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OpenBLAS/lapack-netlib/SRC/sgtrfs.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static real c_b18 = -1.f;
static real c_b19 = 1.f;
/* > \brief \b SGTRFS */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGTRFS + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgtrfs.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgtrfs.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgtrfs.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, */
/* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, */
/* INFO ) */
/* CHARACTER TRANS */
/* INTEGER INFO, LDB, LDX, N, NRHS */
/* INTEGER IPIV( * ), IWORK( * ) */
/* REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), */
/* $ DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ), */
/* $ FERR( * ), WORK( * ), X( LDX, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGTRFS improves the computed solution to a system of linear */
/* > equations when the coefficient matrix is tridiagonal, and provides */
/* > error bounds and backward error estimates for the solution. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \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 = Transpose) */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 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. NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] DL */
/* > \verbatim */
/* > DL is REAL array, dimension (N-1) */
/* > The (n-1) subdiagonal elements of A. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* > D is REAL array, dimension (N) */
/* > The diagonal elements of A. */
/* > \endverbatim */
/* > */
/* > \param[in] DU */
/* > \verbatim */
/* > DU is REAL array, dimension (N-1) */
/* > The (n-1) superdiagonal elements of A. */
/* > \endverbatim */
/* > */
/* > \param[in] DLF */
/* > \verbatim */
/* > DLF is REAL array, dimension (N-1) */
/* > The (n-1) multipliers that define the matrix L from the */
/* > LU factorization of A as computed by SGTTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] DF */
/* > \verbatim */
/* > DF is REAL array, dimension (N) */
/* > The n diagonal elements of the upper triangular matrix U from */
/* > the LU factorization of A. */
/* > \endverbatim */
/* > */
/* > \param[in] DUF */
/* > \verbatim */
/* > DUF is REAL array, dimension (N-1) */
/* > The (n-1) elements of the first superdiagonal of U. */
/* > \endverbatim */
/* > */
/* > \param[in] DU2 */
/* > \verbatim */
/* > DU2 is REAL array, dimension (N-2) */
/* > The (n-2) elements of the second superdiagonal of U. */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > The pivot indices; for 1 <= i <= n, row i of the matrix was */
/* > interchanged with row IPIV(i). IPIV(i) will always be either */
/* > i or i+1; IPIV(i) = i indicates a row interchange was not */
/* > required. */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is REAL 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] X */
/* > \verbatim */
/* > X is REAL array, dimension (LDX,NRHS) */
/* > On entry, the solution matrix X, as computed by SGTTRS. */
/* > On exit, the improved solution matrix X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
/* > \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 REAL array, dimension (3*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* > \par Internal Parameters: */
/* ========================= */
/* > */
/* > \verbatim */
/* > ITMAX is the maximum number of steps of iterative refinement. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realGTcomputational */
/* ===================================================================== */
/* Subroutine */ void sgtrfs_(char *trans, integer *n, integer *nrhs, real *dl,
real *d__, real *du, real *dlf, real *df, real *duf, real *du2,
integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real *
ferr, real *berr, real *work, integer *iwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
integer kase;
real safe1, safe2;
integer i__, j;
real s;
extern logical lsame_(char *, char *);
integer isave[3], count;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *), saxpy_(integer *, real *, real *, integer *, real *,
integer *), slacn2_(integer *, real *, real *, integer *, real *,
integer *, integer *);
extern real slamch_(char *);
integer nz;
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern void slagtm_(
char *, integer *, integer *, real *, real *, real *, real *,
real *, integer *, real *, real *, integer *);
logical notran;
char transn[1], transt[1];
real lstres;
extern /* Subroutine */ void sgttrs_(char *, integer *, integer *, real *,
real *, real *, real *, integer *, real *, integer *, integer *);
real eps;
/* -- 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 */
--dl;
--d__;
--du;
--dlf;
--df;
--duf;
--du2;
--ipiv;
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;
--iwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < f2cmax(1,*n)) {
*info = -13;
} else if (*ldx < f2cmax(1,*n)) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGTRFS", &i__1, (ftnlen)6);
return;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'T';
} else {
*(unsigned char *)transn = 'T';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = 4;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
scopy_(n, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
slagtm_(trans, n, &c__1, &c_b18, &dl[1], &d__[1], &du[1], &x[j *
x_dim1 + 1], ldx, &c_b19, &work[*n + 1], n);
/* Compute abs(op(A))*abs(x) + abs(b) for use in the backward */
/* error bound. */
if (notran) {
if (*n == 1) {
work[1] = (r__1 = b[j * b_dim1 + 1], abs(r__1)) + (r__2 = d__[
1] * x[j * x_dim1 + 1], abs(r__2));
} else {
work[1] = (r__1 = b[j * b_dim1 + 1], abs(r__1)) + (r__2 = d__[
1] * x[j * x_dim1 + 1], abs(r__2)) + (r__3 = du[1] *
x[j * x_dim1 + 2], abs(r__3));
i__2 = *n - 1;
for (i__ = 2; i__ <= i__2; ++i__) {
work[i__] = (r__1 = b[i__ + j * b_dim1], abs(r__1)) + (
r__2 = dl[i__ - 1] * x[i__ - 1 + j * x_dim1], abs(
r__2)) + (r__3 = d__[i__] * x[i__ + j * x_dim1],
abs(r__3)) + (r__4 = du[i__] * x[i__ + 1 + j *
x_dim1], abs(r__4));
/* L30: */
}
work[*n] = (r__1 = b[*n + j * b_dim1], abs(r__1)) + (r__2 =
dl[*n - 1] * x[*n - 1 + j * x_dim1], abs(r__2)) + (
r__3 = d__[*n] * x[*n + j * x_dim1], abs(r__3));
}
} else {
if (*n == 1) {
work[1] = (r__1 = b[j * b_dim1 + 1], abs(r__1)) + (r__2 = d__[
1] * x[j * x_dim1 + 1], abs(r__2));
} else {
work[1] = (r__1 = b[j * b_dim1 + 1], abs(r__1)) + (r__2 = d__[
1] * x[j * x_dim1 + 1], abs(r__2)) + (r__3 = dl[1] *
x[j * x_dim1 + 2], abs(r__3));
i__2 = *n - 1;
for (i__ = 2; i__ <= i__2; ++i__) {
work[i__] = (r__1 = b[i__ + j * b_dim1], abs(r__1)) + (
r__2 = du[i__ - 1] * x[i__ - 1 + j * x_dim1], abs(
r__2)) + (r__3 = d__[i__] * x[i__ + j * x_dim1],
abs(r__3)) + (r__4 = dl[i__] * x[i__ + 1 + j *
x_dim1], abs(r__4));
/* L40: */
}
work[*n] = (r__1 = b[*n + j * b_dim1], abs(r__1)) + (r__2 =
du[*n - 1] * x[*n - 1 + j * x_dim1], abs(r__2)) + (
r__3 = d__[*n] * x[*n + j * x_dim1], abs(r__3));
}
}
/* Compute componentwise relative backward error from formula */
/* f2cmax(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
/* Computing MAX */
r__2 = s, r__3 = (r__1 = work[*n + i__], abs(r__1)) / work[
i__];
s = f2cmax(r__2,r__3);
} else {
/* Computing MAX */
r__2 = s, r__3 = ((r__1 = work[*n + i__], abs(r__1)) + safe1)
/ (work[i__] + safe1);
s = f2cmax(r__2,r__3);
}
/* L50: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
sgttrs_(trans, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[
1], &work[*n + 1], n, info);
saxpy_(n, &c_b19, &work[*n + 1], &c__1, &x[j * x_dim1 + 1], &c__1)
;
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(op(A)))* */
/* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(op(A)) is the inverse of op(A) */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
/* Use SLACN2 to estimate the infinity-norm of the matrix */
/* inv(op(A)) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
work[i__] = (r__1 = work[*n + i__], abs(r__1)) + nz * eps *
work[i__];
} else {
work[i__] = (r__1 = work[*n + i__], abs(r__1)) + nz * eps *
work[i__] + safe1;
}
/* L60: */
}
kase = 0;
L70:
slacn2_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T). */
sgttrs_(transt, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &
ipiv[1], &work[*n + 1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L80: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L90: */
}
sgttrs_(transn, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &
ipiv[1], &work[*n + 1], n, info);
}
goto L70;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
r__2 = lstres, r__3 = (r__1 = x[i__ + j * x_dim1], abs(r__1));
lstres = f2cmax(r__2,r__3);
/* L100: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L110: */
}
return;
/* End of SGTRFS */
} /* sgtrfs_ */
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