510 lines
19 KiB
Fortran
510 lines
19 KiB
Fortran
*> \brief \b SLAHD2
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SLAHD2( IOUNIT, PATH )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER*3 PATH
|
|
* INTEGER IOUNIT
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SLAHD2 prints header information for the different test paths.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] IOUNIT
|
|
*> \verbatim
|
|
*> IOUNIT is INTEGER.
|
|
*> On entry, IOUNIT specifies the unit number to which the
|
|
*> header information should be printed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] PATH
|
|
*> \verbatim
|
|
*> PATH is CHARACTER*3.
|
|
*> On entry, PATH contains the name of the path for which the
|
|
*> header information is to be printed. Current paths are
|
|
*>
|
|
*> SHS, CHS: Non-symmetric eigenproblem.
|
|
*> SST, CST: Symmetric eigenproblem.
|
|
*> SSG, CSG: Symmetric Generalized eigenproblem.
|
|
*> SBD, CBD: Singular Value Decomposition (SVD)
|
|
*> SBB, CBB: General Banded reduction to bidiagonal form
|
|
*>
|
|
*> These paths also are supplied in double precision (replace
|
|
*> leading S by D and leading C by Z in path names).
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup single_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SLAHD2( IOUNIT, PATH )
|
|
*
|
|
* -- LAPACK test routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER*3 PATH
|
|
INTEGER IOUNIT
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Local Scalars ..
|
|
LOGICAL CORZ, SORD
|
|
CHARACTER*2 C2
|
|
INTEGER J
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME, LSAMEN
|
|
EXTERNAL LSAME, LSAMEN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
IF( IOUNIT.LE.0 )
|
|
$ RETURN
|
|
SORD = LSAME( PATH, 'S' ) .OR. LSAME( PATH, 'D' )
|
|
CORZ = LSAME( PATH, 'C' ) .OR. LSAME( PATH, 'Z' )
|
|
IF( .NOT.SORD .AND. .NOT.CORZ ) THEN
|
|
WRITE( IOUNIT, FMT = 9999 )PATH
|
|
END IF
|
|
C2 = PATH( 2: 3 )
|
|
*
|
|
IF( LSAMEN( 2, C2, 'HS' ) ) THEN
|
|
IF( SORD ) THEN
|
|
*
|
|
* Real Non-symmetric Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9998 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9988 )
|
|
WRITE( IOUNIT, FMT = 9987 )
|
|
WRITE( IOUNIT, FMT = 9986 )'pairs ', 'pairs ', 'prs.',
|
|
$ 'prs.'
|
|
WRITE( IOUNIT, FMT = 9985 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9984 )'orthogonal', '''=transpose',
|
|
$ ( '''', J = 1, 6 )
|
|
*
|
|
ELSE
|
|
*
|
|
* Complex Non-symmetric Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9997 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9988 )
|
|
WRITE( IOUNIT, FMT = 9987 )
|
|
WRITE( IOUNIT, FMT = 9986 )'e.vals', 'e.vals', 'e.vs',
|
|
$ 'e.vs'
|
|
WRITE( IOUNIT, FMT = 9985 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9984 )'unitary', '*=conj.transp.',
|
|
$ ( '*', J = 1, 6 )
|
|
END IF
|
|
*
|
|
ELSE IF( LSAMEN( 2, C2, 'ST' ) ) THEN
|
|
*
|
|
IF( SORD ) THEN
|
|
*
|
|
* Real Symmetric Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9996 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9983 )
|
|
WRITE( IOUNIT, FMT = 9982 )
|
|
WRITE( IOUNIT, FMT = 9981 )'Symmetric'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9968 )
|
|
*
|
|
ELSE
|
|
*
|
|
* Complex Hermitian Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9995 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9983 )
|
|
WRITE( IOUNIT, FMT = 9982 )
|
|
WRITE( IOUNIT, FMT = 9981 )'Hermitian'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9967 )
|
|
END IF
|
|
*
|
|
ELSE IF( LSAMEN( 2, C2, 'SG' ) ) THEN
|
|
*
|
|
IF( SORD ) THEN
|
|
*
|
|
* Real Symmetric Generalized Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9992 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9980 )
|
|
WRITE( IOUNIT, FMT = 9979 )
|
|
WRITE( IOUNIT, FMT = 9978 )'Symmetric'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9977 )
|
|
WRITE( IOUNIT, FMT = 9976 )
|
|
*
|
|
ELSE
|
|
*
|
|
* Complex Hermitian Generalized Eigenvalue Problem:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9991 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9980 )
|
|
WRITE( IOUNIT, FMT = 9979 )
|
|
WRITE( IOUNIT, FMT = 9978 )'Hermitian'
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9975 )
|
|
WRITE( IOUNIT, FMT = 9974 )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE IF( LSAMEN( 2, C2, 'BD' ) ) THEN
|
|
*
|
|
IF( SORD ) THEN
|
|
*
|
|
* Real Singular Value Decomposition:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9994 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9973 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9972 )'orthogonal'
|
|
WRITE( IOUNIT, FMT = 9971 )
|
|
ELSE
|
|
*
|
|
* Complex Singular Value Decomposition:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9993 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9973 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9972 )'unitary '
|
|
WRITE( IOUNIT, FMT = 9971 )
|
|
END IF
|
|
*
|
|
ELSE IF( LSAMEN( 2, C2, 'BB' ) ) THEN
|
|
*
|
|
IF( SORD ) THEN
|
|
*
|
|
* Real General Band reduction to bidiagonal form:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9990 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9970 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9969 )'orthogonal'
|
|
ELSE
|
|
*
|
|
* Complex Band reduction to bidiagonal form:
|
|
*
|
|
WRITE( IOUNIT, FMT = 9989 )PATH
|
|
*
|
|
* Matrix types
|
|
*
|
|
WRITE( IOUNIT, FMT = 9970 )
|
|
*
|
|
* Tests performed
|
|
*
|
|
WRITE( IOUNIT, FMT = 9969 )'unitary '
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
WRITE( IOUNIT, FMT = 9999 )PATH
|
|
RETURN
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
9999 FORMAT( 1X, A3, ': no header available' )
|
|
9998 FORMAT( / 1X, A3, ' -- Real Non-symmetric eigenvalue problem' )
|
|
9997 FORMAT( / 1X, A3, ' -- Complex Non-symmetric eigenvalue problem' )
|
|
9996 FORMAT( / 1X, A3, ' -- Real Symmetric eigenvalue problem' )
|
|
9995 FORMAT( / 1X, A3, ' -- Complex Hermitian eigenvalue problem' )
|
|
9994 FORMAT( / 1X, A3, ' -- Real Singular Value Decomposition' )
|
|
9993 FORMAT( / 1X, A3, ' -- Complex Singular Value Decomposition' )
|
|
9992 FORMAT( / 1X, A3, ' -- Real Symmetric Generalized eigenvalue ',
|
|
$ 'problem' )
|
|
9991 FORMAT( / 1X, A3, ' -- Complex Hermitian Generalized eigenvalue ',
|
|
$ 'problem' )
|
|
9990 FORMAT( / 1X, A3, ' -- Real Band reduc. to bidiagonal form' )
|
|
9989 FORMAT( / 1X, A3, ' -- Complex Band reduc. to bidiagonal form' )
|
|
*
|
|
9988 FORMAT( ' Matrix types (see xCHKHS for details): ' )
|
|
*
|
|
9987 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
|
|
$ ' ', ' 5=Diagonal: geometr. spaced entries.',
|
|
$ / ' 2=Identity matrix. ', ' 6=Diagona',
|
|
$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
|
|
$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
|
|
$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
|
|
$ 'mall, evenly spaced.' )
|
|
9986 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
|
|
$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
|
|
$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
|
|
$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
|
|
$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
|
|
$ 'lex ', A6, / ' 12=Well-cond., random complex ', A6, ' ',
|
|
$ ' 17=Ill-cond., large rand. complx ', A4, / ' 13=Ill-condi',
|
|
$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
|
|
$ ' complx ', A4 )
|
|
9985 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
|
|
$ 'with small random entries.', / ' 20=Matrix with large ran',
|
|
$ 'dom entries. ' )
|
|
9984 FORMAT( / ' Tests performed: ', '(H is Hessenberg, T is Schur,',
|
|
$ ' U and Z are ', A, ',', / 20X, A, ', W is a diagonal matr',
|
|
$ 'ix of eigenvalues,', / 20X, 'L and R are the left and rig',
|
|
$ 'ht eigenvector matrices)', / ' 1 = | A - U H U', A1, ' |',
|
|
$ ' / ( |A| n ulp ) ', ' 2 = | I - U U', A1, ' | / ',
|
|
$ '( n ulp )', / ' 3 = | H - Z T Z', A1, ' | / ( |H| n ulp ',
|
|
$ ') ', ' 4 = | I - Z Z', A1, ' | / ( n ulp )',
|
|
$ / ' 5 = | A - UZ T (UZ)', A1, ' | / ( |A| n ulp ) ',
|
|
$ ' 6 = | I - UZ (UZ)', A1, ' | / ( n ulp )', / ' 7 = | T(',
|
|
$ 'e.vects.) - T(no e.vects.) | / ( |T| ulp )', / ' 8 = | W',
|
|
$ '(e.vects.) - W(no e.vects.) | / ( |W| ulp )', / ' 9 = | ',
|
|
$ 'TR - RW | / ( |T| |R| ulp ) ', ' 10 = | LT - WL | / (',
|
|
$ ' |T| |L| ulp )', / ' 11= |HX - XW| / (|H| |X| ulp) (inv.',
|
|
$ 'it)', ' 12= |YH - WY| / (|H| |Y| ulp) (inv.it)' )
|
|
*
|
|
* Symmetric/Hermitian eigenproblem
|
|
*
|
|
9983 FORMAT( ' Matrix types (see xDRVST for details): ' )
|
|
*
|
|
9982 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
|
|
$ ' ', ' 5=Diagonal: clustered entries.', / ' 2=',
|
|
$ 'Identity matrix. ', ' 6=Diagonal: lar',
|
|
$ 'ge, evenly spaced.', / ' 3=Diagonal: evenly spaced entri',
|
|
$ 'es. ', ' 7=Diagonal: small, evenly spaced.', / ' 4=D',
|
|
$ 'iagonal: geometr. spaced entries.' )
|
|
9981 FORMAT( ' Dense ', A, ' Matrices:', / ' 8=Evenly spaced eigen',
|
|
$ 'vals. ', ' 12=Small, evenly spaced eigenvals.',
|
|
$ / ' 9=Geometrically spaced eigenvals. ', ' 13=Matrix ',
|
|
$ 'with random O(1) entries.', / ' 10=Clustered eigenvalues.',
|
|
$ ' ', ' 14=Matrix with large random entries.',
|
|
$ / ' 11=Large, evenly spaced eigenvals. ', ' 15=Matrix ',
|
|
$ 'with small random entries.' )
|
|
*
|
|
* Symmetric/Hermitian Generalized eigenproblem
|
|
*
|
|
9980 FORMAT( ' Matrix types (see xDRVSG for details): ' )
|
|
*
|
|
9979 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
|
|
$ ' ', ' 5=Diagonal: clustered entries.', / ' 2=',
|
|
$ 'Identity matrix. ', ' 6=Diagonal: lar',
|
|
$ 'ge, evenly spaced.', / ' 3=Diagonal: evenly spaced entri',
|
|
$ 'es. ', ' 7=Diagonal: small, evenly spaced.', / ' 4=D',
|
|
$ 'iagonal: geometr. spaced entries.' )
|
|
9978 FORMAT( ' Dense or Banded ', A, ' Matrices: ',
|
|
$ / ' 8=Evenly spaced eigenvals. ',
|
|
$ ' 15=Matrix with small random entries.',
|
|
$ / ' 9=Geometrically spaced eigenvals. ',
|
|
$ ' 16=Evenly spaced eigenvals, KA=1, KB=1.',
|
|
$ / ' 10=Clustered eigenvalues. ',
|
|
$ ' 17=Evenly spaced eigenvals, KA=2, KB=1.',
|
|
$ / ' 11=Large, evenly spaced eigenvals. ',
|
|
$ ' 18=Evenly spaced eigenvals, KA=2, KB=2.',
|
|
$ / ' 12=Small, evenly spaced eigenvals. ',
|
|
$ ' 19=Evenly spaced eigenvals, KA=3, KB=1.',
|
|
$ / ' 13=Matrix with random O(1) entries. ',
|
|
$ ' 20=Evenly spaced eigenvals, KA=3, KB=2.',
|
|
$ / ' 14=Matrix with large random entries.',
|
|
$ ' 21=Evenly spaced eigenvals, KA=3, KB=3.' )
|
|
9977 FORMAT( / ' Tests performed: ',
|
|
$ / '( For each pair (A,B), where A is of the given type ',
|
|
$ / ' and B is a random well-conditioned matrix. D is ',
|
|
$ / ' diagonal, and Z is orthogonal. )',
|
|
$ / ' 1 = SSYGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 2 = SSPGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 3 = SSBGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 4 = SSYGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 5 = SSPGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 6 = SSBGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ' )
|
|
9976 FORMAT( ' 7 = SSYGV, with ITYPE=2 and UPLO=''U'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 8 = SSPGV, with ITYPE=2 and UPLO=''U'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 9 = SSPGV, with ITYPE=2 and UPLO=''L'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '10 = SSPGV, with ITYPE=2 and UPLO=''L'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '11 = SSYGV, with ITYPE=3 and UPLO=''U'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '12 = SSPGV, with ITYPE=3 and UPLO=''U'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '13 = SSYGV, with ITYPE=3 and UPLO=''L'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '14 = SSPGV, with ITYPE=3 and UPLO=''L'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ' )
|
|
9975 FORMAT( / ' Tests performed: ',
|
|
$ / '( For each pair (A,B), where A is of the given type ',
|
|
$ / ' and B is a random well-conditioned matrix. D is ',
|
|
$ / ' diagonal, and Z is unitary. )',
|
|
$ / ' 1 = CHEGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 2 = CHPGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 3 = CHBGV, with ITYPE=1 and UPLO=''U'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 4 = CHEGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 5 = CHPGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 6 = CHBGV, with ITYPE=1 and UPLO=''L'':',
|
|
$ ' | A Z - B Z D | / ( |A| |Z| n ulp ) ' )
|
|
9974 FORMAT( ' 7 = CHEGV, with ITYPE=2 and UPLO=''U'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 8 = CHPGV, with ITYPE=2 and UPLO=''U'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / ' 9 = CHPGV, with ITYPE=2 and UPLO=''L'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '10 = CHPGV, with ITYPE=2 and UPLO=''L'':',
|
|
$ ' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '11 = CHEGV, with ITYPE=3 and UPLO=''U'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '12 = CHPGV, with ITYPE=3 and UPLO=''U'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '13 = CHEGV, with ITYPE=3 and UPLO=''L'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
|
|
$ / '14 = CHPGV, with ITYPE=3 and UPLO=''L'':',
|
|
$ ' | B A Z - Z D | / ( |A| |Z| n ulp ) ' )
|
|
*
|
|
* Singular Value Decomposition
|
|
*
|
|
9973 FORMAT( ' Matrix types (see xCHKBD for details):',
|
|
$ / ' Diagonal matrices:', / ' 1: Zero', 28X,
|
|
$ ' 5: Clustered entries', / ' 2: Identity', 24X,
|
|
$ ' 6: Large, evenly spaced entries',
|
|
$ / ' 3: Evenly spaced entries', 11X,
|
|
$ ' 7: Small, evenly spaced entries',
|
|
$ / ' 4: Geometrically spaced entries',
|
|
$ / ' General matrices:', / ' 8: Evenly spaced sing. vals.',
|
|
$ 7X, '12: Small, evenly spaced sing vals',
|
|
$ / ' 9: Geometrically spaced sing vals ',
|
|
$ '13: Random, O(1) entries', / ' 10: Clustered sing. vals.',
|
|
$ 11X, '14: Random, scaled near overflow',
|
|
$ / ' 11: Large, evenly spaced sing vals ',
|
|
$ '15: Random, scaled near underflow' )
|
|
*
|
|
9972 FORMAT( / ' Test ratios: ',
|
|
$ '(B: bidiagonal, S: diagonal, Q, P, U, and V: ', A10, / 16X,
|
|
$ 'X: m x nrhs, Y = Q'' X, and Z = U'' Y)',
|
|
$ / ' 1: norm( A - Q B P'' ) / ( norm(A) max(m,n) ulp )',
|
|
$ / ' 2: norm( I - Q'' Q ) / ( m ulp )',
|
|
$ / ' 3: norm( I - P'' P ) / ( n ulp )',
|
|
$ / ' 4: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )', /
|
|
$ ' 5: norm( Y - U Z ) / ( norm(Z) max(min(m,n),k) ulp )'
|
|
$ , / ' 6: norm( I - U'' U ) / ( min(m,n) ulp )',
|
|
$ / ' 7: norm( I - V'' V ) / ( min(m,n) ulp )' )
|
|
9971 FORMAT( ' 8: Test ordering of S (0 if nondecreasing, 1/ulp ',
|
|
$ ' otherwise)', /
|
|
$ ' 9: norm( S - S2 ) / ( norm(S) ulp ),',
|
|
$ ' where S2 is computed', / 44X,
|
|
$ 'without computing U and V''',
|
|
$ / ' 10: Sturm sequence test ',
|
|
$ '(0 if sing. vals of B within THRESH of S)',
|
|
$ / ' 11: norm( A - (QU) S (V'' P'') ) / ',
|
|
$ '( norm(A) max(m,n) ulp )', /
|
|
$ ' 12: norm( X - (QU) Z ) / ( |X| max(M,k) ulp )',
|
|
$ / ' 13: norm( I - (QU)''(QU) ) / ( M ulp )',
|
|
$ / ' 14: norm( I - (V'' P'') (P V) ) / ( N ulp )' )
|
|
*
|
|
* Band reduction to bidiagonal form
|
|
*
|
|
9970 FORMAT( ' Matrix types (see xCHKBB for details):',
|
|
$ / ' Diagonal matrices:', / ' 1: Zero', 28X,
|
|
$ ' 5: Clustered entries', / ' 2: Identity', 24X,
|
|
$ ' 6: Large, evenly spaced entries',
|
|
$ / ' 3: Evenly spaced entries', 11X,
|
|
$ ' 7: Small, evenly spaced entries',
|
|
$ / ' 4: Geometrically spaced entries',
|
|
$ / ' General matrices:', / ' 8: Evenly spaced sing. vals.',
|
|
$ 7X, '12: Small, evenly spaced sing vals',
|
|
$ / ' 9: Geometrically spaced sing vals ',
|
|
$ '13: Random, O(1) entries', / ' 10: Clustered sing. vals.',
|
|
$ 11X, '14: Random, scaled near overflow',
|
|
$ / ' 11: Large, evenly spaced sing vals ',
|
|
$ '15: Random, scaled near underflow' )
|
|
*
|
|
9969 FORMAT( / ' Test ratios: ', '(B: upper bidiagonal, Q and P: ',
|
|
$ A10, / 16X, 'C: m x nrhs, PT = P'', Y = Q'' C)',
|
|
$ / ' 1: norm( A - Q B PT ) / ( norm(A) max(m,n) ulp )',
|
|
$ / ' 2: norm( I - Q'' Q ) / ( m ulp )',
|
|
$ / ' 3: norm( I - PT PT'' ) / ( n ulp )',
|
|
$ / ' 4: norm( Y - Q'' C ) / ( norm(Y) max(m,nrhs) ulp )' )
|
|
9968 FORMAT( / ' Tests performed: See sdrvst.f' )
|
|
9967 FORMAT( / ' Tests performed: See cdrvst.f' )
|
|
*
|
|
* End of SLAHD2
|
|
*
|
|
END
|