#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 DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenv alues of L D LT. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DLARRV + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN, */ /* ISPLIT, M, DOL, DOU, MINRGP, */ /* RTOL1, RTOL2, W, WERR, WGAP, */ /* IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, */ /* WORK, IWORK, INFO ) */ /* INTEGER DOL, DOU, INFO, LDZ, M, N */ /* DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU */ /* INTEGER IBLOCK( * ), INDEXW( * ), ISPLIT( * ), */ /* $ ISUPPZ( * ), IWORK( * ) */ /* DOUBLE PRECISION D( * ), GERS( * ), L( * ), W( * ), WERR( * ), */ /* $ WGAP( * ), WORK( * ) */ /* DOUBLE PRECISION Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLARRV computes the eigenvectors of the tridiagonal matrix */ /* > T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T. */ /* > The input eigenvalues should have been computed by DLARRE. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] VL */ /* > \verbatim */ /* > VL is DOUBLE PRECISION */ /* > Lower bound of the interval that contains the desired */ /* > eigenvalues. VL < VU. Needed to compute gaps on the left or right */ /* > end of the extremal eigenvalues in the desired RANGE. */ /* > \endverbatim */ /* > */ /* > \param[in] VU */ /* > \verbatim */ /* > VU is DOUBLE PRECISION */ /* > Upper bound of the interval that contains the desired */ /* > eigenvalues. VL < VU. */ /* > Note: VU is currently not used by this implementation of DLARRV, VU is */ /* > passed to DLARRV because it could be used compute gaps on the right end */ /* > of the extremal eigenvalues. However, with not much initial accuracy in */ /* > LAMBDA and VU, the formula can lead to an overestimation of the right gap */ /* > and thus to inadequately early RQI 'convergence'. This is currently */ /* > prevented this by forcing a small right gap. And so it turns out that VU */ /* > is currently not used by this implementation of DLARRV. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (N) */ /* > On entry, the N diagonal elements of the diagonal matrix D. */ /* > On exit, D may be overwritten. */ /* > \endverbatim */ /* > */ /* > \param[in,out] L */ /* > \verbatim */ /* > L is DOUBLE PRECISION array, dimension (N) */ /* > On entry, the (N-1) subdiagonal elements of the unit */ /* > bidiagonal matrix L are in elements 1 to N-1 of L */ /* > (if the matrix is not split.) At the end of each block */ /* > is stored the corresponding shift as given by DLARRE. */ /* > On exit, L is overwritten. */ /* > \endverbatim */ /* > */ /* > \param[in] PIVMIN */ /* > \verbatim */ /* > PIVMIN is DOUBLE PRECISION */ /* > The minimum pivot allowed in the Sturm sequence. */ /* > \endverbatim */ /* > */ /* > \param[in] ISPLIT */ /* > \verbatim */ /* > ISPLIT is INTEGER array, dimension (N) */ /* > The splitting points, at which T breaks up into blocks. */ /* > The first block consists of rows/columns 1 to */ /* > ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */ /* > through ISPLIT( 2 ), etc. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The total number of input eigenvalues. 0 <= M <= N. */ /* > \endverbatim */ /* > */ /* > \param[in] DOL */ /* > \verbatim */ /* > DOL is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] DOU */ /* > \verbatim */ /* > DOU is INTEGER */ /* > If the user wants to compute only selected eigenvectors from all */ /* > the eigenvalues supplied, he can specify an index range DOL:DOU. */ /* > Or else the setting DOL=1, DOU=M should be applied. */ /* > Note that DOL and DOU refer to the order in which the eigenvalues */ /* > are stored in W. */ /* > If the user wants to compute only selected eigenpairs, then */ /* > the columns DOL-1 to DOU+1 of the eigenvector space Z contain the */ /* > computed eigenvectors. All other columns of Z are set to zero. */ /* > \endverbatim */ /* > */ /* > \param[in] MINRGP */ /* > \verbatim */ /* > MINRGP is DOUBLE PRECISION */ /* > \endverbatim */ /* > */ /* > \param[in] RTOL1 */ /* > \verbatim */ /* > RTOL1 is DOUBLE PRECISION */ /* > \endverbatim */ /* > */ /* > \param[in] RTOL2 */ /* > \verbatim */ /* > RTOL2 is DOUBLE PRECISION */ /* > Parameters for bisection. */ /* > An interval [LEFT,RIGHT] has converged if */ /* > RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */ /* > \endverbatim */ /* > */ /* > \param[in,out] W */ /* > \verbatim */ /* > W is DOUBLE PRECISION array, dimension (N) */ /* > The first M elements of W contain the APPROXIMATE eigenvalues for */ /* > which eigenvectors are to be computed. The eigenvalues */ /* > should be grouped by split-off block and ordered from */ /* > smallest to largest within the block ( The output array */ /* > W from DLARRE is expected here ). Furthermore, they are with */ /* > respect to the shift of the corresponding root representation */ /* > for their block. On exit, W holds the eigenvalues of the */ /* > UNshifted matrix. */ /* > \endverbatim */ /* > */ /* > \param[in,out] WERR */ /* > \verbatim */ /* > WERR is DOUBLE PRECISION array, dimension (N) */ /* > The first M elements contain the semiwidth of the uncertainty */ /* > interval of the corresponding eigenvalue in W */ /* > \endverbatim */ /* > */ /* > \param[in,out] WGAP */ /* > \verbatim */ /* > WGAP is DOUBLE PRECISION array, dimension (N) */ /* > The separation from the right neighbor eigenvalue in W. */ /* > \endverbatim */ /* > */ /* > \param[in] IBLOCK */ /* > \verbatim */ /* > IBLOCK is INTEGER array, dimension (N) */ /* > The indices of the blocks (submatrices) associated with the */ /* > corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue */ /* > W(i) belongs to the first block from the top, =2 if W(i) */ /* > belongs to the second block, etc. */ /* > \endverbatim */ /* > */ /* > \param[in] INDEXW */ /* > \verbatim */ /* > INDEXW is INTEGER array, dimension (N) */ /* > The indices of the eigenvalues within each block (submatrix); */ /* > for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the */ /* > i-th eigenvalue W(i) is the 10-th eigenvalue in the second block. */ /* > \endverbatim */ /* > */ /* > \param[in] GERS */ /* > \verbatim */ /* > GERS is DOUBLE PRECISION array, dimension (2*N) */ /* > The N Gerschgorin intervals (the i-th Gerschgorin interval */ /* > is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should */ /* > be computed from the original UNshifted matrix. */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is DOUBLE PRECISION array, dimension (LDZ, f2cmax(1,M) ) */ /* > If INFO = 0, the first M columns of Z contain the */ /* > orthonormal eigenvectors of the matrix T */ /* > corresponding to the input eigenvalues, with the i-th */ /* > column of Z holding the eigenvector associated with W(i). */ /* > Note: the user must ensure that at least f2cmax(1,M) columns are */ /* > supplied in the array Z. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. LDZ >= 1, and if */ /* > JOBZ = 'V', LDZ >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] ISUPPZ */ /* > \verbatim */ /* > ISUPPZ is INTEGER array, dimension ( 2*f2cmax(1,M) ) */ /* > The support of the eigenvectors in Z, i.e., the indices */ /* > indicating the nonzero elements in Z. The I-th eigenvector */ /* > is nonzero only in elements ISUPPZ( 2*I-1 ) through */ /* > ISUPPZ( 2*I ). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (12*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (7*N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > */ /* > > 0: A problem occurred in DLARRV. */ /* > < 0: One of the called subroutines signaled an internal problem. */ /* > Needs inspection of the corresponding parameter IINFO */ /* > for further information. */ /* > */ /* > =-1: Problem in DLARRB when refining a child's eigenvalues. */ /* > =-2: Problem in DLARRF when computing the RRR of a child. */ /* > When a child is inside a tight cluster, it can be difficult */ /* > to find an RRR. A partial remedy from the user's point of */ /* > view is to make the parameter MINRGP smaller and recompile. */ /* > However, as the orthogonality of the computed vectors is */ /* > proportional to 1/MINRGP, the user should be aware that */ /* > he might be trading in precision when he decreases MINRGP. */ /* > =-3: Problem in DLARRB when refining a single eigenvalue */ /* > after the Rayleigh correction was rejected. */ /* > = 5: The Rayleigh Quotient Iteration failed to converge to */ /* > full accuracy in MAXITR steps. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup doubleOTHERauxiliary */ /* > \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 dlarrv_(integer *n, doublereal *vl, doublereal *vu, doublereal *d__, doublereal *l, doublereal *pivmin, integer *isplit, integer *m, integer *dol, integer *dou, doublereal *minrgp, doublereal *rtol1, doublereal *rtol2, doublereal *w, doublereal *werr, doublereal *wgap, integer *iblock, integer *indexw, doublereal *gers, doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2; logical L__1; /* Local variables */ integer iend, jblk; doublereal lgap; integer done; doublereal rgap, left; integer wend, iter; doublereal bstw; integer minwsize, itmp1, i__, j, k, p, q; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); integer indld; doublereal fudge; integer idone; doublereal sigma; integer iinfo, iindr; doublereal resid; logical eskip; doublereal right; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer nclus, zfrom; doublereal rqtol; integer iindc1, iindc2; extern /* Subroutine */ int dlar1v_(integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, logical *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *); integer miniwsize; logical stp2ii; doublereal lambda; integer ii; doublereal gl; integer im, in; extern doublereal dlamch_(char *); doublereal gu; integer ibegin, indeig; logical needbs; integer indlld; doublereal sgndef, mingma; extern /* Subroutine */ int dlarrb_(integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); integer oldien, oldncl, wbegin, negcnt; doublereal spdiam; integer oldcls; doublereal savgap; integer ndepth; doublereal ssigma; extern /* Subroutine */ int dlarrf_(integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *); logical usedbs; integer iindwk, offset; doublereal gaptol; extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *); integer newcls, oldfst, indwrk, windex, oldlst; logical usedrq; integer newfst, newftt, parity, windmn, windpl, isupmn, newlst, zusedl; doublereal bstres; integer newsiz, zusedu, zusedw; doublereal nrminv, rqcorr; logical tryrqc; integer isupmx; doublereal gap, eps, tau, tol, tmp; integer zto; doublereal ztz; /* -- LAPACK auxiliary routine (version 3.8.0) -- */ /* -- 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 */ --d__; --l; --isplit; --w; --werr; --wgap; --iblock; --indexw; --gers; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --isuppz; --work; --iwork; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n <= 0 || *m <= 0) { return 0; } /* The first N entries of WORK are reserved for the eigenvalues */ indld = *n + 1; indlld = (*n << 1) + 1; indwrk = *n * 3 + 1; minwsize = *n * 12; i__1 = minwsize; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.; /* L5: */ } /* IWORK(IINDR+1:IINDR+N) hold the twist indices R for the */ /* factorization used to compute the FP vector */ iindr = 0; /* IWORK(IINDC1+1:IINC2+N) are used to store the clusters of the current */ /* layer and the one above. */ iindc1 = *n; iindc2 = *n << 1; iindwk = *n * 3 + 1; miniwsize = *n * 7; i__1 = miniwsize; for (i__ = 1; i__ <= i__1; ++i__) { iwork[i__] = 0; /* L10: */ } zusedl = 1; if (*dol > 1) { /* Set lower bound for use of Z */ zusedl = *dol - 1; } zusedu = *m; if (*dou < *m) { /* Set lower bound for use of Z */ zusedu = *dou + 1; } /* The width of the part of Z that is used */ zusedw = zusedu - zusedl + 1; dlaset_("Full", n, &zusedw, &c_b5, &c_b5, &z__[zusedl * z_dim1 + 1], ldz); eps = dlamch_("Precision"); rqtol = eps * 2.; /* Set expert flags for standard code. */ tryrqc = TRUE_; if (*dol == 1 && *dou == *m) { } else { /* Only selected eigenpairs are computed. Since the other evalues */ /* are not refined by RQ iteration, bisection has to compute to full */ /* accuracy. */ *rtol1 = eps * 4.; *rtol2 = eps * 4.; } /* The entries WBEGIN:WEND in W, WERR, WGAP correspond to the */ /* desired eigenvalues. The support of the nonzero eigenvector */ /* entries is contained in the interval IBEGIN:IEND. */ /* Remark that if k eigenpairs are desired, then the eigenvectors */ /* are stored in k contiguous columns of Z. */ /* DONE is the number of eigenvectors already computed */ done = 0; ibegin = 1; wbegin = 1; i__1 = iblock[*m]; for (jblk = 1; jblk <= i__1; ++jblk) { iend = isplit[jblk]; sigma = l[iend]; /* Find the eigenvectors of the submatrix indexed IBEGIN */ /* through IEND. */ wend = wbegin - 1; L15: if (wend < *m) { if (iblock[wend + 1] == jblk) { ++wend; goto L15; } } if (wend < wbegin) { ibegin = iend + 1; goto L170; } else if (wend < *dol || wbegin > *dou) { ibegin = iend + 1; wbegin = wend + 1; goto L170; } /* Find local spectral diameter of the block */ gl = gers[(ibegin << 1) - 1]; gu = gers[ibegin * 2]; i__2 = iend; for (i__ = ibegin + 1; i__ <= i__2; ++i__) { /* Computing MIN */ d__1 = gers[(i__ << 1) - 1]; gl = f2cmin(d__1,gl); /* Computing MAX */ d__1 = gers[i__ * 2]; gu = f2cmax(d__1,gu); /* L20: */ } spdiam = gu - gl; /* OLDIEN is the last index of the previous block */ oldien = ibegin - 1; /* Calculate the size of the current block */ in = iend - ibegin + 1; /* The number of eigenvalues in the current block */ im = wend - wbegin + 1; /* This is for a 1x1 block */ if (ibegin == iend) { ++done; z__[ibegin + wbegin * z_dim1] = 1.; isuppz[(wbegin << 1) - 1] = ibegin; isuppz[wbegin * 2] = ibegin; w[wbegin] += sigma; work[wbegin] = w[wbegin]; ibegin = iend + 1; ++wbegin; goto L170; } /* The desired (shifted) eigenvalues are stored in W(WBEGIN:WEND) */ /* Note that these can be approximations, in this case, the corresp. */ /* entries of WERR give the size of the uncertainty interval. */ /* The eigenvalue approximations will be refined when necessary as */ /* high relative accuracy is required for the computation of the */ /* corresponding eigenvectors. */ dcopy_(&im, &w[wbegin], &c__1, &work[wbegin], &c__1); /* We store in W the eigenvalue approximations w.r.t. the original */ /* matrix T. */ i__2 = im; for (i__ = 1; i__ <= i__2; ++i__) { w[wbegin + i__ - 1] += sigma; /* L30: */ } /* NDEPTH is the current depth of the representation tree */ ndepth = 0; /* PARITY is either 1 or 0 */ parity = 1; /* NCLUS is the number of clusters for the next level of the */ /* representation tree, we start with NCLUS = 1 for the root */ nclus = 1; iwork[iindc1 + 1] = 1; iwork[iindc1 + 2] = im; /* IDONE is the number of eigenvectors already computed in the current */ /* block */ idone = 0; /* loop while( IDONE.LT.IM ) */ /* generate the representation tree for the current block and */ /* compute the eigenvectors */ L40: if (idone < im) { /* This is a crude protection against infinitely deep trees */ if (ndepth > *m) { *info = -2; return 0; } /* breadth first processing of the current level of the representation */ /* tree: OLDNCL = number of clusters on current level */ oldncl = nclus; /* reset NCLUS to count the number of child clusters */ nclus = 0; parity = 1 - parity; if (parity == 0) { oldcls = iindc1; newcls = iindc2; } else { oldcls = iindc2; newcls = iindc1; } /* Process the clusters on the current level */ i__2 = oldncl; for (i__ = 1; i__ <= i__2; ++i__) { j = oldcls + (i__ << 1); /* OLDFST, OLDLST = first, last index of current cluster. */ /* cluster indices start with 1 and are relative */ /* to WBEGIN when accessing W, WGAP, WERR, Z */ oldfst = iwork[j - 1]; oldlst = iwork[j]; if (ndepth > 0) { /* Retrieve relatively robust representation (RRR) of cluster */ /* that has been computed at the previous level */ /* The RRR is stored in Z and overwritten once the eigenvectors */ /* have been computed or when the cluster is refined */ if (*dol == 1 && *dou == *m) { /* Get representation from location of the leftmost evalue */ /* of the cluster */ j = wbegin + oldfst - 1; } else { if (wbegin + oldfst - 1 < *dol) { /* Get representation from the left end of Z array */ j = *dol - 1; } else if (wbegin + oldfst - 1 > *dou) { /* Get representation from the right end of Z array */ j = *dou; } else { j = wbegin + oldfst - 1; } } dcopy_(&in, &z__[ibegin + j * z_dim1], &c__1, &d__[ibegin] , &c__1); i__3 = in - 1; dcopy_(&i__3, &z__[ibegin + (j + 1) * z_dim1], &c__1, &l[ ibegin], &c__1); sigma = z__[iend + (j + 1) * z_dim1]; /* Set the corresponding entries in Z to zero */ dlaset_("Full", &in, &c__2, &c_b5, &c_b5, &z__[ibegin + j * z_dim1], ldz); } /* Compute DL and DLL of current RRR */ i__3 = iend - 1; for (j = ibegin; j <= i__3; ++j) { tmp = d__[j] * l[j]; work[indld - 1 + j] = tmp; work[indlld - 1 + j] = tmp * l[j]; /* L50: */ } if (ndepth > 0) { /* P and Q are index of the first and last eigenvalue to compute */ /* within the current block */ p = indexw[wbegin - 1 + oldfst]; q = indexw[wbegin - 1 + oldlst]; /* Offset for the arrays WORK, WGAP and WERR, i.e., the P-OFFSET */ /* through the Q-OFFSET elements of these arrays are to be used. */ /* OFFSET = P-OLDFST */ offset = indexw[wbegin] - 1; /* perform limited bisection (if necessary) to get approximate */ /* eigenvalues to the precision needed. */ dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin - 1], &p, &q, rtol1, rtol2, &offset, &work[wbegin], &wgap[ wbegin], &werr[wbegin], &work[indwrk], &iwork[ iindwk], pivmin, &spdiam, &in, &iinfo); if (iinfo != 0) { *info = -1; return 0; } /* We also recompute the extremal gaps. W holds all eigenvalues */ /* of the unshifted matrix and must be used for computation */ /* of WGAP, the entries of WORK might stem from RRRs with */ /* different shifts. The gaps from WBEGIN-1+OLDFST to */ /* WBEGIN-1+OLDLST are correctly computed in DLARRB. */ /* However, we only allow the gaps to become greater since */ /* this is what should happen when we decrease WERR */ if (oldfst > 1) { /* Computing MAX */ d__1 = wgap[wbegin + oldfst - 2], d__2 = w[wbegin + oldfst - 1] - werr[wbegin + oldfst - 1] - w[ wbegin + oldfst - 2] - werr[wbegin + oldfst - 2]; wgap[wbegin + oldfst - 2] = f2cmax(d__1,d__2); } if (wbegin + oldlst - 1 < wend) { /* Computing MAX */ d__1 = wgap[wbegin + oldlst - 1], d__2 = w[wbegin + oldlst] - werr[wbegin + oldlst] - w[wbegin + oldlst - 1] - werr[wbegin + oldlst - 1]; wgap[wbegin + oldlst - 1] = f2cmax(d__1,d__2); } /* Each time the eigenvalues in WORK get refined, we store */ /* the newly found approximation with all shifts applied in W */ i__3 = oldlst; for (j = oldfst; j <= i__3; ++j) { w[wbegin + j - 1] = work[wbegin + j - 1] + sigma; /* L53: */ } } /* Process the current node. */ newfst = oldfst; i__3 = oldlst; for (j = oldfst; j <= i__3; ++j) { if (j == oldlst) { /* we are at the right end of the cluster, this is also the */ /* boundary of the child cluster */ newlst = j; } else if (wgap[wbegin + j - 1] >= *minrgp * (d__1 = work[ wbegin + j - 1], abs(d__1))) { /* the right relative gap is big enough, the child cluster */ /* (NEWFST,..,NEWLST) is well separated from the following */ newlst = j; } else { /* inside a child cluster, the relative gap is not */ /* big enough. */ goto L140; } /* Compute size of child cluster found */ newsiz = newlst - newfst + 1; /* NEWFTT is the place in Z where the new RRR or the computed */ /* eigenvector is to be stored */ if (*dol == 1 && *dou == *m) { /* Store representation at location of the leftmost evalue */ /* of the cluster */ newftt = wbegin + newfst - 1; } else { if (wbegin + newfst - 1 < *dol) { /* Store representation at the left end of Z array */ newftt = *dol - 1; } else if (wbegin + newfst - 1 > *dou) { /* Store representation at the right end of Z array */ newftt = *dou; } else { newftt = wbegin + newfst - 1; } } if (newsiz > 1) { /* Current child is not a singleton but a cluster. */ /* Compute and store new representation of child. */ /* Compute left and right cluster gap. */ /* LGAP and RGAP are not computed from WORK because */ /* the eigenvalue approximations may stem from RRRs */ /* different shifts. However, W hold all eigenvalues */ /* of the unshifted matrix. Still, the entries in WGAP */ /* have to be computed from WORK since the entries */ /* in W might be of the same order so that gaps are not */ /* exhibited correctly for very close eigenvalues. */ if (newfst == 1) { /* Computing MAX */ d__1 = 0., d__2 = w[wbegin] - werr[wbegin] - *vl; lgap = f2cmax(d__1,d__2); } else { lgap = wgap[wbegin + newfst - 2]; } rgap = wgap[wbegin + newlst - 1]; /* Compute left- and rightmost eigenvalue of child */ /* to high precision in order to shift as close */ /* as possible and obtain as large relative gaps */ /* as possible */ for (k = 1; k <= 2; ++k) { if (k == 1) { p = indexw[wbegin - 1 + newfst]; } else { p = indexw[wbegin - 1 + newlst]; } offset = indexw[wbegin] - 1; dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin - 1], &p, &p, &rqtol, &rqtol, &offset, & work[wbegin], &wgap[wbegin], &werr[wbegin] , &work[indwrk], &iwork[iindwk], pivmin, & spdiam, &in, &iinfo); /* L55: */ } if (wbegin + newlst - 1 < *dol || wbegin + newfst - 1 > *dou) { /* if the cluster contains no desired eigenvalues */ /* skip the computation of that branch of the rep. tree */ /* We could skip before the refinement of the extremal */ /* eigenvalues of the child, but then the representation */ /* tree could be different from the one when nothing is */ /* skipped. For this reason we skip at this place. */ idone = idone + newlst - newfst + 1; goto L139; } /* Compute RRR of child cluster. */ /* Note that the new RRR is stored in Z */ /* DLARRF needs LWORK = 2*N */ dlarrf_(&in, &d__[ibegin], &l[ibegin], &work[indld + ibegin - 1], &newfst, &newlst, &work[wbegin], &wgap[wbegin], &werr[wbegin], &spdiam, &lgap, &rgap, pivmin, &tau, &z__[ibegin + newftt * z_dim1], &z__[ibegin + (newftt + 1) * z_dim1], &work[indwrk], &iinfo); if (iinfo == 0) { /* a new RRR for the cluster was found by DLARRF */ /* update shift and store it */ ssigma = sigma + tau; z__[iend + (newftt + 1) * z_dim1] = ssigma; /* WORK() are the midpoints and WERR() the semi-width */ /* Note that the entries in W are unchanged. */ i__4 = newlst; for (k = newfst; k <= i__4; ++k) { fudge = eps * 3. * (d__1 = work[wbegin + k - 1], abs(d__1)); work[wbegin + k - 1] -= tau; fudge += eps * 4. * (d__1 = work[wbegin + k - 1], abs(d__1)); /* Fudge errors */ werr[wbegin + k - 1] += fudge; /* Gaps are not fudged. Provided that WERR is small */ /* when eigenvalues are close, a zero gap indicates */ /* that a new representation is needed for resolving */ /* the cluster. A fudge could lead to a wrong decision */ /* of judging eigenvalues 'separated' which in */ /* reality are not. This could have a negative impact */ /* on the orthogonality of the computed eigenvectors. */ /* L116: */ } ++nclus; k = newcls + (nclus << 1); iwork[k - 1] = newfst; iwork[k] = newlst; } else { *info = -2; return 0; } } else { /* Compute eigenvector of singleton */ iter = 0; tol = log((doublereal) in) * 4. * eps; k = newfst; windex = wbegin + k - 1; /* Computing MAX */ i__4 = windex - 1; windmn = f2cmax(i__4,1); /* Computing MIN */ i__4 = windex + 1; windpl = f2cmin(i__4,*m); lambda = work[windex]; ++done; /* Check if eigenvector computation is to be skipped */ if (windex < *dol || windex > *dou) { eskip = TRUE_; goto L125; } else { eskip = FALSE_; } left = work[windex] - werr[windex]; right = work[windex] + werr[windex]; indeig = indexw[windex]; /* Note that since we compute the eigenpairs for a child, */ /* all eigenvalue approximations are w.r.t the same shift. */ /* In this case, the entries in WORK should be used for */ /* computing the gaps since they exhibit even very small */ /* differences in the eigenvalues, as opposed to the */ /* entries in W which might "look" the same. */ if (k == 1) { /* In the case RANGE='I' and with not much initial */ /* accuracy in LAMBDA and VL, the formula */ /* LGAP = MAX( ZERO, (SIGMA - VL) + LAMBDA ) */ /* can lead to an overestimation of the left gap and */ /* thus to inadequately early RQI 'convergence'. */ /* Prevent this by forcing a small left gap. */ /* Computing MAX */ d__1 = abs(left), d__2 = abs(right); lgap = eps * f2cmax(d__1,d__2); } else { lgap = wgap[windmn]; } if (k == im) { /* In the case RANGE='I' and with not much initial */ /* accuracy in LAMBDA and VU, the formula */ /* can lead to an overestimation of the right gap and */ /* thus to inadequately early RQI 'convergence'. */ /* Prevent this by forcing a small right gap. */ /* Computing MAX */ d__1 = abs(left), d__2 = abs(right); rgap = eps * f2cmax(d__1,d__2); } else { rgap = wgap[windex]; } gap = f2cmin(lgap,rgap); if (k == 1 || k == im) { /* The eigenvector support can become wrong */ /* because significant entries could be cut off due to a */ /* large GAPTOL parameter in LAR1V. Prevent this. */ gaptol = 0.; } else { gaptol = gap * eps; } isupmn = in; isupmx = 1; /* Update WGAP so that it holds the minimum gap */ /* to the left or the right. This is crucial in the */ /* case where bisection is used to ensure that the */ /* eigenvalue is refined up to the required precision. */ /* The correct value is restored afterwards. */ savgap = wgap[windex]; wgap[windex] = gap; /* We want to use the Rayleigh Quotient Correction */ /* as often as possible since it converges quadratically */ /* when we are close enough to the desired eigenvalue. */ /* However, the Rayleigh Quotient can have the wrong sign */ /* and lead us away from the desired eigenvalue. In this */ /* case, the best we can do is to use bisection. */ usedbs = FALSE_; usedrq = FALSE_; /* Bisection is initially turned off unless it is forced */ needbs = ! tryrqc; L120: /* Check if bisection should be used to refine eigenvalue */ if (needbs) { /* Take the bisection as new iterate */ usedbs = TRUE_; itmp1 = iwork[iindr + windex]; offset = indexw[wbegin] - 1; d__1 = eps * 2.; dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin - 1], &indeig, &indeig, &c_b5, &d__1, & offset, &work[wbegin], &wgap[wbegin], & werr[wbegin], &work[indwrk], &iwork[ iindwk], pivmin, &spdiam, &itmp1, &iinfo); if (iinfo != 0) { *info = -3; return 0; } lambda = work[windex]; /* Reset twist index from inaccurate LAMBDA to */ /* force computation of true MINGMA */ iwork[iindr + windex] = 0; } /* Given LAMBDA, compute the eigenvector. */ L__1 = ! usedbs; dlar1v_(&in, &c__1, &in, &lambda, &d__[ibegin], &l[ ibegin], &work[indld + ibegin - 1], &work[ indlld + ibegin - 1], pivmin, &gaptol, &z__[ ibegin + windex * z_dim1], &L__1, &negcnt, & ztz, &mingma, &iwork[iindr + windex], &isuppz[ (windex << 1) - 1], &nrminv, &resid, &rqcorr, &work[indwrk]); if (iter == 0) { bstres = resid; bstw = lambda; } else if (resid < bstres) { bstres = resid; bstw = lambda; } /* Computing MIN */ i__4 = isupmn, i__5 = isuppz[(windex << 1) - 1]; isupmn = f2cmin(i__4,i__5); /* Computing MAX */ i__4 = isupmx, i__5 = isuppz[windex * 2]; isupmx = f2cmax(i__4,i__5); ++iter; /* sin alpha <= |resid|/gap */ /* Note that both the residual and the gap are */ /* proportional to the matrix, so ||T|| doesn't play */ /* a role in the quotient */ /* Convergence test for Rayleigh-Quotient iteration */ /* (omitted when Bisection has been used) */ if (resid > tol * gap && abs(rqcorr) > rqtol * abs( lambda) && ! usedbs) { /* We need to check that the RQCORR update doesn't */ /* move the eigenvalue away from the desired one and */ /* towards a neighbor. -> protection with bisection */ if (indeig <= negcnt) { /* The wanted eigenvalue lies to the left */ sgndef = -1.; } else { /* The wanted eigenvalue lies to the right */ sgndef = 1.; } /* We only use the RQCORR if it improves the */ /* the iterate reasonably. */ if (rqcorr * sgndef >= 0. && lambda + rqcorr <= right && lambda + rqcorr >= left) { usedrq = TRUE_; /* Store new midpoint of bisection interval in WORK */ if (sgndef == 1.) { /* The current LAMBDA is on the left of the true */ /* eigenvalue */ left = lambda; /* We prefer to assume that the error estimate */ /* is correct. We could make the interval not */ /* as a bracket but to be modified if the RQCORR */ /* chooses to. In this case, the RIGHT side should */ /* be modified as follows: */ /* RIGHT = MAX(RIGHT, LAMBDA + RQCORR) */ } else { /* The current LAMBDA is on the right of the true */ /* eigenvalue */ right = lambda; /* See comment about assuming the error estimate is */ /* correct above. */ /* LEFT = MIN(LEFT, LAMBDA + RQCORR) */ } work[windex] = (right + left) * .5; /* Take RQCORR since it has the correct sign and */ /* improves the iterate reasonably */ lambda += rqcorr; /* Update width of error interval */ werr[windex] = (right - left) * .5; } else { needbs = TRUE_; } if (right - left < rqtol * abs(lambda)) { /* The eigenvalue is computed to bisection accuracy */ /* compute eigenvector and stop */ usedbs = TRUE_; goto L120; } else if (iter < 10) { goto L120; } else if (iter == 10) { needbs = TRUE_; goto L120; } else { *info = 5; return 0; } } else { stp2ii = FALSE_; if (usedrq && usedbs && bstres <= resid) { lambda = bstw; stp2ii = TRUE_; } if (stp2ii) { /* improve error angle by second step */ L__1 = ! usedbs; dlar1v_(&in, &c__1, &in, &lambda, &d__[ibegin] , &l[ibegin], &work[indld + ibegin - 1], &work[indlld + ibegin - 1], pivmin, &gaptol, &z__[ibegin + windex * z_dim1], &L__1, &negcnt, &ztz, & mingma, &iwork[iindr + windex], & isuppz[(windex << 1) - 1], &nrminv, & resid, &rqcorr, &work[indwrk]); } work[windex] = lambda; } /* Compute FP-vector support w.r.t. whole matrix */ isuppz[(windex << 1) - 1] += oldien; isuppz[windex * 2] += oldien; zfrom = isuppz[(windex << 1) - 1]; zto = isuppz[windex * 2]; isupmn += oldien; isupmx += oldien; /* Ensure vector is ok if support in the RQI has changed */ if (isupmn < zfrom) { i__4 = zfrom - 1; for (ii = isupmn; ii <= i__4; ++ii) { z__[ii + windex * z_dim1] = 0.; /* L122: */ } } if (isupmx > zto) { i__4 = isupmx; for (ii = zto + 1; ii <= i__4; ++ii) { z__[ii + windex * z_dim1] = 0.; /* L123: */ } } i__4 = zto - zfrom + 1; dscal_(&i__4, &nrminv, &z__[zfrom + windex * z_dim1], &c__1); L125: /* Update W */ w[windex] = lambda + sigma; /* Recompute the gaps on the left and right */ /* But only allow them to become larger and not */ /* smaller (which can only happen through "bad" */ /* cancellation and doesn't reflect the theory */ /* where the initial gaps are underestimated due */ /* to WERR being too crude.) */ if (! eskip) { if (k > 1) { /* Computing MAX */ d__1 = wgap[windmn], d__2 = w[windex] - werr[ windex] - w[windmn] - werr[windmn]; wgap[windmn] = f2cmax(d__1,d__2); } if (windex < wend) { /* Computing MAX */ d__1 = savgap, d__2 = w[windpl] - werr[windpl] - w[windex] - werr[windex]; wgap[windex] = f2cmax(d__1,d__2); } } ++idone; } /* here ends the code for the current child */ L139: /* Proceed to any remaining child nodes */ newfst = j + 1; L140: ; } /* L150: */ } ++ndepth; goto L40; } ibegin = iend + 1; wbegin = wend + 1; L170: ; } return 0; /* End of DLARRV */ } /* dlarrv_ */