cgeesx.c

#include<math.h>
#include<stdlib.h>
#include<string.h>
#include<stdio.h>
#include<complex.h>
#ifdefcomplex
#undef complex
#endif
#ifdefI
#undef I
#endif

#if defined(_WIN64)
typedeflong longBLASLONG;
typedefunsigned long longBLASULONG;
#else
typedeflongBLASLONG;
typedefunsigned longBLASULONG;
#endif

#ifdefLAPACK_ILP64
typedefBLASLONGblasint;
#if defined(_WIN64)
#defineblasabs(x) llabs(x)
#else
#defineblasabs(x) labs(x)
#endif
#else
typedefintblasint;
#defineblasabs(x) abs(x)
#endif

typedefblasintinteger;

typedefunsigned intuinteger;
typedefchar*address;
typedefshort intshortint;
typedeffloatreal;
typedefdoubledoublereal;
typedefstruct { realr, i; } complex;
typedefstruct { doublerealr, i; } doublecomplex;
#ifdef_MSC_VER
staticinline_FcomplexCf(complex*z) {_Fcomplexzz={z->r , z->i}; returnzz;}
staticinline_DcomplexCd(doublecomplex*z) {_Dcomplexzz={z->r , z->i};returnzz;}
staticinline_Fcomplex*_pCf(complex*z) {return (_Fcomplex*)z;}
staticinline_Dcomplex*_pCd(doublecomplex*z) {return (_Dcomplex*)z;}
#else
staticinline_ComplexfloatCf(complex*z) {returnz->r+z->i*_Complex_I;}
staticinline_ComplexdoubleCd(doublecomplex*z) {returnz->r+z->i*_Complex_I;}
staticinline_Complexfloat*_pCf(complex*z) {return (_Complexfloat*)z;}
staticinline_Complexdouble*_pCd(doublecomplex*z) {return (_Complexdouble*)z;}
#endif
#definepCf(z) (*_pCf(z))
#definepCd(z) (*_pCd(z))
typedefintlogical;
typedefshort intshortlogical;
typedefcharlogical1;
typedefcharinteger1;

#defineTRUE_ (1)
#defineFALSE_ (0)

/* Extern is for use with -E */
#ifndefExtern
#defineExtern extern
#endif

/* I/O stuff */

typedefintflag;
typedefintftnlen;
typedefintftnint;

/*external read, write*/
typedefstruct
{ flagcierr;
ftnintciunit;
flagciend;
char*cifmt;
ftnintcirec;
} cilist;

/*internal read, write*/
typedefstruct
{ flagicierr;
char*iciunit;
flagiciend;
char*icifmt;
ftninticirlen;
ftninticirnum;
} icilist;

/*open*/
typedefstruct
{ flagoerr;
ftnintounit;
char*ofnm;
ftnlenofnmlen;
char*osta;
char*oacc;
char*ofm;
ftnintorl;
char*oblnk;
} olist;

/*close*/
typedefstruct
{ flagcerr;
ftnintcunit;
char*csta;
} cllist;

/*rewind, backspace, endfile*/
typedefstruct
{ flagaerr;
ftnintaunit;
} alist;

/* inquire */
typedefstruct
{ flaginerr;
ftnintinunit;
char*infile;
ftnleninfilen;
ftnint*inex; /*parameters in standard's order*/
ftnint*inopen;
ftnint*innum;
ftnint*innamed;
char*inname;
ftnleninnamlen;
char*inacc;
ftnleninacclen;
char*inseq;
ftnleninseqlen;
char*indir;
ftnlenindirlen;
char*infmt;
ftnleninfmtlen;
char*inform;
ftnintinformlen;
char*inunf;
ftnleninunflen;
ftnint*inrecl;
ftnint*innrec;
char*inblank;
ftnleninblanklen;
} inlist;

#defineVOID void

unionMultitype { /* for multiple entry points */
integer1g;
shortinth;
integeri;
/* longint j; */
realr;
doublereald;
complexc;
doublecomplexz;
 };

typedefunionMultitypeMultitype;

structVardesc { /* for Namelist */
char*name;
char*addr;
ftnlen*dims;
inttype;
 };
typedefstructVardescVardesc;

structNamelist {
char*name;
Vardesc**vars;
intnvars;
 };
typedefstructNamelistNamelist;

#defineabs(x) ((x) >= 0 ? (x) : -(x))
#definedabs(x) (fabs(x))
#definef2cmin(a,b) ((a) <= (b) ? (a) : (b))
#definef2cmax(a,b) ((a) >= (b) ? (a) : (b))
#definedmin(a,b) (f2cmin(a,b))
#definedmax(a,b) (f2cmax(a,b))
#definebit_test(a,b) ((a) >> (b) & 1)
#definebit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#definebit_set(a,b) ((a) | ((uinteger)1 << (b)))

#defineabort_() { sig_die("Fortran abort routine called", 1); }
#definec_abs(z) (cabsf(Cf(z)))
#definec_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef_MSC_VER
#definec_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]);}
#definez_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
#definec_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#definez_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#definec_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#definec_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#definec_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#definec_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#defined_abs(x) (fabs(*(x)))
#defined_acos(x) (acos(*(x)))
#defined_asin(x) (asin(*(x)))
#defined_atan(x) (atan(*(x)))
#defined_atn2(x, y) (atan2(*(x),*(y)))
#defined_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#definer_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#defined_cos(x) (cos(*(x)))
#defined_cosh(x) (cosh(*(x)))
#defined_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#defined_exp(x) (exp(*(x)))
#defined_imag(z) (cimag(Cd(z)))
#definer_imag(z) (cimagf(Cf(z)))
#defined_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#definer_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#defined_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#definer_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#defined_log(x) (log(*(x)))
#defined_mod(x, y) (fmod(*(x), *(y)))
#defineu_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#defined_nint(x) u_nint(*(x))
#defineu_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#defined_sign(a,b) u_sign(*(a),*(b))
#definer_sign(a,b) u_sign(*(a),*(b))
#defined_sin(x) (sin(*(x)))
#defined_sinh(x) (sinh(*(x)))
#defined_sqrt(x) (sqrt(*(x)))
#defined_tan(x) (tan(*(x)))
#defined_tanh(x) (tanh(*(x)))
#definei_abs(x) abs(*(x))
#definei_dnnt(x) ((integer)u_nint(*(x)))
#definei_len(s, n) (n)
#definei_nint(x) ((integer)u_nint(*(x)))
#definei_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#definepow_dd(ap, bp) ( pow(*(ap), *(bp)))
#definepow_si(B,E) spow_ui(*(B),*(E))
#definepow_ri(B,E) spow_ui(*(B),*(E))
#definepow_di(B,E) dpow_ui(*(B),*(E))
#definepow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#definepow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#definepow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#defines_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++ = ' '; }
#defines_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#defines_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]; }
#definesig_die(s, kill) { exit(1); }
#defines_stop(s, n) {exit(0);}
staticcharjunk[] ="\n@(#)LIBF77 VERSION 19990503\n";
#definez_abs(z) (cabs(Cd(z)))
#definez_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#definez_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#definemyexit_() break;
#definemycycle() continue;
#definemyceiling(w) {ceil(w)}
#definemyhuge(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);}
#definemymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#defineF2C_proc_par_types 1
#ifdef__cplusplus
typedeflogical (*L_fp)(...);
#else
typedeflogical (*L_fp)();
#endif

staticfloatspow_ui(floatx, integern) {
floatpow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
staticdoubledpow_ui(doublex, integern) {
doublepow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#ifdef_MSC_VER
static_Fcomplexcpow_ui(complexx, integern) {
complexpow={1.0,0.0}; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x.r=1/x.r, x.i=1/x.i;
for(u=n; ; ) {
if(u&01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
elsebreak;
 }
 }
_Fcomplexp={pow.r, pow.i};
returnp;
}
#else
static_Complexfloatcpow_ui(_Complexfloatx, integern) {
_Complexfloatpow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#endif
#ifdef_MSC_VER
static_Dcomplexzpow_ui(_Dcomplexx, integern) {
_Dcomplexpow={1.0,0.0}; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x._Val[0] =1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u=n; ; ) {
if(u&01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
elsebreak;
 }
 }
_Dcomplexp= {pow._Val[0], pow._Val[1]};
returnp;
}
#else
static_Complexdoublezpow_ui(_Complexdoublex, integern) {
_Complexdoublepow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#endif
staticintegerpow_ii(integerx, integern) {
integerpow; unsigned long intu;
if (n <= 0) {
if (n==0||x==1) pow=1;
elseif (x!=-1) pow=x==0 ? 1/x : 0;
elsen=-n;
 }
if ((n>0) || !(n==0||x==1||x!=-1)) {
u=n;
for(pow=1; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
staticintegerdmaxloc_(double*w, integers, integere, integer*n)
{
doublem; integeri, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
returnmi-s+1;
}
staticintegersmaxloc_(float*w, integers, integere, integer*n)
{
floatm; integeri, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
returnmi-s+1;
}
staticinlinevoidcdotc_(complex*z, integer*n_, complex*x, integer*incx_, complex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Fcomplexzdotc= {0.0, 0.0};
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=conjf(Cf(&x[i]))._Val[0] *Cf(&y[i])._Val[0];
zdotc._Val[1] +=conjf(Cf(&x[i]))._Val[1] *Cf(&y[i])._Val[1];
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=conjf(Cf(&x[i*incx]))._Val[0] *Cf(&y[i*incy])._Val[0];
zdotc._Val[1] +=conjf(Cf(&x[i*incx]))._Val[1] *Cf(&y[i*incy])._Val[1];
 }
 }
pCf(z) =zdotc;
}
#else
_Complexfloatzdotc=0.0;
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=conjf(Cf(&x[i])) *Cf(&y[i]);
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=conjf(Cf(&x[i*incx])) *Cf(&y[i*incy]);
 }
 }
pCf(z) =zdotc;
}
#endif
staticinlinevoidzdotc_(doublecomplex*z, integer*n_, doublecomplex*x, integer*incx_, doublecomplex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Dcomplexzdotc= {0.0, 0.0};
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=conj(Cd(&x[i]))._Val[0] *Cd(&y[i])._Val[0];
zdotc._Val[1] +=conj(Cd(&x[i]))._Val[1] *Cd(&y[i])._Val[1];
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=conj(Cd(&x[i*incx]))._Val[0] *Cd(&y[i*incy])._Val[0];
zdotc._Val[1] +=conj(Cd(&x[i*incx]))._Val[1] *Cd(&y[i*incy])._Val[1];
 }
 }
pCd(z) =zdotc;
}
#else
_Complexdoublezdotc=0.0;
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=conj(Cd(&x[i])) *Cd(&y[i]);
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=conj(Cd(&x[i*incx])) *Cd(&y[i*incy]);
 }
 }
pCd(z) =zdotc;
}
#endif
staticinlinevoidcdotu_(complex*z, integer*n_, complex*x, integer*incx_, complex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Fcomplexzdotc= {0.0, 0.0};
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=Cf(&x[i])._Val[0] *Cf(&y[i])._Val[0];
zdotc._Val[1] +=Cf(&x[i])._Val[1] *Cf(&y[i])._Val[1];
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=Cf(&x[i*incx])._Val[0] *Cf(&y[i*incy])._Val[0];
zdotc._Val[1] +=Cf(&x[i*incx])._Val[1] *Cf(&y[i*incy])._Val[1];
 }
 }
pCf(z) =zdotc;
}
#else
_Complexfloatzdotc=0.0;
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=Cf(&x[i]) *Cf(&y[i]);
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=Cf(&x[i*incx]) *Cf(&y[i*incy]);
 }
 }
pCf(z) =zdotc;
}
#endif
staticinlinevoidzdotu_(doublecomplex*z, integer*n_, doublecomplex*x, integer*incx_, doublecomplex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Dcomplexzdotc= {0.0, 0.0};
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=Cd(&x[i])._Val[0] *Cd(&y[i])._Val[0];
zdotc._Val[1] +=Cd(&x[i])._Val[1] *Cd(&y[i])._Val[1];
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] +=Cd(&x[i*incx])._Val[0] *Cd(&y[i*incy])._Val[0];
zdotc._Val[1] +=Cd(&x[i*incx])._Val[1] *Cd(&y[i*incy])._Val[1];
 }
 }
pCd(z) =zdotc;
}
#else
_Complexdoublezdotc=0.0;
if (incx==1&&incy==1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=Cd(&x[i]) *Cd(&y[i]);
 }
 } else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc+=Cd(&x[i*incx]) *Cd(&y[i*incy]);
 }
 }
pCd(z) =zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
 You must link the resulting object file with the libraries:
 -lf2c -lm (in that order)
*/





/* Table of constant values */

staticintegerc__1=1;
staticintegerc__0=0;
staticintegerc_n1=-1;

/* > \brief <b> CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 
for GE matrices</b> */

/* =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download CGEESX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeesx.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeesx.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeesx.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/* Definition: */
/* =========== */

/* SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, */
/* VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, */
/* BWORK, INFO ) */

/* CHARACTER JOBVS, SENSE, SORT */
/* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM */
/* REAL RCONDE, RCONDV */
/* LOGICAL BWORK( * ) */
/* REAL RWORK( * ) */
/* COMPLEX A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) */
/* LOGICAL SELECT */
/* EXTERNAL SELECT */


/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGEESX 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. */
/* > \endverbatim */

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

/* > \param[in] JOBVS */
/* > \verbatim */
/* > JOBVS is CHARACTER*1 */
/* > = 'N': Schur vectors are not computed; */
/* > = 'V': Schur vectors are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] SORT */
/* > \verbatim */
/* > SORT is 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). */
/* > \endverbatim */
/* > */
/* > \param[in] SELECT */
/* > \verbatim */
/* > SELECT is a LOGICAL FUNCTION of one COMPLEX 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. */
/* > \endverbatim */
/* > */
/* > \param[in] SENSE */
/* > \verbatim */
/* > SENSE is 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'. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA, N) */
/* > On entry, the N-by-N matrix A. */
/* > On exit, A is overwritten by its Schur form T. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] SDIM */
/* > \verbatim */
/* > SDIM is INTEGER */
/* > If SORT = 'N', SDIM = 0. */
/* > If SORT = 'S', SDIM = number of eigenvalues for which */
/* > SELECT is true. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is COMPLEX array, dimension (N) */
/* > W contains the computed eigenvalues, in the same order */
/* > that they appear on the diagonal of the output Schur form T. */
/* > \endverbatim */
/* > */
/* > \param[out] VS */
/* > \verbatim */
/* > VS is COMPLEX array, dimension (LDVS,N) */
/* > If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
/* > vectors. */
/* > If JOBVS = 'N', VS is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVS */
/* > \verbatim */
/* > LDVS is INTEGER */
/* > The leading dimension of the array VS. LDVS >= 1, and if */
/* > JOBVS = 'V', LDVS >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDE */
/* > \verbatim */
/* > RCONDE is REAL */
/* > 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'. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDV */
/* > \verbatim */
/* > RCONDV is REAL */
/* > If SENSE = 'V' or 'B', RCONDV contains the reciprocal */
/* > condition number for the selected right invariant subspace. */
/* > Not referenced if SENSE = 'N' or 'E'. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX 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(1,2*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. Note also */
/* > that an error is only returned if LWORK < f2cmax(1,2*N), but if */
/* > SENSE = 'E' or 'V' or 'B' this may not be large enough. */
/* > For good performance, LWORK must generally be larger. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates upper bound on the optimal size of the */
/* > array WORK, 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] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BWORK */
/* > \verbatim */
/* > BWORK is LOGICAL array, dimension (N) */
/* > Not referenced if SORT = 'N'. */
/* > \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, 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. */
/* > \endverbatim */

/* Authors: */
/* ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date June 2016 */

/* > \ingroup complexGEeigen */

/* ===================================================================== */
/* Subroutine */voidcgeesx_(char*jobvs, char*sort, L_fpselect, char*
sense, integer*n, complex*a, integer*lda, integer*sdim, complex*
w, complex*vs, integer*ldvs, real*rconde, real*rcondv, complex*
work, integer*lwork, real*rwork, logical*bwork, integer*info)
{
/* System generated locals */
integera_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;

/* Local variables */
integeribal;
realanrm;
integerierr, itau, iwrk, lwrk, i__, icond, ieval;
externlogicallsame_(char*, char*);
extern/* Subroutine */voidccopy_(integer*, complex*, integer*, 
complex*, integer*), cgebak_(char*, char*, integer*, integer
*, integer*, real*, integer*, complex*, integer*, integer*), cgebal_(char*, integer*, complex*, integer*, 
integer*, integer*, real*, integer*), slabad_(real*, 
real*);
logicalscalea;
externrealclange_(char*, integer*, integer*, complex*, integer*, 
real*);
realcscale;
extern/* Subroutine */voidcgehrd_(integer*, integer*, integer*, 
complex*, integer*, complex*, complex*, integer*, integer*),
clascl_(char*, integer*, integer*, real*, real*, integer*, 
integer*, complex*, integer*, integer*);
externrealslamch_(char*);
extern/* Subroutine */voidclacpy_(char*, integer*, integer*, complex
*, integer*, complex*, integer*);
externintxerbla_(char*, integer*, ftnlen);
externintegerilaenv_(integer*, char*, char*, integer*, integer*, 
integer*, integer*, ftnlen, ftnlen);
realbignum;
extern/* Subroutine */voidslascl_(char*, integer*, integer*, real*, 
real*, integer*, integer*, real*, integer*, integer*), chseqr_(char*, char*, integer*, integer*, integer*, 
complex*, integer*, complex*, complex*, integer*, complex*, 
integer*, integer*), cunghr_(integer*, integer
*, integer*, complex*, integer*, complex*, complex*, integer
*, integer*);
logicalwantsb;
extern/* Subroutine */voidctrsen_(char*, char*, logical*, integer*, 
complex*, integer*, complex*, integer*, complex*, integer*, 
real*, real*, complex*, integer*, integer*);
logicalwantse;
integerminwrk, maxwrk;
logicalwantsn;
realsmlnum;
integerhswork;
logicalwantst, lquery, wantsv, wantvs;
integerihi, ilo;
realdum[1], eps;


/* -- 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;
--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");
lquery=*lwork==-1;

if (! wantvs&& ! lsame_(jobvs, "N")) {
*info=-1;
 } elseif (! wantst&& ! lsame_(sort, "N")) {
*info=-2;
 } elseif (! (wantsn||wantse||wantsv||wantsb) || ! wantst&& ! 
wantsn) {
*info=-4;
 } elseif (*n<0) {
*info=-5;
 } elseif (*lda<f2cmax(1,*n)) {
*info=-7;
 } elseif (*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 CHSEQR, 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 CTRSEN later */
/* in the code.) */

if (*info==0) {
if (*n==0) {
minwrk=1;
lwrk=1;
 } else {
maxwrk=*n+*n*ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0, (ftnlen)6, (ftnlen)1);
minwrk=*n << 1;

chseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork=work[1].r;

if (! wantvs) {
maxwrk=f2cmax(maxwrk,hswork);
 } else {
/* Computing MAX */
i__1=maxwrk, i__2=*n+ (*n-1) *ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk=f2cmax(i__1,i__2);
maxwrk=f2cmax(maxwrk,hswork);
 }
lwrk=maxwrk;
if (! wantsn) {
/* Computing MAX */
i__1=lwrk, i__2=*n**n / 2;
lwrk=f2cmax(i__1,i__2);
 }
 }
work[1].r= (real) lwrk, work[1].i=0.f;

if (*lwork<minwrk&& ! lquery) {
*info=-15;
 }
 }

if (*info!=0) {
i__1=-(*info);
xerbla_("CGEESX", &i__1, (ftnlen)6);
return;
 } elseif (lquery) {
return;
 }

/* Quick return if possible */

if (*n==0) {
*sdim=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=clange_("M", n, n, &a[a_offset], lda, dum);
scalea=FALSE_;
if (anrm>0.f&&anrm<smlnum) {
scalea=TRUE_;
cscale=smlnum;
 } elseif (anrm>bignum) {
scalea=TRUE_;
cscale=bignum;
 }
if (scalea) {
clascl_("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;
cgebal_("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;
cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);

if (wantvs) {

/* Copy Householder vectors to VS */

clacpy_("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;
cunghr_(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;
chseqr_("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) {
clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
ierr);
 }