zdrvst.f

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      SUBROUTINE ZDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
     $                   NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
     $                   LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK,
     $                   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, LRWORK, LWORK, NOUNIT,
     $                   NSIZES, NTYPES
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
      DOUBLE PRECISION   D1( * ), D2( * ), D3( * ), RESULT( * ),
     $                   RWORK( * ), WA1( * ), WA2( * ), WA3( * )
      COMPLEX*16         A( LDA, * ), TAU( * ), U( LDU, * ),
     $                   V( LDU, * ), WORK( * ), Z( LDU, * )
*     ..
*
*  Purpose
*  =======
*
*       ZDRVST  checks the Hermitian eigenvalue problem drivers.
*
*               ZHEEVD computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix,
*               using a divide-and-conquer algorithm.
*
*               ZHEEVX computes selected eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix.
*
*               ZHEEVR computes selected eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix
*               using the Relatively Robust Representation where it can.
*
*               ZHPEVD computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix in packed
*               storage, using a divide-and-conquer algorithm.
*
*               ZHPEVX computes selected eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix in packed
*               storage.
*
*               ZHBEVD computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian band matrix,
*               using a divide-and-conquer algorithm.
*
*               ZHBEVX computes selected eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian band matrix.
*
*               ZHEEV computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix.
*
*               ZHPEV computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian matrix in packed
*               storage.
*
*               ZHBEV computes all eigenvalues and, optionally,
*               eigenvectors of a complex Hermitian band matrix.
*
*       When ZDRVST 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 entries
*            1, ..., ULP  and random signs.
*            (ULP = (first number larger than 1) - 1 )
*       (4)  A diagonal matrix with geometrically spaced entries
*            1, ..., ULP  and random signs.
*       (5)  A diagonal matrix with "clustered" entries 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 unitary 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 unitary 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 unitary 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,
*          ZDRVST 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, ZDRVST
*          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 ZDRVST to continue the same random number
*          sequence.
*          Modified.
*
*  THRESH  DOUBLE PRECISION
*          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       COMPLEX*16 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      DOUBLE PRECISION array, dimension (max(NN))
*          The eigenvalues of A, as computed by ZSTEQR simlutaneously
*          with Z.  On exit, the eigenvalues in D1 correspond with the
*          matrix in A.
*          Modified.
*
*  D2      DOUBLE PRECISION array, dimension (max(NN))
*          The eigenvalues of A, as computed by ZSTEQR if Z is not
*          computed.  On exit, the eigenvalues in D2 correspond with
*          the matrix in A.
*          Modified.
*
*  D3      DOUBLE PRECISION array, dimension (max(NN))
*          The eigenvalues of A, as computed by DSTERF.  On exit, the
*          eigenvalues in D3 correspond with the matrix in A.
*          Modified.
*
*  WA1     DOUBLE PRECISION array, dimension
*
*  WA2     DOUBLE PRECISION array, dimension
*
*  WA3     DOUBLE PRECISION array, dimension
*
*  U       COMPLEX*16 array, dimension (LDU, max(NN))
*          The unitary matrix computed by ZHETRD + ZUNGC3.
*          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       COMPLEX*16 array, dimension (LDU, max(NN))
*          The Housholder vectors computed by ZHETRD in reducing A to
*          tridiagonal form.
*          Modified.
*
*  TAU     COMPLEX*16 array, dimension (max(NN))
*          The Householder factors computed by ZHETRD in reducing A
*          to tridiagonal form.
*          Modified.
*
*  Z       COMPLEX*16 array, dimension (LDU, max(NN))
*          The unitary matrix of eigenvectors computed by ZHEEVD,
*          ZHEEVX, ZHPEVD, CHPEVX, ZHBEVD, and CHBEVX.
*          Modified.
*
*  WORK  - COMPLEX*16 array of dimension ( LWORK )
*           Workspace.
*           Modified.
*
*  LWORK - INTEGER
*           The number of entries in WORK.  This must be at least
*           2*max( NN(j), 2 )**2.
*           Not modified.
*
*  RWORK   DOUBLE PRECISION array, dimension (3*max(NN))
*           Workspace.
*           Modified.
*
*  LRWORK - INTEGER
*           The number of entries in RWORK.
*
*  IWORK   INTEGER array, dimension (6*max(NN))
*          Workspace.
*          Modified.
*
*  LIWORK - INTEGER
*           The number of entries in IWORK.
*
*  RESULT  DOUBLE PRECISION array, dimension (??)
*          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  DLATMR, SLATMS, ZHETRD, DORGC3, ZSTEQR, DSTERF,
*              or DORMC2 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 DLAFTS).
*       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) )
*
*  =====================================================================
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, TWO, TEN
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
     $                   TEN = 10.0D+0 )
      DOUBLE PRECISION   HALF
      PARAMETER          ( HALF = ONE / TWO )
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 18 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADNN
      CHARACTER          UPLO
      INTEGER            I, IDIAG, IHBW, IINFO, IL, IMODE, INDWRK, INDX,
     $                   IROW, ITEMP, ITYPE, IU, IUPLO, J, J1, J2, JCOL,
     $                   JSIZE, JTYPE, KD, LGN, LIWEDC, LRWEDC, LWEDC,
     $                   M, M2, M3, MTYPES, N, NERRS, NMATS, NMAX,
     $                   NTEST, NTESTT
      DOUBLE PRECISION   ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
     $                   RTUNFL, TEMP1, TEMP2, TEMP3, ULP, ULPINV, UNFL,
     $                   VL, VU
*     ..
*     .. Local Arrays ..
      INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
     $                   ISEED3( 4 ), KMAGN( MAXTYP ), KMODE( MAXTYP ),
     $                   KTYPE( MAXTYP )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLARND, DSXT1
      EXTERNAL           DLAMCH, DLARND, DSXT1
*     ..
*     .. External Subroutines ..
      EXTERNAL           ALASVM, DLABAD, DLAFTS, XERBLA, ZHBEV, ZHBEVD,
     $                   ZHBEVX, ZHEEV, ZHEEVD, ZHEEVR, ZHEEVX, ZHET21,
     $                   ZHET22, ZHPEV, ZHPEVD, ZHPEVX, ZLACPY, ZLASET,
     $                   ZLATMR, ZLATMS
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, INT, LOG, MAX, MIN, SQRT
*     ..
*     .. Data statements ..