cgbsvx.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> CGBSVX computes the solution to system of linear equations A * X = B for GB matrices</b> */

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

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

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

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

/* SUBROUTINE CGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, */
/* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, */
/* RCOND, FERR, BERR, WORK, RWORK, INFO ) */

/* CHARACTER EQUED, FACT, TRANS */
/* INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS */
/* REAL RCOND */
/* INTEGER IPIV( * ) */
/* REAL BERR( * ), C( * ), FERR( * ), R( * ), */
/* $ RWORK( * ) */
/* COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
/* $ WORK( * ), X( LDX, * ) */


/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGBSVX uses the LU factorization to compute the solution to a complex */
/* > system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */
/* > where A is a band matrix of order N with KL subdiagonals and KU */
/* > superdiagonals, and X and B are N-by-NRHS matrices. */
/* > */
/* > Error bounds on the solution and a condition estimate are also */
/* > provided. */
/* > \endverbatim */

/* > \par Description: */
/* ================= */
/* > */
/* > \verbatim */
/* > */
/* > The following steps are performed by this subroutine: */
/* > */
/* > 1. If FACT = 'E', real scaling factors are computed to equilibrate */
/* > the system: */
/* > TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
/* > TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
/* > TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
/* > Whether or not the system will be equilibrated depends on the */
/* > scaling of the matrix A, but if equilibration is used, A is */
/* > overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
/* > or diag(C)*B (if TRANS = 'T' or 'C'). */
/* > */
/* > 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */
/* > matrix A (after equilibration if FACT = 'E') as */
/* > A = L * U, */
/* > where L is a product of permutation and unit lower triangular */
/* > matrices with KL subdiagonals, and U is upper triangular with */
/* > KL+KU superdiagonals. */
/* > */
/* > 3. If some U(i,i)=0, so that U is exactly singular, then the routine */
/* > returns with INFO = i. Otherwise, the factored form of A is used */
/* > to estimate the condition number of the matrix A. If the */
/* > reciprocal of the condition number is less than machine precision, */
/* > INFO = N+1 is returned as a warning, but the routine still goes on */
/* > to solve for X and compute error bounds as described below. */
/* > */
/* > 4. The system of equations is solved for X using the factored form */
/* > of A. */
/* > */
/* > 5. Iterative refinement is applied to improve the computed solution */
/* > matrix and calculate error bounds and backward error estimates */
/* > for it. */
/* > */
/* > 6. If equilibration was used, the matrix X is premultiplied by */
/* > diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
/* > that it solves the original system before equilibration. */
/* > \endverbatim */

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

/* > \param[in] FACT */
/* > \verbatim */
/* > FACT is CHARACTER*1 */
/* > Specifies whether or not the factored form of the matrix A is */
/* > supplied on entry, and if not, whether the matrix A should be */
/* > equilibrated before it is factored. */
/* > = 'F': On entry, AFB and IPIV contain the factored form of */
/* > A. If EQUED is not 'N', the matrix A has been */
/* > equilibrated with scaling factors given by R and C. */
/* > AB, AFB, and IPIV are not modified. */
/* > = 'N': The matrix A will be copied to AFB and factored. */
/* > = 'E': The matrix A will be equilibrated if necessary, then */
/* > copied to AFB and factored. */
/* > \endverbatim */
/* > */
/* > \param[in] TRANS */
/* > \verbatim */
/* > TRANS is CHARACTER*1 */
/* > Specifies the form of the system of equations. */
/* > = 'N': A * X = B (No transpose) */
/* > = 'T': A**T * X = B (Transpose) */
/* > = 'C': A**H * X = B (Conjugate transpose) */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of linear equations, i.e., the order of the */
/* > matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KL */
/* > \verbatim */
/* > KL is INTEGER */
/* > The number of subdiagonals within the band of A. KL >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KU */
/* > \verbatim */
/* > KU is INTEGER */
/* > The number of superdiagonals within the band of A. KU >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* > NRHS is INTEGER */
/* > The number of right hand sides, i.e., the number of columns */
/* > of the matrices B and X. NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AB */
/* > \verbatim */
/* > AB is COMPLEX array, dimension (LDAB,N) */
/* > On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* > The j-th column of A is stored in the j-th column of the */
/* > array AB as follows: */
/* > AB(KU+1+i-j,j) = A(i,j) for f2cmax(1,j-KU)<=i<=f2cmin(N,j+kl) */
/* > */
/* > If FACT = 'F' and EQUED is not 'N', then A must have been */
/* > equilibrated by the scaling factors in R and/or C. AB is not */
/* > modified if FACT = 'F' or 'N', or if FACT = 'E' and */
/* > EQUED = 'N' on exit. */
/* > */
/* > On exit, if EQUED .ne. 'N', A is scaled as follows: */
/* > EQUED = 'R': A := diag(R) * A */
/* > EQUED = 'C': A := A * diag(C) */
/* > EQUED = 'B': A := diag(R) * A * diag(C). */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AFB */
/* > \verbatim */
/* > AFB is COMPLEX array, dimension (LDAFB,N) */
/* > If FACT = 'F', then AFB is an input argument and on entry */
/* > contains details of the LU factorization of the band matrix */
/* > A, as computed by CGBTRF. U is stored as an upper triangular */
/* > band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */
/* > and the multipliers used during the factorization are stored */
/* > in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */
/* > the factored form of the equilibrated matrix A. */
/* > */
/* > If FACT = 'N', then AFB is an output argument and on exit */
/* > returns details of the LU factorization of A. */
/* > */
/* > If FACT = 'E', then AFB is an output argument and on exit */
/* > returns details of the LU factorization of the equilibrated */
/* > matrix A (see the description of AB for the form of the */
/* > equilibrated matrix). */
/* > \endverbatim */
/* > */
/* > \param[in] LDAFB */
/* > \verbatim */
/* > LDAFB is INTEGER */
/* > The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > If FACT = 'F', then IPIV is an input argument and on entry */
/* > contains the pivot indices from the factorization A = L*U */
/* > as computed by CGBTRF; row i of the matrix was interchanged */
/* > with row IPIV(i). */
/* > */
/* > If FACT = 'N', then IPIV is an output argument and on exit */
/* > contains the pivot indices from the factorization A = L*U */
/* > of the original matrix A. */
/* > */
/* > If FACT = 'E', then IPIV is an output argument and on exit */
/* > contains the pivot indices from the factorization A = L*U */
/* > of the equilibrated matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in,out] EQUED */
/* > \verbatim */
/* > EQUED is CHARACTER*1 */
/* > Specifies the form of equilibration that was done. */
/* > = 'N': No equilibration (always true if FACT = 'N'). */
/* > = 'R': Row equilibration, i.e., A has been premultiplied by */
/* > diag(R). */
/* > = 'C': Column equilibration, i.e., A has been postmultiplied */
/* > by diag(C). */
/* > = 'B': Both row and column equilibration, i.e., A has been */
/* > replaced by diag(R) * A * diag(C). */
/* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* > output argument. */
/* > \endverbatim */
/* > */
/* > \param[in,out] R */
/* > \verbatim */
/* > R is REAL array, dimension (N) */
/* > The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* > is not accessed. R is an input argument if FACT = 'F'; */
/* > otherwise, R is an output argument. If FACT = 'F' and */
/* > EQUED = 'R' or 'B', each element of R must be positive. */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* > C is REAL array, dimension (N) */
/* > The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* > is not accessed. C is an input argument if FACT = 'F'; */
/* > otherwise, C is an output argument. If FACT = 'F' and */
/* > EQUED = 'C' or 'B', each element of C must be positive. */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is COMPLEX array, dimension (LDB,NRHS) */
/* > On entry, the right hand side matrix B. */
/* > On exit, */
/* > if EQUED = 'N', B is not modified; */
/* > if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
/* > diag(R)*B; */
/* > if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
/* > overwritten by diag(C)*B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* > X is COMPLEX array, dimension (LDX,NRHS) */
/* > If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */
/* > to the original system of equations. Note that A and B are */
/* > modified on exit if EQUED .ne. 'N', and the solution to the */
/* > equilibrated system is inv(diag(C))*X if TRANS = 'N' and */
/* > EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */
/* > and EQUED = 'R' or 'B'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] RCOND */
/* > \verbatim */
/* > RCOND is REAL */
/* > The estimate of the reciprocal condition number of the matrix */
/* > A after equilibration (if done). If RCOND is less than the */
/* > machine precision (in particular, if RCOND = 0), the matrix */
/* > is singular to working precision. This condition is */
/* > indicated by a return code of INFO > 0. */
/* > \endverbatim */
/* > */
/* > \param[out] FERR */
/* > \verbatim */
/* > FERR is REAL array, dimension (NRHS) */
/* > The estimated forward error bound for each solution vector */
/* > X(j) (the j-th column of the solution matrix X). */
/* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* > is an estimated upper bound for the magnitude of the largest */
/* > element in (X(j) - XTRUE) divided by the magnitude of the */
/* > largest element in X(j). The estimate is as reliable as */
/* > the estimate for RCOND, and is almost always a slight */
/* > overestimate of the true error. */
/* > \endverbatim */
/* > */
/* > \param[out] BERR */
/* > \verbatim */
/* > BERR is REAL array, dimension (NRHS) */
/* > The componentwise relative backward error of each solution */
/* > vector X(j) (i.e., the smallest relative change in */
/* > any element of A or B that makes X(j) an exact solution). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension (2*N) */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (N) */
/* > On exit, RWORK(1) contains the reciprocal pivot growth */
/* > factor norm(A)/norm(U). The "f2cmax absolute element" norm is */
/* > used. If RWORK(1) is much less than 1, then the stability */
/* > of the LU factorization of the (equilibrated) matrix A */
/* > could be poor. This also means that the solution X, condition */
/* > estimator RCOND, and forward error bound FERR could be */
/* > unreliable. If factorization fails with 0<INFO<=N, then */
/* > RWORK(1) contains the reciprocal pivot growth factor for the */
/* > leading INFO columns of A. */
/* > \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: U(i,i) is exactly zero. The factorization */
/* > has been completed, but the factor U is exactly */
/* > singular, so the solution and error bounds */
/* > could not be computed. RCOND = 0 is returned. */
/* > = N+1: U is nonsingular, but RCOND is less than machine */
/* > precision, meaning that the matrix is singular */
/* > to working precision. Nevertheless, the */
/* > solution and error bounds are computed because */
/* > there are a number of situations where the */
/* > computed solution can be more accurate than the */
/* > value of RCOND would suggest. */
/* > \endverbatim */

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

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

/* > \date April 2012 */

/* > \ingroup complexGBsolve */

/* ===================================================================== */
/* Subroutine */voidcgbsvx_(char*fact, char*trans, integer*n, integer*kl,
integer*ku, integer*nrhs, complex*ab, integer*ldab, complex*afb,
integer*ldafb, integer*ipiv, char*equed, real*r__, real*c__, 
complex*b, integer*ldb, complex*x, integer*ldx, real*rcond, real
*ferr, real*berr, complex*work, real*rwork, integer*info)
{
/* System generated locals */
integerab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
realr__1, r__2;
complexq__1;

/* Local variables */
realamax;
charnorm[1];
integeri__, j;
externlogicallsame_(char*, char*);
realrcmin, rcmax, anorm;
extern/* Subroutine */voidccopy_(integer*, complex*, integer*, 
complex*, integer*);
logicalequil;
integerj1, j2;
externrealclangb_(char*, integer*, integer*, integer*, complex*, 
integer*, real*);
extern/* Subroutine */voidclaqgb_(integer*, integer*, integer*, 
integer*, complex*, integer*, real*, real*, real*, real*, 
real*, char*), cgbcon_(char*, integer*, integer*, 
integer*, complex*, integer*, integer*, real*, real*, 
complex*, real*, integer*);
realcolcnd;
externrealclantb_(char*, char*, char*, integer*, integer*, complex
*, integer*, real*);
extern/* Subroutine */voidcgbequ_(integer*, integer*, integer*, 
integer*, complex*, integer*, real*, real*, real*, real*, 
real*, integer*);
externrealslamch_(char*);
extern/* Subroutine */voidcgbrfs_(char*, integer*, integer*, integer
*, integer*, complex*, integer*, complex*, integer*, integer
*, complex*, integer*, complex*, integer*, real*, real*, 
complex*, real*, integer*), cgbtrf_(integer*, integer
*, integer*, integer*, complex*, integer*, integer*, integer
*);
logicalnofact;
extern/* Subroutine */voidclacpy_(char*, integer*, integer*, complex
*, integer*, complex*, integer*);
externintxerbla_(char*, integer*, ftnlen);
realbignum;
extern/* Subroutine */voidcgbtrs_(char*, integer*, integer*, integer
*, integer*, complex*, integer*, integer*, complex*, integer
*, integer*);
integerinfequ;
logicalcolequ;
realrowcnd;
logicalnotran;
realsmlnum;
logicalrowequ;
realrpvgrw;


/* -- 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..-- */
/* April 2012 */


/* ===================================================================== */
/* Moved setting of INFO = N+1 so INFO does not subsequently get */
/* overwritten. Sven, 17 Mar 05. */
/* ===================================================================== */


/* Parameter adjustments */
ab_dim1=*ldab;
ab_offset=1+ab_dim1*1;
ab-=ab_offset;
afb_dim1=*ldafb;
afb_offset=1+afb_dim1*1;
afb-=afb_offset;
--ipiv;
--r__;
--c__;
b_dim1=*ldb;
b_offset=1+b_dim1*1;
b-=b_offset;
x_dim1=*ldx;
x_offset=1+x_dim1*1;
x-=x_offset;
--ferr;
--berr;
--work;
--rwork;

/* Function Body */
*info=0;
nofact=lsame_(fact, "N");
equil=lsame_(fact, "E");
notran=lsame_(trans, "N");
if (nofact||equil) {
*(unsigned char*)equed='N';
rowequ=FALSE_;
colequ=FALSE_;
 } else {
rowequ=lsame_(equed, "R") ||lsame_(equed, 
"B");
colequ=lsame_(equed, "C") ||lsame_(equed,