zgeev.c

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/* lapack/complex16/zgeev.f -- translated by f2c (version 20050501).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

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

#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"

/* 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;

/*<    >*/
/* Subroutine */ int zgeev_(char *jobvl, char *jobvr, integer *n, 
        doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl, 
        integer *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, 
        integer *lwork, doublereal *rwork, integer *info, ftnlen jobvl_len, 
        ftnlen jobvr_len)
{
    /* 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 */
    integer i__, k, ihi;
    doublereal scl;
    integer ilo;
    doublereal dum[1], eps;
    doublecomplex tmp;
    integer ibal;
    char side[1];
    integer maxb;
    doublereal anrm;
    integer ierr, itau, iwrk, nout;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    logical scalea;
    extern doublereal dlamch_(char *, ftnlen);
    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);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *, ftnlen, ftnlen);
    logical select[1];
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *);
    doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublereal *, ftnlen);
    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);
    integer minwrk, maxwrk=0;
    logical wantvl;
    doublereal smlnum;
    integer hswork, irwork=0;
    extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, 
            integer *, doublecomplex *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, integer *,
             ftnlen, ftnlen), ztrevc_(char *, char *, logical *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, integer *, integer *, doublecomplex *,
             doublereal *, integer *, ftnlen, ftnlen);
    logical lquery, wantvr;
    extern /* Subroutine */ int zunghr_(integer *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *, integer *);
    (void)jobvl_len;
    (void)jobvr_len;

/*  -- 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 .. */
/*<       CHARACTER          JOBVL, JOBVR >*/
/*<       INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N >*/
/*     .. */
/*     .. Array Arguments .. */
/*<       DOUBLE PRECISION   RWORK( * ) >*/
/*<    >*/
/*     .. */

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

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

/*  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. */

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

/*  JOBVL   (input) CHARACTER*1 */
/*          = 'N': left eigenvectors of A are not computed; */
/*          = 'V': left eigenvectors of are computed. */

/*  JOBVR   (input) CHARACTER*1 */
/*          = 'N': right eigenvectors of A are not computed; */
/*          = 'V': right eigenvectors of A are computed. */

/*  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. */

/*  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. */

/*  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 (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 have been computed; */
/*                elements and i+1:N of W contain eigenvalues which have */
/*                converged. */

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

/*     .. Parameters .. */
/*<       DOUBLE PRECISION   ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<       LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR >*/
/*<       CHARACTER          SIDE >*/
/*<    >*/
/*<       DOUBLE PRECISION   ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM >*/
/*<       COMPLEX*16         TMP >*/
/*     .. */
/*     .. Local Arrays .. */
/*<       LOGICAL            SELECT( 1 ) >*/
/*<       DOUBLE PRECISION   DUM( 1 ) >*/
/*     .. */
/*     .. External Subroutines .. */
/*<    >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       INTEGER            IDAMAX, ILAENV >*/
/*<       DOUBLE PRECISION   DLAMCH, DZNRM2, ZLANGE >*/
/*<       EXTERNAL           LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN, SQRT >*/
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

/*<       INFO = 0 >*/
    /* 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;
    --work;
    --rwork;

    /* Function Body */
    *info = 0;
/*<       LQUERY = ( LWORK.EQ.-1 ) >*/
    lquery = *lwork == -1;
/*<       WANTVL = LSAME( JOBVL, 'V' ) >*/
    wantvl = lsame_(jobvl, "V", (ftnlen)1, (ftnlen)1);
/*<       WANTVR = LSAME( JOBVR, 'V' ) >*/
    wantvr = lsame_(jobvr, "V", (ftnlen)1, (ftnlen)1);
/*<       IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN >*/
    if (! wantvl && ! lsame_(jobvl, "N", (ftnlen)1, (ftnlen)1)) {
/*<          INFO = -1 >*/
        *info = -1;
/*<       ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN >*/
    } else if (! wantvr && ! lsame_(jobvr, "N", (ftnlen)1, (ftnlen)1)) {
/*<          INFO = -2 >*/
        *info = -2;
/*<       ELSE IF( N.LT.0 ) THEN >*/
    } else if (*n < 0) {
/*<          INFO = -3 >*/
        *info = -3;
/*<       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN >*/
    } else if (*lda < max(1,*n)) {
/*<          INFO = -5 >*/
        *info = -5;
/*<       ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN >*/
    } else if (*ldvl < 1 || (wantvl && *ldvl < *n)) {
/*<          INFO = -8 >*/
        *info = -8;
/*<       ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN >*/
    } else if (*ldvr < 1 || (wantvr && *ldvr < *n)) {
/*<          INFO = -10 >*/
        *info = -10;
/*<       END IF >*/
    }

/*     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 >*/
    minwrk = 1;
/*<       IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN >*/
    if (*info == 0 && (*lwork >= 1 || lquery)) {
/*<          MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 ) >*/
        maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
                ftnlen)6, (ftnlen)1);
/*<          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN >*/
        if (! wantvl && ! wantvr) {
/*<             MINWRK = MAX( 1, 2*N ) >*/
/* Computing MAX */
            i__1 = 1, i__2 = *n << 1;
            minwrk = max(i__1,i__2);
/*<             MAXB = MAX( ILAENV( 8, 'ZHSEQR', 'EN', N, 1, N, -1 ), 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);
/*<             HSWORK = MAX( K*( K+2 ), 2*N ) >*/
/* Computing MAX */
            i__1 = k * (k + 2), i__2 = *n << 1;
            hswork = max(i__1,i__2);
/*<             MAXWRK = MAX( MAXWRK, HSWORK ) >*/
            maxwrk = max(maxwrk,hswork);
/*<          ELSE >*/
        } else {
/*<             MINWRK = MAX( 1, 2*N ) >*/
/* Computing MAX */
            i__1 = 1, i__2 = *n << 1;
            minwrk = max(i__1,i__2);
/*<    >*/
/* 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);
/*<             MAXB = MAX( ILAENV( 8, 'ZHSEQR', 'SV', N, 1, N, -1 ), 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);
/*<             HSWORK = MAX( K*( K+2 ), 2*N ) >*/
/* Computing MAX */
            i__1 = k * (k + 2), i__2 = *n << 1;
            hswork = max(i__1,i__2);
/*<             MAXWRK = MAX( MAXWRK, HSWORK, 2*N ) >*/
/* Computing MAX */
            i__1 = max(maxwrk,hswork), i__2 = *n << 1;
            maxwrk = max(i__1,i__2);
/*<          END IF >*/
        }
/*<          WORK( 1 ) = MAXWRK >*/
        work[1].r = (doublereal) maxwrk, work[1].i = 0.;
/*<       END IF >*/