ '5. Random, CNDNUM = sqrt(0.1/EPS)', / 4X, $ '2. First column zero', 15X, '6. Random, CNDNUM = 0.1/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 * 9987 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 * 9986 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 * 9985 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)' ) * * PB matrix types * 9984 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 * 9983 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 * 9982 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' ) * * Test ratios * 9981 FORMAT( 3X, I2, ': norm( L * U - A ) / ( N * norm(A) * EPS )' ) 9980 FORMAT( 3X, I2, ': norm( B - A * X ) / ', $ '( norm(A) * norm(X) * EPS )' ) 9979 FORMAT( 3X, I2, ': norm( X - XACT ) / ', $ '( norm(XACT) * CNDNUM * EPS )' ) 9978 FORMAT( 3X, I2, ': norm( X - XACT ) / ', $ '( norm(XACT) * (error bound) )' ) 9977 FORMAT( 3X, I2, ': (backward error) / EPS' ) 9976 FORMAT( 3X, I2, ': RCOND * CNDNUM - 1.0' ) 9975 FORMAT( 3X, I2, ': norm( U'' * U - A ) / ( N * norm(A) * EPS )', $ ', or', / 7X, 'norm( L * L'' - A ) / ( N * norm(A) * EPS )' $ ) 9974 FORMAT( 3X, I2, ': norm( U*D*U'' - A ) / ( N * norm(A) * EPS )', $ ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )' $ ) 9973 FORMAT( 3X, I2, ': norm( U''*D*U - A ) / ( N * norm(A) * EPS )', $ ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )' $ ) 9972 FORMAT( 3X, I2, ': abs( WORK(1) - RPVGRW ) /', $ ' ( max( WORK(1), RPVGRW ) * EPS )' ) * RETURN * * End of ALADHD * END