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OpenBLAS/lapack-netlib/SRC/dtgsen.c

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#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 blasint logical;
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++ */
#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 integer c__1 = 1;
static integer c__2 = 2;
static doublereal c_b28 = 1.;
/* > \brief \b DTGSEN */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DTGSEN + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsen.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsen.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsen.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB, */
/* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL, */
/* PR, DIF, WORK, LWORK, IWORK, LIWORK, INFO ) */
/* LOGICAL WANTQ, WANTZ */
/* INTEGER IJOB, INFO, LDA, LDB, LDQ, LDZ, LIWORK, LWORK, */
/* $ M, N */
/* DOUBLE PRECISION PL, PR */
/* LOGICAL SELECT( * ) */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/* $ B( LDB, * ), BETA( * ), DIF( * ), Q( LDQ, * ), */
/* $ WORK( * ), Z( LDZ, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DTGSEN reorders the generalized real Schur decomposition of a real */
/* > matrix pair (A, B) (in terms of an orthonormal equivalence trans- */
/* > formation Q**T * (A, B) * Z), so that a selected cluster of eigenvalues */
/* > appears in the leading diagonal blocks of the upper quasi-triangular */
/* > matrix A and the upper triangular B. The leading columns of Q and */
/* > Z form orthonormal bases of the corresponding left and right eigen- */
/* > spaces (deflating subspaces). (A, B) must be in generalized real */
/* > Schur canonical form (as returned by DGGES), i.e. A is block upper */
/* > triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper */
/* > triangular. */
/* > */
/* > DTGSEN also computes the generalized eigenvalues */
/* > */
/* > w(j) = (ALPHAR(j) + i*ALPHAI(j))/BETA(j) */
/* > */
/* > of the reordered matrix pair (A, B). */
/* > */
/* > Optionally, DTGSEN computes the estimates of reciprocal condition */
/* > numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11), */
/* > (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) */
/* > between the matrix pairs (A11, B11) and (A22,B22) that correspond to */
/* > the selected cluster and the eigenvalues outside the cluster, resp., */
/* > and norms of "projections" onto left and right eigenspaces w.r.t. */
/* > the selected cluster in the (1,1)-block. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] IJOB */
/* > \verbatim */
/* > IJOB is INTEGER */
/* > Specifies whether condition numbers are required for the */
/* > cluster of eigenvalues (PL and PR) or the deflating subspaces */
/* > (Difu and Difl): */
/* > =0: Only reorder w.r.t. SELECT. No extras. */
/* > =1: Reciprocal of norms of "projections" onto left and right */
/* > eigenspaces w.r.t. the selected cluster (PL and PR). */
/* > =2: Upper bounds on Difu and Difl. F-norm-based estimate */
/* > (DIF(1:2)). */
/* > =3: Estimate of Difu and Difl. 1-norm-based estimate */
/* > (DIF(1:2)). */
/* > About 5 times as expensive as IJOB = 2. */
/* > =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic */
/* > version to get it all. */
/* > =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above) */
/* > \endverbatim */
/* > */
/* > \param[in] WANTQ */
/* > \verbatim */
/* > WANTQ is LOGICAL */
/* > .TRUE. : update the left transformation matrix Q; */
/* > .FALSE.: do not update Q. */
/* > \endverbatim */
/* > */
/* > \param[in] WANTZ */
/* > \verbatim */
/* > WANTZ is LOGICAL */
/* > .TRUE. : update the right transformation matrix Z; */
/* > .FALSE.: do not update Z. */
/* > \endverbatim */
/* > */
/* > \param[in] SELECT */
/* > \verbatim */
/* > SELECT is LOGICAL array, dimension (N) */
/* > SELECT specifies the eigenvalues in the selected cluster. */
/* > To select a real eigenvalue w(j), SELECT(j) must be set to */
/* > .TRUE.. To select a complex conjugate pair of eigenvalues */
/* > w(j) and w(j+1), corresponding to a 2-by-2 diagonal block, */
/* > either SELECT(j) or SELECT(j+1) or both must be set to */
/* > .TRUE.; a complex conjugate pair of eigenvalues must be */
/* > either both included in the cluster or both excluded. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension(LDA,N) */
/* > On entry, the upper quasi-triangular matrix A, with (A, B) in */
/* > generalized real Schur canonical form. */
/* > On exit, A is overwritten by the reordered matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is DOUBLE PRECISION array, dimension(LDB,N) */
/* > On entry, the upper triangular matrix B, with (A, B) in */
/* > generalized real Schur canonical form. */
/* > On exit, B is overwritten by the reordered matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAR */
/* > \verbatim */
/* > ALPHAR is DOUBLE PRECISION array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAI */
/* > \verbatim */
/* > ALPHAI is DOUBLE PRECISION array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* > BETA is DOUBLE PRECISION 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 generalized Schur form of (A,B) were further reduced */
/* > to triangular form using 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. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* > On entry, if WANTQ = .TRUE., Q is an N-by-N matrix. */
/* > On exit, Q has been postmultiplied by the left orthogonal */
/* > transformation matrix which reorder (A, B); The leading M */
/* > columns of Q form orthonormal bases for the specified pair of */
/* > left eigenspaces (deflating subspaces). */
/* > If WANTQ = .FALSE., Q is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* > LDQ is INTEGER */
/* > The leading dimension of the array Q. LDQ >= 1; */
/* > and if WANTQ = .TRUE., LDQ >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */
/* > On entry, if WANTZ = .TRUE., Z is an N-by-N matrix. */
/* > On exit, Z has been postmultiplied by the left orthogonal */
/* > transformation matrix which reorder (A, B); The leading M */
/* > columns of Z form orthonormal bases for the specified pair of */
/* > left eigenspaces (deflating subspaces). */
/* > If WANTZ = .FALSE., Z is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* > LDZ is INTEGER */
/* > The leading dimension of the array Z. LDZ >= 1; */
/* > If WANTZ = .TRUE., LDZ >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The dimension of the specified pair of left and right eigen- */
/* > spaces (deflating subspaces). 0 <= M <= N. */
/* > \endverbatim */
/* > */
/* > \param[out] PL */
/* > \verbatim */
/* > PL is DOUBLE PRECISION */
/* > \endverbatim */
/* > */
/* > \param[out] PR */
/* > \verbatim */
/* > PR is DOUBLE PRECISION */
/* > */
/* > If IJOB = 1, 4 or 5, PL, PR are lower bounds on the */
/* > reciprocal of the norm of "projections" onto left and right */
/* > eigenspaces with respect to the selected cluster. */
/* > 0 < PL, PR <= 1. */
/* > If M = 0 or M = N, PL = PR = 1. */
/* > If IJOB = 0, 2 or 3, PL and PR are not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] DIF */
/* > \verbatim */
/* > DIF is DOUBLE PRECISION array, dimension (2). */
/* > If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl. */
/* > If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on */
/* > Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based */
/* > estimates of Difu and Difl. */
/* > If M = 0 or N, DIF(1:2) = F-norm([A, B]). */
/* > If IJOB = 0 or 1, DIF is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION 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. LWORK >= 4*N+16. */
/* > If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)). */
/* > If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*M*(N-M)). */
/* > */
/* > 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] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* > LIWORK is INTEGER */
/* > The dimension of the array IWORK. LIWORK >= 1. */
/* > If IJOB = 1, 2 or 4, LIWORK >= N+6. */
/* > If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6). */
/* > */
/* > If LIWORK = -1, then a workspace query is assumed; the */
/* > routine only calculates the optimal size of the IWORK array, */
/* > returns this value as the first entry of the IWORK array, and */
/* > no error message related to LIWORK 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. */
/* > =1: Reordering of (A, B) failed because the transformed */
/* > matrix pair (A, B) would be too far from generalized */
/* > Schur form; the problem is very ill-conditioned. */
/* > (A, B) may have been partially reordered. */
/* > If requested, 0 is returned in DIF(*), PL and PR. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup doubleOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > DTGSEN first collects the selected eigenvalues by computing */
/* > orthogonal U and W that move them to the top left corner of (A, B). */
/* > In other words, the selected eigenvalues are the eigenvalues of */
/* > (A11, B11) in: */
/* > */
/* > U**T*(A, B)*W = (A11 A12) (B11 B12) n1 */
/* > ( 0 A22),( 0 B22) n2 */
/* > n1 n2 n1 n2 */
/* > */
/* > where N = n1+n2 and U**T means the transpose of U. The first n1 columns */
/* > of U and W span the specified pair of left and right eigenspaces */
/* > (deflating subspaces) of (A, B). */
/* > */
/* > If (A, B) has been obtained from the generalized real Schur */
/* > decomposition of a matrix pair (C, D) = Q*(A, B)*Z**T, then the */
/* > reordered generalized real Schur form of (C, D) is given by */
/* > */
/* > (C, D) = (Q*U)*(U**T*(A, B)*W)*(Z*W)**T, */
/* > */
/* > and the first n1 columns of Q*U and Z*W span the corresponding */
/* > deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.). */
/* > */
/* > Note that if the selected eigenvalue is sufficiently ill-conditioned, */
/* > then its value may differ significantly from its value before */
/* > reordering. */
/* > */
/* > The reciprocal condition numbers of the left and right eigenspaces */
/* > spanned by the first n1 columns of U and W (or Q*U and Z*W) may */
/* > be returned in DIF(1:2), corresponding to Difu and Difl, resp. */
/* > */
/* > The Difu and Difl are defined as: */
/* > */
/* > Difu[(A11, B11), (A22, B22)] = sigma-f2cmin( Zu ) */
/* > and */
/* > Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)], */
/* > */
/* > where sigma-f2cmin(Zu) is the smallest singular value of the */
/* > (2*n1*n2)-by-(2*n1*n2) matrix */
/* > */
/* > Zu = [ kron(In2, A11) -kron(A22**T, In1) ] */
/* > [ kron(In2, B11) -kron(B22**T, In1) ]. */
/* > */
/* > Here, Inx is the identity matrix of size nx and A22**T is the */
/* > transpose of A22. kron(X, Y) is the Kronecker product between */
/* > the matrices X and Y. */
/* > */
/* > When DIF(2) is small, small changes in (A, B) can cause large changes */
/* > in the deflating subspace. An approximate (asymptotic) bound on the */
/* > maximum angular error in the computed deflating subspaces is */
/* > */
/* > EPS * norm((A, B)) / DIF(2), */
/* > */
/* > where EPS is the machine precision. */
/* > */
/* > The reciprocal norm of the projectors on the left and right */
/* > eigenspaces associated with (A11, B11) may be returned in PL and PR. */
/* > They are computed as follows. First we compute L and R so that */
/* > P*(A, B)*Q is block diagonal, where */
/* > */
/* > P = ( I -L ) n1 Q = ( I R ) n1 */
/* > ( 0 I ) n2 and ( 0 I ) n2 */
/* > n1 n2 n1 n2 */
/* > */
/* > and (L, R) is the solution to the generalized Sylvester equation */
/* > */
/* > A11*R - L*A22 = -A12 */
/* > B11*R - L*B22 = -B12 */
/* > */
/* > Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2). */
/* > An approximate (asymptotic) bound on the average absolute error of */
/* > the selected eigenvalues is */
/* > */
/* > EPS * norm((A, B)) / PL. */
/* > */
/* > There are also global error bounds which valid for perturbations up */
/* > to a certain restriction: A lower bound (x) on the smallest */
/* > F-norm(E,F) for which an eigenvalue of (A11, B11) may move and */
/* > coalesce with an eigenvalue of (A22, B22) under perturbation (E,F), */
/* > (i.e. (A + E, B + F), is */
/* > */
/* > x = f2cmin(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*f2cmax(1/PL,1/PR)). */
/* > */
/* > An approximate bound on x can be computed from DIF(1:2), PL and PR. */
/* > */
/* > If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed */
/* > (L', R') and unperturbed (L, R) left and right deflating subspaces */
/* > associated with the selected cluster in the (1,1)-blocks can be */
/* > bounded as */
/* > */
/* > f2cmax-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2)) */
/* > f2cmax-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2)) */
/* > */
/* > See LAPACK User's Guide section 4.11 or the following references */
/* > for more information. */
/* > */
/* > Note that if the default method for computing the Frobenius-norm- */
/* > based estimate DIF is not wanted (see DLATDF), then the parameter */
/* > IDIFJB (see below) should be changed from 3 to 4 (routine DLATDF */
/* > (IJOB = 2 will be used)). See DTGSYL for more details. */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* > Umea University, S-901 87 Umea, Sweden. */
/* > \par References: */
/* ================ */
/* > */
/* > \verbatim */
/* > */
/* > [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/* > Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/* > M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/* > Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
/* > */
/* > [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/* > Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/* > Estimation: Theory, Algorithms and Software, */
/* > Report UMINF - 94.04, Department of Computing Science, Umea */
/* > University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
/* > Note 87. To appear in Numerical Algorithms, 1996. */
/* > */
/* > [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/* > for Solving the Generalized Sylvester Equation and Estimating the */
/* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/* > Department of Computing Science, Umea University, S-901 87 Umea, */
/* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, */
/* > 1996. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void dtgsen_(integer *ijob, logical *wantq, logical *wantz,
logical *select, integer *n, doublereal *a, integer *lda, doublereal *
b, integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz,
integer *m, doublereal *pl, doublereal *pr, doublereal *dif,
doublereal *work, integer *lwork, integer *iwork, integer *liwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
z_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
integer kase;
logical pair;
integer ierr;
doublereal dsum;
logical swap;
extern /* Subroutine */ void dlag2_(doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
integer i__, k, isave[3];
logical wantd;
integer lwmin;
logical wantp;
integer n1, n2;
extern /* Subroutine */ void dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
logical wantd1, wantd2;
integer kk;
extern doublereal dlamch_(char *);
doublereal dscale;
integer ks;
doublereal rdscal;
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern void dtgexc_(logical *, logical *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, integer *, integer *), dlassq_(integer *,
doublereal *, integer *, doublereal *, doublereal *);
integer liwmin;
extern /* Subroutine */ void dtgsyl_(char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *);
doublereal smlnum;
integer mn2;
logical lquery;
integer ijb;
doublereal eps;
/* -- LAPACK computational routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* Decode and test the input parameters */
/* Parameter adjustments */
--select;
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;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--dif;
--work;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1 || *liwork == -1;
if (*ijob < 0 || *ijob > 5) {
*info = -1;
} else if (*n < 0) {
*info = -5;
} else if (*lda < f2cmax(1,*n)) {
*info = -7;
} else if (*ldb < f2cmax(1,*n)) {
*info = -9;
} else if (*ldq < 1 || *wantq && *ldq < *n) {
*info = -14;
} else if (*ldz < 1 || *wantz && *ldz < *n) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTGSEN", &i__1, (ftnlen)6);
return;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
ierr = 0;
wantp = *ijob == 1 || *ijob >= 4;
wantd1 = *ijob == 2 || *ijob == 4;
wantd2 = *ijob == 3 || *ijob == 5;
wantd = wantd1 || wantd2;
/* Set M to the dimension of the specified pair of deflating */
/* subspaces. */
*m = 0;
pair = FALSE_;
if (! lquery || *ijob != 0) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
if (k < *n) {
if (a[k + 1 + k * a_dim1] == 0.) {
if (select[k]) {
++(*m);
}
} else {
pair = TRUE_;
if (select[k] || select[k + 1]) {
*m += 2;
}
}
} else {
if (select[*n]) {
++(*m);
}
}
}
/* L10: */
}
}
if (*ijob == 1 || *ijob == 2 || *ijob == 4) {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16, i__1 = f2cmax(i__1,i__2), i__2 = (*m <<
1) * (*n - *m);
lwmin = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n + 6;
liwmin = f2cmax(i__1,i__2);
} else if (*ijob == 3 || *ijob == 5) {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16, i__1 = f2cmax(i__1,i__2), i__2 = (*m <<
2) * (*n - *m);
lwmin = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = f2cmax(i__1,i__2), i__2 =
*n + 6;
liwmin = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 2) + 16;
lwmin = f2cmax(i__1,i__2);
liwmin = 1;
}
work[1] = (doublereal) lwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -22;
} else if (*liwork < liwmin && ! lquery) {
*info = -24;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTGSEN", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible. */
if (*m == *n || *m == 0) {
if (wantp) {
*pl = 1.;
*pr = 1.;
}
if (wantd) {
dscale = 0.;
dsum = 1.;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dlassq_(n, &a[i__ * a_dim1 + 1], &c__1, &dscale, &dsum);
dlassq_(n, &b[i__ * b_dim1 + 1], &c__1, &dscale, &dsum);
/* L20: */
}
dif[1] = dscale * sqrt(dsum);
dif[2] = dif[1];
}
goto L60;
}
/* Collect the selected blocks at the top-left corner of (A, B). */
ks = 0;
pair = FALSE_;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
swap = select[k];
if (k < *n) {
if (a[k + 1 + k * a_dim1] != 0.) {
pair = TRUE_;
swap = swap || select[k + 1];
}
}
if (swap) {
++ks;
/* Swap the K-th block to position KS. */
/* Perform the reordering of diagonal blocks in (A, B) */
/* by orthogonal transformation matrices and update */
/* Q and Z accordingly (if requested): */
kk = k;
if (k != ks) {
dtgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &kk,
&ks, &work[1], lwork, &ierr);
}
if (ierr > 0) {
/* Swap is rejected: exit. */
*info = 1;
if (wantp) {
*pl = 0.;
*pr = 0.;
}
if (wantd) {
dif[1] = 0.;
dif[2] = 0.;
}
goto L60;
}
if (pair) {
++ks;
}
}
}
/* L30: */
}
if (wantp) {
/* Solve generalized Sylvester equation for R and L */
/* and compute PL and PR. */
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 0;
dlacpy_("Full", &n1, &n2, &a[i__ * a_dim1 + 1], lda, &work[1], &n1);
dlacpy_("Full", &n1, &n2, &b[i__ * b_dim1 + 1], ldb, &work[n1 * n2 +
1], &n1);
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * a_dim1]
, lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + i__ *
b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], &
work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &ierr);
/* Estimate the reciprocal of norms of "projections" onto left */
/* and right eigenspaces. */
rdscal = 0.;
dsum = 1.;
i__1 = n1 * n2;
dlassq_(&i__1, &work[1], &c__1, &rdscal, &dsum);
*pl = rdscal * sqrt(dsum);
if (*pl == 0.) {
*pl = 1.;
} else {
*pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl));
}
rdscal = 0.;
dsum = 1.;
i__1 = n1 * n2;
dlassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum);
*pr = rdscal * sqrt(dsum);
if (*pr == 0.) {
*pr = 1.;
} else {
*pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr));
}
}
if (wantd) {
/* Compute estimates of Difu and Difl. */
if (wantd1) {
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 3;
/* Frobenius norm-based Difu-estimate. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ *
a_dim1], lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ +
i__ * b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &
dif[1], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
ierr);
/* Frobenius norm-based Difl-estimate. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, &a[
a_offset], lda, &work[1], &n2, &b[i__ + i__ * b_dim1],
ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &dscale,
&dif[2], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
ierr);
} else {
/* Compute 1-norm-based estimates of Difu and Difl using */
/* reversed communication with DLACN2. In each step a */
/* generalized Sylvester equation or a transposed variant */
/* is solved. */
kase = 0;
n1 = *m;
n2 = *n - *m;
i__ = n1 + 1;
ijb = 0;
mn2 = (n1 << 1) * n2;
/* 1-norm-based estimate of Difu. */
L40:
dlacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[1], &kase,
isave);
if (kase != 0) {
if (kase == 1) {
/* Solve generalized Sylvester equation. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
} else {
/* Solve the transposed variant. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("T", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
}
goto L40;
}
dif[1] = dscale / dif[1];
/* 1-norm-based estimate of Difl. */
L50:
dlacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[2], &kase,
isave);
if (kase != 0) {
if (kase == 1) {
/* Solve generalized Sylvester equation. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
&a[a_offset], lda, &work[1], &n2, &b[i__ + i__ *
b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 +
1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
} else {
/* Solve the transposed variant. */
i__1 = *lwork - (n1 << 1) * n2;
dtgsyl_("T", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
&a[a_offset], lda, &work[1], &n2, &b[i__ + i__ *
b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 +
1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 +
1], &i__1, &iwork[1], &ierr);
}
goto L50;
}
dif[2] = dscale / dif[2];
}
}
L60:
/* Compute generalized eigenvalues of reordered pair (A, B) and */
/* normalize the generalized Schur form. */
pair = FALSE_;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (pair) {
pair = FALSE_;
} else {
if (k < *n) {
if (a[k + 1 + k * a_dim1] != 0.) {
pair = TRUE_;
}
}
if (pair) {
/* Compute the eigenvalue(s) at position K. */
work[1] = a[k + k * a_dim1];
work[2] = a[k + 1 + k * a_dim1];
work[3] = a[k + (k + 1) * a_dim1];
work[4] = a[k + 1 + (k + 1) * a_dim1];
work[5] = b[k + k * b_dim1];
work[6] = b[k + 1 + k * b_dim1];
work[7] = b[k + (k + 1) * b_dim1];
work[8] = b[k + 1 + (k + 1) * b_dim1];
d__1 = smlnum * eps;
dlag2_(&work[1], &c__2, &work[5], &c__2, &d__1, &beta[k], &
beta[k + 1], &alphar[k], &alphar[k + 1], &alphai[k]);
alphai[k + 1] = -alphai[k];
} else {
if (d_sign(&c_b28, &b[k + k * b_dim1]) < 0.) {
/* If B(K,K) is negative, make it positive */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
a[k + i__ * a_dim1] = -a[k + i__ * a_dim1];
b[k + i__ * b_dim1] = -b[k + i__ * b_dim1];
if (*wantq) {
q[i__ + k * q_dim1] = -q[i__ + k * q_dim1];
}
/* L70: */
}
}
alphar[k] = a[k + k * a_dim1];
alphai[k] = 0.;
beta[k] = b[k + k * b_dim1];
}
}
/* L80: */
}
work[1] = (doublereal) lwmin;
iwork[1] = liwmin;
return;
/* End of DTGSEN */
} /* dtgsen_ */
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