#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]/Cd(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 ZLAIC1 applies one step of incremental condition estimation. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZLAIC1 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) */ /* INTEGER J, JOB */ /* DOUBLE PRECISION SEST, SESTPR */ /* COMPLEX*16 C, GAMMA, S */ /* COMPLEX*16 W( J ), X( J ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZLAIC1 applies one step of incremental condition estimation in */ /* > its simplest version: */ /* > */ /* > Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j */ /* > lower triangular matrix L, such that */ /* > twonorm(L*x) = sest */ /* > Then ZLAIC1 computes sestpr, s, c such that */ /* > the vector */ /* > [ s*x ] */ /* > xhat = [ c ] */ /* > is an approximate singular vector of */ /* > [ L 0 ] */ /* > Lhat = [ w**H gamma ] */ /* > in the sense that */ /* > twonorm(Lhat*xhat) = sestpr. */ /* > */ /* > Depending on JOB, an estimate for the largest or smallest singular */ /* > value is computed. */ /* > */ /* > Note that [s c]**H and sestpr**2 is an eigenpair of the system */ /* > */ /* > diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] */ /* > [ conjg(gamma) ] */ /* > */ /* > where alpha = x**H * w. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is INTEGER */ /* > = 1: an estimate for the largest singular value is computed. */ /* > = 2: an estimate for the smallest singular value is computed. */ /* > \endverbatim */ /* > */ /* > \param[in] J */ /* > \verbatim */ /* > J is INTEGER */ /* > Length of X and W */ /* > \endverbatim */ /* > */ /* > \param[in] X */ /* > \verbatim */ /* > X is COMPLEX*16 array, dimension (J) */ /* > The j-vector x. */ /* > \endverbatim */ /* > */ /* > \param[in] SEST */ /* > \verbatim */ /* > SEST is DOUBLE PRECISION */ /* > Estimated singular value of j by j matrix L */ /* > \endverbatim */ /* > */ /* > \param[in] W */ /* > \verbatim */ /* > W is COMPLEX*16 array, dimension (J) */ /* > The j-vector w. */ /* > \endverbatim */ /* > */ /* > \param[in] GAMMA */ /* > \verbatim */ /* > GAMMA is COMPLEX*16 */ /* > The diagonal element gamma. */ /* > \endverbatim */ /* > */ /* > \param[out] SESTPR */ /* > \verbatim */ /* > SESTPR is DOUBLE PRECISION */ /* > Estimated singular value of (j+1) by (j+1) matrix Lhat. */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is COMPLEX*16 */ /* > Sine needed in forming xhat. */ /* > \endverbatim */ /* > */ /* > \param[out] C */ /* > \verbatim */ /* > C is COMPLEX*16 */ /* > Cosine needed in forming xhat. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ /* Subroutine */ int zlaic1_(integer *job, integer *j, doublecomplex *x, doublereal *sest, doublecomplex *w, doublecomplex *gamma, doublereal * sestpr, doublecomplex *s, doublecomplex *c__) { /* System generated locals */ doublereal d__1, d__2; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; /* Local variables */ doublecomplex sine; doublereal test, zeta1, zeta2, b, t; doublecomplex alpha; doublereal norma; extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal s1, s2; extern doublereal dlamch_(char *); doublereal absgam, absalp; doublecomplex cosine; doublereal absest, scl, eps, tmp; /* -- LAPACK auxiliary 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 */ /* ===================================================================== */ /* Parameter adjustments */ --w; --x; /* Function Body */ eps = dlamch_("Epsilon"); zdotc_(&z__1, j, &x[1], &c__1, &w[1], &c__1); alpha.r = z__1.r, alpha.i = z__1.i; absalp = z_abs(&alpha); absgam = z_abs(gamma); absest = abs(*sest); if (*job == 1) { /* Estimating largest singular value */ /* special cases */ if (*sest == 0.) { s1 = f2cmax(absgam,absalp); if (s1 == 0.) { s->r = 0., s->i = 0.; c__->r = 1., c__->i = 0.; *sestpr = 0.; } else { z__1.r = alpha.r / s1, z__1.i = alpha.i / s1; s->r = z__1.r, s->i = z__1.i; z__1.r = gamma->r / s1, z__1.i = gamma->i / s1; c__->r = z__1.r, c__->i = z__1.i; d_cnjg(&z__4, s); z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r * z__4.i + s->i * z__4.r; d_cnjg(&z__6, c__); z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r * z__6.i + c__->i * z__6.r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z_sqrt(&z__1, &z__2); tmp = z__1.r; z__1.r = s->r / tmp, z__1.i = s->i / tmp; s->r = z__1.r, s->i = z__1.i; z__1.r = c__->r / tmp, z__1.i = c__->i / tmp; c__->r = z__1.r, c__->i = z__1.i; *sestpr = s1 * tmp; } return 0; } else if (absgam <= eps * absest) { s->r = 1., s->i = 0.; c__->r = 0., c__->i = 0.; tmp = f2cmax(absest,absalp); s1 = absest / tmp; s2 = absalp / tmp; *sestpr = tmp * sqrt(s1 * s1 + s2 * s2); return 0; } else if (absalp <= eps * absest) { s1 = absgam; s2 = absest; if (s1 <= s2) { s->r = 1., s->i = 0.; c__->r = 0., c__->i = 0.; *sestpr = s2; } else { s->r = 0., s->i = 0.; c__->r = 1., c__->i = 0.; *sestpr = s1; } return 0; } else if (absest <= eps * absalp || absest <= eps * absgam) { s1 = absgam; s2 = absalp; if (s1 <= s2) { tmp = s1 / s2; scl = sqrt(tmp * tmp + 1.); *sestpr = s2 * scl; z__2.r = alpha.r / s2, z__2.i = alpha.i / s2; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; s->r = z__1.r, s->i = z__1.i; z__2.r = gamma->r / s2, z__2.i = gamma->i / s2; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; c__->r = z__1.r, c__->i = z__1.i; } else { tmp = s2 / s1; scl = sqrt(tmp * tmp + 1.); *sestpr = s1 * scl; z__2.r = alpha.r / s1, z__2.i = alpha.i / s1; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; s->r = z__1.r, s->i = z__1.i; z__2.r = gamma->r / s1, z__2.i = gamma->i / s1; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; c__->r = z__1.r, c__->i = z__1.i; } return 0; } else { /* normal case */ zeta1 = absalp / absest; zeta2 = absgam / absest; b = (1. - zeta1 * zeta1 - zeta2 * zeta2) * .5; d__1 = zeta1 * zeta1; c__->r = d__1, c__->i = 0.; if (b > 0.) { d__1 = b * b; z__4.r = d__1 + c__->r, z__4.i = c__->i; z_sqrt(&z__3, &z__4); z__2.r = b + z__3.r, z__2.i = z__3.i; z_div(&z__1, c__, &z__2); t = z__1.r; } else { d__1 = b * b; z__3.r = d__1 + c__->r, z__3.i = c__->i; z_sqrt(&z__2, &z__3); z__1.r = z__2.r - b, z__1.i = z__2.i; t = z__1.r; } z__3.r = alpha.r / absest, z__3.i = alpha.i / absest; z__2.r = -z__3.r, z__2.i = -z__3.i; z__1.r = z__2.r / t, z__1.i = z__2.i / t; sine.r = z__1.r, sine.i = z__1.i; z__3.r = gamma->r / absest, z__3.i = gamma->i / absest; z__2.r = -z__3.r, z__2.i = -z__3.i; d__1 = t + 1.; z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1; cosine.r = z__1.r, cosine.i = z__1.i; d_cnjg(&z__4, &sine); z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r * z__4.i + sine.i * z__4.r; d_cnjg(&z__6, &cosine); z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r * z__6.i + cosine.i * z__6.r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z_sqrt(&z__1, &z__2); tmp = z__1.r; z__1.r = sine.r / tmp, z__1.i = sine.i / tmp; s->r = z__1.r, s->i = z__1.i; z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp; c__->r = z__1.r, c__->i = z__1.i; *sestpr = sqrt(t + 1.) * absest; return 0; } } else if (*job == 2) { /* Estimating smallest singular value */ /* special cases */ if (*sest == 0.) { *sestpr = 0.; if (f2cmax(absgam,absalp) == 0.) { sine.r = 1., sine.i = 0.; cosine.r = 0., cosine.i = 0.; } else { d_cnjg(&z__2, gamma); z__1.r = -z__2.r, z__1.i = -z__2.i; sine.r = z__1.r, sine.i = z__1.i; d_cnjg(&z__1, &alpha); cosine.r = z__1.r, cosine.i = z__1.i; } /* Computing MAX */ d__1 = z_abs(&sine), d__2 = z_abs(&cosine); s1 = f2cmax(d__1,d__2); z__1.r = sine.r / s1, z__1.i = sine.i / s1; s->r = z__1.r, s->i = z__1.i; z__1.r = cosine.r / s1, z__1.i = cosine.i / s1; c__->r = z__1.r, c__->i = z__1.i; d_cnjg(&z__4, s); z__3.r = s->r * z__4.r - s->i * z__4.i, z__3.i = s->r * z__4.i + s->i * z__4.r; d_cnjg(&z__6, c__); z__5.r = c__->r * z__6.r - c__->i * z__6.i, z__5.i = c__->r * z__6.i + c__->i * z__6.r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z_sqrt(&z__1, &z__2); tmp = z__1.r; z__1.r = s->r / tmp, z__1.i = s->i / tmp; s->r = z__1.r, s->i = z__1.i; z__1.r = c__->r / tmp, z__1.i = c__->i / tmp; c__->r = z__1.r, c__->i = z__1.i; return 0; } else if (absgam <= eps * absest) { s->r = 0., s->i = 0.; c__->r = 1., c__->i = 0.; *sestpr = absgam; return 0; } else if (absalp <= eps * absest) { s1 = absgam; s2 = absest; if (s1 <= s2) { s->r = 0., s->i = 0.; c__->r = 1., c__->i = 0.; *sestpr = s1; } else { s->r = 1., s->i = 0.; c__->r = 0., c__->i = 0.; *sestpr = s2; } return 0; } else if (absest <= eps * absalp || absest <= eps * absgam) { s1 = absgam; s2 = absalp; if (s1 <= s2) { tmp = s1 / s2; scl = sqrt(tmp * tmp + 1.); *sestpr = absest * (tmp / scl); d_cnjg(&z__4, gamma); z__3.r = z__4.r / s2, z__3.i = z__4.i / s2; z__2.r = -z__3.r, z__2.i = -z__3.i; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; s->r = z__1.r, s->i = z__1.i; d_cnjg(&z__3, &alpha); z__2.r = z__3.r / s2, z__2.i = z__3.i / s2; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; c__->r = z__1.r, c__->i = z__1.i; } else { tmp = s2 / s1; scl = sqrt(tmp * tmp + 1.); *sestpr = absest / scl; d_cnjg(&z__4, gamma); z__3.r = z__4.r / s1, z__3.i = z__4.i / s1; z__2.r = -z__3.r, z__2.i = -z__3.i; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; s->r = z__1.r, s->i = z__1.i; d_cnjg(&z__3, &alpha); z__2.r = z__3.r / s1, z__2.i = z__3.i / s1; z__1.r = z__2.r / scl, z__1.i = z__2.i / scl; c__->r = z__1.r, c__->i = z__1.i; } return 0; } else { /* normal case */ zeta1 = absalp / absest; zeta2 = absgam / absest; /* Computing MAX */ d__1 = zeta1 * zeta1 + 1. + zeta1 * zeta2, d__2 = zeta1 * zeta2 + zeta2 * zeta2; norma = f2cmax(d__1,d__2); /* See if root is closer to zero or to ONE */ test = (zeta1 - zeta2) * 2. * (zeta1 + zeta2) + 1.; if (test >= 0.) { /* root is close to zero, compute directly */ b = (zeta1 * zeta1 + zeta2 * zeta2 + 1.) * .5; d__1 = zeta2 * zeta2; c__->r = d__1, c__->i = 0.; d__2 = b * b; z__2.r = d__2 - c__->r, z__2.i = -c__->i; d__1 = b + sqrt(z_abs(&z__2)); z__1.r = c__->r / d__1, z__1.i = c__->i / d__1; t = z__1.r; z__2.r = alpha.r / absest, z__2.i = alpha.i / absest; d__1 = 1. - t; z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1; sine.r = z__1.r, sine.i = z__1.i; z__3.r = gamma->r / absest, z__3.i = gamma->i / absest; z__2.r = -z__3.r, z__2.i = -z__3.i; z__1.r = z__2.r / t, z__1.i = z__2.i / t; cosine.r = z__1.r, cosine.i = z__1.i; *sestpr = sqrt(t + eps * 4. * eps * norma) * absest; } else { /* root is closer to ONE, shift by that amount */ b = (zeta2 * zeta2 + zeta1 * zeta1 - 1.) * .5; d__1 = zeta1 * zeta1; c__->r = d__1, c__->i = 0.; if (b >= 0.) { z__2.r = -c__->r, z__2.i = -c__->i; d__1 = b * b; z__5.r = d__1 + c__->r, z__5.i = c__->i; z_sqrt(&z__4, &z__5); z__3.r = b + z__4.r, z__3.i = z__4.i; z_div(&z__1, &z__2, &z__3); t = z__1.r; } else { d__1 = b * b; z__3.r = d__1 + c__->r, z__3.i = c__->i; z_sqrt(&z__2, &z__3); z__1.r = b - z__2.r, z__1.i = -z__2.i; t = z__1.r; } z__3.r = alpha.r / absest, z__3.i = alpha.i / absest; z__2.r = -z__3.r, z__2.i = -z__3.i; z__1.r = z__2.r / t, z__1.i = z__2.i / t; sine.r = z__1.r, sine.i = z__1.i; z__3.r = gamma->r / absest, z__3.i = gamma->i / absest; z__2.r = -z__3.r, z__2.i = -z__3.i; d__1 = t + 1.; z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1; cosine.r = z__1.r, cosine.i = z__1.i; *sestpr = sqrt(t + 1. + eps * 4. * eps * norma) * absest; } d_cnjg(&z__4, &sine); z__3.r = sine.r * z__4.r - sine.i * z__4.i, z__3.i = sine.r * z__4.i + sine.i * z__4.r; d_cnjg(&z__6, &cosine); z__5.r = cosine.r * z__6.r - cosine.i * z__6.i, z__5.i = cosine.r * z__6.i + cosine.i * z__6.r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z_sqrt(&z__1, &z__2); tmp = z__1.r; z__1.r = sine.r / tmp, z__1.i = sine.i / tmp; s->r = z__1.r, s->i = z__1.i; z__1.r = cosine.r / tmp, z__1.i = cosine.i / tmp; c__->r = z__1.r, c__->i = z__1.i; return 0; } } return 0; /* End of ZLAIC1 */ } /* zlaic1_ */