sdrvst.f

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      SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
     $                   NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
     $                   WA2, WA3, U, LDU, V, TAU, Z, WORK, LWORK,
     $                   IWORK, LIWORK, RESULT, INFO )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDU, LIWORK, LWORK, NOUNIT, NSIZES,
     $                   NTYPES
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
      REAL               A( LDA, * ), D1( * ), D2( * ), D3( * ),
     $                   D4( * ), EVEIGS( * ), RESULT( * ), TAU( * ),
     $                   U( LDU, * ), V( LDU, * ), WA1( * ), WA2( * ),
     $                   WA3( * ), WORK( * ), Z( LDU, * )
*     ..
*
*  Purpose
*  =======
*
*       SDRVST  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 SDRVST 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 )
*
*  Arguments
*  =========
*
*  NSIZES  INTEGER
*          The number of sizes of matrices to use.  If it is zero,
*          SDRVST 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, SDRVST
*          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 SDRVST 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 simlutaneously
*          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', ... )