LAPACK: TESTING/EIG/slahd2.f Source File

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00001       SUBROUTINE SLAHD2( IOUNIT, PATH )
00002 *
00003 *  -- LAPACK auxiliary test routine (version 2.0) --
00004 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00005 *     November 2006
00006 *
00007 *     .. Scalar Arguments ..
00008       CHARACTER*3        PATH
00009       INTEGER            IOUNIT
00010 *     ..
00011 *
00012 *  Purpose
00013 *  =======
00014 *
00015 *  SLAHD2 prints header information for the different test paths.
00016 *
00017 *  Arguments
00018 *  =========
00019 *
00020 *  IOUNIT  (input) INTEGER.
00021 *          On entry, IOUNIT specifies the unit number to which the
00022 *          header information should be printed.
00023 *
00024 *  PATH    (input) CHARACTER*3.
00025 *          On entry, PATH contains the name of the path for which the
00026 *          header information is to be printed.  Current paths are
00027 *
00028 *             SHS, CHS:  Non-symmetric eigenproblem.
00029 *             SST, CST:  Symmetric eigenproblem.
00030 *             SSG, CSG:  Symmetric Generalized eigenproblem.
00031 *             SBD, CBD:  Singular Value Decomposition (SVD)
00032 *             SBB, CBB:  General Banded reduction to bidiagonal form
00033 *
00034 *          These paths also are supplied in double precision (replace
00035 *          leading S by D and leading C by Z in path names).
00036 *
00037 *  =====================================================================
00038 *
00039 *     .. Local Scalars ..
00040       LOGICAL            CORZ, SORD
00041       CHARACTER*2        C2
00042       INTEGER            J
00043 *     ..
00044 *     .. External Functions ..
00045       LOGICAL            LSAME, LSAMEN
00046       EXTERNAL           LSAME, LSAMEN
00047 *     ..
00048 *     .. Executable Statements ..
00049 *
00050       IF( IOUNIT.LE.0 )
00051      $   RETURN
00052       SORD = LSAME( PATH, 'S' ) .OR. LSAME( PATH, 'D' )
00053       CORZ = LSAME( PATH, 'C' ) .OR. LSAME( PATH, 'Z' )
00054       IF( .NOT.SORD .AND. .NOT.CORZ ) THEN
00055          WRITE( IOUNIT, FMT = 9999 )PATH
00056       END IF
00057       C2 = PATH( 2: 3 )
00058 *
00059       IF( LSAMEN( 2, C2, 'HS' ) ) THEN
00060          IF( SORD ) THEN
00061 *
00062 *           Real Non-symmetric Eigenvalue Problem:
00063 *
00064             WRITE( IOUNIT, FMT = 9998 )PATH
00065 *
00066 *           Matrix types
00067 *
00068             WRITE( IOUNIT, FMT = 9988 )
00069             WRITE( IOUNIT, FMT = 9987 )
00070             WRITE( IOUNIT, FMT = 9986 )'pairs ', 'pairs ', 'prs.',
00071      $         'prs.'
00072             WRITE( IOUNIT, FMT = 9985 )
00073 *
00074 *           Tests performed
00075 *
00076             WRITE( IOUNIT, FMT = 9984 )'orthogonal', '''=transpose',
00077      $         ( '''', J = 1, 6 )
00078 *
00079          ELSE
00080 *
00081 *           Complex Non-symmetric Eigenvalue Problem:
00082 *
00083             WRITE( IOUNIT, FMT = 9997 )PATH
00084 *
00085 *           Matrix types
00086 *
00087             WRITE( IOUNIT, FMT = 9988 )
00088             WRITE( IOUNIT, FMT = 9987 )
00089             WRITE( IOUNIT, FMT = 9986 )'e.vals', 'e.vals', 'e.vs',
00090      $         'e.vs'
00091             WRITE( IOUNIT, FMT = 9985 )
00092 *
00093 *           Tests performed
00094 *
00095             WRITE( IOUNIT, FMT = 9984 )'unitary', '*=conj.transp.',
00096      $         ( '*', J = 1, 6 )
00097          END IF
00098 *
00099       ELSE IF( LSAMEN( 2, C2, 'ST' ) ) THEN
00100 *
00101          IF( SORD ) THEN
00102 *
00103 *           Real Symmetric Eigenvalue Problem:
00104 *
00105             WRITE( IOUNIT, FMT = 9996 )PATH
00106 *
00107 *           Matrix types
00108 *
00109             WRITE( IOUNIT, FMT = 9983 )
00110             WRITE( IOUNIT, FMT = 9982 )
00111             WRITE( IOUNIT, FMT = 9981 )'Symmetric'
00112 *
00113 *           Tests performed
00114 *
00115             WRITE( IOUNIT, FMT = 9968 )
00116 *
00117          ELSE
00118 *
00119 *           Complex Hermitian Eigenvalue Problem:
00120 *
00121             WRITE( IOUNIT, FMT = 9995 )PATH
00122 *
00123 *           Matrix types
00124 *
00125             WRITE( IOUNIT, FMT = 9983 )
00126             WRITE( IOUNIT, FMT = 9982 )
00127             WRITE( IOUNIT, FMT = 9981 )'Hermitian'
00128 *
00129 *           Tests performed
00130 *
00131             WRITE( IOUNIT, FMT = 9967 )
00132          END IF
00133 *
00134       ELSE IF( LSAMEN( 2, C2, 'SG' ) ) THEN
00135 *
00136          IF( SORD ) THEN
00137 *
00138 *           Real Symmetric Generalized Eigenvalue Problem:
00139 *
00140             WRITE( IOUNIT, FMT = 9992 )PATH
00141 *
00142 *           Matrix types
00143 *
00144             WRITE( IOUNIT, FMT = 9980 )
00145             WRITE( IOUNIT, FMT = 9979 )
00146             WRITE( IOUNIT, FMT = 9978 )'Symmetric'
00147 *
00148 *           Tests performed
00149 *
00150             WRITE( IOUNIT, FMT = 9977 )
00151             WRITE( IOUNIT, FMT = 9976 )
00152 *
00153          ELSE
00154 *
00155 *           Complex Hermitian Generalized Eigenvalue Problem:
00156 *
00157             WRITE( IOUNIT, FMT = 9991 )PATH
00158 *
00159 *           Matrix types
00160 *
00161             WRITE( IOUNIT, FMT = 9980 )
00162             WRITE( IOUNIT, FMT = 9979 )
00163             WRITE( IOUNIT, FMT = 9978 )'Hermitian'
00164 *
00165 *           Tests performed
00166 *
00167             WRITE( IOUNIT, FMT = 9975 )
00168             WRITE( IOUNIT, FMT = 9974 )
00169 *
00170          END IF
00171 *
00172       ELSE IF( LSAMEN( 2, C2, 'BD' ) ) THEN
00173 *
00174          IF( SORD ) THEN
00175 *
00176 *           Real Singular Value Decomposition:
00177 *
00178             WRITE( IOUNIT, FMT = 9994 )PATH
00179 *
00180 *           Matrix types
00181 *
00182             WRITE( IOUNIT, FMT = 9973 )
00183 *
00184 *           Tests performed
00185 *
00186             WRITE( IOUNIT, FMT = 9972 )'orthogonal'
00187             WRITE( IOUNIT, FMT = 9971 )
00188          ELSE
00189 *
00190 *           Complex Singular Value Decomposition:
00191 *
00192             WRITE( IOUNIT, FMT = 9993 )PATH
00193 *
00194 *           Matrix types
00195 *
00196             WRITE( IOUNIT, FMT = 9973 )
00197 *
00198 *           Tests performed
00199 *
00200             WRITE( IOUNIT, FMT = 9972 )'unitary   '
00201             WRITE( IOUNIT, FMT = 9971 )
00202          END IF
00203 *
00204       ELSE IF( LSAMEN( 2, C2, 'BB' ) ) THEN
00205 *
00206          IF( SORD ) THEN
00207 *
00208 *           Real General Band reduction to bidiagonal form:
00209 *
00210             WRITE( IOUNIT, FMT = 9990 )PATH
00211 *
00212 *           Matrix types
00213 *
00214             WRITE( IOUNIT, FMT = 9970 )
00215 *
00216 *           Tests performed
00217 *
00218             WRITE( IOUNIT, FMT = 9969 )'orthogonal'
00219          ELSE
00220 *
00221 *           Complex Band reduction to bidiagonal form:
00222 *
00223             WRITE( IOUNIT, FMT = 9989 )PATH
00224 *
00225 *           Matrix types
00226 *
00227             WRITE( IOUNIT, FMT = 9970 )
00228 *
00229 *           Tests performed
00230 *
00231             WRITE( IOUNIT, FMT = 9969 )'unitary   '
00232          END IF
00233 *
00234       ELSE
00235 *
00236          WRITE( IOUNIT, FMT = 9999 )PATH
00237          RETURN
00238       END IF
00239 *
00240       RETURN
00241 *
00242  9999 FORMAT( 1X, A3, ':  no header available' )
00243  9998 FORMAT( / 1X, A3, ' -- Real Non-symmetric eigenvalue problem' )
00244  9997 FORMAT( / 1X, A3, ' -- Complex Non-symmetric eigenvalue problem' )
00245  9996 FORMAT( / 1X, A3, ' -- Real Symmetric eigenvalue problem' )
00246  9995 FORMAT( / 1X, A3, ' -- Complex Hermitian eigenvalue problem' )
00247  9994 FORMAT( / 1X, A3, ' -- Real Singular Value Decomposition' )
00248  9993 FORMAT( / 1X, A3, ' -- Complex Singular Value Decomposition' )
00249  9992 FORMAT( / 1X, A3, ' -- Real Symmetric Generalized eigenvalue ',
00250      $      'problem' )
00251  9991 FORMAT( / 1X, A3, ' -- Complex Hermitian Generalized eigenvalue ',
00252      $      'problem' )
00253  9990 FORMAT( / 1X, A3, ' -- Real Band reduc. to bidiagonal form' )
00254  9989 FORMAT( / 1X, A3, ' -- Complex Band reduc. to bidiagonal form' )
00255 *
00256  9988 FORMAT( ' Matrix types (see xCHKHS for details): ' )
00257 *
00258  9987 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00259      $      '           ', '  5=Diagonal: geometr. spaced entries.',
00260      $      / '  2=Identity matrix.                    ', '  6=Diagona',
00261      $      'l: clustered entries.', / '  3=Transposed Jordan block.  ',
00262      $      '          ', '  7=Diagonal: large, evenly spaced.', / '  ',
00263      $      '4=Diagonal: evenly spaced entries.    ', '  8=Diagonal: s',
00264      $      'mall, evenly spaced.' )
00265  9986 FORMAT( ' Dense, Non-Symmetric Matrices:', / '  9=Well-cond., ev',
00266      $      'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
00267      $      'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
00268      $      ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
00269      $      'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
00270      $      'lex ', A6, / ' 12=Well-cond., random complex ', A6, '   ',
00271      $      ' 17=Ill-cond., large rand. complx ', A4, / ' 13=Ill-condi',
00272      $      'tioned, evenly spaced.     ', ' 18=Ill-cond., small rand.',
00273      $      ' complx ', A4 )
00274  9985 FORMAT( ' 19=Matrix with random O(1) entries.    ', ' 21=Matrix ',
00275      $      'with small random entries.', / ' 20=Matrix with large ran',
00276      $      'dom entries.   ' )
00277  9984 FORMAT( / ' Tests performed:   ', '(H is Hessenberg, T is Schur,',
00278      $      ' U and Z are ', A, ',', / 20X, A, ', W is a diagonal matr',
00279      $      'ix of eigenvalues,', / 20X, 'L and R are the left and rig',
00280      $      'ht eigenvector matrices)', / '  1 = | A - U H U', A1, ' |',
00281      $      ' / ( |A| n ulp )         ', '  2 = | I - U U', A1, ' | / ',
00282      $      '( n ulp )', / '  3 = | H - Z T Z', A1, ' | / ( |H| n ulp ',
00283      $      ')         ', '  4 = | I - Z Z', A1, ' | / ( n ulp )',
00284      $      / '  5 = | A - UZ T (UZ)', A1, ' | / ( |A| n ulp )     ',
00285      $      '  6 = | I - UZ (UZ)', A1, ' | / ( n ulp )', / '  7 = | T(',
00286      $      'e.vects.) - T(no e.vects.) | / ( |T| ulp )', / '  8 = | W',
00287      $      '(e.vects.) - W(no e.vects.) | / ( |W| ulp )', / '  9 = | ',
00288      $      'TR - RW | / ( |T| |R| ulp )     ', ' 10 = | LT - WL | / (',
00289      $      ' |T| |L| ulp )', / ' 11= |HX - XW| / (|H| |X| ulp)  (inv.',
00290      $      'it)', ' 12= |YH - WY| / (|H| |Y| ulp)  (inv.it)' )
00291 *
00292 *     Symmetric/Hermitian eigenproblem
00293 *
00294  9983 FORMAT( ' Matrix types (see xDRVST for details): ' )
00295 *
00296  9982 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00297      $      '           ', '  5=Diagonal: clustered entries.', / '  2=',
00298      $      'Identity matrix.                    ', '  6=Diagonal: lar',
00299      $      'ge, evenly spaced.', / '  3=Diagonal: evenly spaced entri',
00300      $      'es.    ', '  7=Diagonal: small, evenly spaced.', / '  4=D',
00301      $      'iagonal: geometr. spaced entries.' )
00302  9981 FORMAT( ' Dense ', A, ' Matrices:', / '  8=Evenly spaced eigen',
00303      $      'vals.            ', ' 12=Small, evenly spaced eigenvals.',
00304      $      / '  9=Geometrically spaced eigenvals.     ', ' 13=Matrix ',
00305      $      'with random O(1) entries.', / ' 10=Clustered eigenvalues.',
00306      $      '              ', ' 14=Matrix with large random entries.',
00307      $      / ' 11=Large, evenly spaced eigenvals.     ', ' 15=Matrix ',
00308      $      'with small random entries.' )
00309 *
00310 *     Symmetric/Hermitian Generalized eigenproblem
00311 *
00312  9980 FORMAT( ' Matrix types (see xDRVSG for details): ' )
00313 *
00314  9979 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00315      $      '           ', '  5=Diagonal: clustered entries.', / '  2=',
00316      $      'Identity matrix.                    ', '  6=Diagonal: lar',
00317      $      'ge, evenly spaced.', / '  3=Diagonal: evenly spaced entri',
00318      $      'es.    ', '  7=Diagonal: small, evenly spaced.', / '  4=D',
00319      $      'iagonal: geometr. spaced entries.' )
00320  9978 FORMAT( ' Dense or Banded ', A, ' Matrices: ',
00321      $      / '  8=Evenly spaced eigenvals.         ',
00322      $      ' 15=Matrix with small random entries.',
00323      $      / '  9=Geometrically spaced eigenvals.  ',
00324      $      ' 16=Evenly spaced eigenvals, KA=1, KB=1.',
00325      $      / ' 10=Clustered eigenvalues.           ',
00326      $      ' 17=Evenly spaced eigenvals, KA=2, KB=1.',
00327      $      / ' 11=Large, evenly spaced eigenvals.  ',
00328      $      ' 18=Evenly spaced eigenvals, KA=2, KB=2.',
00329      $      / ' 12=Small, evenly spaced eigenvals.  ',
00330      $      ' 19=Evenly spaced eigenvals, KA=3, KB=1.',
00331      $      / ' 13=Matrix with random O(1) entries. ',
00332      $      ' 20=Evenly spaced eigenvals, KA=3, KB=2.',
00333      $      / ' 14=Matrix with large random entries.',
00334      $      ' 21=Evenly spaced eigenvals, KA=3, KB=3.' )
00335  9977 FORMAT( / ' Tests performed:   ',
00336      $      / '( For each pair (A,B), where A is of the given type ',
00337      $      / ' and B is a random well-conditioned matrix. D is ',
00338      $      / ' diagonal, and Z is orthogonal. )',
00339      $      / ' 1 = SSYGV, with ITYPE=1 and UPLO=''U'':',
00340      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00341      $      / ' 2 = SSPGV, with ITYPE=1 and UPLO=''U'':',
00342      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00343      $      / ' 3 = SSBGV, with ITYPE=1 and UPLO=''U'':',
00344      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00345      $      / ' 4 = SSYGV, with ITYPE=1 and UPLO=''L'':',
00346      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00347      $      / ' 5 = SSPGV, with ITYPE=1 and UPLO=''L'':',
00348      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00349      $      / ' 6 = SSBGV, with ITYPE=1 and UPLO=''L'':',
00350      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ' )
00351  9976 FORMAT( ' 7 = SSYGV, with ITYPE=2 and UPLO=''U'':',
00352      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00353      $      / ' 8 = SSPGV, with ITYPE=2 and UPLO=''U'':',
00354      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00355      $      / ' 9 = SSPGV, with ITYPE=2 and UPLO=''L'':',
00356      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00357      $      / '10 = SSPGV, with ITYPE=2 and UPLO=''L'':',
00358      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00359      $      / '11 = SSYGV, with ITYPE=3 and UPLO=''U'':',
00360      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00361      $      / '12 = SSPGV, with ITYPE=3 and UPLO=''U'':',
00362      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00363      $      / '13 = SSYGV, with ITYPE=3 and UPLO=''L'':',
00364      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00365      $      / '14 = SSPGV, with ITYPE=3 and UPLO=''L'':',
00366      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ' )
00367  9975 FORMAT( / ' Tests performed:   ',
00368      $      / '( For each pair (A,B), where A is of the given type ',
00369      $      / ' and B is a random well-conditioned matrix. D is ',
00370      $      / ' diagonal, and Z is unitary. )',
00371      $      / ' 1 = CHEGV, with ITYPE=1 and UPLO=''U'':',
00372      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00373      $      / ' 2 = CHPGV, with ITYPE=1 and UPLO=''U'':',
00374      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00375      $      / ' 3 = CHBGV, with ITYPE=1 and UPLO=''U'':',
00376      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00377      $      / ' 4 = CHEGV, with ITYPE=1 and UPLO=''L'':',
00378      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00379      $      / ' 5 = CHPGV, with ITYPE=1 and UPLO=''L'':',
00380      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ',
00381      $      / ' 6 = CHBGV, with ITYPE=1 and UPLO=''L'':',
00382      $      '  | A Z - B Z D | / ( |A| |Z| n ulp )     ' )
00383  9974 FORMAT( ' 7 = CHEGV, with ITYPE=2 and UPLO=''U'':',
00384      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00385      $      / ' 8 = CHPGV, with ITYPE=2 and UPLO=''U'':',
00386      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00387      $      / ' 9 = CHPGV, with ITYPE=2 and UPLO=''L'':',
00388      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00389      $      / '10 = CHPGV, with ITYPE=2 and UPLO=''L'':',
00390      $      '  | A B Z - Z D | / ( |A| |Z| n ulp )     ',
00391      $      / '11 = CHEGV, with ITYPE=3 and UPLO=''U'':',
00392      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00393      $      / '12 = CHPGV, with ITYPE=3 and UPLO=''U'':',
00394      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00395      $      / '13 = CHEGV, with ITYPE=3 and UPLO=''L'':',
00396      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ',
00397      $      / '14 = CHPGV, with ITYPE=3 and UPLO=''L'':',
00398      $      '  | B A Z - Z D | / ( |A| |Z| n ulp )     ' )
00399 *
00400 *     Singular Value Decomposition
00401 *
00402  9973 FORMAT( ' Matrix types (see xCHKBD for details):',
00403      $      / ' Diagonal matrices:', / '   1: Zero', 28X,
00404      $      ' 5: Clustered entries', / '   2: Identity', 24X,
00405      $      ' 6: Large, evenly spaced entries',
00406      $      / '   3: Evenly spaced entries', 11X,
00407      $      ' 7: Small, evenly spaced entries',
00408      $      / '   4: Geometrically spaced entries',
00409      $      / ' General matrices:', / '   8: Evenly spaced sing. vals.',
00410      $      7X, '12: Small, evenly spaced sing vals',
00411      $      / '   9: Geometrically spaced sing vals  ',
00412      $      '13: Random, O(1) entries', / '  10: Clustered sing. vals.',
00413      $      11X, '14: Random, scaled near overflow',
00414      $      / '  11: Large, evenly spaced sing vals  ',
00415      $      '15: Random, scaled near underflow' )
00416 *
00417  9972 FORMAT( / ' Test ratios:  ',
00418      $      '(B: bidiagonal, S: diagonal, Q, P, U, and V: ', A10, / 16X,
00419      $      'X: m x nrhs, Y = Q'' X, and Z = U'' Y)',
00420      $      / '   1: norm( A - Q B P'' ) / ( norm(A) max(m,n) ulp )',
00421      $      / '   2: norm( I - Q'' Q )   / ( m ulp )',
00422      $      / '   3: norm( I - P'' P )   / ( n ulp )',
00423      $      / '   4: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )', /
00424      $      '   5: norm( Y - U Z )    / ( norm(Z) max(min(m,n),k) ulp )'
00425      $      , / '   6: norm( I - U'' U )   / ( min(m,n) ulp )',
00426      $      / '   7: norm( I - V'' V )   / ( min(m,n) ulp )' )
00427  9971 FORMAT( '   8: Test ordering of S  (0 if nondecreasing, 1/ulp ',
00428      $      ' otherwise)', /
00429      $      '   9: norm( S - S2 )     / ( norm(S) ulp ),',
00430      $      ' where S2 is computed', / 44X,
00431      $      'without computing U and V''',
00432      $      / '  10: Sturm sequence test ',
00433      $      '(0 if sing. vals of B within THRESH of S)',
00434      $      / '  11: norm( A - (QU) S (V'' P'') ) / ',
00435      $      '( norm(A) max(m,n) ulp )', /
00436      $      '  12: norm( X - (QU) Z )         / ( |X| max(M,k) ulp )',
00437      $      / '  13: norm( I - (QU)''(QU) )      / ( M ulp )',
00438      $      / '  14: norm( I - (V'' P'') (P V) )  / ( N ulp )' )
00439 *
00440 *     Band reduction to bidiagonal form
00441 *
00442  9970 FORMAT( ' Matrix types (see xCHKBB for details):',
00443      $      / ' Diagonal matrices:', / '   1: Zero', 28X,
00444      $      ' 5: Clustered entries', / '   2: Identity', 24X,
00445      $      ' 6: Large, evenly spaced entries',
00446      $      / '   3: Evenly spaced entries', 11X,
00447      $      ' 7: Small, evenly spaced entries',
00448      $      / '   4: Geometrically spaced entries',
00449      $      / ' General matrices:', / '   8: Evenly spaced sing. vals.',
00450      $      7X, '12: Small, evenly spaced sing vals',
00451      $      / '   9: Geometrically spaced sing vals  ',
00452      $      '13: Random, O(1) entries', / '  10: Clustered sing. vals.',
00453      $      11X, '14: Random, scaled near overflow',
00454      $      / '  11: Large, evenly spaced sing vals  ',
00455      $      '15: Random, scaled near underflow' )
00456 *
00457  9969 FORMAT( / ' Test ratios:  ', '(B: upper bidiagonal, Q and P: ',
00458      $      A10, / 16X, 'C: m x nrhs, PT = P'', Y = Q'' C)',
00459      $      / ' 1: norm( A - Q B PT ) / ( norm(A) max(m,n) ulp )',
00460      $      / ' 2: norm( I - Q'' Q )   / ( m ulp )',
00461      $      / ' 3: norm( I - PT PT'' )   / ( n ulp )',
00462      $      / ' 4: norm( Y - Q'' C )   / ( norm(Y) max(m,nrhs) ulp )' )
00463  9968 FORMAT( / ' Tests performed:  See sdrvst.f' )
00464  9967 FORMAT( / ' Tests performed:  See cdrvst.f' )
00465 *
00466 *     End of SLAHD2
00467 *
00468       END