#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 ZGGBAL */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZGGBAL + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, */ /* RSCALE, WORK, INFO ) */ /* CHARACTER JOB */ /* INTEGER IHI, ILO, INFO, LDA, LDB, N */ /* DOUBLE PRECISION LSCALE( * ), RSCALE( * ), WORK( * ) */ /* COMPLEX*16 A( LDA, * ), B( LDB, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZGGBAL balances a pair of general complex matrices (A,B). This */ /* > involves, first, permuting A and B by similarity transformations to */ /* > isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N */ /* > elements on the diagonal; and second, applying a diagonal similarity */ /* > transformation to rows and columns ILO to IHI to make the rows */ /* > and columns as close in norm as possible. Both steps are optional. */ /* > */ /* > Balancing may reduce the 1-norm of the matrices, and improve the */ /* > accuracy of the computed eigenvalues and/or eigenvectors in the */ /* > generalized eigenvalue problem A*x = lambda*B*x. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is CHARACTER*1 */ /* > Specifies the operations to be performed on A and B: */ /* > = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 */ /* > and RSCALE(I) = 1.0 for i=1,...,N; */ /* > = 'P': permute only; */ /* > = 'S': scale only; */ /* > = 'B': both permute and scale. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices A and B. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA,N) */ /* > On entry, the input matrix A. */ /* > On exit, A is overwritten by the balanced matrix. */ /* > If JOB = 'N', A is not referenced. */ /* > \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 input matrix B. */ /* > On exit, B is overwritten by the balanced matrix. */ /* > If JOB = 'N', B is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] ILO */ /* > \verbatim */ /* > ILO is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[out] IHI */ /* > \verbatim */ /* > IHI is INTEGER */ /* > ILO and IHI are set to integers such that on exit */ /* > A(i,j) = 0 and B(i,j) = 0 if i > j and */ /* > j = 1,...,ILO-1 or i = IHI+1,...,N. */ /* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */ /* > \endverbatim */ /* > */ /* > \param[out] LSCALE */ /* > \verbatim */ /* > LSCALE is DOUBLE PRECISION array, dimension (N) */ /* > Details of the permutations and scaling factors applied */ /* > to the left side of A and B. If P(j) is the index of the */ /* > row interchanged with row j, and D(j) is the scaling factor */ /* > applied to row j, then */ /* > LSCALE(j) = P(j) for J = 1,...,ILO-1 */ /* > = D(j) for J = ILO,...,IHI */ /* > = P(j) for J = IHI+1,...,N. */ /* > The order in which the interchanges are made is N to IHI+1, */ /* > then 1 to ILO-1. */ /* > \endverbatim */ /* > */ /* > \param[out] RSCALE */ /* > \verbatim */ /* > RSCALE is DOUBLE PRECISION array, dimension (N) */ /* > Details of the permutations and scaling factors applied */ /* > to the right side of A and B. If P(j) is the index of the */ /* > column interchanged with column j, and D(j) is the scaling */ /* > factor applied to column j, then */ /* > RSCALE(j) = P(j) for J = 1,...,ILO-1 */ /* > = D(j) for J = ILO,...,IHI */ /* > = P(j) for J = IHI+1,...,N. */ /* > The order in which the interchanges are made is N to IHI+1, */ /* > then 1 to ILO-1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (lwork) */ /* > lwork must be at least f2cmax(1,6*N) when JOB = 'S' or 'B', and */ /* > at least 1 when JOB = 'N' or 'P'. */ /* > \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 June 2016 */ /* > \ingroup complex16GBcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > See R.C. WARD, Balancing the generalized eigenvalue problem, */ /* > SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int zggbal_(char *job, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, doublereal *work, integer * info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3; /* Local variables */ integer lcab; doublereal beta, coef; integer irab, lrab; doublereal basl, cmax; extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal coef2, coef5; integer i__, j, k, l, m; doublereal gamma, t, alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); doublereal sfmin, sfmax; integer iflow; extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer kount; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer jc; doublereal ta, tb, tc; extern doublereal dlamch_(char *); integer ir, it; doublereal ew; integer nr; doublereal pgamma; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zdscal_( integer *, doublereal *, doublecomplex *, integer *); integer lsfmin; extern integer izamax_(integer *, doublecomplex *, integer *); integer lsfmax, ip1, jp1, lm1; doublereal cab, rab, ewc, cor, sum; integer nrp2, icab; /* -- 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..-- */ /* June 2016 */ /* ===================================================================== */ /* Test the input parameters */ /* 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; --lscale; --rscale; --work; /* Function Body */ *info = 0; if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") && ! lsame_(job, "B")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < f2cmax(1,*n)) { *info = -4; } else if (*ldb < f2cmax(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("ZGGBAL", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { *ilo = 1; *ihi = *n; return 0; } if (*n == 1) { *ilo = 1; *ihi = *n; lscale[1] = 1.; rscale[1] = 1.; return 0; } if (lsame_(job, "N")) { *ilo = 1; *ihi = *n; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { lscale[i__] = 1.; rscale[i__] = 1.; /* L10: */ } return 0; } k = 1; l = *n; if (lsame_(job, "S")) { goto L190; } goto L30; /* Permute the matrices A and B to isolate the eigenvalues. */ /* Find row with one nonzero in columns 1 through L */ L20: l = lm1; if (l != 1) { goto L30; } rscale[1] = 1.; lscale[1] = 1.; goto L190; L30: lm1 = l - 1; for (i__ = l; i__ >= 1; --i__) { i__1 = lm1; for (j = 1; j <= i__1; ++j) { jp1 = j + 1; i__2 = i__ + j * a_dim1; i__3 = i__ + j * b_dim1; if (a[i__2].r != 0. || a[i__2].i != 0. || (b[i__3].r != 0. || b[ i__3].i != 0.)) { goto L50; } /* L40: */ } j = l; goto L70; L50: i__1 = l; for (j = jp1; j <= i__1; ++j) { i__2 = i__ + j * a_dim1; i__3 = i__ + j * b_dim1; if (a[i__2].r != 0. || a[i__2].i != 0. || (b[i__3].r != 0. || b[ i__3].i != 0.)) { goto L80; } /* L60: */ } j = jp1 - 1; L70: m = l; iflow = 1; goto L160; L80: ; } goto L100; /* Find column with one nonzero in rows K through N */ L90: ++k; L100: i__1 = l; for (j = k; j <= i__1; ++j) { i__2 = lm1; for (i__ = k; i__ <= i__2; ++i__) { ip1 = i__ + 1; i__3 = i__ + j * a_dim1; i__4 = i__ + j * b_dim1; if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[ i__4].i != 0.)) { goto L120; } /* L110: */ } i__ = l; goto L140; L120: i__2 = l; for (i__ = ip1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * b_dim1; if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[ i__4].i != 0.)) { goto L150; } /* L130: */ } i__ = ip1 - 1; L140: m = k; iflow = 2; goto L160; L150: ; } goto L190; /* Permute rows M and I */ L160: lscale[m] = (doublereal) i__; if (i__ == m) { goto L170; } i__1 = *n - k + 1; zswap_(&i__1, &a[i__ + k * a_dim1], lda, &a[m + k * a_dim1], lda); i__1 = *n - k + 1; zswap_(&i__1, &b[i__ + k * b_dim1], ldb, &b[m + k * b_dim1], ldb); /* Permute columns M and J */ L170: rscale[m] = (doublereal) j; if (j == m) { goto L180; } zswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1); zswap_(&l, &b[j * b_dim1 + 1], &c__1, &b[m * b_dim1 + 1], &c__1); L180: switch (iflow) { case 1: goto L20; case 2: goto L90; } L190: *ilo = k; *ihi = l; if (lsame_(job, "P")) { i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { lscale[i__] = 1.; rscale[i__] = 1.; /* L195: */ } return 0; } if (*ilo == *ihi) { return 0; } /* Balance the submatrix in rows ILO to IHI. */ nr = *ihi - *ilo + 1; i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { rscale[i__] = 0.; lscale[i__] = 0.; work[i__] = 0.; work[i__ + *n] = 0.; work[i__ + (*n << 1)] = 0.; work[i__ + *n * 3] = 0.; work[i__ + (*n << 2)] = 0.; work[i__ + *n * 5] = 0.; /* L200: */ } /* Compute right side vector in resulting linear equations */ basl = d_lg10(&c_b36); i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { i__2 = *ihi; for (j = *ilo; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; if (a[i__3].r == 0. && a[i__3].i == 0.) { ta = 0.; goto L210; } i__3 = i__ + j * a_dim1; d__3 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__ + j * a_dim1]), abs(d__2)); ta = d_lg10(&d__3) / basl; L210: i__3 = i__ + j * b_dim1; if (b[i__3].r == 0. && b[i__3].i == 0.) { tb = 0.; goto L220; } i__3 = i__ + j * b_dim1; d__3 = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__ + j * b_dim1]), abs(d__2)); tb = d_lg10(&d__3) / basl; L220: work[i__ + (*n << 2)] = work[i__ + (*n << 2)] - ta - tb; work[j + *n * 5] = work[j + *n * 5] - ta - tb; /* L230: */ } /* L240: */ } coef = 1. / (doublereal) (nr << 1); coef2 = coef * coef; coef5 = coef2 * .5; nrp2 = nr + 2; beta = 0.; it = 1; /* Start generalized conjugate gradient iteration */ L250: gamma = ddot_(&nr, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + (*n << 2)] , &c__1) + ddot_(&nr, &work[*ilo + *n * 5], &c__1, &work[*ilo + * n * 5], &c__1); ew = 0.; ewc = 0.; i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { ew += work[i__ + (*n << 2)]; ewc += work[i__ + *n * 5]; /* L260: */ } /* Computing 2nd power */ d__1 = ew; /* Computing 2nd power */ d__2 = ewc; /* Computing 2nd power */ d__3 = ew - ewc; gamma = coef * gamma - coef2 * (d__1 * d__1 + d__2 * d__2) - coef5 * ( d__3 * d__3); if (gamma == 0.) { goto L350; } if (it != 1) { beta = gamma / pgamma; } t = coef5 * (ewc - ew * 3.); tc = coef5 * (ew - ewc * 3.); dscal_(&nr, &beta, &work[*ilo], &c__1); dscal_(&nr, &beta, &work[*ilo + *n], &c__1); daxpy_(&nr, &coef, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + *n], & c__1); daxpy_(&nr, &coef, &work[*ilo + *n * 5], &c__1, &work[*ilo], &c__1); i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { work[i__] += tc; work[i__ + *n] += t; /* L270: */ } /* Apply matrix to vector */ i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { kount = 0; sum = 0.; i__2 = *ihi; for (j = *ilo; j <= i__2; ++j) { i__3 = i__ + j * a_dim1; if (a[i__3].r == 0. && a[i__3].i == 0.) { goto L280; } ++kount; sum += work[j]; L280: i__3 = i__ + j * b_dim1; if (b[i__3].r == 0. && b[i__3].i == 0.) { goto L290; } ++kount; sum += work[j]; L290: ; } work[i__ + (*n << 1)] = (doublereal) kount * work[i__ + *n] + sum; /* L300: */ } i__1 = *ihi; for (j = *ilo; j <= i__1; ++j) { kount = 0; sum = 0.; i__2 = *ihi; for (i__ = *ilo; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; if (a[i__3].r == 0. && a[i__3].i == 0.) { goto L310; } ++kount; sum += work[i__ + *n]; L310: i__3 = i__ + j * b_dim1; if (b[i__3].r == 0. && b[i__3].i == 0.) { goto L320; } ++kount; sum += work[i__ + *n]; L320: ; } work[j + *n * 3] = (doublereal) kount * work[j] + sum; /* L330: */ } sum = ddot_(&nr, &work[*ilo + *n], &c__1, &work[*ilo + (*n << 1)], &c__1) + ddot_(&nr, &work[*ilo], &c__1, &work[*ilo + *n * 3], &c__1); alpha = gamma / sum; /* Determine correction to current iteration */ cmax = 0.; i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { cor = alpha * work[i__ + *n]; if (abs(cor) > cmax) { cmax = abs(cor); } lscale[i__] += cor; cor = alpha * work[i__]; if (abs(cor) > cmax) { cmax = abs(cor); } rscale[i__] += cor; /* L340: */ } if (cmax < .5) { goto L350; } d__1 = -alpha; daxpy_(&nr, &d__1, &work[*ilo + (*n << 1)], &c__1, &work[*ilo + (*n << 2)] , &c__1); d__1 = -alpha; daxpy_(&nr, &d__1, &work[*ilo + *n * 3], &c__1, &work[*ilo + *n * 5], & c__1); pgamma = gamma; ++it; if (it <= nrp2) { goto L250; } /* End generalized conjugate gradient iteration */ L350: sfmin = dlamch_("S"); sfmax = 1. / sfmin; lsfmin = (integer) (d_lg10(&sfmin) / basl + 1.); lsfmax = (integer) (d_lg10(&sfmax) / basl); i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { i__2 = *n - *ilo + 1; irab = izamax_(&i__2, &a[i__ + *ilo * a_dim1], lda); rab = z_abs(&a[i__ + (irab + *ilo - 1) * a_dim1]); i__2 = *n - *ilo + 1; irab = izamax_(&i__2, &b[i__ + *ilo * b_dim1], ldb); /* Computing MAX */ d__1 = rab, d__2 = z_abs(&b[i__ + (irab + *ilo - 1) * b_dim1]); rab = f2cmax(d__1,d__2); d__1 = rab + sfmin; lrab = (integer) (d_lg10(&d__1) / basl + 1.); ir = (integer) (lscale[i__] + d_sign(&c_b72, &lscale[i__])); /* Computing MIN */ i__2 = f2cmax(ir,lsfmin), i__2 = f2cmin(i__2,lsfmax), i__3 = lsfmax - lrab; ir = f2cmin(i__2,i__3); lscale[i__] = pow_di(&c_b36, &ir); icab = izamax_(ihi, &a[i__ * a_dim1 + 1], &c__1); cab = z_abs(&a[icab + i__ * a_dim1]); icab = izamax_(ihi, &b[i__ * b_dim1 + 1], &c__1); /* Computing MAX */ d__1 = cab, d__2 = z_abs(&b[icab + i__ * b_dim1]); cab = f2cmax(d__1,d__2); d__1 = cab + sfmin; lcab = (integer) (d_lg10(&d__1) / basl + 1.); jc = (integer) (rscale[i__] + d_sign(&c_b72, &rscale[i__])); /* Computing MIN */ i__2 = f2cmax(jc,lsfmin), i__2 = f2cmin(i__2,lsfmax), i__3 = lsfmax - lcab; jc = f2cmin(i__2,i__3); rscale[i__] = pow_di(&c_b36, &jc); /* L360: */ } /* Row scaling of matrices A and B */ i__1 = *ihi; for (i__ = *ilo; i__ <= i__1; ++i__) { i__2 = *n - *ilo + 1; zdscal_(&i__2, &lscale[i__], &a[i__ + *ilo * a_dim1], lda); i__2 = *n - *ilo + 1; zdscal_(&i__2, &lscale[i__], &b[i__ + *ilo * b_dim1], ldb); /* L370: */ } /* Column scaling of matrices A and B */ i__1 = *ihi; for (j = *ilo; j <= i__1; ++j) { zdscal_(ihi, &rscale[j], &a[j * a_dim1 + 1], &c__1); zdscal_(ihi, &rscale[j], &b[j * b_dim1 + 1], &c__1); /* L380: */ } return 0; /* End of ZGGBAL */ } /* zggbal_ */