#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 CLAGS2 */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CLAGS2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, */ /* SNV, CSQ, SNQ ) */ /* LOGICAL UPPER */ /* REAL A1, A3, B1, B3, CSQ, CSU, CSV */ /* COMPLEX A2, B2, SNQ, SNU, SNV */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such */ /* > that if ( UPPER ) then */ /* > */ /* > U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 ) */ /* > ( 0 A3 ) ( x x ) */ /* > and */ /* > V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 ) */ /* > ( 0 B3 ) ( x x ) */ /* > */ /* > or if ( .NOT.UPPER ) then */ /* > */ /* > U**H *A*Q = U**H *( A1 0 )*Q = ( x x ) */ /* > ( A2 A3 ) ( 0 x ) */ /* > and */ /* > V**H *B*Q = V**H *( B1 0 )*Q = ( x x ) */ /* > ( B2 B3 ) ( 0 x ) */ /* > where */ /* > */ /* > U = ( CSU SNU ), V = ( CSV SNV ), */ /* > ( -SNU**H CSU ) ( -SNV**H CSV ) */ /* > */ /* > Q = ( CSQ SNQ ) */ /* > ( -SNQ**H CSQ ) */ /* > */ /* > The rows of the transformed A and B are parallel. Moreover, if the */ /* > input 2-by-2 matrix A is not zero, then the transformed (1,1) entry */ /* > of A is not zero. If the input matrices A and B are both not zero, */ /* > then the transformed (2,2) element of B is not zero, except when the */ /* > first rows of input A and B are parallel and the second rows are */ /* > zero. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPPER */ /* > \verbatim */ /* > UPPER is LOGICAL */ /* > = .TRUE.: the input matrices A and B are upper triangular. */ /* > = .FALSE.: the input matrices A and B are lower triangular. */ /* > \endverbatim */ /* > */ /* > \param[in] A1 */ /* > \verbatim */ /* > A1 is REAL */ /* > \endverbatim */ /* > */ /* > \param[in] A2 */ /* > \verbatim */ /* > A2 is COMPLEX */ /* > \endverbatim */ /* > */ /* > \param[in] A3 */ /* > \verbatim */ /* > A3 is REAL */ /* > On entry, A1, A2 and A3 are elements of the input 2-by-2 */ /* > upper (lower) triangular matrix A. */ /* > \endverbatim */ /* > */ /* > \param[in] B1 */ /* > \verbatim */ /* > B1 is REAL */ /* > \endverbatim */ /* > */ /* > \param[in] B2 */ /* > \verbatim */ /* > B2 is COMPLEX */ /* > \endverbatim */ /* > */ /* > \param[in] B3 */ /* > \verbatim */ /* > B3 is REAL */ /* > On entry, B1, B2 and B3 are elements of the input 2-by-2 */ /* > upper (lower) triangular matrix B. */ /* > \endverbatim */ /* > */ /* > \param[out] CSU */ /* > \verbatim */ /* > CSU is REAL */ /* > \endverbatim */ /* > */ /* > \param[out] SNU */ /* > \verbatim */ /* > SNU is COMPLEX */ /* > The desired unitary matrix U. */ /* > \endverbatim */ /* > */ /* > \param[out] CSV */ /* > \verbatim */ /* > CSV is REAL */ /* > \endverbatim */ /* > */ /* > \param[out] SNV */ /* > \verbatim */ /* > SNV is COMPLEX */ /* > The desired unitary matrix V. */ /* > \endverbatim */ /* > */ /* > \param[out] CSQ */ /* > \verbatim */ /* > CSQ is REAL */ /* > \endverbatim */ /* > */ /* > \param[out] SNQ */ /* > \verbatim */ /* > SNQ is COMPLEX */ /* > The desired unitary matrix Q. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complexOTHERauxiliary */ /* ===================================================================== */ /* Subroutine */ int clags2_(logical *upper, real *a1, complex *a2, real *a3, real *b1, complex *b2, real *b3, real *csu, complex *snu, real *csv, complex *snv, real *csq, complex *snq) { /* System generated locals */ real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8; complex q__1, q__2, q__3, q__4, q__5; /* Local variables */ real aua11, aua12, aua21, aua22, avb11, avb12, avb21, avb22, ua11r, ua22r, vb11r, vb22r, a; complex b, c__; real d__; complex r__, d1; real s1, s2, fb, fc; extern /* Subroutine */ int slasv2_(real *, real *, real *, real *, real * , real *, real *, real *, real *), clartg_(complex *, complex *, real *, complex *, complex *); complex ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22; real csl, csr, snl, snr; /* -- 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 */ /* ===================================================================== */ if (*upper) { /* Input matrices A and B are upper triangular matrices */ /* Form matrix C = A*adj(B) = ( a b ) */ /* ( 0 d ) */ a = *a1 * *b3; d__ = *a3 * *b1; q__2.r = *b1 * a2->r, q__2.i = *b1 * a2->i; q__3.r = *a1 * b2->r, q__3.i = *a1 * b2->i; q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i; b.r = q__1.r, b.i = q__1.i; fb = c_abs(&b); /* Transform complex 2-by-2 matrix C to real matrix by unitary */ /* diagonal matrix diag(1,D1). */ d1.r = 1.f, d1.i = 0.f; if (fb != 0.f) { q__1.r = b.r / fb, q__1.i = b.i / fb; d1.r = q__1.r, d1.i = q__1.i; } /* The SVD of real 2 by 2 triangular C */ /* ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 ) */ /* ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T ) */ slasv2_(&a, &fb, &d__, &s1, &s2, &snr, &csr, &snl, &csl); if (abs(csl) >= abs(snl) || abs(csr) >= abs(snr)) { /* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */ /* and (1,2) element of |U|**H *|A| and |V|**H *|B|. */ ua11r = csl * *a1; q__2.r = csl * a2->r, q__2.i = csl * a2->i; q__4.r = snl * d1.r, q__4.i = snl * d1.i; q__3.r = *a3 * q__4.r, q__3.i = *a3 * q__4.i; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; ua12.r = q__1.r, ua12.i = q__1.i; vb11r = csr * *b1; q__2.r = csr * b2->r, q__2.i = csr * b2->i; q__4.r = snr * d1.r, q__4.i = snr * d1.i; q__3.r = *b3 * q__4.r, q__3.i = *b3 * q__4.i; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; vb12.r = q__1.r, vb12.i = q__1.i; aua12 = abs(csl) * ((r__1 = a2->r, abs(r__1)) + (r__2 = r_imag(a2) , abs(r__2))) + abs(snl) * abs(*a3); avb12 = abs(csr) * ((r__1 = b2->r, abs(r__1)) + (r__2 = r_imag(b2) , abs(r__2))) + abs(snr) * abs(*b3); /* zero (1,2) elements of U**H *A and V**H *B */ if (abs(ua11r) + ((r__1 = ua12.r, abs(r__1)) + (r__2 = r_imag(& ua12), abs(r__2))) == 0.f) { q__2.r = vb11r, q__2.i = 0.f; q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &vb12); clartg_(&q__1, &q__3, csq, snq, &r__); } else if (abs(vb11r) + ((r__1 = vb12.r, abs(r__1)) + (r__2 = r_imag(&vb12), abs(r__2))) == 0.f) { q__2.r = ua11r, q__2.i = 0.f; q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &ua12); clartg_(&q__1, &q__3, csq, snq, &r__); } else if (aua12 / (abs(ua11r) + ((r__1 = ua12.r, abs(r__1)) + ( r__2 = r_imag(&ua12), abs(r__2)))) <= avb12 / (abs(vb11r) + ((r__3 = vb12.r, abs(r__3)) + (r__4 = r_imag(&vb12), abs(r__4))))) { q__2.r = ua11r, q__2.i = 0.f; q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &ua12); clartg_(&q__1, &q__3, csq, snq, &r__); } else { q__2.r = vb11r, q__2.i = 0.f; q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &vb12); clartg_(&q__1, &q__3, csq, snq, &r__); } *csu = csl; q__2.r = -d1.r, q__2.i = -d1.i; q__1.r = snl * q__2.r, q__1.i = snl * q__2.i; snu->r = q__1.r, snu->i = q__1.i; *csv = csr; q__2.r = -d1.r, q__2.i = -d1.i; q__1.r = snr * q__2.r, q__1.i = snr * q__2.i; snv->r = q__1.r, snv->i = q__1.i; } else { /* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */ /* and (2,2) element of |U|**H *|A| and |V|**H *|B|. */ r_cnjg(&q__4, &d1); q__3.r = -q__4.r, q__3.i = -q__4.i; q__2.r = snl * q__3.r, q__2.i = snl * q__3.i; q__1.r = *a1 * q__2.r, q__1.i = *a1 * q__2.i; ua21.r = q__1.r, ua21.i = q__1.i; r_cnjg(&q__5, &d1); q__4.r = -q__5.r, q__4.i = -q__5.i; q__3.r = snl * q__4.r, q__3.i = snl * q__4.i; q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i + q__3.i * a2->r; r__1 = csl * *a3; q__1.r = q__2.r + r__1, q__1.i = q__2.i; ua22.r = q__1.r, ua22.i = q__1.i; r_cnjg(&q__4, &d1); q__3.r = -q__4.r, q__3.i = -q__4.i; q__2.r = snr * q__3.r, q__2.i = snr * q__3.i; q__1.r = *b1 * q__2.r, q__1.i = *b1 * q__2.i; vb21.r = q__1.r, vb21.i = q__1.i; r_cnjg(&q__5, &d1); q__4.r = -q__5.r, q__4.i = -q__5.i; q__3.r = snr * q__4.r, q__3.i = snr * q__4.i; q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i + q__3.i * b2->r; r__1 = csr * *b3; q__1.r = q__2.r + r__1, q__1.i = q__2.i; vb22.r = q__1.r, vb22.i = q__1.i; aua22 = abs(snl) * ((r__1 = a2->r, abs(r__1)) + (r__2 = r_imag(a2) , abs(r__2))) + abs(csl) * abs(*a3); avb22 = abs(snr) * ((r__1 = b2->r, abs(r__1)) + (r__2 = r_imag(b2) , abs(r__2))) + abs(csr) * abs(*b3); /* zero (2,2) elements of U**H *A and V**H *B, and then swap. */ if ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&ua21), abs(r__2)) + ((r__3 = ua22.r, abs(r__3)) + (r__4 = r_imag(&ua22), abs(r__4))) == 0.f) { r_cnjg(&q__2, &vb21); q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &vb22); clartg_(&q__1, &q__3, csq, snq, &r__); } else if ((r__1 = vb21.r, abs(r__1)) + (r__2 = r_imag(&vb21), abs(r__2)) + c_abs(&vb22) == 0.f) { r_cnjg(&q__2, &ua21); q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &ua22); clartg_(&q__1, &q__3, csq, snq, &r__); } else if (aua22 / ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(& ua21), abs(r__2)) + ((r__3 = ua22.r, abs(r__3)) + (r__4 = r_imag(&ua22), abs(r__4)))) <= avb22 / ((r__5 = vb21.r, abs(r__5)) + (r__6 = r_imag(&vb21), abs(r__6)) + ((r__7 = vb22.r, abs(r__7)) + (r__8 = r_imag(&vb22), abs(r__8))))) { r_cnjg(&q__2, &ua21); q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &ua22); clartg_(&q__1, &q__3, csq, snq, &r__); } else { r_cnjg(&q__2, &vb21); q__1.r = -q__2.r, q__1.i = -q__2.i; r_cnjg(&q__3, &vb22); clartg_(&q__1, &q__3, csq, snq, &r__); } *csu = snl; q__1.r = csl * d1.r, q__1.i = csl * d1.i; snu->r = q__1.r, snu->i = q__1.i; *csv = snr; q__1.r = csr * d1.r, q__1.i = csr * d1.i; snv->r = q__1.r, snv->i = q__1.i; } } else { /* Input matrices A and B are lower triangular matrices */ /* Form matrix C = A*adj(B) = ( a 0 ) */ /* ( c d ) */ a = *a1 * *b3; d__ = *a3 * *b1; q__2.r = *b3 * a2->r, q__2.i = *b3 * a2->i; q__3.r = *a3 * b2->r, q__3.i = *a3 * b2->i; q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i; c__.r = q__1.r, c__.i = q__1.i; fc = c_abs(&c__); /* Transform complex 2-by-2 matrix C to real matrix by unitary */ /* diagonal matrix diag(d1,1). */ d1.r = 1.f, d1.i = 0.f; if (fc != 0.f) { q__1.r = c__.r / fc, q__1.i = c__.i / fc; d1.r = q__1.r, d1.i = q__1.i; } /* The SVD of real 2 by 2 triangular C */ /* ( CSL -SNL )*( A 0 )*( CSR SNR ) = ( R 0 ) */ /* ( SNL CSL ) ( C D ) ( -SNR CSR ) ( 0 T ) */ slasv2_(&a, &fc, &d__, &s1, &s2, &snr, &csr, &snl, &csl); if (abs(csr) >= abs(snr) || abs(csl) >= abs(snl)) { /* Compute the (2,1) and (2,2) elements of U**H *A and V**H *B, */ /* and (2,1) element of |U|**H *|A| and |V|**H *|B|. */ q__4.r = -d1.r, q__4.i = -d1.i; q__3.r = snr * q__4.r, q__3.i = snr * q__4.i; q__2.r = *a1 * q__3.r, q__2.i = *a1 * q__3.i; q__5.r = csr * a2->r, q__5.i = csr * a2->i; q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i; ua21.r = q__1.r, ua21.i = q__1.i; ua22r = csr * *a3; q__4.r = -d1.r, q__4.i = -d1.i; q__3.r = snl * q__4.r, q__3.i = snl * q__4.i; q__2.r = *b1 * q__3.r, q__2.i = *b1 * q__3.i; q__5.r = csl * b2->r, q__5.i = csl * b2->i; q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i; vb21.r = q__1.r, vb21.i = q__1.i; vb22r = csl * *b3; aua21 = abs(snr) * abs(*a1) + abs(csr) * ((r__1 = a2->r, abs(r__1) ) + (r__2 = r_imag(a2), abs(r__2))); avb21 = abs(snl) * abs(*b1) + abs(csl) * ((r__1 = b2->r, abs(r__1) ) + (r__2 = r_imag(b2), abs(r__2))); /* zero (2,1) elements of U**H *A and V**H *B. */ if ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(&ua21), abs(r__2)) + abs(ua22r) == 0.f) { q__1.r = vb22r, q__1.i = 0.f; clartg_(&q__1, &vb21, csq, snq, &r__); } else if ((r__1 = vb21.r, abs(r__1)) + (r__2 = r_imag(&vb21), abs(r__2)) + abs(vb22r) == 0.f) { q__1.r = ua22r, q__1.i = 0.f; clartg_(&q__1, &ua21, csq, snq, &r__); } else if (aua21 / ((r__1 = ua21.r, abs(r__1)) + (r__2 = r_imag(& ua21), abs(r__2)) + abs(ua22r)) <= avb21 / ((r__3 = vb21.r, abs(r__3)) + (r__4 = r_imag(&vb21), abs(r__4)) + abs(vb22r))) { q__1.r = ua22r, q__1.i = 0.f; clartg_(&q__1, &ua21, csq, snq, &r__); } else { q__1.r = vb22r, q__1.i = 0.f; clartg_(&q__1, &vb21, csq, snq, &r__); } *csu = csr; r_cnjg(&q__3, &d1); q__2.r = -q__3.r, q__2.i = -q__3.i; q__1.r = snr * q__2.r, q__1.i = snr * q__2.i; snu->r = q__1.r, snu->i = q__1.i; *csv = csl; r_cnjg(&q__3, &d1); q__2.r = -q__3.r, q__2.i = -q__3.i; q__1.r = snl * q__2.r, q__1.i = snl * q__2.i; snv->r = q__1.r, snv->i = q__1.i; } else { /* Compute the (1,1) and (1,2) elements of U**H *A and V**H *B, */ /* and (1,1) element of |U|**H *|A| and |V|**H *|B|. */ r__1 = csr * *a1; r_cnjg(&q__4, &d1); q__3.r = snr * q__4.r, q__3.i = snr * q__4.i; q__2.r = q__3.r * a2->r - q__3.i * a2->i, q__2.i = q__3.r * a2->i + q__3.i * a2->r; q__1.r = r__1 + q__2.r, q__1.i = q__2.i; ua11.r = q__1.r, ua11.i = q__1.i; r_cnjg(&q__3, &d1); q__2.r = snr * q__3.r, q__2.i = snr * q__3.i; q__1.r = *a3 * q__2.r, q__1.i = *a3 * q__2.i; ua12.r = q__1.r, ua12.i = q__1.i; r__1 = csl * *b1; r_cnjg(&q__4, &d1); q__3.r = snl * q__4.r, q__3.i = snl * q__4.i; q__2.r = q__3.r * b2->r - q__3.i * b2->i, q__2.i = q__3.r * b2->i + q__3.i * b2->r; q__1.r = r__1 + q__2.r, q__1.i = q__2.i; vb11.r = q__1.r, vb11.i = q__1.i; r_cnjg(&q__3, &d1); q__2.r = snl * q__3.r, q__2.i = snl * q__3.i; q__1.r = *b3 * q__2.r, q__1.i = *b3 * q__2.i; vb12.r = q__1.r, vb12.i = q__1.i; aua11 = abs(csr) * abs(*a1) + abs(snr) * ((r__1 = a2->r, abs(r__1) ) + (r__2 = r_imag(a2), abs(r__2))); avb11 = abs(csl) * abs(*b1) + abs(snl) * ((r__1 = b2->r, abs(r__1) ) + (r__2 = r_imag(b2), abs(r__2))); /* zero (1,1) elements of U**H *A and V**H *B, and then swap. */ if ((r__1 = ua11.r, abs(r__1)) + (r__2 = r_imag(&ua11), abs(r__2)) + ((r__3 = ua12.r, abs(r__3)) + (r__4 = r_imag(&ua12), abs(r__4))) == 0.f) { clartg_(&vb12, &vb11, csq, snq, &r__); } else if ((r__1 = vb11.r, abs(r__1)) + (r__2 = r_imag(&vb11), abs(r__2)) + ((r__3 = vb12.r, abs(r__3)) + (r__4 = r_imag( &vb12), abs(r__4))) == 0.f) { clartg_(&ua12, &ua11, csq, snq, &r__); } else if (aua11 / ((r__1 = ua11.r, abs(r__1)) + (r__2 = r_imag(& ua11), abs(r__2)) + ((r__3 = ua12.r, abs(r__3)) + (r__4 = r_imag(&ua12), abs(r__4)))) <= avb11 / ((r__5 = vb11.r, abs(r__5)) + (r__6 = r_imag(&vb11), abs(r__6)) + ((r__7 = vb12.r, abs(r__7)) + (r__8 = r_imag(&vb12), abs(r__8))))) { clartg_(&ua12, &ua11, csq, snq, &r__); } else { clartg_(&vb12, &vb11, csq, snq, &r__); } *csu = snr; r_cnjg(&q__2, &d1); q__1.r = csr * q__2.r, q__1.i = csr * q__2.i; snu->r = q__1.r, snu->i = q__1.i; *csv = snl; r_cnjg(&q__2, &d1); q__1.r = csl * q__2.r, q__1.i = csl * q__2.i; snv->r = q__1.r, snv->i = q__1.i; } } return 0; /* End of CLAGS2 */ } /* clags2_ */