#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(_Fcomplex x, integer n) { _Fcomplex 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 = _FCmulcc(pow,x) ; if(u >>= 1) x = _FCmulcc(x,x); else break; } } return pow; } #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 = _Cmulcc(pow,x); if(u >>= 1) x = _Cmulcc(x,x); else break; } } return pow; } #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 CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CLAESY + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 ) */ /* COMPLEX A, B, C, CS1, EVSCAL, RT1, RT2, SN1 */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix */ /* > ( ( A, B );( B, C ) ) */ /* > provided the norm of the matrix of eigenvectors is larger than */ /* > some threshold value. */ /* > */ /* > RT1 is the eigenvalue of larger absolute value, and RT2 of */ /* > smaller absolute value. If the eigenvectors are computed, then */ /* > on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence */ /* > */ /* > [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ] */ /* > [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ] */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX */ /* > The ( 1, 1 ) element of input matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX */ /* > The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element */ /* > is also given by B, since the 2-by-2 matrix is symmetric. */ /* > \endverbatim */ /* > */ /* > \param[in] C */ /* > \verbatim */ /* > C is COMPLEX */ /* > The ( 2, 2 ) element of input matrix. */ /* > \endverbatim */ /* > */ /* > \param[out] RT1 */ /* > \verbatim */ /* > RT1 is COMPLEX */ /* > The eigenvalue of larger modulus. */ /* > \endverbatim */ /* > */ /* > \param[out] RT2 */ /* > \verbatim */ /* > RT2 is COMPLEX */ /* > The eigenvalue of smaller modulus. */ /* > \endverbatim */ /* > */ /* > \param[out] EVSCAL */ /* > \verbatim */ /* > EVSCAL is COMPLEX */ /* > The complex value by which the eigenvector matrix was scaled */ /* > to make it orthonormal. If EVSCAL is zero, the eigenvectors */ /* > were not computed. This means one of two things: the 2-by-2 */ /* > matrix could not be diagonalized, or the norm of the matrix */ /* > of eigenvectors before scaling was larger than the threshold */ /* > value THRESH (set below). */ /* > \endverbatim */ /* > */ /* > \param[out] CS1 */ /* > \verbatim */ /* > CS1 is COMPLEX */ /* > \endverbatim */ /* > */ /* > \param[out] SN1 */ /* > \verbatim */ /* > SN1 is COMPLEX */ /* > If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector */ /* > for RT1. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complexSYauxiliary */ /* ===================================================================== */ /* Subroutine */ int claesy_(complex *a, complex *b, complex *c__, complex * rt1, complex *rt2, complex *evscal, complex *cs1, complex *sn1) { /* System generated locals */ real r__1, r__2; complex q__1, q__2, q__3, q__4, q__5, q__6, q__7; /* Local variables */ real babs, tabs; complex s, t; real z__, evnorm; complex 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 */ /* ===================================================================== */ /* Special case: The matrix is actually diagonal. */ /* To avoid divide by zero later, we treat this case separately. */ if (c_abs(b) == 0.f) { rt1->r = a->r, rt1->i = a->i; rt2->r = c__->r, rt2->i = c__->i; if (c_abs(rt1) < c_abs(rt2)) { tmp.r = rt1->r, tmp.i = rt1->i; rt1->r = rt2->r, rt1->i = rt2->i; rt2->r = tmp.r, rt2->i = tmp.i; cs1->r = 0.f, cs1->i = 0.f; sn1->r = 1.f, sn1->i = 0.f; } else { cs1->r = 1.f, cs1->i = 0.f; sn1->r = 0.f, sn1->i = 0.f; } } else { /* Compute the eigenvalues and eigenvectors. */ /* The characteristic equation is */ /* lambda **2 - (A+C) lambda + (A*C - B*B) */ /* and we solve it using the quadratic formula. */ q__2.r = a->r + c__->r, q__2.i = a->i + c__->i; q__1.r = q__2.r * .5f, q__1.i = q__2.i * .5f; s.r = q__1.r, s.i = q__1.i; q__2.r = a->r - c__->r, q__2.i = a->i - c__->i; q__1.r = q__2.r * .5f, q__1.i = q__2.i * .5f; t.r = q__1.r, t.i = q__1.i; /* Take the square root carefully to avoid over/under flow. */ babs = c_abs(b); tabs = c_abs(&t); z__ = f2cmax(babs,tabs); if (z__ > 0.f) { q__5.r = t.r / z__, q__5.i = t.i / z__; pow_ci(&q__4, &q__5, &c__2); q__7.r = b->r / z__, q__7.i = b->i / z__; pow_ci(&q__6, &q__7, &c__2); q__3.r = q__4.r + q__6.r, q__3.i = q__4.i + q__6.i; c_sqrt(&q__2, &q__3); q__1.r = z__ * q__2.r, q__1.i = z__ * q__2.i; t.r = q__1.r, t.i = q__1.i; } /* Compute the two eigenvalues. RT1 and RT2 are exchanged */ /* if necessary so that RT1 will have the greater magnitude. */ q__1.r = s.r + t.r, q__1.i = s.i + t.i; rt1->r = q__1.r, rt1->i = q__1.i; q__1.r = s.r - t.r, q__1.i = s.i - t.i; rt2->r = q__1.r, rt2->i = q__1.i; if (c_abs(rt1) < c_abs(rt2)) { tmp.r = rt1->r, tmp.i = rt1->i; rt1->r = rt2->r, rt1->i = rt2->i; rt2->r = tmp.r, rt2->i = tmp.i; } /* Choose CS1 = 1 and SN1 to satisfy the first equation, then */ /* scale the components of this eigenvector so that the matrix */ /* of eigenvectors X satisfies X * X**T = I . (No scaling is */ /* done if the norm of the eigenvalue matrix is less than THRESH.) */ q__2.r = rt1->r - a->r, q__2.i = rt1->i - a->i; c_div(&q__1, &q__2, b); sn1->r = q__1.r, sn1->i = q__1.i; tabs = c_abs(sn1); if (tabs > 1.f) { /* Computing 2nd power */ r__2 = 1.f / tabs; r__1 = r__2 * r__2; q__5.r = sn1->r / tabs, q__5.i = sn1->i / tabs; pow_ci(&q__4, &q__5, &c__2); q__3.r = r__1 + q__4.r, q__3.i = q__4.i; c_sqrt(&q__2, &q__3); q__1.r = tabs * q__2.r, q__1.i = tabs * q__2.i; t.r = q__1.r, t.i = q__1.i; } else { q__3.r = sn1->r * sn1->r - sn1->i * sn1->i, q__3.i = sn1->r * sn1->i + sn1->i * sn1->r; q__2.r = q__3.r + 1.f, q__2.i = q__3.i + 0.f; c_sqrt(&q__1, &q__2); t.r = q__1.r, t.i = q__1.i; } evnorm = c_abs(&t); if (evnorm >= .1f) { c_div(&q__1, &c_b1, &t); evscal->r = q__1.r, evscal->i = q__1.i; cs1->r = evscal->r, cs1->i = evscal->i; q__1.r = sn1->r * evscal->r - sn1->i * evscal->i, q__1.i = sn1->r * evscal->i + sn1->i * evscal->r; sn1->r = q__1.r, sn1->i = q__1.i; } else { evscal->r = 0.f, evscal->i = 0.f; } } return 0; /* End of CLAESY */ } /* claesy_ */