#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 CHBTRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CHBTRD_HB2ST + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, */ /* D, E, HOUS, LHOUS, WORK, LWORK, INFO ) */ /* #if defined(_OPENMP) */ /* use omp_lib */ /* #endif */ /* IMPLICIT NONE */ /* CHARACTER STAGE1, UPLO, VECT */ /* INTEGER N, KD, IB, LDAB, LHOUS, LWORK, INFO */ /* REAL D( * ), E( * ) */ /* COMPLEX AB( LDAB, * ), HOUS( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric */ /* > tridiagonal form T by a unitary similarity transformation: */ /* > Q**H * A * Q = T. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] STAGE1 */ /* > \verbatim */ /* > STAGE1 is CHARACTER*1 */ /* > = 'N': "No": to mention that the stage 1 of the reduction */ /* > from dense to band using the chetrd_he2hb routine */ /* > was not called before this routine to reproduce AB. */ /* > In other term this routine is called as standalone. */ /* > = 'Y': "Yes": to mention that the stage 1 of the */ /* > reduction from dense to band using the chetrd_he2hb */ /* > routine has been called to produce AB (e.g., AB is */ /* > the output of chetrd_he2hb. */ /* > \endverbatim */ /* > */ /* > \param[in] VECT */ /* > \verbatim */ /* > VECT is CHARACTER*1 */ /* > = 'N': No need for the Housholder representation, */ /* > and thus LHOUS is of size f2cmax(1, 4*N); */ /* > = 'V': the Householder representation is needed to */ /* > either generate or to apply Q later on, */ /* > then LHOUS is to be queried and computed. */ /* > (NOT AVAILABLE IN THIS RELEASE). */ /* > \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] KD */ /* > \verbatim */ /* > KD is INTEGER */ /* > The number of superdiagonals of the matrix A if UPLO = 'U', */ /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] AB */ /* > \verbatim */ /* > AB is COMPLEX array, dimension (LDAB,N) */ /* > On entry, the upper or lower triangle of the Hermitian band */ /* > matrix A, stored in the first KD+1 rows of the array. The */ /* > j-th column of A is stored in the j-th column of the array AB */ /* > as follows: */ /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */ /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */ /* > On exit, the diagonal elements of AB are overwritten by the */ /* > diagonal elements of the tridiagonal matrix T; if KD > 0, the */ /* > elements on the first superdiagonal (if UPLO = 'U') or the */ /* > first subdiagonal (if UPLO = 'L') are overwritten by the */ /* > off-diagonal elements of T; the rest of AB is overwritten by */ /* > values generated during the reduction. */ /* > \endverbatim */ /* > */ /* > \param[in] LDAB */ /* > \verbatim */ /* > LDAB is INTEGER */ /* > The leading dimension of the array AB. LDAB >= KD+1. */ /* > \endverbatim */ /* > */ /* > \param[out] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > The diagonal elements of the tridiagonal matrix T. */ /* > \endverbatim */ /* > */ /* > \param[out] E */ /* > \verbatim */ /* > E is REAL array, dimension (N-1) */ /* > The off-diagonal elements of the tridiagonal matrix T: */ /* > E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */ /* > \endverbatim */ /* > */ /* > \param[out] HOUS */ /* > \verbatim */ /* > HOUS is COMPLEX array, dimension LHOUS, that */ /* > store the Householder representation. */ /* > \endverbatim */ /* > */ /* > \param[in] LHOUS */ /* > \verbatim */ /* > LHOUS is INTEGER */ /* > The dimension of the array HOUS. LHOUS = MAX(1, dimension) */ /* > If LWORK = -1, or LHOUS=-1, */ /* > then a query is assumed; the routine */ /* > only calculates the optimal size of the HOUS array, returns */ /* > this value as the first entry of the HOUS array, and no error */ /* > message related to LHOUS is issued by XERBLA. */ /* > LHOUS = MAX(1, dimension) where */ /* > dimension = 4*N if VECT='N' */ /* > not available now if VECT='H' */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK = MAX(1, dimension) */ /* > If LWORK = -1, or LHOUS=-1, */ /* > then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > LWORK = MAX(1, dimension) where */ /* > dimension = (2KD+1)*N + KD*NTHREADS */ /* > where KD is the blocking size of the reduction, */ /* > FACTOPTNB is the blocking used by the QR or LQ */ /* > algorithm, usually FACTOPTNB=128 is a good choice */ /* > NTHREADS is the number of threads used when */ /* > openMP compilation is enabled, otherwise =1. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date November 2017 */ /* > \ingroup complexOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Implemented by Azzam Haidar. */ /* > */ /* > All details are available on technical report, SC11, SC13 papers. */ /* > */ /* > Azzam Haidar, Hatem Ltaief, and Jack Dongarra. */ /* > Parallel reduction to condensed forms for symmetric eigenvalue problems */ /* > using aggregated fine-grained and memory-aware kernels. In Proceedings */ /* > of 2011 International Conference for High Performance Computing, */ /* > Networking, Storage and Analysis (SC '11), New York, NY, USA, */ /* > Article 8 , 11 pages. */ /* > http://doi.acm.org/10.1145/2063384.2063394 */ /* > */ /* > A. Haidar, J. Kurzak, P. Luszczek, 2013. */ /* > An improved parallel singular value algorithm and its implementation */ /* > for multicore hardware, In Proceedings of 2013 International Conference */ /* > for High Performance Computing, Networking, Storage and Analysis (SC '13). */ /* > Denver, Colorado, USA, 2013. */ /* > Article 90, 12 pages. */ /* > http://doi.acm.org/10.1145/2503210.2503292 */ /* > */ /* > A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. */ /* > A novel hybrid CPU-GPU generalized eigensolver for electronic structure */ /* > calculations based on fine-grained memory aware tasks. */ /* > International Journal of High Performance Computing Applications. */ /* > Volume 28 Issue 2, Pages 196-209, May 2014. */ /* > http://hpc.sagepub.com/content/28/2/196 */ /* > */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int chetrd_hb2st_(char *stage1, char *vect, char *uplo, integer *n, integer *kd, complex *ab, integer *ldab, real *d__, real * e, complex *hous, integer *lhous, complex *work, integer *lwork, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5; real r__1; complex q__1; /* Local variables */ integer inda; extern integer ilaenv2stage_(integer *, char *, char *, integer *, integer *, integer *, integer *); integer thed, indv, myid, indw, apos, dpos, abofdpos, nthreads, i__, k, m, edind, debug; extern logical lsame_(char *, char *); integer lhmin, sicev, sizea, shift, stind, colpt, lwmin, awpos; logical wantq, upper; integer grsiz, ttype, stepercol, ed, ib; extern /* Subroutine */ int chb2st_kernels_(char *, logical *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *); integer st, abdpos; extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen); integer thgrid, thgrnb, indtau; real abstmp; integer ofdpos, blklastind; extern /* Subroutine */ int mecago_(); logical lquery, afters1; integer lda, tid, ldv; complex tmp; integer stt, sweepid, nbtiles, sizetau, thgrsiz; /* -- LAPACK computational routine (version 3.8.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2017 */ /* ===================================================================== */ /* Determine the minimal workspace size required. */ /* Test the input parameters */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --d__; --e; --hous; --work; /* Function Body */ debug = 0; *info = 0; afters1 = lsame_(stage1, "Y"); wantq = lsame_(vect, "V"); upper = lsame_(uplo, "U"); lquery = *lwork == -1 || *lhous == -1; /* Determine the block size, the workspace size and the hous size. */ ib = ilaenv2stage_(&c__2, "CHETRD_HB2ST", vect, n, kd, &c_n1, &c_n1); lhmin = ilaenv2stage_(&c__3, "CHETRD_HB2ST", vect, n, kd, &ib, &c_n1); lwmin = ilaenv2stage_(&c__4, "CHETRD_HB2ST", vect, n, kd, &ib, &c_n1); if (! afters1 && ! lsame_(stage1, "N")) { *info = -1; } else if (! lsame_(vect, "N")) { *info = -2; } else if (! upper && ! lsame_(uplo, "L")) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*kd < 0) { *info = -5; } else if (*ldab < *kd + 1) { *info = -7; } else if (*lhous < lhmin && ! lquery) { *info = -11; } else if (*lwork < lwmin && ! lquery) { *info = -13; } if (*info == 0) { hous[1].r = (real) lhmin, hous[1].i = 0.f; work[1].r = (real) lwmin, work[1].i = 0.f; } if (*info != 0) { i__1 = -(*info); xerbla_("CHETRD_HB2ST", &i__1, (ftnlen)12); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { hous[1].r = 1.f, hous[1].i = 0.f; work[1].r = 1.f, work[1].i = 0.f; return 0; } /* Determine pointer position */ ldv = *kd + ib; sizetau = *n << 1; sicev = *n << 1; indtau = 1; indv = indtau + sizetau; lda = (*kd << 1) + 1; sizea = lda * *n; inda = 1; indw = inda + sizea; nthreads = 1; tid = 0; if (upper) { apos = inda + *kd; awpos = inda; dpos = apos + *kd; ofdpos = dpos - 1; abdpos = *kd + 1; abofdpos = *kd; } else { apos = inda; awpos = inda + *kd + 1; dpos = apos; ofdpos = dpos + 1; abdpos = 1; abofdpos = 2; } /* Case KD=0: */ /* The matrix is diagonal. We just copy it (convert to "real" for */ /* complex because D is double and the imaginary part should be 0) */ /* and store it in D. A sequential code here is better or */ /* in a parallel environment it might need two cores for D and E */ if (*kd == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = abdpos + i__ * ab_dim1; d__[i__] = ab[i__2].r; /* L30: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { e[i__] = 0.f; /* L40: */ } hous[1].r = 1.f, hous[1].i = 0.f; work[1].r = 1.f, work[1].i = 0.f; return 0; } /* Case KD=1: */ /* The matrix is already Tridiagonal. We have to make diagonal */ /* and offdiagonal elements real, and store them in D and E. */ /* For that, for real precision just copy the diag and offdiag */ /* to D and E while for the COMPLEX case the bulge chasing is */ /* performed to convert the hermetian tridiagonal to symmetric */ /* tridiagonal. A simpler coversion formula might be used, but then */ /* updating the Q matrix will be required and based if Q is generated */ /* or not this might complicate the story. */ if (*kd == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = abdpos + i__ * ab_dim1; d__[i__] = ab[i__2].r; /* L50: */ } /* make off-diagonal elements real and copy them to E */ if (upper) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = abofdpos + (i__ + 1) * ab_dim1; tmp.r = ab[i__2].r, tmp.i = ab[i__2].i; abstmp = c_abs(&tmp); i__2 = abofdpos + (i__ + 1) * ab_dim1; ab[i__2].r = abstmp, ab[i__2].i = 0.f; e[i__] = abstmp; if (abstmp != 0.f) { q__1.r = tmp.r / abstmp, q__1.i = tmp.i / abstmp; tmp.r = q__1.r, tmp.i = q__1.i; } else { tmp.r = 1.f, tmp.i = 0.f; } if (i__ < *n - 1) { i__2 = abofdpos + (i__ + 2) * ab_dim1; i__3 = abofdpos + (i__ + 2) * ab_dim1; q__1.r = ab[i__3].r * tmp.r - ab[i__3].i * tmp.i, q__1.i = ab[i__3].r * tmp.i + ab[i__3].i * tmp.r; ab[i__2].r = q__1.r, ab[i__2].i = q__1.i; } /* IF( WANTZ ) THEN */ /* CALL CSCAL( N, CONJG( TMP ), Q( 1, I+1 ), 1 ) */ /* END IF */ /* L60: */ } } else { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = abofdpos + i__ * ab_dim1; tmp.r = ab[i__2].r, tmp.i = ab[i__2].i; abstmp = c_abs(&tmp); i__2 = abofdpos + i__ * ab_dim1; ab[i__2].r = abstmp, ab[i__2].i = 0.f; e[i__] = abstmp; if (abstmp != 0.f) { q__1.r = tmp.r / abstmp, q__1.i = tmp.i / abstmp; tmp.r = q__1.r, tmp.i = q__1.i; } else { tmp.r = 1.f, tmp.i = 0.f; } if (i__ < *n - 1) { i__2 = abofdpos + (i__ + 1) * ab_dim1; i__3 = abofdpos + (i__ + 1) * ab_dim1; q__1.r = ab[i__3].r * tmp.r - ab[i__3].i * tmp.i, q__1.i = ab[i__3].r * tmp.i + ab[i__3].i * tmp.r; ab[i__2].r = q__1.r, ab[i__2].i = q__1.i; } /* IF( WANTQ ) THEN */ /* CALL CSCAL( N, TMP, Q( 1, I+1 ), 1 ) */ /* END IF */ /* L70: */ } } hous[1].r = 1.f, hous[1].i = 0.f; work[1].r = 1.f, work[1].i = 0.f; return 0; } /* Main code start here. */ /* Reduce the hermitian band of A to a tridiagonal matrix. */ thgrsiz = *n; grsiz = 1; shift = 3; r__1 = (real) (*n) / (real) (*kd) + .5f; nbtiles = r_int(&r__1); r__1 = (real) shift / (real) grsiz + .5f; stepercol = r_int(&r__1); r__1 = (real) (*n - 1) / (real) thgrsiz + .5f; thgrnb = r_int(&r__1); i__1 = *kd + 1; clacpy_("A", &i__1, n, &ab[ab_offset], ldab, &work[apos], &lda) ; claset_("A", kd, n, &c_b1, &c_b1, &work[awpos], &lda); /* openMP parallelisation start here */ /* main bulge chasing loop */ i__1 = thgrnb; for (thgrid = 1; thgrid <= i__1; ++thgrid) { stt = (thgrid - 1) * thgrsiz + 1; /* Computing MIN */ i__2 = stt + thgrsiz - 1, i__3 = *n - 1; thed = f2cmin(i__2,i__3); i__2 = *n - 1; for (i__ = stt; i__ <= i__2; ++i__) { ed = f2cmin(i__,thed); if (stt > ed) { myexit_(); } i__3 = stepercol; for (m = 1; m <= i__3; ++m) { st = stt; i__4 = ed; for (sweepid = st; sweepid <= i__4; ++sweepid) { i__5 = grsiz; for (k = 1; k <= i__5; ++k) { myid = (i__ - sweepid) * (stepercol * grsiz) + (m - 1) * grsiz + k; if (myid == 1) { ttype = 1; } else { ttype = myid % 2 + 2; } if (ttype == 2) { colpt = myid / 2 * *kd + sweepid; stind = colpt - *kd + 1; edind = f2cmin(colpt,*n); blklastind = colpt; } else { colpt = (myid + 1) / 2 * *kd + sweepid; stind = colpt - *kd + 1; edind = f2cmin(colpt,*n); if (stind >= edind - 1 && edind == *n) { blklastind = *n; } else { blklastind = 0; } } /* Call the kernel */ chb2st_kernels_(uplo, &wantq, &ttype, &stind, &edind, &sweepid, n, kd, &ib, &work[inda], &lda, & hous[indv], &hous[indtau], &ldv, &work[indw + tid * *kd]); if (blklastind >= *n - 1) { ++stt; myexit_(); } /* L140: */ } /* L130: */ } /* L120: */ } /* L110: */ } /* L100: */ } /* Copy the diagonal from A to D. Note that D is REAL thus only */ /* the Real part is needed, the imaginary part should be zero. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = dpos + (i__ - 1) * lda; d__[i__] = work[i__2].r; /* L150: */ } /* Copy the off diagonal from A to E. Note that E is REAL thus only */ /* the Real part is needed, the imaginary part should be zero. */ if (upper) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ofdpos + i__ * lda; e[i__] = work[i__2].r; /* L160: */ } } else { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ofdpos + (i__ - 1) * lda; e[i__] = work[i__2].r; /* L170: */ } } hous[1].r = (real) lhmin, hous[1].i = 0.f; work[1].r = (real) lwmin, work[1].i = 0.f; return 0; /* End of CHETRD_HB2ST */ } /* chetrd_hb2st__ */