cdrvsx.f3

!>
!>    CDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
!>    expert driver CGEESX.
!>
!>    CDRVSX uses both test matrices generated randomly depending on
!>    data supplied in the calling sequence, as well as on data
!>    read from an input file and including precomputed condition
!>    numbers to which it compares the ones it computes.
!>
!>    When CDRVSX is called, a number of matrix  () and a
!>    number of matrix  are specified.  For each size ()
!>    and each type of matrix, one matrix will be generated and used
!>    to test the nonsymmetric eigenroutines.  For each matrix, 15
!>    tests will be performed:
!>
!>    (1)     0 if T is in Schur form, 1/ulp otherwise
!>           (no sorting of eigenvalues)
!>
!>    (2)     | A - VS T VS' | / ( n |A| ulp )
!>
!>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
!>      form  (no sorting of eigenvalues).
!>
!>    (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
!>
!>    (4)     0     if W are eigenvalues of T
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (5)     0     if T(with VS) = T(without VS),
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (7)     0 if T is in Schur form, 1/ulp otherwise
!>            (with sorting of eigenvalues)
!>
!>    (8)     | A - VS T VS' | / ( n |A| ulp )
!>
!>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
!>      form  (with sorting of eigenvalues).
!>
!>    (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
!>
!>    (10)    0     if W are eigenvalues of T
!>            1/ulp otherwise
!>            If workspace sufficient, also compare W with and
!>            without reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (11)    0     if T(with VS) = T(without VS),
!>            1/ulp otherwise
!>            If workspace sufficient, also compare T with and without
!>            reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
!>            1/ulp otherwise
!>            If workspace sufficient, also compare VS with and without
!>            reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (13)    if sorting worked and SDIM is the number of
!>            eigenvalues which were SELECTed
!>            If workspace sufficient, also compare SDIM with and
!>            without reciprocal condition numbers
!>
!>    (14)    if RCONDE the same no matter if VS and/or RCONDV computed
!>
!>    (15)    if RCONDV the same no matter if VS and/or RCONDE computed
!>
!>    The  are specified by an array NN(1:NSIZES); the value of
!>    each element NN(j) specifies one size.
!>    The  are specified by a logical array DOTYPE( 1:NTYPES );
!>    if DOTYPE(j) is .TRUE., then matrix type  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  entries 1, ULP, ..., ULP
!>         and random complex angles.
!>
!>    (7)  Same as (4), but multiplied by a constant near
!>         the overflow threshold
!>    (8)  Same as (4), but multiplied by a constant near
!>         the 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 orthogonal and
!>         T has  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  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 a constant
!>         near the overflow threshold
!>    (18) Same as (16), but multiplied by a constant
!>         near the underflow threshold
!>
!>    (19) Nonsymmetric matrix with random entries chosen from (-1,1).
!>         If N is at least 4, all entries in first two rows and last
!>         row, and first column and last two columns are zero.
!>    (20) Same as (19), but multiplied by a constant
!>         near the overflow threshold
!>    (21) Same as (19), but multiplied by a constant
!>         near the underflow threshold
!>
!>    In addition, an input file will be read from logical unit number
!>    NIUNIT. The file contains matrices along with precomputed
!>    eigenvalues and reciprocal condition numbers for the eigenvalue
!>    average and right invariant subspace. For these matrices, in
!>    addition to tests (1) to (15) we will compute the following two
!>    tests:
!>
!>   (16)  |RCONDE - RCDEIN| / cond(RCONDE)
!>
!>      RCONDE is the reciprocal average eigenvalue condition number
!>      computed by CGEESX and RCDEIN (the precomputed true value)
!>      is supplied as input.  cond(RCONDE) is the condition number
!>      of RCONDE, and takes errors in computing RCONDE into account,
!>      so that the resulting quantity should be O(ULP). cond(RCONDE)
!>      is essentially given by norm(A)/RCONDV.
!>
!>   (17)  |RCONDV - RCDVIN| / cond(RCONDV)
!>
!>      RCONDV is the reciprocal right invariant subspace condition
!>      number computed by CGEESX and RCDVIN (the precomputed true
!>      value) is supplied as input. cond(RCONDV) is the condition
!>      number of RCONDV, and takes errors in computing RCONDV into
!>      account, so that the resulting quantity should be O(ULP).
!>      cond(RCONDV) is essentially given by norm(A)/RCONDE.
!> 

NSIZES

!>          NSIZES is INTEGER
!>          The number of sizes of matrices to use.  NSIZES must be at
!>          least zero. If it is zero, no randomly generated matrices
!>          are tested, but any test matrices read from NIUNIT will be
!>          tested.
!> 

NN

!>          NN is 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.
!> 

NTYPES

!>          NTYPES is INTEGER
!>          The number of elements in DOTYPE. NTYPES must be at least
!>          zero. If it is zero, no randomly generated test matrices
!>          are tested, but and test matrices read from NIUNIT will be
!>          tested. 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. .
!> 

DOTYPE

!>          DOTYPE is 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.
!> 

ISEED

!>          ISEED is 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 CDRVSX to continue the same random number
!>          sequence.
!> 

THRESH

!>          THRESH is REAL
!>          A test will count as  if the , 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.
!> 

NIUNIT

!>          NIUNIT is INTEGER
!>          The FORTRAN unit number for reading in the data file of
!>          problems to solve.
!> 

NOUNIT

!>          NOUNIT is INTEGER
!>          The FORTRAN unit number for printing out error messages
!>          (e.g., if a routine returns INFO not equal to 0.)
!> 

A

!>          A is COMPLEX 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.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of A, and H. LDA must be at
!>          least 1 and at least max( NN ).
!> 

H

!>          H is COMPLEX array, dimension (LDA, max(NN))
!>          Another copy of the test matrix A, modified by CGEESX.
!> 

HT

!>          HT is COMPLEX array, dimension (LDA, max(NN))
!>          Yet another copy of the test matrix A, modified by CGEESX.
!> 

W

!>          W is COMPLEX array, dimension (max(NN))
!>          The computed eigenvalues of A.
!> 

WT

!>          WT is COMPLEX array, dimension (max(NN))
!>          Like W, this array contains the eigenvalues of A,
!>          but those computed when CGEESX only computes a partial
!>          eigendecomposition, i.e. not Schur vectors
!> 

WTMP

!>          WTMP is COMPLEX array, dimension (max(NN))
!>          More temporary storage for eigenvalues.
!> 

VS

!>          VS is COMPLEX array, dimension (LDVS, max(NN))
!>          VS holds the computed Schur vectors.
!> 

LDVS

!>          LDVS is INTEGER
!>          Leading dimension of VS. Must be at least max(1,max(NN)).
!> 

VS1

!>          VS1 is COMPLEX array, dimension (LDVS, max(NN))
!>          VS1 holds another copy of the computed Schur vectors.
!> 

RESULT

!>          RESULT is REAL array, dimension (17)
!>          The values computed by the 17 tests described above.
!>          The values are currently limited to 1/ulp, to avoid overflow.
!> 

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The number of entries in WORK.  This must be at least
!>          max(1,2*NN(j)**2) for all j.
!> 

RWORK

!>          RWORK is REAL array, dimension (max(NN))
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (max(NN))
!> 

INFO

!>          INFO is INTEGER
!>          If 0,  successful exit.
!>            <0,  input parameter -INFO is incorrect
!>            >0,  CLATMR, CLATMS, CLATME or CGET24 returned an error
!>                 code and INFO is its absolute value
!>
!>-----------------------------------------------------------------------
!>
!>     Some Local Variables and Parameters:
!>     ---- ----- --------- --- ----------
!>     ZERO, ONE       Real 0 and 1.
!>     MAXTYP          The number of types defined.
!>     NMAX            Largest value in NN.
!>     NERRS           The number of tests which have exceeded THRESH
!>     COND, CONDS,
!>     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.
!>     RTULP, RTULPI   Square roots of the previous 4 values.
!>             The following four arrays decode JTYPE:
!>     KTYPE(j)        The general type (1-10) for type .
!>     KMODE(j)        The MODE value to be passed to the matrix
!>                     generator for type .
!>     KMAGN(j)        The order of magnitude ( O(1),
!>                     O(overflow^(1/2) ), O(underflow^(1/2) )
!>     KCONDS(j)       Selectw whether CONDS is to be 1 or
!>                     1/sqrt(ulp).  (0 means irrelevant.)
!> 

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