#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 CHETRD_HE2HB */ /* @generated from zhetrd_he2hb.f, fortran z -> c, Wed Dec 7 08:22:40 2016 */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CHETRD_HE2HB + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CHETRD_HE2HB( UPLO, N, KD, A, LDA, AB, LDAB, TAU, */ /* WORK, LWORK, INFO ) */ /* IMPLICIT NONE */ /* CHARACTER UPLO */ /* INTEGER INFO, LDA, LDAB, LWORK, N, KD */ /* COMPLEX A( LDA, * ), AB( LDAB, * ), */ /* TAU( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CHETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian */ /* > band-diagonal form AB by a unitary similarity transformation: */ /* > Q**H * A * Q = AB. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \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 reduced matrix if UPLO = 'U', */ /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */ /* > The reduced matrix is stored in the array AB. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX 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, and the strictly lower */ /* > triangular part of A is not referenced. If UPLO = 'L', the */ /* > leading N-by-N lower triangular part of A contains the lower */ /* > triangular part of the matrix A, and the strictly upper */ /* > triangular part of A is not referenced. */ /* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ /* > of A are overwritten by the corresponding elements of the */ /* > tridiagonal matrix T, and the elements above the first */ /* > superdiagonal, with the array TAU, represent the unitary */ /* > matrix Q as a product of elementary reflectors; if UPLO */ /* > = 'L', the diagonal and first subdiagonal of A are over- */ /* > written by the corresponding elements of the tridiagonal */ /* > matrix T, and the elements below the first subdiagonal, with */ /* > the array TAU, represent the unitary matrix Q as a product */ /* > of elementary reflectors. See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] AB */ /* > \verbatim */ /* > AB is COMPLEX array, dimension (LDAB,N) */ /* > On exit, 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). */ /* > \endverbatim */ /* > */ /* > \param[in] LDAB */ /* > \verbatim */ /* > LDAB is INTEGER */ /* > The leading dimension of the array AB. LDAB >= KD+1. */ /* > \endverbatim */ /* > */ /* > \param[out] TAU */ /* > \verbatim */ /* > TAU is COMPLEX array, dimension (N-KD) */ /* > The scalar factors of the elementary reflectors (see Further */ /* > Details). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (LWORK) */ /* > On exit, if INFO = 0, or if LWORK=-1, */ /* > WORK(1) returns the size of LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK which should be calculated */ /* > by a workspace query. LWORK = MAX(1, LWORK_QUERY) */ /* > If LWORK = -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_QUERY = N*KD + N*f2cmax(KD,FACTOPTNB) + 2*KD*KD */ /* > where FACTOPTNB is the blocking used by the QR or LQ */ /* > algorithm, usually FACTOPTNB=128 is a good choice otherwise */ /* > putting LWORK=-1 will provide the size of WORK. */ /* > \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 complexHEcomputational */ /* > \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 */ /* > */ /* > \verbatim */ /* > */ /* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ /* > reflectors */ /* > */ /* > Q = H(k)**H . . . H(2)**H H(1)**H, where k = n-kd. */ /* > */ /* > Each H(i) has the form */ /* > */ /* > H(i) = I - tau * v * v**H */ /* > */ /* > where tau is a complex scalar, and v is a complex vector with */ /* > v(1:i+kd-1) = 0 and v(i+kd) = 1; conjg(v(i+kd+1:n)) is stored on exit in */ /* > A(i,i+kd+1:n), and tau in TAU(i). */ /* > */ /* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ /* > reflectors */ /* > */ /* > Q = H(1) H(2) . . . H(k), where k = n-kd. */ /* > */ /* > Each H(i) has the form */ /* > */ /* > H(i) = I - tau * v * v**H */ /* > */ /* > where tau is a complex scalar, and v is a complex vector with */ /* > v(kd+1:i) = 0 and v(i+kd+1) = 1; v(i+kd+2:n) is stored on exit in */ /* > A(i+kd+2:n,i), and tau in TAU(i). */ /* > */ /* > The contents of A on exit are illustrated by the following examples */ /* > with n = 5: */ /* > */ /* > if UPLO = 'U': if UPLO = 'L': */ /* > */ /* > ( ab ab/v1 v1 v1 v1 ) ( ab ) */ /* > ( ab ab/v2 v2 v2 ) ( ab/v1 ab ) */ /* > ( ab ab/v3 v3 ) ( v1 ab/v2 ab ) */ /* > ( ab ab/v4 ) ( v1 v2 ab/v3 ab ) */ /* > ( ab ) ( v1 v2 v3 ab/v4 ab ) */ /* > */ /* > where d and e denote diagonal and off-diagonal elements of T, and vi */ /* > denotes an element of the vector defining H(i). */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int chetrd_he2hb_(char *uplo, integer *n, integer *kd, complex *a, integer *lda, complex *ab, integer *ldab, complex *tau, complex *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5; complex q__1; /* Local variables */ extern integer ilaenv2stage_(integer *, char *, char *, integer *, integer *, integer *, integer *); integer tpos, wpos, s1pos, s2pos, i__, j; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), chemm_(char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); integer lwmin; logical upper; extern /* Subroutine */ int cher2k_(char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, real *, complex *, integer *); integer lk, pk, pn, lt; extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *); integer lw; extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), clarft_( char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen); integer ls1; logical lquery; integer ls2, ldt, ldw, lds1, lds2; /* -- 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 */ /* and test the input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --tau; --work; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); lquery = *lwork == -1; lwmin = ilaenv2stage_(&c__4, "CHETRD_HE2HB", "", n, kd, &c_n1, &c_n1); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kd < 0) { *info = -3; } else if (*lda < f2cmax(1,*n)) { *info = -5; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = *kd + 1; if (*ldab < f2cmax(i__1,i__2)) { *info = -7; } else if (*lwork < lwmin && ! lquery) { *info = -10; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHETRD_HE2HB", &i__1, (ftnlen)12); return 0; } else if (lquery) { work[1].r = (real) lwmin, work[1].i = 0.f; return 0; } /* Quick return if possible */ /* Copy the upper/lower portion of A into AB */ if (*n <= *kd + 1) { if (upper) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MIN */ i__2 = *kd + 1; lk = f2cmin(i__2,i__); ccopy_(&lk, &a[i__ - lk + 1 + i__ * a_dim1], &c__1, &ab[*kd + 1 - lk + 1 + i__ * ab_dim1], &c__1); /* L100: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MIN */ i__2 = *kd + 1, i__3 = *n - i__ + 1; lk = f2cmin(i__2,i__3); ccopy_(&lk, &a[i__ + i__ * a_dim1], &c__1, &ab[i__ * ab_dim1 + 1], &c__1); /* L110: */ } } work[1].r = 1.f, work[1].i = 0.f; return 0; } /* Determine the pointer position for the workspace */ ldt = *kd; lds1 = *kd; lt = ldt * *kd; lw = *n * *kd; ls1 = lds1 * *kd; ls2 = lwmin - lt - lw - ls1; /* LS2 = N*MAX(KD,FACTOPTNB) */ tpos = 1; wpos = tpos + lt; s1pos = wpos + lw; s2pos = s1pos + ls1; if (upper) { ldw = *kd; lds2 = *kd; } else { ldw = *n; lds2 = *n; } /* Set the workspace of the triangular matrix T to zero once such a */ /* way every time T is generated the upper/lower portion will be always zero */ claset_("A", &ldt, kd, &c_b1, &c_b1, &work[tpos], &ldt); if (upper) { i__1 = *n - *kd; i__2 = *kd; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { pn = *n - i__ - *kd + 1; /* Computing MIN */ i__3 = *n - i__ - *kd + 1; pk = f2cmin(i__3,*kd); /* Compute the LQ factorization of the current block */ cgelqf_(kd, &pn, &a[i__ + (i__ + *kd) * a_dim1], lda, &tau[i__], & work[s2pos], &ls2, &iinfo); /* Copy the upper portion of A into AB */ i__3 = i__ + pk - 1; for (j = i__; j <= i__3; ++j) { /* Computing MIN */ i__4 = *kd, i__5 = *n - j; lk = f2cmin(i__4,i__5) + 1; i__4 = *ldab - 1; ccopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * ab_dim1], &i__4); /* L20: */ } claset_("Lower", &pk, &pk, &c_b1, &c_b2, &a[i__ + (i__ + *kd) * a_dim1], lda); /* Form the matrix T */ clarft_("Forward", "Rowwise", &pn, &pk, &a[i__ + (i__ + *kd) * a_dim1], lda, &tau[i__], &work[tpos], &ldt); /* Compute W: */ cgemm_("Conjugate", "No transpose", &pk, &pn, &pk, &c_b2, &work[ tpos], &ldt, &a[i__ + (i__ + *kd) * a_dim1], lda, &c_b1, & work[s2pos], &lds2); chemm_("Right", uplo, &pk, &pn, &c_b2, &a[i__ + *kd + (i__ + *kd) * a_dim1], lda, &work[s2pos], &lds2, &c_b1, &work[wpos], & ldw); cgemm_("No transpose", "Conjugate", &pk, &pk, &pn, &c_b2, &work[ wpos], &ldw, &work[s2pos], &lds2, &c_b1, &work[s1pos], & lds1); q__1.r = -.5f, q__1.i = 0.f; cgemm_("No transpose", "No transpose", &pk, &pn, &pk, &q__1, & work[s1pos], &lds1, &a[i__ + (i__ + *kd) * a_dim1], lda, & c_b2, &work[wpos], &ldw); /* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */ /* an update of the form: A := A - V'*W - W'*V */ q__1.r = -1.f, q__1.i = 0.f; cher2k_(uplo, "Conjugate", &pn, &pk, &q__1, &a[i__ + (i__ + *kd) * a_dim1], lda, &work[wpos], &ldw, &c_b33, &a[i__ + *kd + ( i__ + *kd) * a_dim1], lda); /* L10: */ } /* Copy the upper band to AB which is the band storage matrix */ i__2 = *n; for (j = *n - *kd + 1; j <= i__2; ++j) { /* Computing MIN */ i__1 = *kd, i__3 = *n - j; lk = f2cmin(i__1,i__3) + 1; i__1 = *ldab - 1; ccopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * ab_dim1], & i__1); /* L30: */ } } else { /* Reduce the lower triangle of A to lower band matrix */ i__2 = *n - *kd; i__1 = *kd; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { pn = *n - i__ - *kd + 1; /* Computing MIN */ i__3 = *n - i__ - *kd + 1; pk = f2cmin(i__3,*kd); /* Compute the QR factorization of the current block */ cgeqrf_(&pn, kd, &a[i__ + *kd + i__ * a_dim1], lda, &tau[i__], & work[s2pos], &ls2, &iinfo); /* Copy the upper portion of A into AB */ i__3 = i__ + pk - 1; for (j = i__; j <= i__3; ++j) { /* Computing MIN */ i__4 = *kd, i__5 = *n - j; lk = f2cmin(i__4,i__5) + 1; ccopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], & c__1); /* L50: */ } claset_("Upper", &pk, &pk, &c_b1, &c_b2, &a[i__ + *kd + i__ * a_dim1], lda); /* Form the matrix T */ clarft_("Forward", "Columnwise", &pn, &pk, &a[i__ + *kd + i__ * a_dim1], lda, &tau[i__], &work[tpos], &ldt); /* Compute W: */ cgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b2, &a[ i__ + *kd + i__ * a_dim1], lda, &work[tpos], &ldt, &c_b1, &work[s2pos], &lds2); chemm_("Left", uplo, &pn, &pk, &c_b2, &a[i__ + *kd + (i__ + *kd) * a_dim1], lda, &work[s2pos], &lds2, &c_b1, &work[wpos], & ldw); cgemm_("Conjugate", "No transpose", &pk, &pk, &pn, &c_b2, &work[ s2pos], &lds2, &work[wpos], &ldw, &c_b1, &work[s1pos], & lds1); q__1.r = -.5f, q__1.i = 0.f; cgemm_("No transpose", "No transpose", &pn, &pk, &pk, &q__1, &a[ i__ + *kd + i__ * a_dim1], lda, &work[s1pos], &lds1, & c_b2, &work[wpos], &ldw); /* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */ /* an update of the form: A := A - V*W' - W*V' */ q__1.r = -1.f, q__1.i = 0.f; cher2k_(uplo, "No transpose", &pn, &pk, &q__1, &a[i__ + *kd + i__ * a_dim1], lda, &work[wpos], &ldw, &c_b33, &a[i__ + *kd + (i__ + *kd) * a_dim1], lda); /* ================================================================== */ /* RESTORE A FOR COMPARISON AND CHECKING TO BE REMOVED */ /* DO 45 J = I, I+PK-1 */ /* LK = MIN( KD, N-J ) + 1 */ /* CALL CCOPY( LK, AB( 1, J ), 1, A( J, J ), 1 ) */ /* 45 CONTINUE */ /* ================================================================== */ /* L40: */ } /* Copy the lower band to AB which is the band storage matrix */ i__1 = *n; for (j = *n - *kd + 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = *kd, i__3 = *n - j; lk = f2cmin(i__2,i__3) + 1; ccopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], & c__1); /* L60: */ } } work[1].r = (real) lwmin, work[1].i = 0.f; return 0; /* End of CHETRD_HE2HB */ } /* chetrd_he2hb__ */