#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 SSPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SSPEVX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, */ /* ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, */ /* INFO ) */ /* CHARACTER JOBZ, RANGE, UPLO */ /* INTEGER IL, INFO, IU, LDZ, M, N */ /* REAL ABSTOL, VL, VU */ /* INTEGER IFAIL( * ), IWORK( * ) */ /* REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SSPEVX computes selected eigenvalues and, optionally, eigenvectors */ /* > of a real symmetric matrix A in packed storage. Eigenvalues/vectors */ /* > can be selected by specifying either a range of values or a range of */ /* > indices for the desired eigenvalues. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBZ */ /* > \verbatim */ /* > JOBZ is CHARACTER*1 */ /* > = 'N': Compute eigenvalues only; */ /* > = 'V': Compute eigenvalues and eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] RANGE */ /* > \verbatim */ /* > RANGE is CHARACTER*1 */ /* > = 'A': all eigenvalues will be found; */ /* > = 'V': all eigenvalues in the half-open interval (VL,VU] */ /* > will be found; */ /* > = 'I': the IL-th through IU-th eigenvalues will be found. */ /* > \endverbatim */ /* > */ /* > \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,out] AP */ /* > \verbatim */ /* > AP is REAL array, dimension (N*(N+1)/2) */ /* > On entry, the upper or lower triangle of the symmetric matrix */ /* > A, packed columnwise in a linear array. The j-th column of A */ /* > is stored in the array AP as follows: */ /* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ /* > if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ /* > */ /* > On exit, AP is overwritten by values generated during the */ /* > reduction to tridiagonal form. If UPLO = 'U', the diagonal */ /* > and first superdiagonal of the tridiagonal matrix T overwrite */ /* > the corresponding elements of A, and if UPLO = 'L', the */ /* > diagonal and first subdiagonal of T overwrite the */ /* > corresponding elements of A. */ /* > \endverbatim */ /* > */ /* > \param[in] VL */ /* > \verbatim */ /* > VL is REAL */ /* > If RANGE='V', the lower bound of the interval to */ /* > be searched for eigenvalues. VL < VU. */ /* > Not referenced if RANGE = 'A' or 'I'. */ /* > \endverbatim */ /* > */ /* > \param[in] VU */ /* > \verbatim */ /* > VU is REAL */ /* > If RANGE='V', the upper bound of the interval to */ /* > be searched for eigenvalues. VL < VU. */ /* > Not referenced if RANGE = 'A' or 'I'. */ /* > \endverbatim */ /* > */ /* > \param[in] IL */ /* > \verbatim */ /* > IL is INTEGER */ /* > If RANGE='I', the index of the */ /* > smallest eigenvalue to be returned. */ /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ /* > Not referenced if RANGE = 'A' or 'V'. */ /* > \endverbatim */ /* > */ /* > \param[in] IU */ /* > \verbatim */ /* > IU is INTEGER */ /* > If RANGE='I', the index of the */ /* > largest eigenvalue to be returned. */ /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ /* > Not referenced if RANGE = 'A' or 'V'. */ /* > \endverbatim */ /* > */ /* > \param[in] ABSTOL */ /* > \verbatim */ /* > ABSTOL is REAL */ /* > The absolute error tolerance for the eigenvalues. */ /* > An approximate eigenvalue is accepted as converged */ /* > when it is determined to lie in an interval [a,b] */ /* > of width less than or equal to */ /* > */ /* > ABSTOL + EPS * f2cmax( |a|,|b| ) , */ /* > */ /* > where EPS is the machine precision. If ABSTOL is less than */ /* > or equal to zero, then EPS*|T| will be used in its place, */ /* > where |T| is the 1-norm of the tridiagonal matrix obtained */ /* > by reducing AP to tridiagonal form. */ /* > */ /* > Eigenvalues will be computed most accurately when ABSTOL is */ /* > set to twice the underflow threshold 2*SLAMCH('S'), not zero. */ /* > If this routine returns with INFO>0, indicating that some */ /* > eigenvectors did not converge, try setting ABSTOL to */ /* > 2*SLAMCH('S'). */ /* > */ /* > See "Computing Small Singular Values of Bidiagonal Matrices */ /* > with Guaranteed High Relative Accuracy," by Demmel and */ /* > Kahan, LAPACK Working Note #3. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The total number of eigenvalues found. 0 <= M <= N. */ /* > If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ /* > \endverbatim */ /* > */ /* > \param[out] W */ /* > \verbatim */ /* > W is REAL array, dimension (N) */ /* > If INFO = 0, the selected eigenvalues in ascending order. */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is REAL array, dimension (LDZ, f2cmax(1,M)) */ /* > If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ /* > contain the orthonormal eigenvectors of the matrix A */ /* > corresponding to the selected eigenvalues, with the i-th */ /* > column of Z holding the eigenvector associated with W(i). */ /* > If an eigenvector fails to converge, then that column of Z */ /* > contains the latest approximation to the eigenvector, and the */ /* > index of the eigenvector is returned in IFAIL. */ /* > If JOBZ = 'N', then Z is not referenced. */ /* > Note: the user must ensure that at least f2cmax(1,M) columns are */ /* > supplied in the array Z; if RANGE = 'V', the exact value of M */ /* > is not known in advance and an upper bound must be used. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. LDZ >= 1, and if */ /* > JOBZ = 'V', LDZ >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (8*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (5*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IFAIL */ /* > \verbatim */ /* > IFAIL is INTEGER array, dimension (N) */ /* > If JOBZ = 'V', then if INFO = 0, the first M elements of */ /* > IFAIL are zero. If INFO > 0, then IFAIL contains the */ /* > indices of the eigenvectors that failed to converge. */ /* > If JOBZ = 'N', then IFAIL 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: if INFO = i, then i eigenvectors failed to converge. */ /* > Their indices are stored in array IFAIL. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup realOTHEReigen */ /* ===================================================================== */ /* Subroutine */ int sspevx_(char *jobz, char *range, char *uplo, integer *n, real *ap, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, real *w, real *z__, integer *ldz, real *work, integer * iwork, integer *ifail, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Local variables */ integer indd, inde; real anrm; integer imax; real rmin, rmax; logical test; integer itmp1, i__, j, indee; real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); char order[1]; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ); logical wantz; integer jj; logical alleig, indeig; integer iscale, indibl; logical valeig; extern real slamch_(char *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real abstll, bignum; integer indtau, indisp, indiwo, indwrk; extern real slansp_(char *, char *, integer *, real *, real *); extern /* Subroutine */ int sstein_(integer *, real *, real *, integer *, real *, integer *, integer *, real *, integer *, real *, integer * , integer *, integer *), ssterf_(integer *, real *, real *, integer *); integer nsplit; extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); real smlnum; extern /* Subroutine */ int sopgtr_(char *, integer *, real *, real *, real *, integer *, real *, integer *), ssptrd_(char *, integer *, real *, real *, real *, real *, integer *), ssteqr_(char *, integer *, real *, real *, real *, integer *, real *, integer *), sopmtr_(char *, char *, char *, integer *, integer *, real *, real *, real *, integer *, real *, integer *); real eps, vll, vuu, tmp1; /* -- LAPACK driver 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..-- */ /* June 2016 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; --iwork; --ifail; /* Function Body */ wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -7; } } else if (indeig) { if (*il < 1 || *il > f2cmax(1,*n)) { *info = -8; } else if (*iu < f2cmin(*n,*il) || *iu > *n) { *info = -9; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -14; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSPEVX", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; w[1] = ap[1]; } else { if (*vl < ap[1] && *vu >= ap[1]) { *m = 1; w[1] = ap[1]; } } if (wantz) { z__[z_dim1 + 1] = 1.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = f2cmin(r__1,r__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } else { vll = 0.f; vuu = 0.f; } anrm = slansp_("M", uplo, n, &ap[1], &work[1]); if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { i__1 = *n * (*n + 1) / 2; sscal_(&i__1, &sigma, &ap[1], &c__1); if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. */ indtau = 1; inde = indtau + *n; indd = inde + *n; indwrk = indd + *n; ssptrd_(uplo, n, &ap[1], &work[indd], &work[inde], &work[indtau], &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal */ /* to zero, then call SSTERF or SOPGTR and SSTEQR. If this fails */ /* for some eigenvalue, then try SSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.f) { scopy_(n, &work[indd], &c__1, &w[1], &c__1); indee = indwrk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssterf_(n, &w[1], &work[indee], info); } else { sopgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, & work[indwrk], &iinfo); i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[ indwrk], info); if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; /* L10: */ } } } if (*info == 0) { *m = *n; goto L20; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwo = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[ inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[ indwrk], &iwork[indiwo], info); if (wantz) { sstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[ indisp], &z__[z_offset], ldz, &work[indwrk], &iwork[indiwo], & ifail[1], info); /* Apply orthogonal matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by SSTEIN. */ sopmtr_("L", uplo, "N", n, m, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[indwrk], &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L20: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } /* If eigenvalues are not in order, then sort them, along with */ /* eigenvectors. */ if (wantz) { i__1 = *m - 1; for (j = 1; j <= i__1; ++j) { i__ = 0; tmp1 = w[j]; i__2 = *m; for (jj = j + 1; jj <= i__2; ++jj) { if (w[jj] < tmp1) { i__ = jj; tmp1 = w[jj]; } /* L30: */ } if (i__ != 0) { itmp1 = iwork[indibl + i__ - 1]; w[i__] = w[j]; iwork[indibl + i__ - 1] = iwork[indibl + j - 1]; w[j] = tmp1; iwork[indibl + j - 1] = itmp1; sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L40: */ } } return 0; /* End of SSPEVX */ } /* sspevx_ */