コード例 #1
0
ファイル: zgeesx.c プロジェクト: MichaelH13/sdkpub
/* Subroutine */ int zgeesx_(char *jobvs, char *sort, L_fp select, char *
	sense, integer *n, doublecomplex *a, integer *lda, integer *sdim, 
	doublecomplex *w, doublecomplex *vs, integer *ldvs, doublereal *
	rconde, doublereal *rcondv, doublecomplex *work, integer *lwork, 
	doublereal *rwork, logical *bwork, integer *info)
{
/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the   
    eigenvalues, the Schur form T, and, optionally, the matrix of Schur   
    vectors Z.  This gives the Schur factorization A = Z*T*(Z**H).   

    Optionally, it also orders the eigenvalues on the diagonal of the   
    Schur form so that selected eigenvalues are at the top left;   
    computes a reciprocal condition number for the average of the   
    selected eigenvalues (RCONDE); and computes a reciprocal condition   
    number for the right invariant subspace corresponding to the   
    selected eigenvalues (RCONDV).  The leading columns of Z form an   
    orthonormal basis for this invariant subspace.   

    For further explanation of the reciprocal condition numbers RCONDE   
    and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where   
    these quantities are called s and sep respectively).   

    A complex matrix is in Schur form if it is upper triangular.   

    Arguments   
    =========   

    JOBVS   (input) CHARACTER*1   
            = 'N': Schur vectors are not computed;   
            = 'V': Schur vectors are computed.   

    SORT    (input) CHARACTER*1   
            Specifies whether or not to order the eigenvalues on the   
            diagonal of the Schur form.   
            = 'N': Eigenvalues are not ordered;   
            = 'S': Eigenvalues are ordered (see SELECT).   

    SELECT  (input) LOGICAL FUNCTION of one COMPLEX*16 argument   
            SELECT must be declared EXTERNAL in the calling subroutine.   
            If SORT = 'S', SELECT is used to select eigenvalues to order   
            to the top left of the Schur form.   
            If SORT = 'N', SELECT is not referenced.   
            An eigenvalue W(j) is selected if SELECT(W(j)) is true.   

    SENSE   (input) CHARACTER*1   
            Determines which reciprocal condition numbers are computed.   
            = 'N': None are computed;   
            = 'E': Computed for average of selected eigenvalues only;   
            = 'V': Computed for selected right invariant subspace only;   
            = 'B': Computed for both.   
            If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.   

    N       (input) INTEGER   
            The order of the matrix A. N >= 0.   

    A       (input/output) COMPLEX*16 array, dimension (LDA, N)   
            On entry, the N-by-N matrix A.   
            On exit, A is overwritten by its Schur form T.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.  LDA >= max(1,N).   

    SDIM    (output) INTEGER   
            If SORT = 'N', SDIM = 0.   
            If SORT = 'S', SDIM = number of eigenvalues for which   
                           SELECT is true.   

    W       (output) COMPLEX*16 array, dimension (N)   
            W contains the computed eigenvalues, in the same order   
            that they appear on the diagonal of the output Schur form T.   

    VS      (output) COMPLEX*16 array, dimension (LDVS,N)   
            If JOBVS = 'V', VS contains the unitary matrix Z of Schur   
            vectors.   
            If JOBVS = 'N', VS is not referenced.   

    LDVS    (input) INTEGER   
            The leading dimension of the array VS.  LDVS >= 1, and if   
            JOBVS = 'V', LDVS >= N.   

    RCONDE  (output) DOUBLE PRECISION   
            If SENSE = 'E' or 'B', RCONDE contains the reciprocal   
            condition number for the average of the selected eigenvalues.   
            Not referenced if SENSE = 'N' or 'V'.   

    RCONDV  (output) DOUBLE PRECISION   
            If SENSE = 'V' or 'B', RCONDV contains the reciprocal   
            condition number for the selected right invariant subspace.   
            Not referenced if SENSE = 'N' or 'E'.   

    WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.  LWORK >= max(1,2*N).   
            Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),   
            where SDIM is the number of selected eigenvalues computed by   
            this routine.  Note that 2*SDIM*(N-SDIM) <= N*N/2.   
            For good performance, LWORK must generally be larger.   

    RWORK   (workspace) DOUBLE PRECISION array, dimension (N)   

    BWORK   (workspace) LOGICAL array, dimension (N)   
            Not referenced if SORT = 'N'.   

    INFO    (output) INTEGER   
            = 0: successful exit   
            < 0: if INFO = -i, the i-th argument had an illegal value.   
            > 0: if INFO = i, and i is   
               <= N: the QR algorithm failed to compute all the   
                     eigenvalues; elements 1:ILO-1 and i+1:N of W   
                     contain those eigenvalues which have converged; if   
                     JOBVS = 'V', VS contains the transformation which   
                     reduces A to its partially converged Schur form.   
               = N+1: the eigenvalues could not be reordered because some   
                     eigenvalues were too close to separate (the problem   
                     is very ill-conditioned);   
               = N+2: after reordering, roundoff changed values of some   
                     complex eigenvalues so that leading eigenvalues in   
                     the Schur form no longer satisfy SELECT=.TRUE.  This   
                     could also be caused by underflow due to scaling.   

    =====================================================================   


       Test the input arguments   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c__0 = 0;
    static integer c__8 = 8;
    static integer c_n1 = -1;
    static integer c__4 = 4;
    
    /* System generated locals */
    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer ibal, maxb;
    static doublereal anrm;
    static integer ierr, itau, iwrk, i__, k, icond, ieval;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    static logical scalea;
    extern doublereal dlamch_(char *);
    static doublereal cscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *), zgebak_(char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublecomplex *, 
	    integer *, integer *), zgebal_(char *, integer *, 
	    doublecomplex *, integer *, integer *, integer *, doublereal *, 
	    integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    static doublereal bignum;
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *);
    static logical wantsb, wantse;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    static integer minwrk, maxwrk;
    static logical wantsn;
    static doublereal smlnum;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    static integer hswork;
    extern /* Subroutine */ int zunghr_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *);
    static logical wantst, wantsv, wantvs;
    extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, integer *, integer *);
    static integer ihi, ilo;
    static doublereal dum[1], eps;


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --w;
    vs_dim1 = *ldvs;
    vs_offset = 1 + vs_dim1 * 1;
    vs -= vs_offset;
    --work;
    --rwork;
    --bwork;

    /* Function Body */
    *info = 0;
    wantvs = lsame_(jobvs, "V");
    wantst = lsame_(sort, "S");
    wantsn = lsame_(sense, "N");
    wantse = lsame_(sense, "E");
    wantsv = lsame_(sense, "V");
    wantsb = lsame_(sense, "B");
    if (! wantvs && ! lsame_(jobvs, "N")) {
	*info = -1;
    } else if (! wantst && ! lsame_(sort, "N")) {
	*info = -2;
    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
	    wantsn) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < max(1,*n)) {
	*info = -7;
    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
	*info = -11;
    }

/*     Compute workspace   
        (Note: Comments in the code beginning "Workspace:" describe the   
         minimal amount of real workspace needed at that point in the   
         code, as well as the preferred amount for good performance.   
         CWorkspace refers to complex workspace, and RWorkspace to real   
         workspace. NB refers to the optimal block size for the   
         immediately following subroutine, as returned by ILAENV.   
         HSWORK refers to the workspace preferred by ZHSEQR, as   
         calculated below. HSWORK is computed assuming ILO=1 and IHI=N,   
         the worst case.   
         If SENSE = 'E', 'V' or 'B', then the amount of workspace needed   
         depends on SDIM, which is computed by the routine ZTRSEN later   
         in the code.) */

    minwrk = 1;
    if (*info == 0 && *lwork >= 1) {
	maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
		ftnlen)6, (ftnlen)1);
/* Computing MAX */
	i__1 = 1, i__2 = *n << 1;
	minwrk = max(i__1,i__2);
	if (! wantvs) {
/* Computing MAX */
	    i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, (ftnlen)
		    6, (ftnlen)2);
	    maxb = max(i__1,2);
/* Computing MIN   
   Computing MAX */
	    i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
		    c_n1, (ftnlen)6, (ftnlen)2);
	    i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
	    k = min(i__1,i__2);
/* Computing MAX */
	    i__1 = k * (k + 2), i__2 = *n << 1;
	    hswork = max(i__1,i__2);
/* Computing MAX */
	    i__1 = max(maxwrk,hswork);
	    maxwrk = max(i__1,1);
	} else {
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", 
		    " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = ilaenv_(&c__8, "ZHSEQR", "SV", n, &c__1, n, &c_n1, (ftnlen)
		    6, (ftnlen)2);
	    maxb = max(i__1,2);
/* Computing MIN   
   Computing MAX */
	    i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SV", n, &c__1, n, &
		    c_n1, (ftnlen)6, (ftnlen)2);
	    i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
	    k = min(i__1,i__2);
/* Computing MAX */
	    i__1 = k * (k + 2), i__2 = *n << 1;
	    hswork = max(i__1,i__2);
/* Computing MAX */
	    i__1 = max(maxwrk,hswork);
	    maxwrk = max(i__1,1);
	}
	work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    }
    if (*lwork < minwrk) {
	*info = -15;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGEESX", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	*sdim = 0;
	return 0;
    }

/*     Get machine constants */

    eps = dlamch_("P");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
	scalea = TRUE_;
	cscale = smlnum;
    } else if (anrm > bignum) {
	scalea = TRUE_;
	cscale = bignum;
    }
    if (scalea) {
	zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
		ierr);
    }


/*     Permute the matrix to make it more nearly triangular   
       (CWorkspace: none)   
       (RWorkspace: need N) */

    ibal = 1;
    zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);

/*     Reduce to upper Hessenberg form   
       (CWorkspace: need 2*N, prefer N+N*NB)   
       (RWorkspace: none) */

    itau = 1;
    iwrk = *n + itau;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
	     &ierr);

    if (wantvs) {

/*        Copy Householder vectors to VS */

	zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
		;

/*        Generate unitary matrix in VS   
          (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)   
          (RWorkspace: none) */

	i__1 = *lwork - iwrk + 1;
	zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
		 &i__1, &ierr);
    }

    *sdim = 0;

/*     Perform QR iteration, accumulating Schur vectors in VS if desired   
       (CWorkspace: need 1, prefer HSWORK (see comments) )   
       (RWorkspace: none) */

    iwrk = itau;
    i__1 = *lwork - iwrk + 1;
    zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
	    vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
    if (ieval > 0) {
	*info = ieval;
    }

/*     Sort eigenvalues if desired */

    if (wantst && *info == 0) {
	if (scalea) {
	    zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
		    ierr);
	}
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    bwork[i__] = (*select)(&w[i__]);
/* L10: */
	}

/*        Reorder eigenvalues, transform Schur vectors, and compute   
          reciprocal condition numbers   
          (CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM)   
                       otherwise, need none )   
          (RWorkspace: none) */

	i__1 = *lwork - iwrk + 1;
	ztrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
		 ldvs, &w[1], sdim, rconde, rcondv, &work[iwrk], &i__1, &
		icond);
	if (! wantsn) {
/* Computing MAX */
	    i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
	    maxwrk = max(i__1,i__2);
	}
	if (icond == -14) {

/*           Not enough complex workspace */

	    *info = -15;
	}
    }

    if (wantvs) {

/*        Undo balancing   
          (CWorkspace: none)   
          (RWorkspace: need N) */

	zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset], 
		ldvs, &ierr);
    }

    if (scalea) {

/*        Undo scaling for the Schur form of A */

	zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
		ierr);
	i__1 = *lda + 1;
	zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
	if ((wantsv || wantsb) && *info == 0) {
	    dum[0] = *rcondv;
	    dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
		    c__1, &ierr);
	    *rcondv = dum[0];
	}
    }

    work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    return 0;

/*     End of ZGEESX */

} /* zgeesx_ */
コード例 #2
0
/* Subroutine */ int zerrhs_(char *path, integer *nunit)
{
    /* Format strings */
    static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
	    "rror exits\002,\002 (\002,i3,\002 tests done)\002)";
    static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
	    "ts of the error \002,\002exits ***\002)";

    /* System generated locals */
    integer i__1;
    doublereal d__1;

    /* Local variables */
    doublecomplex a[9]	/* was [3][3] */, c__[9]	/* was [3][3] */;
    integer i__, j, m;
    doublereal s[3];
    doublecomplex w[9], x[3];
    char c2[2];
    integer nt;
    doublecomplex vl[9]	/* was [3][3] */, vr[9]	/* was [3][3] */;
    doublereal rw[3];
    integer ihi, ilo;
    logical sel[3];
    doublecomplex tau[3];
    integer info, ifaill[3];
    extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublecomplex *, integer *, 
	    integer *), zgebal_(char *, integer *, 
	    doublecomplex *, integer *, integer *, integer *, doublereal *, 
	    integer *);
    integer ifailr[3];
    extern logical lsamen_(integer *, char *, char *);
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), chkxer_(char *, integer *, integer *, 
	    logical *, logical *), zhsein_(char *, char *, char *, 
	    logical *, integer *, doublecomplex *, integer *, doublecomplex *, 
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublecomplex *, doublereal *, integer *, integer *, 
	    integer *), zhseqr_(char *, char *, 
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, integer *), ztrevc_(char *, char *, 
	    logical *, integer *, doublecomplex *, integer *, doublecomplex *, 
	     integer *, doublecomplex *, integer *, integer *, integer *, 
	    doublecomplex *, doublereal *, integer *), 
	    zunghr_(integer *, integer *, integer *, doublecomplex *, integer 
	    *, doublecomplex *, doublecomplex *, integer *, integer *), 
	    zunmhr_(char *, char *, integer *, integer *, integer *, integer *
, doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___1 = { 0, 0, 0, 0, 0 };
    static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___23 = { 0, 0, 0, fmt_9998, 0 };



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

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

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

/*  ZERRHS tests the error exits for ZGEBAK, CGEBAL, CGEHRD, ZUNGHR, */
/*  ZUNMHR, ZHSEQR, CHSEIN, and ZTREVC. */

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

/*  PATH    (input) CHARACTER*3 */
/*          The LAPACK path name for the routines to be tested. */

/*  NUNIT   (input) INTEGER */
/*          The unit number for output. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Executable Statements .. */

    infoc_1.nout = *nunit;
    io___1.ciunit = infoc_1.nout;
    s_wsle(&io___1);
    e_wsle();
    s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);

/*     Set the variables to innocuous values. */

    for (j = 1; j <= 3; ++j) {
	for (i__ = 1; i__ <= 3; ++i__) {
	    i__1 = i__ + j * 3 - 4;
	    d__1 = 1. / (doublereal) (i__ + j);
	    a[i__1].r = d__1, a[i__1].i = 0.;
/* L10: */
	}
	sel[j - 1] = TRUE_;
/* L20: */
    }
    infoc_1.ok = TRUE_;
    nt = 0;

/*     Test error exits of the nonsymmetric eigenvalue routines. */

    if (lsamen_(&c__2, c2, "HS")) {

/*        ZGEBAL */

	s_copy(srnamc_1.srnamt, "ZGEBAL", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zgebal_("/", &c__0, a, &c__1, &ilo, &ihi, s, &info);
	chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zgebal_("N", &c_n1, a, &c__1, &ilo, &ihi, s, &info);
	chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zgebal_("N", &c__2, a, &c__1, &ilo, &ihi, s, &info);
	chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 3;

/*        ZGEBAK */

	s_copy(srnamc_1.srnamt, "ZGEBAK", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zgebak_("/", "R", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zgebak_("N", "/", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zgebak_("N", "R", &c_n1, &c__1, &c__0, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zgebak_("N", "R", &c__0, &c__0, &c__0, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zgebak_("N", "R", &c__0, &c__2, &c__0, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zgebak_("N", "R", &c__2, &c__2, &c__1, s, &c__0, a, &c__2, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zgebak_("N", "R", &c__0, &c__1, &c__1, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zgebak_("N", "R", &c__0, &c__1, &c__0, s, &c_n1, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 9;
	zgebak_("N", "R", &c__2, &c__1, &c__2, s, &c__0, a, &c__1, &info);
	chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 9;

/*        ZGEHRD */

	s_copy(srnamc_1.srnamt, "ZGEHRD", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zgehrd_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zgehrd_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zgehrd_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zgehrd_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zgehrd_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zgehrd_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__2, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zgehrd_(&c__2, &c__1, &c__2, a, &c__2, tau, w, &c__1, &info);
	chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 7;

/*        ZUNGHR */

	s_copy(srnamc_1.srnamt, "ZUNGHR", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zunghr_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zunghr_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zunghr_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zunghr_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zunghr_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zunghr_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zunghr_(&c__3, &c__1, &c__3, a, &c__3, tau, w, &c__1, &info);
	chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 7;

/*        ZUNMHR */

	s_copy(srnamc_1.srnamt, "ZUNMHR", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zunmhr_("/", "N", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zunmhr_("L", "/", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zunmhr_("L", "N", &c_n1, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zunmhr_("L", "N", &c__0, &c_n1, &c__1, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zunmhr_("L", "N", &c__0, &c__0, &c__0, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zunmhr_("L", "N", &c__0, &c__0, &c__2, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zunmhr_("L", "N", &c__1, &c__2, &c__2, &c__1, a, &c__1, tau, c__, &
		c__1, w, &c__2, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zunmhr_("R", "N", &c__2, &c__1, &c__2, &c__1, a, &c__1, tau, c__, &
		c__2, w, &c__2, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zunmhr_("L", "N", &c__1, &c__1, &c__1, &c__0, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zunmhr_("L", "N", &c__0, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	zunmhr_("R", "N", &c__1, &c__0, &c__1, &c__1, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zunmhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
		c__2, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	zunmhr_("R", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 11;
	zunmhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__2, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 13;
	zunmhr_("L", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
		c__1, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 13;
	zunmhr_("R", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
		c__2, w, &c__1, &info);
	chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 16;

/*        ZHSEQR */

	s_copy(srnamc_1.srnamt, "ZHSEQR", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zhseqr_("/", "N", &c__0, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zhseqr_("E", "/", &c__0, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zhseqr_("E", "N", &c_n1, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zhseqr_("E", "N", &c__0, &c__0, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	zhseqr_("E", "N", &c__0, &c__2, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zhseqr_("E", "N", &c__1, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zhseqr_("E", "N", &c__1, &c__1, &c__2, a, &c__1, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zhseqr_("E", "N", &c__2, &c__1, &c__2, a, &c__1, x, c__, &c__2, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	zhseqr_("E", "V", &c__2, &c__1, &c__2, a, &c__2, x, c__, &c__1, w, &
		c__1, &info);
	chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 9;

/*        ZHSEIN */

	s_copy(srnamc_1.srnamt, "ZHSEIN", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	zhsein_("/", "N", "N", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1, 
		&c__0, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	zhsein_("R", "/", "N", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1, 
		&c__0, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 3;
	zhsein_("R", "N", "/", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1, 
		&c__0, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 5;
	zhsein_("R", "N", "N", sel, &c_n1, a, &c__1, x, vl, &c__1, vr, &c__1, 
		&c__0, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 7;
	zhsein_("R", "N", "N", sel, &c__2, a, &c__1, x, vl, &c__1, vr, &c__2, 
		&c__4, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	zhsein_("L", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__1, 
		&c__4, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 12;
	zhsein_("R", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__1, 
		&c__4, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 13;
	zhsein_("R", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__2, 
		&c__1, &m, w, rw, ifaill, ifailr, &info);
	chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 8;

/*        ZTREVC */

	s_copy(srnamc_1.srnamt, "ZTREVC", (ftnlen)32, (ftnlen)6);
	infoc_1.infot = 1;
	ztrevc_("/", "A", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 2;
	ztrevc_("L", "/", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 4;
	ztrevc_("L", "A", sel, &c_n1, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 6;
	ztrevc_("L", "A", sel, &c__2, a, &c__1, vl, &c__2, vr, &c__1, &c__4, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 8;
	ztrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 10;
	ztrevc_("R", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	infoc_1.infot = 11;
	ztrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__2, vr, &c__1, &c__1, &
		m, w, rw, &info);
	chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
		infoc_1.ok);
	nt += 7;
    }

/*     Print a summary line. */

    if (infoc_1.ok) {
	io___22.ciunit = infoc_1.nout;
	s_wsfe(&io___22);
	do_fio(&c__1, path, (ftnlen)3);
	do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
	e_wsfe();
    } else {
	io___23.ciunit = infoc_1.nout;
	s_wsfe(&io___23);
	do_fio(&c__1, path, (ftnlen)3);
	e_wsfe();
    }


    return 0;

/*     End of ZERRHS */

} /* zerrhs_ */
コード例 #3
0
ファイル: zgeevx.c プロジェクト: flame/libflame
/* Subroutine */
int zgeevx_(char *balanc, char *jobvl, char *jobvr, char * sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm, doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer * lwork, doublereal *rwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;
    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);
    /* Local variables */
    integer i__, k;
    char job[1];
    doublereal scl, dum[1], eps;
    doublecomplex tmp;
    char side[1];
    doublereal anrm;
    integer ierr, itau, iwrk, nout, icond;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    logical scalea;
    extern doublereal dlamch_(char *);
    doublereal cscale;
    extern /* Subroutine */
    int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), zgebak_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublecomplex *, integer *, integer *), zgebal_(char *, integer *, doublecomplex *, integer *, integer *, integer *, doublereal *, integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */
    int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
    logical select[1];
    extern /* Subroutine */
    int zdscal_(integer *, doublereal *, doublecomplex *, integer *);
    doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *);
    extern /* Subroutine */
    int zgehrd_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    integer minwrk, maxwrk;
    logical wantvl, wntsnb;
    integer hswork;
    logical wntsne;
    doublereal smlnum;
    extern /* Subroutine */
    int zhseqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    logical lquery, wantvr;
    extern /* Subroutine */
    int ztrevc_(char *, char *, logical *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, doublecomplex *, doublereal *, integer *), ztrsna_(char *, char *, logical *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *), zunghr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *);
    logical wntsnn, wntsnv;
    /* -- LAPACK driver routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. Local Arrays .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test the input arguments */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --scale;
    --rconde;
    --rcondv;
    --work;
    --rwork;
    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    wantvl = lsame_(jobvl, "V");
    wantvr = lsame_(jobvr, "V");
    wntsnn = lsame_(sense, "N");
    wntsne = lsame_(sense, "E");
    wntsnv = lsame_(sense, "V");
    wntsnb = lsame_(sense, "B");
    if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") || lsame_(balanc, "B")))
    {
        *info = -1;
    }
    else if (! wantvl && ! lsame_(jobvl, "N"))
    {
        *info = -2;
    }
    else if (! wantvr && ! lsame_(jobvr, "N"))
    {
        *info = -3;
    }
    else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb) && ! (wantvl && wantvr))
    {
        *info = -4;
    }
    else if (*n < 0)
    {
        *info = -5;
    }
    else if (*lda < max(1,*n))
    {
        *info = -7;
    }
    else if (*ldvl < 1 || wantvl && *ldvl < *n)
    {
        *info = -10;
    }
    else if (*ldvr < 1 || wantvr && *ldvr < *n)
    {
        *info = -12;
    }
    /* 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. */
    /* CWorkspace refers to complex workspace, and RWorkspace to real */
    /* workspace. NB refers to the optimal block size for the */
    /* immediately following subroutine, as returned by ILAENV. */
    /* HSWORK refers to the workspace preferred by ZHSEQR, as */
    /* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
    /* the worst case.) */
    if (*info == 0)
    {
        if (*n == 0)
        {
            minwrk = 1;
            maxwrk = 1;
        }
        else
        {
            maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, & c__0);
            if (wantvl)
            {
                zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[1], &c_n1, info);
            }
            else if (wantvr)
            {
                zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[1], &c_n1, info);
            }
            else
            {
                if (wntsnn)
                {
                    zhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info);
                }
                else
                {
                    zhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info);
                }
            }
            hswork = (integer) work[1].r;
            if (! wantvl && ! wantvr)
            {
                minwrk = *n << 1;
                if (! (wntsnn || wntsne))
                {
                    /* Computing MAX */
                    i__1 = minwrk;
                    i__2 = *n * *n + (*n << 1); // , expr subst
                    minwrk = max(i__1,i__2);
                }
                maxwrk = max(maxwrk,hswork);
                if (! (wntsnn || wntsne))
                {
                    /* Computing MAX */
                    i__1 = maxwrk;
                    i__2 = *n * *n + (*n << 1); // , expr subst
                    maxwrk = max(i__1,i__2);
                }
            }
            else
            {
                minwrk = *n << 1;
                if (! (wntsnn || wntsne))
                {
                    /* Computing MAX */
                    i__1 = minwrk;
                    i__2 = *n * *n + (*n << 1); // , expr subst
                    minwrk = max(i__1,i__2);
                }
                maxwrk = max(maxwrk,hswork);
                /* Computing MAX */
                i__1 = maxwrk;
                i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", " ", n, &c__1, n, &c_n1); // , expr subst
                maxwrk = max(i__1,i__2);
                if (! (wntsnn || wntsne))
                {
                    /* Computing MAX */
                    i__1 = maxwrk;
                    i__2 = *n * *n + (*n << 1); // , expr subst
                    maxwrk = max(i__1,i__2);
                }
                /* Computing MAX */
                i__1 = maxwrk;
                i__2 = *n << 1; // , expr subst
                maxwrk = max(i__1,i__2);
            }
            maxwrk = max(maxwrk,minwrk);
        }
        work[1].r = (doublereal) maxwrk;
        work[1].i = 0.; // , expr subst
        if (*lwork < minwrk && ! lquery)
        {
            *info = -20;
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZGEEVX", &i__1);
        return 0;
    }
    else if (lquery)
    {
        return 0;
    }
    /* Quick return if possible */
    if (*n == 0)
    {
        return 0;
    }
    /* Get machine constants */
    eps = dlamch_("P");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;
    /* Scale A if max element outside range [SMLNUM,BIGNUM] */
    icond = 0;
    anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum)
    {
        scalea = TRUE_;
        cscale = smlnum;
    }
    else if (anrm > bignum)
    {
        scalea = TRUE_;
        cscale = bignum;
    }
    if (scalea)
    {
        zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & ierr);
    }
    /* Balance the matrix and compute ABNRM */
    zgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
    *abnrm = zlange_("1", n, n, &a[a_offset], lda, dum);
    if (scalea)
    {
        dum[0] = *abnrm;
        dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, & ierr);
        *abnrm = dum[0];
    }
    /* Reduce to upper Hessenberg form */
    /* (CWorkspace: need 2*N, prefer N+N*NB) */
    /* (RWorkspace: none) */
    itau = 1;
    iwrk = itau + *n;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, & ierr);
    if (wantvl)
    {
        /* Want left eigenvectors */
        /* Copy Householder vectors to VL */
        *(unsigned char *)side = 'L';
        zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl) ;
        /* Generate unitary matrix in VL */
        /* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
        /* (RWorkspace: none) */
        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], & i__1, &ierr);
        /* Perform QR iteration, accumulating Schur vectors in VL */
        /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /* (RWorkspace: none) */
        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[iwrk], &i__1, info);
        if (wantvr)
        {
            /* Want left and right eigenvectors */
            /* Copy Schur vectors to VR */
            *(unsigned char *)side = 'B';
            zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
        }
    }
    else if (wantvr)
    {
        /* Want right eigenvectors */
        /* Copy Householder vectors to VR */
        *(unsigned char *)side = 'R';
        zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr) ;
        /* Generate unitary matrix in VR */
        /* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
        /* (RWorkspace: none) */
        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], & i__1, &ierr);
        /* Perform QR iteration, accumulating Schur vectors in VR */
        /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /* (RWorkspace: none) */
        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info);
    }
    else
    {
        /* Compute eigenvalues only */
        /* If condition numbers desired, compute Schur form */
        if (wntsnn)
        {
            *(unsigned char *)job = 'E';
        }
        else
        {
            *(unsigned char *)job = 'S';
        }
        /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /* (RWorkspace: none) */
        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info);
    }
    /* If INFO > 0 from ZHSEQR, then quit */
    if (*info > 0)
    {
        goto L50;
    }
    if (wantvl || wantvr)
    {
        /* Compute left and/or right eigenvectors */
        /* (CWorkspace: need 2*N) */
        /* (RWorkspace: need N) */
        ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], & ierr);
    }
    /* Compute condition numbers if desired */
    /* (CWorkspace: need N*N+2*N unless SENSE = 'E') */
    /* (RWorkspace: need 2*N unless SENSE = 'E') */
    if (! wntsnn)
    {
        ztrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout, &work[iwrk], n, &rwork[1], &icond);
    }
    if (wantvl)
    {
        /* Undo balancing of left eigenvectors */
        zgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl, &ierr);
        /* Normalize left eigenvectors and make largest component real */
        i__1 = *n;
        for (i__ = 1;
                i__ <= i__1;
                ++i__)
        {
            scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
            zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
            i__2 = *n;
            for (k = 1;
                    k <= i__2;
                    ++k)
            {
                i__3 = k + i__ * vl_dim1;
                /* Computing 2nd power */
                d__1 = vl[i__3].r;
                /* Computing 2nd power */
                d__2 = d_imag(&vl[k + i__ * vl_dim1]);
                rwork[k] = d__1 * d__1 + d__2 * d__2;
                /* L10: */
            }
            k = idamax_(n, &rwork[1], &c__1);
            d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
            d__1 = sqrt(rwork[k]);
            z__1.r = z__2.r / d__1;
            z__1.i = z__2.i / d__1; // , expr subst
            tmp.r = z__1.r;
            tmp.i = z__1.i; // , expr subst
            zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
            i__2 = k + i__ * vl_dim1;
            i__3 = k + i__ * vl_dim1;
            d__1 = vl[i__3].r;
            z__1.r = d__1;
            z__1.i = 0.; // , expr subst
            vl[i__2].r = z__1.r;
            vl[i__2].i = z__1.i; // , expr subst
            /* L20: */
        }
    }
    if (wantvr)
    {
        /* Undo balancing of right eigenvectors */
        zgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr, &ierr);
        /* Normalize right eigenvectors and make largest component real */
        i__1 = *n;
        for (i__ = 1;
                i__ <= i__1;
                ++i__)
        {
            scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
            zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
            i__2 = *n;
            for (k = 1;
                    k <= i__2;
                    ++k)
            {
                i__3 = k + i__ * vr_dim1;
                /* Computing 2nd power */
                d__1 = vr[i__3].r;
                /* Computing 2nd power */
                d__2 = d_imag(&vr[k + i__ * vr_dim1]);
                rwork[k] = d__1 * d__1 + d__2 * d__2;
                /* L30: */
            }
            k = idamax_(n, &rwork[1], &c__1);
            d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
            d__1 = sqrt(rwork[k]);
            z__1.r = z__2.r / d__1;
            z__1.i = z__2.i / d__1; // , expr subst
            tmp.r = z__1.r;
            tmp.i = z__1.i; // , expr subst
            zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
            i__2 = k + i__ * vr_dim1;
            i__3 = k + i__ * vr_dim1;
            d__1 = vr[i__3].r;
            z__1.r = d__1;
            z__1.i = 0.; // , expr subst
            vr[i__2].r = z__1.r;
            vr[i__2].i = z__1.i; // , expr subst
            /* L40: */
        }
    }
    /* Undo scaling if necessary */
L50:
    if (scalea)
    {
        i__1 = *n - *info;
        /* Computing MAX */
        i__3 = *n - *info;
        i__2 = max(i__3,1);
        zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1] , &i__2, &ierr);
        if (*info == 0)
        {
            if ((wntsnv || wntsnb) && icond == 0)
            {
                dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[ 1], n, &ierr);
            }
        }
        else
        {
            i__1 = *ilo - 1;
            zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n, &ierr);
        }
    }
    work[1].r = (doublereal) maxwrk;
    work[1].i = 0.; // , expr subst
    return 0;
    /* End of ZGEEVX */
}
コード例 #4
0
ファイル: zchkhs.c プロジェクト: 3deggi/levmar-ndk
/* Subroutine */ int zchkhs_(integer *nsizes, integer *nn, integer *ntypes, 
	logical *dotype, integer *iseed, doublereal *thresh, integer *nounit, 
	doublecomplex *a, integer *lda, doublecomplex *h__, doublecomplex *t1, 
	 doublecomplex *t2, doublecomplex *u, integer *ldu, doublecomplex *
	z__, doublecomplex *uz, doublecomplex *w1, doublecomplex *w3, 
	doublecomplex *evectl, doublecomplex *evectr, doublecomplex *evecty, 
	doublecomplex *evectx, doublecomplex *uu, doublecomplex *tau, 
	doublecomplex *work, integer *nwork, doublereal *rwork, integer *
	iwork, logical *select, doublereal *result, integer *info)
{
    /* Initialized data */

    static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
    static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
    static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
    static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };

    /* Format strings */
    static char fmt_9999[] = "(\002 ZCHKHS: \002,a,\002 returned INFO=\002,i"
	    "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
	    "(\002,3(i5,\002,\002),i5,\002)\002)";
    static char fmt_9998[] = "(\002 ZCHKHS: \002,a,\002 Eigenvectors from"
	    " \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
	    "error=\002,0p,g10.3,\002,\002,9x,\002N=\002,i6,\002, JTYPE=\002,"
	    "i6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
    static char fmt_9997[] = "(\002 ZCHKHS: Selected \002,a,\002 Eigenvector"
	    "s from \002,a,\002 do not match other eigenvectors \002,9x,\002N="
	    "\002,i6,\002, JTYPE=\002,i6,\002, ISEED=(\002,3(i5,\002,\002),i5,"
	    "\002)\002)";

    /* System generated locals */
    integer a_dim1, a_offset, evectl_dim1, evectl_offset, evectr_dim1, 
	    evectr_offset, evectx_dim1, evectx_offset, evecty_dim1, 
	    evecty_offset, h_dim1, h_offset, t1_dim1, t1_offset, t2_dim1, 
	    t2_offset, u_dim1, u_offset, uu_dim1, uu_offset, uz_dim1, 
	    uz_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    doublereal d__1, d__2;
    doublecomplex z__1;

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

    /* Local variables */
    integer i__, j, k, n, n1, jj, in, ihi, ilo;
    doublereal ulp, cond;
    integer jcol, nmax;
    doublereal unfl, ovfl, temp1, temp2;
    logical badnn, match;
    integer imode;
    doublereal dumma[4];
    integer iinfo;
    doublereal conds;
    extern /* Subroutine */ int zget10_(integer *, integer *, doublecomplex *, 
	     integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublereal *, doublereal *);
    doublereal aninv, anorm;
    extern /* Subroutine */ int zget22_(char *, char *, char *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, doublereal *, doublereal *), zgemm_(char *, char *, integer *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, integer *, 
	     doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    integer nmats, jsize, nerrs, itype, jtype, ntest;
    extern /* Subroutine */ int zhst01_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublereal *, doublereal *), zcopy_(integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *);
    doublereal rtulp;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    doublecomplex cdumma[4];
    integer idumma[1];
    extern /* Subroutine */ int dlafts_(char *, integer *, integer *, integer 
	    *, integer *, doublereal *, integer *, doublereal *, integer *, 
	    integer *);
    integer ioldsd[4];
    extern /* Subroutine */ int xerbla_(char *, integer *), zgehrd_(
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, integer *), dlasum_(
	    char *, integer *, integer *, integer *), zlatme_(integer 
	    *, char *, integer *, doublecomplex *, integer *, doublereal *, 
	    doublecomplex *, char *, char *, char *, char *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, doublereal *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), zhsein_(char *, char *, char *, 
	    logical *, integer *, doublecomplex *, integer *, doublecomplex *, 
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublecomplex *, doublereal *, integer *, integer *, 
	    integer *), zlacpy_(char *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *), zlatmr_(
	    integer *, integer *, char *, integer *, char *, doublecomplex *, 
	    integer *, doublereal *, doublecomplex *, char *, char *, 
	    doublecomplex *, integer *, doublereal *, doublecomplex *, 
	    integer *, doublereal *, char *, integer *, integer *, integer *, 
	    doublereal *, doublereal *, char *, doublecomplex *, integer *, 
	    integer *, integer *);
    doublereal rtunfl, rtovfl, rtulpi, ulpinv;
    integer mtypes, ntestt;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, 
	     char *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, char *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), ztrevc_(char 
	    *, char *, logical *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *, 
	     integer *, doublecomplex *, doublereal *, integer *), zunghr_(integer *, integer *, integer *, doublecomplex *, 
	     integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zunmhr_(char *, char *, integer *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___35 = { 0, 0, 0, fmt_9999, 0 };
    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_9999, 0 };
    static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___50 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___54 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___55 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___56 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___57 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___58 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___59 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___60 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___61 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___62 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___63 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___64 = { 0, 0, 0, fmt_9999, 0 };



/*  -- LAPACK test routine (version 3.1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     February 2007 */

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

/*  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: */
/*     ---- ----- --------- --- ---------- */

/*     ZERO, ONE       Real 0 and 1. */
/*     MAXTYP          The number of types defined. */
/*     MTEST           The number of tests defined: care must be taken */
/*                     that (1) the size of RESULT, (2) the number of */
/*                     tests actually performed, and (3) MTEST agree. */
/*     NTEST           The number of tests performed on this matrix */
/*                     so far.  This should be less than MTEST, and */
/*                     equal to it by the last test.  It will be less */
/*                     if any of the routines being tested indicates */
/*                     that it could not compute the matrices that */
/*                     would be tested. */
/*     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, 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. */
/*     RTOVFL, RTUNFL, */
/*     RTULP, RTULPI   Square roots of the previous 4 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) ) */
/*     KCONDS(j)       Selects whether CONDS is to be 1 or */
/*                     1/sqrt(ulp).  (0 means irrelevant.) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --nn;
    --dotype;
    --iseed;
    t2_dim1 = *lda;
    t2_offset = 1 + t2_dim1;
    t2 -= t2_offset;
    t1_dim1 = *lda;
    t1_offset = 1 + t1_dim1;
    t1 -= t1_offset;
    h_dim1 = *lda;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    uu_dim1 = *ldu;
    uu_offset = 1 + uu_dim1;
    uu -= uu_offset;
    evectx_dim1 = *ldu;
    evectx_offset = 1 + evectx_dim1;
    evectx -= evectx_offset;
    evecty_dim1 = *ldu;
    evecty_offset = 1 + evecty_dim1;
    evecty -= evecty_offset;
    evectr_dim1 = *ldu;
    evectr_offset = 1 + evectr_dim1;
    evectr -= evectr_offset;
    evectl_dim1 = *ldu;
    evectl_offset = 1 + evectl_dim1;
    evectl -= evectl_offset;
    uz_dim1 = *ldu;
    uz_offset = 1 + uz_dim1;
    uz -= uz_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    --w1;
    --w3;
    --tau;
    --work;
    --rwork;
    --iwork;
    --select;
    --result;

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

/*     Check for errors */

    ntestt = 0;
    *info = 0;

    badnn = FALSE_;
    nmax = 0;
    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: */
    }

/*     Check for errors */

    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 (*ldu <= 1 || *ldu < nmax) {
	*info = -14;
    } else if ((nmax << 2) * nmax + 2 > *nwork) {
	*info = -26;
    }

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

/*     Quick return if possible */

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

/*     More important constants */

    unfl = dlamch_("Safe minimum");
    ovfl = dlamch_("Overflow");
    dlabad_(&unfl, &ovfl);
    ulp = dlamch_("Epsilon") * dlamch_("Base");
    ulpinv = 1. / ulp;
    rtunfl = sqrt(unfl);
    rtovfl = sqrt(ovfl);
    rtulp = sqrt(ulp);
    rtulpi = 1. / rtulp;

/*     Loop over sizes, types */

    nerrs = 0;
    nmats = 0;

    i__1 = *nsizes;
    for (jsize = 1; jsize <= i__1; ++jsize) {
	n = nn[jsize];
	n1 = max(1,n);
	aninv = 1. / (doublereal) n1;

	if (*nsizes != 1) {
	    mtypes = min(21,*ntypes);
	} else {
	    mtypes = min(22,*ntypes);
	}

	i__2 = mtypes;
	for (jtype = 1; jtype <= i__2; ++jtype) {
	    if (! dotype[jtype]) {
		goto L250;
	    }
	    ++nmats;
	    ntest = 0;

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

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

/*           Initialize RESULT */

	    for (j = 1; j <= 14; ++j) {
		result[j] = 0.;
/* L30: */
	    }

/*           Compute "A" */

/*           Control parameters: */

/*           KMAGN  KCONDS  KMODE        KTYPE */
/*       =1  O(1)   1       clustered 1  zero */
/*       =2  large  large   clustered 2  identity */
/*       =3  small          exponential  Jordan */
/*       =4                 arithmetic   diagonal, (w/ eigenvalues) */
/*       =5                 random log   hermitian, w/ eigenvalues */
/*       =6                 random       general, w/ eigenvalues */
/*       =7                              random diagonal */
/*       =8                              random hermitian */
/*       =9                              random general */
/*       =10                             random triangular */

	    if (mtypes > 21) {
		goto L100;
	    }

	    itype = ktype[jtype - 1];
	    imode = kmode[jtype - 1];

/*           Compute norm */

	    switch (kmagn[jtype - 1]) {
		case 1:  goto L40;
		case 2:  goto L50;
		case 3:  goto L60;
	    }

L40:
	    anorm = 1.;
	    goto L70;

L50:
	    anorm = rtovfl * ulp * aninv;
	    goto L70;

L60:
	    anorm = rtunfl * n * ulpinv;
	    goto L70;

L70:

	    zlaset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
	    iinfo = 0;
	    cond = ulpinv;

/*           Special Matrices */

	    if (itype == 1) {

/*              Zero */

		iinfo = 0;
	    } else if (itype == 2) {

/*              Identity */

		i__3 = n;
		for (jcol = 1; jcol <= i__3; ++jcol) {
		    i__4 = jcol + jcol * a_dim1;
		    a[i__4].r = anorm, a[i__4].i = 0.;
/* L80: */
		}

	    } else if (itype == 3) {

/*              Jordan Block */

		i__3 = n;
		for (jcol = 1; jcol <= i__3; ++jcol) {
		    i__4 = jcol + jcol * a_dim1;
		    a[i__4].r = anorm, a[i__4].i = 0.;
		    if (jcol > 1) {
			i__4 = jcol + (jcol - 1) * a_dim1;
			a[i__4].r = 1., a[i__4].i = 0.;
		    }
/* L90: */
		}

	    } else if (itype == 4) {

/*              Diagonal Matrix, [Eigen]values Specified */

		zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &imode, &cond, 
			&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
			n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
			c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
			1], &iinfo);

	    } else if (itype == 5) {

/*              Hermitian, eigenvalues specified */

		zlatms_(&n, &n, "D", &iseed[1], "H", &rwork[1], &imode, &cond, 
			 &anorm, &n, &n, "N", &a[a_offset], lda, &work[1], &
			iinfo);

	    } else if (itype == 6) {

/*              General, eigenvalues specified */

		if (kconds[jtype - 1] == 1) {
		    conds = 1.;
		} else if (kconds[jtype - 1] == 2) {
		    conds = rtulpi;
		} else {
		    conds = 0.;
		}

		zlatme_(&n, "D", &iseed[1], &work[1], &imode, &cond, &c_b2, 
			" ", "T", "T", "T", &rwork[1], &c__4, &conds, &n, &n, 
			&anorm, &a[a_offset], lda, &work[n + 1], &iinfo);

	    } else if (itype == 7) {

/*              Diagonal, random eigenvalues */

		zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27, 
			&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
			n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
			c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
			1], &iinfo);

	    } else if (itype == 8) {

/*              Hermitian, random eigenvalues */

		zlatmr_(&n, &n, "D", &iseed[1], "H", &work[1], &c__6, &c_b27, 
			&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
			n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
			c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
			iinfo);

	    } else if (itype == 9) {

/*              General, random eigenvalues */

		zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27, 
			&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
			n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
			c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
			iinfo);

	    } else if (itype == 10) {

/*              Triangular, random eigenvalues */

		zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27, 
			&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
			n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &c__0, &
			c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
			iinfo);

	    } else {

		iinfo = 1;
	    }

	    if (iinfo != 0) {
		io___35.ciunit = *nounit;
		s_wsfe(&io___35);
		do_fio(&c__1, "Generator", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		return 0;
	    }

L100:

/*           Call ZGEHRD to compute H and U, do tests. */

	    zlacpy_(" ", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
	    ntest = 1;

	    ilo = 1;
	    ihi = n;

	    i__3 = *nwork - n;
	    zgehrd_(&n, &ilo, &ihi, &h__[h_offset], lda, &work[1], &work[n + 
		    1], &i__3, &iinfo);

	    if (iinfo != 0) {
		result[1] = ulpinv;
		io___38.ciunit = *nounit;
		s_wsfe(&io___38);
		do_fio(&c__1, "ZGEHRD", (ftnlen)6);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

	    i__3 = n - 1;
	    for (j = 1; j <= i__3; ++j) {
		i__4 = j + 1 + j * uu_dim1;
		uu[i__4].r = 0., uu[i__4].i = 0.;
		i__4 = n;
		for (i__ = j + 2; i__ <= i__4; ++i__) {
		    i__5 = i__ + j * u_dim1;
		    i__6 = i__ + j * h_dim1;
		    u[i__5].r = h__[i__6].r, u[i__5].i = h__[i__6].i;
		    i__5 = i__ + j * uu_dim1;
		    i__6 = i__ + j * h_dim1;
		    uu[i__5].r = h__[i__6].r, uu[i__5].i = h__[i__6].i;
		    i__5 = i__ + j * h_dim1;
		    h__[i__5].r = 0., h__[i__5].i = 0.;
/* L110: */
		}
/* L120: */
	    }
	    i__3 = n - 1;
	    zcopy_(&i__3, &work[1], &c__1, &tau[1], &c__1);
	    i__3 = *nwork - n;
	    zunghr_(&n, &ilo, &ihi, &u[u_offset], ldu, &work[1], &work[n + 1], 
		     &i__3, &iinfo);
	    ntest = 2;

	    zhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &h__[h_offset], lda, &
		    u[u_offset], ldu, &work[1], nwork, &rwork[1], &result[1]);

/*           Call ZHSEQR to compute T1, T2 and Z, do tests. */

/*           Eigenvalues only (W3) */

	    zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
	    ntest = 3;
	    result[3] = ulpinv;

	    zhseqr_("E", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w3[1], &
		    uz[uz_offset], ldu, &work[1], nwork, &iinfo);
	    if (iinfo != 0) {
		io___40.ciunit = *nounit;
		s_wsfe(&io___40);
		do_fio(&c__1, "ZHSEQR(E)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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();
		if (iinfo <= n + 2) {
		    *info = abs(iinfo);
		    goto L240;
		}
	    }

/*           Eigenvalues (W1) and Full Schur Form (T2) */

	    zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);

	    zhseqr_("S", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w1[1], &
		    uz[uz_offset], ldu, &work[1], nwork, &iinfo);
	    if (iinfo != 0 && iinfo <= n + 2) {
		io___41.ciunit = *nounit;
		s_wsfe(&io___41);
		do_fio(&c__1, "ZHSEQR(S)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

/*           Eigenvalues (W1), Schur Form (T1), and Schur Vectors (UZ) */

	    zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t1[t1_offset], lda);
	    zlacpy_(" ", &n, &n, &u[u_offset], ldu, &uz[uz_offset], ldu);

	    zhseqr_("S", "V", &n, &ilo, &ihi, &t1[t1_offset], lda, &w1[1], &
		    uz[uz_offset], ldu, &work[1], nwork, &iinfo);
	    if (iinfo != 0 && iinfo <= n + 2) {
		io___42.ciunit = *nounit;
		s_wsfe(&io___42);
		do_fio(&c__1, "ZHSEQR(V)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

/*           Compute Z = U' UZ */

	    zgemm_("C", "N", &n, &n, &n, &c_b2, &u[u_offset], ldu, &uz[
		    uz_offset], ldu, &c_b1, &z__[z_offset], ldu);
	    ntest = 8;

/*           Do Tests 3: | H - Z T Z' | / ( |H| n ulp ) */
/*                and 4: | I - Z Z' | / ( n ulp ) */

	    zhst01_(&n, &ilo, &ihi, &h__[h_offset], lda, &t1[t1_offset], lda, 
		    &z__[z_offset], ldu, &work[1], nwork, &rwork[1], &result[
		    3]);

/*           Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp ) */
/*                and 6: | I - UZ (UZ)' | / ( n ulp ) */

	    zhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &t1[t1_offset], lda, &
		    uz[uz_offset], ldu, &work[1], nwork, &rwork[1], &result[5]
);

/*           Do Test 7: | T2 - T1 | / ( |T| n ulp ) */

	    zget10_(&n, &n, &t2[t2_offset], lda, &t1[t1_offset], lda, &work[1]
, &rwork[1], &result[7]);

/*           Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) */

	    temp1 = 0.;
	    temp2 = 0.;
	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
		d__1 = temp1, d__2 = z_abs(&w1[j]), d__1 = max(d__1,d__2), 
			d__2 = z_abs(&w3[j]);
		temp1 = max(d__1,d__2);
/* Computing MAX */
		i__4 = j;
		i__5 = j;
		z__1.r = w1[i__4].r - w3[i__5].r, z__1.i = w1[i__4].i - w3[
			i__5].i;
		d__1 = temp2, d__2 = z_abs(&z__1);
		temp2 = max(d__1,d__2);
/* L130: */
	    }

/* Computing MAX */
	    d__1 = unfl, d__2 = ulp * max(temp1,temp2);
	    result[8] = temp2 / max(d__1,d__2);

/*           Compute the Left and Right Eigenvectors of T */

/*           Compute the Right eigenvector Matrix: */

	    ntest = 9;
	    result[9] = ulpinv;

/*           Select every other eigenvector */

	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
		select[j] = FALSE_;
/* L140: */
	    }
	    i__3 = n;
	    for (j = 1; j <= i__3; j += 2) {
		select[j] = TRUE_;
/* L150: */
	    }
	    ztrevc_("Right", "All", &select[1], &n, &t1[t1_offset], lda, 
		    cdumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[
		    1], &rwork[1], &iinfo);
	    if (iinfo != 0) {
		io___47.ciunit = *nounit;
		s_wsfe(&io___47);
		do_fio(&c__1, "ZTREVC(R,A)", (ftnlen)11);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

/*           Test 9:  | TR - RW | / ( |T| |R| ulp ) */

	    zget22_("N", "N", "N", &n, &t1[t1_offset], lda, &evectr[
		    evectr_offset], ldu, &w1[1], &work[1], &rwork[1], dumma);
	    result[9] = dumma[0];
	    if (dumma[1] > *thresh) {
		io___49.ciunit = *nounit;
		s_wsfe(&io___49);
		do_fio(&c__1, "Right", (ftnlen)5);
		do_fio(&c__1, "ZTREVC", (ftnlen)6);
		do_fio(&c__1, (char *)&dumma[1], (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();
	    }

/*           Compute selected right eigenvectors and confirm that */
/*           they agree with previous right eigenvectors */

	    ztrevc_("Right", "Some", &select[1], &n, &t1[t1_offset], lda, 
		    cdumma, ldu, &evectl[evectl_offset], ldu, &n, &in, &work[
		    1], &rwork[1], &iinfo);
	    if (iinfo != 0) {
		io___50.ciunit = *nounit;
		s_wsfe(&io___50);
		do_fio(&c__1, "ZTREVC(R,S)", (ftnlen)11);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

	    k = 1;
	    match = TRUE_;
	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
		if (select[j]) {
		    i__4 = n;
		    for (jj = 1; jj <= i__4; ++jj) {
			i__5 = jj + j * evectr_dim1;
			i__6 = jj + k * evectl_dim1;
			if (evectr[i__5].r != evectl[i__6].r || evectr[i__5]
				.i != evectl[i__6].i) {
			    match = FALSE_;
			    goto L180;
			}
/* L160: */
		    }
		    ++k;
		}
/* L170: */
	    }
L180:
	    if (! match) {
		io___54.ciunit = *nounit;
		s_wsfe(&io___54);
		do_fio(&c__1, "Right", (ftnlen)5);
		do_fio(&c__1, "ZTREVC", (ftnlen)6);
		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();
	    }

/*           Compute the Left eigenvector Matrix: */

	    ntest = 10;
	    result[10] = ulpinv;
	    ztrevc_("Left", "All", &select[1], &n, &t1[t1_offset], lda, &
		    evectl[evectl_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
	    if (iinfo != 0) {
		io___55.ciunit = *nounit;
		s_wsfe(&io___55);
		do_fio(&c__1, "ZTREVC(L,A)", (ftnlen)11);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

/*           Test 10:  | LT - WL | / ( |T| |L| ulp ) */

	    zget22_("C", "N", "C", &n, &t1[t1_offset], lda, &evectl[
		    evectl_offset], ldu, &w1[1], &work[1], &rwork[1], &dumma[
		    2]);
	    result[10] = dumma[2];
	    if (dumma[3] > *thresh) {
		io___56.ciunit = *nounit;
		s_wsfe(&io___56);
		do_fio(&c__1, "Left", (ftnlen)4);
		do_fio(&c__1, "ZTREVC", (ftnlen)6);
		do_fio(&c__1, (char *)&dumma[3], (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();
	    }

/*           Compute selected left eigenvectors and confirm that */
/*           they agree with previous left eigenvectors */

	    ztrevc_("Left", "Some", &select[1], &n, &t1[t1_offset], lda, &
		    evectr[evectr_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
	    if (iinfo != 0) {
		io___57.ciunit = *nounit;
		s_wsfe(&io___57);
		do_fio(&c__1, "ZTREVC(L,S)", (ftnlen)11);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		goto L240;
	    }

	    k = 1;
	    match = TRUE_;
	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
		if (select[j]) {
		    i__4 = n;
		    for (jj = 1; jj <= i__4; ++jj) {
			i__5 = jj + j * evectl_dim1;
			i__6 = jj + k * evectr_dim1;
			if (evectl[i__5].r != evectr[i__6].r || evectl[i__5]
				.i != evectr[i__6].i) {
			    match = FALSE_;
			    goto L210;
			}
/* L190: */
		    }
		    ++k;
		}
/* L200: */
	    }
L210:
	    if (! match) {
		io___58.ciunit = *nounit;
		s_wsfe(&io___58);
		do_fio(&c__1, "Left", (ftnlen)4);
		do_fio(&c__1, "ZTREVC", (ftnlen)6);
		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();
	    }

/*           Call ZHSEIN for Right eigenvectors of H, do test 11 */

	    ntest = 11;
	    result[11] = ulpinv;
	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
		select[j] = TRUE_;
/* L220: */
	    }

	    zhsein_("Right", "Qr", "Ninitv", &select[1], &n, &h__[h_offset], 
		    lda, &w3[1], cdumma, ldu, &evectx[evectx_offset], ldu, &
		    n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
		    iinfo);
	    if (iinfo != 0) {
		io___59.ciunit = *nounit;
		s_wsfe(&io___59);
		do_fio(&c__1, "ZHSEIN(R)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		if (iinfo < 0) {
		    goto L240;
		}
	    } else {

/*              Test 11:  | HX - XW | / ( |H| |X| ulp ) */

/*                        (from inverse iteration) */

		zget22_("N", "N", "N", &n, &h__[h_offset], lda, &evectx[
			evectx_offset], ldu, &w3[1], &work[1], &rwork[1], 
			dumma);
		if (dumma[0] < ulpinv) {
		    result[11] = dumma[0] * aninv;
		}
		if (dumma[1] > *thresh) {
		    io___60.ciunit = *nounit;
		    s_wsfe(&io___60);
		    do_fio(&c__1, "Right", (ftnlen)5);
		    do_fio(&c__1, "ZHSEIN", (ftnlen)6);
		    do_fio(&c__1, (char *)&dumma[1], (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();
		}
	    }

/*           Call ZHSEIN for Left eigenvectors of H, do test 12 */

	    ntest = 12;
	    result[12] = ulpinv;
	    i__3 = n;
	    for (j = 1; j <= i__3; ++j) {
		select[j] = TRUE_;
/* L230: */
	    }

	    zhsein_("Left", "Qr", "Ninitv", &select[1], &n, &h__[h_offset], 
		    lda, &w3[1], &evecty[evecty_offset], ldu, cdumma, ldu, &
		    n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
		    iinfo);
	    if (iinfo != 0) {
		io___61.ciunit = *nounit;
		s_wsfe(&io___61);
		do_fio(&c__1, "ZHSEIN(L)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		if (iinfo < 0) {
		    goto L240;
		}
	    } else {

/*              Test 12:  | YH - WY | / ( |H| |Y| ulp ) */

/*                        (from inverse iteration) */

		zget22_("C", "N", "C", &n, &h__[h_offset], lda, &evecty[
			evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
			dumma[2]);
		if (dumma[2] < ulpinv) {
		    result[12] = dumma[2] * aninv;
		}
		if (dumma[3] > *thresh) {
		    io___62.ciunit = *nounit;
		    s_wsfe(&io___62);
		    do_fio(&c__1, "Left", (ftnlen)4);
		    do_fio(&c__1, "ZHSEIN", (ftnlen)6);
		    do_fio(&c__1, (char *)&dumma[3], (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();
		}
	    }

/*           Call ZUNMHR for Right eigenvectors of A, do test 13 */

	    ntest = 13;
	    result[13] = ulpinv;

	    zunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evectx[evectx_offset], ldu, &work[1], 
		    nwork, &iinfo);
	    if (iinfo != 0) {
		io___63.ciunit = *nounit;
		s_wsfe(&io___63);
		do_fio(&c__1, "ZUNMHR(L)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		if (iinfo < 0) {
		    goto L240;
		}
	    } else {

/*              Test 13:  | AX - XW | / ( |A| |X| ulp ) */

/*                        (from inverse iteration) */

		zget22_("N", "N", "N", &n, &a[a_offset], lda, &evectx[
			evectx_offset], ldu, &w3[1], &work[1], &rwork[1], 
			dumma);
		if (dumma[0] < ulpinv) {
		    result[13] = dumma[0] * aninv;
		}
	    }

/*           Call ZUNMHR for Left eigenvectors of A, do test 14 */

	    ntest = 14;
	    result[14] = ulpinv;

	    zunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evecty[evecty_offset], ldu, &work[1], 
		    nwork, &iinfo);
	    if (iinfo != 0) {
		io___64.ciunit = *nounit;
		s_wsfe(&io___64);
		do_fio(&c__1, "ZUNMHR(L)", (ftnlen)9);
		do_fio(&c__1, (char *)&iinfo, (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(iinfo);
		if (iinfo < 0) {
		    goto L240;
		}
	    } else {

/*              Test 14:  | YA - WY | / ( |A| |Y| ulp ) */

/*                        (from inverse iteration) */

		zget22_("C", "N", "C", &n, &a[a_offset], lda, &evecty[
			evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
			dumma[2]);
		if (dumma[2] < ulpinv) {
		    result[14] = dumma[2] * aninv;
		}
	    }

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

L240:

	    ntestt += ntest;
	    dlafts_("ZHS", &n, &n, &jtype, &ntest, &result[1], ioldsd, thresh, 
		     nounit, &nerrs);

L250:
	    ;
	}
/* L260: */
    }

/*     Summary */

    dlasum_("ZHS", nounit, &nerrs, &ntestt);

    return 0;


/*     End of ZCHKHS */

} /* zchkhs_ */
コード例 #5
0
ファイル: zgees.c プロジェクト: Electrostatics/FETK
/* Subroutine */ int zgees_(char *jobvs, char *sort, L_fp select, integer *n, 
	doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w, 
	doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork,
	 doublereal *rwork, logical *bwork, integer *info, ftnlen jobvs_len, 
	ftnlen sort_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    static integer i__, k;
    static doublereal s;
    static integer ihi, ilo;
    static doublereal dum[1], eps, sep;
    static integer ibal, maxb;
    static doublereal anrm;
    static integer ierr, itau, iwrk, icond, ieval;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    static logical scalea;
    extern doublereal dlamch_(char *, ftnlen);
    static doublereal cscale;
    extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublecomplex *, integer *, 
	    integer *, ftnlen, ftnlen), zgebal_(char *, integer *, 
	    doublecomplex *, integer *, integer *, integer *, doublereal *, 
	    integer *, ftnlen), xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *, ftnlen);
    static doublereal bignum;
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *, ftnlen), zlacpy_(char *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     ftnlen);
    static integer minwrk, maxwrk;
    static doublereal smlnum;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *,
	     ftnlen, ftnlen);
    static integer hswork;
    extern /* Subroutine */ int zunghr_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *);
    static logical wantst, lquery, wantvs;
    extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, integer *, integer *, ftnlen, ftnlen);


/*  -- LAPACK driver routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

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

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

/*  ZGEES computes for an N-by-N complex nonsymmetric matrix A, the */
/*  eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
/*  vectors Z.  This gives the Schur factorization A = Z*T*(Z**H). */

/*  Optionally, it also orders the eigenvalues on the diagonal of the */
/*  Schur form so that selected eigenvalues are at the top left. */
/*  The leading columns of Z then form an orthonormal basis for the */
/*  invariant subspace corresponding to the selected eigenvalues. */

/*  A complex matrix is in Schur form if it is upper triangular. */

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

/*  JOBVS   (input) CHARACTER*1 */
/*          = 'N': Schur vectors are not computed; */
/*          = 'V': Schur vectors are computed. */

/*  SORT    (input) CHARACTER*1 */
/*          Specifies whether or not to order the eigenvalues on the */
/*          diagonal of the Schur form. */
/*          = 'N': Eigenvalues are not ordered: */
/*          = 'S': Eigenvalues are ordered (see SELECT). */

/*  SELECT  (input) LOGICAL FUNCTION of one COMPLEX*16 argument */
/*          SELECT must be declared EXTERNAL in the calling subroutine. */
/*          If SORT = 'S', SELECT is used to select eigenvalues to order */
/*          to the top left of the Schur form. */
/*          IF SORT = 'N', SELECT is not referenced. */
/*          The eigenvalue W(j) is selected if SELECT(W(j)) is true. */

/*  N       (input) INTEGER */
/*          The order of the matrix A. N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, the N-by-N matrix A. */
/*          On exit, A has been overwritten by its Schur form T. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  SDIM    (output) INTEGER */
/*          If SORT = 'N', SDIM = 0. */
/*          If SORT = 'S', SDIM = number of eigenvalues for which */
/*                         SELECT is true. */

/*  W       (output) COMPLEX*16 array, dimension (N) */
/*          W contains the computed eigenvalues, in the same order that */
/*          they appear on the diagonal of the output Schur form T. */

/*  VS      (output) COMPLEX*16 array, dimension (LDVS,N) */
/*          If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
/*          vectors. */
/*          If JOBVS = 'N', VS is not referenced. */

/*  LDVS    (input) INTEGER */
/*          The leading dimension of the array VS.  LDVS >= 1; if */
/*          JOBVS = 'V', LDVS >= N. */

/*  WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK.  LWORK >= max(1,2*N). */
/*          For good performance, LWORK must generally be larger. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */

/*  BWORK   (workspace) LOGICAL array, dimension (N) */
/*          Not referenced if SORT = 'N'. */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value. */
/*          > 0: if INFO = i, and i is */
/*               <= N:  the QR algorithm failed to compute all the */
/*                      eigenvalues; elements 1:ILO-1 and i+1:N of W */
/*                      contain those eigenvalues which have converged; */
/*                      if JOBVS = 'V', VS contains the matrix which */
/*                      reduces A to its partially converged Schur form. */
/*               = N+1: the eigenvalues could not be reordered because */
/*                      some eigenvalues were too close to separate (the */
/*                      problem is very ill-conditioned); */
/*               = N+2: after reordering, roundoff changed values of */
/*                      some complex eigenvalues so that leading */
/*                      eigenvalues in the Schur form no longer satisfy */
/*                      SELECT = .TRUE..  This could also be caused by */
/*                      underflow due to scaling. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    vs_dim1 = *ldvs;
    vs_offset = 1 + vs_dim1;
    vs -= vs_offset;
    --work;
    --rwork;
    --bwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    wantvs = lsame_(jobvs, "V", (ftnlen)1, (ftnlen)1);
    wantst = lsame_(sort, "S", (ftnlen)1, (ftnlen)1);
    if (! wantvs && ! lsame_(jobvs, "N", (ftnlen)1, (ftnlen)1)) {
	*info = -1;
    } else if (! wantst && ! lsame_(sort, "N", (ftnlen)1, (ftnlen)1)) {
	*info = -2;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
	*info = -10;
    }

/*     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. */
/*       CWorkspace refers to complex workspace, and RWorkspace to real */
/*       workspace. NB refers to the optimal block size for the */
/*       immediately following subroutine, as returned by ILAENV. */
/*       HSWORK refers to the workspace preferred by ZHSEQR, as */
/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/*       the worst case.) */

    minwrk = 1;
    if (*info == 0 && (*lwork >= 1 || lquery)) {
	maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
		ftnlen)6, (ftnlen)1);
/* Computing MAX */
	i__1 = 1, i__2 = *n << 1;
	minwrk = max(i__1,i__2);
	if (! wantvs) {
/* Computing MAX */
	    i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, (ftnlen)
		    6, (ftnlen)2);
	    maxb = max(i__1,2);
/* Computing MIN */
/* Computing MAX */
	    i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
		    c_n1, (ftnlen)6, (ftnlen)2);
	    i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
	    k = min(i__1,i__2);
/* Computing MAX */
	    i__1 = k * (k + 2), i__2 = *n << 1;
	    hswork = max(i__1,i__2);
/* Computing MAX */
	    i__1 = max(maxwrk,hswork);
	    maxwrk = max(i__1,1);
	} else {
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", 
		    " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = ilaenv_(&c__8, "ZHSEQR", "EN", n, &c__1, n, &c_n1, (ftnlen)
		    6, (ftnlen)2);
	    maxb = max(i__1,2);
/* Computing MIN */
/* Computing MAX */
	    i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
		    c_n1, (ftnlen)6, (ftnlen)2);
	    i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
	    k = min(i__1,i__2);
/* Computing MAX */
	    i__1 = k * (k + 2), i__2 = *n << 1;
	    hswork = max(i__1,i__2);
/* Computing MAX */
	    i__1 = max(maxwrk,hswork);
	    maxwrk = max(i__1,1);
	}
	work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    }
    if (*lwork < minwrk && ! lquery) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGEES ", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	*sdim = 0;
	return 0;
    }

/*     Get machine constants */

    eps = dlamch_("P", (ftnlen)1);
    smlnum = dlamch_("S", (ftnlen)1);
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = zlange_("M", n, n, &a[a_offset], lda, dum, (ftnlen)1);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
	scalea = TRUE_;
	cscale = smlnum;
    } else if (anrm > bignum) {
	scalea = TRUE_;
	cscale = bignum;
    }
    if (scalea) {
	zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
		ierr, (ftnlen)1);
    }

/*     Permute the matrix to make it more nearly triangular */
/*     (CWorkspace: none) */
/*     (RWorkspace: need N) */

    ibal = 1;
    zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr, (
	    ftnlen)1);

/*     Reduce to upper Hessenberg form */
/*     (CWorkspace: need 2*N, prefer N+N*NB) */
/*     (RWorkspace: none) */

    itau = 1;
    iwrk = *n + itau;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
	     &ierr);

    if (wantvs) {

/*        Copy Householder vectors to VS */

	zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs, (ftnlen)1)
		;

/*        Generate unitary matrix in VS */
/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/*        (RWorkspace: none) */

	i__1 = *lwork - iwrk + 1;
	zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
		 &i__1, &ierr);
    }

    *sdim = 0;

/*     Perform QR iteration, accumulating Schur vectors in VS if desired */
/*     (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/*     (RWorkspace: none) */

    iwrk = itau;
    i__1 = *lwork - iwrk + 1;
    zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
	    vs_offset], ldvs, &work[iwrk], &i__1, &ieval, (ftnlen)1, (ftnlen)
	    1);
    if (ieval > 0) {
	*info = ieval;
    }

/*     Sort eigenvalues if desired */

    if (wantst && *info == 0) {
	if (scalea) {
	    zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
		    ierr, (ftnlen)1);
	}
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    bwork[i__] = (*select)(&w[i__]);
/* L10: */
	}

/*        Reorder eigenvalues and transform Schur vectors */
/*        (CWorkspace: none) */
/*        (RWorkspace: none) */

	i__1 = *lwork - iwrk + 1;
	ztrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset], 
		ldvs, &w[1], sdim, &s, &sep, &work[iwrk], &i__1, &icond, (
		ftnlen)1, (ftnlen)1);
    }

    if (wantvs) {

/*        Undo balancing */
/*        (CWorkspace: none) */
/*        (RWorkspace: need N) */

	zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset], 
		ldvs, &ierr, (ftnlen)1, (ftnlen)1);
    }

    if (scalea) {

/*        Undo scaling for the Schur form of A */

	zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
		ierr, (ftnlen)1);
	i__1 = *lda + 1;
	zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
    }

    work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    return 0;

/*     End of ZGEES */

} /* zgees_ */
コード例 #6
0
ファイル: zgeevx.c プロジェクト: Jell/image-recognition
/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char *
                             sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w,
                             doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr,
                             integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm,
                             doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer *
                             lwork, doublereal *rwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
            i__2, i__3;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, k;
    char job[1];
    doublereal scl, dum[1], eps;
    doublecomplex tmp;
    char side[1];
    doublereal anrm;
    integer ierr, itau, iwrk, nout, icond;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
                                       doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    logical scalea;
    extern doublereal dlamch_(char *);
    doublereal cscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
                                        doublereal *, doublereal *, integer *, integer *, doublereal *,
                                        integer *, integer *), zgebak_(char *, char *, integer *,
                                                integer *, integer *, doublereal *, integer *, doublecomplex *,
                                                integer *, integer *), zgebal_(char *, integer *,
                                                        doublecomplex *, integer *, integer *, integer *, doublereal *,
                                                        integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
                           integer *, integer *);
    logical select[1];
    extern /* Subroutine */ int zdscal_(integer *, doublereal *,
                                        doublecomplex *, integer *);
    doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
                              integer *, doublereal *);
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, doublecomplex *,
                                        integer *, integer *), zlascl_(char *, integer *, integer *,
                                                doublereal *, doublereal *, integer *, integer *, doublecomplex *,
                                                integer *, integer *), zlacpy_(char *, integer *,
                                                        integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    integer minwrk, maxwrk;
    logical wantvl, wntsnb;
    integer hswork;
    logical wntsne;
    doublereal smlnum;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
                                        integer *, doublecomplex *, integer *, doublecomplex *,
                                        doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    logical lquery, wantvr;
    extern /* Subroutine */ int ztrevc_(char *, char *, logical *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, integer *,
                                        doublecomplex *, integer *, integer *, integer *, doublecomplex *,
                                        doublereal *, integer *), ztrsna_(char *, char *,
                                                logical *, integer *, doublecomplex *, integer *, doublecomplex *
                                                , integer *, doublecomplex *, integer *, doublereal *, doublereal
                                                *, integer *, integer *, doublecomplex *, integer *, doublereal *,
                                                integer *), zunghr_(integer *, integer *,
                                                        integer *, doublecomplex *, integer *, doublecomplex *,
                                                        doublecomplex *, integer *, integer *);
    logical wntsnn, wntsnv;


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

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

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

    /*  ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */
    /*  eigenvalues and, optionally, the left and/or right eigenvectors. */

    /*  Optionally also, it computes a balancing transformation to improve */
    /*  the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
    /*  SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */
    /*  (RCONDE), and reciprocal condition numbers for the right */
    /*  eigenvectors (RCONDV). */

    /*  The right eigenvector v(j) of A satisfies */
    /*                   A * v(j) = lambda(j) * v(j) */
    /*  where lambda(j) is its eigenvalue. */
    /*  The left eigenvector u(j) of A satisfies */
    /*                u(j)**H * A = lambda(j) * u(j)**H */
    /*  where u(j)**H denotes the conjugate transpose of u(j). */

    /*  The computed eigenvectors are normalized to have Euclidean norm */
    /*  equal to 1 and largest component real. */

    /*  Balancing a matrix means permuting the rows and columns to make it */
    /*  more nearly upper triangular, and applying a diagonal similarity */
    /*  transformation D * A * D**(-1), where D is a diagonal matrix, to */
    /*  make its rows and columns closer in norm and the condition numbers */
    /*  of its eigenvalues and eigenvectors smaller.  The computed */
    /*  reciprocal condition numbers correspond to the balanced matrix. */
    /*  Permuting rows and columns will not change the condition numbers */
    /*  (in exact arithmetic) but diagonal scaling will.  For further */
    /*  explanation of balancing, see section 4.10.2 of the LAPACK */
    /*  Users' Guide. */

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

    /*  BALANC  (input) CHARACTER*1 */
    /*          Indicates how the input matrix should be diagonally scaled */
    /*          and/or permuted to improve the conditioning of its */
    /*          eigenvalues. */
    /*          = 'N': Do not diagonally scale or permute; */
    /*          = 'P': Perform permutations to make the matrix more nearly */
    /*                 upper triangular. Do not diagonally scale; */
    /*          = 'S': Diagonally scale the matrix, ie. replace A by */
    /*                 D*A*D**(-1), where D is a diagonal matrix chosen */
    /*                 to make the rows and columns of A more equal in */
    /*                 norm. Do not permute; */
    /*          = 'B': Both diagonally scale and permute A. */

    /*          Computed reciprocal condition numbers will be for the matrix */
    /*          after balancing and/or permuting. Permuting does not change */
    /*          condition numbers (in exact arithmetic), but balancing does. */

    /*  JOBVL   (input) CHARACTER*1 */
    /*          = 'N': left eigenvectors of A are not computed; */
    /*          = 'V': left eigenvectors of A are computed. */
    /*          If SENSE = 'E' or 'B', JOBVL must = 'V'. */

    /*  JOBVR   (input) CHARACTER*1 */
    /*          = 'N': right eigenvectors of A are not computed; */
    /*          = 'V': right eigenvectors of A are computed. */
    /*          If SENSE = 'E' or 'B', JOBVR must = 'V'. */

    /*  SENSE   (input) CHARACTER*1 */
    /*          Determines which reciprocal condition numbers are computed. */
    /*          = 'N': None are computed; */
    /*          = 'E': Computed for eigenvalues only; */
    /*          = 'V': Computed for right eigenvectors only; */
    /*          = 'B': Computed for eigenvalues and right eigenvectors. */

    /*          If SENSE = 'E' or 'B', both left and right eigenvectors */
    /*          must also be computed (JOBVL = 'V' and JOBVR = 'V'). */

    /*  N       (input) INTEGER */
    /*          The order of the matrix A. N >= 0. */

    /*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
    /*          On entry, the N-by-N matrix A. */
    /*          On exit, A has been overwritten.  If JOBVL = 'V' or */
    /*          JOBVR = 'V', A contains the Schur form of the balanced */
    /*          version of the matrix A. */

    /*  LDA     (input) INTEGER */
    /*          The leading dimension of the array A.  LDA >= max(1,N). */

    /*  W       (output) COMPLEX*16 array, dimension (N) */
    /*          W contains the computed eigenvalues. */

    /*  VL      (output) COMPLEX*16 array, dimension (LDVL,N) */
    /*          If JOBVL = 'V', the left eigenvectors u(j) are stored one */
    /*          after another in the columns of VL, in the same order */
    /*          as their eigenvalues. */
    /*          If JOBVL = 'N', VL is not referenced. */
    /*          u(j) = VL(:,j), the j-th column of VL. */

    /*  LDVL    (input) INTEGER */
    /*          The leading dimension of the array VL.  LDVL >= 1; if */
    /*          JOBVL = 'V', LDVL >= N. */

    /*  VR      (output) COMPLEX*16 array, dimension (LDVR,N) */
    /*          If JOBVR = 'V', the right eigenvectors v(j) are stored one */
    /*          after another in the columns of VR, in the same order */
    /*          as their eigenvalues. */
    /*          If JOBVR = 'N', VR is not referenced. */
    /*          v(j) = VR(:,j), the j-th column of VR. */

    /*  LDVR    (input) INTEGER */
    /*          The leading dimension of the array VR.  LDVR >= 1; if */
    /*          JOBVR = 'V', LDVR >= N. */

    /*  ILO     (output) INTEGER */
    /*  IHI     (output) INTEGER */
    /*          ILO and IHI are integer values determined when A was */
    /*          balanced.  The balanced A(i,j) = 0 if I > J and */
    /*          J = 1,...,ILO-1 or I = IHI+1,...,N. */

    /*  SCALE   (output) DOUBLE PRECISION array, dimension (N) */
    /*          Details of the permutations and scaling factors applied */
    /*          when balancing A.  If P(j) is the index of the row and column */
    /*          interchanged with row and column j, and D(j) is the scaling */
    /*          factor applied to row and column j, then */
    /*          SCALE(J) = P(J),    for J = 1,...,ILO-1 */
    /*                   = D(J),    for J = ILO,...,IHI */
    /*                   = P(J)     for J = IHI+1,...,N. */
    /*          The order in which the interchanges are made is N to IHI+1, */
    /*          then 1 to ILO-1. */

    /*  ABNRM   (output) DOUBLE PRECISION */
    /*          The one-norm of the balanced matrix (the maximum */
    /*          of the sum of absolute values of elements of any column). */

    /*  RCONDE  (output) DOUBLE PRECISION array, dimension (N) */
    /*          RCONDE(j) is the reciprocal condition number of the j-th */
    /*          eigenvalue. */

    /*  RCONDV  (output) DOUBLE PRECISION array, dimension (N) */
    /*          RCONDV(j) is the reciprocal condition number of the j-th */
    /*          right eigenvector. */

    /*  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
    /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

    /*  LWORK   (input) INTEGER */
    /*          The dimension of the array WORK.  If SENSE = 'N' or 'E', */
    /*          LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', */
    /*          LWORK >= N*N+2*N. */
    /*          For good performance, LWORK must generally be larger. */

    /*          If LWORK = -1, then a workspace query is assumed; the routine */
    /*          only calculates the optimal size of the WORK array, returns */
    /*          this value as the first entry of the WORK array, and no error */
    /*          message related to LWORK is issued by XERBLA. */

    /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N) */

    /*  INFO    (output) INTEGER */
    /*          = 0:  successful exit */
    /*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
    /*          > 0:  if INFO = i, the QR algorithm failed to compute all the */
    /*                eigenvalues, and no eigenvectors or condition numbers */
    /*                have been computed; elements 1:ILO-1 and i+1:N of W */
    /*                contain eigenvalues which have converged. */

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

    /*     .. Parameters .. */
    /*     .. */
    /*     .. Local Scalars .. */
    /*     .. */
    /*     .. Local Arrays .. */
    /*     .. */
    /*     .. External Subroutines .. */
    /*     .. */
    /*     .. External Functions .. */
    /*     .. */
    /*     .. Intrinsic Functions .. */
    /*     .. */
    /*     .. Executable Statements .. */

    /*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --scale;
    --rconde;
    --rcondv;
    --work;
    --rwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    wantvl = lsame_(jobvl, "V");
    wantvr = lsame_(jobvr, "V");
    wntsnn = lsame_(sense, "N");
    wntsne = lsame_(sense, "E");
    wntsnv = lsame_(sense, "V");
    wntsnb = lsame_(sense, "B");
    if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P")
            || lsame_(balanc, "B"))) {
        *info = -1;
    } else if (! wantvl && ! lsame_(jobvl, "N")) {
        *info = -2;
    } else if (! wantvr && ! lsame_(jobvr, "N")) {
        *info = -3;
    } else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
               && ! (wantvl && wantvr)) {
        *info = -4;
    } else if (*n < 0) {
        *info = -5;
    } else if (*lda < max(1,*n)) {
        *info = -7;
    } else if (*ldvl < 1 || wantvl && *ldvl < *n) {
        *info = -10;
    } else if (*ldvr < 1 || wantvr && *ldvr < *n) {
        *info = -12;
    }

    /*     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. */
    /*       CWorkspace refers to complex workspace, and RWorkspace to real */
    /*       workspace. NB refers to the optimal block size for the */
    /*       immediately following subroutine, as returned by ILAENV. */
    /*       HSWORK refers to the workspace preferred by ZHSEQR, as */
    /*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
    /*       the worst case.) */

    if (*info == 0) {
        if (*n == 0) {
            minwrk = 1;
            maxwrk = 1;
        } else {
            maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &
                                       c__0);

            if (wantvl) {
                zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
                            vl_offset], ldvl, &work[1], &c_n1, info);
            } else if (wantvr) {
                zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
                            vr_offset], ldvr, &work[1], &c_n1, info);
            } else {
                if (wntsnn) {
                    zhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
                            vr[vr_offset], ldvr, &work[1], &c_n1, info);
                } else {
                    zhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
                            vr[vr_offset], ldvr, &work[1], &c_n1, info);
                }
            }
            hswork = (integer) work[1].r;

            if (! wantvl && ! wantvr) {
                minwrk = *n << 1;
                if (! (wntsnn || wntsne)) {
                    /* Computing MAX */
                    i__1 = minwrk, i__2 = *n * *n + (*n << 1);
                    minwrk = max(i__1,i__2);
                }
                maxwrk = max(maxwrk,hswork);
                if (! (wntsnn || wntsne)) {
                    /* Computing MAX */
                    i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
                    maxwrk = max(i__1,i__2);
                }
            } else {
                minwrk = *n << 1;
                if (! (wntsnn || wntsne)) {
                    /* Computing MAX */
                    i__1 = minwrk, i__2 = *n * *n + (*n << 1);
                    minwrk = max(i__1,i__2);
                }
                maxwrk = max(maxwrk,hswork);
                /* Computing MAX */
                i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
                                      " ", n, &c__1, n, &c_n1);
                maxwrk = max(i__1,i__2);
                if (! (wntsnn || wntsne)) {
                    /* Computing MAX */
                    i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
                    maxwrk = max(i__1,i__2);
                }
                /* Computing MAX */
                i__1 = maxwrk, i__2 = *n << 1;
                maxwrk = max(i__1,i__2);
            }
            maxwrk = max(maxwrk,minwrk);
        }
        work[1].r = (doublereal) maxwrk, work[1].i = 0.;

        if (*lwork < minwrk && ! lquery) {
            *info = -20;
        }
    }

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

    /*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

    /*     Get machine constants */

    eps = dlamch_("P");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;

    /*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    icond = 0;
    anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
        scalea = TRUE_;
        cscale = smlnum;
    } else if (anrm > bignum) {
        scalea = TRUE_;
        cscale = bignum;
    }
    if (scalea) {
        zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
                ierr);
    }

    /*     Balance the matrix and compute ABNRM */

    zgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
    *abnrm = zlange_("1", n, n, &a[a_offset], lda, dum);
    if (scalea) {
        dum[0] = *abnrm;
        dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
                ierr);
        *abnrm = dum[0];
    }

    /*     Reduce to upper Hessenberg form */
    /*     (CWorkspace: need 2*N, prefer N+N*NB) */
    /*     (RWorkspace: none) */

    itau = 1;
    iwrk = itau + *n;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
            ierr);

    if (wantvl) {

        /*        Want left eigenvectors */
        /*        Copy Householder vectors to VL */

        *(unsigned char *)side = 'L';
        zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
        ;

        /*        Generate unitary matrix in VL */
        /*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
        /*        (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
                i__1, &ierr);

        /*        Perform QR iteration, accumulating Schur vectors in VL */
        /*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /*        (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[
                    vl_offset], ldvl, &work[iwrk], &i__1, info);

        if (wantvr) {

            /*           Want left and right eigenvectors */
            /*           Copy Schur vectors to VR */

            *(unsigned char *)side = 'B';
            zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
        }

    } else if (wantvr) {

        /*        Want right eigenvectors */
        /*        Copy Householder vectors to VR */

        *(unsigned char *)side = 'R';
        zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
        ;

        /*        Generate unitary matrix in VR */
        /*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
        /*        (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
                i__1, &ierr);

        /*        Perform QR iteration, accumulating Schur vectors in VR */
        /*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /*        (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
                    vr_offset], ldvr, &work[iwrk], &i__1, info);

    } else {

        /*        Compute eigenvalues only */
        /*        If condition numbers desired, compute Schur form */

        if (wntsnn) {
            *(unsigned char *)job = 'E';
        } else {
            *(unsigned char *)job = 'S';
        }

        /*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
        /*        (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
                    vr_offset], ldvr, &work[iwrk], &i__1, info);
    }

    /*     If INFO > 0 from ZHSEQR, then quit */

    if (*info > 0) {
        goto L50;
    }

    if (wantvl || wantvr) {

        /*        Compute left and/or right eigenvectors */
        /*        (CWorkspace: need 2*N) */
        /*        (RWorkspace: need N) */

        ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
                &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], &
                ierr);
    }

    /*     Compute condition numbers if desired */
    /*     (CWorkspace: need N*N+2*N unless SENSE = 'E') */
    /*     (RWorkspace: need 2*N unless SENSE = 'E') */

    if (! wntsnn) {
        ztrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset],
                ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout,
                &work[iwrk], n, &rwork[1], &icond);
    }

    if (wantvl) {

        /*        Undo balancing of left eigenvectors */

        zgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
                &ierr);

        /*        Normalize left eigenvectors and make largest component real */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
            zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
            i__2 = *n;
            for (k = 1; k <= i__2; ++k) {
                i__3 = k + i__ * vl_dim1;
                /* Computing 2nd power */
                d__1 = vl[i__3].r;
                /* Computing 2nd power */
                d__2 = d_imag(&vl[k + i__ * vl_dim1]);
                rwork[k] = d__1 * d__1 + d__2 * d__2;
                /* L10: */
            }
            k = idamax_(n, &rwork[1], &c__1);
            d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
            d__1 = sqrt(rwork[k]);
            z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
            tmp.r = z__1.r, tmp.i = z__1.i;
            zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
            i__2 = k + i__ * vl_dim1;
            i__3 = k + i__ * vl_dim1;
            d__1 = vl[i__3].r;
            z__1.r = d__1, z__1.i = 0.;
            vl[i__2].r = z__1.r, vl[i__2].i = z__1.i;
            /* L20: */
        }
    }

    if (wantvr) {

        /*        Undo balancing of right eigenvectors */

        zgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
                &ierr);

        /*        Normalize right eigenvectors and make largest component real */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
            zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
            i__2 = *n;
            for (k = 1; k <= i__2; ++k) {
                i__3 = k + i__ * vr_dim1;
                /* Computing 2nd power */
                d__1 = vr[i__3].r;
                /* Computing 2nd power */
                d__2 = d_imag(&vr[k + i__ * vr_dim1]);
                rwork[k] = d__1 * d__1 + d__2 * d__2;
                /* L30: */
            }
            k = idamax_(n, &rwork[1], &c__1);
            d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
            d__1 = sqrt(rwork[k]);
            z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
            tmp.r = z__1.r, tmp.i = z__1.i;
            zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
            i__2 = k + i__ * vr_dim1;
            i__3 = k + i__ * vr_dim1;
            d__1 = vr[i__3].r;
            z__1.r = d__1, z__1.i = 0.;
            vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
            /* L40: */
        }
    }

    /*     Undo scaling if necessary */

L50:
    if (scalea) {
        i__1 = *n - *info;
        /* Computing MAX */
        i__3 = *n - *info;
        i__2 = max(i__3,1);
        zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
                , &i__2, &ierr);
        if (*info == 0) {
            if ((wntsnv || wntsnb) && icond == 0) {
                dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
                            1], n, &ierr);
            }
        } else {
            i__1 = *ilo - 1;
            zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
                    &ierr);
        }
    }

    work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    return 0;

    /*     End of ZGEEVX */

} /* zgeevx_ */
コード例 #7
0
ファイル: zlaqr2.c プロジェクト: flame/libflame
/* Subroutine */
int zlaqr2_(logical *wantt, logical *wantz, integer *n, integer *ktop, integer *kbot, integer *nw, doublecomplex *h__, integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, integer *ldz, integer *ns, integer *nd, doublecomplex *sh, doublecomplex *v, integer *ldv, integer *nh, doublecomplex *t, integer *ldt, integer *nv, doublecomplex *wv, integer *ldwv, doublecomplex *work, integer *lwork)
{
    /* System generated locals */
    integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1, wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;
    doublecomplex z__1, z__2;
    /* Builtin functions */
    double d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);
    /* Local variables */
    integer i__, j;
    doublecomplex s;
    integer jw;
    doublereal foo;
    integer kln;
    doublecomplex tau;
    integer knt;
    doublereal ulp;
    integer lwk1, lwk2;
    doublecomplex beta;
    integer kcol, info, ifst, ilst, ltop, krow;
    extern /* Subroutine */
    int zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *);
    integer infqr;
    extern /* Subroutine */
    int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *);
    integer kwtop;
    extern /* Subroutine */
    int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    doublereal safmin, safmax;
    extern /* Subroutine */
    int zgehrd_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *), zlahqr_(logical *, logical *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *);
    doublereal smlnum;
    extern /* Subroutine */
    int ztrexc_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, integer *);
    integer lwkopt;
    extern /* Subroutine */
    int zunmhr_(char *, char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer * );
    /* -- LAPACK auxiliary routine (version 3.4.2) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* September 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ================================================================ */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Statement Functions .. */
    /* .. */
    /* .. Statement Function definitions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* ==== Estimate optimal workspace. ==== */
    /* Parameter adjustments */
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --sh;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    wv_dim1 = *ldwv;
    wv_offset = 1 + wv_dim1;
    wv -= wv_offset;
    --work;
    /* Function Body */
    /* Computing MIN */
    i__1 = *nw;
    i__2 = *kbot - *ktop + 1; // , expr subst
    jw = min(i__1,i__2);
    if (jw <= 2)
    {
        lwkopt = 1;
    }
    else
    {
        /* ==== Workspace query call to ZGEHRD ==== */
        i__1 = jw - 1;
        zgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], & c_n1, &info);
        lwk1 = (integer) work[1].r;
        /* ==== Workspace query call to ZUNMHR ==== */
        i__1 = jw - 1;
        zunmhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[1], &c_n1, &info);
        lwk2 = (integer) work[1].r;
        /* ==== Optimal workspace ==== */
        lwkopt = jw + max(lwk1,lwk2);
    }
    /* ==== Quick return in case of workspace query. ==== */
    if (*lwork == -1)
    {
        d__1 = (doublereal) lwkopt;
        z__1.r = d__1;
        z__1.i = 0.; // , expr subst
        work[1].r = z__1.r;
        work[1].i = z__1.i; // , expr subst
        return 0;
    }
    /* ==== Nothing to do ... */
    /* ... for an empty active block ... ==== */
    *ns = 0;
    *nd = 0;
    work[1].r = 1.;
    work[1].i = 0.; // , expr subst
    if (*ktop > *kbot)
    {
        return 0;
    }
    /* ... nor for an empty deflation window. ==== */
    if (*nw < 1)
    {
        return 0;
    }
    /* ==== Machine constants ==== */
    safmin = dlamch_("SAFE MINIMUM");
    safmax = 1. / safmin;
    dlabad_(&safmin, &safmax);
    ulp = dlamch_("PRECISION");
    smlnum = safmin * ((doublereal) (*n) / ulp);
    /* ==== Setup deflation window ==== */
    /* Computing MIN */
    i__1 = *nw;
    i__2 = *kbot - *ktop + 1; // , expr subst
    jw = min(i__1,i__2);
    kwtop = *kbot - jw + 1;
    if (kwtop == *ktop)
    {
        s.r = 0.;
        s.i = 0.; // , expr subst
    }
    else
    {
        i__1 = kwtop + (kwtop - 1) * h_dim1;
        s.r = h__[i__1].r;
        s.i = h__[i__1].i; // , expr subst
    }
    if (*kbot == kwtop)
    {
        /* ==== 1-by-1 deflation window: not much to do ==== */
        i__1 = kwtop;
        i__2 = kwtop + kwtop * h_dim1;
        sh[i__1].r = h__[i__2].r;
        sh[i__1].i = h__[i__2].i; // , expr subst
        *ns = 1;
        *nd = 0;
        /* Computing MAX */
        i__1 = kwtop + kwtop * h_dim1;
        d__5 = smlnum;
        d__6 = ulp * ((d__1 = h__[i__1].r, f2c_abs(d__1)) + (d__2 = d_imag(&h__[kwtop + kwtop * h_dim1]), f2c_abs(d__2))); // , expr subst
        if ((d__3 = s.r, f2c_abs(d__3)) + (d__4 = d_imag(&s), f2c_abs(d__4)) <= max( d__5,d__6))
        {
            *ns = 0;
            *nd = 1;
            if (kwtop > *ktop)
            {
                i__1 = kwtop + (kwtop - 1) * h_dim1;
                h__[i__1].r = 0.;
                h__[i__1].i = 0.; // , expr subst
            }
        }
        work[1].r = 1.;
        work[1].i = 0.; // , expr subst
        return 0;
    }
    /* ==== Convert to spike-triangular form. (In case of a */
    /* . rare QR failure, this routine continues to do */
    /* . aggressive early deflation using that part of */
    /* . the deflation window that converged using INFQR */
    /* . here and there to keep track.) ==== */
    zlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset], ldt);
    i__1 = jw - 1;
    i__2 = *ldh + 1;
    i__3 = *ldt + 1;
    zcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], & i__3);
    zlaset_("A", &jw, &jw, &c_b1, &c_b2, &v[v_offset], ldv);
    zlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
    /* ==== Deflation detection loop ==== */
    *ns = jw;
    ilst = infqr + 1;
    i__1 = jw;
    for (knt = infqr + 1;
            knt <= i__1;
            ++knt)
    {
        /* ==== Small spike tip deflation test ==== */
        i__2 = *ns + *ns * t_dim1;
        foo = (d__1 = t[i__2].r, f2c_abs(d__1)) + (d__2 = d_imag(&t[*ns + *ns * t_dim1]), f2c_abs(d__2));
        if (foo == 0.)
        {
            foo = (d__1 = s.r, f2c_abs(d__1)) + (d__2 = d_imag(&s), f2c_abs(d__2));
        }
        i__2 = *ns * v_dim1 + 1;
        /* Computing MAX */
        d__5 = smlnum;
        d__6 = ulp * foo; // , expr subst
        if (((d__1 = s.r, f2c_abs(d__1)) + (d__2 = d_imag(&s), f2c_abs(d__2))) * (( d__3 = v[i__2].r, f2c_abs(d__3)) + (d__4 = d_imag(&v[*ns * v_dim1 + 1]), f2c_abs(d__4))) <= max(d__5,d__6))
        {
            /* ==== One more converged eigenvalue ==== */
            --(*ns);
        }
        else
        {
            /* ==== One undeflatable eigenvalue. Move it up out of the */
            /* . way. (ZTREXC can not fail in this case.) ==== */
            ifst = *ns;
            ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, & ilst, &info);
            ++ilst;
        }
        /* L10: */
    }
    /* ==== Return to Hessenberg form ==== */
    if (*ns == 0)
    {
        s.r = 0.;
        s.i = 0.; // , expr subst
    }
    if (*ns < jw)
    {
        /* ==== sorting the diagonal of T improves accuracy for */
        /* . graded matrices. ==== */
        i__1 = *ns;
        for (i__ = infqr + 1;
                i__ <= i__1;
                ++i__)
        {
            ifst = i__;
            i__2 = *ns;
            for (j = i__ + 1;
                    j <= i__2;
                    ++j)
            {
                i__3 = j + j * t_dim1;
                i__4 = ifst + ifst * t_dim1;
                if ((d__1 = t[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&t[j + j * t_dim1]), f2c_abs(d__2)) > (d__3 = t[i__4].r, f2c_abs(d__3)) + (d__4 = d_imag(&t[ifst + ifst * t_dim1]), f2c_abs(d__4)) )
                {
                    ifst = j;
                }
                /* L20: */
            }
            ilst = i__;
            if (ifst != ilst)
            {
                ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &ilst, &info);
            }
            /* L30: */
        }
    }
    /* ==== Restore shift/eigenvalue array from T ==== */
    i__1 = jw;
    for (i__ = infqr + 1;
            i__ <= i__1;
            ++i__)
    {
        i__2 = kwtop + i__ - 1;
        i__3 = i__ + i__ * t_dim1;
        sh[i__2].r = t[i__3].r;
        sh[i__2].i = t[i__3].i; // , expr subst
        /* L40: */
    }
    if (*ns < jw || s.r == 0. && s.i == 0.)
    {
        if (*ns > 1 && (s.r != 0. || s.i != 0.))
        {
            /* ==== Reflect spike back into lower triangle ==== */
            zcopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
            i__1 = *ns;
            for (i__ = 1;
                    i__ <= i__1;
                    ++i__)
            {
                i__2 = i__;
                d_cnjg(&z__1, &work[i__]);
                work[i__2].r = z__1.r;
                work[i__2].i = z__1.i; // , expr subst
                /* L50: */
            }
            beta.r = work[1].r;
            beta.i = work[1].i; // , expr subst
            zlarfg_(ns, &beta, &work[2], &c__1, &tau);
            work[1].r = 1.;
            work[1].i = 0.; // , expr subst
            i__1 = jw - 2;
            i__2 = jw - 2;
            zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &t[t_dim1 + 3], ldt);
            d_cnjg(&z__1, &tau);
            zlarf_("L", ns, &jw, &work[1], &c__1, &z__1, &t[t_offset], ldt, & work[jw + 1]);
            zlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, & work[jw + 1]);
            zlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, & work[jw + 1]);
            i__1 = *lwork - jw;
            zgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1] , &i__1, &info);
        }
        /* ==== Copy updated reduced window into place ==== */
        if (kwtop > 1)
        {
            i__1 = kwtop + (kwtop - 1) * h_dim1;
            d_cnjg(&z__2, &v[v_dim1 + 1]);
            z__1.r = s.r * z__2.r - s.i * z__2.i;
            z__1.i = s.r * z__2.i + s.i * z__2.r; // , expr subst
            h__[i__1].r = z__1.r;
            h__[i__1].i = z__1.i; // , expr subst
        }
        zlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1] , ldh);
        i__1 = jw - 1;
        i__2 = *ldt + 1;
        i__3 = *ldh + 1;
        zcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1], &i__3);
        /* ==== Accumulate orthogonal matrix in order update */
        /* . H and Z, if requested. ==== */
        if (*ns > 1 && (s.r != 0. || s.i != 0.))
        {
            i__1 = *lwork - jw;
            zunmhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[jw + 1], &i__1, &info);
        }
        /* ==== Update vertical slab in H ==== */
        if (*wantt)
        {
            ltop = 1;
        }
        else
        {
            ltop = *ktop;
        }
        i__1 = kwtop - 1;
        i__2 = *nv;
        for (krow = ltop;
                i__2 < 0 ? krow >= i__1 : krow <= i__1;
                krow += i__2)
        {
            /* Computing MIN */
            i__3 = *nv;
            i__4 = kwtop - krow; // , expr subst
            kln = min(i__3,i__4);
            zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &h__[krow + kwtop * h_dim1], ldh, &v[v_offset], ldv, &c_b1, &wv[wv_offset], ldwv);
            zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop * h_dim1], ldh);
            /* L60: */
        }
        /* ==== Update horizontal slab in H ==== */
        if (*wantt)
        {
            i__2 = *n;
            i__1 = *nh;
            for (kcol = *kbot + 1;
                    i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
                    kcol += i__1)
            {
                /* Computing MIN */
                i__3 = *nh;
                i__4 = *n - kcol + 1; // , expr subst
                kln = min(i__3,i__4);
                zgemm_("C", "N", &jw, &kln, &jw, &c_b2, &v[v_offset], ldv, & h__[kwtop + kcol * h_dim1], ldh, &c_b1, &t[t_offset], ldt);
                zlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol * h_dim1], ldh);
                /* L70: */
            }
        }
        /* ==== Update vertical slab in Z ==== */
        if (*wantz)
        {
            i__1 = *ihiz;
            i__2 = *nv;
            for (krow = *iloz;
                    i__2 < 0 ? krow >= i__1 : krow <= i__1;
                    krow += i__2)
            {
                /* Computing MIN */
                i__3 = *nv;
                i__4 = *ihiz - krow + 1; // , expr subst
                kln = min(i__3,i__4);
                zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &z__[krow + kwtop * z_dim1], ldz, &v[v_offset], ldv, &c_b1, &wv[wv_offset] , ldwv);
                zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow + kwtop * z_dim1], ldz);
                /* L80: */
            }
        }
    }
    /* ==== Return the number of deflations ... ==== */
    *nd = jw - *ns;
    /* ==== ... and the number of shifts. (Subtracting */
    /* . INFQR from the spike length takes care */
    /* . of the case of a rare QR failure while */
    /* . calculating eigenvalues of the deflation */
    /* . window.) ==== */
    *ns -= infqr;
    /* ==== Return optimal workspace. ==== */
    d__1 = (doublereal) lwkopt;
    z__1.r = d__1;
    z__1.i = 0.; // , expr subst
    work[1].r = z__1.r;
    work[1].i = z__1.i; // , expr subst
    /* ==== End of ZLAQR2 ==== */
    return 0;
}
コード例 #8
0
ファイル: zlaqr3.c プロジェクト: 3deggi/levmar-ndk
/* Subroutine */ int zlaqr3_(logical *wantt, logical *wantz, integer *n, 
	integer *ktop, integer *kbot, integer *nw, doublecomplex *h__, 
	integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, 
	integer *ldz, integer *ns, integer *nd, doublecomplex *sh, 
	doublecomplex *v, integer *ldv, integer *nh, doublecomplex *t, 
	integer *ldt, integer *nv, doublecomplex *wv, integer *ldwv, 
	doublecomplex *work, integer *lwork)
{
    /* System generated locals */
    integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1, 
	    wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, j;
    doublecomplex s;
    integer jw;
    doublereal foo;
    integer kln;
    doublecomplex tau;
    integer knt;
    doublereal ulp;
    integer lwk1, lwk2, lwk3;
    doublecomplex beta;
    integer kcol, info, nmin, ifst, ilst, ltop, krow;
    extern /* Subroutine */ int zlarf_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *);
    integer infqr;
    extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    integer kwtop;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), dlabad_(doublereal *, doublereal *), 
	    zlaqr4_(logical *, logical *, integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *, 
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
);
    extern doublereal dlamch_(char *);
    doublereal safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    doublereal safmax;
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zlarfg_(integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *), zlahqr_(logical *, 
	    logical *, integer *, integer *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, integer *, doublecomplex *, 
	     integer *, integer *), zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *);
    doublereal smlnum;
    extern /* Subroutine */ int ztrexc_(char *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, integer *, integer *, 
	    integer *);
    integer lwkopt;
    extern /* Subroutine */ int zunmhr_(char *, char *, integer *, integer *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *, 
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
);


/*  -- LAPACK auxiliary routine (version 3.2.1)                        -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/*  -- April 2009                                                      -- */

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

/*     ****************************************************************** */
/*     Aggressive early deflation: */

/*     This subroutine accepts as input an upper Hessenberg matrix */
/*     H and performs an unitary similarity transformation */
/*     designed to detect and deflate fully converged eigenvalues from */
/*     a trailing principal submatrix.  On output H has been over- */
/*     written by a new Hessenberg matrix that is a perturbation of */
/*     an unitary similarity transformation of H.  It is to be */
/*     hoped that the final version of H has many zero subdiagonal */
/*     entries. */

/*     ****************************************************************** */
/*     WANTT   (input) LOGICAL */
/*          If .TRUE., then the Hessenberg matrix H is fully updated */
/*          so that the triangular Schur factor may be */
/*          computed (in cooperation with the calling subroutine). */
/*          If .FALSE., then only enough of H is updated to preserve */
/*          the eigenvalues. */

/*     WANTZ   (input) LOGICAL */
/*          If .TRUE., then the unitary matrix Z is updated so */
/*          so that the unitary Schur factor may be computed */
/*          (in cooperation with the calling subroutine). */
/*          If .FALSE., then Z is not referenced. */

/*     N       (input) INTEGER */
/*          The order of the matrix H and (if WANTZ is .TRUE.) the */
/*          order of the unitary matrix Z. */

/*     KTOP    (input) INTEGER */
/*          It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
/*          KBOT and KTOP together determine an isolated block */
/*          along the diagonal of the Hessenberg matrix. */

/*     KBOT    (input) INTEGER */
/*          It is assumed without a check that either */
/*          KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together */
/*          determine an isolated block along the diagonal of the */
/*          Hessenberg matrix. */

/*     NW      (input) INTEGER */
/*          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1). */

/*     H       (input/output) COMPLEX*16 array, dimension (LDH,N) */
/*          On input the initial N-by-N section of H stores the */
/*          Hessenberg matrix undergoing aggressive early deflation. */
/*          On output H has been transformed by a unitary */
/*          similarity transformation, perturbed, and the returned */
/*          to Hessenberg form that (it is to be hoped) has some */
/*          zero subdiagonal entries. */

/*     LDH     (input) integer */
/*          Leading dimension of H just as declared in the calling */
/*          subroutine.  N .LE. LDH */

/*     ILOZ    (input) INTEGER */
/*     IHIZ    (input) INTEGER */
/*          Specify the rows of Z to which transformations must be */
/*          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N. */

/*     Z       (input/output) COMPLEX*16 array, dimension (LDZ,N) */
/*          IF WANTZ is .TRUE., then on output, the unitary */
/*          similarity transformation mentioned above has been */
/*          accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. */
/*          If WANTZ is .FALSE., then Z is unreferenced. */

/*     LDZ     (input) integer */
/*          The leading dimension of Z just as declared in the */
/*          calling subroutine.  1 .LE. LDZ. */

/*     NS      (output) integer */
/*          The number of unconverged (ie approximate) eigenvalues */
/*          returned in SR and SI that may be used as shifts by the */
/*          calling subroutine. */

/*     ND      (output) integer */
/*          The number of converged eigenvalues uncovered by this */
/*          subroutine. */

/*     SH      (output) COMPLEX*16 array, dimension KBOT */
/*          On output, approximate eigenvalues that may */
/*          be used for shifts are stored in SH(KBOT-ND-NS+1) */
/*          through SR(KBOT-ND).  Converged eigenvalues are */
/*          stored in SH(KBOT-ND+1) through SH(KBOT). */

/*     V       (workspace) COMPLEX*16 array, dimension (LDV,NW) */
/*          An NW-by-NW work array. */

/*     LDV     (input) integer scalar */
/*          The leading dimension of V just as declared in the */
/*          calling subroutine.  NW .LE. LDV */

/*     NH      (input) integer scalar */
/*          The number of columns of T.  NH.GE.NW. */

/*     T       (workspace) COMPLEX*16 array, dimension (LDT,NW) */

/*     LDT     (input) integer */
/*          The leading dimension of T just as declared in the */
/*          calling subroutine.  NW .LE. LDT */

/*     NV      (input) integer */
/*          The number of rows of work array WV available for */
/*          workspace.  NV.GE.NW. */

/*     WV      (workspace) COMPLEX*16 array, dimension (LDWV,NW) */

/*     LDWV    (input) integer */
/*          The leading dimension of W just as declared in the */
/*          calling subroutine.  NW .LE. LDV */

/*     WORK    (workspace) COMPLEX*16 array, dimension LWORK. */
/*          On exit, WORK(1) is set to an estimate of the optimal value */
/*          of LWORK for the given values of N, NW, KTOP and KBOT. */

/*     LWORK   (input) integer */
/*          The dimension of the work array WORK.  LWORK = 2*NW */
/*          suffices, but greater efficiency may result from larger */
/*          values of LWORK. */

/*          If LWORK = -1, then a workspace query is assumed; ZLAQR3 */
/*          only estimates the optimal workspace size for the given */
/*          values of N, NW, KTOP and KBOT.  The estimate is returned */
/*          in WORK(1).  No error message related to LWORK is issued */
/*          by XERBLA.  Neither H nor Z are accessed. */

/*     ================================================================ */
/*     Based on contributions by */
/*        Karen Braman and Ralph Byers, Department of Mathematics, */
/*        University of Kansas, USA */

/*     ================================================================ */
/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     ==== Estimate optimal workspace. ==== */

    /* Parameter adjustments */
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --sh;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    wv_dim1 = *ldwv;
    wv_offset = 1 + wv_dim1;
    wv -= wv_offset;
    --work;

    /* Function Body */
/* Computing MIN */
    i__1 = *nw, i__2 = *kbot - *ktop + 1;
    jw = min(i__1,i__2);
    if (jw <= 2) {
	lwkopt = 1;
    } else {

/*        ==== Workspace query call to ZGEHRD ==== */

	i__1 = jw - 1;
	zgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
		c_n1, &info);
	lwk1 = (integer) work[1].r;

/*        ==== Workspace query call to ZUNMHR ==== */

	i__1 = jw - 1;
	zunmhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], 
		 &v[v_offset], ldv, &work[1], &c_n1, &info);
	lwk2 = (integer) work[1].r;

/*        ==== Workspace query call to ZLAQR4 ==== */

	zlaqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[1], 
		&c__1, &jw, &v[v_offset], ldv, &work[1], &c_n1, &infqr);
	lwk3 = (integer) work[1].r;

/*        ==== Optimal workspace ==== */

/* Computing MAX */
	i__1 = jw + max(lwk1,lwk2);
	lwkopt = max(i__1,lwk3);
    }

/*     ==== Quick return in case of workspace query. ==== */

    if (*lwork == -1) {
	d__1 = (doublereal) lwkopt;
	z__1.r = d__1, z__1.i = 0.;
	work[1].r = z__1.r, work[1].i = z__1.i;
	return 0;
    }

/*     ==== Nothing to do ... */
/*     ... for an empty active block ... ==== */
    *ns = 0;
    *nd = 0;
    work[1].r = 1., work[1].i = 0.;
    if (*ktop > *kbot) {
	return 0;
    }
/*     ... nor for an empty deflation window. ==== */
    if (*nw < 1) {
	return 0;
    }

/*     ==== Machine constants ==== */

    safmin = dlamch_("SAFE MINIMUM");
    safmax = 1. / safmin;
    dlabad_(&safmin, &safmax);
    ulp = dlamch_("PRECISION");
    smlnum = safmin * ((doublereal) (*n) / ulp);

/*     ==== Setup deflation window ==== */

/* Computing MIN */
    i__1 = *nw, i__2 = *kbot - *ktop + 1;
    jw = min(i__1,i__2);
    kwtop = *kbot - jw + 1;
    if (kwtop == *ktop) {
	s.r = 0., s.i = 0.;
    } else {
	i__1 = kwtop + (kwtop - 1) * h_dim1;
	s.r = h__[i__1].r, s.i = h__[i__1].i;
    }

    if (*kbot == kwtop) {

/*        ==== 1-by-1 deflation window: not much to do ==== */

	i__1 = kwtop;
	i__2 = kwtop + kwtop * h_dim1;
	sh[i__1].r = h__[i__2].r, sh[i__1].i = h__[i__2].i;
	*ns = 1;
	*nd = 0;
/* Computing MAX */
	i__1 = kwtop + kwtop * h_dim1;
	d__5 = smlnum, d__6 = ulp * ((d__1 = h__[i__1].r, abs(d__1)) + (d__2 =
		 d_imag(&h__[kwtop + kwtop * h_dim1]), abs(d__2)));
	if ((d__3 = s.r, abs(d__3)) + (d__4 = d_imag(&s), abs(d__4)) <= max(
		d__5,d__6)) {
	    *ns = 0;
	    *nd = 1;
	    if (kwtop > *ktop) {
		i__1 = kwtop + (kwtop - 1) * h_dim1;
		h__[i__1].r = 0., h__[i__1].i = 0.;
	    }
	}
	work[1].r = 1., work[1].i = 0.;
	return 0;
    }

/*     ==== Convert to spike-triangular form.  (In case of a */
/*     .    rare QR failure, this routine continues to do */
/*     .    aggressive early deflation using that part of */
/*     .    the deflation window that converged using INFQR */
/*     .    here and there to keep track.) ==== */

    zlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset], 
	    ldt);
    i__1 = jw - 1;
    i__2 = *ldh + 1;
    i__3 = *ldt + 1;
    zcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
	    i__3);

    zlaset_("A", &jw, &jw, &c_b1, &c_b2, &v[v_offset], ldv);
    nmin = ilaenv_(&c__12, "ZLAQR3", "SV", &jw, &c__1, &jw, lwork);
    if (jw > nmin) {
	zlaqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[
		kwtop], &c__1, &jw, &v[v_offset], ldv, &work[1], lwork, &
		infqr);
    } else {
	zlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[
		kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
    }

/*     ==== Deflation detection loop ==== */

    *ns = jw;
    ilst = infqr + 1;
    i__1 = jw;
    for (knt = infqr + 1; knt <= i__1; ++knt) {

/*        ==== Small spike tip deflation test ==== */

	i__2 = *ns + *ns * t_dim1;
	foo = (d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[*ns + *ns * 
		t_dim1]), abs(d__2));
	if (foo == 0.) {
	    foo = (d__1 = s.r, abs(d__1)) + (d__2 = d_imag(&s), abs(d__2));
	}
	i__2 = *ns * v_dim1 + 1;
/* Computing MAX */
	d__5 = smlnum, d__6 = ulp * foo;
	if (((d__1 = s.r, abs(d__1)) + (d__2 = d_imag(&s), abs(d__2))) * ((
		d__3 = v[i__2].r, abs(d__3)) + (d__4 = d_imag(&v[*ns * v_dim1 
		+ 1]), abs(d__4))) <= max(d__5,d__6)) {

/*           ==== One more converged eigenvalue ==== */

	    --(*ns);
	} else {

/*           ==== One undeflatable eigenvalue.  Move it up out of the */
/*           .    way.   (ZTREXC can not fail in this case.) ==== */

	    ifst = *ns;
	    ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &
		    ilst, &info);
	    ++ilst;
	}
/* L10: */
    }

/*        ==== Return to Hessenberg form ==== */

    if (*ns == 0) {
	s.r = 0., s.i = 0.;
    }

    if (*ns < jw) {

/*        ==== sorting the diagonal of T improves accuracy for */
/*        .    graded matrices.  ==== */

	i__1 = *ns;
	for (i__ = infqr + 1; i__ <= i__1; ++i__) {
	    ifst = i__;
	    i__2 = *ns;
	    for (j = i__ + 1; j <= i__2; ++j) {
		i__3 = j + j * t_dim1;
		i__4 = ifst + ifst * t_dim1;
		if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[j + j * 
			t_dim1]), abs(d__2)) > (d__3 = t[i__4].r, abs(d__3)) 
			+ (d__4 = d_imag(&t[ifst + ifst * t_dim1]), abs(d__4))
			) {
		    ifst = j;
		}
/* L20: */
	    }
	    ilst = i__;
	    if (ifst != ilst) {
		ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, 
			 &ilst, &info);
	    }
/* L30: */
	}
    }

/*     ==== Restore shift/eigenvalue array from T ==== */

    i__1 = jw;
    for (i__ = infqr + 1; i__ <= i__1; ++i__) {
	i__2 = kwtop + i__ - 1;
	i__3 = i__ + i__ * t_dim1;
	sh[i__2].r = t[i__3].r, sh[i__2].i = t[i__3].i;
/* L40: */
    }


    if (*ns < jw || s.r == 0. && s.i == 0.) {
	if (*ns > 1 && (s.r != 0. || s.i != 0.)) {

/*           ==== Reflect spike back into lower triangle ==== */

	    zcopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
	    i__1 = *ns;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		i__2 = i__;
		d_cnjg(&z__1, &work[i__]);
		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L50: */
	    }
	    beta.r = work[1].r, beta.i = work[1].i;
	    zlarfg_(ns, &beta, &work[2], &c__1, &tau);
	    work[1].r = 1., work[1].i = 0.;

	    i__1 = jw - 2;
	    i__2 = jw - 2;
	    zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &t[t_dim1 + 3], ldt);

	    d_cnjg(&z__1, &tau);
	    zlarf_("L", ns, &jw, &work[1], &c__1, &z__1, &t[t_offset], ldt, &
		    work[jw + 1]);
	    zlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
		    work[jw + 1]);
	    zlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
		    work[jw + 1]);

	    i__1 = *lwork - jw;
	    zgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
	}

/*        ==== Copy updated reduced window into place ==== */

	if (kwtop > 1) {
	    i__1 = kwtop + (kwtop - 1) * h_dim1;
	    d_cnjg(&z__2, &v[v_dim1 + 1]);
	    z__1.r = s.r * z__2.r - s.i * z__2.i, z__1.i = s.r * z__2.i + s.i 
		    * z__2.r;
	    h__[i__1].r = z__1.r, h__[i__1].i = z__1.i;
	}
	zlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
	i__1 = jw - 1;
	i__2 = *ldt + 1;
	i__3 = *ldh + 1;
	zcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1], 
		 &i__3);

/*        ==== Accumulate orthogonal matrix in order update */
/*        .    H and Z, if requested.  ==== */

	if (*ns > 1 && (s.r != 0. || s.i != 0.)) {
	    i__1 = *lwork - jw;
	    zunmhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1], 
		     &v[v_offset], ldv, &work[jw + 1], &i__1, &info);
	}

/*        ==== Update vertical slab in H ==== */

	if (*wantt) {
	    ltop = 1;
	} else {
	    ltop = *ktop;
	}
	i__1 = kwtop - 1;
	i__2 = *nv;
	for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow += 
		i__2) {
/* Computing MIN */
	    i__3 = *nv, i__4 = kwtop - krow;
	    kln = min(i__3,i__4);
	    zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &h__[krow + kwtop * 
		    h_dim1], ldh, &v[v_offset], ldv, &c_b1, &wv[wv_offset], 
		    ldwv);
	    zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop * 
		    h_dim1], ldh);
/* L60: */
	}

/*        ==== Update horizontal slab in H ==== */

	if (*wantt) {
	    i__2 = *n;
	    i__1 = *nh;
	    for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2; 
		    kcol += i__1) {
/* Computing MIN */
		i__3 = *nh, i__4 = *n - kcol + 1;
		kln = min(i__3,i__4);
		zgemm_("C", "N", &jw, &kln, &jw, &c_b2, &v[v_offset], ldv, &
			h__[kwtop + kcol * h_dim1], ldh, &c_b1, &t[t_offset], 
			ldt);
		zlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
			 h_dim1], ldh);
/* L70: */
	    }
	}

/*        ==== Update vertical slab in Z ==== */

	if (*wantz) {
	    i__1 = *ihiz;
	    i__2 = *nv;
	    for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
		     i__2) {
/* Computing MIN */
		i__3 = *nv, i__4 = *ihiz - krow + 1;
		kln = min(i__3,i__4);
		zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &z__[krow + kwtop * 
			z_dim1], ldz, &v[v_offset], ldv, &c_b1, &wv[wv_offset]
, ldwv);
		zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow + 
			kwtop * z_dim1], ldz);
/* L80: */
	    }
	}
    }

/*     ==== Return the number of deflations ... ==== */

    *nd = jw - *ns;

/*     ==== ... and the number of shifts. (Subtracting */
/*     .    INFQR from the spike length takes care */
/*     .    of the case of a rare QR failure while */
/*     .    calculating eigenvalues of the deflation */
/*     .    window.)  ==== */

    *ns -= infqr;

/*      ==== Return optimal workspace. ==== */

    d__1 = (doublereal) lwkopt;
    z__1.r = d__1, z__1.i = 0.;
    work[1].r = z__1.r, work[1].i = z__1.i;

/*     ==== End of ZLAQR3 ==== */

    return 0;
} /* zlaqr3_ */
コード例 #9
0
ファイル: zgeevx.c プロジェクト: deepakantony/vispack
/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char *
                             sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w,
                             doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr,
                             integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm,
                             doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer *
                             lwork, doublereal *rwork, integer *info)
{
    /*  -- LAPACK driver routine (version 2.0) --
           Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
           Courant Institute, Argonne National Lab, and Rice University
           September 30, 1994


        Purpose
        =======

        ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
        eigenvalues and, optionally, the left and/or right eigenvectors.

        Optionally also, it computes a balancing transformation to improve
        the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
        SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
        (RCONDE), and reciprocal condition numbers for the right
        eigenvectors (RCONDV).

        The right eigenvector v(j) of A satisfies
                         A * v(j) = lambda(j) * v(j)
        where lambda(j) is its eigenvalue.
        The left eigenvector u(j) of A satisfies
                      u(j)**H * A = lambda(j) * u(j)**H
        where u(j)**H denotes the conjugate transpose of u(j).

        The computed eigenvectors are normalized to have Euclidean norm
        equal to 1 and largest component real.

        Balancing a matrix means permuting the rows and columns to make it
        more nearly upper triangular, and applying a diagonal similarity
        transformation D * A * D**(-1), where D is a diagonal matrix, to
        make its rows and columns closer in norm and the condition numbers
        of its eigenvalues and eigenvectors smaller.  The computed
        reciprocal condition numbers correspond to the balanced matrix.
        Permuting rows and columns will not change the condition numbers
        (in exact arithmetic) but diagonal scaling will.  For further
        explanation of balancing, see section 4.10.2 of the LAPACK
        Users' Guide.

        Arguments
        =========

        BALANC  (input) CHARACTER*1
                Indicates how the input matrix should be diagonally scaled
                and/or permuted to improve the conditioning of its
                eigenvalues.
                = 'N': Do not diagonally scale or permute;
                = 'P': Perform permutations to make the matrix more nearly
                       upper triangular. Do not diagonally scale;
                = 'S': Diagonally scale the matrix, ie. replace A by
                       D*A*D**(-1), where D is a diagonal matrix chosen
                       to make the rows and columns of A more equal in
                       norm. Do not permute;
                = 'B': Both diagonally scale and permute A.

                Computed reciprocal condition numbers will be for the matrix

                after balancing and/or permuting. Permuting does not change
                condition numbers (in exact arithmetic), but balancing does.


        JOBVL   (input) CHARACTER*1
                = 'N': left eigenvectors of A are not computed;
                = 'V': left eigenvectors of A are computed.
                If SENSE = 'E' or 'B', JOBVL must = 'V'.

        JOBVR   (input) CHARACTER*1
                = 'N': right eigenvectors of A are not computed;
                = 'V': right eigenvectors of A are computed.
                If SENSE = 'E' or 'B', JOBVR must = 'V'.

        SENSE   (input) CHARACTER*1
                Determines which reciprocal condition numbers are computed.
                = 'N': None are computed;
                = 'E': Computed for eigenvalues only;
                = 'V': Computed for right eigenvectors only;
                = 'B': Computed for eigenvalues and right eigenvectors.

                If SENSE = 'E' or 'B', both left and right eigenvectors
                must also be computed (JOBVL = 'V' and JOBVR = 'V').

        N       (input) INTEGER
                The order of the matrix A. N >= 0.

        A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A.
                On exit, A has been overwritten.  If JOBVL = 'V' or
                JOBVR = 'V', A contains the Schur form of the balanced
                version of the matrix A.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        W       (output) COMPLEX*16 array, dimension (N)
                W contains the computed eigenvalues.

        VL      (output) COMPLEX*16 array, dimension (LDVL,N)
                If JOBVL = 'V', the left eigenvectors u(j) are stored one
                after another in the columns of VL, in the same order
                as their eigenvalues.
                If JOBVL = 'N', VL is not referenced.
                u(j) = VL(:,j), the j-th column of VL.

        LDVL    (input) INTEGER
                The leading dimension of the array VL.  LDVL >= 1; if
                JOBVL = 'V', LDVL >= N.

        VR      (output) COMPLEX*16 array, dimension (LDVR,N)
                If JOBVR = 'V', the right eigenvectors v(j) are stored one
                after another in the columns of VR, in the same order
                as their eigenvalues.
                If JOBVR = 'N', VR is not referenced.
                v(j) = VR(:,j), the j-th column of VR.

        LDVR    (input) INTEGER
                The leading dimension of the array VR.  LDVR >= 1; if
                JOBVR = 'V', LDVR >= N.

        ILO,IHI (output) INTEGER
                ILO and IHI are integer values determined when A was
                balanced.  The balanced A(i,j) = 0 if I > J and
                J = 1,...,ILO-1 or I = IHI+1,...,N.

        SCALE   (output) DOUBLE PRECISION array, dimension (N)
                Details of the permutations and scaling factors applied
                when balancing A.  If P(j) is the index of the row and column

                interchanged with row and column j, and D(j) is the scaling
                factor applied to row and column j, then
                SCALE(J) = P(J),    for J = 1,...,ILO-1
                         = D(J),    for J = ILO,...,IHI
                         = P(J)     for J = IHI+1,...,N.
                The order in which the interchanges are made is N to IHI+1,
                then 1 to ILO-1.

        ABNRM   (output) DOUBLE PRECISION
                The one-norm of the balanced matrix (the maximum
                of the sum of absolute values of elements of any column).

        RCONDE  (output) DOUBLE PRECISION array, dimension (N)
                RCONDE(j) is the reciprocal condition number of the j-th
                eigenvalue.

        RCONDV  (output) DOUBLE PRECISION array, dimension (N)
                RCONDV(j) is the reciprocal condition number of the j-th
                right eigenvector.

        WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK.  If SENSE = 'N' or 'E',
                LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',
                LWORK >= N*N+2*N.
                For good performance, LWORK must generally be larger.

        RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value.
                > 0:  if INFO = i, the QR algorithm failed to compute all the

                      eigenvalues, and no eigenvectors or condition numbers
                      have been computed; elements 1:ILO-1 and i+1:N of W
                      contain eigenvalues which have converged.

        =====================================================================



           Test the input arguments


       Parameter adjustments
           Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c__0 = 0;
    static integer c__8 = 8;
    static integer c_n1 = -1;
    static integer c__4 = 4;

    /* System generated locals */
    integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
            i__2, i__3, i__4;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;
    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);
    /* Local variables */
    static char side[1];
    static integer maxb;
    static doublereal anrm;
    static integer ierr, itau, iwrk, nout, i, k, icond;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
                                       doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    static logical scalea;
    extern doublereal dlamch_(char *);
    static doublereal cscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
                                        doublereal *, doublereal *, integer *, integer *, doublereal *,
                                        integer *, integer *), zgebak_(char *, char *, integer *,
                                                integer *, integer *, doublereal *, integer *, doublecomplex *,
                                                integer *, integer *), zgebal_(char *, integer *,
                                                        doublecomplex *, integer *, integer *, integer *, doublereal *,
                                                        integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
                           integer *, integer *, ftnlen, ftnlen);
    static logical select[1];
    extern /* Subroutine */ int zdscal_(integer *, doublereal *,
                                        doublecomplex *, integer *);
    static doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
                              integer *, doublereal *);
    extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, doublecomplex *,
                                        integer *, integer *), zlascl_(char *, integer *, integer *,
                                                doublereal *, doublereal *, integer *, integer *, doublecomplex *,
                                                integer *, integer *), zlacpy_(char *, integer *,
                                                        integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    static integer minwrk, maxwrk;
    static logical wantvl, wntsnb;
    static integer hswork;
    static logical wntsne;
    static doublereal smlnum;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
                                        integer *, doublecomplex *, integer *, doublecomplex *,
                                        doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    static logical wantvr;
    extern /* Subroutine */ int ztrevc_(char *, char *, logical *, integer *,
                                        doublecomplex *, integer *, doublecomplex *, integer *,
                                        doublecomplex *, integer *, integer *, integer *, doublecomplex *,
                                        doublereal *, integer *), ztrsna_(char *, char *,
                                                logical *, integer *, doublecomplex *, integer *, doublecomplex *
                                                , integer *, doublecomplex *, integer *, doublereal *, doublereal
                                                *, integer *, integer *, doublecomplex *, integer *, doublereal *,
                                                integer *), zunghr_(integer *, integer *,
                                                        integer *, doublecomplex *, integer *, doublecomplex *,
                                                        doublecomplex *, integer *, integer *);
    static logical wntsnn, wntsnv;
    static char job[1];
    static doublereal scl, dum[1], eps;
    static doublecomplex tmp;



#define DUM(I) dum[(I)]
#define W(I) w[(I)-1]
#define SCALE(I) scale[(I)-1]
#define RCONDE(I) rconde[(I)-1]
#define RCONDV(I) rcondv[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define VL(I,J) vl[(I)-1 + ((J)-1)* ( *ldvl)]
#define VR(I,J) vr[(I)-1 + ((J)-1)* ( *ldvr)]

    *info = 0;
    wantvl = lsame_(jobvl, "V");
    wantvr = lsame_(jobvr, "V");
    wntsnn = lsame_(sense, "N");
    wntsne = lsame_(sense, "E");
    wntsnv = lsame_(sense, "V");
    wntsnb = lsame_(sense, "B");
    if (! (lsame_(balanc, "N") || lsame_(balanc, "S") ||
            lsame_(balanc, "P") || lsame_(balanc, "B"))) {
        *info = -1;
    } else if (! wantvl && ! lsame_(jobvl, "N")) {
        *info = -2;
    } else if (! wantvr && ! lsame_(jobvr, "N")) {
        *info = -3;
    } else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
               && ! (wantvl && wantvr)) {
        *info = -4;
    } else if (*n < 0) {
        *info = -5;
    } else if (*lda < max(1,*n)) {
        *info = -7;
    } else if (*ldvl < 1 || wantvl && *ldvl < *n) {
        *info = -10;
    } else if (*ldvr < 1 || wantvr && *ldvr < *n) {
        *info = -12;
    }

    /*     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.
             CWorkspace refers to complex workspace, and RWorkspace to real
             workspace. NB refers to the optimal block size for the
             immediately following subroutine, as returned by ILAENV.
             HSWORK refers to the workspace preferred by ZHSEQR, as
             calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
             the worst case.) */

    minwrk = 1;
    if (*info == 0 && *lwork >= 1) {
        maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0,
                                   6L, 1L);
        if (! wantvl && ! wantvr) {
            /* Computing MAX */
            i__1 = 1, i__2 = *n << 1;
            minwrk = max(i__1,i__2);
            if (! (wntsnn || wntsne)) {
                /* Computing MAX */
                i__1 = minwrk, i__2 = *n * *n + (*n << 1);
                minwrk = max(i__1,i__2);
            }
            /* Computing MAX */
            i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, 6L, 2L);
            maxb = max(i__1,2);
            if (wntsnn) {
                /* Computing MIN
                   Computing MAX */
                i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
                                         c_n1, 6L, 2L);
                i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
                k = min(i__1,i__2);
            } else {
                /* Computing MIN
                   Computing MAX */
                i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
                                         c_n1, 6L, 2L);
                i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
                k = min(i__1,i__2);
            }
            /* Computing MAX */
            i__1 = k * (k + 2), i__2 = *n << 1;
            hswork = max(i__1,i__2);
            /* Computing MAX */
            i__1 = max(maxwrk,1);
            maxwrk = max(i__1,hswork);
            if (! (wntsnn || wntsne)) {
                /* Computing MAX */
                i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
                maxwrk = max(i__1,i__2);
            }
        } else {
            /* Computing MAX */
            i__1 = 1, i__2 = *n << 1;
            minwrk = max(i__1,i__2);
            if (! (wntsnn || wntsne)) {
                /* Computing MAX */
                i__1 = minwrk, i__2 = *n * *n + (*n << 1);
                minwrk = max(i__1,i__2);
            }
            /* Computing MAX */
            i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, 6L, 2L);
            maxb = max(i__1,2);
            /* Computing MIN
               Computing MAX */
            i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
                                     c_n1, 6L, 2L);
            i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
            k = min(i__1,i__2);
            /* Computing MAX */
            i__1 = k * (k + 2), i__2 = *n << 1;
            hswork = max(i__1,i__2);
            /* Computing MAX */
            i__1 = max(maxwrk,1);
            maxwrk = max(i__1,hswork);
            /* Computing MAX */
            i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
                                  " ", n, &c__1, n, &c_n1, 6L, 1L);
            maxwrk = max(i__1,i__2);
            if (! (wntsnn || wntsne)) {
                /* Computing MAX */
                i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
                maxwrk = max(i__1,i__2);
            }
            /* Computing MAX */
            i__1 = maxwrk, i__2 = *n << 1, i__1 = max(i__1,i__2);
            maxwrk = max(i__1,1);
        }
        WORK(1).r = (doublereal) maxwrk, WORK(1).i = 0.;
    }
    if (*lwork < minwrk) {
        *info = -20;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGEEVX", &i__1);
        return 0;
    }

    /*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

    /*     Get machine constants */

    eps = dlamch_("P");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;

    /*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    icond = 0;
    anrm = zlange_("M", n, n, &A(1,1), lda, dum);
    scalea = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
        scalea = TRUE_;
        cscale = smlnum;
    } else if (anrm > bignum) {
        scalea = TRUE_;
        cscale = bignum;
    }
    if (scalea) {
        zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &A(1,1), lda, &
                ierr);
    }

    /*     Balance the matrix and compute ABNRM */

    zgebal_(balanc, n, &A(1,1), lda, ilo, ihi, &SCALE(1), &ierr);
    *abnrm = zlange_("1", n, n, &A(1,1), lda, dum);
    if (scalea) {
        DUM(0) = *abnrm;
        dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
                ierr);
        *abnrm = DUM(0);
    }

    /*     Reduce to upper Hessenberg form
           (CWorkspace: need 2*N, prefer N+N*NB)
           (RWorkspace: none) */

    itau = 1;
    iwrk = itau + *n;
    i__1 = *lwork - iwrk + 1;
    zgehrd_(n, ilo, ihi, &A(1,1), lda, &WORK(itau), &WORK(iwrk), &i__1, &
            ierr);

    if (wantvl) {

        /*        Want left eigenvectors
                  Copy Householder vectors to VL */

        *(unsigned char *)side = 'L';
        zlacpy_("L", n, n, &A(1,1), lda, &VL(1,1), ldvl);

        /*        Generate unitary matrix in VL
                  (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
                  (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &VL(1,1), ldvl, &WORK(itau), &WORK(iwrk), &
                i__1, &ierr);

        /*        Perform QR iteration, accumulating Schur vectors in VL
                  (CWorkspace: need 1, prefer HSWORK (see comments) )
                  (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &A(1,1), lda, &W(1), &VL(1,1), ldvl, &WORK(iwrk), &i__1, info);

        if (wantvr) {

            /*           Want left and right eigenvectors
                         Copy Schur vectors to VR */

            *(unsigned char *)side = 'B';
            zlacpy_("F", n, n, &VL(1,1), ldvl, &VR(1,1), ldvr)
            ;
        }

    } else if (wantvr) {

        /*        Want right eigenvectors
                  Copy Householder vectors to VR */

        *(unsigned char *)side = 'R';
        zlacpy_("L", n, n, &A(1,1), lda, &VR(1,1), ldvr);

        /*        Generate unitary matrix in VR
                  (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
                  (RWorkspace: none) */

        i__1 = *lwork - iwrk + 1;
        zunghr_(n, ilo, ihi, &VR(1,1), ldvr, &WORK(itau), &WORK(iwrk), &
                i__1, &ierr);

        /*        Perform QR iteration, accumulating Schur vectors in VR
                  (CWorkspace: need 1, prefer HSWORK (see comments) )
                  (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_("S", "V", n, ilo, ihi, &A(1,1), lda, &W(1), &VR(1,1), ldvr, &WORK(iwrk), &i__1, info);

    } else {

        /*        Compute eigenvalues only
                  If condition numbers desired, compute Schur form */

        if (wntsnn) {
            *(unsigned char *)job = 'E';
        } else {
            *(unsigned char *)job = 'S';
        }

        /*        (CWorkspace: need 1, prefer HSWORK (see comments) )
                  (RWorkspace: none) */

        iwrk = itau;
        i__1 = *lwork - iwrk + 1;
        zhseqr_(job, "N", n, ilo, ihi, &A(1,1), lda, &W(1), &VR(1,1), ldvr, &WORK(iwrk), &i__1, info);
    }

    /*     If INFO > 0 from ZHSEQR, then quit */

    if (*info > 0) {
        goto L50;
    }

    if (wantvl || wantvr) {

        /*        Compute left and/or right eigenvectors
                  (CWorkspace: need 2*N)
                  (RWorkspace: need N) */

        ztrevc_(side, "B", select, n, &A(1,1), lda, &VL(1,1), ldvl,
                &VR(1,1), ldvr, n, &nout, &WORK(iwrk), &RWORK(1), &
                ierr);
    }

    /*     Compute condition numbers if desired
           (CWorkspace: need N*N+2*N unless SENSE = 'E')
           (RWorkspace: need 2*N unless SENSE = 'E') */

    if (! wntsnn) {
        ztrsna_(sense, "A", select, n, &A(1,1), lda, &VL(1,1),
                ldvl, &VR(1,1), ldvr, &RCONDE(1), &RCONDV(1), n, &nout,
                &WORK(iwrk), n, &RWORK(1), &icond);
    }

    if (wantvl) {

        /*        Undo balancing of left eigenvectors */

        zgebak_(balanc, "L", n, ilo, ihi, &SCALE(1), n, &VL(1,1), ldvl,
                &ierr);

        /*        Normalize left eigenvectors and make largest component real
        */

        i__1 = *n;
        for (i = 1; i <= *n; ++i) {
            scl = 1. / dznrm2_(n, &VL(1,i), &c__1);
            zdscal_(n, &scl, &VL(1,i), &c__1);
            i__2 = *n;
            for (k = 1; k <= *n; ++k) {
                i__3 = k + i * vl_dim1;
                /* Computing 2nd power */
                d__1 = VL(k,i).r;
                /* Computing 2nd power */
                d__2 = d_imag(&VL(k,i));
                RWORK(k) = d__1 * d__1 + d__2 * d__2;
                /* L10: */
            }
            k = idamax_(n, &RWORK(1), &c__1);
            d_cnjg(&z__2, &VL(k,i));
            d__1 = sqrt(RWORK(k));
            z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
            tmp.r = z__1.r, tmp.i = z__1.i;
            zscal_(n, &tmp, &VL(1,i), &c__1);
            i__2 = k + i * vl_dim1;
            i__3 = k + i * vl_dim1;
            d__1 = VL(k,i).r;
            z__1.r = d__1, z__1.i = 0.;
            VL(k,i).r = z__1.r, VL(k,i).i = z__1.i;
            /* L20: */
        }
    }

    if (wantvr) {

        /*        Undo balancing of right eigenvectors */

        zgebak_(balanc, "R", n, ilo, ihi, &SCALE(1), n, &VR(1,1), ldvr,
                &ierr);

        /*        Normalize right eigenvectors and make largest component real
         */

        i__1 = *n;
        for (i = 1; i <= *n; ++i) {
            scl = 1. / dznrm2_(n, &VR(1,i), &c__1);
            zdscal_(n, &scl, &VR(1,i), &c__1);
            i__2 = *n;
            for (k = 1; k <= *n; ++k) {
                i__3 = k + i * vr_dim1;
                /* Computing 2nd power */
                d__1 = VR(k,i).r;
                /* Computing 2nd power */
                d__2 = d_imag(&VR(k,i));
                RWORK(k) = d__1 * d__1 + d__2 * d__2;
                /* L30: */
            }
            k = idamax_(n, &RWORK(1), &c__1);
            d_cnjg(&z__2, &VR(k,i));
            d__1 = sqrt(RWORK(k));
            z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
            tmp.r = z__1.r, tmp.i = z__1.i;
            zscal_(n, &tmp, &VR(1,i), &c__1);
            i__2 = k + i * vr_dim1;
            i__3 = k + i * vr_dim1;
            d__1 = VR(k,i).r;
            z__1.r = d__1, z__1.i = 0.;
            VR(k,i).r = z__1.r, VR(k,i).i = z__1.i;
            /* L40: */
        }
    }

    /*     Undo scaling if necessary */

L50:
    if (scalea) {
        i__1 = *n - *info;
        /* Computing MAX */
        i__3 = *n - *info;
        i__2 = max(i__3,1);
        zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &W(*info + 1)
                , &i__2, &ierr);
        if (*info == 0) {
            if ((wntsnv || wntsnb) && icond == 0) {
                dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &RCONDV(
                            1), n, &ierr);
            }
        } else {
            i__1 = *ilo - 1;
            zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &W(1), n,
                    &ierr);
        }
    }

    WORK(1).r = (doublereal) maxwrk, WORK(1).i = 0.;
    return 0;

    /*     End of ZGEEVX */

} /* zgeevx_ */