cgebal.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)
*/


/* -- translated by f2c (version 20000121).
 You must link the resulting object file with the libraries:
 -lf2c -lm (in that order)
*/



/* -- 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;

/* > \brief \b CGEBAL */

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

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

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

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

/* SUBROUTINE CGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) */

/* CHARACTER JOB */
/* INTEGER IHI, ILO, INFO, LDA, N */
/* REAL SCALE( * ) */
/* COMPLEX A( LDA, * ) */


/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGEBAL balances a general complex matrix A. This involves, first, */
/* > permuting A by a similarity transformation to isolate eigenvalues */
/* > in the first 1 to ILO-1 and last IHI+1 to N elements on the */
/* > diagonal; and second, applying a diagonal similarity transformation */
/* > to rows and columns ILO to IHI to make the rows and columns as */
/* > close in norm as possible. Both steps are optional. */
/* > */
/* > Balancing may reduce the 1-norm of the matrix, and improve the */
/* > accuracy of the computed eigenvalues and/or eigenvectors. */
/* > \endverbatim */

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

/* > \param[in] JOB */
/* > \verbatim */
/* > JOB is CHARACTER*1 */
/* > Specifies the operations to be performed on A: */
/* > = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
/* > for i = 1,...,N; */
/* > = 'P': permute only; */
/* > = 'S': scale only; */
/* > = 'B': both permute and scale. */
/* > \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 input matrix A. */
/* > On exit, A is overwritten by the balanced matrix. */
/* > If JOB = 'N', A is not referenced. */
/* > See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ILO */
/* > \verbatim */
/* > ILO is INTEGER */
/* > \endverbatim */
/* > \param[out] IHI */
/* > \verbatim */
/* > IHI is INTEGER */
/* > ILO and IHI are set to integers such that on exit */
/* > A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
/* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
/* > \endverbatim */
/* > */
/* > \param[out] SCALE */
/* > \verbatim */
/* > SCALE is REAL array, dimension (N) */
/* > Details of the permutations and scaling factors applied to */
/* > 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. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup complexGEcomputational */

/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The permutations consist of row and column interchanges which put */
/* > the matrix in the form */
/* > */
/* > ( T1 X Y ) */
/* > P A P = ( 0 B Z ) */
/* > ( 0 0 T2 ) */
/* > */
/* > where T1 and T2 are upper triangular matrices whose eigenvalues lie */
/* > along the diagonal. The column indices ILO and IHI mark the starting */
/* > and ending columns of the submatrix B. Balancing consists of applying */
/* > a diagonal similarity transformation inv(D) * B * D to make the */
/* > 1-norms of each row of B and its corresponding column nearly equal. */
/* > The output matrix is */
/* > */
/* > ( T1 X*D Y ) */
/* > ( 0 inv(D)*B*D inv(D)*Z ). */
/* > ( 0 0 T2 ) */
/* > */
/* > Information about the permutations P and the diagonal matrix D is */
/* > returned in the vector SCALE. */
/* > */
/* > This subroutine is based on the EISPACK routine CBAL. */
/* > */
/* > Modified by Tzu-Yi Chen, Computer Science Division, University of */
/* > California at Berkeley, USA */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */intcgebal_(char*job, integer*n, complex*a, integer*lda, 
integer*ilo, integer*ihi, real*scale, integer*info)
{
/* System generated locals */
integera_dim1, a_offset, i__1, i__2, i__3;
realr__1, r__2;

/* Local variables */
integeriexc;
realc__, f, g;
integeri__, j, k, l, m;
realr__, s;
externlogicallsame_(char*, char*);
extern/* Subroutine */intcswap_(integer*, complex*, integer*, 
complex*, integer*);
realsfmin1, sfmin2, sfmax1, sfmax2, ca;
externrealscnrm2_(integer*, complex*, integer*);
realra;
externintegericamax_(integer*, complex*, integer*);
externrealslamch_(char*);
extern/* Subroutine */intcsscal_(integer*, real*, complex*, integer
*), xerbla_(char*, integer*, ftnlen);
externlogicalsisnan_(real*);
logicalnoconv;
integerica, ira;


/* -- LAPACK computational 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..-- */
/* December 2016 */


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


/* Test the input parameters */

/* Parameter adjustments */
a_dim1=*lda;
a_offset=1+a_dim1*1;
a-=a_offset;
--scale;

/* Function Body */
*info=0;
if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") 
&& ! lsame_(job, "B")) {
*info=-1;
 } elseif (*n<0) {
*info=-2;
 } elseif (*lda<f2cmax(1,*n)) {
*info=-4;
 }
if (*info!=0) {
i__1=-(*info);
xerbla_("CGEBAL", &i__1, (ftnlen)6);
return0;
 }

k=1;
l=*n;

if (*n==0) {
 goto L210;
 }

if (lsame_(job, "N")) {
i__1=*n;
for (i__=1; i__ <= i__1; ++i__) {
scale[i__] =1.f;
/* L10: */
 }
 goto L210;
 }

if (lsame_(job, "S")) {
 goto L120;
 }

/* Permutation to isolate eigenvalues if possible */

 goto L50;

/* Row and column exchange. */

L20:
scale[m] = (real) j;
if (j==m) {
 goto L30;
 }

cswap_(&l, &a[j*a_dim1+1], &c__1, &a[m*a_dim1+1], &c__1);
i__1=*n-k+1;
cswap_(&i__1, &a[j+k*a_dim1], lda, &a[m+k*a_dim1], lda);

L30:
switch (iexc) {
case1: goto L40;
case2: goto L80;
 }

/* Search for rows isolating an eigenvalue and push them down. */

L40:
if (l==1) {
 goto L210;
 }
--l;

L50:
for (j=l; j >= 1; --j) {

i__1=l;
for (i__=1; i__ <= i__1; ++i__) {
if (i__==j) {
 goto L60;
 }
i__2=j+i__*a_dim1;
if (a[i__2].r!=0.f||r_imag(&a[j+i__*a_dim1]) !=0.f) {
 goto L70;
 }
L60:
 ;
 }

m=l;
iexc=1;
 goto L20;
L70:
 ;
 }

 goto L90;

/* Search for columns isolating an eigenvalue and push them left. */

L80:
++k;

L90:
i__1=l;
for (j=k; j <= i__1; ++j) {

i__2=l;
for (i__=k; i__ <= i__2; ++i__) {
if (i__==j) {
 goto L100;
 }
i__3=i__+j*a_dim1;
if (a[i__3].r!=0.f||r_imag(&a[i__+j*a_dim1]) !=0.f) {
 goto L110;
 }
L100:
 ;
 }

m=k;
iexc=2;
 goto L20;
L110:
 ;
 }

L120:
i__1=l;
for (i__=k; i__ <= i__1; ++i__) {
scale[i__] =1.f;
/* L130: */
 }

if (lsame_(job, "P")) {
 goto L210;
 }

/* Balance the submatrix in rows K to L. */

/* Iterative loop for norm reduction */

sfmin1=slamch_("S") / slamch_("P");
sfmax1=1.f / sfmin1;
sfmin2=sfmin1*2.f;
sfmax2=1.f / sfmin2;
L140:
noconv=FALSE_;

i__1=l;
for (i__=k; i__ <= i__1; ++i__) {

i__2=l-k+1;
c__=scnrm2_(&i__2, &a[k+i__*a_dim1], &c__1);
i__2=l-k+1;
r__=scnrm2_(&i__2, &a[i__+k*a_dim1], lda);
ica=icamax_(&l, &a[i__*a_dim1+1], &c__1);
ca=c_abs(&a[ica+i__*a_dim1]);
i__2=*n-k+1;
ira=icamax_(&i__2, &a[i__+k*a_dim1], lda);
ra=c_abs(&a[i__+ (ira+k-1) *a_dim1]);

/* Guard against zero C or R due to underflow. */

if (c__==0.f||r__==0.f) {
 goto L200;
 }
g=r__ / 2.f;
f=1.f;
s=c__+r__;
L160:
/* Computing MAX */
r__1=f2cmax(f,c__);
/* Computing MIN */
r__2=f2cmin(r__,g);
if (c__ >= g||f2cmax(r__1,ca) >= sfmax2||f2cmin(r__2,ra) <= sfmin2) {
 goto L170;
 }
r__1=c__+f+ca+r__+g+ra;
if (sisnan_(&r__1)) {

/* Exit if NaN to avoid infinite loop */

*info=-3;
i__2=-(*info);
xerbla_("CGEBAL", &i__2, (ftnlen)6);
return0;
 }
f *= 2.f;
c__ *= 2.f;
ca *= 2.f;
r__ /= 2.f;
g /= 2.f;
ra /= 2.f;
 goto L160;

L170:
g=c__ / 2.f;
L180:
/* Computing MIN */
r__1=f2cmin(f,c__), r__1=f2cmin(r__1,g);
if (g<r__||f2cmax(r__,ra) >= sfmax2||f2cmin(r__1,ca) <= sfmin2) {
 goto L190;
 }
f /= 2.f;
c__ /= 2.f;
g /= 2.f;
ca /= 2.f;
r__ *= 2.f;
ra *= 2.f;
 goto L180;

/* Now balance. */

L190:
if (c__+r__ >= s*.95f) {
 goto L200;
 }
if (f<1.f&&scale[i__] <1.f) {
if (f*scale[i__] <= sfmin1) {
 goto L200;
 }
 }
if (f>1.f&&scale[i__] >1.f) {
if (scale[i__] >= sfmax1 / f) {
 goto L200;
 }
 }
g=1.f / f;
scale[i__] *= f;
noconv=TRUE_;

i__2=*n-k+1;
csscal_(&i__2, &g, &a[i__+k*a_dim1], lda);
csscal_(&l, &f, &a[i__*a_dim1+1], &c__1);

L200:
 ;
 }

if (noconv) {
 goto L140;
 }

L210:
*ilo=k;
*ihi=l;

return0;

/* End of CGEBAL */

} /* cgebal_ */