#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 ZHBTRD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZHBTRD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, */ /* WORK, INFO ) */ /* CHARACTER UPLO, VECT */ /* INTEGER INFO, KD, LDAB, LDQ, N */ /* DOUBLE PRECISION D( * ), E( * ) */ /* COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZHBTRD 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] VECT */ /* > \verbatim */ /* > VECT is CHARACTER*1 */ /* > = 'N': do not form Q; */ /* > = 'V': form Q; */ /* > = 'U': update a matrix X, by forming X*Q. */ /* > \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*16 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 DOUBLE PRECISION array, dimension (N) */ /* > The diagonal elements of the tridiagonal matrix T. */ /* > \endverbatim */ /* > */ /* > \param[out] E */ /* > \verbatim */ /* > E is DOUBLE PRECISION 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[in,out] Q */ /* > \verbatim */ /* > Q is COMPLEX*16 array, dimension (LDQ,N) */ /* > On entry, if VECT = 'U', then Q must contain an N-by-N */ /* > matrix X; if VECT = 'N' or 'V', then Q need not be set. */ /* > */ /* > On exit: */ /* > if VECT = 'V', Q contains the N-by-N unitary matrix Q; */ /* > if VECT = 'U', Q contains the product X*Q; */ /* > if VECT = 'N', the array Q is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. */ /* > LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 array, dimension (N) */ /* > \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 December 2016 */ /* > \ingroup complex16OTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Modified by Linda Kaufman, Bell Labs. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int zhbtrd_(char *vect, char *uplo, integer *n, integer *kd, doublecomplex *ab, integer *ldab, doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *work, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1; doublecomplex z__1; /* Local variables */ integer inca, jend, lend, jinc; doublereal abst; integer incx, last; doublecomplex temp; extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *); integer j1end, j1inc, i__, j, k, l; doublecomplex t; integer iqend; extern logical lsame_(char *, char *); extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); logical initq, wantq, upper; integer i2, j1, j2; extern /* Subroutine */ int zlar2v_(integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *); integer nq, nr, iqaend; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zlacgv_( integer *, doublecomplex *, integer *); integer kd1; extern /* Subroutine */ int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *), zlargv_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *), zlartv_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *); integer ibl, iqb, kdn, jin, nrt, kdm1; /* -- LAPACK computational 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..-- */ /* December 2016 */ /* ===================================================================== */ /* Test the input parameters */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --d__; --e; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; --work; /* Function Body */ initq = lsame_(vect, "V"); wantq = initq || lsame_(vect, "U"); upper = lsame_(uplo, "U"); kd1 = *kd + 1; kdm1 = *kd - 1; incx = *ldab - 1; iqend = 1; *info = 0; if (! wantq && ! lsame_(vect, "N")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*kd < 0) { *info = -4; } else if (*ldab < kd1) { *info = -6; } else if (*ldq < f2cmax(1,*n) && wantq) { *info = -10; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHBTRD", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Initialize Q to the unit matrix, if needed */ if (initq) { zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq); } /* Wherever possible, plane rotations are generated and applied in */ /* vector operations of length NR over the index set J1:J2:KD1. */ /* The real cosines and complex sines of the plane rotations are */ /* stored in the arrays D and WORK. */ inca = kd1 * *ldab; /* Computing MIN */ i__1 = *n - 1; kdn = f2cmin(i__1,*kd); if (upper) { if (*kd > 1) { /* Reduce to complex Hermitian tridiagonal form, working with */ /* the upper triangle */ nr = 0; j1 = kdn + 2; j2 = 1; i__1 = kd1 + ab_dim1; i__2 = kd1 + ab_dim1; d__1 = ab[i__2].r; ab[i__1].r = d__1, ab[i__1].i = 0.; i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { /* Reduce i-th row of matrix to tridiagonal form */ for (k = kdn + 1; k >= 2; --k) { j1 += kdn; j2 += kdn; if (nr > 0) { /* generate plane rotations to annihilate nonzero */ /* elements which have been created outside the band */ zlargv_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &inca, & work[j1], &kd1, &d__[j1], &kd1); /* apply rotations from the right */ /* Dependent on the the number of diagonals either */ /* ZLARTV or ZROT is used */ if (nr >= (*kd << 1) - 1) { i__2 = *kd - 1; for (l = 1; l <= i__2; ++l) { zlartv_(&nr, &ab[l + 1 + (j1 - 1) * ab_dim1], &inca, &ab[l + j1 * ab_dim1], &inca, & d__[j1], &work[j1], &kd1); /* L10: */ } } else { jend = j1 + (nr - 1) * kd1; i__2 = jend; i__3 = kd1; for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <= i__2; jinc += i__3) { zrot_(&kdm1, &ab[(jinc - 1) * ab_dim1 + 2], & c__1, &ab[jinc * ab_dim1 + 1], &c__1, &d__[jinc], &work[jinc]); /* L20: */ } } } if (k > 2) { if (k <= *n - i__ + 1) { /* generate plane rotation to annihilate a(i,i+k-1) */ /* within the band */ zlartg_(&ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1] , &ab[*kd - k + 2 + (i__ + k - 1) * ab_dim1], &d__[i__ + k - 1], &work[i__ + k - 1], &temp); i__3 = *kd - k + 3 + (i__ + k - 2) * ab_dim1; ab[i__3].r = temp.r, ab[i__3].i = temp.i; /* apply rotation from the right */ i__3 = k - 3; zrot_(&i__3, &ab[*kd - k + 4 + (i__ + k - 2) * ab_dim1], &c__1, &ab[*kd - k + 3 + (i__ + k - 1) * ab_dim1], &c__1, &d__[i__ + k - 1], &work[i__ + k - 1]); } ++nr; j1 = j1 - kdn - 1; } /* apply plane rotations from both sides to diagonal */ /* blocks */ if (nr > 0) { zlar2v_(&nr, &ab[kd1 + (j1 - 1) * ab_dim1], &ab[kd1 + j1 * ab_dim1], &ab[*kd + j1 * ab_dim1], &inca, &d__[j1], &work[j1], &kd1); } /* apply plane rotations from the left */ if (nr > 0) { zlacgv_(&nr, &work[j1], &kd1); if ((*kd << 1) - 1 < nr) { /* Dependent on the the number of diagonals either */ /* ZLARTV or ZROT is used */ i__3 = *kd - 1; for (l = 1; l <= i__3; ++l) { if (j2 + l > *n) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { zlartv_(&nrt, &ab[*kd - l + (j1 + l) * ab_dim1], &inca, &ab[*kd - l + 1 + (j1 + l) * ab_dim1], &inca, & d__[j1], &work[j1], &kd1); } /* L30: */ } } else { j1end = j1 + kd1 * (nr - 2); if (j1end >= j1) { i__3 = j1end; i__2 = kd1; for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <= i__3; jin += i__2) { i__4 = *kd - 1; zrot_(&i__4, &ab[*kd - 1 + (jin + 1) * ab_dim1], &incx, &ab[*kd + (jin + 1) * ab_dim1], &incx, &d__[jin], & work[jin]); /* L40: */ } } /* Computing MIN */ i__2 = kdm1, i__3 = *n - j2; lend = f2cmin(i__2,i__3); last = j1end + kd1; if (lend > 0) { zrot_(&lend, &ab[*kd - 1 + (last + 1) * ab_dim1], &incx, &ab[*kd + (last + 1) * ab_dim1], &incx, &d__[last], &work[ last]); } } } if (wantq) { /* accumulate product of plane rotations in Q */ if (initq) { /* take advantage of the fact that Q was */ /* initially the Identity matrix */ iqend = f2cmax(iqend,j2); /* Computing MAX */ i__2 = 0, i__3 = k - 3; i2 = f2cmax(i__2,i__3); iqaend = i__ * *kd + 1; if (k == 2) { iqaend += *kd; } iqaend = f2cmin(iqaend,iqend); i__2 = j2; i__3 = kd1; for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) { ibl = i__ - i2 / kdm1; ++i2; /* Computing MAX */ i__4 = 1, i__5 = j - ibl; iqb = f2cmax(i__4,i__5); nq = iqaend + 1 - iqb; /* Computing MIN */ i__4 = iqaend + *kd; iqaend = f2cmin(i__4,iqend); d_cnjg(&z__1, &work[j]); zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1, &q[iqb + j * q_dim1], &c__1, &d__[j], &z__1); /* L50: */ } } else { i__3 = j2; i__2 = kd1; for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) { d_cnjg(&z__1, &work[j]); zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[ j * q_dim1 + 1], &c__1, &d__[j], & z__1); /* L60: */ } } } if (j2 + kdn > *n) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 = j2 - kdn - 1; } i__2 = j2; i__3 = kd1; for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) { /* create nonzero element a(j-1,j+kd) outside the band */ /* and store it in WORK */ i__4 = j + *kd; i__5 = j; i__6 = (j + *kd) * ab_dim1 + 1; z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i * ab[i__6].i, z__1.i = work[i__5].r * ab[i__6] .i + work[i__5].i * ab[i__6].r; work[i__4].r = z__1.r, work[i__4].i = z__1.i; i__4 = (j + *kd) * ab_dim1 + 1; i__5 = j; i__6 = (j + *kd) * ab_dim1 + 1; z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] * ab[i__6].i; ab[i__4].r = z__1.r, ab[i__4].i = z__1.i; /* L70: */ } /* L80: */ } /* L90: */ } } if (*kd > 0) { /* make off-diagonal elements real and copy them to E */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__3 = *kd + (i__ + 1) * ab_dim1; t.r = ab[i__3].r, t.i = ab[i__3].i; abst = z_abs(&t); i__3 = *kd + (i__ + 1) * ab_dim1; ab[i__3].r = abst, ab[i__3].i = 0.; e[i__] = abst; if (abst != 0.) { z__1.r = t.r / abst, z__1.i = t.i / abst; t.r = z__1.r, t.i = z__1.i; } else { t.r = 1., t.i = 0.; } if (i__ < *n - 1) { i__3 = *kd + (i__ + 2) * ab_dim1; i__2 = *kd + (i__ + 2) * ab_dim1; z__1.r = ab[i__2].r * t.r - ab[i__2].i * t.i, z__1.i = ab[ i__2].r * t.i + ab[i__2].i * t.r; ab[i__3].r = z__1.r, ab[i__3].i = z__1.i; } if (wantq) { d_cnjg(&z__1, &t); zscal_(n, &z__1, &q[(i__ + 1) * q_dim1 + 1], &c__1); } /* L100: */ } } else { /* set E to zero if original matrix was diagonal */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { e[i__] = 0.; /* L110: */ } } /* copy diagonal elements to D */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__3 = i__; i__2 = kd1 + i__ * ab_dim1; d__[i__3] = ab[i__2].r; /* L120: */ } } else { if (*kd > 1) { /* Reduce to complex Hermitian tridiagonal form, working with */ /* the lower triangle */ nr = 0; j1 = kdn + 2; j2 = 1; i__1 = ab_dim1 + 1; i__3 = ab_dim1 + 1; d__1 = ab[i__3].r; ab[i__1].r = d__1, ab[i__1].i = 0.; i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { /* Reduce i-th column of matrix to tridiagonal form */ for (k = kdn + 1; k >= 2; --k) { j1 += kdn; j2 += kdn; if (nr > 0) { /* generate plane rotations to annihilate nonzero */ /* elements which have been created outside the band */ zlargv_(&nr, &ab[kd1 + (j1 - kd1) * ab_dim1], &inca, & work[j1], &kd1, &d__[j1], &kd1); /* apply plane rotations from one side */ /* Dependent on the the number of diagonals either */ /* ZLARTV or ZROT is used */ if (nr > (*kd << 1) - 1) { i__3 = *kd - 1; for (l = 1; l <= i__3; ++l) { zlartv_(&nr, &ab[kd1 - l + (j1 - kd1 + l) * ab_dim1], &inca, &ab[kd1 - l + 1 + ( j1 - kd1 + l) * ab_dim1], &inca, &d__[ j1], &work[j1], &kd1); /* L130: */ } } else { jend = j1 + kd1 * (nr - 1); i__3 = jend; i__2 = kd1; for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <= i__3; jinc += i__2) { zrot_(&kdm1, &ab[*kd + (jinc - *kd) * ab_dim1] , &incx, &ab[kd1 + (jinc - *kd) * ab_dim1], &incx, &d__[jinc], &work[ jinc]); /* L140: */ } } } if (k > 2) { if (k <= *n - i__ + 1) { /* generate plane rotation to annihilate a(i+k-1,i) */ /* within the band */ zlartg_(&ab[k - 1 + i__ * ab_dim1], &ab[k + i__ * ab_dim1], &d__[i__ + k - 1], &work[i__ + k - 1], &temp); i__2 = k - 1 + i__ * ab_dim1; ab[i__2].r = temp.r, ab[i__2].i = temp.i; /* apply rotation from the left */ i__2 = k - 3; i__3 = *ldab - 1; i__4 = *ldab - 1; zrot_(&i__2, &ab[k - 2 + (i__ + 1) * ab_dim1], & i__3, &ab[k - 1 + (i__ + 1) * ab_dim1], & i__4, &d__[i__ + k - 1], &work[i__ + k - 1]); } ++nr; j1 = j1 - kdn - 1; } /* apply plane rotations from both sides to diagonal */ /* blocks */ if (nr > 0) { zlar2v_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], & inca, &d__[j1], &work[j1], &kd1); } /* apply plane rotations from the right */ /* Dependent on the the number of diagonals either */ /* ZLARTV or ZROT is used */ if (nr > 0) { zlacgv_(&nr, &work[j1], &kd1); if (nr > (*kd << 1) - 1) { i__2 = *kd - 1; for (l = 1; l <= i__2; ++l) { if (j2 + l > *n) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { zlartv_(&nrt, &ab[l + 2 + (j1 - 1) * ab_dim1], &inca, &ab[l + 1 + j1 * ab_dim1], &inca, &d__[j1], &work[ j1], &kd1); } /* L150: */ } } else { j1end = j1 + kd1 * (nr - 2); if (j1end >= j1) { i__2 = j1end; i__3 = kd1; for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 : j1inc <= i__2; j1inc += i__3) { zrot_(&kdm1, &ab[(j1inc - 1) * ab_dim1 + 3], &c__1, &ab[j1inc * ab_dim1 + 2], &c__1, &d__[j1inc], &work[ j1inc]); /* L160: */ } } /* Computing MIN */ i__3 = kdm1, i__2 = *n - j2; lend = f2cmin(i__3,i__2); last = j1end + kd1; if (lend > 0) { zrot_(&lend, &ab[(last - 1) * ab_dim1 + 3], & c__1, &ab[last * ab_dim1 + 2], &c__1, &d__[last], &work[last]); } } } if (wantq) { /* accumulate product of plane rotations in Q */ if (initq) { /* take advantage of the fact that Q was */ /* initially the Identity matrix */ iqend = f2cmax(iqend,j2); /* Computing MAX */ i__3 = 0, i__2 = k - 3; i2 = f2cmax(i__3,i__2); iqaend = i__ * *kd + 1; if (k == 2) { iqaend += *kd; } iqaend = f2cmin(iqaend,iqend); i__3 = j2; i__2 = kd1; for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) { ibl = i__ - i2 / kdm1; ++i2; /* Computing MAX */ i__4 = 1, i__5 = j - ibl; iqb = f2cmax(i__4,i__5); nq = iqaend + 1 - iqb; /* Computing MIN */ i__4 = iqaend + *kd; iqaend = f2cmin(i__4,iqend); zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1, &q[iqb + j * q_dim1], &c__1, &d__[j], &work[j]); /* L170: */ } } else { i__2 = j2; i__3 = kd1; for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) { zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[ j * q_dim1 + 1], &c__1, &d__[j], & work[j]); /* L180: */ } } } if (j2 + kdn > *n) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 = j2 - kdn - 1; } i__3 = j2; i__2 = kd1; for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) { /* create nonzero element a(j+kd,j-1) outside the */ /* band and store it in WORK */ i__4 = j + *kd; i__5 = j; i__6 = kd1 + j * ab_dim1; z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i * ab[i__6].i, z__1.i = work[i__5].r * ab[i__6] .i + work[i__5].i * ab[i__6].r; work[i__4].r = z__1.r, work[i__4].i = z__1.i; i__4 = kd1 + j * ab_dim1; i__5 = j; i__6 = kd1 + j * ab_dim1; z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] * ab[i__6].i; ab[i__4].r = z__1.r, ab[i__4].i = z__1.i; /* L190: */ } /* L200: */ } /* L210: */ } } if (*kd > 0) { /* make off-diagonal elements real and copy them to E */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ * ab_dim1 + 2; t.r = ab[i__2].r, t.i = ab[i__2].i; abst = z_abs(&t); i__2 = i__ * ab_dim1 + 2; ab[i__2].r = abst, ab[i__2].i = 0.; e[i__] = abst; if (abst != 0.) { z__1.r = t.r / abst, z__1.i = t.i / abst; t.r = z__1.r, t.i = z__1.i; } else { t.r = 1., t.i = 0.; } if (i__ < *n - 1) { i__2 = (i__ + 1) * ab_dim1 + 2; i__3 = (i__ + 1) * ab_dim1 + 2; z__1.r = ab[i__3].r * t.r - ab[i__3].i * t.i, z__1.i = ab[ i__3].r * t.i + ab[i__3].i * t.r; ab[i__2].r = z__1.r, ab[i__2].i = z__1.i; } if (wantq) { zscal_(n, &t, &q[(i__ + 1) * q_dim1 + 1], &c__1); } /* L220: */ } } else { /* set E to zero if original matrix was diagonal */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { e[i__] = 0.; /* L230: */ } } /* copy diagonal elements to D */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__ * ab_dim1 + 1; d__[i__2] = ab[i__3].r; /* L240: */ } } return 0; /* End of ZHBTRD */ } /* zhbtrd_ */