SDRVST2STG  checks the symmetric eigenvalue problem drivers.


              SSTEV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric tridiagonal matrix.


              SSTEVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric tridiagonal matrix.


              SSTEVR computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric tridiagonal matrix


              using the Relatively Robust Representation where it can.


              SSYEV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix.


              SSYEVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix.


              SSYEVR computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix


              using the Relatively Robust Representation where it can.


              SSPEV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix in packed


              storage.


              SSPEVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix in packed


              storage.


              SSBEV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric band matrix.


              SSBEVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric band matrix.


              SSYEVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix using


              a divide and conquer algorithm.


              SSPEVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric matrix in packed


              storage, using a divide and conquer algorithm.


              SSBEVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric band matrix,


              using a divide and conquer algorithm.


      When SDRVST2STG is called, a number of matrix 'sizes' ('n's') and a


      number of matrix 'types' are specified.  For each size ('n')


      and each type of matrix, one matrix will be generated and used


      to test the appropriate drivers.  For each matrix and each


      driver routine called, the following tests will be performed:


      (1)     | A - Z D Z' | / ( |A| n ulp )


      (2)     | I - Z Z' | / ( n ulp )


      (3)     | D1 - D2 | / ( |D1| ulp )


      where Z is the matrix of eigenvectors returned when the


      eigenvector option is given and D1 and D2 are the eigenvalues


      returned with and without the eigenvector option.


      The 'sizes' are specified by an array NN(1:NSIZES); the value of


      each element NN(j) specifies one size.


      The 'types' are specified by a logical array DOTYPE( 1:NTYPES );


      if DOTYPE(j) is .TRUE., then matrix type 'j' will be generated.


      Currently, the list of possible types is:


      (1)  The zero matrix.


      (2)  The identity matrix.


      (3)  A diagonal matrix with evenly spaced eigenvalues


           1, ..., ULP  and random signs.


           (ULP = (first number larger than 1) - 1 )


      (4)  A diagonal matrix with geometrically spaced eigenvalues


           1, ..., ULP  and random signs.


      (5)  A diagonal matrix with 'clustered' eigenvalues


           1, ULP, ..., ULP and random signs.


      (6)  Same as (4), but multiplied by SQRT( overflow threshold )


      (7)  Same as (4), but multiplied by SQRT( underflow threshold )


      (8)  A matrix of the form  U' D U, where U is orthogonal and


           D has evenly spaced entries 1, ..., ULP with random signs


           on the diagonal.


      (9)  A matrix of the form  U' D U, where U is orthogonal and


           D has geometrically spaced entries 1, ..., ULP with random


           signs on the diagonal.


      (10) A matrix of the form  U' D U, where U is orthogonal and


           D has 'clustered' entries 1, ULP,..., ULP with random


           signs on the diagonal.


      (11) Same as (8), but multiplied by SQRT( overflow threshold )


      (12) Same as (8), but multiplied by SQRT( underflow threshold )


      (13) Symmetric matrix with random entries chosen from (-1,1).


      (14) Same as (13), but multiplied by SQRT( overflow threshold )


      (15) Same as (13), but multiplied by SQRT( underflow threshold )


      (16) A band matrix with half bandwidth randomly chosen between


           0 and N-1, with evenly spaced eigenvalues 1, ..., ULP


           with random signs.


      (17) Same as (16), but multiplied by SQRT( overflow threshold )


      (18) Same as (16), but multiplied by SQRT( underflow threshold )

  NSIZES  INTEGER


          The number of sizes of matrices to use.  If it is zero,


          SDRVST2STG does nothing.  It must be at least zero.


          Not modified.


  NN      INTEGER array, dimension (NSIZES)


          An array containing the sizes to be used for the matrices.


          Zero values will be skipped.  The values must be at least


          zero.


          Not modified.


  NTYPES  INTEGER


          The number of elements in DOTYPE.   If it is zero, SDRVST2STG


          does nothing.  It must be at least zero.  If it is MAXTYP+1


          and NSIZES is 1, then an additional type, MAXTYP+1 is


          defined, which is to use whatever matrix is in A.  This


          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and


          DOTYPE(MAXTYP+1) is .TRUE. .


          Not modified.


  DOTYPE  LOGICAL array, dimension (NTYPES)


          If DOTYPE(j) is .TRUE., then for each size in NN a


          matrix of that size and of type j will be generated.


          If NTYPES is smaller than the maximum number of types


          defined (PARAMETER MAXTYP), then types NTYPES+1 through


          MAXTYP will not be generated.  If NTYPES is larger


          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)


          will be ignored.


          Not modified.


  ISEED   INTEGER array, dimension (4)


          On entry ISEED specifies the seed of the random number


          generator. The array elements should be between 0 and 4095;


          if not they will be reduced mod 4096.  Also, ISEED(4) must


          be odd.  The random number generator uses a linear


          congruential sequence limited to small integers, and so


          should produce machine independent random numbers. The


          values of ISEED are changed on exit, and can be used in the


          next call to SDRVST2STG to continue the same random number


          sequence.


          Modified.


  THRESH  REAL


          A test will count as 'failed' if the 'error', computed as


          described above, exceeds THRESH.  Note that the error


          is scaled to be O(1), so THRESH should be a reasonably


          small multiple of 1, e.g., 10 or 100.  In particular,


          it should not depend on the precision (single vs. double)


          or the size of the matrix.  It must be at least zero.


          Not modified.


  NOUNIT  INTEGER


          The FORTRAN unit number for printing out error messages


          (e.g., if a routine returns IINFO not equal to 0.)


          Not modified.


  A       REAL             array, dimension (LDA , max(NN))


          Used to hold the matrix whose eigenvalues are to be


          computed.  On exit, A contains the last matrix actually


          used.


          Modified.


  LDA     INTEGER


          The leading dimension of A.  It must be at


          least 1 and at least max( NN ).


          Not modified.


  D1      REAL             array, dimension (max(NN))


          The eigenvalues of A, as computed by SSTEQR simultaneously


          with Z.  On exit, the eigenvalues in D1 correspond with the


          matrix in A.


          Modified.


  D2      REAL             array, dimension (max(NN))


          The eigenvalues of A, as computed by SSTEQR if Z is not


          computed.  On exit, the eigenvalues in D2 correspond with


          the matrix in A.


          Modified.


  D3      REAL             array, dimension (max(NN))


          The eigenvalues of A, as computed by SSTERF.  On exit, the


          eigenvalues in D3 correspond with the matrix in A.


          Modified.


  D4      REAL             array, dimension


  EVEIGS  REAL array, dimension (max(NN))


          The eigenvalues as computed by SSTEV('N', ... )


          (I reserve the right to change this to the output of


          whichever algorithm computes the most accurate eigenvalues).


  WA1     REAL array, dimension


  WA2     REAL array, dimension


  WA3     REAL array, dimension


  U       REAL             array, dimension (LDU, max(NN))


          The orthogonal matrix computed by SSYTRD + SORGTR.


          Modified.


  LDU     INTEGER


          The leading dimension of U, Z, and V.  It must be at


          least 1 and at least max( NN ).


          Not modified.


  V       REAL             array, dimension (LDU, max(NN))


          The Housholder vectors computed by SSYTRD in reducing A to


          tridiagonal form.


          Modified.


  TAU     REAL array, dimension (max(NN))


          The Householder factors computed by SSYTRD in reducing A


          to tridiagonal form.


          Modified.


  Z       REAL             array, dimension (LDU, max(NN))


          The orthogonal matrix of eigenvectors computed by SSTEQR,


          SPTEQR, and SSTEIN.


          Modified.


  WORK    REAL array, dimension (LWORK)


          Workspace.


          Modified.


  LWORK   INTEGER


          The number of entries in WORK.  This must be at least


          1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2


          where Nmax = max( NN(j), 2 ) and lg = log base 2.


          Not modified.


  IWORK   INTEGER array,


             dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax )


          where Nmax = max( NN(j), 2 ) and lg = log base 2.


          Workspace.


          Modified.


  RESULT  REAL array, dimension (105)


          The values computed by the tests described above.


          The values are currently limited to 1/ulp, to avoid


          overflow.


          Modified.


  INFO    INTEGER


          If 0, then everything ran OK.


           -1: NSIZES < 0


           -2: Some NN(j) < 0


           -3: NTYPES < 0


           -5: THRESH < 0


           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).


          -16: LDU < 1 or LDU < NMAX.


          -21: LWORK too small.


          If  SLATMR, SLATMS, SSYTRD, SORGTR, SSTEQR, SSTERF,


              or SORMTR returns an error code, the


              absolute value of it is returned.


          Modified.
-----------------------------------------------------------------------


       Some Local Variables and Parameters:


       ---- ----- --------- --- ----------


       ZERO, ONE       Real 0 and 1.


       MAXTYP          The number of types defined.


       NTEST           The number of tests performed, or which can


                       be performed so far, for the current matrix.


       NTESTT          The total number of tests performed so far.


       NMAX            Largest value in NN.


       NMATS           The number of matrices generated so far.


       NERRS           The number of tests which have exceeded THRESH


                       so far (computed by SLAFTS).


       COND, IMODE     Values to be passed to the matrix generators.


       ANORM           Norm of A; passed to matrix generators.


       OVFL, UNFL      Overflow and underflow thresholds.


       ULP, ULPINV     Finest relative precision and its inverse.


       RTOVFL, RTUNFL  Square roots of the previous 2 values.


               The following four arrays decode JTYPE:


       KTYPE(j)        The general type (1-10) for type 'j'.


       KMODE(j)        The MODE value to be passed to the matrix


                       generator for type 'j'.


       KMAGN(j)        The order of magnitude ( O(1),


                       O(overflow^(1/2) ), O(underflow^(1/2) )


     The tests performed are:                 Routine tested


    1= | A - U S U' | / ( |A| n ulp )         SSTEV('V', ... )


    2= | I - U U' | / ( n ulp )               SSTEV('V', ... )


    3= |D(with Z) - D(w/o Z)| / (|D| ulp)     SSTEV('N', ... )


    4= | A - U S U' | / ( |A| n ulp )         SSTEVX('V','A', ... )


    5= | I - U U' | / ( n ulp )               SSTEVX('V','A', ... )


    6= |D(with Z) - EVEIGS| / (|D| ulp)       SSTEVX('N','A', ... )


    7= | A - U S U' | / ( |A| n ulp )         SSTEVR('V','A', ... )


    8= | I - U U' | / ( n ulp )               SSTEVR('V','A', ... )


    9= |D(with Z) - EVEIGS| / (|D| ulp)       SSTEVR('N','A', ... )


    10= | A - U S U' | / ( |A| n ulp )        SSTEVX('V','I', ... )


    11= | I - U U' | / ( n ulp )              SSTEVX('V','I', ... )


    12= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSTEVX('N','I', ... )


    13= | A - U S U' | / ( |A| n ulp )        SSTEVX('V','V', ... )


    14= | I - U U' | / ( n ulp )              SSTEVX('V','V', ... )


    15= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSTEVX('N','V', ... )


    16= | A - U S U' | / ( |A| n ulp )        SSTEVD('V', ... )


    17= | I - U U' | / ( n ulp )              SSTEVD('V', ... )


    18= |D(with Z) - EVEIGS| / (|D| ulp)      SSTEVD('N', ... )


    19= | A - U S U' | / ( |A| n ulp )        SSTEVR('V','I', ... )


    20= | I - U U' | / ( n ulp )              SSTEVR('V','I', ... )


    21= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSTEVR('N','I', ... )


    22= | A - U S U' | / ( |A| n ulp )        SSTEVR('V','V', ... )


    23= | I - U U' | / ( n ulp )              SSTEVR('V','V', ... )


    24= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSTEVR('N','V', ... )


    25= | A - U S U' | / ( |A| n ulp )        SSYEV('L','V', ... )


    26= | I - U U' | / ( n ulp )              SSYEV('L','V', ... )


    27= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEV_2STAGE('L','N', ... )


    28= | A - U S U' | / ( |A| n ulp )        SSYEVX('L','V','A', ... )


    29= | I - U U' | / ( n ulp )              SSYEVX('L','V','A', ... )


    30= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX_2STAGE('L','N','A', ... )


    31= | A - U S U' | / ( |A| n ulp )        SSYEVX('L','V','I', ... )


    32= | I - U U' | / ( n ulp )              SSYEVX('L','V','I', ... )


    33= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX_2STAGE('L','N','I', ... )


    34= | A - U S U' | / ( |A| n ulp )        SSYEVX('L','V','V', ... )


    35= | I - U U' | / ( n ulp )              SSYEVX('L','V','V', ... )


    36= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX_2STAGE('L','N','V', ... )


    37= | A - U S U' | / ( |A| n ulp )        SSPEV('L','V', ... )


    38= | I - U U' | / ( n ulp )              SSPEV('L','V', ... )


    39= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEV('L','N', ... )


    40= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','A', ... )


    41= | I - U U' | / ( n ulp )              SSPEVX('L','V','A', ... )


    42= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','A', ... )


    43= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','I', ... )


    44= | I - U U' | / ( n ulp )              SSPEVX('L','V','I', ... )


    45= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','I', ... )


    46= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','V', ... )


    47= | I - U U' | / ( n ulp )              SSPEVX('L','V','V', ... )


    48= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','V', ... )


    49= | A - U S U' | / ( |A| n ulp )        SSBEV('L','V', ... )


    50= | I - U U' | / ( n ulp )              SSBEV('L','V', ... )


    51= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEV_2STAGE('L','N', ... )


    52= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','A', ... )


    53= | I - U U' | / ( n ulp )              SSBEVX('L','V','A', ... )


    54= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX_2STAGE('L','N','A', ... )


    55= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','I', ... )


    56= | I - U U' | / ( n ulp )              SSBEVX('L','V','I', ... )


    57= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX_2STAGE('L','N','I', ... )


    58= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','V', ... )


    59= | I - U U' | / ( n ulp )              SSBEVX('L','V','V', ... )


    60= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX_2STAGE('L','N','V', ... )


    61= | A - U S U' | / ( |A| n ulp )        SSYEVD('L','V', ... )


    62= | I - U U' | / ( n ulp )              SSYEVD('L','V', ... )


    63= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVD_2STAGE('L','N', ... )


    64= | A - U S U' | / ( |A| n ulp )        SSPEVD('L','V', ... )


    65= | I - U U' | / ( n ulp )              SSPEVD('L','V', ... )


    66= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVD('L','N', ... )


    67= | A - U S U' | / ( |A| n ulp )        SSBEVD('L','V', ... )


    68= | I - U U' | / ( n ulp )              SSBEVD('L','V', ... )


    69= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVD_2STAGE('L','N', ... )


    70= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','A', ... )


    71= | I - U U' | / ( n ulp )              SSYEVR('L','V','A', ... )


    72= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR_2STAGE('L','N','A', ... )


    73= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','I', ... )


    74= | I - U U' | / ( n ulp )              SSYEVR('L','V','I', ... )


    75= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR_2STAGE('L','N','I', ... )


    76= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','V', ... )


    77= | I - U U' | / ( n ulp )              SSYEVR('L','V','V', ... )


    78= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR_2STAGE('L','N','V', ... )


    Tests 25 through 78 are repeated (as tests 79 through 132)


    with UPLO='U'


    To be added in 1999


    79= | A - U S U' | / ( |A| n ulp )        SSPEVR('L','V','A', ... )


    80= | I - U U' | / ( n ulp )              SSPEVR('L','V','A', ... )


    81= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','A', ... )


    82= | A - U S U' | / ( |A| n ulp )        SSPEVR('L','V','I', ... )


    83= | I - U U' | / ( n ulp )              SSPEVR('L','V','I', ... )


    84= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','I', ... )


    85= | A - U S U' | / ( |A| n ulp )        SSPEVR('L','V','V', ... )


    86= | I - U U' | / ( n ulp )              SSPEVR('L','V','V', ... )


    87= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','V', ... )


    88= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','A', ... )


    89= | I - U U' | / ( n ulp )              SSBEVR('L','V','A', ... )


    90= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','A', ... )


    91= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','I', ... )


    92= | I - U U' | / ( n ulp )              SSBEVR('L','V','I', ... )


    93= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','I', ... )


    94= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','V', ... )


    95= | I - U U' | / ( n ulp )              SSBEVR('L','V','V', ... )


    96= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','V', ... )

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