|
- #include <math.h>
- #include <stdlib.h>
- #include <string.h>
- #include <stdio.h>
- #include <complex.h>
- #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]/Cd(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i]) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i]) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- /* -- translated by f2c (version 20000121).
- You must link the resulting object file with the libraries:
- -lf2c -lm (in that order)
- */
-
-
-
-
- /* Table of constant values */
-
- static doublecomplex c_b1 = {0.,0.};
- static doublecomplex c_b2 = {1.,0.};
- static integer c__1 = 1;
-
- /* > \brief \b ZTGEVC */
-
- /* =========== DOCUMENTATION =========== */
-
- /* Online html documentation available at */
- /* http://www.netlib.org/lapack/explore-html/ */
-
- /* > \htmlonly */
- /* > Download ZTGEVC + dependencies */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgevc.
- f"> */
- /* > [TGZ]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgevc.
- f"> */
- /* > [ZIP]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgevc.
- f"> */
- /* > [TXT]</a> */
- /* > \endhtmlonly */
-
- /* Definition: */
- /* =========== */
-
- /* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */
- /* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) */
-
- /* CHARACTER HOWMNY, SIDE */
- /* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */
- /* LOGICAL SELECT( * ) */
- /* DOUBLE PRECISION RWORK( * ) */
- /* COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */
- /* $ VR( LDVR, * ), WORK( * ) */
-
-
-
- /* > \par Purpose: */
- /* ============= */
- /* > */
- /* > \verbatim */
- /* > */
- /* > ZTGEVC computes some or all of the right and/or left eigenvectors of */
- /* > a pair of complex matrices (S,P), where S and P are upper triangular. */
- /* > Matrix pairs of this type are produced by the generalized Schur */
- /* > factorization of a complex matrix pair (A,B): */
- /* > */
- /* > A = Q*S*Z**H, B = Q*P*Z**H */
- /* > */
- /* > as computed by ZGGHRD + ZHGEQZ. */
- /* > */
- /* > The right eigenvector x and the left eigenvector y of (S,P) */
- /* > corresponding to an eigenvalue w are defined by: */
- /* > */
- /* > S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
- /* > */
- /* > where y**H denotes the conjugate tranpose of y. */
- /* > The eigenvalues are not input to this routine, but are computed */
- /* > directly from the diagonal elements of S and P. */
- /* > */
- /* > This routine returns the matrices X and/or Y of right and left */
- /* > eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
- /* > where Z and Q are input matrices. */
- /* > If Q and Z are the unitary factors from the generalized Schur */
- /* > factorization of a matrix pair (A,B), then Z*X and Q*Y */
- /* > are the matrices of right and left eigenvectors of (A,B). */
- /* > \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, */
- /* > specified by the logical array SELECT. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] SELECT */
- /* > \verbatim */
- /* > SELECT is LOGICAL array, dimension (N) */
- /* > If HOWMNY='S', SELECT specifies the eigenvectors to be */
- /* > computed. The eigenvector corresponding to the j-th */
- /* > eigenvalue is computed if SELECT(j) = .TRUE.. */
- /* > Not referenced if HOWMNY = 'A' or 'B'. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] N */
- /* > \verbatim */
- /* > N is INTEGER */
- /* > The order of the matrices S and P. N >= 0. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] S */
- /* > \verbatim */
- /* > S is COMPLEX*16 array, dimension (LDS,N) */
- /* > The upper triangular matrix S from a generalized Schur */
- /* > factorization, as computed by ZHGEQZ. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDS */
- /* > \verbatim */
- /* > LDS is INTEGER */
- /* > The leading dimension of array S. LDS >= f2cmax(1,N). */
- /* > \endverbatim */
- /* > */
- /* > \param[in] P */
- /* > \verbatim */
- /* > P is COMPLEX*16 array, dimension (LDP,N) */
- /* > The upper triangular matrix P from a generalized Schur */
- /* > factorization, as computed by ZHGEQZ. P must have real */
- /* > diagonal elements. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDP */
- /* > \verbatim */
- /* > LDP is INTEGER */
- /* > The leading dimension of array P. LDP >= f2cmax(1,N). */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] VL */
- /* > \verbatim */
- /* > VL is COMPLEX*16 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 unitary matrix Q */
- /* > of left Schur vectors returned by ZHGEQZ). */
- /* > On exit, if SIDE = 'L' or 'B', VL contains: */
- /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
- /* > if HOWMNY = 'B', the matrix Q*Y; */
- /* > if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
- /* > SELECT, stored consecutively in the columns of */
- /* > VL, in the same order as their eigenvalues. */
- /* > Not referenced if SIDE = 'R'. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDVL */
- /* > \verbatim */
- /* > LDVL is INTEGER */
- /* > The leading dimension of array VL. LDVL >= 1, and if */
- /* > SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] VR */
- /* > \verbatim */
- /* > VR is COMPLEX*16 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 unitary matrix Z */
- /* > of right Schur vectors returned by ZHGEQZ). */
- /* > On exit, if SIDE = 'R' or 'B', VR contains: */
- /* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
- /* > if HOWMNY = 'B', the matrix Z*X; */
- /* > if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
- /* > SELECT, stored consecutively in the columns of */
- /* > VR, in the same order as their eigenvalues. */
- /* > 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 eigenvector occupies one column. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] WORK */
- /* > \verbatim */
- /* > WORK is COMPLEX*16 array, dimension (2*N) */
- /* > \endverbatim */
- /* > */
- /* > \param[out] RWORK */
- /* > \verbatim */
- /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
- /* > \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 December 2016 */
-
- /* > \ingroup complex16GEcomputational */
-
- /* ===================================================================== */
- /* Subroutine */ void ztgevc_(char *side, char *howmny, logical *select,
- integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer
- *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
- ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork,
- integer *info)
- {
- /* System generated locals */
- integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
- vr_offset, i__1, i__2, i__3, i__4, i__5;
- doublereal d__1, d__2, d__3, d__4, d__5, d__6;
- doublecomplex z__1, z__2, z__3, z__4;
-
- /* Local variables */
- integer ibeg, ieig, iend;
- doublereal dmin__;
- integer isrc;
- doublereal temp;
- doublecomplex suma, sumb;
- doublereal xmax;
- doublecomplex d__;
- integer i__, j;
- doublereal scale;
- logical ilall;
- integer iside;
- doublereal sbeta;
- extern logical lsame_(char *, char *);
- doublereal small;
- logical compl;
- doublereal anorm, bnorm;
- logical compr;
- extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
- doublecomplex *, doublecomplex *, integer *, doublecomplex *,
- integer *, doublecomplex *, doublecomplex *, integer *);
- doublecomplex ca, cb;
- extern /* Subroutine */ void dlabad_(doublereal *, doublereal *);
- logical ilbbad;
- doublereal acoefa;
- integer je;
- doublereal bcoefa, acoeff;
- doublecomplex bcoeff;
- logical ilback;
- integer im;
- doublereal ascale, bscale;
- extern doublereal dlamch_(char *);
- integer jr;
- doublecomplex salpha;
- doublereal safmin;
- extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
- doublereal bignum;
- logical ilcomp;
- extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
- doublecomplex *);
- integer ihwmny;
- doublereal big;
- logical lsa, lsb;
- doublereal ulp;
- doublecomplex sum;
-
-
- /* -- LAPACK computational 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 */
-
-
-
- /* ===================================================================== */
-
-
- /* Decode and Test the input parameters */
-
- /* Parameter adjustments */
- --select;
- s_dim1 = *lds;
- s_offset = 1 + s_dim1 * 1;
- s -= s_offset;
- p_dim1 = *ldp;
- p_offset = 1 + p_dim1 * 1;
- p -= p_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;
- --rwork;
-
- /* Function Body */
- if (lsame_(howmny, "A")) {
- ihwmny = 1;
- ilall = TRUE_;
- ilback = FALSE_;
- } else if (lsame_(howmny, "S")) {
- ihwmny = 2;
- ilall = FALSE_;
- ilback = FALSE_;
- } else if (lsame_(howmny, "B")) {
- ihwmny = 3;
- ilall = TRUE_;
- ilback = TRUE_;
- } else {
- ihwmny = -1;
- }
-
- if (lsame_(side, "R")) {
- iside = 1;
- compl = FALSE_;
- compr = TRUE_;
- } else if (lsame_(side, "L")) {
- iside = 2;
- compl = TRUE_;
- compr = FALSE_;
- } else if (lsame_(side, "B")) {
- iside = 3;
- compl = TRUE_;
- compr = TRUE_;
- } else {
- iside = -1;
- }
-
- *info = 0;
- if (iside < 0) {
- *info = -1;
- } else if (ihwmny < 0) {
- *info = -2;
- } else if (*n < 0) {
- *info = -4;
- } else if (*lds < f2cmax(1,*n)) {
- *info = -6;
- } else if (*ldp < f2cmax(1,*n)) {
- *info = -8;
- }
- if (*info != 0) {
- i__1 = -(*info);
- xerbla_("ZTGEVC", &i__1, (ftnlen)6);
- return;
- }
-
- /* Count the number of eigenvectors */
-
- if (! ilall) {
- im = 0;
- i__1 = *n;
- for (j = 1; j <= i__1; ++j) {
- if (select[j]) {
- ++im;
- }
- /* L10: */
- }
- } else {
- im = *n;
- }
-
- /* Check diagonal of B */
-
- ilbbad = FALSE_;
- i__1 = *n;
- for (j = 1; j <= i__1; ++j) {
- if (d_imag(&p[j + j * p_dim1]) != 0.) {
- ilbbad = TRUE_;
- }
- /* L20: */
- }
-
- if (ilbbad) {
- *info = -7;
- } else if (compl && *ldvl < *n || *ldvl < 1) {
- *info = -10;
- } else if (compr && *ldvr < *n || *ldvr < 1) {
- *info = -12;
- } else if (*mm < im) {
- *info = -13;
- }
- if (*info != 0) {
- i__1 = -(*info);
- xerbla_("ZTGEVC", &i__1, (ftnlen)6);
- return;
- }
-
- /* Quick return if possible */
-
- *m = im;
- if (*n == 0) {
- return;
- }
-
- /* Machine Constants */
-
- safmin = dlamch_("Safe minimum");
- big = 1. / safmin;
- dlabad_(&safmin, &big);
- ulp = dlamch_("Epsilon") * dlamch_("Base");
- small = safmin * *n / ulp;
- big = 1. / small;
- bignum = 1. / (safmin * *n);
-
- /* Compute the 1-norm of each column of the strictly upper triangular */
- /* part of A and B to check for possible overflow in the triangular */
- /* solver. */
-
- i__1 = s_dim1 + 1;
- anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]),
- abs(d__2));
- i__1 = p_dim1 + 1;
- bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]),
- abs(d__2));
- rwork[1] = 0.;
- rwork[*n + 1] = 0.;
- i__1 = *n;
- for (j = 2; j <= i__1; ++j) {
- rwork[j] = 0.;
- rwork[*n + j] = 0.;
- i__2 = j - 1;
- for (i__ = 1; i__ <= i__2; ++i__) {
- i__3 = i__ + j * s_dim1;
- rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__
- + j * s_dim1]), abs(d__2));
- i__3 = i__ + j * p_dim1;
- rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(&
- p[i__ + j * p_dim1]), abs(d__2));
- /* L30: */
- }
- /* Computing MAX */
- i__2 = j + j * s_dim1;
- d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + (
- d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2)));
- anorm = f2cmax(d__3,d__4);
- /* Computing MAX */
- i__2 = j + j * p_dim1;
- d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) +
- (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2)));
- bnorm = f2cmax(d__3,d__4);
- /* L40: */
- }
-
- ascale = 1. / f2cmax(anorm,safmin);
- bscale = 1. / f2cmax(bnorm,safmin);
-
- /* Left eigenvectors */
-
- if (compl) {
- ieig = 0;
-
- /* Main loop over eigenvalues */
-
- i__1 = *n;
- for (je = 1; je <= i__1; ++je) {
- if (ilall) {
- ilcomp = TRUE_;
- } else {
- ilcomp = select[je];
- }
- if (ilcomp) {
- ++ieig;
-
- i__2 = je + je * s_dim1;
- i__3 = je + je * p_dim1;
- if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
- * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r,
- abs(d__1)) <= safmin) {
-
- /* Singular matrix pencil -- return unit eigenvector */
-
- i__2 = *n;
- for (jr = 1; jr <= i__2; ++jr) {
- i__3 = jr + ieig * vl_dim1;
- vl[i__3].r = 0., vl[i__3].i = 0.;
- /* L50: */
- }
- i__2 = ieig + ieig * vl_dim1;
- vl[i__2].r = 1., vl[i__2].i = 0.;
- goto L140;
- }
-
- /* Non-singular eigenvalue: */
- /* Compute coefficients a and b in */
- /* H */
- /* y ( a A - b B ) = 0 */
-
- /* Computing MAX */
- i__2 = je + je * s_dim1;
- i__3 = je + je * p_dim1;
- d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je
- + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
- p[i__3].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
- temp = 1. / f2cmax(d__4,safmin);
- i__2 = je + je * s_dim1;
- z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i;
- z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
- salpha.r = z__1.r, salpha.i = z__1.i;
- i__2 = je + je * p_dim1;
- sbeta = temp * p[i__2].r * bscale;
- acoeff = sbeta * ascale;
- z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
-
- /* Scale to avoid underflow */
-
- lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
- lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
- abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
- + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
-
- scale = 1.;
- if (lsa) {
- scale = small / abs(sbeta) * f2cmin(anorm,big);
- }
- if (lsb) {
- /* Computing MAX */
- d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
- + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
- bnorm,big);
- scale = f2cmax(d__3,d__4);
- }
- if (lsa || lsb) {
- /* Computing MIN */
- /* Computing MAX */
- d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
- d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
- d_imag(&bcoeff), abs(d__2));
- d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
- scale = f2cmin(d__3,d__4);
- if (lsa) {
- acoeff = ascale * (scale * sbeta);
- } else {
- acoeff = scale * acoeff;
- }
- if (lsb) {
- z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
- z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
- } else {
- z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
- }
- }
-
- acoefa = abs(acoeff);
- bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
- bcoeff), abs(d__2));
- xmax = 1.;
- i__2 = *n;
- for (jr = 1; jr <= i__2; ++jr) {
- i__3 = jr;
- work[i__3].r = 0., work[i__3].i = 0.;
- /* L60: */
- }
- i__2 = je;
- work[i__2].r = 1., work[i__2].i = 0.;
- /* Computing MAX */
- d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
- d__1 = f2cmax(d__1,d__2);
- dmin__ = f2cmax(d__1,safmin);
-
- /* H */
- /* Triangular solve of (a A - b B) y = 0 */
-
- /* H */
- /* (rowwise in (a A - b B) , or columnwise in a A - b B) */
-
- i__2 = *n;
- for (j = je + 1; j <= i__2; ++j) {
-
- /* Compute */
- /* j-1 */
- /* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
- /* k=je */
- /* (Scale if necessary) */
-
- temp = 1. / xmax;
- if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum *
- temp) {
- i__3 = j - 1;
- for (jr = je; jr <= i__3; ++jr) {
- i__4 = jr;
- i__5 = jr;
- z__1.r = temp * work[i__5].r, z__1.i = temp *
- work[i__5].i;
- work[i__4].r = z__1.r, work[i__4].i = z__1.i;
- /* L70: */
- }
- xmax = 1.;
- }
- suma.r = 0., suma.i = 0.;
- sumb.r = 0., sumb.i = 0.;
-
- i__3 = j - 1;
- for (jr = je; jr <= i__3; ++jr) {
- d_cnjg(&z__3, &s[jr + j * s_dim1]);
- i__4 = jr;
- z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
- .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
- work[i__4].r;
- z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i;
- suma.r = z__1.r, suma.i = z__1.i;
- d_cnjg(&z__3, &p[jr + j * p_dim1]);
- i__4 = jr;
- z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
- .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
- work[i__4].r;
- z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i;
- sumb.r = z__1.r, sumb.i = z__1.i;
- /* L80: */
- }
- z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i;
- d_cnjg(&z__4, &bcoeff);
- z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i =
- z__4.r * sumb.i + z__4.i * sumb.r;
- z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
- sum.r = z__1.r, sum.i = z__1.i;
-
- /* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
-
- /* with scaling and perturbation of the denominator */
-
- i__3 = j + j * s_dim1;
- z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i;
- i__4 = j + j * p_dim1;
- z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
- z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
- .r;
- z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
- d_cnjg(&z__1, &z__2);
- d__.r = z__1.r, d__.i = z__1.i;
- if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
- d__2)) <= dmin__) {
- z__1.r = dmin__, z__1.i = 0.;
- d__.r = z__1.r, d__.i = z__1.i;
- }
-
- if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
- d__2)) < 1.) {
- if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum),
- abs(d__2)) >= bignum * ((d__3 = d__.r, abs(
- d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) {
- temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 =
- d_imag(&sum), abs(d__2)));
- i__3 = j - 1;
- for (jr = je; jr <= i__3; ++jr) {
- i__4 = jr;
- i__5 = jr;
- z__1.r = temp * work[i__5].r, z__1.i = temp *
- work[i__5].i;
- work[i__4].r = z__1.r, work[i__4].i = z__1.i;
- /* L90: */
- }
- xmax = temp * xmax;
- z__1.r = temp * sum.r, z__1.i = temp * sum.i;
- sum.r = z__1.r, sum.i = z__1.i;
- }
- }
- i__3 = j;
- z__2.r = -sum.r, z__2.i = -sum.i;
- zladiv_(&z__1, &z__2, &d__);
- work[i__3].r = z__1.r, work[i__3].i = z__1.i;
- /* Computing MAX */
- i__3 = j;
- d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
- d__2 = d_imag(&work[j]), abs(d__2));
- xmax = f2cmax(d__3,d__4);
- /* L100: */
- }
-
- /* Back transform eigenvector if HOWMNY='B'. */
-
- if (ilback) {
- i__2 = *n + 1 - je;
- zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl,
- &work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
- isrc = 2;
- ibeg = 1;
- } else {
- isrc = 1;
- ibeg = je;
- }
-
- /* Copy and scale eigenvector into column of VL */
-
- xmax = 0.;
- i__2 = *n;
- for (jr = ibeg; jr <= i__2; ++jr) {
- /* Computing MAX */
- i__3 = (isrc - 1) * *n + jr;
- d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
- d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
- d__2));
- xmax = f2cmax(d__3,d__4);
- /* L110: */
- }
-
- if (xmax > safmin) {
- temp = 1. / xmax;
- i__2 = *n;
- for (jr = ibeg; jr <= i__2; ++jr) {
- i__3 = jr + ieig * vl_dim1;
- i__4 = (isrc - 1) * *n + jr;
- z__1.r = temp * work[i__4].r, z__1.i = temp * work[
- i__4].i;
- vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
- /* L120: */
- }
- } else {
- ibeg = *n + 1;
- }
-
- i__2 = ibeg - 1;
- for (jr = 1; jr <= i__2; ++jr) {
- i__3 = jr + ieig * vl_dim1;
- vl[i__3].r = 0., vl[i__3].i = 0.;
- /* L130: */
- }
-
- }
- L140:
- ;
- }
- }
-
- /* Right eigenvectors */
-
- if (compr) {
- ieig = im + 1;
-
- /* Main loop over eigenvalues */
-
- for (je = *n; je >= 1; --je) {
- if (ilall) {
- ilcomp = TRUE_;
- } else {
- ilcomp = select[je];
- }
- if (ilcomp) {
- --ieig;
-
- i__1 = je + je * s_dim1;
- i__2 = je + je * p_dim1;
- if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
- * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r,
- abs(d__1)) <= safmin) {
-
- /* Singular matrix pencil -- return unit eigenvector */
-
- i__1 = *n;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr + ieig * vr_dim1;
- vr[i__2].r = 0., vr[i__2].i = 0.;
- /* L150: */
- }
- i__1 = ieig + ieig * vr_dim1;
- vr[i__1].r = 1., vr[i__1].i = 0.;
- goto L250;
- }
-
- /* Non-singular eigenvalue: */
- /* Compute coefficients a and b in */
-
- /* ( a A - b B ) x = 0 */
-
- /* Computing MAX */
- i__1 = je + je * s_dim1;
- i__2 = je + je * p_dim1;
- d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je
- + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
- p[i__2].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
- temp = 1. / f2cmax(d__4,safmin);
- i__1 = je + je * s_dim1;
- z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i;
- z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
- salpha.r = z__1.r, salpha.i = z__1.i;
- i__1 = je + je * p_dim1;
- sbeta = temp * p[i__1].r * bscale;
- acoeff = sbeta * ascale;
- z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
-
- /* Scale to avoid underflow */
-
- lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
- lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
- abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
- + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
-
- scale = 1.;
- if (lsa) {
- scale = small / abs(sbeta) * f2cmin(anorm,big);
- }
- if (lsb) {
- /* Computing MAX */
- d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
- + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
- bnorm,big);
- scale = f2cmax(d__3,d__4);
- }
- if (lsa || lsb) {
- /* Computing MIN */
- /* Computing MAX */
- d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
- d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
- d_imag(&bcoeff), abs(d__2));
- d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
- scale = f2cmin(d__3,d__4);
- if (lsa) {
- acoeff = ascale * (scale * sbeta);
- } else {
- acoeff = scale * acoeff;
- }
- if (lsb) {
- z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
- z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
- } else {
- z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
- bcoeff.r = z__1.r, bcoeff.i = z__1.i;
- }
- }
-
- acoefa = abs(acoeff);
- bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
- bcoeff), abs(d__2));
- xmax = 1.;
- i__1 = *n;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr;
- work[i__2].r = 0., work[i__2].i = 0.;
- /* L160: */
- }
- i__1 = je;
- work[i__1].r = 1., work[i__1].i = 0.;
- /* Computing MAX */
- d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
- d__1 = f2cmax(d__1,d__2);
- dmin__ = f2cmax(d__1,safmin);
-
- /* Triangular solve of (a A - b B) x = 0 (columnwise) */
-
- /* WORK(1:j-1) contains sums w, */
- /* WORK(j+1:JE) contains x */
-
- i__1 = je - 1;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr;
- i__3 = jr + je * s_dim1;
- z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i;
- i__4 = jr + je * p_dim1;
- z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
- z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
- .r;
- z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
- work[i__2].r = z__1.r, work[i__2].i = z__1.i;
- /* L170: */
- }
- i__1 = je;
- work[i__1].r = 1., work[i__1].i = 0.;
-
- for (j = je - 1; j >= 1; --j) {
-
- /* Form x(j) := - w(j) / d */
- /* with scaling and perturbation of the denominator */
-
- i__1 = j + j * s_dim1;
- z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i;
- i__2 = j + j * p_dim1;
- z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i,
- z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
- .r;
- z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
- d__.r = z__1.r, d__.i = z__1.i;
- if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
- d__2)) <= dmin__) {
- z__1.r = dmin__, z__1.i = 0.;
- d__.r = z__1.r, d__.i = z__1.i;
- }
-
- if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
- d__2)) < 1.) {
- i__1 = j;
- if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
- &work[j]), abs(d__2)) >= bignum * ((d__3 =
- d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
- d__4)))) {
- i__1 = j;
- temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
- d__2 = d_imag(&work[j]), abs(d__2)));
- i__1 = je;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr;
- i__3 = jr;
- z__1.r = temp * work[i__3].r, z__1.i = temp *
- work[i__3].i;
- work[i__2].r = z__1.r, work[i__2].i = z__1.i;
- /* L180: */
- }
- }
- }
-
- i__1 = j;
- i__2 = j;
- z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
- zladiv_(&z__1, &z__2, &d__);
- work[i__1].r = z__1.r, work[i__1].i = z__1.i;
-
- if (j > 1) {
-
- /* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
-
- i__1 = j;
- if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
- &work[j]), abs(d__2)) > 1.) {
- i__1 = j;
- temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
- d__2 = d_imag(&work[j]), abs(d__2)));
- if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >=
- bignum * temp) {
- i__1 = je;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr;
- i__3 = jr;
- z__1.r = temp * work[i__3].r, z__1.i =
- temp * work[i__3].i;
- work[i__2].r = z__1.r, work[i__2].i =
- z__1.i;
- /* L190: */
- }
- }
- }
-
- i__1 = j;
- z__1.r = acoeff * work[i__1].r, z__1.i = acoeff *
- work[i__1].i;
- ca.r = z__1.r, ca.i = z__1.i;
- i__1 = j;
- z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
- i__1].i, z__1.i = bcoeff.r * work[i__1].i +
- bcoeff.i * work[i__1].r;
- cb.r = z__1.r, cb.i = z__1.i;
- i__1 = j - 1;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr;
- i__3 = jr;
- i__4 = jr + j * s_dim1;
- z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i,
- z__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
- .r;
- z__2.r = work[i__3].r + z__3.r, z__2.i = work[
- i__3].i + z__3.i;
- i__5 = jr + j * p_dim1;
- z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i,
- z__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
- .r;
- z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
- z__4.i;
- work[i__2].r = z__1.r, work[i__2].i = z__1.i;
- /* L200: */
- }
- }
- /* L210: */
- }
-
- /* Back transform eigenvector if HOWMNY='B'. */
-
- if (ilback) {
- zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
- &c__1, &c_b1, &work[*n + 1], &c__1);
- isrc = 2;
- iend = *n;
- } else {
- isrc = 1;
- iend = je;
- }
-
- /* Copy and scale eigenvector into column of VR */
-
- xmax = 0.;
- i__1 = iend;
- for (jr = 1; jr <= i__1; ++jr) {
- /* Computing MAX */
- i__2 = (isrc - 1) * *n + jr;
- d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
- d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
- d__2));
- xmax = f2cmax(d__3,d__4);
- /* L220: */
- }
-
- if (xmax > safmin) {
- temp = 1. / xmax;
- i__1 = iend;
- for (jr = 1; jr <= i__1; ++jr) {
- i__2 = jr + ieig * vr_dim1;
- i__3 = (isrc - 1) * *n + jr;
- z__1.r = temp * work[i__3].r, z__1.i = temp * work[
- i__3].i;
- vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
- /* L230: */
- }
- } else {
- iend = 0;
- }
-
- i__1 = *n;
- for (jr = iend + 1; jr <= i__1; ++jr) {
- i__2 = jr + ieig * vr_dim1;
- vr[i__2].r = 0., vr[i__2].i = 0.;
- /* L240: */
- }
-
- }
- L250:
- ;
- }
- }
-
- return;
-
- /* End of ZTGEVC */
-
- } /* ztgevc_ */
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