#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 ZGGHRD */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZGGHRD + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, */ /* LDQ, Z, LDZ, INFO ) */ /* CHARACTER COMPQ, COMPZ */ /* INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N */ /* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */ /* $ Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper */ /* > Hessenberg form using unitary transformations, where A is a */ /* > general matrix and B is upper triangular. The form of the */ /* > generalized eigenvalue problem is */ /* > A*x = lambda*B*x, */ /* > and B is typically made upper triangular by computing its QR */ /* > factorization and moving the unitary matrix Q to the left side */ /* > of the equation. */ /* > */ /* > This subroutine simultaneously reduces A to a Hessenberg matrix H: */ /* > Q**H*A*Z = H */ /* > and transforms B to another upper triangular matrix T: */ /* > Q**H*B*Z = T */ /* > in order to reduce the problem to its standard form */ /* > H*y = lambda*T*y */ /* > where y = Z**H*x. */ /* > */ /* > The unitary matrices Q and Z are determined as products of Givens */ /* > rotations. They may either be formed explicitly, or they may be */ /* > postmultiplied into input matrices Q1 and Z1, so that */ /* > Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H */ /* > Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H */ /* > If Q1 is the unitary matrix from the QR factorization of B in the */ /* > original equation A*x = lambda*B*x, then ZGGHRD reduces the original */ /* > problem to generalized Hessenberg form. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] COMPQ */ /* > \verbatim */ /* > COMPQ is CHARACTER*1 */ /* > = 'N': do not compute Q; */ /* > = 'I': Q is initialized to the unit matrix, and the */ /* > unitary matrix Q is returned; */ /* > = 'V': Q must contain a unitary matrix Q1 on entry, */ /* > and the product Q1*Q is returned. */ /* > \endverbatim */ /* > */ /* > \param[in] COMPZ */ /* > \verbatim */ /* > COMPZ is CHARACTER*1 */ /* > = 'N': do not compute Z; */ /* > = 'I': Z is initialized to the unit matrix, and the */ /* > unitary matrix Z is returned; */ /* > = 'V': Z must contain a unitary matrix Z1 on entry, */ /* > and the product Z1*Z is returned. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices A and B. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] ILO */ /* > \verbatim */ /* > ILO is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] IHI */ /* > \verbatim */ /* > IHI is INTEGER */ /* > */ /* > ILO and IHI mark the rows and columns of A which are to be */ /* > reduced. It is assumed that A is already upper triangular */ /* > in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are */ /* > normally set by a previous call to ZGGBAL; otherwise they */ /* > should be set to 1 and N respectively. */ /* > 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA, N) */ /* > On entry, the N-by-N general matrix to be reduced. */ /* > On exit, the upper triangle and the first subdiagonal of A */ /* > are overwritten with the upper Hessenberg matrix H, and the */ /* > rest is set to zero. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is COMPLEX*16 array, dimension (LDB, N) */ /* > On entry, the N-by-N upper triangular matrix B. */ /* > On exit, the upper triangular matrix T = Q**H B Z. The */ /* > elements below the diagonal are set to zero. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] Q */ /* > \verbatim */ /* > Q is COMPLEX*16 array, dimension (LDQ, N) */ /* > On entry, if COMPQ = 'V', the unitary matrix Q1, typically */ /* > from the QR factorization of B. */ /* > On exit, if COMPQ='I', the unitary matrix Q, and if */ /* > COMPQ = 'V', the product Q1*Q. */ /* > Not referenced if COMPQ='N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. */ /* > LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Z */ /* > \verbatim */ /* > Z is COMPLEX*16 array, dimension (LDZ, N) */ /* > On entry, if COMPZ = 'V', the unitary matrix Z1. */ /* > On exit, if COMPZ='I', the unitary matrix Z, and if */ /* > COMPZ = 'V', the product Z1*Z. */ /* > Not referenced if COMPZ='N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. */ /* > LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. */ /* > \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 */ /* > */ /* > This routine reduces A to Hessenberg and B to triangular form by */ /* > an unblocked reduction, as described in _Matrix_Computations_, */ /* > by Golub and van Loan (Johns Hopkins Press). */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int zgghrd_(char *compq, char *compz, integer *n, integer * ilo, integer *ihi, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2, i__3; doublecomplex z__1; /* Local variables */ integer jcol, jrow; extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *); doublereal c__; doublecomplex s; extern logical lsame_(char *, char *); doublecomplex ctemp; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); integer icompq, icompz; extern /* Subroutine */ int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *); logical ilq, ilz; /* -- 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 */ /* ===================================================================== */ /* Decode COMPQ */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; /* Function Body */ if (lsame_(compq, "N")) { ilq = FALSE_; icompq = 1; } else if (lsame_(compq, "V")) { ilq = TRUE_; icompq = 2; } else if (lsame_(compq, "I")) { ilq = TRUE_; icompq = 3; } else { icompq = 0; } /* Decode COMPZ */ if (lsame_(compz, "N")) { ilz = FALSE_; icompz = 1; } else if (lsame_(compz, "V")) { ilz = TRUE_; icompz = 2; } else if (lsame_(compz, "I")) { ilz = TRUE_; icompz = 3; } else { icompz = 0; } /* Test the input parameters. */ *info = 0; if (icompq <= 0) { *info = -1; } else if (icompz <= 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ilo < 1) { *info = -4; } else if (*ihi > *n || *ihi < *ilo - 1) { *info = -5; } else if (*lda < f2cmax(1,*n)) { *info = -7; } else if (*ldb < f2cmax(1,*n)) { *info = -9; } else if (ilq && *ldq < *n || *ldq < 1) { *info = -11; } else if (ilz && *ldz < *n || *ldz < 1) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("ZGGHRD", &i__1, (ftnlen)6); return 0; } /* Initialize Q and Z if desired. */ if (icompq == 3) { zlaset_("Full", n, n, &c_b2, &c_b1, &q[q_offset], ldq); } if (icompz == 3) { zlaset_("Full", n, n, &c_b2, &c_b1, &z__[z_offset], ldz); } /* Quick return if possible */ if (*n <= 1) { return 0; } /* Zero out lower triangle of B */ i__1 = *n - 1; for (jcol = 1; jcol <= i__1; ++jcol) { i__2 = *n; for (jrow = jcol + 1; jrow <= i__2; ++jrow) { i__3 = jrow + jcol * b_dim1; b[i__3].r = 0., b[i__3].i = 0.; /* L10: */ } /* L20: */ } /* Reduce A and B */ i__1 = *ihi - 2; for (jcol = *ilo; jcol <= i__1; ++jcol) { i__2 = jcol + 2; for (jrow = *ihi; jrow >= i__2; --jrow) { /* Step 1: rotate rows JROW-1, JROW to kill A(JROW,JCOL) */ i__3 = jrow - 1 + jcol * a_dim1; ctemp.r = a[i__3].r, ctemp.i = a[i__3].i; zlartg_(&ctemp, &a[jrow + jcol * a_dim1], &c__, &s, &a[jrow - 1 + jcol * a_dim1]); i__3 = jrow + jcol * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; i__3 = *n - jcol; zrot_(&i__3, &a[jrow - 1 + (jcol + 1) * a_dim1], lda, &a[jrow + ( jcol + 1) * a_dim1], lda, &c__, &s); i__3 = *n + 2 - jrow; zrot_(&i__3, &b[jrow - 1 + (jrow - 1) * b_dim1], ldb, &b[jrow + ( jrow - 1) * b_dim1], ldb, &c__, &s); if (ilq) { d_cnjg(&z__1, &s); zrot_(n, &q[(jrow - 1) * q_dim1 + 1], &c__1, &q[jrow * q_dim1 + 1], &c__1, &c__, &z__1); } /* Step 2: rotate columns JROW, JROW-1 to kill B(JROW,JROW-1) */ i__3 = jrow + jrow * b_dim1; ctemp.r = b[i__3].r, ctemp.i = b[i__3].i; zlartg_(&ctemp, &b[jrow + (jrow - 1) * b_dim1], &c__, &s, &b[jrow + jrow * b_dim1]); i__3 = jrow + (jrow - 1) * b_dim1; b[i__3].r = 0., b[i__3].i = 0.; zrot_(ihi, &a[jrow * a_dim1 + 1], &c__1, &a[(jrow - 1) * a_dim1 + 1], &c__1, &c__, &s); i__3 = jrow - 1; zrot_(&i__3, &b[jrow * b_dim1 + 1], &c__1, &b[(jrow - 1) * b_dim1 + 1], &c__1, &c__, &s); if (ilz) { zrot_(n, &z__[jrow * z_dim1 + 1], &c__1, &z__[(jrow - 1) * z_dim1 + 1], &c__1, &c__, &s); } /* L30: */ } /* L40: */ } return 0; /* End of ZGGHRD */ } /* zgghrd_ */