#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 STREVC3 */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download STREVC3 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE STREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, */ /* VR, LDVR, MM, M, WORK, LWORK, INFO ) */ /* CHARACTER HOWMNY, SIDE */ /* INTEGER INFO, LDT, LDVL, LDVR, LWORK, M, MM, N */ /* LOGICAL SELECT( * ) */ /* REAL T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > STREVC3 computes some or all of the right and/or left eigenvectors of */ /* > a real upper quasi-triangular matrix T. */ /* > Matrices of this type are produced by the Schur factorization of */ /* > a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. */ /* > */ /* > The right eigenvector x and the left eigenvector y of T corresponding */ /* > to an eigenvalue w are defined by: */ /* > */ /* > T*x = w*x, (y**T)*T = w*(y**T) */ /* > */ /* > where y**T denotes the transpose of the vector y. */ /* > The eigenvalues are not input to this routine, but are read directly */ /* > from the diagonal blocks of T. */ /* > */ /* > This routine returns the matrices X and/or Y of right and left */ /* > eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */ /* > input matrix. If Q is the orthogonal factor that reduces a matrix */ /* > A to Schur form T, then Q*X and Q*Y are the matrices of right and */ /* > left eigenvectors of A. */ /* > */ /* > This uses a Level 3 BLAS version of the back transformation. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > = 'R': compute right eigenvectors only; */ /* > = 'L': compute left eigenvectors only; */ /* > = 'B': compute both right and left eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] HOWMNY */ /* > \verbatim */ /* > HOWMNY is CHARACTER*1 */ /* > = 'A': compute all right and/or left eigenvectors; */ /* > = 'B': compute all right and/or left eigenvectors, */ /* > backtransformed by the matrices in VR and/or VL; */ /* > = 'S': compute selected right and/or left eigenvectors, */ /* > as indicated by the logical array SELECT. */ /* > \endverbatim */ /* > */ /* > \param[in,out] SELECT */ /* > \verbatim */ /* > SELECT is LOGICAL array, dimension (N) */ /* > If HOWMNY = 'S', SELECT specifies the eigenvectors to be */ /* > computed. */ /* > If w(j) is a real eigenvalue, the corresponding real */ /* > eigenvector is computed if SELECT(j) is .TRUE.. */ /* > If w(j) and w(j+1) are the real and imaginary parts of a */ /* > complex eigenvalue, the corresponding complex eigenvector is */ /* > computed if either SELECT(j) or SELECT(j+1) is .TRUE., and */ /* > on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to */ /* > .FALSE.. */ /* > Not referenced if HOWMNY = 'A' or 'B'. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix T. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] T */ /* > \verbatim */ /* > T is REAL array, dimension (LDT,N) */ /* > The upper quasi-triangular matrix T in Schur canonical form. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] VL */ /* > \verbatim */ /* > VL is REAL array, dimension (LDVL,MM) */ /* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */ /* > contain an N-by-N matrix Q (usually the orthogonal matrix Q */ /* > of Schur vectors returned by SHSEQR). */ /* > On exit, if SIDE = 'L' or 'B', VL contains: */ /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */ /* > if HOWMNY = 'B', the matrix Q*Y; */ /* > if HOWMNY = 'S', the left eigenvectors of T specified by */ /* > SELECT, stored consecutively in the columns */ /* > of VL, in the same order as their */ /* > eigenvalues. */ /* > A complex eigenvector corresponding to a complex eigenvalue */ /* > is stored in two consecutive columns, the first holding the */ /* > real part, and the second the imaginary part. */ /* > Not referenced if SIDE = 'R'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of the array VL. */ /* > LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VR */ /* > \verbatim */ /* > VR is REAL array, dimension (LDVR,MM) */ /* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */ /* > contain an N-by-N matrix Q (usually the orthogonal matrix Q */ /* > of Schur vectors returned by SHSEQR). */ /* > On exit, if SIDE = 'R' or 'B', VR contains: */ /* > if HOWMNY = 'A', the matrix X of right eigenvectors of T; */ /* > if HOWMNY = 'B', the matrix Q*X; */ /* > if HOWMNY = 'S', the right eigenvectors of T specified by */ /* > SELECT, stored consecutively in the columns */ /* > of VR, in the same order as their */ /* > eigenvalues. */ /* > A complex eigenvector corresponding to a complex eigenvalue */ /* > is stored in two consecutive columns, the first holding the */ /* > real part and the second the imaginary part. */ /* > Not referenced if SIDE = 'L'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. */ /* > LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. */ /* > \endverbatim */ /* > */ /* > \param[in] MM */ /* > \verbatim */ /* > MM is INTEGER */ /* > The number of columns in the arrays VL and/or VR. MM >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of columns in the arrays VL and/or VR actually */ /* > used to store the eigenvectors. */ /* > If HOWMNY = 'A' or 'B', M is set to N. */ /* > Each selected real eigenvector occupies one column and each */ /* > selected complex eigenvector occupies two columns. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MAX(1,LWORK)) */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of array WORK. LWORK >= f2cmax(1,3*N). */ /* > For optimum performance, LWORK >= N + 2*N*NB, where NB is */ /* > the optimal blocksize. */ /* > */ /* > 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] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date November 2017 */ /* @generated from dtrevc3.f, fortran d -> s, Tue Apr 19 01:47:44 2016 */ /* > \ingroup realOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The algorithm used in this program is basically backward (forward) */ /* > substitution, with scaling to make the the code robust against */ /* > possible overflow. */ /* > */ /* > Each eigenvector is normalized so that the element of largest */ /* > magnitude has magnitude 1; here the magnitude of a complex number */ /* > (x,y) is taken to be |x| + |y|. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int strevc3_(char *side, char *howmny, logical *select, integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, real *work, integer *lwork, integer *info) { /* System generated locals */ address a__1[2]; integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1[2], i__2, i__3, i__4; real r__1, r__2, r__3, r__4; char ch__1[2]; /* Local variables */ real beta, emax; logical pair, allv; integer ierr; real unfl, ovfl, smin; extern real sdot_(integer *, real *, integer *, real *, integer *); logical over; real vmax; integer jnxt, i__, j, k; real scale, x[4] /* was [2][2] */; extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); real remax; logical leftv; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); logical bothv; real vcrit; logical somev; integer j1, j2; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); real xnorm; extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, real *, integer *); integer iscomplex[128]; extern /* Subroutine */ int slaln2_(logical *, integer *, integer *, real *, real *, real *, integer *, real *, real *, real *, integer *, real *, real *, real *, integer *, real *, real *, integer *); integer nb, ii, ki; extern /* Subroutine */ int slabad_(real *, real *); integer ip, is, iv; real wi; extern real slamch_(char *); real wr; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); real bignum; extern integer isamax_(integer *, real *, integer *); extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); logical rightv; integer ki2, maxwrk; real smlnum; logical lquery; real rec, ulp; /* -- LAPACK computational routine (version 3.8.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2017 */ /* ===================================================================== */ /* Decode and test the input parameters */ /* Parameter adjustments */ --select; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --work; /* Function Body */ bothv = lsame_(side, "B"); rightv = lsame_(side, "R") || bothv; leftv = lsame_(side, "L") || bothv; allv = lsame_(howmny, "A"); over = lsame_(howmny, "B"); somev = lsame_(howmny, "S"); *info = 0; /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = howmny; s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); nb = ilaenv_(&c__1, "STREVC", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)2); maxwrk = *n + (*n << 1) * nb; work[1] = (real) maxwrk; lquery = *lwork == -1; if (! rightv && ! leftv) { *info = -1; } else if (! allv && ! over && ! somev) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*ldt < f2cmax(1,*n)) { *info = -6; } else if (*ldvl < 1 || leftv && *ldvl < *n) { *info = -8; } else if (*ldvr < 1 || rightv && *ldvr < *n) { *info = -10; } else /* if(complicated condition) */ { /* Computing MAX */ i__2 = 1, i__3 = *n * 3; if (*lwork < f2cmax(i__2,i__3) && ! lquery) { *info = -14; } else { /* Set M to the number of columns required to store the selected */ /* eigenvectors, standardize the array SELECT if necessary, and */ /* test MM. */ if (somev) { *m = 0; pair = FALSE_; i__2 = *n; for (j = 1; j <= i__2; ++j) { if (pair) { pair = FALSE_; select[j] = FALSE_; } else { if (j < *n) { if (t[j + 1 + j * t_dim1] == 0.f) { if (select[j]) { ++(*m); } } else { pair = TRUE_; if (select[j] || select[j + 1]) { select[j] = TRUE_; *m += 2; } } } else { if (select[*n]) { ++(*m); } } } /* L10: */ } } else { *m = *n; } if (*mm < *m) { *info = -11; } } } if (*info != 0) { i__2 = -(*info); xerbla_("STREVC3", &i__2, (ftnlen)7); return 0; } else if (lquery) { return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* Use blocked version of back-transformation if sufficient workspace. */ /* Zero-out the workspace to avoid potential NaN propagation. */ if (over && *lwork >= *n + (*n << 4)) { nb = (*lwork - *n) / (*n << 1); nb = f2cmin(nb,128); i__2 = (nb << 1) + 1; slaset_("F", n, &i__2, &c_b17, &c_b17, &work[1], n); } else { nb = 1; } /* Set the constants to control overflow. */ unfl = slamch_("Safe minimum"); ovfl = 1.f / unfl; slabad_(&unfl, &ovfl); ulp = slamch_("Precision"); smlnum = unfl * (*n / ulp); bignum = (1.f - ulp) / smlnum; /* Compute 1-norm of each column of strictly upper triangular */ /* part of T to control overflow in triangular solver. */ work[1] = 0.f; i__2 = *n; for (j = 2; j <= i__2; ++j) { work[j] = 0.f; i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { work[j] += (r__1 = t[i__ + j * t_dim1], abs(r__1)); /* L20: */ } /* L30: */ } /* Index IP is used to specify the real or complex eigenvalue: */ /* IP = 0, real eigenvalue, */ /* 1, first of conjugate complex pair: (wr,wi) */ /* -1, second of conjugate complex pair: (wr,wi) */ /* ISCOMPLEX array stores IP for each column in current block. */ if (rightv) { /* ============================================================ */ /* Compute right eigenvectors. */ /* IV is index of column in current block. */ /* For complex right vector, uses IV-1 for real part and IV for complex part. */ /* Non-blocked version always uses IV=2; */ /* blocked version starts with IV=NB, goes down to 1 or 2. */ /* (Note the "0-th" column is used for 1-norms computed above.) */ iv = 2; if (nb > 2) { iv = nb; } ip = 0; is = *m; for (ki = *n; ki >= 1; --ki) { if (ip == -1) { /* previous iteration (ki+1) was second of conjugate pair, */ /* so this ki is first of conjugate pair; skip to end of loop */ ip = 1; goto L140; } else if (ki == 1) { /* last column, so this ki must be real eigenvalue */ ip = 0; } else if (t[ki + (ki - 1) * t_dim1] == 0.f) { /* zero on sub-diagonal, so this ki is real eigenvalue */ ip = 0; } else { /* non-zero on sub-diagonal, so this ki is second of conjugate pair */ ip = -1; } if (somev) { if (ip == 0) { if (! select[ki]) { goto L140; } } else { if (! select[ki - 1]) { goto L140; } } } /* Compute the KI-th eigenvalue (WR,WI). */ wr = t[ki + ki * t_dim1]; wi = 0.f; if (ip != 0) { wi = sqrt((r__1 = t[ki + (ki - 1) * t_dim1], abs(r__1))) * sqrt((r__2 = t[ki - 1 + ki * t_dim1], abs(r__2))); } /* Computing MAX */ r__1 = ulp * (abs(wr) + abs(wi)); smin = f2cmax(r__1,smlnum); if (ip == 0) { /* -------------------------------------------------------- */ /* Real right eigenvector */ work[ki + iv * *n] = 1.f; /* Form right-hand side. */ i__2 = ki - 1; for (k = 1; k <= i__2; ++k) { work[k + iv * *n] = -t[k + ki * t_dim1]; /* L50: */ } /* Solve upper quasi-triangular system: */ /* [ T(1:KI-1,1:KI-1) - WR ]*X = SCALE*WORK. */ jnxt = ki - 1; for (j = ki - 1; j >= 1; --j) { if (j > jnxt) { goto L60; } j1 = j; j2 = j; jnxt = j - 1; if (j > 1) { if (t[j + (j - 1) * t_dim1] != 0.f) { j1 = j - 1; jnxt = j - 2; } } if (j1 == j2) { /* 1-by-1 diagonal block */ slaln2_(&c_false, &c__1, &c__1, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + iv * *n], n, &wr, &c_b17, x, &c__2, &scale, & xnorm, &ierr); /* Scale X(1,1) to avoid overflow when updating */ /* the right-hand side. */ if (xnorm > 1.f) { if (work[j] > bignum / xnorm) { x[0] /= xnorm; scale /= xnorm; } } /* Scale if necessary */ if (scale != 1.f) { sscal_(&ki, &scale, &work[iv * *n + 1], &c__1); } work[j + iv * *n] = x[0]; /* Update right-hand side */ i__2 = j - 1; r__1 = -x[0]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ iv * *n + 1], &c__1); } else { /* 2-by-2 diagonal block */ slaln2_(&c_false, &c__2, &c__1, &smin, &c_b29, &t[j - 1 + (j - 1) * t_dim1], ldt, &c_b29, &c_b29, & work[j - 1 + iv * *n], n, &wr, &c_b17, x, & c__2, &scale, &xnorm, &ierr); /* Scale X(1,1) and X(2,1) to avoid overflow when */ /* updating the right-hand side. */ if (xnorm > 1.f) { /* Computing MAX */ r__1 = work[j - 1], r__2 = work[j]; beta = f2cmax(r__1,r__2); if (beta > bignum / xnorm) { x[0] /= xnorm; x[1] /= xnorm; scale /= xnorm; } } /* Scale if necessary */ if (scale != 1.f) { sscal_(&ki, &scale, &work[iv * *n + 1], &c__1); } work[j - 1 + iv * *n] = x[0]; work[j + iv * *n] = x[1]; /* Update right-hand side */ i__2 = j - 2; r__1 = -x[0]; saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1, &work[iv * *n + 1], &c__1); i__2 = j - 2; r__1 = -x[1]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ iv * *n + 1], &c__1); } L60: ; } /* Copy the vector x or Q*x to VR and normalize. */ if (! over) { /* ------------------------------ */ /* no back-transform: copy x to VR and normalize. */ scopy_(&ki, &work[iv * *n + 1], &c__1, &vr[is * vr_dim1 + 1], &c__1); ii = isamax_(&ki, &vr[is * vr_dim1 + 1], &c__1); remax = 1.f / (r__1 = vr[ii + is * vr_dim1], abs(r__1)); sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1); i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { vr[k + is * vr_dim1] = 0.f; /* L70: */ } } else if (nb == 1) { /* ------------------------------ */ /* version 1: back-transform each vector with GEMV, Q*x. */ if (ki > 1) { i__2 = ki - 1; sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, & work[iv * *n + 1], &c__1, &work[ki + iv * *n], &vr[ki * vr_dim1 + 1], &c__1); } ii = isamax_(n, &vr[ki * vr_dim1 + 1], &c__1); remax = 1.f / (r__1 = vr[ii + ki * vr_dim1], abs(r__1)); sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1); } else { /* ------------------------------ */ /* version 2: back-transform block of vectors with GEMM */ /* zero out below vector */ i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { work[k + iv * *n] = 0.f; } iscomplex[iv - 1] = ip; /* back-transform and normalization is done below */ } } else { /* -------------------------------------------------------- */ /* Complex right eigenvector. */ /* Initial solve */ /* [ ( T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I*WI) ]*X = 0. */ /* [ ( T(KI, KI-1) T(KI, KI) ) ] */ if ((r__1 = t[ki - 1 + ki * t_dim1], abs(r__1)) >= (r__2 = t[ ki + (ki - 1) * t_dim1], abs(r__2))) { work[ki - 1 + (iv - 1) * *n] = 1.f; work[ki + iv * *n] = wi / t[ki - 1 + ki * t_dim1]; } else { work[ki - 1 + (iv - 1) * *n] = -wi / t[ki + (ki - 1) * t_dim1]; work[ki + iv * *n] = 1.f; } work[ki + (iv - 1) * *n] = 0.f; work[ki - 1 + iv * *n] = 0.f; /* Form right-hand side. */ i__2 = ki - 2; for (k = 1; k <= i__2; ++k) { work[k + (iv - 1) * *n] = -work[ki - 1 + (iv - 1) * *n] * t[k + (ki - 1) * t_dim1]; work[k + iv * *n] = -work[ki + iv * *n] * t[k + ki * t_dim1]; /* L80: */ } /* Solve upper quasi-triangular system: */ /* [ T(1:KI-2,1:KI-2) - (WR+i*WI) ]*X = SCALE*(WORK+i*WORK2) */ jnxt = ki - 2; for (j = ki - 2; j >= 1; --j) { if (j > jnxt) { goto L90; } j1 = j; j2 = j; jnxt = j - 1; if (j > 1) { if (t[j + (j - 1) * t_dim1] != 0.f) { j1 = j - 1; jnxt = j - 2; } } if (j1 == j2) { /* 1-by-1 diagonal block */ slaln2_(&c_false, &c__1, &c__2, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + ( iv - 1) * *n], n, &wr, &wi, x, &c__2, &scale, &xnorm, &ierr); /* Scale X(1,1) and X(1,2) to avoid overflow when */ /* updating the right-hand side. */ if (xnorm > 1.f) { if (work[j] > bignum / xnorm) { x[0] /= xnorm; x[2] /= xnorm; scale /= xnorm; } } /* Scale if necessary */ if (scale != 1.f) { sscal_(&ki, &scale, &work[(iv - 1) * *n + 1], & c__1); sscal_(&ki, &scale, &work[iv * *n + 1], &c__1); } work[j + (iv - 1) * *n] = x[0]; work[j + iv * *n] = x[2]; /* Update the right-hand side */ i__2 = j - 1; r__1 = -x[0]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ (iv - 1) * *n + 1], &c__1); i__2 = j - 1; r__1 = -x[2]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ iv * *n + 1], &c__1); } else { /* 2-by-2 diagonal block */ slaln2_(&c_false, &c__2, &c__2, &smin, &c_b29, &t[j - 1 + (j - 1) * t_dim1], ldt, &c_b29, &c_b29, & work[j - 1 + (iv - 1) * *n], n, &wr, &wi, x, & c__2, &scale, &xnorm, &ierr); /* Scale X to avoid overflow when updating */ /* the right-hand side. */ if (xnorm > 1.f) { /* Computing MAX */ r__1 = work[j - 1], r__2 = work[j]; beta = f2cmax(r__1,r__2); if (beta > bignum / xnorm) { rec = 1.f / xnorm; x[0] *= rec; x[2] *= rec; x[1] *= rec; x[3] *= rec; scale *= rec; } } /* Scale if necessary */ if (scale != 1.f) { sscal_(&ki, &scale, &work[(iv - 1) * *n + 1], & c__1); sscal_(&ki, &scale, &work[iv * *n + 1], &c__1); } work[j - 1 + (iv - 1) * *n] = x[0]; work[j + (iv - 1) * *n] = x[1]; work[j - 1 + iv * *n] = x[2]; work[j + iv * *n] = x[3]; /* Update the right-hand side */ i__2 = j - 2; r__1 = -x[0]; saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1, &work[(iv - 1) * *n + 1], &c__1); i__2 = j - 2; r__1 = -x[1]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ (iv - 1) * *n + 1], &c__1); i__2 = j - 2; r__1 = -x[2]; saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1, &work[iv * *n + 1], &c__1); i__2 = j - 2; r__1 = -x[3]; saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[ iv * *n + 1], &c__1); } L90: ; } /* Copy the vector x or Q*x to VR and normalize. */ if (! over) { /* ------------------------------ */ /* no back-transform: copy x to VR and normalize. */ scopy_(&ki, &work[(iv - 1) * *n + 1], &c__1, &vr[(is - 1) * vr_dim1 + 1], &c__1); scopy_(&ki, &work[iv * *n + 1], &c__1, &vr[is * vr_dim1 + 1], &c__1); emax = 0.f; i__2 = ki; for (k = 1; k <= i__2; ++k) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = vr[k + (is - 1) * vr_dim1] , abs(r__1)) + (r__2 = vr[k + is * vr_dim1], abs(r__2)); emax = f2cmax(r__3,r__4); /* L100: */ } remax = 1.f / emax; sscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1); sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1); i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { vr[k + (is - 1) * vr_dim1] = 0.f; vr[k + is * vr_dim1] = 0.f; /* L110: */ } } else if (nb == 1) { /* ------------------------------ */ /* version 1: back-transform each vector with GEMV, Q*x. */ if (ki > 2) { i__2 = ki - 2; sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, & work[(iv - 1) * *n + 1], &c__1, &work[ki - 1 + (iv - 1) * *n], &vr[(ki - 1) * vr_dim1 + 1], &c__1); i__2 = ki - 2; sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, & work[iv * *n + 1], &c__1, &work[ki + iv * *n], &vr[ki * vr_dim1 + 1], &c__1); } else { sscal_(n, &work[ki - 1 + (iv - 1) * *n], &vr[(ki - 1) * vr_dim1 + 1], &c__1); sscal_(n, &work[ki + iv * *n], &vr[ki * vr_dim1 + 1], &c__1); } emax = 0.f; i__2 = *n; for (k = 1; k <= i__2; ++k) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = vr[k + (ki - 1) * vr_dim1] , abs(r__1)) + (r__2 = vr[k + ki * vr_dim1], abs(r__2)); emax = f2cmax(r__3,r__4); /* L120: */ } remax = 1.f / emax; sscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1); sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1); } else { /* ------------------------------ */ /* version 2: back-transform block of vectors with GEMM */ /* zero out below vector */ i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { work[k + (iv - 1) * *n] = 0.f; work[k + iv * *n] = 0.f; } iscomplex[iv - 2] = -ip; iscomplex[iv - 1] = ip; --iv; /* back-transform and normalization is done below */ } } if (nb > 1) { /* -------------------------------------------------------- */ /* Blocked version of back-transform */ /* For complex case, KI2 includes both vectors (KI-1 and KI) */ if (ip == 0) { ki2 = ki; } else { ki2 = ki - 1; } /* Columns IV:NB of work are valid vectors. */ /* When the number of vectors stored reaches NB-1 or NB, */ /* or if this was last vector, do the GEMM */ if (iv <= 2 || ki2 == 1) { i__2 = nb - iv + 1; i__3 = ki2 + nb - iv; sgemm_("N", "N", n, &i__2, &i__3, &c_b29, &vr[vr_offset], ldvr, &work[iv * *n + 1], n, &c_b17, &work[(nb + iv) * *n + 1], n); /* normalize vectors */ i__2 = nb; for (k = iv; k <= i__2; ++k) { if (iscomplex[k - 1] == 0) { /* real eigenvector */ ii = isamax_(n, &work[(nb + k) * *n + 1], &c__1); remax = 1.f / (r__1 = work[ii + (nb + k) * *n], abs(r__1)); } else if (iscomplex[k - 1] == 1) { /* first eigenvector of conjugate pair */ emax = 0.f; i__3 = *n; for (ii = 1; ii <= i__3; ++ii) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = work[ii + (nb + k) * *n], abs(r__1)) + (r__2 = work[ii + (nb + k + 1) * *n], abs(r__2)); emax = f2cmax(r__3,r__4); } remax = 1.f / emax; /* else if ISCOMPLEX(K).EQ.-1 */ /* second eigenvector of conjugate pair */ /* reuse same REMAX as previous K */ } sscal_(n, &remax, &work[(nb + k) * *n + 1], &c__1); } i__2 = nb - iv + 1; slacpy_("F", n, &i__2, &work[(nb + iv) * *n + 1], n, &vr[ ki2 * vr_dim1 + 1], ldvr); iv = nb; } else { --iv; } } /* blocked back-transform */ --is; if (ip != 0) { --is; } L140: ; } } if (leftv) { /* ============================================================ */ /* Compute left eigenvectors. */ /* IV is index of column in current block. */ /* For complex left vector, uses IV for real part and IV+1 for complex part. */ /* Non-blocked version always uses IV=1; */ /* blocked version starts with IV=1, goes up to NB-1 or NB. */ /* (Note the "0-th" column is used for 1-norms computed above.) */ iv = 1; ip = 0; is = 1; i__2 = *n; for (ki = 1; ki <= i__2; ++ki) { if (ip == 1) { /* previous iteration (ki-1) was first of conjugate pair, */ /* so this ki is second of conjugate pair; skip to end of loop */ ip = -1; goto L260; } else if (ki == *n) { /* last column, so this ki must be real eigenvalue */ ip = 0; } else if (t[ki + 1 + ki * t_dim1] == 0.f) { /* zero on sub-diagonal, so this ki is real eigenvalue */ ip = 0; } else { /* non-zero on sub-diagonal, so this ki is first of conjugate pair */ ip = 1; } if (somev) { if (! select[ki]) { goto L260; } } /* Compute the KI-th eigenvalue (WR,WI). */ wr = t[ki + ki * t_dim1]; wi = 0.f; if (ip != 0) { wi = sqrt((r__1 = t[ki + (ki + 1) * t_dim1], abs(r__1))) * sqrt((r__2 = t[ki + 1 + ki * t_dim1], abs(r__2))); } /* Computing MAX */ r__1 = ulp * (abs(wr) + abs(wi)); smin = f2cmax(r__1,smlnum); if (ip == 0) { /* -------------------------------------------------------- */ /* Real left eigenvector */ work[ki + iv * *n] = 1.f; /* Form right-hand side. */ i__3 = *n; for (k = ki + 1; k <= i__3; ++k) { work[k + iv * *n] = -t[ki + k * t_dim1]; /* L160: */ } /* Solve transposed quasi-triangular system: */ /* [ T(KI+1:N,KI+1:N) - WR ]**T * X = SCALE*WORK */ vmax = 1.f; vcrit = bignum; jnxt = ki + 1; i__3 = *n; for (j = ki + 1; j <= i__3; ++j) { if (j < jnxt) { goto L170; } j1 = j; j2 = j; jnxt = j + 1; if (j < *n) { if (t[j + 1 + j * t_dim1] != 0.f) { j2 = j + 1; jnxt = j + 2; } } if (j1 == j2) { /* 1-by-1 diagonal block */ /* Scale if necessary to avoid overflow when forming */ /* the right-hand side. */ if (work[j] > vcrit) { rec = 1.f / vmax; i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1); vmax = 1.f; vcrit = bignum; } i__4 = j - ki - 1; work[j + iv * *n] -= sdot_(&i__4, &t[ki + 1 + j * t_dim1], &c__1, &work[ki + 1 + iv * *n], & c__1); /* Solve [ T(J,J) - WR ]**T * X = WORK */ slaln2_(&c_false, &c__1, &c__1, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + iv * *n], n, &wr, &c_b17, x, &c__2, &scale, & xnorm, &ierr); /* Scale if necessary */ if (scale != 1.f) { i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1); } work[j + iv * *n] = x[0]; /* Computing MAX */ r__2 = (r__1 = work[j + iv * *n], abs(r__1)); vmax = f2cmax(r__2,vmax); vcrit = bignum / vmax; } else { /* 2-by-2 diagonal block */ /* Scale if necessary to avoid overflow when forming */ /* the right-hand side. */ /* Computing MAX */ r__1 = work[j], r__2 = work[j + 1]; beta = f2cmax(r__1,r__2); if (beta > vcrit) { rec = 1.f / vmax; i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1); vmax = 1.f; vcrit = bignum; } i__4 = j - ki - 1; work[j + iv * *n] -= sdot_(&i__4, &t[ki + 1 + j * t_dim1], &c__1, &work[ki + 1 + iv * *n], & c__1); i__4 = j - ki - 1; work[j + 1 + iv * *n] -= sdot_(&i__4, &t[ki + 1 + (j + 1) * t_dim1], &c__1, &work[ki + 1 + iv * *n] , &c__1); /* Solve */ /* [ T(J,J)-WR T(J,J+1) ]**T * X = SCALE*( WORK1 ) */ /* [ T(J+1,J) T(J+1,J+1)-WR ] ( WORK2 ) */ slaln2_(&c_true, &c__2, &c__1, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + iv * *n], n, &wr, &c_b17, x, &c__2, &scale, & xnorm, &ierr); /* Scale if necessary */ if (scale != 1.f) { i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1); } work[j + iv * *n] = x[0]; work[j + 1 + iv * *n] = x[1]; /* Computing MAX */ r__3 = (r__1 = work[j + iv * *n], abs(r__1)), r__4 = ( r__2 = work[j + 1 + iv * *n], abs(r__2)), r__3 = f2cmax(r__3,r__4); vmax = f2cmax(r__3,vmax); vcrit = bignum / vmax; } L170: ; } /* Copy the vector x or Q*x to VL and normalize. */ if (! over) { /* ------------------------------ */ /* no back-transform: copy x to VL and normalize. */ i__3 = *n - ki + 1; scopy_(&i__3, &work[ki + iv * *n], &c__1, &vl[ki + is * vl_dim1], &c__1); i__3 = *n - ki + 1; ii = isamax_(&i__3, &vl[ki + is * vl_dim1], &c__1) + ki - 1; remax = 1.f / (r__1 = vl[ii + is * vl_dim1], abs(r__1)); i__3 = *n - ki + 1; sscal_(&i__3, &remax, &vl[ki + is * vl_dim1], &c__1); i__3 = ki - 1; for (k = 1; k <= i__3; ++k) { vl[k + is * vl_dim1] = 0.f; /* L180: */ } } else if (nb == 1) { /* ------------------------------ */ /* version 1: back-transform each vector with GEMV, Q*x. */ if (ki < *n) { i__3 = *n - ki; sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 1) * vl_dim1 + 1], ldvl, &work[ki + 1 + iv * *n], &c__1, & work[ki + iv * *n], &vl[ki * vl_dim1 + 1], & c__1); } ii = isamax_(n, &vl[ki * vl_dim1 + 1], &c__1); remax = 1.f / (r__1 = vl[ii + ki * vl_dim1], abs(r__1)); sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1); } else { /* ------------------------------ */ /* version 2: back-transform block of vectors with GEMM */ /* zero out above vector */ /* could go from KI-NV+1 to KI-1 */ i__3 = ki - 1; for (k = 1; k <= i__3; ++k) { work[k + iv * *n] = 0.f; } iscomplex[iv - 1] = ip; /* back-transform and normalization is done below */ } } else { /* -------------------------------------------------------- */ /* Complex left eigenvector. */ /* Initial solve: */ /* [ ( T(KI,KI) T(KI,KI+1) )**T - (WR - I* WI) ]*X = 0. */ /* [ ( T(KI+1,KI) T(KI+1,KI+1) ) ] */ if ((r__1 = t[ki + (ki + 1) * t_dim1], abs(r__1)) >= (r__2 = t[ki + 1 + ki * t_dim1], abs(r__2))) { work[ki + iv * *n] = wi / t[ki + (ki + 1) * t_dim1]; work[ki + 1 + (iv + 1) * *n] = 1.f; } else { work[ki + iv * *n] = 1.f; work[ki + 1 + (iv + 1) * *n] = -wi / t[ki + 1 + ki * t_dim1]; } work[ki + 1 + iv * *n] = 0.f; work[ki + (iv + 1) * *n] = 0.f; /* Form right-hand side. */ i__3 = *n; for (k = ki + 2; k <= i__3; ++k) { work[k + iv * *n] = -work[ki + iv * *n] * t[ki + k * t_dim1]; work[k + (iv + 1) * *n] = -work[ki + 1 + (iv + 1) * *n] * t[ki + 1 + k * t_dim1]; /* L190: */ } /* Solve transposed quasi-triangular system: */ /* [ T(KI+2:N,KI+2:N)**T - (WR-i*WI) ]*X = WORK1+i*WORK2 */ vmax = 1.f; vcrit = bignum; jnxt = ki + 2; i__3 = *n; for (j = ki + 2; j <= i__3; ++j) { if (j < jnxt) { goto L200; } j1 = j; j2 = j; jnxt = j + 1; if (j < *n) { if (t[j + 1 + j * t_dim1] != 0.f) { j2 = j + 1; jnxt = j + 2; } } if (j1 == j2) { /* 1-by-1 diagonal block */ /* Scale if necessary to avoid overflow when */ /* forming the right-hand side elements. */ if (work[j] > vcrit) { rec = 1.f / vmax; i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1); i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + (iv + 1) * *n], & c__1); vmax = 1.f; vcrit = bignum; } i__4 = j - ki - 2; work[j + iv * *n] -= sdot_(&i__4, &t[ki + 2 + j * t_dim1], &c__1, &work[ki + 2 + iv * *n], & c__1); i__4 = j - ki - 2; work[j + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2 + j * t_dim1], &c__1, &work[ki + 2 + (iv + 1) * * n], &c__1); /* Solve [ T(J,J)-(WR-i*WI) ]*(X11+i*X12)= WK+I*WK2 */ r__1 = -wi; slaln2_(&c_false, &c__1, &c__2, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + iv * *n], n, &wr, &r__1, x, &c__2, &scale, & xnorm, &ierr); /* Scale if necessary */ if (scale != 1.f) { i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1); i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + (iv + 1) * *n], & c__1); } work[j + iv * *n] = x[0]; work[j + (iv + 1) * *n] = x[2]; /* Computing MAX */ r__3 = (r__1 = work[j + iv * *n], abs(r__1)), r__4 = ( r__2 = work[j + (iv + 1) * *n], abs(r__2)), r__3 = f2cmax(r__3,r__4); vmax = f2cmax(r__3,vmax); vcrit = bignum / vmax; } else { /* 2-by-2 diagonal block */ /* Scale if necessary to avoid overflow when forming */ /* the right-hand side elements. */ /* Computing MAX */ r__1 = work[j], r__2 = work[j + 1]; beta = f2cmax(r__1,r__2); if (beta > vcrit) { rec = 1.f / vmax; i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1); i__4 = *n - ki + 1; sscal_(&i__4, &rec, &work[ki + (iv + 1) * *n], & c__1); vmax = 1.f; vcrit = bignum; } i__4 = j - ki - 2; work[j + iv * *n] -= sdot_(&i__4, &t[ki + 2 + j * t_dim1], &c__1, &work[ki + 2 + iv * *n], & c__1); i__4 = j - ki - 2; work[j + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2 + j * t_dim1], &c__1, &work[ki + 2 + (iv + 1) * * n], &c__1); i__4 = j - ki - 2; work[j + 1 + iv * *n] -= sdot_(&i__4, &t[ki + 2 + (j + 1) * t_dim1], &c__1, &work[ki + 2 + iv * *n] , &c__1); i__4 = j - ki - 2; work[j + 1 + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2 + (j + 1) * t_dim1], &c__1, &work[ki + 2 + ( iv + 1) * *n], &c__1); /* Solve 2-by-2 complex linear equation */ /* [ (T(j,j) T(j,j+1) )**T - (wr-i*wi)*I ]*X = SCALE*B */ /* [ (T(j+1,j) T(j+1,j+1)) ] */ r__1 = -wi; slaln2_(&c_true, &c__2, &c__2, &smin, &c_b29, &t[j + j * t_dim1], ldt, &c_b29, &c_b29, &work[j + iv * *n], n, &wr, &r__1, x, &c__2, &scale, & xnorm, &ierr); /* Scale if necessary */ if (scale != 1.f) { i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1); i__4 = *n - ki + 1; sscal_(&i__4, &scale, &work[ki + (iv + 1) * *n], & c__1); } work[j + iv * *n] = x[0]; work[j + (iv + 1) * *n] = x[2]; work[j + 1 + iv * *n] = x[1]; work[j + 1 + (iv + 1) * *n] = x[3]; /* Computing MAX */ r__1 = abs(x[0]), r__2 = abs(x[2]), r__1 = f2cmax(r__1, r__2), r__2 = abs(x[1]), r__1 = f2cmax(r__1,r__2) , r__2 = abs(x[3]), r__1 = f2cmax(r__1,r__2); vmax = f2cmax(r__1,vmax); vcrit = bignum / vmax; } L200: ; } /* Copy the vector x or Q*x to VL and normalize. */ if (! over) { /* ------------------------------ */ /* no back-transform: copy x to VL and normalize. */ i__3 = *n - ki + 1; scopy_(&i__3, &work[ki + iv * *n], &c__1, &vl[ki + is * vl_dim1], &c__1); i__3 = *n - ki + 1; scopy_(&i__3, &work[ki + (iv + 1) * *n], &c__1, &vl[ki + ( is + 1) * vl_dim1], &c__1); emax = 0.f; i__3 = *n; for (k = ki; k <= i__3; ++k) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = vl[k + is * vl_dim1], abs( r__1)) + (r__2 = vl[k + (is + 1) * vl_dim1], abs(r__2)); emax = f2cmax(r__3,r__4); /* L220: */ } remax = 1.f / emax; i__3 = *n - ki + 1; sscal_(&i__3, &remax, &vl[ki + is * vl_dim1], &c__1); i__3 = *n - ki + 1; sscal_(&i__3, &remax, &vl[ki + (is + 1) * vl_dim1], &c__1) ; i__3 = ki - 1; for (k = 1; k <= i__3; ++k) { vl[k + is * vl_dim1] = 0.f; vl[k + (is + 1) * vl_dim1] = 0.f; /* L230: */ } } else if (nb == 1) { /* ------------------------------ */ /* version 1: back-transform each vector with GEMV, Q*x. */ if (ki < *n - 1) { i__3 = *n - ki - 1; sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 2) * vl_dim1 + 1], ldvl, &work[ki + 2 + iv * *n], &c__1, & work[ki + iv * *n], &vl[ki * vl_dim1 + 1], & c__1); i__3 = *n - ki - 1; sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 2) * vl_dim1 + 1], ldvl, &work[ki + 2 + (iv + 1) * *n], & c__1, &work[ki + 1 + (iv + 1) * *n], &vl[(ki + 1) * vl_dim1 + 1], &c__1); } else { sscal_(n, &work[ki + iv * *n], &vl[ki * vl_dim1 + 1], &c__1); sscal_(n, &work[ki + 1 + (iv + 1) * *n], &vl[(ki + 1) * vl_dim1 + 1], &c__1); } emax = 0.f; i__3 = *n; for (k = 1; k <= i__3; ++k) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = vl[k + ki * vl_dim1], abs( r__1)) + (r__2 = vl[k + (ki + 1) * vl_dim1], abs(r__2)); emax = f2cmax(r__3,r__4); /* L240: */ } remax = 1.f / emax; sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1); sscal_(n, &remax, &vl[(ki + 1) * vl_dim1 + 1], &c__1); } else { /* ------------------------------ */ /* version 2: back-transform block of vectors with GEMM */ /* zero out above vector */ /* could go from KI-NV+1 to KI-1 */ i__3 = ki - 1; for (k = 1; k <= i__3; ++k) { work[k + iv * *n] = 0.f; work[k + (iv + 1) * *n] = 0.f; } iscomplex[iv - 1] = ip; iscomplex[iv] = -ip; ++iv; /* back-transform and normalization is done below */ } } if (nb > 1) { /* -------------------------------------------------------- */ /* Blocked version of back-transform */ /* For complex case, KI2 includes both vectors (KI and KI+1) */ if (ip == 0) { ki2 = ki; } else { ki2 = ki + 1; } /* Columns 1:IV of work are valid vectors. */ /* When the number of vectors stored reaches NB-1 or NB, */ /* or if this was last vector, do the GEMM */ if (iv >= nb - 1 || ki2 == *n) { i__3 = *n - ki2 + iv; sgemm_("N", "N", n, &iv, &i__3, &c_b29, &vl[(ki2 - iv + 1) * vl_dim1 + 1], ldvl, &work[ki2 - iv + 1 + *n], n, &c_b17, &work[(nb + 1) * *n + 1], n); /* normalize vectors */ i__3 = iv; for (k = 1; k <= i__3; ++k) { if (iscomplex[k - 1] == 0) { /* real eigenvector */ ii = isamax_(n, &work[(nb + k) * *n + 1], &c__1); remax = 1.f / (r__1 = work[ii + (nb + k) * *n], abs(r__1)); } else if (iscomplex[k - 1] == 1) { /* first eigenvector of conjugate pair */ emax = 0.f; i__4 = *n; for (ii = 1; ii <= i__4; ++ii) { /* Computing MAX */ r__3 = emax, r__4 = (r__1 = work[ii + (nb + k) * *n], abs(r__1)) + (r__2 = work[ii + (nb + k + 1) * *n], abs(r__2)); emax = f2cmax(r__3,r__4); } remax = 1.f / emax; /* else if ISCOMPLEX(K).EQ.-1 */ /* second eigenvector of conjugate pair */ /* reuse same REMAX as previous K */ } sscal_(n, &remax, &work[(nb + k) * *n + 1], &c__1); } slacpy_("F", n, &iv, &work[(nb + 1) * *n + 1], n, &vl[( ki2 - iv + 1) * vl_dim1 + 1], ldvl); iv = 1; } else { ++iv; } } /* blocked back-transform */ ++is; if (ip != 0) { ++is; } L260: ; } } return 0; /* End of STREVC3 */ } /* strevc3_ */