zchkhs.f

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      SUBROUTINE ZCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
     $                   NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
     $                   W3, EVECTL, EVECTR, EVECTY, EVECTX, UU, TAU,
     $                   WORK, NWORK, RWORK, IWORK, SELECT, RESULT,
     $                   INFO )
*
*  -- LAPACK test routine (version 3.1.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     February 2007
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * ), SELECT( * )
      INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
      DOUBLE PRECISION   RESULT( 14 ), RWORK( * )
      COMPLEX*16         A( LDA, * ), EVECTL( LDU, * ),
     $                   EVECTR( LDU, * ), EVECTX( LDU, * ),
     $                   EVECTY( LDU, * ), H( LDA, * ), T1( LDA, * ),
     $                   T2( LDA, * ), TAU( * ), U( LDU, * ),
     $                   UU( LDU, * ), UZ( LDU, * ), W1( * ), W3( * ),
     $                   WORK( * ), Z( LDU, * )
*     ..
*
*  Purpose
*  =======
*
*     ZCHKHS  checks the nonsymmetric eigenvalue problem routines.
*
*             ZGEHRD factors A as  U H U' , where ' means conjugate
*             transpose, H is hessenberg, and U is unitary.
*
*             ZUNGHR generates the unitary matrix U.
*
*             ZUNMHR multiplies a matrix by the unitary matrix U.
*
*             ZHSEQR factors H as  Z T Z' , where Z is unitary and T
*             is upper triangular.  It also computes the eigenvalues,
*             w(1), ..., w(n); we define a diagonal matrix W whose
*             (diagonal) entries are the eigenvalues.
*
*             ZTREVC computes the left eigenvector matrix L and the
*             right eigenvector matrix R for the matrix T.  The
*             columns of L are the complex conjugates of the left
*             eigenvectors of T.  The columns of R are the right
*             eigenvectors of T.  L is lower triangular, and R is
*             upper triangular.
*
*             ZHSEIN computes the left eigenvector matrix Y and the
*             right eigenvector matrix X for the matrix H.  The
*             columns of Y are the complex conjugates of the left
*             eigenvectors of H.  The columns of X are the right
*             eigenvectors of H.  Y is lower triangular, and X is
*             upper triangular.
*
*     When ZCHKHS 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 nonsymmetric eigenroutines.  For each matrix, 14
*     tests will be performed:
*
*     (1)     | A - U H U**H | / ( |A| n ulp )
*
*     (2)     | I - UU**H | / ( n ulp )
*
*     (3)     | H - Z T Z**H | / ( |H| n ulp )
*
*     (4)     | I - ZZ**H | / ( n ulp )
*
*     (5)     | A - UZ H (UZ)**H | / ( |A| n ulp )
*
*     (6)     | I - UZ (UZ)**H | / ( n ulp )
*
*     (7)     | T(Z computed) - T(Z not computed) | / ( |T| ulp )
*
*     (8)     | W(Z computed) - W(Z not computed) | / ( |W| ulp )
*
*     (9)     | TR - RW | / ( |T| |R| ulp )
*
*     (10)    | L**H T - W**H L | / ( |T| |L| ulp )
*
*     (11)    | HX - XW | / ( |H| |X| ulp )
*
*     (12)    | Y**H H - W**H Y | / ( |H| |Y| ulp )
*
*     (13)    | AX - XW | / ( |A| |X| ulp )
*
*     (14)    | Y**H A - W**H Y | / ( |A| |Y| ulp )
*
*     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 (transposed) Jordan block, with 1's on the diagonal.
*
*     (4)  A diagonal matrix with evenly spaced entries
*          1, ..., ULP  and random complex angles.
*          (ULP = (first number larger than 1) - 1 )
*     (5)  A diagonal matrix with geometrically spaced entries
*          1, ..., ULP  and random complex angles.
*     (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
*          and random complex angles.
*
*     (7)  Same as (4), but multiplied by SQRT( overflow threshold )
*     (8)  Same as (4), but multiplied by SQRT( underflow threshold )
*
*     (9)  A matrix of the form  U' T U, where U is unitary and
*          T has evenly spaced entries 1, ..., ULP with random complex
*          angles on the diagonal and random O(1) entries in the upper
*          triangle.
*
*     (10) A matrix of the form  U' T U, where U is unitary and
*          T has geometrically spaced entries 1, ..., ULP with random
*          complex angles on the diagonal and random O(1) entries in
*          the upper triangle.
*
*     (11) A matrix of the form  U' T U, where U is unitary and
*          T has "clustered" entries 1, ULP,..., ULP with random
*          complex angles on the diagonal and random O(1) entries in
*          the upper triangle.
*
*     (12) A matrix of the form  U' T U, where U is unitary and
*          T has complex eigenvalues randomly chosen from
*          ULP < |z| < 1   and random O(1) entries in the upper
*          triangle.
*
*     (13) A matrix of the form  X' T X, where X has condition
*          SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
*          with random complex angles on the diagonal and random O(1)
*          entries in the upper triangle.
*
*     (14) A matrix of the form  X' T X, where X has condition
*          SQRT( ULP ) and T has geometrically spaced entries
*          1, ..., ULP with random complex angles on the diagonal
*          and random O(1) entries in the upper triangle.
*
*     (15) A matrix of the form  X' T X, where X has condition
*          SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
*          with random complex angles on the diagonal and random O(1)
*          entries in the upper triangle.
*
*     (16) A matrix of the form  X' T X, where X has condition
*          SQRT( ULP ) and T has complex eigenvalues randomly chosen
*          from   ULP < |z| < 1   and random O(1) entries in the upper
*          triangle.
*
*     (17) Same as (16), but multiplied by SQRT( overflow threshold )
*     (18) Same as (16), but multiplied by SQRT( underflow threshold )
*
*     (19) Nonsymmetric matrix with random entries chosen from |z| < 1
*     (20) Same as (19), but multiplied by SQRT( overflow threshold )
*     (21) Same as (19), but multiplied by SQRT( underflow threshold )
*
*  Arguments
*  ==========
*
*  NSIZES - INTEGER
*           The number of sizes of matrices to use.  If it is zero,
*           ZCHKHS 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, ZCHKHS
*           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 ZCHKHS 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, H, T1 and T2.  It must be at
*           least 1 and at least max( NN ).
*           Not modified.
*
*  H      - COMPLEX*16 array, dimension (LDA,max(NN))
*           The upper hessenberg matrix computed by ZGEHRD.  On exit,
*           H contains the Hessenberg form of the matrix in A.
*           Modified.
*
*  T1     - COMPLEX*16 array, dimension (LDA,max(NN))
*           The Schur (="quasi-triangular") matrix computed by ZHSEQR
*           if Z is computed.  On exit, T1 contains the Schur form of
*           the matrix in A.
*           Modified.
*
*  T2     - COMPLEX*16 array, dimension (LDA,max(NN))
*           The Schur matrix computed by ZHSEQR when Z is not computed.
*           This should be identical to T1.
*           Modified.
*
*  LDU    - INTEGER
*           The leading dimension of U, Z, UZ and UU.  It must be at
*           least 1 and at least max( NN ).
*           Not modified.
*
*  U      - COMPLEX*16 array, dimension (LDU,max(NN))
*           The unitary matrix computed by ZGEHRD.
*           Modified.
*
*  Z      - COMPLEX*16 array, dimension (LDU,max(NN))
*           The unitary matrix computed by ZHSEQR.
*           Modified.
*
*  UZ     - COMPLEX*16 array, dimension (LDU,max(NN))
*           The product of U times Z.
*           Modified.
*
*  W1     - COMPLEX*16 array, dimension (max(NN))
*           The eigenvalues of A, as computed by a full Schur
*           decomposition H = Z T Z'.  On exit, W1 contains the
*           eigenvalues of the matrix in A.
*           Modified.
*
*  W3     - COMPLEX*16 array, dimension (max(NN))
*           The eigenvalues of A, as computed by a partial Schur
*           decomposition (Z not computed, T only computed as much
*           as is necessary for determining eigenvalues).  On exit,
*           W3 contains the eigenvalues of the matrix in A, possibly
*           perturbed by ZHSEIN.
*           Modified.
*
*  EVECTL - COMPLEX*16 array, dimension (LDU,max(NN))
*           The conjugate transpose of the (upper triangular) left
*           eigenvector matrix for the matrix in T1.
*           Modified.
*
*  EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN))
*           The (upper triangular) right eigenvector matrix for the
*           matrix in T1.
*           Modified.
*
*  EVECTY - COMPLEX*16 array, dimension (LDU,max(NN))
*           The conjugate transpose of the left eigenvector matrix
*           for the matrix in H.
*           Modified.
*
*  EVECTX - COMPLEX*16 array, dimension (LDU,max(NN))
*           The right eigenvector matrix for the matrix in H.
*           Modified.
*
*  UU     - COMPLEX*16 array, dimension (LDU,max(NN))
*           Details of the unitary matrix computed by ZGEHRD.
*           Modified.
*
*  TAU    - COMPLEX*16 array, dimension (max(NN))
*           Further details of the unitary matrix computed by ZGEHRD.
*           Modified.
*
*  WORK   - COMPLEX*16 array, dimension (NWORK)
*           Workspace.
*           Modified.
*
*  NWORK  - INTEGER
*           The number of entries in WORK.  NWORK >= 4*NN(j)*NN(j) + 2.
*
*  RWORK  - DOUBLE PRECISION array, dimension (max(NN))
*           Workspace.  Could be equivalenced to IWORK, but not SELECT.
*           Modified.
*
*  IWORK  - INTEGER array, dimension (max(NN))
*           Workspace.
*           Modified.
*
*  SELECT - LOGICAL array, dimension (max(NN))
*           Workspace.  Could be equivalenced to IWORK, but not RWORK.
*           Modified.
*
*  RESULT - DOUBLE PRECISION array, dimension (14)
*           The values computed by the fourteen 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
*            -6: THRESH < 0
*            -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
*           -14: LDU < 1 or LDU < NMAX.
*           -26: NWORK too small.
*           If  ZLATMR, CLATMS, or CLATME returns an error code, the
*               absolute value of it is returned.
*           If 1, then ZHSEQR could not find all the shifts.
*           If 2, then the EISPACK code (for small blocks) failed.
*           If >2, then 30*N iterations were not enough to find an
*               eigenvalue or to decompose the problem.
*           Modified.
*
*-----------------------------------------------------------------------
*
*     Some Local Variables and Parameters:
*     ---- ----- --------- --- ----------
*