#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 DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DLASV2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) */ /* DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLASV2 computes the singular value decomposition of a 2-by-2 */ /* > triangular matrix */ /* > [ F G ] */ /* > [ 0 H ]. */ /* > On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the */ /* > smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and */ /* > right singular vectors for abs(SSMAX), giving the decomposition */ /* > */ /* > [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] */ /* > [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] F */ /* > \verbatim */ /* > F is DOUBLE PRECISION */ /* > The (1,1) element of the 2-by-2 matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] G */ /* > \verbatim */ /* > G is DOUBLE PRECISION */ /* > The (1,2) element of the 2-by-2 matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] H */ /* > \verbatim */ /* > H is DOUBLE PRECISION */ /* > The (2,2) element of the 2-by-2 matrix. */ /* > \endverbatim */ /* > */ /* > \param[out] SSMIN */ /* > \verbatim */ /* > SSMIN is DOUBLE PRECISION */ /* > abs(SSMIN) is the smaller singular value. */ /* > \endverbatim */ /* > */ /* > \param[out] SSMAX */ /* > \verbatim */ /* > SSMAX is DOUBLE PRECISION */ /* > abs(SSMAX) is the larger singular value. */ /* > \endverbatim */ /* > */ /* > \param[out] SNL */ /* > \verbatim */ /* > SNL is DOUBLE PRECISION */ /* > \endverbatim */ /* > */ /* > \param[out] CSL */ /* > \verbatim */ /* > CSL is DOUBLE PRECISION */ /* > The vector (CSL, SNL) is a unit left singular vector for the */ /* > singular value abs(SSMAX). */ /* > \endverbatim */ /* > */ /* > \param[out] SNR */ /* > \verbatim */ /* > SNR is DOUBLE PRECISION */ /* > \endverbatim */ /* > */ /* > \param[out] CSR */ /* > \verbatim */ /* > CSR is DOUBLE PRECISION */ /* > The vector (CSR, SNR) is a unit right singular vector for the */ /* > singular value abs(SSMAX). */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup OTHERauxiliary */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Any input parameter may be aliased with any output parameter. */ /* > */ /* > Barring over/underflow and assuming a guard digit in subtraction, all */ /* > output quantities are correct to within a few units in the last */ /* > place (ulps). */ /* > */ /* > In IEEE arithmetic, the code works correctly if one matrix element is */ /* > infinite. */ /* > */ /* > Overflow will not occur unless the largest singular value itself */ /* > overflows or is within a few ulps of overflow. (On machines with */ /* > partial overflow, like the Cray, overflow may occur if the largest */ /* > singular value is within a factor of 2 of overflow.) */ /* > */ /* > Underflow is harmless if underflow is gradual. Otherwise, results */ /* > may correspond to a matrix modified by perturbations of size near */ /* > the underflow threshold. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * csr, doublereal *snl, doublereal *csl) { /* System generated locals */ doublereal d__1; /* Local variables */ integer pmax; doublereal temp; logical swap; doublereal a, d__, l, m, r__, s, t, tsign, fa, ga, ha; extern doublereal dlamch_(char *); doublereal ft, gt, ht, mm; logical gasmal; doublereal tt, clt, crt, slt, srt; /* -- 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 */ /* ===================================================================== */ ft = *f; fa = abs(ft); ht = *h__; ha = abs(*h__); /* PMAX points to the maximum absolute element of matrix */ /* PMAX = 1 if F largest in absolute values */ /* PMAX = 2 if G largest in absolute values */ /* PMAX = 3 if H largest in absolute values */ pmax = 1; swap = ha > fa; if (swap) { pmax = 3; temp = ft; ft = ht; ht = temp; temp = fa; fa = ha; ha = temp; /* Now FA .ge. HA */ } gt = *g; ga = abs(gt); if (ga == 0.) { /* Diagonal matrix */ *ssmin = ha; *ssmax = fa; clt = 1.; crt = 1.; slt = 0.; srt = 0.; } else { gasmal = TRUE_; if (ga > fa) { pmax = 2; if (fa / ga < dlamch_("EPS")) { /* Case of very large GA */ gasmal = FALSE_; *ssmax = ga; if (ha > 1.) { *ssmin = fa / (ga / ha); } else { *ssmin = fa / ga * ha; } clt = 1.; slt = ht / gt; srt = 1.; crt = ft / gt; } } if (gasmal) { /* Normal case */ d__ = fa - ha; if (d__ == fa) { /* Copes with infinite F or H */ l = 1.; } else { l = d__ / fa; } /* Note that 0 .le. L .le. 1 */ m = gt / ft; /* Note that abs(M) .le. 1/macheps */ t = 2. - l; /* Note that T .ge. 1 */ mm = m * m; tt = t * t; s = sqrt(tt + mm); /* Note that 1 .le. S .le. 1 + 1/macheps */ if (l == 0.) { r__ = abs(m); } else { r__ = sqrt(l * l + mm); } /* Note that 0 .le. R .le. 1 + 1/macheps */ a = (s + r__) * .5; /* Note that 1 .le. A .le. 1 + abs(M) */ *ssmin = ha / a; *ssmax = fa * a; if (mm == 0.) { /* Note that M is very tiny */ if (l == 0.) { t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >); } else { t = gt / d_sign(&d__, &ft) + m / t; } } else { t = (m / (s + t) + m / (r__ + l)) * (a + 1.); } l = sqrt(t * t + 4.); crt = 2. / l; srt = t / l; clt = (crt + srt * m) / a; slt = ht / ft * srt / a; } } if (swap) { *csl = srt; *snl = crt; *csr = slt; *snr = clt; } else { *csl = clt; *snl = slt; *csr = crt; *snr = srt; } /* Correct signs of SSMAX and SSMIN */ if (pmax == 1) { tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f); } if (pmax == 2) { tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g); } if (pmax == 3) { tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__); } *ssmax = d_sign(ssmax, &tsign); d__1 = tsign * d_sign(&c_b4, f) * d_sign(&c_b4, h__); *ssmin = d_sign(ssmin, &d__1); return 0; /* End of DLASV2 */ } /* dlasv2_ */