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OpenBLAS/lapack-netlib/SRC/sggevx.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 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);}
#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)}
/* -- 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__0 = 0;
static real c_b57 = 0.f;
static real c_b58 = 1.f;
/* > \brief <b> SGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
rices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGGEVX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggevx.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggevx.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggevx.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB, */
/* ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, ILO, */
/* IHI, LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, */
/* RCONDV, WORK, LWORK, IWORK, BWORK, INFO ) */
/* CHARACTER BALANC, JOBVL, JOBVR, SENSE */
/* INTEGER IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N */
/* REAL ABNRM, BBNRM */
/* LOGICAL BWORK( * ) */
/* INTEGER IWORK( * ) */
/* REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/* $ B( LDB, * ), BETA( * ), LSCALE( * ), */
/* $ RCONDE( * ), RCONDV( * ), RSCALE( * ), */
/* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B) */
/* > the generalized eigenvalues, and optionally, the left and/or right */
/* > generalized eigenvectors. */
/* > */
/* > Optionally also, it computes a balancing transformation to improve */
/* > the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* > LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for */
/* > the eigenvalues (RCONDE), and reciprocal condition numbers for the */
/* > right eigenvectors (RCONDV). */
/* > */
/* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/* > lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */
/* > singular. It is usually represented as the pair (alpha,beta), as */
/* > there is a reasonable interpretation for beta=0, and even for both */
/* > being zero. */
/* > */
/* > The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */
/* > of (A,B) satisfies */
/* > */
/* > A * v(j) = lambda(j) * B * v(j) . */
/* > */
/* > The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */
/* > of (A,B) satisfies */
/* > */
/* > u(j)**H * A = lambda(j) * u(j)**H * B. */
/* > */
/* > where u(j)**H is the conjugate-transpose of u(j). */
/* > */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] BALANC */
/* > \verbatim */
/* > BALANC is CHARACTER*1 */
/* > Specifies the balance option to be performed. */
/* > = 'N': do not diagonally scale or permute; */
/* > = 'P': permute only; */
/* > = 'S': scale only; */
/* > = 'B': both permute and scale. */
/* > Computed reciprocal condition numbers will be for the */
/* > matrices after permuting and/or balancing. Permuting does */
/* > not change condition numbers (in exact arithmetic), but */
/* > balancing does. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVL */
/* > \verbatim */
/* > JOBVL is CHARACTER*1 */
/* > = 'N': do not compute the left generalized eigenvectors; */
/* > = 'V': compute the left generalized eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVR */
/* > \verbatim */
/* > JOBVR is CHARACTER*1 */
/* > = 'N': do not compute the right generalized eigenvectors; */
/* > = 'V': compute the right generalized eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] SENSE */
/* > \verbatim */
/* > SENSE is CHARACTER*1 */
/* > Determines which reciprocal condition numbers are computed. */
/* > = 'N': none are computed; */
/* > = 'E': computed for eigenvalues only; */
/* > = 'V': computed for eigenvectors only; */
/* > = 'B': computed for eigenvalues and eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices A, B, VL, and VR. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA, N) */
/* > On entry, the matrix A in the pair (A,B). */
/* > On exit, A has been overwritten. If JOBVL='V' or JOBVR='V' */
/* > or both, then A contains the first part of the real Schur */
/* > form of the "balanced" versions of the input A and B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB, N) */
/* > On entry, the matrix B in the pair (A,B). */
/* > On exit, B has been overwritten. If JOBVL='V' or JOBVR='V' */
/* > or both, then B contains the second part of the real Schur */
/* > form of the "balanced" versions of the input A and B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAR */
/* > \verbatim */
/* > ALPHAR is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAI */
/* > \verbatim */
/* > ALPHAI is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* > BETA is REAL array, dimension (N) */
/* > On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* > be the generalized eigenvalues. If ALPHAI(j) is zero, then */
/* > the j-th eigenvalue is real; if positive, then the j-th and */
/* > (j+1)-st eigenvalues are a complex conjugate pair, with */
/* > ALPHAI(j+1) negative. */
/* > */
/* > Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/* > may easily over- or underflow, and BETA(j) may even be zero. */
/* > Thus, the user should avoid naively computing the ratio */
/* > ALPHA/BETA. However, ALPHAR and ALPHAI will be always less */
/* > than and usually comparable with norm(A) in magnitude, and */
/* > BETA always less than and usually comparable with norm(B). */
/* > \endverbatim */
/* > */
/* > \param[out] VL */
/* > \verbatim */
/* > VL is REAL array, dimension (LDVL,N) */
/* > If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* > after another in the columns of VL, in the same order as */
/* > their eigenvalues. If the j-th eigenvalue is real, then */
/* > u(j) = VL(:,j), the j-th column of VL. If the j-th and */
/* > (j+1)-th eigenvalues form a complex conjugate pair, then */
/* > u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
/* > Each eigenvector will be scaled so the largest component have */
/* > abs(real part) + abs(imag. part) = 1. */
/* > Not referenced if JOBVL = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* > LDVL is INTEGER */
/* > The leading dimension of the matrix VL. LDVL >= 1, and */
/* > if JOBVL = 'V', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VR */
/* > \verbatim */
/* > VR is REAL array, dimension (LDVR,N) */
/* > If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* > after another in the columns of VR, in the same order as */
/* > their eigenvalues. If the j-th eigenvalue is real, then */
/* > v(j) = VR(:,j), the j-th column of VR. If the j-th and */
/* > (j+1)-th eigenvalues form a complex conjugate pair, then */
/* > v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
/* > Each eigenvector will be scaled so the largest component have */
/* > abs(real part) + abs(imag. part) = 1. */
/* > Not referenced if JOBVR = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* > LDVR is INTEGER */
/* > The leading dimension of the matrix VR. LDVR >= 1, and */
/* > if JOBVR = 'V', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] ILO */
/* > \verbatim */
/* > ILO is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[out] IHI */
/* > \verbatim */
/* > IHI is INTEGER */
/* > ILO and IHI are integer values such that on exit */
/* > A(i,j) = 0 and B(i,j) = 0 if i > j and */
/* > j = 1,...,ILO-1 or i = IHI+1,...,N. */
/* > If BALANC = 'N' or 'S', ILO = 1 and IHI = N. */
/* > \endverbatim */
/* > */
/* > \param[out] LSCALE */
/* > \verbatim */
/* > LSCALE is REAL array, dimension (N) */
/* > Details of the permutations and scaling factors applied */
/* > to the left side of A and B. If PL(j) is the index of the */
/* > row interchanged with row j, and DL(j) is the scaling */
/* > factor applied to row j, then */
/* > LSCALE(j) = PL(j) for j = 1,...,ILO-1 */
/* > = DL(j) for j = ILO,...,IHI */
/* > = PL(j) for j = IHI+1,...,N. */
/* > The order in which the interchanges are made is N to IHI+1, */
/* > then 1 to ILO-1. */
/* > \endverbatim */
/* > */
/* > \param[out] RSCALE */
/* > \verbatim */
/* > RSCALE is REAL array, dimension (N) */
/* > Details of the permutations and scaling factors applied */
/* > to the right side of A and B. If PR(j) is the index of the */
/* > column interchanged with column j, and DR(j) is the scaling */
/* > factor applied to column j, then */
/* > RSCALE(j) = PR(j) for j = 1,...,ILO-1 */
/* > = DR(j) for j = ILO,...,IHI */
/* > = PR(j) for j = IHI+1,...,N */
/* > The order in which the interchanges are made is N to IHI+1, */
/* > then 1 to ILO-1. */
/* > \endverbatim */
/* > */
/* > \param[out] ABNRM */
/* > \verbatim */
/* > ABNRM is REAL */
/* > The one-norm of the balanced matrix A. */
/* > \endverbatim */
/* > */
/* > \param[out] BBNRM */
/* > \verbatim */
/* > BBNRM is REAL */
/* > The one-norm of the balanced matrix B. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDE */
/* > \verbatim */
/* > RCONDE is REAL array, dimension (N) */
/* > If SENSE = 'E' or 'B', the reciprocal condition numbers of */
/* > the eigenvalues, stored in consecutive elements of the array. */
/* > For a complex conjugate pair of eigenvalues two consecutive */
/* > elements of RCONDE are set to the same value. Thus RCONDE(j), */
/* > RCONDV(j), and the j-th columns of VL and VR all correspond */
/* > to the j-th eigenpair. */
/* > If SENSE = 'N' or 'V', RCONDE is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDV */
/* > \verbatim */
/* > RCONDV is REAL array, dimension (N) */
/* > If SENSE = 'V' or 'B', the estimated reciprocal condition */
/* > numbers of the eigenvectors, stored in consecutive elements */
/* > of the array. For a complex eigenvector two consecutive */
/* > elements of RCONDV are set to the same value. If the */
/* > eigenvalues cannot be reordered to compute RCONDV(j), */
/* > RCONDV(j) is set to 0; this can only occur when the true */
/* > value would be very small anyway. */
/* > If SENSE = 'N' or 'E', RCONDV is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK >= f2cmax(1,2*N). */
/* > If BALANC = 'S' or 'B', or JOBVL = 'V', or JOBVR = 'V', */
/* > LWORK >= f2cmax(1,6*N). */
/* > If SENSE = 'E', LWORK >= f2cmax(1,10*N). */
/* > If SENSE = 'V' or 'B', LWORK >= 2*N*N+8*N+16. */
/* > */
/* > 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 (N+6) */
/* > If SENSE = 'E', IWORK is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] BWORK */
/* > \verbatim */
/* > BWORK is LOGICAL array, dimension (N) */
/* > If SENSE = 'N', BWORK is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > = 1,...,N: */
/* > The QZ iteration failed. No eigenvectors have been */
/* > calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/* > should be correct for j=INFO+1,...,N. */
/* > > N: =N+1: other than QZ iteration failed in SHGEQZ. */
/* > =N+2: error return from STGEVC. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date April 2012 */
/* > \ingroup realGEeigen */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Balancing a matrix pair (A,B) includes, first, permuting rows and */
/* > columns to isolate eigenvalues, second, applying diagonal similarity */
/* > transformation to the rows and columns to make the rows and columns */
/* > as close in norm as possible. The computed reciprocal condition */
/* > numbers correspond to the balanced matrix. Permuting rows and columns */
/* > will not change the condition numbers (in exact arithmetic) but */
/* > diagonal scaling will. For further explanation of balancing, see */
/* > section 4.11.1.2 of LAPACK Users' Guide. */
/* > */
/* > An approximate error bound on the chordal distance between the i-th */
/* > computed generalized eigenvalue w and the corresponding exact */
/* > eigenvalue lambda is */
/* > */
/* > chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I) */
/* > */
/* > An approximate error bound for the angle between the i-th computed */
/* > eigenvector VL(i) or VR(i) is given by */
/* > */
/* > EPS * norm(ABNRM, BBNRM) / DIF(i). */
/* > */
/* > For further explanation of the reciprocal condition numbers RCONDE */
/* > and RCONDV, see section 4.11 of LAPACK User's Guide. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void sggevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, integer *n, real *a, integer *lda, real *b, integer *ldb, real
*alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr,
integer *ldvr, integer *ilo, integer *ihi, real *lscale, real *rscale,
real *abnrm, real *bbnrm, real *rconde, real *rcondv, real *work,
integer *lwork, integer *iwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
logical pair;
real anrm, bnrm;
integer ierr, itau;
real temp;
logical ilvl, ilvr;
integer iwrk, iwrk1, i__, j, m;
extern logical lsame_(char *, char *);
integer icols;
logical noscl;
integer irows, jc;
extern /* Subroutine */ void slabad_(real *, real *);
integer in, mm, jr;
extern /* Subroutine */ void sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
logical ilascl, ilbscl;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern void sgghrd_(
char *, char *, integer *, integer *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, integer *,
integer *);
logical ldumma[1];
char chtemp[1];
real bignum;
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern real slamch_(char *);
integer ijobvl;
extern real slange_(char *, integer *, integer *, real *, integer *, real
*);
extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
logical wantsb;
extern /* Subroutine */ void slaset_(char *, integer *, integer *, real *,
real *, real *, integer *);
real anrmto;
logical wantse;
real bnrmto;
extern /* Subroutine */ void shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *), stgevc_(char *,
char *, logical *, integer *, real *, integer *, real *, integer *
, real *, integer *, real *, integer *, integer *, integer *,
real *, integer *), stgsna_(char *, char *,
logical *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, real *, integer *,
integer *, real *, integer *, integer *, integer *);
integer minwrk, maxwrk;
logical wantsn;
real smlnum;
extern /* Subroutine */ void sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
logical lquery, wantsv;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
real eps;
logical ilv;
/* -- LAPACK driver 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..-- */
/* April 2012 */
/* ===================================================================== */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--lscale;
--rscale;
--rconde;
--rcondv;
--work;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
noscl = lsame_(balanc, "N") || lsame_(balanc, "P");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (! (noscl || lsame_(balanc, "S") || lsame_(
balanc, "B"))) {
*info = -1;
} else if (ijobvl <= 0) {
*info = -2;
} else if (ijobvr <= 0) {
*info = -3;
} else if (! (wantsn || wantse || wantsb || wantsv)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < f2cmax(1,*n)) {
*info = -7;
} else if (*ldb < f2cmax(1,*n)) {
*info = -9;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -14;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -16;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. The workspace is */
/* computed assuming ILO = 1 and IHI = N, the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
if (noscl && ! ilv) {
minwrk = *n << 1;
} else {
minwrk = *n * 6;
}
if (wantse) {
minwrk = *n * 10;
} else if (wantsv || wantsb) {
minwrk = (*n << 1) * (*n + 4) + 16;
}
maxwrk = minwrk;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &
c__1, n, &c__0, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SORMQR", " ", n, &
c__1, n, &c__0, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
if (ilvl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SORGQR",
" ", n, &c__1, n, &c__0, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__1,i__2);
}
}
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -26;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGEVX", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n == 0) {
return;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute and/or balance the matrix pair (A,B) */
/* (Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise) */
sggbal_(balanc, n, &a[a_offset], lda, &b[b_offset], ldb, ilo, ihi, &
lscale[1], &rscale[1], &work[1], &ierr);
/* Compute ABNRM and BBNRM */
*abnrm = slange_("1", n, n, &a[a_offset], lda, &work[1]);
if (ilascl) {
work[1] = *abnrm;
slascl_("G", &c__0, &c__0, &anrmto, &anrm, &c__1, &c__1, &work[1], &
c__1, &ierr);
*abnrm = work[1];
}
*bbnrm = slange_("1", n, n, &b[b_offset], ldb, &work[1]);
if (ilbscl) {
work[1] = *bbnrm;
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, &c__1, &c__1, &work[1], &
c__1, &ierr);
*bbnrm = work[1];
}
/* Reduce B to triangular form (QR decomposition of B) */
/* (Workspace: need N, prefer N*NB ) */
irows = *ihi + 1 - *ilo;
if (ilv || ! wantsn) {
icols = *n + 1 - *ilo;
} else {
icols = irows;
}
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b[*ilo + *ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to A */
/* (Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b[*ilo + *ilo * b_dim1], ldb, &
work[itau], &a[*ilo + *ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr);
/* Initialize VL and/or VR */
/* (Workspace: need N, prefer N*NB) */
if (ilvl) {
slaset_("Full", n, n, &c_b57, &c_b58, &vl[vl_offset], ldvl)
;
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[*ilo + 1 + *ilo * b_dim1], ldb, &vl[
*ilo + 1 + *ilo * vl_dim1], ldvl);
}
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vl[*ilo + *ilo * vl_dim1], ldvl, &
work[itau], &work[iwrk], &i__1, &ierr);
}
if (ilvr) {
slaset_("Full", n, n, &c_b57, &c_b58, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
if (ilv || ! wantsn) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a[*ilo + *ilo * a_dim1],
lda, &b[*ilo + *ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &ierr);
}
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/* Schur forms and Schur vectors) */
/* (Workspace: need N) */
if (ilv || ! wantsn) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
shgeqz_(chtemp, jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset]
, ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], ldvl, &
vr[vr_offset], ldvr, &work[1], lwork, &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L130;
}
/* Compute Eigenvectors and estimate condition numbers if desired */
/* (Workspace: STGEVC: need 6*N */
/* STGSNA: need 2*N*(N+2)+16 if SENSE = 'V' or 'B', */
/* need N otherwise ) */
if (ilv || ! wantsn) {
if (ilv) {
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &
work[1], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L130;
}
}
if (! wantsn) {
/* compute eigenvectors (STGEVC) and estimate condition */
/* numbers (STGSNA). Note that the definition of the condition */
/* number is not invariant under transformation (u,v) to */
/* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized */
/* Schur form (S,T), Q and Z are orthogonal matrices. In order */
/* to avoid using extra 2*N*N workspace, we have to recalculate */
/* eigenvectors and estimate one condition numbers at a time. */
pair = FALSE_;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (pair) {
pair = FALSE_;
goto L20;
}
mm = 1;
if (i__ < *n) {
if (a[i__ + 1 + i__ * a_dim1] != 0.f) {
pair = TRUE_;
mm = 2;
}
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
bwork[j] = FALSE_;
/* L10: */
}
if (mm == 1) {
bwork[i__] = TRUE_;
} else if (mm == 2) {
bwork[i__] = TRUE_;
bwork[i__ + 1] = TRUE_;
}
iwrk = mm * *n + 1;
iwrk1 = iwrk + mm * *n;
/* Compute a pair of left and right eigenvectors. */
/* (compute workspace: need up to 4*N + 6*N) */
if (wantse || wantsb) {
stgevc_("B", "S", &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &work[1], n, &work[iwrk], n, &mm,
&m, &work[iwrk1], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L130;
}
}
i__2 = *lwork - iwrk1 + 1;
stgsna_(sense, "S", &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &work[1], n, &work[iwrk], n, &rconde[
i__], &rcondv[i__], &mm, &m, &work[iwrk1], &i__2, &
iwork[1], &ierr);
L20:
;
}
}
}
/* Undo balancing on VL and VR and normalization */
/* (Workspace: none needed) */
if (ilvl) {
sggbak_(balanc, "L", n, ilo, ihi, &lscale[1], &rscale[1], n, &vl[
vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L70;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1], abs(
r__1));
temp = f2cmax(r__2,r__3);
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1], abs(
r__1)) + (r__2 = vl[jr + (jc + 1) * vl_dim1], abs(
r__2));
temp = f2cmax(r__3,r__4);
/* L40: */
}
}
if (temp < smlnum) {
goto L70;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
/* L50: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L60: */
}
}
L70:
;
}
}
if (ilvr) {
sggbak_(balanc, "R", n, ilo, ihi, &lscale[1], &rscale[1], n, &vr[
vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L120;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1], abs(
r__1));
temp = f2cmax(r__2,r__3);
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1], abs(
r__1)) + (r__2 = vr[jr + (jc + 1) * vr_dim1], abs(
r__2));
temp = f2cmax(r__3,r__4);
/* L90: */
}
}
if (temp < smlnum) {
goto L120;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
/* L100: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L110: */
}
}
L120:
;
}
}
/* Undo scaling if necessary */
L130:
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
work[1] = (real) maxwrk;
return;
/* End of SGGEVX */
} /* sggevx_ */
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