#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]/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++ */ #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 ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZLAED8 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, */ /* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, */ /* GIVCOL, GIVNUM, INFO ) */ /* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ */ /* DOUBLE PRECISION RHO */ /* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */ /* $ INDXQ( * ), PERM( * ) */ /* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), */ /* $ Z( * ) */ /* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZLAED8 merges the two sets of eigenvalues together into a single */ /* > sorted set. Then it tries to deflate the size of the problem. */ /* > There are two ways in which deflation can occur: when two or more */ /* > eigenvalues are close together or if there is a tiny element in the */ /* > Z vector. For each such occurrence the order of the related secular */ /* > equation problem is reduced by one. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[out] K */ /* > \verbatim */ /* > K is INTEGER */ /* > Contains the number of non-deflated eigenvalues. */ /* > This is the order of the related secular equation. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] QSIZ */ /* > \verbatim */ /* > QSIZ is INTEGER */ /* > The dimension of the unitary matrix used to reduce */ /* > the dense or band matrix to tridiagonal form. */ /* > QSIZ >= N if ICOMPQ = 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Q */ /* > \verbatim */ /* > Q is COMPLEX*16 array, dimension (LDQ,N) */ /* > On entry, Q contains the eigenvectors of the partially solved */ /* > system which has been previously updated in matrix */ /* > multiplies with other partially solved eigensystems. */ /* > On exit, Q contains the trailing (N-K) updated eigenvectors */ /* > (those which were deflated) in its last N-K columns. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. LDQ >= f2cmax( 1, N ). */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (N) */ /* > On entry, D contains the eigenvalues of the two submatrices to */ /* > be combined. On exit, D contains the trailing (N-K) updated */ /* > eigenvalues (those which were deflated) sorted into increasing */ /* > order. */ /* > \endverbatim */ /* > */ /* > \param[in,out] RHO */ /* > \verbatim */ /* > RHO is DOUBLE PRECISION */ /* > Contains the off diagonal element associated with the rank-1 */ /* > cut which originally split the two submatrices which are now */ /* > being recombined. RHO is modified during the computation to */ /* > the value required by DLAED3. */ /* > \endverbatim */ /* > */ /* > \param[in] CUTPNT */ /* > \verbatim */ /* > CUTPNT is INTEGER */ /* > Contains the location of the last eigenvalue in the leading */ /* > sub-matrix. MIN(1,N) <= CUTPNT <= N. */ /* > \endverbatim */ /* > */ /* > \param[in] Z */ /* > \verbatim */ /* > Z is DOUBLE PRECISION array, dimension (N) */ /* > On input this vector contains the updating vector (the last */ /* > row of the first sub-eigenvector matrix and the first row of */ /* > the second sub-eigenvector matrix). The contents of Z are */ /* > destroyed during the updating process. */ /* > \endverbatim */ /* > */ /* > \param[out] DLAMDA */ /* > \verbatim */ /* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ /* > Contains a copy of the first K eigenvalues which will be used */ /* > by DLAED3 to form the secular equation. */ /* > \endverbatim */ /* > */ /* > \param[out] Q2 */ /* > \verbatim */ /* > Q2 is COMPLEX*16 array, dimension (LDQ2,N) */ /* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ /* > Contains a copy of the first K eigenvectors which will be used */ /* > by DLAED7 in a matrix multiply (DGEMM) to update the new */ /* > eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ2 */ /* > \verbatim */ /* > LDQ2 is INTEGER */ /* > The leading dimension of the array Q2. LDQ2 >= f2cmax( 1, N ). */ /* > \endverbatim */ /* > */ /* > \param[out] W */ /* > \verbatim */ /* > W is DOUBLE PRECISION array, dimension (N) */ /* > This will hold the first k values of the final */ /* > deflation-altered z-vector and will be passed to DLAED3. */ /* > \endverbatim */ /* > */ /* > \param[out] INDXP */ /* > \verbatim */ /* > INDXP is INTEGER array, dimension (N) */ /* > This will contain the permutation used to place deflated */ /* > values of D at the end of the array. On output INDXP(1:K) */ /* > points to the nondeflated D-values and INDXP(K+1:N) */ /* > points to the deflated eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[out] INDX */ /* > \verbatim */ /* > INDX is INTEGER array, dimension (N) */ /* > This will contain the permutation used to sort the contents of */ /* > D into ascending order. */ /* > \endverbatim */ /* > */ /* > \param[in] INDXQ */ /* > \verbatim */ /* > INDXQ is INTEGER array, dimension (N) */ /* > This contains the permutation which separately sorts the two */ /* > sub-problems in D into ascending order. Note that elements in */ /* > the second half of this permutation must first have CUTPNT */ /* > added to their values in order to be accurate. */ /* > \endverbatim */ /* > */ /* > \param[out] PERM */ /* > \verbatim */ /* > PERM is INTEGER array, dimension (N) */ /* > Contains the permutations (from deflation and sorting) to be */ /* > applied to each eigenblock. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVPTR */ /* > \verbatim */ /* > GIVPTR is INTEGER */ /* > Contains the number of Givens rotations which took place in */ /* > this subproblem. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVCOL */ /* > \verbatim */ /* > GIVCOL is INTEGER array, dimension (2, N) */ /* > Each pair of numbers indicates a pair of columns to take place */ /* > in a Givens rotation. */ /* > \endverbatim */ /* > */ /* > \param[out] GIVNUM */ /* > \verbatim */ /* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */ /* > Each number indicates the S value to be used in the */ /* > corresponding Givens rotation. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, integer *indxq, integer *perm, integer *givptr, integer *givcol, doublereal *givnum, integer *info) { /* System generated locals */ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; doublereal d__1; /* Local variables */ integer jlam, imax, jmax; doublereal c__; integer i__, j; doublereal s, t; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer k2, n1, n2; extern /* Subroutine */ int zdrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zcopy_( integer *, doublecomplex *, integer *, doublecomplex *, integer *) ; extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *); integer jp; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), xerbla_(char *, integer *, ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer n1p1; doublereal eps, tau, tol; /* -- 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 */ q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; --d__; --z__; --dlamda; q2_dim1 = *ldq2; q2_offset = 1 + q2_dim1 * 1; q2 -= q2_offset; --w; --indxp; --indx; --indxq; --perm; givcol -= 3; givnum -= 3; /* Function Body */ *info = 0; if (*n < 0) { *info = -2; } else if (*qsiz < *n) { *info = -3; } else if (*ldq < f2cmax(1,*n)) { *info = -5; } else if (*cutpnt < f2cmin(1,*n) || *cutpnt > *n) { *info = -8; } else if (*ldq2 < f2cmax(1,*n)) { *info = -12; } if (*info != 0) { i__1 = -(*info); xerbla_("ZLAED8", &i__1, (ftnlen)6); return 0; } /* Need to initialize GIVPTR to O here in case of quick exit */ /* to prevent an unspecified code behavior (usually sigfault) */ /* when IWORK array on entry to *stedc is not zeroed */ /* (or at least some IWORK entries which used in *laed7 for GIVPTR). */ *givptr = 0; /* Quick return if possible */ if (*n == 0) { return 0; } n1 = *cutpnt; n2 = *n - n1; n1p1 = n1 + 1; if (*rho < 0.) { dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } /* Normalize z so that norm(z) = 1 */ t = 1. / sqrt(2.); i__1 = *n; for (j = 1; j <= i__1; ++j) { indx[j] = j; /* L10: */ } dscal_(n, &t, &z__[1], &c__1); *rho = (d__1 = *rho * 2., abs(d__1)); /* Sort the eigenvalues into increasing order */ i__1 = *n; for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { indxq[i__] += *cutpnt; /* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = d__[indxq[i__]]; w[i__] = z__[indxq[i__]]; /* L30: */ } i__ = 1; j = *cutpnt + 1; dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = dlamda[indx[i__]]; z__[i__] = w[indx[i__]]; /* L40: */ } /* Calculate the allowable deflation tolerance */ imax = idamax_(n, &z__[1], &c__1); jmax = idamax_(n, &d__[1], &c__1); eps = dlamch_("Epsilon"); tol = eps * 8. * (d__1 = d__[jmax], abs(d__1)); /* If the rank-1 modifier is small enough, no more needs to be done */ /* -- except to reorganize Q so that its columns correspond with the */ /* elements in D. */ if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { *k = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { perm[j] = indxq[indx[j]]; zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] , &c__1); /* L50: */ } zlacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq); return 0; } /* If there are multiple eigenvalues then the problem deflates. Here */ /* the number of equal eigenvalues are found. As each equal */ /* eigenvalue is found, an elementary reflector is computed to rotate */ /* the corresponding eigensubspace so that the corresponding */ /* components of Z are zero in this new basis. */ *k = 0; k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ --k2; indxp[k2] = j; if (j == *n) { goto L100; } } else { jlam = j; goto L70; } /* L60: */ } L70: ++j; if (j > *n) { goto L90; } if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ --k2; indxp[k2] = j; } else { /* Check if eigenvalues are close enough to allow deflation. */ s = z__[jlam]; c__ = z__[j]; /* Find sqrt(a**2+b**2) without overflow or */ /* destructive underflow. */ tau = dlapy2_(&c__, &s); t = d__[j] - d__[jlam]; c__ /= tau; s = -s / tau; if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { /* Deflation is possible. */ z__[j] = tau; z__[jlam] = 0.; /* Record the appropriate Givens rotation */ ++(*givptr); givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; givcol[(*givptr << 1) + 2] = indxq[indx[j]]; givnum[(*givptr << 1) + 1] = c__; givnum[(*givptr << 1) + 2] = s; zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[ indx[j]] * q_dim1 + 1], &c__1, &c__, &s); t = d__[jlam] * c__ * c__ + d__[j] * s * s; d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; d__[jlam] = t; --k2; i__ = 1; L80: if (k2 + i__ <= *n) { if (d__[jlam] < d__[indxp[k2 + i__]]) { indxp[k2 + i__ - 1] = indxp[k2 + i__]; indxp[k2 + i__] = jlam; ++i__; goto L80; } else { indxp[k2 + i__ - 1] = jlam; } } else { indxp[k2 + i__ - 1] = jlam; } jlam = j; } else { ++(*k); w[*k] = z__[jlam]; dlamda[*k] = d__[jlam]; indxp[*k] = jlam; jlam = j; } } goto L70; L90: /* Record the last eigenvalue. */ ++(*k); w[*k] = z__[jlam]; dlamda[*k] = d__[jlam]; indxp[*k] = jlam; L100: /* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ /* and Q2 respectively. The eigenvalues/vectors which were not */ /* deflated go into the first K slots of DLAMDA and Q2 respectively, */ /* while those which were deflated go into the last N - K slots. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { jp = indxp[j]; dlamda[j] = d__[jp]; perm[j] = indxq[indx[jp]]; zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], & c__1); /* L110: */ } /* The deflated eigenvalues and their corresponding vectors go back */ /* into the last N - K slots of D and Q respectively. */ if (*k < *n) { i__1 = *n - *k; dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); i__1 = *n - *k; zlacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + 1) * q_dim1 + 1], ldq); } return 0; /* End of ZLAED8 */ } /* zlaed8_ */