#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 CHEEQUB */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CHEEQUB + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CHEEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO ) */ /* INTEGER INFO, LDA, N */ /* REAL AMAX, SCOND */ /* CHARACTER UPLO */ /* COMPLEX A( LDA, * ), WORK( * ) */ /* REAL S( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CHEEQUB computes row and column scalings intended to equilibrate a */ /* > Hermitian matrix A (with respect to the Euclidean norm) and reduce */ /* > its condition number. The scale factors S are computed by the BIN */ /* > algorithm (see references) so that the scaled matrix B with elements */ /* > B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of */ /* > the smallest possible condition number over all possible diagonal */ /* > scalings. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > = 'U': Upper triangle of A is stored; */ /* > = 'L': Lower triangle of A is stored. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > The N-by-N Hermitian matrix whose scaling factors are to be */ /* > computed. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is REAL array, dimension (N) */ /* > If INFO = 0, S contains the scale factors for A. */ /* > \endverbatim */ /* > */ /* > \param[out] SCOND */ /* > \verbatim */ /* > SCOND is REAL */ /* > If INFO = 0, S contains the ratio of the smallest S(i) to */ /* > the largest S(i). If SCOND >= 0.1 and AMAX is neither too */ /* > large nor too small, it is not worth scaling by S. */ /* > \endverbatim */ /* > */ /* > \param[out] AMAX */ /* > \verbatim */ /* > AMAX is REAL */ /* > Largest absolute value of any matrix element. If AMAX is */ /* > very close to overflow or very close to underflow, the */ /* > matrix should be scaled. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (2*N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: if INFO = i, the i-th diagonal element is nonpositive. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date April 2012 */ /* > \ingroup complexHEcomputational */ /* > \par References: */ /* ================ */ /* > */ /* > Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n */ /* > Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n */ /* > DOI 10.1023/B:NUMA.0000016606.32820.69 \n */ /* > Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 */ /* > */ /* ===================================================================== */ /* Subroutine */ int cheequb_(char *uplo, integer *n, complex *a, integer * lda, real *s, real *scond, real *amax, complex *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2, r__3, r__4; doublereal d__1; complex q__1, q__2, q__3, q__4; /* Local variables */ real base; integer iter; real smin, smax, d__; integer i__, j; real t, u, scale; extern logical lsame_(char *, char *); real c0, c1, c2, sumsq, si; logical up; extern real slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real bignum; extern /* Subroutine */ int classq_(integer *, complex *, integer *, real *, real *); real smlnum, avg, std, tol; /* -- LAPACK computational 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..-- */ /* April 2012 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --s; --work; /* Function Body */ *info = 0; if (! (lsame_(uplo, "U") || lsame_(uplo, "L"))) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < f2cmax(1,*n)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("CHEEQUB", &i__1, (ftnlen)7); return 0; } up = lsame_(uplo, "U"); *amax = 0.f; /* Quick return if possible. */ if (*n == 0) { *scond = 1.f; return 0; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { s[i__] = 0.f; } *amax = 0.f; if (up) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = s[i__], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); s[i__] = f2cmax(r__3,r__4); /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = s[j], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); s[j] = f2cmax(r__3,r__4); /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = *amax, r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); *amax = f2cmax(r__3,r__4); } /* Computing MAX */ i__2 = j + j * a_dim1; r__3 = s[j], r__4 = (r__1 = a[i__2].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2)); s[j] = f2cmax(r__3,r__4); /* Computing MAX */ i__2 = j + j * a_dim1; r__3 = *amax, r__4 = (r__1 = a[i__2].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2)); *amax = f2cmax(r__3,r__4); } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = j + j * a_dim1; r__3 = s[j], r__4 = (r__1 = a[i__2].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2)); s[j] = f2cmax(r__3,r__4); /* Computing MAX */ i__2 = j + j * a_dim1; r__3 = *amax, r__4 = (r__1 = a[i__2].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2)); *amax = f2cmax(r__3,r__4); i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = s[i__], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); s[i__] = f2cmax(r__3,r__4); /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = s[j], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); s[j] = f2cmax(r__3,r__4); /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = *amax, r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); *amax = f2cmax(r__3,r__4); } } } i__1 = *n; for (j = 1; j <= i__1; ++j) { s[j] = 1.f / s[j]; } tol = 1.f / sqrt(*n * 2.f); for (iter = 1; iter <= 100; ++iter) { scale = 0.f; sumsq = 0.f; /* beta = |A|s */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; work[i__2].r = 0.f, work[i__2].i = 0.f; } if (up) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__ + j * a_dim1; r__3 = ((r__1 = a[i__5].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) * s[j]; q__1.r = work[i__4].r + r__3, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; i__3 = j; i__4 = j; i__5 = i__ + j * a_dim1; r__3 = ((r__1 = a[i__5].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) * s[i__]; q__1.r = work[i__4].r + r__3, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } i__2 = j; i__3 = j; i__4 = j + j * a_dim1; r__3 = ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2))) * s[j]; q__1.r = work[i__3].r + r__3, q__1.i = work[i__3].i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; i__4 = j + j * a_dim1; r__3 = ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[j + j * a_dim1]), abs(r__2))) * s[j]; q__1.r = work[i__3].r + r__3, q__1.i = work[i__3].i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__ + j * a_dim1; r__3 = ((r__1 = a[i__5].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) * s[j]; q__1.r = work[i__4].r + r__3, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; i__3 = j; i__4 = j; i__5 = i__ + j * a_dim1; r__3 = ((r__1 = a[i__5].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) * s[i__]; q__1.r = work[i__4].r + r__3, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } } } /* avg = s^T beta / n */ avg = 0.f; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; q__2.r = s[i__2] * work[i__3].r, q__2.i = s[i__2] * work[i__3].i; q__1.r = avg + q__2.r, q__1.i = q__2.i; avg = q__1.r; } avg /= *n; std = 0.f; i__1 = *n << 1; for (i__ = *n + 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__ - *n; i__4 = i__ - *n; q__2.r = s[i__3] * work[i__4].r, q__2.i = s[i__3] * work[i__4].i; q__1.r = q__2.r - avg, q__1.i = q__2.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } classq_(n, &work[*n + 1], &c__1, &scale, &sumsq); std = scale * sqrt(sumsq / *n); if (std < tol * avg) { goto L999; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * a_dim1; t = (r__1 = a[i__2].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + i__ * a_dim1]), abs(r__2)); si = s[i__]; c2 = (*n - 1) * t; i__2 = *n - 2; i__3 = i__; r__1 = t * si; q__2.r = work[i__3].r - r__1, q__2.i = work[i__3].i; d__1 = (doublereal) i__2; q__1.r = d__1 * q__2.r, q__1.i = d__1 * q__2.i; c1 = q__1.r; r__1 = -(t * si) * si; i__2 = i__; d__1 = 2.; q__4.r = d__1 * work[i__2].r, q__4.i = d__1 * work[i__2].i; q__3.r = si * q__4.r, q__3.i = si * q__4.i; q__2.r = r__1 + q__3.r, q__2.i = q__3.i; r__2 = *n * avg; q__1.r = q__2.r - r__2, q__1.i = q__2.i; c0 = q__1.r; d__ = c1 * c1 - c0 * 4 * c2; if (d__ <= 0.f) { *info = -1; return 0; } si = c0 * -2 / (c1 + sqrt(d__)); d__ = si - s[i__]; u = 0.f; if (up) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; t = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[j + i__ * a_dim1]), abs(r__2)); u += s[j] * t; i__3 = j; i__4 = j; r__1 = d__ * t; q__1.r = work[i__4].r + r__1, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; t = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); u += s[j] * t; i__3 = j; i__4 = j; r__1 = d__ * t; q__1.r = work[i__4].r + r__1, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } } else { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; t = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), abs(r__2)); u += s[j] * t; i__3 = j; i__4 = j; r__1 = d__ * t; q__1.r = work[i__4].r + r__1, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j + i__ * a_dim1; t = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[j + i__ * a_dim1]), abs(r__2)); u += s[j] * t; i__3 = j; i__4 = j; r__1 = d__ * t; q__1.r = work[i__4].r + r__1, q__1.i = work[i__4].i; work[i__3].r = q__1.r, work[i__3].i = q__1.i; } } i__2 = i__; q__4.r = u + work[i__2].r, q__4.i = work[i__2].i; q__3.r = d__ * q__4.r, q__3.i = d__ * q__4.i; d__1 = (doublereal) (*n); q__2.r = q__3.r / d__1, q__2.i = q__3.i / d__1; q__1.r = avg + q__2.r, q__1.i = q__2.i; avg = q__1.r; s[i__] = si; } } L999: smlnum = slamch_("SAFEMIN"); bignum = 1.f / smlnum; smin = bignum; smax = 0.f; t = 1.f / sqrt(avg); base = slamch_("B"); u = 1.f / log(base); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = (integer) (u * log(s[i__] * t)); s[i__] = pow_ri(&base, &i__2); /* Computing MIN */ r__1 = smin, r__2 = s[i__]; smin = f2cmin(r__1,r__2); /* Computing MAX */ r__1 = smax, r__2 = s[i__]; smax = f2cmax(r__1,r__2); } *scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum); return 0; } /* cheequb_ */