#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 SSTEVR 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 SSTEVR + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, */ /* M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, */ /* LIWORK, INFO ) */ /* CHARACTER JOBZ, RANGE */ /* INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N */ /* REAL ABSTOL, VL, VU */ /* INTEGER ISUPPZ( * ), IWORK( * ) */ /* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SSTEVR computes selected eigenvalues and, optionally, eigenvectors */ /* > of a real symmetric tridiagonal matrix T. Eigenvalues and */ /* > eigenvectors can be selected by specifying either a range of values */ /* > or a range of indices for the desired eigenvalues. */ /* > */ /* > Whenever possible, SSTEVR calls SSTEMR to compute the */ /* > eigenspectrum using Relatively Robust Representations. SSTEMR */ /* > computes eigenvalues by the dqds algorithm, while orthogonal */ /* > eigenvectors are computed from various "good" L D L^T representations */ /* > (also known as Relatively Robust Representations). Gram-Schmidt */ /* > orthogonalization is avoided as far as possible. More specifically, */ /* > the various steps of the algorithm are as follows. For the i-th */ /* > unreduced block of T, */ /* > (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T */ /* > is a relatively robust representation, */ /* > (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high */ /* > relative accuracy by the dqds algorithm, */ /* > (c) If there is a cluster of close eigenvalues, "choose" sigma_i */ /* > close to the cluster, and go to step (a), */ /* > (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, */ /* > compute the corresponding eigenvector by forming a */ /* > rank-revealing twisted factorization. */ /* > The desired accuracy of the output can be specified by the input */ /* > parameter ABSTOL. */ /* > */ /* > For more details, see "A new O(n^2) algorithm for the symmetric */ /* > tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, */ /* > Computer Science Division Technical Report No. UCB//CSD-97-971, */ /* > UC Berkeley, May 1997. */ /* > */ /* > */ /* > Note 1 : SSTEVR calls SSTEMR when the full spectrum is requested */ /* > on machines which conform to the ieee-754 floating point standard. */ /* > SSTEVR calls SSTEBZ and SSTEIN on non-ieee machines and */ /* > when partial spectrum requests are made. */ /* > */ /* > Normal execution of SSTEMR may create NaNs and infinities and */ /* > hence may abort due to a floating point exception in environments */ /* > which do not handle NaNs and infinities in the ieee standard default */ /* > manner. */ /* > \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. */ /* > For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and */ /* > SSTEIN are called */ /* > \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 n diagonal elements of the tridiagonal matrix */ /* > A. */ /* > On exit, D may be multiplied by a constant factor chosen */ /* > to avoid over/underflow in computing the eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[in,out] E */ /* > \verbatim */ /* > E is REAL array, dimension (f2cmax(1,N-1)) */ /* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ /* > matrix A in elements 1 to N-1 of E. */ /* > On exit, E may be multiplied by a constant factor chosen */ /* > to avoid over/underflow in computing the eigenvalues. */ /* > \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 A to tridiagonal form. */ /* > */ /* > See "Computing Small Singular Values of Bidiagonal Matrices */ /* > with Guaranteed High Relative Accuracy," by Demmel and */ /* > Kahan, LAPACK Working Note #3. */ /* > */ /* > If high relative accuracy is important, set ABSTOL to */ /* > SLAMCH( 'Safe minimum' ). Doing so will guarantee that */ /* > eigenvalues are computed to high relative accuracy when */ /* > possible in future releases. The current code does not */ /* > make any guarantees about high relative accuracy, but */ /* > future releases will. See J. Barlow and J. Demmel, */ /* > "Computing Accurate Eigensystems of Scaled Diagonally */ /* > Dominant Matrices", LAPACK Working Note #7, for a discussion */ /* > of which matrices define their eigenvalues to high relative */ /* > accuracy. */ /* > \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) */ /* > The first M elements contain 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). */ /* > 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] ISUPPZ */ /* > \verbatim */ /* > ISUPPZ is INTEGER array, dimension ( 2*f2cmax(1,M) ) */ /* > The support of the eigenvectors in Z, i.e., the indices */ /* > indicating the nonzero elements in Z. The i-th eigenvector */ /* > is nonzero only in elements ISUPPZ( 2*i-1 ) through */ /* > ISUPPZ( 2*i ). */ /* > Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal (and */ /* > minimal) LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= 20*N. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal sizes of the WORK and IWORK */ /* > arrays, returns these values as the first entries of the WORK */ /* > and IWORK arrays, and no error message related to LWORK or */ /* > LIWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ /* > On exit, if INFO = 0, IWORK(1) returns the optimal (and */ /* > minimal) LIWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LIWORK */ /* > \verbatim */ /* > LIWORK is INTEGER */ /* > The dimension of the array IWORK. LIWORK >= 10*N. */ /* > */ /* > If LIWORK = -1, then a workspace query is assumed; the */ /* > routine only calculates the optimal sizes of the WORK and */ /* > IWORK arrays, returns these values as the first entries of */ /* > the WORK and IWORK arrays, and no error message related to */ /* > LWORK or LIWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: Internal error */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup realOTHEReigen */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Inderjit Dhillon, IBM Almaden, USA \n */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* > Ken Stanley, Computer Science Division, University of */ /* > California at Berkeley, USA \n */ /* > Jason Riedy, Computer Science Division, University of */ /* > California at Berkeley, USA \n */ /* > */ /* ===================================================================== */ /* Subroutine */ int sstevr_(char *jobz, char *range, integer *n, real *d__, real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, real *w, real *z__, integer *ldz, integer *isuppz, real * work, integer *lwork, integer *iwork, integer *liwork, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Local variables */ integer imax; real rmin, rmax; logical test; real tnrm; integer i__, j; real sigma; extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); char order[1]; integer lwmin; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ); logical wantz; integer jj; logical alleig, indeig; integer iscale, ieeeok, indibl, indifl; logical valeig; extern real slamch_(char *); real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real bignum; integer indisp, indiwo, liwmin; logical tryrac; extern real slanst_(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 sstemr_(char *, char *, integer *, real *, real *, real *, real *, integer *, integer *, integer *, real *, real *, integer *, integer *, integer *, logical *, real *, integer *, integer *, integer *, integer *); logical lquery; 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 */ --d__; --e; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --isuppz; --work; --iwork; /* Function Body */ ieeeok = ilaenv_(&c__10, "SSTEVR", "N", &c__1, &c__2, &c__3, &c__4, ( ftnlen)6, (ftnlen)1); wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lquery = *lwork == -1 || *liwork == -1; /* Computing MAX */ i__1 = 1, i__2 = *n * 20; lwmin = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *n * 10; liwmin = f2cmax(i__1,i__2); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (*n < 0) { *info = -3; } 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) { work[1] = (real) lwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -17; } else if (*liwork < liwmin && ! lquery) { *info = -19; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSTEVR", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; w[1] = d__[1]; } else { if (*vl < d__[1] && *vu >= d__[1]) { *m = 1; w[1] = d__[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; if (valeig) { vll = *vl; vuu = *vu; } tnrm = slanst_("M", n, &d__[1], &e[1]); if (tnrm > 0.f && tnrm < rmin) { iscale = 1; sigma = rmin / tnrm; } else if (tnrm > rmax) { iscale = 1; sigma = rmax / tnrm; } if (iscale == 1) { sscal_(n, &sigma, &d__[1], &c__1); i__1 = *n - 1; sscal_(&i__1, &sigma, &e[1], &c__1); if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Initialize indices into workspaces. Note: These indices are used only */ /* if SSTERF or SSTEMR fail. */ /* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and */ /* stores the block indices of each of the M<=N eigenvalues. */ indibl = 1; /* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and */ /* stores the starting and finishing indices of each block. */ indisp = indibl + *n; /* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors */ /* that corresponding to eigenvectors that fail to converge in */ /* SSTEIN. This information is discarded; if any fail, the driver */ /* returns INFO > 0. */ indifl = indisp + *n; /* INDIWO is the offset of the remaining integer workspace. */ indiwo = indisp + *n; /* If all eigenvalues are desired, then */ /* call SSTERF or SSTEMR. If this fails for some eigenvalue, then */ /* try SSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && ieeeok == 1) { i__1 = *n - 1; scopy_(&i__1, &e[1], &c__1, &work[1], &c__1); if (! wantz) { scopy_(n, &d__[1], &c__1, &w[1], &c__1); ssterf_(n, &w[1], &work[1], info); } else { scopy_(n, &d__[1], &c__1, &work[*n + 1], &c__1); if (*abstol <= *n * 2.f * eps) { tryrac = TRUE_; } else { tryrac = FALSE_; } i__1 = *lwork - (*n << 1); sstemr_(jobz, "A", n, &work[*n + 1], &work[1], vl, vu, il, iu, m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &work[ (*n << 1) + 1], &i__1, &iwork[1], liwork, info); } if (*info == 0) { *m = *n; goto L10; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } sstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, & nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[1], &iwork[ indiwo], info); if (wantz) { sstein_(n, &d__[1], &e[1], m, &w[1], &iwork[indibl], &iwork[indisp], & z__[z_offset], ldz, &work[1], &iwork[indiwo], &iwork[indifl], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L10: 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]; } /* L20: */ } if (i__ != 0) { w[i__] = w[j]; w[j] = tmp1; sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); } /* L30: */ } } /* Causes problems with tests 19 & 20: */ /* IF (wantz .and. INDEIG ) Z( 1,1) = Z(1,1) / 1.002 + .002 */ work[1] = (real) lwmin; iwork[1] = liwmin; return 0; /* End of SSTEVR */ } /* sstevr_ */