#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 SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLASQ2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLASQ2( N, Z, INFO ) */ /* INTEGER INFO, N */ /* REAL Z( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLASQ2 computes all the eigenvalues of the symmetric positive */ /* > definite tridiagonal matrix associated with the qd array Z to high */ /* > relative accuracy are computed to high relative accuracy, in the */ /* > absence of denormalization, underflow and overflow. */ /* > */ /* > To see the relation of Z to the tridiagonal matrix, let L be a */ /* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */ /* > let U be an upper bidiagonal matrix with 1's above and diagonal */ /* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */ /* > symmetric tridiagonal to which it is similar. */ /* > */ /* > Note : SLASQ2 defines a logical variable, IEEE, which is true */ /* > on machines which follow ieee-754 floating-point standard in their */ /* > handling of infinities and NaNs, and false otherwise. This variable */ /* > is passed to SLASQ3. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of rows and columns in the matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Z */ /* > \verbatim */ /* > Z is REAL array, dimension ( 4*N ) */ /* > On entry Z holds the qd array. On exit, entries 1 to N hold */ /* > the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */ /* > trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */ /* > N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */ /* > holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */ /* > shifts that failed. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if the i-th argument is a scalar and had an illegal */ /* > value, then INFO = -i, if the i-th argument is an */ /* > array and the j-entry had an illegal value, then */ /* > INFO = -(i*100+j) */ /* > > 0: the algorithm failed */ /* > = 1, a split was marked by a positive value in E */ /* > = 2, current block of Z not diagonalized after 100*N */ /* > iterations (in inner while loop). On exit Z holds */ /* > a qd array with the same eigenvalues as the given Z. */ /* > = 3, termination criterion of outer while loop not met */ /* > (program created more than N unreduced blocks) */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup auxOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Local Variables: I0:N0 defines a current unreduced segment of Z. */ /* > The shifts are accumulated in SIGMA. Iteration count is in ITER. */ /* > Ping-pong is controlled by PP (alternates between 0 and 1). */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int slasq2_(integer *n, real *z__, integer *info) { /* System generated locals */ integer i__1, i__2, i__3; real r__1, r__2; /* Local variables */ logical ieee; integer nbig; real dmin__, emin, emax; integer kmin, ndiv, iter; real qmin, temp, qmax, zmax; integer splt; real dmin1, dmin2, d__, e, g; integer k; real s, t; integer nfail; real desig, trace, sigma; integer iinfo; real tempe, tempq; integer i0, i1, i4, n0, n1, ttype; extern /* Subroutine */ int slasq3_(integer *, integer *, real *, integer *, real *, real *, real *, real *, integer *, integer *, integer * , logical *, integer *, real *, real *, real *, real *, real *, real *, real *); real dn; integer pp; real deemin; extern real slamch_(char *); integer iwhila, iwhilb; real oldemn, safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real dn1, dn2; extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); real dee, eps, tau, tol; integer ipn4; real tol2; /* -- 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 arguments. */ /* (in case SLASQ2 is not called by SLASQ1) */ /* Parameter adjustments */ --z__; /* Function Body */ *info = 0; eps = slamch_("Precision"); safmin = slamch_("Safe minimum"); tol = eps * 100.f; /* Computing 2nd power */ r__1 = tol; tol2 = r__1 * r__1; if (*n < 0) { *info = -1; xerbla_("SLASQ2", &c__1, (ftnlen)6); return 0; } else if (*n == 0) { return 0; } else if (*n == 1) { /* 1-by-1 case. */ if (z__[1] < 0.f) { *info = -201; xerbla_("SLASQ2", &c__2, (ftnlen)6); } return 0; } else if (*n == 2) { /* 2-by-2 case. */ if (z__[1] < 0.f) { *info = -201; xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } else if (z__[2] < 0.f) { *info = -202; xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } else if (z__[3] < 0.f) { *info = -203; xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } else if (z__[3] > z__[1]) { d__ = z__[3]; z__[3] = z__[1]; z__[1] = d__; } z__[5] = z__[1] + z__[2] + z__[3]; if (z__[2] > z__[3] * tol2) { t = (z__[1] - z__[3] + z__[2]) * .5f; s = z__[3] * (z__[2] / t); if (s <= t) { s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.f) + 1.f))); } else { s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s))); } t = z__[1] + (s + z__[2]); z__[3] *= z__[1] / t; z__[1] = t; } z__[2] = z__[3]; z__[6] = z__[2] + z__[1]; return 0; } /* Check for negative data and compute sums of q's and e's. */ z__[*n * 2] = 0.f; emin = z__[2]; qmax = 0.f; zmax = 0.f; d__ = 0.f; e = 0.f; i__1 = *n - 1 << 1; for (k = 1; k <= i__1; k += 2) { if (z__[k] < 0.f) { *info = -(k + 200); xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } else if (z__[k + 1] < 0.f) { *info = -(k + 201); xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } d__ += z__[k]; e += z__[k + 1]; /* Computing MAX */ r__1 = qmax, r__2 = z__[k]; qmax = f2cmax(r__1,r__2); /* Computing MIN */ r__1 = emin, r__2 = z__[k + 1]; emin = f2cmin(r__1,r__2); /* Computing MAX */ r__1 = f2cmax(qmax,zmax), r__2 = z__[k + 1]; zmax = f2cmax(r__1,r__2); /* L10: */ } if (z__[(*n << 1) - 1] < 0.f) { *info = -((*n << 1) + 199); xerbla_("SLASQ2", &c__2, (ftnlen)6); return 0; } d__ += z__[(*n << 1) - 1]; /* Computing MAX */ r__1 = qmax, r__2 = z__[(*n << 1) - 1]; qmax = f2cmax(r__1,r__2); zmax = f2cmax(qmax,zmax); /* Check for diagonality. */ if (e == 0.f) { i__1 = *n; for (k = 2; k <= i__1; ++k) { z__[k] = z__[(k << 1) - 1]; /* L20: */ } slasrt_("D", n, &z__[1], &iinfo); z__[(*n << 1) - 1] = d__; return 0; } trace = d__ + e; /* Check for zero data. */ if (trace == 0.f) { z__[(*n << 1) - 1] = 0.f; return 0; } /* Check whether the machine is IEEE conformable. */ /* IEEE = ILAENV( 10, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND. */ /* $ ILAENV( 11, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 */ /* [11/15/2008] The case IEEE=.TRUE. has a problem in single precision with */ /* some the test matrices of type 16. The double precision code is fine. */ ieee = FALSE_; /* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */ for (k = *n << 1; k >= 2; k += -2) { z__[k * 2] = 0.f; z__[(k << 1) - 1] = z__[k]; z__[(k << 1) - 2] = 0.f; z__[(k << 1) - 3] = z__[k - 1]; /* L30: */ } i0 = 1; n0 = *n; /* Reverse the qd-array, if warranted. */ if (z__[(i0 << 2) - 3] * 1.5f < z__[(n0 << 2) - 3]) { ipn4 = i0 + n0 << 2; i__1 = i0 + n0 - 1 << 1; for (i4 = i0 << 2; i4 <= i__1; i4 += 4) { temp = z__[i4 - 3]; z__[i4 - 3] = z__[ipn4 - i4 - 3]; z__[ipn4 - i4 - 3] = temp; temp = z__[i4 - 1]; z__[i4 - 1] = z__[ipn4 - i4 - 5]; z__[ipn4 - i4 - 5] = temp; /* L40: */ } } /* Initial split checking via dqd and Li's test. */ pp = 0; for (k = 1; k <= 2; ++k) { d__ = z__[(n0 << 2) + pp - 3]; i__1 = (i0 << 2) + pp; for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) { if (z__[i4 - 1] <= tol2 * d__) { z__[i4 - 1] = 0.f; d__ = z__[i4 - 3]; } else { d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1])); } /* L50: */ } /* dqd maps Z to ZZ plus Li's test. */ emin = z__[(i0 << 2) + pp + 1]; d__ = z__[(i0 << 2) + pp - 3]; i__1 = (n0 - 1 << 2) + pp; for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) { z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1]; if (z__[i4 - 1] <= tol2 * d__) { z__[i4 - 1] = 0.f; z__[i4 - (pp << 1) - 2] = d__; z__[i4 - (pp << 1)] = 0.f; d__ = z__[i4 + 1]; } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2]; z__[i4 - (pp << 1)] = z__[i4 - 1] * temp; d__ *= temp; } else { z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - ( pp << 1) - 2]); d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]); } /* Computing MIN */ r__1 = emin, r__2 = z__[i4 - (pp << 1)]; emin = f2cmin(r__1,r__2); /* L60: */ } z__[(n0 << 2) - pp - 2] = d__; /* Now find qmax. */ qmax = z__[(i0 << 2) - pp - 2]; i__1 = (n0 << 2) - pp - 2; for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) { /* Computing MAX */ r__1 = qmax, r__2 = z__[i4]; qmax = f2cmax(r__1,r__2); /* L70: */ } /* Prepare for the next iteration on K. */ pp = 1 - pp; /* L80: */ } /* Initialise variables to pass to SLASQ3. */ ttype = 0; dmin1 = 0.f; dmin2 = 0.f; dn = 0.f; dn1 = 0.f; dn2 = 0.f; g = 0.f; tau = 0.f; iter = 2; nfail = 0; ndiv = n0 - i0 << 1; i__1 = *n + 1; for (iwhila = 1; iwhila <= i__1; ++iwhila) { if (n0 < 1) { goto L170; } /* While array unfinished do */ /* E(N0) holds the value of SIGMA when submatrix in I0:N0 */ /* splits from the rest of the array, but is negated. */ desig = 0.f; if (n0 == *n) { sigma = 0.f; } else { sigma = -z__[(n0 << 2) - 1]; } if (sigma < 0.f) { *info = 1; return 0; } /* Find last unreduced submatrix's top index I0, find QMAX and */ /* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */ emax = 0.f; if (n0 > i0) { emin = (r__1 = z__[(n0 << 2) - 5], abs(r__1)); } else { emin = 0.f; } qmin = z__[(n0 << 2) - 3]; qmax = qmin; for (i4 = n0 << 2; i4 >= 8; i4 += -4) { if (z__[i4 - 5] <= 0.f) { goto L100; } if (qmin >= emax * 4.f) { /* Computing MIN */ r__1 = qmin, r__2 = z__[i4 - 3]; qmin = f2cmin(r__1,r__2); /* Computing MAX */ r__1 = emax, r__2 = z__[i4 - 5]; emax = f2cmax(r__1,r__2); } /* Computing MAX */ r__1 = qmax, r__2 = z__[i4 - 7] + z__[i4 - 5]; qmax = f2cmax(r__1,r__2); /* Computing MIN */ r__1 = emin, r__2 = z__[i4 - 5]; emin = f2cmin(r__1,r__2); /* L90: */ } i4 = 4; L100: i0 = i4 / 4; pp = 0; if (n0 - i0 > 1) { dee = z__[(i0 << 2) - 3]; deemin = dee; kmin = i0; i__2 = (n0 << 2) - 3; for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) { dee = z__[i4] * (dee / (dee + z__[i4 - 2])); if (dee <= deemin) { deemin = dee; kmin = (i4 + 3) / 4; } /* L110: */ } if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * .5f) { ipn4 = i0 + n0 << 2; pp = 2; i__2 = i0 + n0 - 1 << 1; for (i4 = i0 << 2; i4 <= i__2; i4 += 4) { temp = z__[i4 - 3]; z__[i4 - 3] = z__[ipn4 - i4 - 3]; z__[ipn4 - i4 - 3] = temp; temp = z__[i4 - 2]; z__[i4 - 2] = z__[ipn4 - i4 - 2]; z__[ipn4 - i4 - 2] = temp; temp = z__[i4 - 1]; z__[i4 - 1] = z__[ipn4 - i4 - 5]; z__[ipn4 - i4 - 5] = temp; temp = z__[i4]; z__[i4] = z__[ipn4 - i4 - 4]; z__[ipn4 - i4 - 4] = temp; /* L120: */ } } } /* Put -(initial shift) into DMIN. */ /* Computing MAX */ r__1 = 0.f, r__2 = qmin - sqrt(qmin) * 2.f * sqrt(emax); dmin__ = -f2cmax(r__1,r__2); /* Now I0:N0 is unreduced. */ /* PP = 0 for ping, PP = 1 for pong. */ /* PP = 2 indicates that flipping was applied to the Z array and */ /* and that the tests for deflation upon entry in SLASQ3 */ /* should not be performed. */ nbig = (n0 - i0 + 1) * 100; i__2 = nbig; for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) { if (i0 > n0) { goto L150; } /* While submatrix unfinished take a good dqds step. */ slasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, & nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, & dn1, &dn2, &g, &tau); pp = 1 - pp; /* When EMIN is very small check for splits. */ if (pp == 0 && n0 - i0 >= 3) { if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * sigma) { splt = i0 - 1; qmax = z__[(i0 << 2) - 3]; emin = z__[(i0 << 2) - 1]; oldemn = z__[i0 * 4]; i__3 = n0 - 3 << 2; for (i4 = i0 << 2; i4 <= i__3; i4 += 4) { if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= tol2 * sigma) { z__[i4 - 1] = -sigma; splt = i4 / 4; qmax = 0.f; emin = z__[i4 + 3]; oldemn = z__[i4 + 4]; } else { /* Computing MAX */ r__1 = qmax, r__2 = z__[i4 + 1]; qmax = f2cmax(r__1,r__2); /* Computing MIN */ r__1 = emin, r__2 = z__[i4 - 1]; emin = f2cmin(r__1,r__2); /* Computing MIN */ r__1 = oldemn, r__2 = z__[i4]; oldemn = f2cmin(r__1,r__2); } /* L130: */ } z__[(n0 << 2) - 1] = emin; z__[n0 * 4] = oldemn; i0 = splt + 1; } } /* L140: */ } *info = 2; /* Maximum number of iterations exceeded, restore the shift */ /* SIGMA and place the new d's and e's in a qd array. */ /* This might need to be done for several blocks */ i1 = i0; n1 = n0; L145: tempq = z__[(i0 << 2) - 3]; z__[(i0 << 2) - 3] += sigma; i__2 = n0; for (k = i0 + 1; k <= i__2; ++k) { tempe = z__[(k << 2) - 5]; z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7]; tempq = z__[(k << 2) - 3]; z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << 2) - 5]; } /* Prepare to do this on the previous block if there is one */ if (i1 > 1) { n1 = i1 - 1; while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.f) { --i1; } if (i1 >= 1) { sigma = -z__[(n1 << 2) - 1]; goto L145; } } i__2 = *n; for (k = 1; k <= i__2; ++k) { z__[(k << 1) - 1] = z__[(k << 2) - 3]; /* Only the block 1..N0 is unfinished. The rest of the e's */ /* must be essentially zero, although sometimes other data */ /* has been stored in them. */ if (k < n0) { z__[k * 2] = z__[(k << 2) - 1]; } else { z__[k * 2] = 0.f; } } return 0; /* end IWHILB */ L150: /* L160: */ ; } *info = 3; return 0; /* end IWHILA */ L170: /* Move q's to the front. */ i__1 = *n; for (k = 2; k <= i__1; ++k) { z__[k] = z__[(k << 2) - 3]; /* L180: */ } /* Sort and compute sum of eigenvalues. */ slasrt_("D", n, &z__[1], &iinfo); e = 0.f; for (k = *n; k >= 1; --k) { e += z__[k]; /* L190: */ } /* Store trace, sum(eigenvalues) and information on performance. */ z__[(*n << 1) + 1] = trace; z__[(*n << 1) + 2] = e; z__[(*n << 1) + 3] = (real) iter; /* Computing 2nd power */ i__1 = *n; z__[(*n << 1) + 4] = (real) ndiv / (real) (i__1 * i__1); z__[(*n << 1) + 5] = nfail * 100.f / (real) iter; return 0; /* End of SLASQ2 */ } /* slasq2_ */