#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 SGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm) */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGGES3 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, */ /* $ LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, */ /* $ VSR, LDVSR, WORK, LWORK, BWORK, INFO ) */ /* CHARACTER JOBVSL, JOBVSR, SORT */ /* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM */ /* LOGICAL BWORK( * ) */ /* REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */ /* $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), */ /* $ VSR( LDVSR, * ), WORK( * ) */ /* LOGICAL SELCTG */ /* EXTERNAL SELCTG */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGGES3 computes for a pair of N-by-N real nonsymmetric matrices (A,B), */ /* > the generalized eigenvalues, the generalized real Schur form (S,T), */ /* > optionally, the left and/or right matrices of Schur vectors (VSL and */ /* > VSR). This gives the generalized Schur factorization */ /* > */ /* > (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) */ /* > */ /* > Optionally, it also orders the eigenvalues so that a selected cluster */ /* > of eigenvalues appears in the leading diagonal blocks of the upper */ /* > quasi-triangular matrix S and the upper triangular matrix T.The */ /* > leading columns of VSL and VSR then form an orthonormal basis for the */ /* > corresponding left and right eigenspaces (deflating subspaces). */ /* > */ /* > (If only the generalized eigenvalues are needed, use the driver */ /* > SGGEV instead, which is faster.) */ /* > */ /* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */ /* > or a ratio alpha/beta = w, such that A - w*B is singular. It is */ /* > usually represented as the pair (alpha,beta), as there is a */ /* > reasonable interpretation for beta=0 or both being zero. */ /* > */ /* > A pair of matrices (S,T) is in generalized real Schur form if T is */ /* > upper triangular with non-negative diagonal and S is block upper */ /* > triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond */ /* > to real generalized eigenvalues, while 2-by-2 blocks of S will be */ /* > "standardized" by making the corresponding elements of T have the */ /* > form: */ /* > [ a 0 ] */ /* > [ 0 b ] */ /* > */ /* > and the pair of corresponding 2-by-2 blocks in S and T will have a */ /* > complex conjugate pair of generalized eigenvalues. */ /* > */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBVSL */ /* > \verbatim */ /* > JOBVSL is CHARACTER*1 */ /* > = 'N': do not compute the left Schur vectors; */ /* > = 'V': compute the left Schur vectors. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVSR */ /* > \verbatim */ /* > JOBVSR is CHARACTER*1 */ /* > = 'N': do not compute the right Schur vectors; */ /* > = 'V': compute the right Schur vectors. */ /* > \endverbatim */ /* > */ /* > \param[in] SORT */ /* > \verbatim */ /* > SORT is CHARACTER*1 */ /* > Specifies whether or not to order the eigenvalues on the */ /* > diagonal of the generalized Schur form. */ /* > = 'N': Eigenvalues are not ordered; */ /* > = 'S': Eigenvalues are ordered (see SELCTG); */ /* > \endverbatim */ /* > */ /* > \param[in] SELCTG */ /* > \verbatim */ /* > SELCTG is a LOGICAL FUNCTION of three REAL arguments */ /* > SELCTG must be declared EXTERNAL in the calling subroutine. */ /* > If SORT = 'N', SELCTG is not referenced. */ /* > If SORT = 'S', SELCTG is used to select eigenvalues to sort */ /* > to the top left of the Schur form. */ /* > An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */ /* > SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */ /* > one of a complex conjugate pair of eigenvalues is selected, */ /* > then both complex eigenvalues are selected. */ /* > */ /* > Note that in the ill-conditioned case, a selected complex */ /* > eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), */ /* > BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 */ /* > in this case. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices A, B, VSL, and VSR. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA, N) */ /* > On entry, the first of the pair of matrices. */ /* > On exit, A has been overwritten by its generalized Schur */ /* > form S. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB, N) */ /* > On entry, the second of the pair of matrices. */ /* > On exit, B has been overwritten by its generalized Schur */ /* > form T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] SDIM */ /* > \verbatim */ /* > SDIM is INTEGER */ /* > If SORT = 'N', SDIM = 0. */ /* > If SORT = 'S', SDIM = number of eigenvalues (after sorting) */ /* > for which SELCTG is true. (Complex conjugate pairs for which */ /* > SELCTG is true for either eigenvalue count as 2.) */ /* > \endverbatim */ /* > */ /* > \param[out] ALPHAR */ /* > \verbatim */ /* > ALPHAR is REAL array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] ALPHAI */ /* > \verbatim */ /* > ALPHAI is REAL array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] BETA */ /* > \verbatim */ /* > BETA is REAL array, dimension (N) */ /* > On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */ /* > be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i, */ /* > and BETA(j),j=1,...,N are the diagonals of the complex Schur */ /* > form (S,T) that would result if the 2-by-2 diagonal blocks of */ /* > the real Schur form of (A,B) were further reduced to */ /* > triangular form using 2-by-2 complex unitary transformations. */ /* > If ALPHAI(j) is zero, then the j-th eigenvalue is real; if */ /* > positive, then the j-th and (j+1)-st eigenvalues are a */ /* > complex conjugate pair, with ALPHAI(j+1) negative. */ /* > */ /* > Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */ /* > may easily over- or underflow, and BETA(j) may even be zero. */ /* > Thus, the user should avoid naively computing the ratio. */ /* > However, ALPHAR and ALPHAI will be always less than and */ /* > usually comparable with norm(A) in magnitude, and BETA always */ /* > less than and usually comparable with norm(B). */ /* > \endverbatim */ /* > */ /* > \param[out] VSL */ /* > \verbatim */ /* > VSL is REAL array, dimension (LDVSL,N) */ /* > If JOBVSL = 'V', VSL will contain the left Schur vectors. */ /* > Not referenced if JOBVSL = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVSL */ /* > \verbatim */ /* > LDVSL is INTEGER */ /* > The leading dimension of the matrix VSL. LDVSL >=1, and */ /* > if JOBVSL = 'V', LDVSL >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] VSR */ /* > \verbatim */ /* > VSR is REAL array, dimension (LDVSR,N) */ /* > If JOBVSR = 'V', VSR will contain the right Schur vectors. */ /* > Not referenced if JOBVSR = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVSR */ /* > \verbatim */ /* > LDVSR is INTEGER */ /* > The leading dimension of the matrix VSR. LDVSR >= 1, and */ /* > if JOBVSR = 'V', LDVSR >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] BWORK */ /* > \verbatim */ /* > BWORK is LOGICAL array, dimension (N) */ /* > Not referenced if SORT = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > = 1,...,N: */ /* > The QZ iteration failed. (A,B) are not in Schur */ /* > form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */ /* > be correct for j=INFO+1,...,N. */ /* > > N: =N+1: other than QZ iteration failed in SHGEQZ. */ /* > =N+2: after reordering, roundoff changed values of */ /* > some complex eigenvalues so that leading */ /* > eigenvalues in the Generalized Schur form no */ /* > longer satisfy SELCTG=.TRUE. This could also */ /* > be caused due to scaling. */ /* > =N+3: reordering failed in STGSEN. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date January 2015 */ /* > \ingroup realGEeigen */ /* ===================================================================== */ /* Subroutine */ int sgges3_(char *jobvsl, char *jobvsr, char *sort, L_fp selctg, integer *n, real *a, integer *lda, real *b, integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *work, integer *lwork, logical *bwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, vsr_dim1, vsr_offset, i__1, i__2; real r__1; /* Local variables */ real anrm, bnrm; integer idum[1], ierr, itau, iwrk; real pvsl, pvsr; integer i__; extern logical lsame_(char *, char *); integer ileft, icols; logical cursl, ilvsl, ilvsr; integer irows; extern /* Subroutine */ int sgghd3_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , real *, integer *, real *, integer *, integer *) ; logical lst2sl; extern /* Subroutine */ int slabad_(real *, real *); integer ip; extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, integer * ), sggbal_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, real *, real *, integer *); logical ilascl, ilbscl; extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real safmax, bignum; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); integer ijobvl, iright; extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *); integer ijobvr; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); real anrmto, bnrmto; logical lastsl; extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real * , real *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), stgsen_(integer *, logical *, logical *, logical *, integer *, real *, integer *, real *, integer *, real *, real *, real *, real *, integer *, real *, integer *, integer *, real *, real *, real *, real *, integer *, integer *, integer *, integer *); real smlnum; extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *); logical wantst, lquery; integer lwkopt; extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *); real dif[2]; integer ihi, ilo; real eps; /* -- LAPACK driver routine (version 3.6.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* January 2015 */ /* ===================================================================== */ /* Decode the input arguments */ /* 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; --alphar; --alphai; --beta; vsl_dim1 = *ldvsl; vsl_offset = 1 + vsl_dim1 * 1; vsl -= vsl_offset; vsr_dim1 = *ldvsr; vsr_offset = 1 + vsr_dim1 * 1; vsr -= vsr_offset; --work; --bwork; /* Function Body */ if (lsame_(jobvsl, "N")) { ijobvl = 1; ilvsl = FALSE_; } else if (lsame_(jobvsl, "V")) { ijobvl = 2; ilvsl = TRUE_; } else { ijobvl = -1; ilvsl = FALSE_; } if (lsame_(jobvsr, "N")) { ijobvr = 1; ilvsr = FALSE_; } else if (lsame_(jobvsr, "V")) { ijobvr = 2; ilvsr = TRUE_; } else { ijobvr = -1; ilvsr = FALSE_; } wantst = lsame_(sort, "S"); /* Test the input arguments */ *info = 0; lquery = *lwork == -1; if (ijobvl <= 0) { *info = -1; } else if (ijobvr <= 0) { *info = -2; } else if (! wantst && ! lsame_(sort, "N")) { *info = -3; } else if (*n < 0) { *info = -5; } else if (*lda < f2cmax(1,*n)) { *info = -7; } else if (*ldb < f2cmax(1,*n)) { *info = -9; } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) { *info = -15; } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) { *info = -17; } else if (*lwork < *n * 6 + 16 && ! lquery) { *info = -19; } /* Compute workspace */ if (*info == 0) { sgeqrf_(n, n, &b[b_offset], ldb, &work[1], &work[1], &c_n1, &ierr); /* Computing MAX */ i__1 = *n * 6 + 16, i__2 = *n * 3 + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); sormqr_("L", "T", n, n, n, &b[b_offset], ldb, &work[1], &a[a_offset], lda, &work[1], &c_n1, &ierr); /* Computing MAX */ i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); if (ilvsl) { sorgqr_(n, n, n, &vsl[vsl_offset], ldvsl, &work[1], &work[1], & c_n1, &ierr); /* Computing MAX */ i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); } sgghd3_(jobvsl, jobvsr, n, &c__1, n, &a[a_offset], lda, &b[b_offset], ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[ 1], &c_n1, &ierr); /* Computing MAX */ i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); shgeqz_("S", jobvsl, jobvsr, n, &c__1, n, &a[a_offset], lda, &b[ b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[ vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[1], &c_n1, &ierr); /* Computing MAX */ i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); if (wantst) { stgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, & b[b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[ vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pvsl, &pvsr, dif, &work[1], &c_n1, idum, &c__1, &ierr); /* Computing MAX */ i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1]; lwkopt = f2cmax(i__1,i__2); } work[1] = (real) lwkopt; } if (*info != 0) { i__1 = -(*info); xerbla_("SGGES3 ", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { *sdim = 0; return 0; } /* Get machine constants */ eps = slamch_("P"); safmin = slamch_("S"); safmax = 1.f / safmin; slabad_(&safmin, &safmax); smlnum = sqrt(safmin) / eps; bignum = 1.f / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]); ilascl = FALSE_; if (anrm > 0.f && anrm < smlnum) { anrmto = smlnum; ilascl = TRUE_; } else if (anrm > bignum) { anrmto = bignum; ilascl = TRUE_; } if (ilascl) { slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, & ierr); } /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */ bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]); ilbscl = FALSE_; if (bnrm > 0.f && bnrm < smlnum) { bnrmto = smlnum; ilbscl = TRUE_; } else if (bnrm > bignum) { bnrmto = bignum; ilbscl = TRUE_; } if (ilbscl) { slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, & ierr); } /* Permute the matrix to make it more nearly triangular */ ileft = 1; iright = *n + 1; iwrk = iright + *n; sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[ ileft], &work[iright], &work[iwrk], &ierr); /* Reduce B to triangular form (QR decomposition of B) */ irows = ihi + 1 - ilo; icols = *n + 1 - ilo; itau = iwrk; iwrk = itau + irows; i__1 = *lwork + 1 - iwrk; sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[ iwrk], &i__1, &ierr); /* Apply the orthogonal transformation to matrix A */ i__1 = *lwork + 1 - iwrk; sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, & work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, & ierr); /* Initialize VSL */ if (ilvsl) { slaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl); if (irows > 1) { i__1 = irows - 1; i__2 = irows - 1; slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ ilo + 1 + ilo * vsl_dim1], ldvsl); } i__1 = *lwork + 1 - iwrk; sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, & work[itau], &work[iwrk], &i__1, &ierr); } /* Initialize VSR */ if (ilvsr) { slaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr); } /* Reduce to generalized Hessenberg form */ i__1 = *lwork + 1 - iwrk; sgghd3_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk] , &i__1, &ierr); /* Perform QZ algorithm, computing Schur vectors if desired */ iwrk = itau; i__1 = *lwork + 1 - iwrk; shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[ b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset] , ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &ierr); if (ierr != 0) { if (ierr > 0 && ierr <= *n) { *info = ierr; } else if (ierr > *n && ierr <= *n << 1) { *info = ierr - *n; } else { *info = *n + 1; } goto L40; } /* Sort eigenvalues ALPHA/BETA if desired */ *sdim = 0; if (wantst) { /* Undo scaling on eigenvalues before SELCTGing */ if (ilascl) { slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &ierr); slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &ierr); } if (ilbscl) { slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &ierr); } /* Select eigenvalues */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]); /* L10: */ } i__1 = *lwork - iwrk + 1; stgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[ vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pvsl, & pvsr, dif, &work[iwrk], &i__1, idum, &c__1, &ierr); if (ierr == 1) { *info = *n + 3; } } /* Apply back-permutation to VSL and VSR */ if (ilvsl) { sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[ vsl_offset], ldvsl, &ierr); } if (ilvsr) { sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[ vsr_offset], ldvsr, &ierr); } /* Check if unscaling would cause over/underflow, if so, rescale */ /* (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */ /* B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */ if (ilascl) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (alphai[i__] != 0.f) { if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[ i__] > anrm / anrmto) { work[1] = (r__1 = a[i__ + i__ * a_dim1] / alphar[i__], abs(r__1)); beta[i__] *= work[1]; alphar[i__] *= work[1]; alphai[i__] *= work[1]; } else if (alphai[i__] / safmax > anrmto / anrm || safmin / alphai[i__] > anrm / anrmto) { work[1] = (r__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[ i__], abs(r__1)); beta[i__] *= work[1]; alphar[i__] *= work[1]; alphai[i__] *= work[1]; } } /* L50: */ } } if (ilbscl) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (alphai[i__] != 0.f) { if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__] > bnrm / bnrmto) { work[1] = (r__1 = b[i__ + i__ * b_dim1] / beta[i__], abs( r__1)); beta[i__] *= work[1]; alphar[i__] *= work[1]; alphai[i__] *= work[1]; } } /* L60: */ } } /* Undo scaling */ if (ilascl) { slascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, & ierr); slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, & ierr); slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, & ierr); } if (ilbscl) { slascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, & ierr); slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, & ierr); } if (wantst) { /* Check if reordering is correct */ lastsl = TRUE_; lst2sl = TRUE_; *sdim = 0; ip = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]); if (alphai[i__] == 0.f) { if (cursl) { ++(*sdim); } ip = 0; if (cursl && ! lastsl) { *info = *n + 2; } } else { if (ip == 1) { /* Last eigenvalue of conjugate pair */ cursl = cursl || lastsl; lastsl = cursl; if (cursl) { *sdim += 2; } ip = -1; if (cursl && ! lst2sl) { *info = *n + 2; } } else { /* First eigenvalue of conjugate pair */ ip = 1; } } lst2sl = lastsl; lastsl = cursl; /* L30: */ } } L40: work[1] = (real) lwkopt; return 0; /* End of SGGES3 */ } /* sgges3_ */