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OpenBLAS/lapack-netlib/SRC/zla_gbrfsx_extended.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]/Cd(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 pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(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);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#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)}
/* procedure parameter types for -A and -C++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
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;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
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];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -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;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, 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];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, 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];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {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
_Complex float zdotc = 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
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {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
_Complex double zdotc = 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
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {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
_Complex float zdotc = 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
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {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
_Complex double zdotc = 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 */
static integer c__1 = 1;
static doublecomplex c_b6 = {-1.,0.};
static doublecomplex c_b8 = {1.,0.};
static doublereal c_b31 = 1.;
/* > \brief \b ZLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general
banded matrices by performing extra-precise iterative refinement and provides error bounds and backwar
d error estimates for the solution. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZLA_GBRFSX_EXTENDED + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbr
fsx_extended.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbr
fsx_extended.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbr
fsx_extended.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, */
/* NRHS, AB, LDAB, AFB, LDAFB, IPIV, */
/* COLEQU, C, B, LDB, Y, LDY, */
/* BERR_OUT, N_NORMS, ERR_BNDS_NORM, */
/* ERR_BNDS_COMP, RES, AYB, DY, */
/* Y_TAIL, RCOND, ITHRESH, RTHRESH, */
/* DZ_UB, IGNORE_CWISE, INFO ) */
/* INTEGER INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS, */
/* $ PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH */
/* LOGICAL COLEQU, IGNORE_CWISE */
/* DOUBLE PRECISION RTHRESH, DZ_UB */
/* INTEGER IPIV( * ) */
/* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
/* $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * ) */
/* DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ), */
/* $ ERR_BNDS_NORM( NRHS, * ), */
/* $ ERR_BNDS_COMP( NRHS, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZLA_GBRFSX_EXTENDED improves the computed solution to a system of */
/* > linear equations by performing extra-precise iterative refinement */
/* > and provides error bounds and backward error estimates for the solution. */
/* > This subroutine is called by ZGBRFSX to perform iterative refinement. */
/* > In addition to normwise error bound, the code provides maximum */
/* > componentwise error bound if possible. See comments for ERR_BNDS_NORM */
/* > and ERR_BNDS_COMP for details of the error bounds. Note that this */
/* > subroutine is only resonsible for setting the second fields of */
/* > ERR_BNDS_NORM and ERR_BNDS_COMP. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] PREC_TYPE */
/* > \verbatim */
/* > PREC_TYPE is INTEGER */
/* > Specifies the intermediate precision to be used in refinement. */
/* > The value is defined by ILAPREC(P) where P is a CHARACTER and P */
/* > = 'S': Single */
/* > = 'D': Double */
/* > = 'I': Indigenous */
/* > = 'X' or 'E': Extra */
/* > \endverbatim */
/* > */
/* > \param[in] TRANS_TYPE */
/* > \verbatim */
/* > TRANS_TYPE is INTEGER */
/* > Specifies the transposition operation on A. */
/* > The value is defined by ILATRANS(T) where T is a CHARACTER and T */
/* > = 'N': No transpose */
/* > = 'T': Transpose */
/* > = 'C': 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 */
/* > matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] AB */
/* > \verbatim */
/* > AB is COMPLEX*16 array, dimension (LDAB,N) */
/* > On entry, the N-by-N matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array A. LDAB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] AFB */
/* > \verbatim */
/* > AFB is COMPLEX*16 array, dimension (LDAF,N) */
/* > The factors L and U from the factorization */
/* > A = P*L*U as computed by ZGBTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAFB */
/* > \verbatim */
/* > LDAFB is INTEGER */
/* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > The pivot indices from the factorization A = P*L*U */
/* > as computed by ZGBTRF; row i of the matrix was interchanged */
/* > with row IPIV(i). */
/* > \endverbatim */
/* > */
/* > \param[in] COLEQU */
/* > \verbatim */
/* > COLEQU is LOGICAL */
/* > If .TRUE. then column equilibration was done to A before calling */
/* > this routine. This is needed to compute the solution and error */
/* > bounds correctly. */
/* > \endverbatim */
/* > */
/* > \param[in] C */
/* > \verbatim */
/* > C is DOUBLE PRECISION array, dimension (N) */
/* > The column scale factors for A. If COLEQU = .FALSE., C */
/* > is not accessed. If C is input, each element of C should be a power */
/* > of the radix to ensure a reliable solution and error estimates. */
/* > Scaling by powers of the radix does not cause rounding errors unless */
/* > the result underflows or overflows. Rounding errors during scaling */
/* > lead to refining with a matrix that is not equivalent to the */
/* > input matrix, producing error estimates that may not be */
/* > reliable. */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
/* > The right-hand-side matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] Y */
/* > \verbatim */
/* > Y is COMPLEX*16 array, dimension (LDY,NRHS) */
/* > On entry, the solution matrix X, as computed by ZGBTRS. */
/* > On exit, the improved solution matrix Y. */
/* > \endverbatim */
/* > */
/* > \param[in] LDY */
/* > \verbatim */
/* > LDY is INTEGER */
/* > The leading dimension of the array Y. LDY >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] BERR_OUT */
/* > \verbatim */
/* > BERR_OUT is DOUBLE PRECISION array, dimension (NRHS) */
/* > On exit, BERR_OUT(j) contains the componentwise relative backward */
/* > error for right-hand-side j from the formula */
/* > f2cmax(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* > where abs(Z) is the componentwise absolute value of the matrix */
/* > or vector Z. This is computed by ZLA_LIN_BERR. */
/* > \endverbatim */
/* > */
/* > \param[in] N_NORMS */
/* > \verbatim */
/* > N_NORMS is INTEGER */
/* > Determines which error bounds to return (see ERR_BNDS_NORM */
/* > and ERR_BNDS_COMP). */
/* > If N_NORMS >= 1 return normwise error bounds. */
/* > If N_NORMS >= 2 return componentwise error bounds. */
/* > \endverbatim */
/* > */
/* > \param[in,out] ERR_BNDS_NORM */
/* > \verbatim */
/* > ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* > For each right-hand side, this array contains information about */
/* > various error bounds and condition numbers corresponding to the */
/* > normwise relative error, which is defined as follows: */
/* > */
/* > Normwise relative error in the ith solution vector: */
/* > max_j (abs(XTRUE(j,i) - X(j,i))) */
/* > ------------------------------ */
/* > max_j abs(X(j,i)) */
/* > */
/* > The array is indexed by the type of error information as described */
/* > below. There currently are up to three pieces of information */
/* > returned. */
/* > */
/* > The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* > right-hand side. */
/* > */
/* > The second index in ERR_BNDS_NORM(:,err) contains the following */
/* > three fields: */
/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* > reciprocal condition number is less than the threshold */
/* > sqrt(n) * slamch('Epsilon'). */
/* > */
/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
/* > almost certainly within a factor of 10 of the true error */
/* > so long as the next entry is greater than the threshold */
/* > sqrt(n) * slamch('Epsilon'). This error bound should only */
/* > be trusted if the previous boolean is true. */
/* > */
/* > err = 3 Reciprocal condition number: Estimated normwise */
/* > reciprocal condition number. Compared with the threshold */
/* > sqrt(n) * slamch('Epsilon') to determine if the error */
/* > estimate is "guaranteed". These reciprocal condition */
/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* > appropriately scaled matrix Z. */
/* > Let Z = S*A, where S scales each row by a power of the */
/* > radix so all absolute row sums of Z are approximately 1. */
/* > */
/* > This subroutine is only responsible for setting the second field */
/* > above. */
/* > See Lapack Working Note 165 for further details and extra */
/* > cautions. */
/* > \endverbatim */
/* > */
/* > \param[in,out] ERR_BNDS_COMP */
/* > \verbatim */
/* > ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* > For each right-hand side, this array contains information about */
/* > various error bounds and condition numbers corresponding to the */
/* > componentwise relative error, which is defined as follows: */
/* > */
/* > Componentwise relative error in the ith solution vector: */
/* > abs(XTRUE(j,i) - X(j,i)) */
/* > max_j ---------------------- */
/* > abs(X(j,i)) */
/* > */
/* > The array is indexed by the right-hand side i (on which the */
/* > componentwise relative error depends), and the type of error */
/* > information as described below. There currently are up to three */
/* > pieces of information returned for each right-hand side. If */
/* > componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* > ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most */
/* > the first (:,N_ERR_BNDS) entries are returned. */
/* > */
/* > The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* > right-hand side. */
/* > */
/* > The second index in ERR_BNDS_COMP(:,err) contains the following */
/* > three fields: */
/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* > reciprocal condition number is less than the threshold */
/* > sqrt(n) * slamch('Epsilon'). */
/* > */
/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
/* > almost certainly within a factor of 10 of the true error */
/* > so long as the next entry is greater than the threshold */
/* > sqrt(n) * slamch('Epsilon'). This error bound should only */
/* > be trusted if the previous boolean is true. */
/* > */
/* > err = 3 Reciprocal condition number: Estimated componentwise */
/* > reciprocal condition number. Compared with the threshold */
/* > sqrt(n) * slamch('Epsilon') to determine if the error */
/* > estimate is "guaranteed". These reciprocal condition */
/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* > appropriately scaled matrix Z. */
/* > Let Z = S*(A*diag(x)), where x is the solution for the */
/* > current right-hand side and S scales each row of */
/* > A*diag(x) by a power of the radix so all absolute row */
/* > sums of Z are approximately 1. */
/* > */
/* > This subroutine is only responsible for setting the second field */
/* > above. */
/* > See Lapack Working Note 165 for further details and extra */
/* > cautions. */
/* > \endverbatim */
/* > */
/* > \param[in] RES */
/* > \verbatim */
/* > RES is COMPLEX*16 array, dimension (N) */
/* > Workspace to hold the intermediate residual. */
/* > \endverbatim */
/* > */
/* > \param[in] AYB */
/* > \verbatim */
/* > AYB is DOUBLE PRECISION array, dimension (N) */
/* > Workspace. */
/* > \endverbatim */
/* > */
/* > \param[in] DY */
/* > \verbatim */
/* > DY is COMPLEX*16 array, dimension (N) */
/* > Workspace to hold the intermediate solution. */
/* > \endverbatim */
/* > */
/* > \param[in] Y_TAIL */
/* > \verbatim */
/* > Y_TAIL is COMPLEX*16 array, dimension (N) */
/* > Workspace to hold the trailing bits of the intermediate solution. */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* > RCOND is DOUBLE PRECISION */
/* > Reciprocal scaled condition number. This is an estimate of the */
/* > reciprocal Skeel condition number of the matrix A after */
/* > equilibration (if done). If this is less than the machine */
/* > precision (in particular, if it is zero), the matrix is singular */
/* > to working precision. Note that the error may still be small even */
/* > if this number is very small and the matrix appears ill- */
/* > conditioned. */
/* > \endverbatim */
/* > */
/* > \param[in] ITHRESH */
/* > \verbatim */
/* > ITHRESH is INTEGER */
/* > The maximum number of residual computations allowed for */
/* > refinement. The default is 10. For 'aggressive' set to 100 to */
/* > permit convergence using approximate factorizations or */
/* > factorizations other than LU. If the factorization uses a */
/* > technique other than Gaussian elimination, the guarantees in */
/* > ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */
/* > \endverbatim */
/* > */
/* > \param[in] RTHRESH */
/* > \verbatim */
/* > RTHRESH is DOUBLE PRECISION */
/* > Determines when to stop refinement if the error estimate stops */
/* > decreasing. Refinement will stop when the next solution no longer */
/* > satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */
/* > the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */
/* > default value is 0.5. For 'aggressive' set to 0.9 to permit */
/* > convergence on extremely ill-conditioned matrices. See LAWN 165 */
/* > for more details. */
/* > \endverbatim */
/* > */
/* > \param[in] DZ_UB */
/* > \verbatim */
/* > DZ_UB is DOUBLE PRECISION */
/* > Determines when to start considering componentwise convergence. */
/* > Componentwise convergence is only considered after each component */
/* > of the solution Y is stable, which we definte as the relative */
/* > change in each component being less than DZ_UB. The default value */
/* > is 0.25, requiring the first bit to be stable. See LAWN 165 for */
/* > more details. */
/* > \endverbatim */
/* > */
/* > \param[in] IGNORE_CWISE */
/* > \verbatim */
/* > IGNORE_CWISE is LOGICAL */
/* > If .TRUE. then ignore componentwise convergence. Default value */
/* > is .FALSE.. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: Successful exit. */
/* > < 0: if INFO = -i, the ith argument to ZGBTRS had an illegal */
/* > value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2017 */
/* > \ingroup complex16GBcomputational */
/* ===================================================================== */
/* Subroutine */ void zla_gbrfsx_extended_(integer *prec_type__, integer *
trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs,
doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb,
integer *ipiv, logical *colequ, doublereal *c__, doublecomplex *b,
integer *ldb, doublecomplex *y, integer *ldy, doublereal *berr_out__,
integer *n_norms__, doublereal *err_bnds_norm__, doublereal *
err_bnds_comp__, doublecomplex *res, doublereal *ayb, doublecomplex *
dy, doublecomplex *y_tail__, doublereal *rcond, integer *ithresh,
doublereal *rthresh, doublereal *dz_ub__, logical *ignore_cwise__,
integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
char ch__1[1];
/* Local variables */
doublereal dx_x__, dz_z__, ymin;
extern /* Subroutine */ void zla_lin_berr_(integer *, integer *, integer *
, doublecomplex *, doublereal *, doublereal *);
doublereal dxratmax, dzratmax;
extern /* Subroutine */ void blas_zgbmv_x_(integer *, integer *, integer *
, integer *, integer *, doublecomplex *, doublecomplex *, integer
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
integer y_prec_state__, i__, j, m;
extern /* Subroutine */ void blas_zgbmv2_x_(integer *, integer *, integer
*, integer *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *),
zla_gbamv_(integer *, integer *, integer *, integer *, integer *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, integer *);
doublereal dxrat;
logical incr_prec__;
doublereal dzrat;
extern /* Subroutine */ void zgbmv_(char *, integer *, integer *, integer *
, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
char trans[1];
doublereal normx, normy;
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal myhugeval, prev_dz_z__;
extern doublereal dlamch_(char *);
doublereal yk, final_dx_x__, final_dz_z__, normdx;
extern /* Subroutine */ void zgbtrs_(char *, integer *, integer *, integer
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *), zla_wwaddw_(
integer *, doublecomplex *, doublecomplex *, doublecomplex *);
extern /* Character */ VOID chla_transtype_(char *, integer *);
doublereal prevnormdx;
integer cnt;
doublereal dyk, eps;
integer x_state__, z_state__;
doublereal incr_thresh__;
/* -- LAPACK computational routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2017 */
/* ===================================================================== */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1;
err_bnds_norm__ -= err_bnds_norm_offset;
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;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
if (*info != 0) {
return;
}
chla_transtype_(ch__1, trans_type__);
*(unsigned char *)trans = *(unsigned char *)&ch__1[0];
eps = dlamch_("Epsilon");
myhugeval = dlamch_("Overflow");
/* Force MYHUGEVAL to Inf */
myhugeval *= myhugeval;
/* Using MYHUGEVAL may lead to spurious underflows. */
incr_thresh__ = (doublereal) (*n) * eps;
m = *kl + *ku + 1;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
y_prec_state__ = 1;
if (y_prec_state__ == 2) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
y_tail__[i__3].r = 0., y_tail__[i__3].i = 0.;
}
}
dxrat = 0.;
dxratmax = 0.;
dzrat = 0.;
dzratmax = 0.;
final_dx_x__ = myhugeval;
final_dz_z__ = myhugeval;
prevnormdx = myhugeval;
prev_dz_z__ = myhugeval;
dz_z__ = myhugeval;
dx_x__ = myhugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1; cnt <= i__2; ++cnt) {
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0) {
zgbmv_(trans, &m, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[
j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1);
} else if (y_prec_state__ == 1) {
blas_zgbmv_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, &
res[1], &c__1, prec_type__);
} else {
blas_zgbmv2_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
ab_offset], ldab, &y[j * y_dim1 + 1], &y_tail__[1], &
c__1, &c_b8, &res[1], &c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
zcopy_(n, &res[1], &c__1, &dy[1], &c__1);
zgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
, &dy[1], n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.;
normy = 0.;
normdx = 0.;
dz_z__ = 0.;
ymin = myhugeval;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * y_dim1;
yk = (d__1 = y[i__4].r, abs(d__1)) + (d__2 = d_imag(&y[i__ +
j * y_dim1]), abs(d__2));
i__4 = i__;
dyk = (d__1 = dy[i__4].r, abs(d__1)) + (d__2 = d_imag(&dy[i__]
), abs(d__2));
if (yk != 0.) {
/* Computing MAX */
d__1 = dz_z__, d__2 = dyk / yk;
dz_z__ = f2cmax(d__1,d__2);
} else if (dyk != 0.) {
dz_z__ = myhugeval;
}
ymin = f2cmin(ymin,yk);
normy = f2cmax(normy,yk);
if (*colequ) {
/* Computing MAX */
d__1 = normx, d__2 = yk * c__[i__];
normx = f2cmax(d__1,d__2);
/* Computing MAX */
d__1 = normdx, d__2 = dyk * c__[i__];
normdx = f2cmax(d__1,d__2);
} else {
normx = normy;
normdx = f2cmax(normdx,dyk);
}
}
if (normx != 0.) {
dx_x__ = normdx / normx;
} else if (normdx == 0.) {
dx_x__ = 0.;
} else {
dx_x__ = myhugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria. */
if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy
&& y_prec_state__ < 2) {
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh) {
x_state__ = 1;
}
if (x_state__ == 1) {
if (dx_x__ <= eps) {
x_state__ = 2;
} else if (dxrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
x_state__ = 3;
}
} else {
if (dxrat > dxratmax) {
dxratmax = dxrat;
}
}
if (x_state__ > 1) {
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__) {
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh) {
z_state__ = 1;
}
if (z_state__ == 1) {
if (dz_z__ <= eps) {
z_state__ = 2;
} else if (dz_z__ > *dz_ub__) {
z_state__ = 0;
dzratmax = 0.;
final_dz_z__ = myhugeval;
} else if (dzrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
z_state__ = 3;
}
} else {
if (dzrat > dzratmax) {
dzratmax = dzrat;
}
}
if (z_state__ > 1) {
final_dz_z__ = dz_z__;
}
}
/* Exit if both normwise and componentwise stopped working, */
/* but if componentwise is unstable, let it go at least two */
/* iterations. */
if (x_state__ != 1) {
if (*ignore_cwise__) {
goto L666;
}
if (z_state__ == 3 || z_state__ == 2) {
goto L666;
}
if (z_state__ == 0 && cnt > 1) {
goto L666;
}
}
if (incr_prec__) {
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
y_tail__[i__4].r = 0., y_tail__[i__4].i = 0.;
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2) {
zaxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
} else {
zla_wwaddw_(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't CALL MYEXIT. */
L666:
/* Set final_* when cnt hits ithresh. */
if (x_state__ == 1) {
final_dx_x__ = dx_x__;
}
if (z_state__ == 1) {
final_dz_z__ = dz_z__;
}
/* Compute error bounds. */
if (*n_norms__ >= 1) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / (
1 - dxratmax);
}
if (*n_norms__ >= 2) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / (
1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* f2cmax(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
zgbmv_(trans, n, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[j *
y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
ayb[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__
+ j * b_dim1]), abs(d__2));
}
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
zla_gbamv_(trans_type__, n, n, kl, ku, &c_b31, &ab[ab_offset], ldab,
&y[j * y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1);
zla_lin_berr_(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return;
} /* zla_gbrfsx_extended__ */
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