ddrgev.c

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/* ddrgev.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c__0 = 0;
static doublereal c_b17 = 0.;
static integer c__2 = 2;
static doublereal c_b23 = 1.;
static integer c__3 = 3;
static integer c__4 = 4;
static logical c_true = TRUE_;
static logical c_false = FALSE_;

/* Subroutine */ int ddrgev_(integer *nsizes, integer *nn, integer *ntypes, 
        logical *dotype, integer *iseed, doublereal *thresh, integer *nounit, 
        doublereal *a, integer *lda, doublereal *b, doublereal *s, doublereal 
        *t, doublereal *q, integer *ldq, doublereal *z__, doublereal *qe, 
        integer *ldqe, doublereal *alphar, doublereal *alphai, doublereal *
        beta, doublereal *alphr1, doublereal *alphi1, doublereal *beta1, 
        doublereal *work, integer *lwork, doublereal *result, integer *info)
{
    /* Initialized data */

    static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
            2,2,2,3 };
    static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
            2,3,2,1 };
    static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
            1,1,1,1 };
    static integer iasign[26] = { 0,0,0,0,0,0,2,0,2,2,0,0,2,2,2,0,2,0,0,0,2,2,
            2,2,2,0 };
    static integer ibsign[26] = { 0,0,0,0,0,0,0,2,0,0,2,2,0,0,2,0,2,0,0,0,0,0,
            0,0,0,0 };
    static integer kz1[6] = { 0,1,2,1,3,3 };
    static integer kz2[6] = { 0,0,1,2,1,1 };
    static integer kadd[6] = { 0,0,0,0,3,2 };
    static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
            4,4,4,0 };
    static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
            8,8,8,8,8,0 };
    static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
            3,3,3,1 };
    static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
            4,4,4,1 };
    static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
            3,3,2,1 };

    /* Format strings */
    static char fmt_9999[] = "(\002 DDRGEV: \002,a,\002 returned INFO=\002,i"
            "6,\002.\002,/3x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
            "(\002,4(i4,\002,\002),i5,\002)\002)";
    static char fmt_9998[] = "(\002 DDRGEV: \002,a,\002 Eigenvectors from"
            " \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
            "error=\002,0p,g10.3,\002,\002,3x,\002N=\002,i4,\002, JTYPE=\002,"
            "i3,\002, ISEED=(\002,4(i4,\002,\002),i5,\002)\002)";
    static char fmt_9997[] = "(/1x,a3,\002 -- Real Generalized eigenvalue pr"
            "oblem driver\002)";
    static char fmt_9996[] = "(\002 Matrix types (see DDRGEV for details):"
            " \002)";
    static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
            "osed Jordan block)\002,/\002   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I"
            ")  5=(J',J')  \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
            "onal Matrices:  ( \002,\002D=diag(0,1,2,...) )\002,/\002   7=(D,"
            "I)   9=(large*D, small*I\002,\002)  11=(large*I, small*D)  13=(l"
            "arge*D, large*I)\002,/\002   8=(I,D)  10=(small*D, large*I)  12="
            "(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002  15"
            "=(D, reversed D)\002)";
    static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
            "atrices U, V:\002,/\002  16=Transposed Jordan Blocks            "
            " 19=geometric \002,\002alpha, beta=0,1\002,/\002  17=arithm. alp"
            "ha&beta             \002,\002      20=arithmetic alpha, beta=0,"
            "1\002,/\002  18=clustered \002,\002alpha, beta=0,1            21"
            "=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
            "/\002  22=(large, small)   \002,\00223=(small,large)    24=(smal"
            "l,small)    25=(large,large)\002,/\002  26=random O(1) matrices"
            ".\002)";
    static char fmt_9993[] = "(/\002 Tests performed:    \002,/\002 1 = max "
            "| ( b A - a B )'*l | / const.,\002,/\002 2 = | |VR(i)| - 1 | / u"
            "lp,\002,/\002 3 = max | ( b A - a B )*r | / const.\002,/\002 4 ="
            " | |VL(i)| - 1 | / ulp,\002,/\002 5 = 0 if W same no matter if r"
            " or l computed,\002,/\002 6 = 0 if l same no matter if l compute"
            "d,\002,/\002 7 = 0 if r same no matter if r computed,\002,/1x)";
    static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
            ",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
            ",0p,f8.2)";
    static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
            ",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
            ",1p,d10.3)";

    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, qe_dim1, 
            qe_offset, s_dim1, s_offset, t_dim1, t_offset, z_dim1, z_offset, 
            i__1, i__2, i__3, i__4;
    doublereal d__1;

    /* Builtin functions */
    double d_sign(doublereal *, doublereal *);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);

    /* Local variables */
    integer i__, j, n, n1, jc, in, jr;
    doublereal ulp;
    integer iadd, ierr, nmax;
    logical badnn;
    extern /* Subroutine */ int dget52_(logical *, integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *), dggev_(char *, char *, integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, integer *, integer *);
    doublereal rmagn[4];
    integer nmats, jsize, nerrs, jtype;
    extern /* Subroutine */ int dlatm4_(integer *, integer *, integer *, 
            integer *, integer *, doublereal *, doublereal *, doublereal *, 
            integer *, integer *, doublereal *, integer *), dorm2r_(char *, 
            char *, integer *, integer *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *);
    extern doublereal dlarnd_(integer *, integer *);
    doublereal safmin;
    integer ioldsd[4];
    doublereal safmax;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *), 
            alasvm_(char *, integer *, integer *, integer *, integer *), dlaset_(char *, integer *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *), xerbla_(char *, 
            integer *);
    integer minwrk, maxwrk;
    doublereal ulpinv;
    integer mtypes, ntestt;

    /* Fortran I/O blocks */
    static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___44 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___45 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___46 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___47 = { 0, 0, 0, fmt_9996, 0 };
    static cilist io___48 = { 0, 0, 0, fmt_9995, 0 };
    static cilist io___49 = { 0, 0, 0, fmt_9994, 0 };
    static cilist io___50 = { 0, 0, 0, fmt_9993, 0 };
    static cilist io___51 = { 0, 0, 0, fmt_9992, 0 };
    static cilist io___52 = { 0, 0, 0, fmt_9991, 0 };



/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DDRGEV checks the nonsymmetric generalized eigenvalue problem driver */
/*  routine DGGEV. */

/*  DGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the */
/*  generalized eigenvalues and, optionally, the left and right */
/*  eigenvectors. */

/*  A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/*  or a ratio  alpha/beta = w, such that A - w*B is singular.  It is */
/*  usually represented as the pair (alpha,beta), as there is reasonalbe */
/*  interpretation for beta=0, and even for both being zero. */

/*  A right generalized eigenvector corresponding to a generalized */
/*  eigenvalue  w  for a pair of matrices (A,B) is a vector r  such that */
/*  (A - wB) * r = 0.  A left generalized eigenvector is a vector l such */
/*  that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l. */

/*  When DDRGEV 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, a pair of matrices (A, B) will be generated */
/*  and used for testing.  For each matrix pair, the following tests */
/*  will be performed and compared with the threshhold THRESH. */

/*  Results from DGGEV: */

/*  (1)  max over all left eigenvalue/-vector pairs (alpha/beta,l) of */

/*       | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) ) */

/*       where VL**H is the conjugate-transpose of VL. */

/*  (2)  | |VL(i)| - 1 | / ulp and whether largest component real */

/*       VL(i) denotes the i-th column of VL. */

/*  (3)  max over all left eigenvalue/-vector pairs (alpha/beta,r) of */

/*       | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) ) */

/*  (4)  | |VR(i)| - 1 | / ulp and whether largest component real */

/*       VR(i) denotes the i-th column of VR. */

/*  (5)  W(full) = W(partial) */
/*       W(full) denotes the eigenvalues computed when both l and r */
/*       are also computed, and W(partial) denotes the eigenvalues */
/*       computed when only W, only W and r, or only W and l are */
/*       computed. */

/*  (6)  VL(full) = VL(partial) */
/*       VL(full) denotes the left eigenvectors computed when both l */
/*       and r are computed, and VL(partial) denotes the result */
/*       when only l is computed. */

/*  (7)  VR(full) = VR(partial) */
/*       VR(full) denotes the right eigenvectors computed when both l */
/*       and r are also computed, and VR(partial) denotes the result */
/*       when only l is computed. */


/*  Test Matrices */
/*  ---- -------- */

/*  The sizes of the test matrices 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)  ( 0, 0 )         (a pair of zero matrices) */

/*  (2)  ( I, 0 )         (an identity and a zero matrix) */

/*  (3)  ( 0, I )         (an identity and a zero matrix) */

/*  (4)  ( I, I )         (a pair of identity matrices) */

/*          t   t */
/*  (5)  ( J , J  )       (a pair of transposed Jordan blocks) */

/*                                      t                ( I   0  ) */
/*  (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t ) */
/*                                   ( 0   I  )          ( 0   J  ) */
/*                        and I is a k x k identity and J a (k+1)x(k+1) */
/*                        Jordan block; k=(N-1)/2 */

/*  (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal */
/*                        matrix with those diagonal entries.) */
/*  (8)  ( I, D ) */

/*  (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big */

/*  (10) ( small*D, big*I ) */

/*  (11) ( big*I, small*D ) */

/*  (12) ( small*I, big*D ) */

/*  (13) ( big*D, big*I ) */

/*  (14) ( small*D, small*I ) */

/*  (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/*                         D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/*            t   t */
/*  (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices. */

/*  (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices */
/*                         with random O(1) entries above the diagonal */
/*                         and diagonal entries diag(T1) = */
/*                         ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/*                         ( 0, N-3, N-4,..., 1, 0, 0 ) */

/*  (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/*                         diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/*                         s = machine precision. */

/*  (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/*                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */

/*                                                         N-5 */
/*  (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 ) */
/*                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */

/*  (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/*                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/*                         where r1,..., r(N-4) are random. */

/*  (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/*                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */

/*  (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/*                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */

/*  (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/*                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */

/*  (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/*                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */

/*  (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular */
/*                          matrices. */


/*  Arguments */
/*  ========= */

/*  NSIZES  (input) INTEGER */
/*          The number of sizes of matrices to use.  If it is zero, */
/*          DDRGES does nothing.  NSIZES >= 0. */

/*  NN      (input) INTEGER array, dimension (NSIZES) */
/*          An array containing the sizes to be used for the matrices. */
/*          Zero values will be skipped.  NN >= 0. */

/*  NTYPES  (input) INTEGER */
/*          The number of elements in DOTYPE.   If it is zero, DDRGES */
/*          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. . */

/*  DOTYPE  (input) 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   (input/output) 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 DDRGES to continue the same random number */
/*          sequence. */

/*  THRESH  (input) 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. */

/*  NOUNIT  (input) INTEGER */
/*          The FORTRAN unit number for printing out error messages */
/*          (e.g., if a routine returns IERR not equal to 0.) */

/*  A       (input/workspace) DOUBLE PRECISION array, */
/*                                       dimension(LDA, max(NN)) */
/*          Used to hold the original A matrix.  Used as input only */
/*          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/*          DOTYPE(MAXTYP+1)=.TRUE. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of A, B, S, and T. */
/*          It must be at least 1 and at least max( NN ). */

/*  B       (input/workspace) DOUBLE PRECISION array, */
/*                                       dimension(LDA, max(NN)) */
/*          Used to hold the original B matrix.  Used as input only */
/*          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/*          DOTYPE(MAXTYP+1)=.TRUE. */

/*  S       (workspace) DOUBLE PRECISION array, */
/*                                 dimension (LDA, max(NN)) */
/*          The Schur form matrix computed from A by DGGES.  On exit, S */
/*          contains the Schur form matrix corresponding to the matrix */
/*          in A. */

/*  T       (workspace) DOUBLE PRECISION array, */
/*                                 dimension (LDA, max(NN)) */
/*          The upper triangular matrix computed from B by DGGES. */

/*  Q       (workspace) DOUBLE PRECISION array, */
/*                                 dimension (LDQ, max(NN)) */
/*          The (left) eigenvectors matrix computed by DGGEV. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of Q and Z. It must */
/*          be at least 1 and at least max( NN ). */

/*  Z       (workspace) DOUBLE PRECISION array, dimension( LDQ, max(NN) ) */
/*          The (right) orthogonal matrix computed by DGGES. */

/*  QE      (workspace) DOUBLE PRECISION array, dimension( LDQ, max(NN) ) */
/*          QE holds the computed right or left eigenvectors. */

/*  LDQE    (input) INTEGER */
/*          The leading dimension of QE. LDQE >= max(1,max(NN)). */

/*  ALPHAR  (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*  ALPHAI  (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*  BETA    (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*          The generalized eigenvalues of (A,B) computed by DGGEV. */
/*          ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th */
/*          generalized eigenvalue of A and B. */

/*  ALPHR1  (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*  ALPHI1  (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*  BETA1   (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/*          Like ALPHAR, ALPHAI, BETA, these arrays contain the */
/*          eigenvalues of A and B, but those computed when DGGEV only */
/*          computes a partial eigendecomposition, i.e. not the */
/*          eigenvalues and left and right eigenvectors. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          The number of entries in WORK.  LWORK >= MAX( 8*N, N*(N+1) ). */

/*  RESULT  (output) DOUBLE PRECISION array, dimension (2) */
/*          The values computed by the tests described above. */
/*          The values are currently limited to 1/ulp, to avoid overflow. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          > 0:  A routine returned an error code.  INFO is the */
/*                absolute value of the INFO value returned. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --nn;
    --dotype;
    --iseed;
    t_dim1 = *lda;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    s_dim1 = *lda;
    s_offset = 1 + s_dim1;
    s -= s_offset;
    b_dim1 = *lda;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    z_dim1 = *ldq;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    qe_dim1 = *ldqe;
    qe_offset = 1 + qe_dim1;
    qe -= qe_offset;
    --alphar;
    --alphai;
    --beta;
    --alphr1;
    --alphi1;
    --beta1;
    --work;
    --result;

    /* Function Body */
/*     .. */
/*     .. Executable Statements .. */

/*     Check for errors */

    *info = 0;

    badnn = FALSE_;
    nmax = 1;
    i__1 = *nsizes;
    for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
        i__2 = nmax, i__3 = nn[j];
        nmax = max(i__2,i__3);
        if (nn[j] < 0) {
            badnn = TRUE_;
        }
/* L10: */
    }

    if (*nsizes < 0) {
        *info = -1;
    } else if (badnn) {
        *info = -2;
    } else if (*ntypes < 0) {
        *info = -3;
    } else if (*thresh < 0.) {
        *info = -6;
    } else if (*lda <= 1 || *lda < nmax) {
        *info = -9;
    } else if (*ldq <= 1 || *ldq < nmax) {
        *info = -14;
    } else if (*ldqe <= 1 || *ldqe < nmax) {
        *info = -17;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace needed at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV. */

    minwrk = 1;
    if (*info == 0 && *lwork >= 1) {
/* Computing MAX */
        i__1 = 1, i__2 = nmax << 3, i__1 = max(i__1,i__2), i__2 = nmax * (
                nmax + 1);
        minwrk = max(i__1,i__2);
        maxwrk = nmax * 7 + nmax * ilaenv_(&c__1, "DGEQRF", " ", &nmax, &c__1, 
                 &nmax, &c__0);
/* Computing MAX */
        i__1 = maxwrk, i__2 = nmax * (nmax + 1);
        maxwrk = max(i__1,i__2);
        work[1] = (doublereal) maxwrk;
    }

    if (*lwork < minwrk) {
        *info = -25;
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DDRGEV", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*nsizes == 0 || *ntypes == 0) {
        return 0;
    }

    safmin = dlamch_("Safe minimum");
    ulp = dlamch_("Epsilon") * dlamch_("Base");
    safmin /= ulp;
    safmax = 1. / safmin;
    dlabad_(&safmin, &safmax);
    ulpinv = 1. / ulp;

/*     The values RMAGN(2:3) depend on N, see below. */

    rmagn[0] = 0.;
    rmagn[1] = 1.;

/*     Loop over sizes, types */

    ntestt = 0;
    nerrs = 0;
    nmats = 0;

    i__1 = *nsizes;
    for (jsize = 1; jsize <= i__1; ++jsize) {
        n = nn[jsize];
        n1 = max(1,n);
        rmagn[2] = safmax * ulp / (doublereal) n1;
        rmagn[3] = safmin * ulpinv * n1;

        if (*nsizes != 1) {
            mtypes = min(26,*ntypes);
        } else {
            mtypes = min(27,*ntypes);
        }

        i__2 = mtypes;
        for (jtype = 1; jtype <= i__2; ++jtype) {
            if (! dotype[jtype]) {
                goto L210;
            }
            ++nmats;

/*           Save ISEED in case of an error. */

            for (j = 1; j <= 4; ++j) {
                ioldsd[j - 1] = iseed[j];
/* L20: */
            }

/*           Generate test matrices A and B */

/*           Description of control parameters: */

/*           KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/*                   =3 means random. */
/*           KATYPE: the "type" to be passed to DLATM4 for computing A. */
/*           KAZERO: the pattern of zeros on the diagonal for A: */
/*                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/*                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/*                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of */
/*                   non-zero entries.) */
/*           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/*                   =2: large, =3: small. */
/*           IASIGN: 1 if the diagonal elements of A are to be */
/*                   multiplied by a random magnitude 1 number, =2 if */
/*                   randomly chosen diagonal blocks are to be rotated */
/*                   to form 2x2 blocks. */
/*           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. */
/*           KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/*           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/*           RMAGN: used to implement KAMAGN and KBMAGN. */

            if (mtypes > 26) {
                goto L100;
            }
            ierr = 0;
            if (kclass[jtype - 1] < 3) {

/*              Generate A (w/o rotation) */

                if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
                    in = ((n - 1) / 2 << 1) + 1;
                    if (in != n) {
                        dlaset_("Full", &n, &n, &c_b17, &c_b17, &a[a_offset], 
                                lda);
                    }
                } else {
                    in = n;
                }
                dlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1], 
                        &kz2[kazero[jtype - 1] - 1], &iasign[jtype - 1], &
                        rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype - 
                        1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
                        a_offset], lda);
                iadd = kadd[kazero[jtype - 1] - 1];
                if (iadd > 0 && iadd <= n) {
                    a[iadd + iadd * a_dim1] = 1.;
                }

/*              Generate B (w/o rotation) */

                if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
                    in = ((n - 1) / 2 << 1) + 1;
                    if (in != n) {
                        dlaset_("Full", &n, &n, &c_b17, &c_b17, &b[b_offset], 
                                lda);
                    }
                } else {
                    in = n;
                }
                dlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1], 
                        &kz2[kbzero[jtype - 1] - 1], &ibsign[jtype - 1], &
                        rmagn[kbmagn[jtype - 1]], &c_b23, &rmagn[ktrian[jtype 
                        - 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
                        b_offset], lda);
                iadd = kadd[kbzero[jtype - 1] - 1];
                if (iadd != 0 && iadd <= n) {
                    b[iadd + iadd * b_dim1] = 1.;
                }

                if (kclass[jtype - 1] == 2 && n > 0) {

/*                 Include rotations */

/*                 Generate Q, Z as Householder transformations times */
/*                 a diagonal matrix. */

                    i__3 = n - 1;
                    for (jc = 1; jc <= i__3; ++jc) {
                        i__4 = n;
                        for (jr = jc; jr <= i__4; ++jr) {
                            q[jr + jc * q_dim1] = dlarnd_(&c__3, &iseed[1]);
                            z__[jr + jc * z_dim1] = dlarnd_(&c__3, &iseed[1]);
/* L30: */
                        }
                        i__4 = n + 1 - jc;
                        dlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc * 
                                q_dim1], &c__1, &work[jc]);
                        work[(n << 1) + jc] = d_sign(&c_b23, &q[jc + jc * 
                                q_dim1]);
                        q[jc + jc * q_dim1] = 1.;
                        i__4 = n + 1 - jc;
                        dlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 + 
                                jc * z_dim1], &c__1, &work[n + jc]);
                        work[n * 3 + jc] = d_sign(&c_b23, &z__[jc + jc * 
                                z_dim1]);
                        z__[jc + jc * z_dim1] = 1.;
/* L40: */
                    }
                    q[n + n * q_dim1] = 1.;
                    work[n] = 0.;
                    d__1 = dlarnd_(&c__2, &iseed[1]);
                    work[n * 3] = d_sign(&c_b23, &d__1);
                    z__[n + n * z_dim1] = 1.;
                    work[n * 2] = 0.;
                    d__1 = dlarnd_(&c__2, &iseed[1]);
                    work[n * 4] = d_sign(&c_b23, &d__1);

/*                 Apply the diagonal matrices */

                    i__3 = n;
                    for (jc = 1; jc <= i__3; ++jc) {
                        i__4 = n;
                        for (jr = 1; jr <= i__4; ++jr) {
                            a[jr + jc * a_dim1] = work[(n << 1) + jr] * work[
                                    n * 3 + jc] * a[jr + jc * a_dim1];
                            b[jr + jc * b_dim1] = work[(n << 1) + jr] * work[
                                    n * 3 + jc] * b[jr + jc * b_dim1];
/* L50: */
                        }
/* L60: */
                    }
                    i__3 = n - 1;
                    dorm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
                            1], &a[a_offset], lda, &work[(n << 1) + 1], &ierr);
                    if (ierr != 0) {
                        goto L90;
                    }
                    i__3 = n - 1;
                    dorm2r_("R", "T", &n, &n, &i__3, &z__[z_offset], ldq, &
                            work[n + 1], &a[a_offset], lda, &work[(n << 1) + 
                            1], &ierr);
                    if (ierr != 0) {
                        goto L90;
                    }
                    i__3 = n - 1;
                    dorm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
                            1], &b[b_offset], lda, &work[(n << 1) + 1], &ierr);
                    if (ierr != 0) {
                        goto L90;
                    }
                    i__3 = n - 1;
                    dorm2r_("R", "T", &n, &n, &i__3, &z__[z_offset], ldq, &
                            work[n + 1], &b[b_offset], lda, &work[(n << 1) + 
                            1], &ierr);
                    if (ierr != 0) {
                        goto L90;
                    }
                }
            } else {

/*              Random matrices */

                i__3 = n;
                for (jc = 1; jc <= i__3; ++jc) {
                    i__4 = n;
                    for (jr = 1; jr <= i__4; ++jr) {
                        a[jr + jc * a_dim1] = rmagn[kamagn[jtype - 1]] * 
                                dlarnd_(&c__2, &iseed[1]);
                        b[jr + jc * b_dim1] = rmagn[kbmagn[jtype - 1]] * 
                                dlarnd_(&c__2, &iseed[1]);
/* L70: */
                    }
/* L80: */
                }
            }

L90:

            if (ierr != 0) {
                io___38.ciunit = *nounit;
                s_wsfe(&io___38);
                do_fio(&c__1, "Generator", (ftnlen)9);
                do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
                *info = abs(ierr);
                return 0;
            }

L100:

            for (i__ = 1; i__ <= 7; ++i__) {
                result[i__] = -1.;
/* L110: */
            }

/*           Call DGGEV to compute eigenvalues and eigenvectors. */

            dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
            dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
            dggev_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
                    alphar[1], &alphai[1], &beta[1], &q[q_offset], ldq, &z__[
                    z_offset], ldq, &work[1], lwork, &ierr);
            if (ierr != 0 && ierr != n + 1) {
                result[1] = ulpinv;
                io___40.ciunit = *nounit;
                s_wsfe(&io___40);
                do_fio(&c__1, "DGGEV1", (ftnlen)6);
                do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
                *info = abs(ierr);
                goto L190;
            }

/*           Do the tests (1) and (2) */

            dget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &q[
                    q_offset], ldq, &alphar[1], &alphai[1], &beta[1], &work[1]
, &result[1]);
            if (result[2] > *thresh) {
                io___41.ciunit = *nounit;
                s_wsfe(&io___41);
                do_fio(&c__1, "Left", (ftnlen)4);
                do_fio(&c__1, "DGGEV1", (ftnlen)6);
                do_fio(&c__1, (char *)&result[2], (ftnlen)sizeof(doublereal));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
            }

/*           Do the tests (3) and (4) */

            dget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &z__[
                    z_offset], ldq, &alphar[1], &alphai[1], &beta[1], &work[1]
, &result[3]);
            if (result[4] > *thresh) {
                io___42.ciunit = *nounit;
                s_wsfe(&io___42);
                do_fio(&c__1, "Right", (ftnlen)5);
                do_fio(&c__1, "DGGEV1", (ftnlen)6);
                do_fio(&c__1, (char *)&result[4], (ftnlen)sizeof(doublereal));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
            }

/*           Do the test (5) */

            dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
            dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
            dggev_("N", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
                    alphr1[1], &alphi1[1], &beta1[1], &q[q_offset], ldq, &z__[
                    z_offset], ldq, &work[1], lwork, &ierr);
            if (ierr != 0 && ierr != n + 1) {
                result[1] = ulpinv;
                io___43.ciunit = *nounit;
                s_wsfe(&io___43);
                do_fio(&c__1, "DGGEV2", (ftnlen)6);
                do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
                *info = abs(ierr);
                goto L190;
            }

            i__3 = n;
            for (j = 1; j <= i__3; ++j) {
                if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
                        j] != beta1[j]) {
                    result[5] = ulpinv;
                }
/* L120: */
            }

/*           Do the test (6): Compute eigenvalues and left eigenvectors, */
/*           and test them */

            dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
            dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
            dggev_("V", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
                    alphr1[1], &alphi1[1], &beta1[1], &qe[qe_offset], ldqe, &
                    z__[z_offset], ldq, &work[1], lwork, &ierr);
            if (ierr != 0 && ierr != n + 1) {
                result[1] = ulpinv;
                io___44.ciunit = *nounit;
                s_wsfe(&io___44);
                do_fio(&c__1, "DGGEV3", (ftnlen)6);
                do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
                *info = abs(ierr);
                goto L190;
            }

            i__3 = n;
            for (j = 1; j <= i__3; ++j) {
                if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
                        j] != beta1[j]) {
                    result[6] = ulpinv;
                }
/* L130: */
            }

            i__3 = n;
            for (j = 1; j <= i__3; ++j) {
                i__4 = n;
                for (jc = 1; jc <= i__4; ++jc) {
                    if (q[j + jc * q_dim1] != qe[j + jc * qe_dim1]) {
                        result[6] = ulpinv;
                    }
/* L140: */
                }
/* L150: */
            }

/*           DO the test (7): Compute eigenvalues and right eigenvectors, */
/*           and test them */

            dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
            dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
            dggev_("N", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
                    alphr1[1], &alphi1[1], &beta1[1], &q[q_offset], ldq, &qe[
                    qe_offset], ldqe, &work[1], lwork, &ierr);
            if (ierr != 0 && ierr != n + 1) {
                result[1] = ulpinv;
                io___45.ciunit = *nounit;
                s_wsfe(&io___45);
                do_fio(&c__1, "DGGEV4", (ftnlen)6);
                do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
                do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
                e_wsfe();
                *info = abs(ierr);
                goto L190;
            }

            i__3 = n;
            for (j = 1; j <= i__3; ++j) {
                if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
                        j] != beta1[j]) {
                    result[7] = ulpinv;
                }
/* L160: */
            }

            i__3 = n;
            for (j = 1; j <= i__3; ++j) {
                i__4 = n;
                for (jc = 1; jc <= i__4; ++jc) {
                    if (z__[j + jc * z_dim1] != qe[j + jc * qe_dim1]) {
                        result[7] = ulpinv;
                    }
/* L170: */
                }
/* L180: */
            }

/*           End of Loop -- Check for RESULT(j) > THRESH */

L190:

            ntestt += 7;

/*           Print out tests which fail. */

            for (jr = 1; jr <= 7; ++jr) {
                if (result[jr] >= *thresh) {

/*                 If this is the first test to fail, */
/*                 print a header to the data file. */

                    if (nerrs == 0) {
                        io___46.ciunit = *nounit;
                        s_wsfe(&io___46);
                        do_fio(&c__1, "DGV", (ftnlen)3);
                        e_wsfe();

/*                    Matrix types */

                        io___47.ciunit = *nounit;
                        s_wsfe(&io___47);
                        e_wsfe();
                        io___48.ciunit = *nounit;
                        s_wsfe(&io___48);
                        e_wsfe();
                        io___49.ciunit = *nounit;
                        s_wsfe(&io___49);
                        do_fio(&c__1, "Orthogonal", (ftnlen)10);
                        e_wsfe();

/*                    Tests performed */

                        io___50.ciunit = *nounit;
                        s_wsfe(&io___50);
                        e_wsfe();

                    }
                    ++nerrs;
                    if (result[jr] < 1e4) {
                        io___51.ciunit = *nounit;
                        s_wsfe(&io___51);
                        do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
                                ;
                        do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
                                integer));
                        do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
                                doublereal));
                        e_wsfe();
                    } else {
                        io___52.ciunit = *nounit;
                        s_wsfe(&io___52);
                        do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
                                ;
                        do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
                                integer));
                        do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
                        do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
                                doublereal));
                        e_wsfe();
                    }
                }
/* L200: */
            }

L210:
            ;
        }
/* L220: */
    }

/*     Summary */

    alasvm_("DGV", nounit, &nerrs, &ntestt, &c__0);

    work[1] = (doublereal) maxwrk;

    return 0;







/*     End of DDRGEV */

} /* ddrgev_ */