#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 SSTEQR */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SSTEQR + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */ /* CHARACTER COMPZ */ /* INTEGER INFO, LDZ, N */ /* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SSTEQR computes all eigenvalues and, optionally, eigenvectors of a */ /* > symmetric tridiagonal matrix using the implicit QL or QR method. */ /* > The eigenvectors of a full or band symmetric matrix can also be found */ /* > if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to */ /* > tridiagonal form. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] COMPZ */ /* > \verbatim */ /* > COMPZ is CHARACTER*1 */ /* > = 'N': Compute eigenvalues only. */ /* > = 'V': Compute eigenvalues and eigenvectors of the original */ /* > symmetric matrix. On entry, Z must contain the */ /* > orthogonal matrix used to reduce the original matrix */ /* > to tridiagonal form. */ /* > = 'I': Compute eigenvalues and eigenvectors of the */ /* > tridiagonal matrix. Z is initialized to the identity */ /* > matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > On entry, the diagonal elements of the tridiagonal matrix. */ /* > On exit, if INFO = 0, the eigenvalues in ascending order. */ /* > \endverbatim */ /* > */ /* > \param[in,out] E */ /* > \verbatim */ /* > E is REAL array, dimension (N-1) */ /* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ /* > matrix. */ /* > On exit, E has been destroyed. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Z */ /* > \verbatim */ /* > Z is REAL array, dimension (LDZ, N) */ /* > On entry, if COMPZ = 'V', then Z contains the orthogonal */ /* > matrix used in the reduction to tridiagonal form. */ /* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ /* > orthonormal eigenvectors of the original symmetric matrix, */ /* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ /* > of the symmetric tridiagonal matrix. */ /* > If COMPZ = 'N', then Z is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. LDZ >= 1, and if */ /* > eigenvectors are desired, then LDZ >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (f2cmax(1,2*N-2)) */ /* > If COMPZ = 'N', then WORK is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: the algorithm has failed to find all the eigenvalues in */ /* > a total of 30*N iterations; if INFO = i, then i */ /* > elements of E have not converged to zero; on exit, D */ /* > and E contain the elements of a symmetric tridiagonal */ /* > matrix which is orthogonally similar to the original */ /* > matrix. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int ssteqr_(char *compz, integer *n, real *d__, real *e, real *z__, integer *ldz, real *work, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Local variables */ integer lend, jtot; extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *) ; real b, c__, f, g; integer i__, j, k, l, m; real p, r__, s; extern logical lsame_(char *, char *); real anorm; extern /* Subroutine */ int slasr_(char *, char *, char *, integer *, integer *, real *, real *, real *, integer *); integer l1; extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, integer *); integer lendm1, lendp1; extern /* Subroutine */ int slaev2_(real *, real *, real *, real *, real * , real *, real *); extern real slapy2_(real *, real *); integer ii, mm, iscale; extern real slamch_(char *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real safmax; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); integer lendsv; extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real * ), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); real ssfmin; integer nmaxit, icompz; real ssfmax; extern real slanst_(char *, integer *, real *, real *); extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); integer lm1, mm1, nm1; real rt1, rt2, eps; integer lsv; real tst, eps2; /* -- 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 */ --d__; --e; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; /* Function Body */ *info = 0; if (lsame_(compz, "N")) { icompz = 0; } else if (lsame_(compz, "V")) { icompz = 1; } else if (lsame_(compz, "I")) { icompz = 2; } else { icompz = -1; } if (icompz < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < f2cmax(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("SSTEQR", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (icompz == 2) { z__[z_dim1 + 1] = 1.f; } return 0; } /* Determine the unit roundoff and over/underflow thresholds. */ eps = slamch_("E"); /* Computing 2nd power */ r__1 = eps; eps2 = r__1 * r__1; safmin = slamch_("S"); safmax = 1.f / safmin; ssfmax = sqrt(safmax) / 3.f; ssfmin = sqrt(safmin) / eps2; /* Compute the eigenvalues and eigenvectors of the tridiagonal */ /* matrix. */ if (icompz == 2) { slaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz); } nmaxit = *n * 30; jtot = 0; /* Determine where the matrix splits and choose QL or QR iteration */ /* for each block, according to whether top or bottom diagonal */ /* element is smaller. */ l1 = 1; nm1 = *n - 1; L10: if (l1 > *n) { goto L160; } if (l1 > 1) { e[l1 - 1] = 0.f; } if (l1 <= nm1) { i__1 = nm1; for (m = l1; m <= i__1; ++m) { tst = (r__1 = e[m], abs(r__1)); if (tst == 0.f) { goto L30; } if (tst <= sqrt((r__1 = d__[m], abs(r__1))) * sqrt((r__2 = d__[m + 1], abs(r__2))) * eps) { e[m] = 0.f; goto L30; } /* L20: */ } } m = *n; L30: l = l1; lsv = l; lend = m; lendsv = lend; l1 = m + 1; if (lend == l) { goto L10; } /* Scale submatrix in rows and columns L to LEND */ i__1 = lend - l + 1; anorm = slanst_("M", &i__1, &d__[l], &e[l]); iscale = 0; if (anorm == 0.f) { goto L10; } if (anorm > ssfmax) { iscale = 1; i__1 = lend - l + 1; slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, info); i__1 = lend - l; slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, info); } else if (anorm < ssfmin) { iscale = 2; i__1 = lend - l + 1; slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, info); i__1 = lend - l; slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, info); } /* Choose between QL and QR iteration */ if ((r__1 = d__[lend], abs(r__1)) < (r__2 = d__[l], abs(r__2))) { lend = lsv; l = lendsv; } if (lend > l) { /* QL Iteration */ /* Look for small subdiagonal element. */ L40: if (l != lend) { lendm1 = lend - 1; i__1 = lendm1; for (m = l; m <= i__1; ++m) { /* Computing 2nd power */ r__2 = (r__1 = e[m], abs(r__1)); tst = r__2 * r__2; if (tst <= eps2 * (r__1 = d__[m], abs(r__1)) * (r__2 = d__[m + 1], abs(r__2)) + safmin) { goto L60; } /* L50: */ } } m = lend; L60: if (m < lend) { e[m] = 0.f; } p = d__[l]; if (m == l) { goto L80; } /* If remaining matrix is 2-by-2, use SLAE2 or SLAEV2 */ /* to compute its eigensystem. */ if (m == l + 1) { if (icompz > 0) { slaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); work[l] = c__; work[*n - 1 + l] = s; slasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], & z__[l * z_dim1 + 1], ldz); } else { slae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); } d__[l] = rt1; d__[l + 1] = rt2; e[l] = 0.f; l += 2; if (l <= lend) { goto L40; } goto L140; } if (jtot == nmaxit) { goto L140; } ++jtot; /* Form shift. */ g = (d__[l + 1] - p) / (e[l] * 2.f); r__ = slapy2_(&g, &c_b10); g = d__[m] - p + e[l] / (g + r_sign(&r__, &g)); s = 1.f; c__ = 1.f; p = 0.f; /* Inner loop */ mm1 = m - 1; i__1 = l; for (i__ = mm1; i__ >= i__1; --i__) { f = s * e[i__]; b = c__ * e[i__]; slartg_(&g, &f, &c__, &s, &r__); if (i__ != m - 1) { e[i__ + 1] = r__; } g = d__[i__ + 1] - p; r__ = (d__[i__] - g) * s + c__ * 2.f * b; p = s * r__; d__[i__ + 1] = g + p; g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = -s; } /* L70: */ } /* If eigenvectors are desired, then apply saved rotations. */ if (icompz > 0) { mm = m - l + 1; slasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l * z_dim1 + 1], ldz); } d__[l] -= p; e[l] = g; goto L40; /* Eigenvalue found. */ L80: d__[l] = p; ++l; if (l <= lend) { goto L40; } goto L140; } else { /* QR Iteration */ /* Look for small superdiagonal element. */ L90: if (l != lend) { lendp1 = lend + 1; i__1 = lendp1; for (m = l; m >= i__1; --m) { /* Computing 2nd power */ r__2 = (r__1 = e[m - 1], abs(r__1)); tst = r__2 * r__2; if (tst <= eps2 * (r__1 = d__[m], abs(r__1)) * (r__2 = d__[m - 1], abs(r__2)) + safmin) { goto L110; } /* L100: */ } } m = lend; L110: if (m > lend) { e[m - 1] = 0.f; } p = d__[l]; if (m == l) { goto L130; } /* If remaining matrix is 2-by-2, use SLAE2 or SLAEV2 */ /* to compute its eigensystem. */ if (m == l - 1) { if (icompz > 0) { slaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) ; work[m] = c__; work[*n - 1 + m] = s; slasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], & z__[(l - 1) * z_dim1 + 1], ldz); } else { slae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); } d__[l - 1] = rt1; d__[l] = rt2; e[l - 1] = 0.f; l += -2; if (l >= lend) { goto L90; } goto L140; } if (jtot == nmaxit) { goto L140; } ++jtot; /* Form shift. */ g = (d__[l - 1] - p) / (e[l - 1] * 2.f); r__ = slapy2_(&g, &c_b10); g = d__[m] - p + e[l - 1] / (g + r_sign(&r__, &g)); s = 1.f; c__ = 1.f; p = 0.f; /* Inner loop */ lm1 = l - 1; i__1 = lm1; for (i__ = m; i__ <= i__1; ++i__) { f = s * e[i__]; b = c__ * e[i__]; slartg_(&g, &f, &c__, &s, &r__); if (i__ != m) { e[i__ - 1] = r__; } g = d__[i__] - p; r__ = (d__[i__ + 1] - g) * s + c__ * 2.f * b; p = s * r__; d__[i__] = g + p; g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = s; } /* L120: */ } /* If eigenvectors are desired, then apply saved rotations. */ if (icompz > 0) { mm = l - m + 1; slasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m * z_dim1 + 1], ldz); } d__[l] -= p; e[lm1] = g; goto L90; /* Eigenvalue found. */ L130: d__[l] = p; --l; if (l >= lend) { goto L90; } goto L140; } /* Undo scaling if necessary */ L140: if (iscale == 1) { i__1 = lendsv - lsv + 1; slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], n, info); i__1 = lendsv - lsv; slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, info); } else if (iscale == 2) { i__1 = lendsv - lsv + 1; slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], n, info); i__1 = lendsv - lsv; slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, info); } /* Check for no convergence to an eigenvalue after a total */ /* of N*MAXIT iterations. */ if (jtot < nmaxit) { goto L10; } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (e[i__] != 0.f) { ++(*info); } /* L150: */ } goto L190; /* Order eigenvalues and eigenvectors. */ L160: if (icompz == 0) { /* Use Quick Sort */ slasrt_("I", n, &d__[1], info); } else { /* Use Selection Sort to minimize swaps of eigenvectors */ i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; k = i__; p = d__[i__]; i__2 = *n; for (j = ii; j <= i__2; ++j) { if (d__[j] < p) { k = j; p = d__[j]; } /* L170: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } /* L180: */ } } L190: return 0; /* End of SSTEQR */ } /* ssteqr_ */