#include #include #include #include #include #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 int logical; typedef short int shortlogical; 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 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++ */ #define F2C_proc_par_types 1 #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 \brief \b SLARRF finds a new relatively robust representation such that at least one of the eigenvalues i s relatively isolated. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLARRF + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLARRF( N, D, L, LD, CLSTRT, CLEND, */ /* W, WGAP, WERR, */ /* SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, */ /* DPLUS, LPLUS, WORK, INFO ) */ /* INTEGER CLSTRT, CLEND, INFO, N */ /* REAL CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM */ /* REAL D( * ), DPLUS( * ), L( * ), LD( * ), */ /* $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > Given the initial representation L D L^T and its cluster of close */ /* > eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... */ /* > W( CLEND ), SLARRF finds a new relatively robust representation */ /* > L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the */ /* > eigenvalues of L(+) D(+) L(+)^T is relatively isolated. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix (subblock, if the matrix split). */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > The N diagonal elements of the diagonal matrix D. */ /* > \endverbatim */ /* > */ /* > \param[in] L */ /* > \verbatim */ /* > L is REAL array, dimension (N-1) */ /* > The (N-1) subdiagonal elements of the unit bidiagonal */ /* > matrix L. */ /* > \endverbatim */ /* > */ /* > \param[in] LD */ /* > \verbatim */ /* > LD is REAL array, dimension (N-1) */ /* > The (N-1) elements L(i)*D(i). */ /* > \endverbatim */ /* > */ /* > \param[in] CLSTRT */ /* > \verbatim */ /* > CLSTRT is INTEGER */ /* > The index of the first eigenvalue in the cluster. */ /* > \endverbatim */ /* > */ /* > \param[in] CLEND */ /* > \verbatim */ /* > CLEND is INTEGER */ /* > The index of the last eigenvalue in the cluster. */ /* > \endverbatim */ /* > */ /* > \param[in] W */ /* > \verbatim */ /* > W is REAL array, dimension */ /* > dimension is >= (CLEND-CLSTRT+1) */ /* > The eigenvalue APPROXIMATIONS of L D L^T in ascending order. */ /* > W( CLSTRT ) through W( CLEND ) form the cluster of relatively */ /* > close eigenalues. */ /* > \endverbatim */ /* > */ /* > \param[in,out] WGAP */ /* > \verbatim */ /* > WGAP is REAL array, dimension */ /* > dimension is >= (CLEND-CLSTRT+1) */ /* > The separation from the right neighbor eigenvalue in W. */ /* > \endverbatim */ /* > */ /* > \param[in] WERR */ /* > \verbatim */ /* > WERR is REAL array, dimension */ /* > dimension is >= (CLEND-CLSTRT+1) */ /* > WERR contain the semiwidth of the uncertainty */ /* > interval of the corresponding eigenvalue APPROXIMATION in W */ /* > \endverbatim */ /* > */ /* > \param[in] SPDIAM */ /* > \verbatim */ /* > SPDIAM is REAL */ /* > estimate of the spectral diameter obtained from the */ /* > Gerschgorin intervals */ /* > \endverbatim */ /* > */ /* > \param[in] CLGAPL */ /* > \verbatim */ /* > CLGAPL is REAL */ /* > \endverbatim */ /* > */ /* > \param[in] CLGAPR */ /* > \verbatim */ /* > CLGAPR is REAL */ /* > absolute gap on each end of the cluster. */ /* > Set by the calling routine to protect against shifts too close */ /* > to eigenvalues outside the cluster. */ /* > \endverbatim */ /* > */ /* > \param[in] PIVMIN */ /* > \verbatim */ /* > PIVMIN is REAL */ /* > The minimum pivot allowed in the Sturm sequence. */ /* > \endverbatim */ /* > */ /* > \param[out] SIGMA */ /* > \verbatim */ /* > SIGMA is REAL */ /* > The shift used to form L(+) D(+) L(+)^T. */ /* > \endverbatim */ /* > */ /* > \param[out] DPLUS */ /* > \verbatim */ /* > DPLUS is REAL array, dimension (N) */ /* > The N diagonal elements of the diagonal matrix D(+). */ /* > \endverbatim */ /* > */ /* > \param[out] LPLUS */ /* > \verbatim */ /* > LPLUS is REAL array, dimension (N-1) */ /* > The first (N-1) elements of LPLUS contain the subdiagonal */ /* > elements of the unit bidiagonal matrix L(+). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (2*N) */ /* > Workspace. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > Signals processing OK (=0) or failure (=1) */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup OTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Beresford Parlett, University of California, Berkeley, USA \n */ /* > Jim Demmel, University of California, Berkeley, USA \n */ /* > Inderjit Dhillon, University of Texas, Austin, USA \n */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* > Christof Voemel, University of California, Berkeley, USA */ /* ===================================================================== */ /* Subroutine */ int slarrf_(integer *n, real *d__, real *l, real *ld, integer *clstrt, integer *clend, real *w, real *wgap, real *werr, real *spdiam, real *clgapl, real *clgapr, real *pivmin, real *sigma, real *dplus, real *lplus, real *work, integer *info) { /* System generated locals */ integer i__1; real r__1, r__2, r__3; /* Local variables */ real growthbound, fail, fact, oldp; integer indx; real prod; integer ktry; real fail2; integer i__; real s, avgap, ldmax, rdmax; integer shift; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); real bestshift, smlgrowth; logical dorrr1; real ldelta; extern real slamch_(char *); logical nofail; real mingap, lsigma, rdelta; logical forcer; real rsigma, clwdth; extern logical sisnan_(real *); logical sawnan1, sawnan2; real eps, tmp; logical tryrrr1; real max1, max2, rrr1, rrr2, znm2; /* -- LAPACK auxiliary 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 2016 */ /* ===================================================================== */ /* Parameter adjustments */ --work; --lplus; --dplus; --werr; --wgap; --w; --ld; --l; --d__; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n <= 0) { return 0; } fact = 2.f; eps = slamch_("Precision"); shift = 0; forcer = FALSE_; /* Note that we cannot guarantee that for any of the shifts tried, */ /* the factorization has a small or even moderate element growth. */ /* There could be Ritz values at both ends of the cluster and despite */ /* backing off, there are examples where all factorizations tried */ /* (in IEEE mode, allowing zero pivots & infinities) have INFINITE */ /* element growth. */ /* For this reason, we should use PIVMIN in this subroutine so that at */ /* least the L D L^T factorization exists. It can be checked afterwards */ /* whether the element growth caused bad residuals/orthogonality. */ /* Decide whether the code should accept the best among all */ /* representations despite large element growth or signal INFO=1 */ /* Setting NOFAIL to .FALSE. for quick fix for bug 113 */ nofail = FALSE_; /* Compute the average gap length of the cluster */ clwdth = (r__1 = w[*clend] - w[*clstrt], abs(r__1)) + werr[*clend] + werr[ *clstrt]; avgap = clwdth / (real) (*clend - *clstrt); mingap = f2cmin(*clgapl,*clgapr); /* Initial values for shifts to both ends of cluster */ /* Computing MIN */ r__1 = w[*clstrt], r__2 = w[*clend]; lsigma = f2cmin(r__1,r__2) - werr[*clstrt]; /* Computing MAX */ r__1 = w[*clstrt], r__2 = w[*clend]; rsigma = f2cmax(r__1,r__2) + werr[*clend]; /* Use a small fudge to make sure that we really shift to the outside */ lsigma -= abs(lsigma) * 2.f * eps; rsigma += abs(rsigma) * 2.f * eps; /* Compute upper bounds for how much to back off the initial shifts */ ldmax = mingap * .25f + *pivmin * 2.f; rdmax = mingap * .25f + *pivmin * 2.f; /* Computing MAX */ r__1 = avgap, r__2 = wgap[*clstrt]; ldelta = f2cmax(r__1,r__2) / fact; /* Computing MAX */ r__1 = avgap, r__2 = wgap[*clend - 1]; rdelta = f2cmax(r__1,r__2) / fact; /* Initialize the record of the best representation found */ s = slamch_("S"); smlgrowth = 1.f / s; fail = (real) (*n - 1) * mingap / (*spdiam * eps); fail2 = (real) (*n - 1) * mingap / (*spdiam * sqrt(eps)); bestshift = lsigma; /* while (KTRY <= KTRYMAX) */ ktry = 0; growthbound = *spdiam * 8.f; L5: sawnan1 = FALSE_; sawnan2 = FALSE_; /* Ensure that we do not back off too much of the initial shifts */ ldelta = f2cmin(ldmax,ldelta); rdelta = f2cmin(rdmax,rdelta); /* Compute the element growth when shifting to both ends of the cluster */ /* accept the shift if there is no element growth at one of the two ends */ /* Left end */ s = -lsigma; dplus[1] = d__[1] + s; if (abs(dplus[1]) < *pivmin) { dplus[1] = -(*pivmin); /* Need to set SAWNAN1 because refined RRR test should not be used */ /* in this case */ sawnan1 = TRUE_; } max1 = abs(dplus[1]); i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { lplus[i__] = ld[i__] / dplus[i__]; s = s * lplus[i__] * l[i__] - lsigma; dplus[i__ + 1] = d__[i__ + 1] + s; if ((r__1 = dplus[i__ + 1], abs(r__1)) < *pivmin) { dplus[i__ + 1] = -(*pivmin); /* Need to set SAWNAN1 because refined RRR test should not be used */ /* in this case */ sawnan1 = TRUE_; } /* Computing MAX */ r__2 = max1, r__3 = (r__1 = dplus[i__ + 1], abs(r__1)); max1 = f2cmax(r__2,r__3); /* L6: */ } sawnan1 = sawnan1 || sisnan_(&max1); if (forcer || max1 <= growthbound && ! sawnan1) { *sigma = lsigma; shift = 1; goto L100; } /* Right end */ s = -rsigma; work[1] = d__[1] + s; if (abs(work[1]) < *pivmin) { work[1] = -(*pivmin); /* Need to set SAWNAN2 because refined RRR test should not be used */ /* in this case */ sawnan2 = TRUE_; } max2 = abs(work[1]); i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { work[*n + i__] = ld[i__] / work[i__]; s = s * work[*n + i__] * l[i__] - rsigma; work[i__ + 1] = d__[i__ + 1] + s; if ((r__1 = work[i__ + 1], abs(r__1)) < *pivmin) { work[i__ + 1] = -(*pivmin); /* Need to set SAWNAN2 because refined RRR test should not be used */ /* in this case */ sawnan2 = TRUE_; } /* Computing MAX */ r__2 = max2, r__3 = (r__1 = work[i__ + 1], abs(r__1)); max2 = f2cmax(r__2,r__3); /* L7: */ } sawnan2 = sawnan2 || sisnan_(&max2); if (forcer || max2 <= growthbound && ! sawnan2) { *sigma = rsigma; shift = 2; goto L100; } /* If we are at this point, both shifts led to too much element growth */ /* Record the better of the two shifts (provided it didn't lead to NaN) */ if (sawnan1 && sawnan2) { /* both MAX1 and MAX2 are NaN */ goto L50; } else { if (! sawnan1) { indx = 1; if (max1 <= smlgrowth) { smlgrowth = max1; bestshift = lsigma; } } if (! sawnan2) { if (sawnan1 || max2 <= max1) { indx = 2; } if (max2 <= smlgrowth) { smlgrowth = max2; bestshift = rsigma; } } } /* If we are here, both the left and the right shift led to */ /* element growth. If the element growth is moderate, then */ /* we may still accept the representation, if it passes a */ /* refined test for RRR. This test supposes that no NaN occurred. */ /* Moreover, we use the refined RRR test only for isolated clusters. */ if (clwdth < mingap / 128.f && f2cmin(max1,max2) < fail2 && ! sawnan1 && ! sawnan2) { dorrr1 = TRUE_; } else { dorrr1 = FALSE_; } tryrrr1 = TRUE_; if (tryrrr1 && dorrr1) { if (indx == 1) { tmp = (r__1 = dplus[*n], abs(r__1)); znm2 = 1.f; prod = 1.f; oldp = 1.f; for (i__ = *n - 1; i__ >= 1; --i__) { if (prod <= eps) { prod = dplus[i__ + 1] * work[*n + i__ + 1] / (dplus[i__] * work[*n + i__]) * oldp; } else { prod *= (r__1 = work[*n + i__], abs(r__1)); } oldp = prod; /* Computing 2nd power */ r__1 = prod; znm2 += r__1 * r__1; /* Computing MAX */ r__2 = tmp, r__3 = (r__1 = dplus[i__] * prod, abs(r__1)); tmp = f2cmax(r__2,r__3); /* L15: */ } rrr1 = tmp / (*spdiam * sqrt(znm2)); if (rrr1 <= 8.f) { *sigma = lsigma; shift = 1; goto L100; } } else if (indx == 2) { tmp = (r__1 = work[*n], abs(r__1)); znm2 = 1.f; prod = 1.f; oldp = 1.f; for (i__ = *n - 1; i__ >= 1; --i__) { if (prod <= eps) { prod = work[i__ + 1] * lplus[i__ + 1] / (work[i__] * lplus[i__]) * oldp; } else { prod *= (r__1 = lplus[i__], abs(r__1)); } oldp = prod; /* Computing 2nd power */ r__1 = prod; znm2 += r__1 * r__1; /* Computing MAX */ r__2 = tmp, r__3 = (r__1 = work[i__] * prod, abs(r__1)); tmp = f2cmax(r__2,r__3); /* L16: */ } rrr2 = tmp / (*spdiam * sqrt(znm2)); if (rrr2 <= 8.f) { *sigma = rsigma; shift = 2; goto L100; } } } L50: if (ktry < 1) { /* If we are here, both shifts failed also the RRR test. */ /* Back off to the outside */ /* Computing MAX */ r__1 = lsigma - ldelta, r__2 = lsigma - ldmax; lsigma = f2cmax(r__1,r__2); /* Computing MIN */ r__1 = rsigma + rdelta, r__2 = rsigma + rdmax; rsigma = f2cmin(r__1,r__2); ldelta *= 2.f; rdelta *= 2.f; ++ktry; goto L5; } else { /* None of the representations investigated satisfied our */ /* criteria. Take the best one we found. */ if (smlgrowth < fail || nofail) { lsigma = bestshift; rsigma = bestshift; forcer = TRUE_; goto L5; } else { *info = 1; return 0; } } L100: if (shift == 1) { } else if (shift == 2) { /* store new L and D back into DPLUS, LPLUS */ scopy_(n, &work[1], &c__1, &dplus[1], &c__1); i__1 = *n - 1; scopy_(&i__1, &work[*n + 1], &c__1, &lplus[1], &c__1); } return 0; /* End of SLARRF */ } /* slarrf_ */