#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]/Cd(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 ZHEEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat rices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZHEEVR + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, */ /* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, */ /* RWORK, LRWORK, IWORK, LIWORK, INFO ) */ /* CHARACTER JOBZ, RANGE, UPLO */ /* INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK, */ /* $ M, N */ /* DOUBLE PRECISION ABSTOL, VL, VU */ /* INTEGER ISUPPZ( * ), IWORK( * ) */ /* DOUBLE PRECISION RWORK( * ), W( * ) */ /* COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZHEEVR computes selected eigenvalues and, optionally, eigenvectors */ /* > of a complex Hermitian matrix A. Eigenvalues and eigenvectors can */ /* > be selected by specifying either a range of values or a range of */ /* > indices for the desired eigenvalues. */ /* > */ /* > ZHEEVR first reduces the matrix A to tridiagonal form T with a call */ /* > to ZHETRD. Then, whenever possible, ZHEEVR calls ZSTEMR to compute */ /* > eigenspectrum using Relatively Robust Representations. ZSTEMR */ /* > 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 each unreduced block (submatrix) of T, */ /* > (a) Compute T - sigma I = L D L^T, so that L and D */ /* > define all the wanted eigenvalues to high relative accuracy. */ /* > This means that small relative changes in the entries of D and L */ /* > cause only small relative changes in the eigenvalues and */ /* > eigenvectors. The standard (unfactored) representation of the */ /* > tridiagonal matrix T does not have this property in general. */ /* > (b) Compute the eigenvalues to suitable accuracy. */ /* > If the eigenvectors are desired, the algorithm attains full */ /* > accuracy of the computed eigenvalues only right before */ /* > the corresponding vectors have to be computed, see steps c) and d). */ /* > (c) For each cluster of close eigenvalues, select a new */ /* > shift close to the cluster, find a new factorization, and refine */ /* > the shifted eigenvalues to suitable accuracy. */ /* > (d) For each eigenvalue with a large enough relative separation compute */ /* > the corresponding eigenvector by forming a rank revealing twisted */ /* > factorization. Go back to (c) for any clusters that remain. */ /* > */ /* > The desired accuracy of the output can be specified by the input */ /* > parameter ABSTOL. */ /* > */ /* > For more details, see DSTEMR's documentation and: */ /* > - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations */ /* > to compute orthogonal eigenvectors of symmetric tridiagonal matrices," */ /* > Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. */ /* > - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and */ /* > Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, */ /* > 2004. Also LAPACK Working Note 154. */ /* > - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric */ /* > tridiagonal eigenvalue/eigenvector problem", */ /* > Computer Science Division Technical Report No. UCB/CSD-97-971, */ /* > UC Berkeley, May 1997. */ /* > */ /* > */ /* > Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested */ /* > on machines which conform to the ieee-754 floating point standard. */ /* > ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and */ /* > when partial spectrum requests are made. */ /* > */ /* > Normal execution of ZSTEMR 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, DSTEBZ and */ /* > ZSTEIN are called */ /* > \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] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA, N) */ /* > On entry, the Hermitian matrix A. If UPLO = 'U', the */ /* > leading N-by-N upper triangular part of A contains the */ /* > upper triangular part of the matrix A. If UPLO = 'L', */ /* > the leading N-by-N lower triangular part of A contains */ /* > the lower triangular part of the matrix A. */ /* > On exit, the lower triangle (if UPLO='L') or the upper */ /* > triangle (if UPLO='U') of A, including the diagonal, is */ /* > destroyed. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] VL */ /* > \verbatim */ /* > VL is DOUBLE PRECISION */ /* > 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 DOUBLE PRECISION */ /* > 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 DOUBLE PRECISION */ /* > 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 */ /* > DLAMCH( '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 DOUBLE PRECISION array, dimension (N) */ /* > The first M elements contain the selected eigenvalues in */ /* > ascending order. */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is COMPLEX*16 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 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] 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 ). This is an output of ZSTEMR (tridiagonal */ /* > matrix). The support of the eigenvectors of A is typically */ /* > 1:N because of the unitary transformations applied by ZUNMTR. */ /* > Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The length of the array WORK. LWORK >= f2cmax(1,2*N). */ /* > For optimal efficiency, LWORK >= (NB+1)*N, */ /* > where NB is the f2cmax of the blocksize for ZHETRD and for */ /* > ZUNMTR as returned by ILAENV. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal sizes of the WORK, RWORK and */ /* > IWORK arrays, returns these values as the first entries of */ /* > the WORK, RWORK and IWORK arrays, and no error message */ /* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */ /* > On exit, if INFO = 0, RWORK(1) returns the optimal */ /* > (and minimal) LRWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LRWORK */ /* > \verbatim */ /* > LRWORK is INTEGER */ /* > The length of the array RWORK. LRWORK >= f2cmax(1,24*N). */ /* > */ /* > If LRWORK = -1, then a workspace query is assumed; the */ /* > routine only calculates the optimal sizes of the WORK, RWORK */ /* > and IWORK arrays, returns these values as the first entries */ /* > of the WORK, RWORK and IWORK arrays, and no error message */ /* > related to LWORK or LRWORK 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 >= f2cmax(1,10*N). */ /* > */ /* > If LIWORK = -1, then a workspace query is assumed; the */ /* > routine only calculates the optimal sizes of the WORK, RWORK */ /* > and IWORK arrays, returns these values as the first entries */ /* > of the WORK, RWORK and IWORK arrays, and no error message */ /* > related to LWORK or LRWORK 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 complex16HEeigen */ /* > \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 zheevr_(char *jobz, char *range, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * w, doublecomplex *z__, integer *ldz, integer *isuppz, doublecomplex * work, integer *lwork, doublereal *rwork, integer *lrwork, integer * iwork, integer *liwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; /* Local variables */ doublereal anrm; integer imax; doublereal rmin, rmax; logical test; integer itmp1, i__, j; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); integer indrd, indre; doublereal sigma; extern logical lsame_(char *, char *); integer iinfo; char order[1]; integer indwk; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer lwmin; logical lower, wantz; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer nb, jj; extern doublereal dlamch_(char *); logical alleig, indeig; integer iscale, ieeeok, indibl, indrdd, indifl, indree; logical valeig; doublereal safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zdscal_( integer *, doublereal *, doublecomplex *, integer *); doublereal abstll, bignum; integer indtau, indisp; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *); integer indiwo, indwkn; extern /* Subroutine */ int dstebz_(char *, char *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); integer indrwk, liwmin; extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, integer *, integer *); logical tryrac; integer lrwmin, llwrkn, llwork, nsplit; doublereal smlnum; extern /* Subroutine */ int zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *); logical lquery; integer lwkopt; extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zstemr_(char *, char *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, doublereal *, doublecomplex *, integer *, integer *, integer *, logical *, doublereal *, integer *, integer *, integer *, integer *), zunmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ); doublereal eps, vll, vuu; integer llrwork; doublereal 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 */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --isuppz; --work; --rwork; --iwork; /* Function Body */ ieeeok = ilaenv_(&c__10, "ZHEEVR", "N", &c__1, &c__2, &c__3, &c__4, ( ftnlen)6, (ftnlen)1); lower = lsame_(uplo, "L"); wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; /* Computing MAX */ i__1 = 1, i__2 = *n * 24; lrwmin = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *n * 10; liwmin = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *n << 1; lwmin = f2cmax(i__1,i__2); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (lower || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*lda < f2cmax(1,*n)) { *info = -6; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -8; } } else if (indeig) { if (*il < 1 || *il > f2cmax(1,*n)) { *info = -9; } else if (*iu < f2cmin(*n,*il) || *iu > *n) { *info = -10; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -15; } } if (*info == 0) { nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = nb, i__2 = ilaenv_(&c__1, "ZUNMTR", uplo, n, &c_n1, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); nb = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = (nb + 1) * *n; lwkopt = f2cmax(i__1,lwmin); work[1].r = (doublereal) lwkopt, work[1].i = 0.; rwork[1] = (doublereal) lrwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -18; } else if (*lrwork < lrwmin && ! lquery) { *info = -20; } else if (*liwork < liwmin && ! lquery) { *info = -22; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZHEEVR", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { work[1].r = 1., work[1].i = 0.; return 0; } if (*n == 1) { work[1].r = 2., work[1].i = 0.; if (alleig || indeig) { *m = 1; i__1 = a_dim1 + 1; w[1] = a[i__1].r; } else { i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; if (*vl < a[i__1].r && *vu >= a[i__2].r) { *m = 1; i__1 = a_dim1 + 1; w[1] = a[i__1].r; } } if (wantz) { i__1 = z_dim1 + 1; z__[i__1].r = 1., z__[i__1].i = 0.; isuppz[1] = 1; isuppz[2] = 1; } return 0; } /* Get machine constants. */ safmin = dlamch_("Safe minimum"); eps = dlamch_("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin)); rmax = f2cmin(d__1,d__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = zlansy_("M", uplo, n, &a[a_offset], lda, &rwork[1]); if (anrm > 0. && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { if (lower) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j + 1; zdscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1); /* L10: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { zdscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1); /* L20: */ } } if (*abstol > 0.) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Initialize indices into workspaces. Note: The IWORK indices are */ /* used only if DSTERF or ZSTEMR fail. */ /* WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the */ /* elementary reflectors used in ZHETRD. */ indtau = 1; /* INDWK is the starting offset of the remaining complex workspace, */ /* and LLWORK is the remaining complex workspace size. */ indwk = indtau + *n; llwork = *lwork - indwk + 1; /* RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal */ /* entries. */ indrd = 1; /* RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the */ /* tridiagonal matrix from ZHETRD. */ indre = indrd + *n; /* RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over */ /* -written by ZSTEMR (the DSTERF path copies the diagonal to W). */ indrdd = indre + *n; /* RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over */ /* -written while computing the eigenvalues in DSTERF and ZSTEMR. */ indree = indrdd + *n; /* INDRWK is the starting offset of the left-over real workspace, and */ /* LLRWORK is the remaining workspace size. */ indrwk = indree + *n; llrwork = *lrwork - indrwk + 1; /* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and */ /* stores the block indices of each of the M<=N eigenvalues. */ indibl = 1; /* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ 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 */ /* DSTEIN. 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 = indifl + *n; /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ zhetrd_(uplo, n, &a[a_offset], lda, &rwork[indrd], &rwork[indre], &work[ indtau], &work[indwk], &llwork, &iinfo); /* If all eigenvalues are desired */ /* then call DSTERF or ZSTEMR and ZUNMTR. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && ieeeok == 1) { if (! wantz) { dcopy_(n, &rwork[indrd], &c__1, &w[1], &c__1); i__1 = *n - 1; dcopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1); dsterf_(n, &w[1], &rwork[indree], info); } else { i__1 = *n - 1; dcopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1); dcopy_(n, &rwork[indrd], &c__1, &rwork[indrdd], &c__1); if (*abstol <= *n * 2. * eps) { tryrac = TRUE_; } else { tryrac = FALSE_; } zstemr_(jobz, "A", n, &rwork[indrdd], &rwork[indree], vl, vu, il, iu, m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &rwork[indrwk], &llrwork, &iwork[1], liwork, info); /* Apply unitary matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by ZSTEMR. */ if (wantz && *info == 0) { indwkn = indwk; llwrkn = *lwork - indwkn + 1; zunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau] , &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo); } } if (*info == 0) { *m = *n; goto L30; } *info = 0; } /* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */ /* Also call DSTEBZ and ZSTEIN if ZSTEMR fails. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indrd], & rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], & rwork[indrwk], &iwork[indiwo], info); if (wantz) { zstein_(n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], & iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[ indiwo], &iwork[indifl], info); /* Apply unitary matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by ZSTEIN. */ indwkn = indwk; llwrkn = *lwork - indwkn + 1; zunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[ z_offset], ldz, &work[indwkn], &llwrkn, &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L30: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__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]; } /* L40: */ } 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; zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); } /* L50: */ } } /* Set WORK(1) to optimal workspace size. */ work[1].r = (doublereal) lwkopt, work[1].i = 0.; rwork[1] = (doublereal) lrwmin; iwork[1] = liwmin; return 0; /* End of ZHEEVR */ } /* zheevr_ */