LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlahd2.f
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00001 *> \brief \b DLAHD2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DLAHD2( IOUNIT, PATH )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER*3        PATH
00015 *       INTEGER            IOUNIT
00016 *       ..
00017 *  
00018 *
00019 *> \par Purpose:
00020 *  =============
00021 *>
00022 *> \verbatim
00023 *>
00024 *> DLAHD2 prints header information for the different test paths.
00025 *> \endverbatim
00026 *
00027 *  Arguments:
00028 *  ==========
00029 *
00030 *> \param[in] IOUNIT
00031 *> \verbatim
00032 *>          IOUNIT is INTEGER.
00033 *>          On entry, IOUNIT specifies the unit number to which the
00034 *>          header information should be printed.
00035 *> \endverbatim
00036 *>
00037 *> \param[in] PATH
00038 *> \verbatim
00039 *>          PATH is CHARACTER*3.
00040 *>          On entry, PATH contains the name of the path for which the
00041 *>          header information is to be printed.  Current paths are
00042 *>
00043 *>             DHS, ZHS:  Non-symmetric eigenproblem.
00044 *>             DST, ZST:  Symmetric eigenproblem.
00045 *>             DSG, ZSG:  Symmetric Generalized eigenproblem.
00046 *>             DBD, ZBD:  Singular Value Decomposition (SVD)
00047 *>             DBB, ZBB:  General Banded reduction to bidiagonal form
00048 *>
00049 *>          These paths also are supplied in double precision (replace
00050 *>          leading S by D and leading C by Z in path names).
00051 *> \endverbatim
00052 *
00053 *  Authors:
00054 *  ========
00055 *
00056 *> \author Univ. of Tennessee 
00057 *> \author Univ. of California Berkeley 
00058 *> \author Univ. of Colorado Denver 
00059 *> \author NAG Ltd. 
00060 *
00061 *> \date November 2011
00062 *
00063 *> \ingroup double_eig
00064 *
00065 *  =====================================================================
00066       SUBROUTINE DLAHD2( IOUNIT, PATH )
00067 *
00068 *  -- LAPACK test routine (version 3.4.0) --
00069 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00070 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00071 *     November 2011
00072 *
00073 *     .. Scalar Arguments ..
00074       CHARACTER*3        PATH
00075       INTEGER            IOUNIT
00076 *     ..
00077 *
00078 *  =====================================================================
00079 *
00080 *     .. Local Scalars ..
00081       LOGICAL            CORZ, SORD
00082       CHARACTER*2        C2
00083       INTEGER            J
00084 *     ..
00085 *     .. External Functions ..
00086       LOGICAL            LSAME, LSAMEN
00087       EXTERNAL           LSAME, LSAMEN
00088 *     ..
00089 *     .. Executable Statements ..
00090 *
00091       IF( IOUNIT.LE.0 )
00092      $   RETURN
00093       SORD = LSAME( PATH, 'S' ) .OR. LSAME( PATH, 'D' )
00094       CORZ = LSAME( PATH, 'C' ) .OR. LSAME( PATH, 'Z' )
00095       IF( .NOT.SORD .AND. .NOT.CORZ ) THEN
00096          WRITE( IOUNIT, FMT = 9999 )PATH
00097       END IF
00098       C2 = PATH( 2: 3 )
00099 *
00100       IF( LSAMEN( 2, C2, 'HS' ) ) THEN
00101          IF( SORD ) THEN
00102 *
00103 *           Real Non-symmetric Eigenvalue Problem:
00104 *
00105             WRITE( IOUNIT, FMT = 9998 )PATH
00106 *
00107 *           Matrix types
00108 *
00109             WRITE( IOUNIT, FMT = 9988 )
00110             WRITE( IOUNIT, FMT = 9987 )
00111             WRITE( IOUNIT, FMT = 9986 )'pairs ', 'pairs ', 'prs.',
00112      $         'prs.'
00113             WRITE( IOUNIT, FMT = 9985 )
00114 *
00115 *           Tests performed
00116 *
00117             WRITE( IOUNIT, FMT = 9984 )'orthogonal', '''=transpose',
00118      $         ( '''', J = 1, 6 )
00119 *
00120          ELSE
00121 *
00122 *           Complex Non-symmetric Eigenvalue Problem:
00123 *
00124             WRITE( IOUNIT, FMT = 9997 )PATH
00125 *
00126 *           Matrix types
00127 *
00128             WRITE( IOUNIT, FMT = 9988 )
00129             WRITE( IOUNIT, FMT = 9987 )
00130             WRITE( IOUNIT, FMT = 9986 )'e.vals', 'e.vals', 'e.vs',
00131      $         'e.vs'
00132             WRITE( IOUNIT, FMT = 9985 )
00133 *
00134 *           Tests performed
00135 *
00136             WRITE( IOUNIT, FMT = 9984 )'unitary', '*=conj.transp.',
00137      $         ( '*', J = 1, 6 )
00138          END IF
00139 *
00140       ELSE IF( LSAMEN( 2, C2, 'ST' ) ) THEN
00141 *
00142          IF( SORD ) THEN
00143 *
00144 *           Real Symmetric Eigenvalue Problem:
00145 *
00146             WRITE( IOUNIT, FMT = 9996 )PATH
00147 *
00148 *           Matrix types
00149 *
00150             WRITE( IOUNIT, FMT = 9983 )
00151             WRITE( IOUNIT, FMT = 9982 )
00152             WRITE( IOUNIT, FMT = 9981 )'Symmetric'
00153 *
00154 *           Tests performed
00155 *
00156             WRITE( IOUNIT, FMT = 9968 )
00157 *
00158          ELSE
00159 *
00160 *           Complex Hermitian Eigenvalue Problem:
00161 *
00162             WRITE( IOUNIT, FMT = 9995 )PATH
00163 *
00164 *           Matrix types
00165 *
00166             WRITE( IOUNIT, FMT = 9983 )
00167             WRITE( IOUNIT, FMT = 9982 )
00168             WRITE( IOUNIT, FMT = 9981 )'Hermitian'
00169 *
00170 *           Tests performed
00171 *
00172             WRITE( IOUNIT, FMT = 9967 )
00173          END IF
00174 *
00175       ELSE IF( LSAMEN( 2, C2, 'SG' ) ) THEN
00176 *
00177          IF( SORD ) THEN
00178 *
00179 *           Real Symmetric Generalized Eigenvalue Problem:
00180 *
00181             WRITE( IOUNIT, FMT = 9992 )PATH
00182 *
00183 *           Matrix types
00184 *
00185             WRITE( IOUNIT, FMT = 9980 )
00186             WRITE( IOUNIT, FMT = 9979 )
00187             WRITE( IOUNIT, FMT = 9978 )'Symmetric'
00188 *
00189 *           Tests performed
00190 *
00191             WRITE( IOUNIT, FMT = 9977 )
00192             WRITE( IOUNIT, FMT = 9976 )
00193 *
00194          ELSE
00195 *
00196 *           Complex Hermitian Generalized Eigenvalue Problem:
00197 *
00198             WRITE( IOUNIT, FMT = 9991 )PATH
00199 *
00200 *           Matrix types
00201 *
00202             WRITE( IOUNIT, FMT = 9980 )
00203             WRITE( IOUNIT, FMT = 9979 )
00204             WRITE( IOUNIT, FMT = 9978 )'Hermitian'
00205 *
00206 *           Tests performed
00207 *
00208             WRITE( IOUNIT, FMT = 9975 )
00209             WRITE( IOUNIT, FMT = 9974 )
00210 *
00211          END IF
00212 *
00213       ELSE IF( LSAMEN( 2, C2, 'BD' ) ) THEN
00214 *
00215          IF( SORD ) THEN
00216 *
00217 *           Real Singular Value Decomposition:
00218 *
00219             WRITE( IOUNIT, FMT = 9994 )PATH
00220 *
00221 *           Matrix types
00222 *
00223             WRITE( IOUNIT, FMT = 9973 )
00224 *
00225 *           Tests performed
00226 *
00227             WRITE( IOUNIT, FMT = 9972 )'orthogonal'
00228             WRITE( IOUNIT, FMT = 9971 )
00229          ELSE
00230 *
00231 *           Complex Singular Value Decomposition:
00232 *
00233             WRITE( IOUNIT, FMT = 9993 )PATH
00234 *
00235 *           Matrix types
00236 *
00237             WRITE( IOUNIT, FMT = 9973 )
00238 *
00239 *           Tests performed
00240 *
00241             WRITE( IOUNIT, FMT = 9972 )'unitary   '
00242             WRITE( IOUNIT, FMT = 9971 )
00243          END IF
00244 *
00245       ELSE IF( LSAMEN( 2, C2, 'BB' ) ) THEN
00246 *
00247          IF( SORD ) THEN
00248 *
00249 *           Real General Band reduction to bidiagonal form:
00250 *
00251             WRITE( IOUNIT, FMT = 9990 )PATH
00252 *
00253 *           Matrix types
00254 *
00255             WRITE( IOUNIT, FMT = 9970 )
00256 *
00257 *           Tests performed
00258 *
00259             WRITE( IOUNIT, FMT = 9969 )'orthogonal'
00260          ELSE
00261 *
00262 *           Complex Band reduction to bidiagonal form:
00263 *
00264             WRITE( IOUNIT, FMT = 9989 )PATH
00265 *
00266 *           Matrix types
00267 *
00268             WRITE( IOUNIT, FMT = 9970 )
00269 *
00270 *           Tests performed
00271 *
00272             WRITE( IOUNIT, FMT = 9969 )'unitary   '
00273          END IF
00274 *
00275       ELSE
00276 *
00277          WRITE( IOUNIT, FMT = 9999 )PATH
00278          RETURN
00279       END IF
00280 *
00281       RETURN
00282 *
00283  9999 FORMAT( 1X, A3, ':  no header available' )
00284  9998 FORMAT( / 1X, A3, ' -- Real Non-symmetric eigenvalue problem' )
00285  9997 FORMAT( / 1X, A3, ' -- Complex Non-symmetric eigenvalue problem' )
00286  9996 FORMAT( / 1X, A3, ' -- Real Symmetric eigenvalue problem' )
00287  9995 FORMAT( / 1X, A3, ' -- Complex Hermitian eigenvalue problem' )
00288  9994 FORMAT( / 1X, A3, ' -- Real Singular Value Decomposition' )
00289  9993 FORMAT( / 1X, A3, ' -- Complex Singular Value Decomposition' )
00290  9992 FORMAT( / 1X, A3, ' -- Real Symmetric Generalized eigenvalue ',
00291      $      'problem' )
00292  9991 FORMAT( / 1X, A3, ' -- Complex Hermitian Generalized eigenvalue ',
00293      $      'problem' )
00294  9990 FORMAT( / 1X, A3, ' -- Real Band reduc. to bidiagonal form' )
00295  9989 FORMAT( / 1X, A3, ' -- Complex Band reduc. to bidiagonal form' )
00296 *
00297  9988 FORMAT( ' Matrix types (see xCHKHS for details): ' )
00298 *
00299  9987 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00300      $      '           ', '  5=Diagonal: geometr. spaced entries.',
00301      $      / '  2=Identity matrix.                    ', '  6=Diagona',
00302      $      'l: clustered entries.', / '  3=Transposed Jordan block.  ',
00303      $      '          ', '  7=Diagonal: large, evenly spaced.', / '  ',
00304      $      '4=Diagonal: evenly spaced entries.    ', '  8=Diagonal: s',
00305      $      'mall, evenly spaced.' )
00306  9986 FORMAT( ' Dense, Non-Symmetric Matrices:', / '  9=Well-cond., ev',
00307      $      'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
00308      $      'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
00309      $      ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
00310      $      'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
00311      $      'lex ', A6, / ' 12=Well-cond., random complex ', A6, '   ',
00312      $      ' 17=Ill-cond., large rand. complx ', A4, / ' 13=Ill-condi',
00313      $      'tioned, evenly spaced.     ', ' 18=Ill-cond., small rand.',
00314      $      ' complx ', A4 )
00315  9985 FORMAT( ' 19=Matrix with random O(1) entries.    ', ' 21=Matrix ',
00316      $      'with small random entries.', / ' 20=Matrix with large ran',
00317      $      'dom entries.   ' )
00318  9984 FORMAT( / ' Tests performed:   ', '(H is Hessenberg, T is Schur,',
00319      $      ' U and Z are ', A, ',', / 20X, A, ', W is a diagonal matr',
00320      $      'ix of eigenvalues,', / 20X, 'L and R are the left and rig',
00321      $      'ht eigenvector matrices)', / '  1 = | A - U H U', A1, ' |',
00322      $      ' / ( |A| n ulp )         ', '  2 = | I - U U', A1, ' | / ',
00323      $      '( n ulp )', / '  3 = | H - Z T Z', A1, ' | / ( |H| n ulp ',
00324      $      ')         ', '  4 = | I - Z Z', A1, ' | / ( n ulp )',
00325      $      / '  5 = | A - UZ T (UZ)', A1, ' | / ( |A| n ulp )     ',
00326      $      '  6 = | I - UZ (UZ)', A1, ' | / ( n ulp )', / '  7 = | T(',
00327      $      'e.vects.) - T(no e.vects.) | / ( |T| ulp )', / '  8 = | W',
00328      $      '(e.vects.) - W(no e.vects.) | / ( |W| ulp )', / '  9 = | ',
00329      $      'TR - RW | / ( |T| |R| ulp )     ', ' 10 = | LT - WL | / (',
00330      $      ' |T| |L| ulp )', / ' 11= |HX - XW| / (|H| |X| ulp)  (inv.',
00331      $      'it)', ' 12= |YH - WY| / (|H| |Y| ulp)  (inv.it)' )
00332 *
00333 *     Symmetric/Hermitian eigenproblem
00334 *
00335  9983 FORMAT( ' Matrix types (see xDRVST for details): ' )
00336 *
00337  9982 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00338      $      '           ', '  5=Diagonal: clustered entries.', / '  2=',
00339      $      'Identity matrix.                    ', '  6=Diagonal: lar',
00340      $      'ge, evenly spaced.', / '  3=Diagonal: evenly spaced entri',
00341      $      'es.    ', '  7=Diagonal: small, evenly spaced.', / '  4=D',
00342      $      'iagonal: geometr. spaced entries.' )
00343  9981 FORMAT( ' Dense ', A, ' Matrices:', / '  8=Evenly spaced eigen',
00344      $      'vals.            ', ' 12=Small, evenly spaced eigenvals.',
00345      $      / '  9=Geometrically spaced eigenvals.     ', ' 13=Matrix ',
00346      $      'with random O(1) entries.', / ' 10=Clustered eigenvalues.',
00347      $      '              ', ' 14=Matrix with large random entries.',
00348      $      / ' 11=Large, evenly spaced eigenvals.     ', ' 15=Matrix ',
00349      $      'with small random entries.' )
00350 *
00351 *     Symmetric/Hermitian Generalized eigenproblem
00352 *
00353  9980 FORMAT( ' Matrix types (see xDRVSG for details): ' )
00354 *
00355  9979 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00356      $      '           ', '  5=Diagonal: clustered entries.', / '  2=',
00357      $      'Identity matrix.                    ', '  6=Diagonal: lar',
00358      $      'ge, evenly spaced.', / '  3=Diagonal: evenly spaced entri',
00359      $      'es.    ', '  7=Diagonal: small, evenly spaced.', / '  4=D',
00360      $      'iagonal: geometr. spaced entries.' )
00361  9978 FORMAT( ' Dense or Banded ', A, ' Matrices: ',
00362      $      / '  8=Evenly spaced eigenvals.         ',
00363      $      ' 15=Matrix with small random entries.',
00364      $      / '  9=Geometrically spaced eigenvals.  ',
00365      $      ' 16=Evenly spaced eigenvals, KA=1, KB=1.',
00366      $      / ' 10=Clustered eigenvalues.           ',
00367      $      ' 17=Evenly spaced eigenvals, KA=2, KB=1.',
00368      $      / ' 11=Large, evenly spaced eigenvals.  ',
00369      $      ' 18=Evenly spaced eigenvals, KA=2, KB=2.',
00370      $      / ' 12=Small, evenly spaced eigenvals.  ',
00371      $      ' 19=Evenly spaced eigenvals, KA=3, KB=1.',
00372      $      / ' 13=Matrix with random O(1) entries. ',
00373      $      ' 20=Evenly spaced eigenvals, KA=3, KB=2.',
00374      $      / ' 14=Matrix with large random entries.',
00375      $      ' 21=Evenly spaced eigenvals, KA=3, KB=3.' )
00376  9977 FORMAT( / ' Tests performed:   ',
00377      $      / '( For each pair (A,B), where A is of the given type ',
00378      $      / ' and B is a random well-conditioned matrix. D is ',
00379      $      / ' diagonal, and Z is orthogonal. )',
00380      $      / ' 1 = DSYGV, with ITYPE=1 and UPLO=''U'':',
00381      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00382      $      / ' 2 = DSPGV, with ITYPE=1 and UPLO=''U'':',
00383      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00384      $      / ' 3 = DSBGV, with ITYPE=1 and UPLO=''U'':',
00385      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00386      $      / ' 4 = DSYGV, with ITYPE=1 and UPLO=''L'':',
00387      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00388      $      / ' 5 = DSPGV, with ITYPE=1 and UPLO=''L'':',
00389      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00390      $      / ' 6 = DSBGV, with ITYPE=1 and UPLO=''L'':',
00391      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ' )
00392  9976 FORMAT( ' 7 = DSYGV, with ITYPE=2 and UPLO=''U'':',
00393      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00394      $      / ' 8 = DSPGV, with ITYPE=2 and UPLO=''U'':',
00395      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00396      $      / ' 9 = DSPGV, with ITYPE=2 and UPLO=''L'':',
00397      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00398      $      / '10 = DSPGV, with ITYPE=2 and UPLO=''L'':',
00399      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00400      $      / '11 = DSYGV, with ITYPE=3 and UPLO=''U'':',
00401      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00402      $      / '12 = DSPGV, with ITYPE=3 and UPLO=''U'':',
00403      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00404      $      / '13 = DSYGV, with ITYPE=3 and UPLO=''L'':',
00405      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00406      $      / '14 = DSPGV, with ITYPE=3 and UPLO=''L'':',
00407      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ' )
00408  9975 FORMAT( / ' Tests performed:   ',
00409      $      / '( For each pair (A,B), where A is of the given type ',
00410      $      / ' and B is a random well-conditioned matrix. D is ',
00411      $      / ' diagonal, and Z is unitary. )',
00412      $      / ' 1 = ZHEGV, with ITYPE=1 and UPLO=''U'':',
00413      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00414      $      / ' 2 = ZHPGV, with ITYPE=1 and UPLO=''U'':',
00415      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00416      $      / ' 3 = ZHBGV, with ITYPE=1 and UPLO=''U'':',
00417      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00418      $      / ' 4 = ZHEGV, with ITYPE=1 and UPLO=''L'':',
00419      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00420      $      / ' 5 = ZHPGV, with ITYPE=1 and UPLO=''L'':',
00421      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00422      $      / ' 6 = ZHBGV, with ITYPE=1 and UPLO=''L'':',
00423      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ' )
00424  9974 FORMAT( ' 7 = ZHEGV, with ITYPE=2 and UPLO=''U'':',
00425      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00426      $      / ' 8 = ZHPGV, with ITYPE=2 and UPLO=''U'':',
00427      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00428      $      / ' 9 = ZHPGV, with ITYPE=2 and UPLO=''L'':',
00429      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00430      $      / '10 = ZHPGV, with ITYPE=2 and UPLO=''L'':',
00431      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00432      $      / '11 = ZHEGV, with ITYPE=3 and UPLO=''U'':',
00433      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00434      $      / '12 = ZHPGV, with ITYPE=3 and UPLO=''U'':',
00435      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00436      $      / '13 = ZHEGV, with ITYPE=3 and UPLO=''L'':',
00437      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00438      $      / '14 = ZHPGV, with ITYPE=3 and UPLO=''L'':',
00439      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ' )
00440 *
00441 *     Singular Value Decomposition
00442 *
00443  9973 FORMAT( ' Matrix types (see xCHKBD for details):',
00444      $      / ' Diagonal matrices:', / '   1: Zero', 28X,
00445      $      ' 5: Clustered entries', / '   2: Identity', 24X,
00446      $      ' 6: Large, evenly spaced entries',
00447      $      / '   3: Evenly spaced entries', 11X,
00448      $      ' 7: Small, evenly spaced entries',
00449      $      / '   4: Geometrically spaced entries',
00450      $      / ' General matrices:', / '   8: Evenly spaced sing. vals.',
00451      $      7X, '12: Small, evenly spaced sing vals',
00452      $      / '   9: Geometrically spaced sing vals  ',
00453      $      '13: Random, O(1) entries', / '  10: Clustered sing. vals.',
00454      $      11X, '14: Random, scaled near overflow',
00455      $      / '  11: Large, evenly spaced sing vals  ',
00456      $      '15: Random, scaled near underflow' )
00457 *
00458  9972 FORMAT( / ' Test ratios:  ',
00459      $      '(B: bidiagonal, S: diagonal, Q, P, U, and V: ', A10, / 16X,
00460      $      'X: m x nrhs, Y = Q'' X, and Z = U'' Y)',
00461      $      / '   1: norm( A - Q B P'' ) / ( norm(A) max(m,n) ulp )',
00462      $      / '   2: norm( I - Q'' Q )   / ( m ulp )',
00463      $      / '   3: norm( I - P'' P )   / ( n ulp )',
00464      $      / '   4: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )', /
00465      $      '   5: norm( Y - U Z )    / ( norm(Z) max(min(m,n),k) ulp )'
00466      $      , / '   6: norm( I - U'' U )   / ( min(m,n) ulp )',
00467      $      / '   7: norm( I - V'' V )   / ( min(m,n) ulp )' )
00468  9971 FORMAT( '   8: Test ordering of S  (0 if nondecreasing, 1/ulp ',
00469      $      ' otherwise)', /
00470      $      '   9: norm( S - S2 )     / ( norm(S) ulp ),',
00471      $      ' where S2 is computed', / 44X,
00472      $      'without computing U and V''',
00473      $      / '  10: Sturm sequence test ',
00474      $      '(0 if sing. vals of B within THRESH of S)',
00475      $      / '  11: norm( A - (QU) S (V'' P'') ) / ',
00476      $      '( norm(A) max(m,n) ulp )', /
00477      $      '  12: norm( X - (QU) Z )         / ( |X| max(M,k) ulp )',
00478      $      / '  13: norm( I - (QU)''(QU) )      / ( M ulp )',
00479      $      / '  14: norm( I - (V'' P'') (P V) )  / ( N ulp )' )
00480 *
00481 *     Band reduction to bidiagonal form
00482 *
00483  9970 FORMAT( ' Matrix types (see xCHKBB for details):',
00484      $      / ' Diagonal matrices:', / '   1: Zero', 28X,
00485      $      ' 5: Clustered entries', / '   2: Identity', 24X,
00486      $      ' 6: Large, evenly spaced entries',
00487      $      / '   3: Evenly spaced entries', 11X,
00488      $      ' 7: Small, evenly spaced entries',
00489      $      / '   4: Geometrically spaced entries',
00490      $      / ' General matrices:', / '   8: Evenly spaced sing. vals.',
00491      $      7X, '12: Small, evenly spaced sing vals',
00492      $      / '   9: Geometrically spaced sing vals  ',
00493      $      '13: Random, O(1) entries', / '  10: Clustered sing. vals.',
00494      $      11X, '14: Random, scaled near overflow',
00495      $      / '  11: Large, evenly spaced sing vals  ',
00496      $      '15: Random, scaled near underflow' )
00497 *
00498  9969 FORMAT( / ' Test ratios:  ', '(B: upper bidiagonal, Q and P: ',
00499      $      A10, / 16X, 'C: m x nrhs, PT = P'', Y = Q'' C)',
00500      $      / ' 1: norm( A - Q B PT ) / ( norm(A) max(m,n) ulp )',
00501      $      / ' 2: norm( I - Q'' Q )   / ( m ulp )',
00502      $      / ' 3: norm( I - PT PT'' )   / ( n ulp )',
00503      $      / ' 4: norm( Y - Q'' C )   / ( norm(Y) max(m,nrhs) ulp )' )
00504  9968 FORMAT( / ' Tests performed:  See sdrvst.f' )
00505  9967 FORMAT( / ' Tests performed:  See cdrvst.f' )
00506 *
00507 *     End of DLAHD2
00508 *
00509       END
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