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OpenBLAS/lapack-netlib/SRC/sgeev.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
/* > \brief <b> SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matr
ices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGEEV + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgeev.f
"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgeev.f
"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgeev.f
"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, */
/* LDVR, WORK, LWORK, INFO ) */
/* CHARACTER JOBVL, JOBVR */
/* INTEGER INFO, LDA, LDVL, LDVR, LWORK, N */
/* REAL A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), */
/* $ WI( * ), WORK( * ), WR( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGEEV computes for an N-by-N real 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. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBVL */
/* > \verbatim */
/* > JOBVL is CHARACTER*1 */
/* > = 'N': left eigenvectors of A are not computed; */
/* > = 'V': left eigenvectors of A are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVR */
/* > \verbatim */
/* > JOBVR is CHARACTER*1 */
/* > = 'N': right eigenvectors of A are not computed; */
/* > = 'V': right eigenvectors of A are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,N) */
/* > On entry, the N-by-N matrix A. */
/* > On exit, A has been overwritten. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WR */
/* > \verbatim */
/* > WR is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] WI */
/* > \verbatim */
/* > WI is REAL array, dimension (N) */
/* > WR and WI contain the real and imaginary parts, */
/* > respectively, of the computed eigenvalues. Complex */
/* > conjugate pairs of eigenvalues appear consecutively */
/* > with the eigenvalue having the positive imaginary part */
/* > first. */
/* > \endverbatim */
/* > */
/* > \param[out] VL */
/* > \verbatim */
/* > VL is REAL 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. */
/* > If the j-th eigenvalue is real, then u(j) = VL(:,j), */
/* > the j-th column of VL. */
/* > If the j-th and (j+1)-st eigenvalues form a complex */
/* > conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and */
/* > u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* > LDVL is INTEGER */
/* > The leading dimension of the array VL. LDVL >= 1; if */
/* > JOBVL = 'V', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VR */
/* > \verbatim */
/* > VR is REAL 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. */
/* > If the j-th eigenvalue is real, then v(j) = VR(:,j), */
/* > the j-th column of VR. */
/* > If the j-th and (j+1)-st eigenvalues form a complex */
/* > conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and */
/* > v(j+1) = VR(:,j) - i*VR(:,j+1). */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* > LDVR is INTEGER */
/* > The leading dimension of the array VR. LDVR >= 1; if */
/* > JOBVR = 'V', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK >= f2cmax(1,3*N), and */
/* > if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*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. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is 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 i+1:N of WR and WI contain eigenvalues which */
/* > have converged. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* @generated from dgeev.f, fortran d -> s, Tue Apr 19 01:47:44 2016 */
/* > \ingroup realGEeigen */
/* ===================================================================== */
/* Subroutine */ void sgeev_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *wr, real *wi, real *vl, integer *ldvl, real *vr,
integer *ldvr, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
real r__1, r__2;
/* Local variables */
integer ibal;
char side[1];
real anrm;
integer ierr, itau, iwrk, nout;
extern /* Subroutine */ void srot_(integer *, real *, integer *, real *,
integer *, real *, real *);
extern real snrm2_(integer *, real *, integer *);
integer i__, k;
real r__;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
extern real slapy2_(real *, real *);
real cs;
extern /* Subroutine */ void slabad_(real *, real *);
logical scalea;
real cscale;
extern /* Subroutine */ void sgebak_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, integer *), sgebal_(char *, integer *, real *, integer *,
integer *, integer *, real *, integer *);
real sn;
extern real slamch_(char *), slange_(char *, integer *, integer *,
real *, integer *, real *);
extern /* Subroutine */ void sgehrd_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
logical select[1];
real bignum;
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slartg_(real *, real *,
real *, real *, real *), sorghr_(integer *, integer *, integer *,
real *, integer *, real *, real *, integer *, integer *), shseqr_(
char *, char *, integer *, integer *, integer *, real *, integer *
, real *, real *, real *, integer *, real *, integer *, integer *);
integer minwrk, maxwrk;
logical wantvl;
real smlnum;
integer hswork;
logical lquery, wantvr;
extern /* Subroutine */ void strevc3_(char *, char *, logical *, integer *,
real *, integer *, real *, integer *, real *, integer *, integer
*, integer *, real *, integer *, integer *);
integer ihi;
real scl;
integer ilo;
real dum[1], eps;
integer lwork_trevc__;
/* -- LAPACK driver routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--wr;
--wi;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -1;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < f2cmax(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -9;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -11;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by SHSEQR, 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 << 1) + *n * ilaenv_(&c__1, "SGEHRD", " ", n, &c__1,
n, &c__0, (ftnlen)6, (ftnlen)1);
if (wantvl) {
minwrk = *n << 2;
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"SORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = f2cmax(i__1,i__2);
shseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = *
n + hswork;
maxwrk = f2cmax(i__1,i__2);
strevc3_("L", "B", select, n, &a[a_offset], lda, &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
work[1], &c_n1, &ierr);
lwork_trevc__ = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + lwork_trevc__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 2;
maxwrk = f2cmax(i__1,i__2);
} else if (wantvr) {
minwrk = *n << 2;
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"SORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = f2cmax(i__1,i__2);
shseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = *
n + hswork;
maxwrk = f2cmax(i__1,i__2);
strevc3_("R", "B", select, n, &a[a_offset], lda, &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
work[1], &c_n1, &ierr);
lwork_trevc__ = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + lwork_trevc__;
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 2;
maxwrk = f2cmax(i__1,i__2);
} else {
minwrk = *n * 3;
shseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = *
n + hswork;
maxwrk = f2cmax(i__1,i__2);
}
maxwrk = f2cmax(maxwrk,minwrk);
}
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEEV ", &i__1, (ftnlen)5);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n == 0) {
return;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
slascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix */
/* (Workspace: need N) */
ibal = 1;
sgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
itau = ibal + *n;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
sgehrd_(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';
slacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate orthogonal matrix in VL */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
sorghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
shseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[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';
slacpy_("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';
slacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate orthogonal matrix in VR */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
sorghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
shseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &
vr[vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
shseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &
vr[vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO .NE. 0 from SHSEQR, then quit */
if (*info != 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (Workspace: need 4*N, prefer N + N + 2*N*NB) */
i__1 = *lwork - iwrk + 1;
strevc3_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &i__1, &
ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
/* (Workspace: need N) */
sgebak_("B", "L", n, &ilo, &ihi, &work[ibal], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.f) {
scl = 1.f / snrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
sscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
} else if (wi[i__] > 0.f) {
r__1 = snrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
r__2 = snrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
scl = 1.f / slapy2_(&r__1, &r__2);
sscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
sscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
r__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
r__2 = vl[k + (i__ + 1) * vl_dim1];
work[iwrk + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L10: */
}
k = isamax_(n, &work[iwrk], &c__1);
slartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1],
&cs, &sn, &r__);
srot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) *
vl_dim1 + 1], &c__1, &cs, &sn);
vl[k + (i__ + 1) * vl_dim1] = 0.f;
}
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
/* (Workspace: need N) */
sgebak_("B", "R", n, &ilo, &ihi, &work[ibal], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.f) {
scl = 1.f / snrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
sscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
} else if (wi[i__] > 0.f) {
r__1 = snrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
r__2 = snrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
scl = 1.f / slapy2_(&r__1, &r__2);
sscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
sscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
r__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
r__2 = vr[k + (i__ + 1) * vr_dim1];
work[iwrk + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L30: */
}
k = isamax_(n, &work[iwrk], &c__1);
slartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
&cs, &sn, &r__);
srot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) *
vr_dim1 + 1], &c__1, &cs, &sn);
vr[k + (i__ + 1) * vr_dim1] = 0.f;
}
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = f2cmax(i__3,1);
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info +
1], &i__2, &ierr);
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = f2cmax(i__3,1);
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*info +
1], &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1],
n, &ierr);
i__1 = ilo - 1;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1],
n, &ierr);
}
}
work[1] = (real) maxwrk;
return;
/* End of SGEEV */
} /* sgeev_ */
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