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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 >*/
}
/*< IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN >*/
if (*lwork < minwrk && ! lquery) {
/*< INFO = -12 >*/
*info = -12;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZGEEV ', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZGEEV ", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< >*/
if (*n == 0) {
return 0;
}
/* Get machine constants */
/*< EPS = DLAMCH( 'P' ) >*/
eps = dlamch_("P", (ftnlen)1);
/*< SMLNUM = DLAMCH( 'S' ) >*/
smlnum = dlamch_("S", (ftnlen)1);
/*< BIGNUM = ONE / SMLNUM >*/
bignum = 1. / smlnum;
/*< CALL DLABAD( SMLNUM, BIGNUM ) >*/
dlabad_(&smlnum, &bignum);
/*< SMLNUM = SQRT( SMLNUM ) / EPS >*/
smlnum = sqrt(smlnum) / eps;
/*< BIGNUM = ONE / SMLNUM >*/
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
/*< ANRM = ZLANGE( 'M', N, N, A, LDA, DUM ) >*/
anrm = zlange_("M", n, n, &a[a_offset], lda, dum, (ftnlen)1);
/*< SCALEA = .FALSE. >*/
scalea = FALSE_;
/*< IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN >*/
if (anrm > 0. && anrm < smlnum) {
/*< SCALEA = .TRUE. >*/
scalea = TRUE_;
/*< CSCALE = SMLNUM >*/
cscale = smlnum;
/*< ELSE IF( ANRM.GT.BIGNUM ) THEN >*/
} else if (anrm > bignum) {
/*< SCALEA = .TRUE. >*/
scalea = TRUE_;
/*< CSCALE = BIGNUM >*/
cscale = bignum;
/*< END IF >*/
}
/*< >*/
if (scalea) {
zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
}
/* Balance the matrix */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
/*< IBAL = 1 >*/
ibal = 1;
/*< CALL ZGEBAL( 'B', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR ) >*/
zgebal_("B", 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 >*/
itau = 1;
/*< IWRK = ITAU + N >*/
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 ) THEN >*/
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
/*< SIDE = 'L' >*/
*(unsigned char *)side = 'L';
/*< CALL ZLACPY( 'L', N, N, A, LDA, VL, LDVL ) >*/
zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl, (ftnlen)1)
;
/* 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 >*/
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, (ftnlen)1, (
ftnlen)1);
/*< IF( WANTVR ) THEN >*/
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
/*< SIDE = 'B' >*/
*(unsigned char *)side = 'B';
/*< CALL ZLACPY( 'F', N, N, VL, LDVL, VR, LDVR ) >*/
zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, (
ftnlen)1);
/*< END IF >*/
}
/*< ELSE IF( WANTVR ) THEN >*/
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
/*< SIDE = 'R' >*/
*(unsigned char *)side = 'R';
/*< CALL ZLACPY( 'L', N, N, A, LDA, VR, LDVR ) >*/
zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr, (ftnlen)1)
;
/* 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 >*/
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, (ftnlen)1, (
ftnlen)1);
/*< ELSE >*/
} else {
/* Compute eigenvalues only */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
/*< IWRK = ITAU >*/
iwrk = itau;
/*< >*/
i__1 = *lwork - iwrk + 1;
zhseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info, (ftnlen)1, (
ftnlen)1);
/*< END IF >*/
}
/* If INFO > 0 from ZHSEQR, then quit */
/*< >*/
if (*info > 0) {
goto L50;
}
/*< IF( WANTVL .OR. WANTVR ) THEN >*/
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need 2*N) */
/*< IRWORK = IBAL + N >*/
irwork = ibal + *n;
/*< >*/
ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[irwork],
&ierr, (ftnlen)1, (ftnlen)1);
/*< END IF >*/
}
/*< IF( WANTVL ) THEN >*/
if (wantvl) {
/* Undo balancing of left eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
/*< >*/
zgebak_("B", "L", n, &ilo, &ihi, &rwork[ibal], n, &vl[vl_offset],
ldvl, &ierr, (ftnlen)1, (ftnlen)1);
/* Normalize left eigenvectors and make largest component real */
/*< DO 20 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< SCL = ONE / DZNRM2( N, VL( 1, I ), 1 ) >*/
scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
/*< CALL ZDSCAL( N, SCL, VL( 1, I ), 1 ) >*/
zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
/*< DO 10 K = 1, N >*/
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[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< K = IDAMAX( N, RWORK( IRWORK ), 1 ) >*/
k = idamax_(n, &rwork[irwork], &c__1);
/*< TMP = DCONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) >*/
d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
d__1 = sqrt(rwork[irwork + k - 1]);
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;
/*< CALL ZSCAL( N, TMP, VL( 1, I ), 1 ) >*/
zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
/*< VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO ) >*/
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;
/*< 20 CONTINUE >*/
/* L20: */
}
/*< END IF >*/
}
/*< IF( WANTVR ) THEN >*/
if (wantvr) {
/* Undo balancing of right eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
/*< >*/
zgebak_("B", "R", n, &ilo, &ihi, &rwork[ibal], n, &vr[vr_offset],
ldvr, &ierr, (ftnlen)1, (ftnlen)1);
/* Normalize right eigenvectors and make largest component real */
/*< DO 40 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< SCL = ONE / DZNRM2( N, VR( 1, I ), 1 ) >*/
scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
/*< CALL ZDSCAL( N, SCL, VR( 1, I ), 1 ) >*/
zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
/*< DO 30 K = 1, N >*/
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[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< K = IDAMAX( N, RWORK( IRWORK ), 1 ) >*/
k = idamax_(n, &rwork[irwork], &c__1);
/*< TMP = DCONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) >*/
d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
d__1 = sqrt(rwork[irwork + k - 1]);
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;
/*< CALL ZSCAL( N, TMP, VR( 1, I ), 1 ) >*/
zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
/*< VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO ) >*/
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;
/*< 40 CONTINUE >*/
/* L40: */
}
/*< END IF >*/
}
/* Undo scaling if necessary */
/*< 50 CONTINUE >*/
L50:
/*< IF( SCALEA ) THEN >*/
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, (ftnlen)1);
/*< IF( INFO.GT.0 ) THEN >*/
if (*info > 0) {
/*< CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR ) >*/
i__1 = ilo - 1;
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr, (ftnlen)1);
/*< END IF >*/
}
/*< END IF >*/
}
/*< WORK( 1 ) = MAXWRK >*/
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZGEEV */
/*< END >*/
} /* zgeev_ */
#ifdef __cplusplus
}
#endif
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