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OpenBLAS/lapack-netlib/SRC/strevc3.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 int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<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_n1 = -1;
static integer c__2 = 2;
static real c_b17 = 0.f;
static logical c_false = FALSE_;
static real c_b29 = 1.f;
static logical c_true = TRUE_;
/* > \brief \b STREVC3 */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download STREVC3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strevc3
.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/strevc3
.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/strevc3
.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE STREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, */
/* VR, LDVR, MM, M, WORK, LWORK, INFO ) */
/* CHARACTER HOWMNY, SIDE */
/* INTEGER INFO, LDT, LDVL, LDVR, LWORK, M, MM, N */
/* LOGICAL SELECT( * ) */
/* REAL T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */
/* $ WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > STREVC3 computes some or all of the right and/or left eigenvectors of */
/* > a real upper quasi-triangular matrix T. */
/* > Matrices of this type are produced by the Schur factorization of */
/* > a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. */
/* > */
/* > The right eigenvector x and the left eigenvector y of T corresponding */
/* > to an eigenvalue w are defined by: */
/* > */
/* > T*x = w*x, (y**T)*T = w*(y**T) */
/* > */
/* > where y**T denotes the transpose of the vector y. */
/* > The eigenvalues are not input to this routine, but are read directly */
/* > from the diagonal blocks of T. */
/* > */
/* > This routine returns the matrices X and/or Y of right and left */
/* > eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
/* > input matrix. If Q is the orthogonal factor that reduces a matrix */
/* > A to Schur form T, then Q*X and Q*Y are the matrices of right and */
/* > left eigenvectors of A. */
/* > */
/* > This uses a Level 3 BLAS version of the back transformation. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] SIDE */
/* > \verbatim */
/* > SIDE is CHARACTER*1 */
/* > = 'R': compute right eigenvectors only; */
/* > = 'L': compute left eigenvectors only; */
/* > = 'B': compute both right and left eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] HOWMNY */
/* > \verbatim */
/* > HOWMNY is CHARACTER*1 */
/* > = 'A': compute all right and/or left eigenvectors; */
/* > = 'B': compute all right and/or left eigenvectors, */
/* > backtransformed by the matrices in VR and/or VL; */
/* > = 'S': compute selected right and/or left eigenvectors, */
/* > as indicated by the logical array SELECT. */
/* > \endverbatim */
/* > */
/* > \param[in,out] SELECT */
/* > \verbatim */
/* > SELECT is LOGICAL array, dimension (N) */
/* > If HOWMNY = 'S', SELECT specifies the eigenvectors to be */
/* > computed. */
/* > If w(j) is a real eigenvalue, the corresponding real */
/* > eigenvector is computed if SELECT(j) is .TRUE.. */
/* > If w(j) and w(j+1) are the real and imaginary parts of a */
/* > complex eigenvalue, the corresponding complex eigenvector is */
/* > computed if either SELECT(j) or SELECT(j+1) is .TRUE., and */
/* > on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to */
/* > .FALSE.. */
/* > Not referenced if HOWMNY = 'A' or 'B'. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix T. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] T */
/* > \verbatim */
/* > T is REAL array, dimension (LDT,N) */
/* > The upper quasi-triangular matrix T in Schur canonical form. */
/* > \endverbatim */
/* > */
/* > \param[in] LDT */
/* > \verbatim */
/* > LDT is INTEGER */
/* > The leading dimension of the array T. LDT >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] VL */
/* > \verbatim */
/* > VL is REAL array, dimension (LDVL,MM) */
/* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/* > contain an N-by-N matrix Q (usually the orthogonal matrix Q */
/* > of Schur vectors returned by SHSEQR). */
/* > On exit, if SIDE = 'L' or 'B', VL contains: */
/* > if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
/* > if HOWMNY = 'B', the matrix Q*Y; */
/* > if HOWMNY = 'S', the left eigenvectors of T specified by */
/* > SELECT, stored consecutively in the columns */
/* > of VL, in the same order as their */
/* > eigenvalues. */
/* > A complex eigenvector corresponding to a complex eigenvalue */
/* > is stored in two consecutive columns, the first holding the */
/* > real part, and the second the imaginary part. */
/* > Not referenced if SIDE = 'R'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* > LDVL is INTEGER */
/* > The leading dimension of the array VL. */
/* > LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VR */
/* > \verbatim */
/* > VR is REAL array, dimension (LDVR,MM) */
/* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/* > contain an N-by-N matrix Q (usually the orthogonal matrix Q */
/* > of Schur vectors returned by SHSEQR). */
/* > On exit, if SIDE = 'R' or 'B', VR contains: */
/* > if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
/* > if HOWMNY = 'B', the matrix Q*X; */
/* > if HOWMNY = 'S', the right eigenvectors of T specified by */
/* > SELECT, stored consecutively in the columns */
/* > of VR, in the same order as their */
/* > eigenvalues. */
/* > A complex eigenvector corresponding to a complex eigenvalue */
/* > is stored in two consecutive columns, the first holding the */
/* > real part and the second the imaginary part. */
/* > Not referenced if SIDE = 'L'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* > LDVR is INTEGER */
/* > The leading dimension of the array VR. */
/* > LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[in] MM */
/* > \verbatim */
/* > MM is INTEGER */
/* > The number of columns in the arrays VL and/or VR. MM >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of columns in the arrays VL and/or VR actually */
/* > used to store the eigenvectors. */
/* > If HOWMNY = 'A' or 'B', M is set to N. */
/* > Each selected real eigenvector occupies one column and each */
/* > selected complex eigenvector occupies two columns. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of array WORK. LWORK >= f2cmax(1,3*N). */
/* > For optimum performance, LWORK >= N + 2*N*NB, where NB is */
/* > the optimal blocksize. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2017 */
/* @generated from dtrevc3.f, fortran d -> s, Tue Apr 19 01:47:44 2016 */
/* > \ingroup realOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The algorithm used in this program is basically backward (forward) */
/* > substitution, with scaling to make the the code robust against */
/* > possible overflow. */
/* > */
/* > Each eigenvector is normalized so that the element of largest */
/* > magnitude has magnitude 1; here the magnitude of a complex number */
/* > (x,y) is taken to be |x| + |y|. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void strevc3_(char *side, char *howmny, logical *select,
integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr,
integer *ldvr, integer *mm, integer *m, real *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1[2],
i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
char ch__1[2];
/* Local variables */
real beta, emax;
logical pair, allv;
integer ierr;
real unfl, ovfl, smin;
extern real sdot_(integer *, real *, integer *, real *, integer *);
logical over;
real vmax;
integer jnxt, i__, j, k;
real scale, x[4] /* was [2][2] */;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *),
sgemm_(char *, char *, integer *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
real remax;
logical leftv;
extern /* Subroutine */ void sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
logical bothv;
real vcrit;
logical somev;
integer j1, j2;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *);
real xnorm;
extern /* Subroutine */ void saxpy_(integer *, real *, real *, integer *,
real *, integer *);
integer iscomplex[128];
extern /* Subroutine */ void slaln2_(logical *, integer *, integer *, real
*, real *, real *, integer *, real *, real *, real *, integer *,
real *, real *, real *, integer *, real *, real *, integer *);
integer nb, ii, ki;
extern /* Subroutine */ void slabad_(real *, real *);
integer ip, is, iv;
real wi;
extern real slamch_(char *);
real wr;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
real bignum;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
logical rightv;
integer ki2, maxwrk;
real smlnum;
logical lquery;
real rec, ulp;
/* -- LAPACK computational routine (version 3.8.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2017 */
/* ===================================================================== */
/* Decode and test the input parameters */
/* Parameter adjustments */
--select;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
/* Function Body */
bothv = lsame_(side, "B");
rightv = lsame_(side, "R") || bothv;
leftv = lsame_(side, "L") || bothv;
allv = lsame_(howmny, "A");
over = lsame_(howmny, "B");
somev = lsame_(howmny, "S");
*info = 0;
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = howmny;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
nb = ilaenv_(&c__1, "STREVC", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)2);
maxwrk = *n + (*n << 1) * nb;
work[1] = (real) maxwrk;
lquery = *lwork == -1;
if (! rightv && ! leftv) {
*info = -1;
} else if (! allv && ! over && ! somev) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*ldt < f2cmax(1,*n)) {
*info = -6;
} else if (*ldvl < 1 || leftv && *ldvl < *n) {
*info = -8;
} else if (*ldvr < 1 || rightv && *ldvr < *n) {
*info = -10;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = 1, i__3 = *n * 3;
if (*lwork < f2cmax(i__2,i__3) && ! lquery) {
*info = -14;
} else {
/* Set M to the number of columns required to store the selected */
/* eigenvectors, standardize the array SELECT if necessary, and */
/* test MM. */
if (somev) {
*m = 0;
pair = FALSE_;
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (pair) {
pair = FALSE_;
select[j] = FALSE_;
} else {
if (j < *n) {
if (t[j + 1 + j * t_dim1] == 0.f) {
if (select[j]) {
++(*m);
}
} else {
pair = TRUE_;
if (select[j] || select[j + 1]) {
select[j] = TRUE_;
*m += 2;
}
}
} else {
if (select[*n]) {
++(*m);
}
}
}
/* L10: */
}
} else {
*m = *n;
}
if (*mm < *m) {
*info = -11;
}
}
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("STREVC3", &i__2, (ftnlen)7);
return;
} else if (lquery) {
return;
}
/* Quick return if possible. */
if (*n == 0) {
return;
}
/* Use blocked version of back-transformation if sufficient workspace. */
/* Zero-out the workspace to avoid potential NaN propagation. */
if (over && *lwork >= *n + (*n << 4)) {
nb = (*lwork - *n) / (*n << 1);
nb = f2cmin(nb,128);
i__2 = (nb << 1) + 1;
slaset_("F", n, &i__2, &c_b17, &c_b17, &work[1], n);
} else {
nb = 1;
}
/* Set the constants to control overflow. */
unfl = slamch_("Safe minimum");
ovfl = 1.f / unfl;
slabad_(&unfl, &ovfl);
ulp = slamch_("Precision");
smlnum = unfl * (*n / ulp);
bignum = (1.f - ulp) / smlnum;
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
work[1] = 0.f;
i__2 = *n;
for (j = 2; j <= i__2; ++j) {
work[j] = 0.f;
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
work[j] += (r__1 = t[i__ + j * t_dim1], abs(r__1));
/* L20: */
}
/* L30: */
}
/* Index IP is used to specify the real or complex eigenvalue: */
/* IP = 0, real eigenvalue, */
/* 1, first of conjugate complex pair: (wr,wi) */
/* -1, second of conjugate complex pair: (wr,wi) */
/* ISCOMPLEX array stores IP for each column in current block. */
if (rightv) {
/* ============================================================ */
/* Compute right eigenvectors. */
/* IV is index of column in current block. */
/* For complex right vector, uses IV-1 for real part and IV for complex part. */
/* Non-blocked version always uses IV=2; */
/* blocked version starts with IV=NB, goes down to 1 or 2. */
/* (Note the "0-th" column is used for 1-norms computed above.) */
iv = 2;
if (nb > 2) {
iv = nb;
}
ip = 0;
is = *m;
for (ki = *n; ki >= 1; --ki) {
if (ip == -1) {
/* previous iteration (ki+1) was second of conjugate pair, */
/* so this ki is first of conjugate pair; skip to end of loop */
ip = 1;
goto L140;
} else if (ki == 1) {
/* last column, so this ki must be real eigenvalue */
ip = 0;
} else if (t[ki + (ki - 1) * t_dim1] == 0.f) {
/* zero on sub-diagonal, so this ki is real eigenvalue */
ip = 0;
} else {
/* non-zero on sub-diagonal, so this ki is second of conjugate pair */
ip = -1;
}
if (somev) {
if (ip == 0) {
if (! select[ki]) {
goto L140;
}
} else {
if (! select[ki - 1]) {
goto L140;
}
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.f;
if (ip != 0) {
wi = sqrt((r__1 = t[ki + (ki - 1) * t_dim1], abs(r__1))) *
sqrt((r__2 = t[ki - 1 + ki * t_dim1], abs(r__2)));
}
/* Computing MAX */
r__1 = ulp * (abs(wr) + abs(wi));
smin = f2cmax(r__1,smlnum);
if (ip == 0) {
/* -------------------------------------------------------- */
/* Real right eigenvector */
work[ki + iv * *n] = 1.f;
/* Form right-hand side. */
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
work[k + iv * *n] = -t[k + ki * t_dim1];
/* L50: */
}
/* Solve upper quasi-triangular system: */
/* [ T(1:KI-1,1:KI-1) - WR ]*X = SCALE*WORK. */
jnxt = ki - 1;
for (j = ki - 1; j >= 1; --j) {
if (j > jnxt) {
goto L60;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.f) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
slaln2_(&c_false, &c__1, &c__1, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j +
iv * *n], n, &wr, &c_b17, x, &c__2, &scale, &
xnorm, &ierr);
/* Scale X(1,1) to avoid overflow when updating */
/* the right-hand side. */
if (xnorm > 1.f) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[iv * *n + 1], &c__1);
}
work[j + iv * *n] = x[0];
/* Update right-hand side */
i__2 = j - 1;
r__1 = -x[0];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
iv * *n + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
slaln2_(&c_false, &c__2, &c__1, &smin, &c_b29, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b29, &c_b29, &
work[j - 1 + iv * *n], n, &wr, &c_b17, x, &
c__2, &scale, &xnorm, &ierr);
/* Scale X(1,1) and X(2,1) to avoid overflow when */
/* updating the right-hand side. */
if (xnorm > 1.f) {
/* Computing MAX */
r__1 = work[j - 1], r__2 = work[j];
beta = f2cmax(r__1,r__2);
if (beta > bignum / xnorm) {
x[0] /= xnorm;
x[1] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[iv * *n + 1], &c__1);
}
work[j - 1 + iv * *n] = x[0];
work[j + iv * *n] = x[1];
/* Update right-hand side */
i__2 = j - 2;
r__1 = -x[0];
saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[iv * *n + 1], &c__1);
i__2 = j - 2;
r__1 = -x[1];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
iv * *n + 1], &c__1);
}
L60:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
/* ------------------------------ */
/* no back-transform: copy x to VR and normalize. */
scopy_(&ki, &work[iv * *n + 1], &c__1, &vr[is * vr_dim1 +
1], &c__1);
ii = isamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vr[ii + is * vr_dim1], abs(r__1));
sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
vr[k + is * vr_dim1] = 0.f;
/* L70: */
}
} else if (nb == 1) {
/* ------------------------------ */
/* version 1: back-transform each vector with GEMV, Q*x. */
if (ki > 1) {
i__2 = ki - 1;
sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, &
work[iv * *n + 1], &c__1, &work[ki + iv * *n],
&vr[ki * vr_dim1 + 1], &c__1);
}
ii = isamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vr[ii + ki * vr_dim1], abs(r__1));
sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
} else {
/* ------------------------------ */
/* version 2: back-transform block of vectors with GEMM */
/* zero out below vector */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
work[k + iv * *n] = 0.f;
}
iscomplex[iv - 1] = ip;
/* back-transform and normalization is done below */
}
} else {
/* -------------------------------------------------------- */
/* Complex right eigenvector. */
/* Initial solve */
/* [ ( T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I*WI) ]*X = 0. */
/* [ ( T(KI, KI-1) T(KI, KI) ) ] */
if ((r__1 = t[ki - 1 + ki * t_dim1], abs(r__1)) >= (r__2 = t[
ki + (ki - 1) * t_dim1], abs(r__2))) {
work[ki - 1 + (iv - 1) * *n] = 1.f;
work[ki + iv * *n] = wi / t[ki - 1 + ki * t_dim1];
} else {
work[ki - 1 + (iv - 1) * *n] = -wi / t[ki + (ki - 1) *
t_dim1];
work[ki + iv * *n] = 1.f;
}
work[ki + (iv - 1) * *n] = 0.f;
work[ki - 1 + iv * *n] = 0.f;
/* Form right-hand side. */
i__2 = ki - 2;
for (k = 1; k <= i__2; ++k) {
work[k + (iv - 1) * *n] = -work[ki - 1 + (iv - 1) * *n] *
t[k + (ki - 1) * t_dim1];
work[k + iv * *n] = -work[ki + iv * *n] * t[k + ki *
t_dim1];
/* L80: */
}
/* Solve upper quasi-triangular system: */
/* [ T(1:KI-2,1:KI-2) - (WR+i*WI) ]*X = SCALE*(WORK+i*WORK2) */
jnxt = ki - 2;
for (j = ki - 2; j >= 1; --j) {
if (j > jnxt) {
goto L90;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.f) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
slaln2_(&c_false, &c__1, &c__2, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j + (
iv - 1) * *n], n, &wr, &wi, x, &c__2, &scale,
&xnorm, &ierr);
/* Scale X(1,1) and X(1,2) to avoid overflow when */
/* updating the right-hand side. */
if (xnorm > 1.f) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
x[2] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[(iv - 1) * *n + 1], &
c__1);
sscal_(&ki, &scale, &work[iv * *n + 1], &c__1);
}
work[j + (iv - 1) * *n] = x[0];
work[j + iv * *n] = x[2];
/* Update the right-hand side */
i__2 = j - 1;
r__1 = -x[0];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
(iv - 1) * *n + 1], &c__1);
i__2 = j - 1;
r__1 = -x[2];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
iv * *n + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
slaln2_(&c_false, &c__2, &c__2, &smin, &c_b29, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b29, &c_b29, &
work[j - 1 + (iv - 1) * *n], n, &wr, &wi, x, &
c__2, &scale, &xnorm, &ierr);
/* Scale X to avoid overflow when updating */
/* the right-hand side. */
if (xnorm > 1.f) {
/* Computing MAX */
r__1 = work[j - 1], r__2 = work[j];
beta = f2cmax(r__1,r__2);
if (beta > bignum / xnorm) {
rec = 1.f / xnorm;
x[0] *= rec;
x[2] *= rec;
x[1] *= rec;
x[3] *= rec;
scale *= rec;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[(iv - 1) * *n + 1], &
c__1);
sscal_(&ki, &scale, &work[iv * *n + 1], &c__1);
}
work[j - 1 + (iv - 1) * *n] = x[0];
work[j + (iv - 1) * *n] = x[1];
work[j - 1 + iv * *n] = x[2];
work[j + iv * *n] = x[3];
/* Update the right-hand side */
i__2 = j - 2;
r__1 = -x[0];
saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[(iv - 1) * *n + 1], &c__1);
i__2 = j - 2;
r__1 = -x[1];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
(iv - 1) * *n + 1], &c__1);
i__2 = j - 2;
r__1 = -x[2];
saxpy_(&i__2, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[iv * *n + 1], &c__1);
i__2 = j - 2;
r__1 = -x[3];
saxpy_(&i__2, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
iv * *n + 1], &c__1);
}
L90:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
/* ------------------------------ */
/* no back-transform: copy x to VR and normalize. */
scopy_(&ki, &work[(iv - 1) * *n + 1], &c__1, &vr[(is - 1)
* vr_dim1 + 1], &c__1);
scopy_(&ki, &work[iv * *n + 1], &c__1, &vr[is * vr_dim1 +
1], &c__1);
emax = 0.f;
i__2 = ki;
for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vr[k + (is - 1) * vr_dim1]
, abs(r__1)) + (r__2 = vr[k + is * vr_dim1],
abs(r__2));
emax = f2cmax(r__3,r__4);
/* L100: */
}
remax = 1.f / emax;
sscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1);
sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
vr[k + (is - 1) * vr_dim1] = 0.f;
vr[k + is * vr_dim1] = 0.f;
/* L110: */
}
} else if (nb == 1) {
/* ------------------------------ */
/* version 1: back-transform each vector with GEMV, Q*x. */
if (ki > 2) {
i__2 = ki - 2;
sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, &
work[(iv - 1) * *n + 1], &c__1, &work[ki - 1
+ (iv - 1) * *n], &vr[(ki - 1) * vr_dim1 + 1],
&c__1);
i__2 = ki - 2;
sgemv_("N", n, &i__2, &c_b29, &vr[vr_offset], ldvr, &
work[iv * *n + 1], &c__1, &work[ki + iv * *n],
&vr[ki * vr_dim1 + 1], &c__1);
} else {
sscal_(n, &work[ki - 1 + (iv - 1) * *n], &vr[(ki - 1)
* vr_dim1 + 1], &c__1);
sscal_(n, &work[ki + iv * *n], &vr[ki * vr_dim1 + 1],
&c__1);
}
emax = 0.f;
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vr[k + (ki - 1) * vr_dim1]
, abs(r__1)) + (r__2 = vr[k + ki * vr_dim1],
abs(r__2));
emax = f2cmax(r__3,r__4);
/* L120: */
}
remax = 1.f / emax;
sscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1);
sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
} else {
/* ------------------------------ */
/* version 2: back-transform block of vectors with GEMM */
/* zero out below vector */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
work[k + (iv - 1) * *n] = 0.f;
work[k + iv * *n] = 0.f;
}
iscomplex[iv - 2] = -ip;
iscomplex[iv - 1] = ip;
--iv;
/* back-transform and normalization is done below */
}
}
if (nb > 1) {
/* -------------------------------------------------------- */
/* Blocked version of back-transform */
/* For complex case, KI2 includes both vectors (KI-1 and KI) */
if (ip == 0) {
ki2 = ki;
} else {
ki2 = ki - 1;
}
/* Columns IV:NB of work are valid vectors. */
/* When the number of vectors stored reaches NB-1 or NB, */
/* or if this was last vector, do the GEMM */
if (iv <= 2 || ki2 == 1) {
i__2 = nb - iv + 1;
i__3 = ki2 + nb - iv;
sgemm_("N", "N", n, &i__2, &i__3, &c_b29, &vr[vr_offset],
ldvr, &work[iv * *n + 1], n, &c_b17, &work[(nb +
iv) * *n + 1], n);
/* normalize vectors */
i__2 = nb;
for (k = iv; k <= i__2; ++k) {
if (iscomplex[k - 1] == 0) {
/* real eigenvector */
ii = isamax_(n, &work[(nb + k) * *n + 1], &c__1);
remax = 1.f / (r__1 = work[ii + (nb + k) * *n],
abs(r__1));
} else if (iscomplex[k - 1] == 1) {
/* first eigenvector of conjugate pair */
emax = 0.f;
i__3 = *n;
for (ii = 1; ii <= i__3; ++ii) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = work[ii + (nb + k)
* *n], abs(r__1)) + (r__2 = work[ii
+ (nb + k + 1) * *n], abs(r__2));
emax = f2cmax(r__3,r__4);
}
remax = 1.f / emax;
/* else if ISCOMPLEX(K).EQ.-1 */
/* second eigenvector of conjugate pair */
/* reuse same REMAX as previous K */
}
sscal_(n, &remax, &work[(nb + k) * *n + 1], &c__1);
}
i__2 = nb - iv + 1;
slacpy_("F", n, &i__2, &work[(nb + iv) * *n + 1], n, &vr[
ki2 * vr_dim1 + 1], ldvr);
iv = nb;
} else {
--iv;
}
}
/* blocked back-transform */
--is;
if (ip != 0) {
--is;
}
L140:
;
}
}
if (leftv) {
/* ============================================================ */
/* Compute left eigenvectors. */
/* IV is index of column in current block. */
/* For complex left vector, uses IV for real part and IV+1 for complex part. */
/* Non-blocked version always uses IV=1; */
/* blocked version starts with IV=1, goes up to NB-1 or NB. */
/* (Note the "0-th" column is used for 1-norms computed above.) */
iv = 1;
ip = 0;
is = 1;
i__2 = *n;
for (ki = 1; ki <= i__2; ++ki) {
if (ip == 1) {
/* previous iteration (ki-1) was first of conjugate pair, */
/* so this ki is second of conjugate pair; skip to end of loop */
ip = -1;
goto L260;
} else if (ki == *n) {
/* last column, so this ki must be real eigenvalue */
ip = 0;
} else if (t[ki + 1 + ki * t_dim1] == 0.f) {
/* zero on sub-diagonal, so this ki is real eigenvalue */
ip = 0;
} else {
/* non-zero on sub-diagonal, so this ki is first of conjugate pair */
ip = 1;
}
if (somev) {
if (! select[ki]) {
goto L260;
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.f;
if (ip != 0) {
wi = sqrt((r__1 = t[ki + (ki + 1) * t_dim1], abs(r__1))) *
sqrt((r__2 = t[ki + 1 + ki * t_dim1], abs(r__2)));
}
/* Computing MAX */
r__1 = ulp * (abs(wr) + abs(wi));
smin = f2cmax(r__1,smlnum);
if (ip == 0) {
/* -------------------------------------------------------- */
/* Real left eigenvector */
work[ki + iv * *n] = 1.f;
/* Form right-hand side. */
i__3 = *n;
for (k = ki + 1; k <= i__3; ++k) {
work[k + iv * *n] = -t[ki + k * t_dim1];
/* L160: */
}
/* Solve transposed quasi-triangular system: */
/* [ T(KI+1:N,KI+1:N) - WR ]**T * X = SCALE*WORK */
vmax = 1.f;
vcrit = bignum;
jnxt = ki + 1;
i__3 = *n;
for (j = ki + 1; j <= i__3; ++j) {
if (j < jnxt) {
goto L170;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.f) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side. */
if (work[j] > vcrit) {
rec = 1.f / vmax;
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__4 = j - ki - 1;
work[j + iv * *n] -= sdot_(&i__4, &t[ki + 1 + j *
t_dim1], &c__1, &work[ki + 1 + iv * *n], &
c__1);
/* Solve [ T(J,J) - WR ]**T * X = WORK */
slaln2_(&c_false, &c__1, &c__1, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j +
iv * *n], n, &wr, &c_b17, x, &c__2, &scale, &
xnorm, &ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1);
}
work[j + iv * *n] = x[0];
/* Computing MAX */
r__2 = (r__1 = work[j + iv * *n], abs(r__1));
vmax = f2cmax(r__2,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side. */
/* Computing MAX */
r__1 = work[j], r__2 = work[j + 1];
beta = f2cmax(r__1,r__2);
if (beta > vcrit) {
rec = 1.f / vmax;
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__4 = j - ki - 1;
work[j + iv * *n] -= sdot_(&i__4, &t[ki + 1 + j *
t_dim1], &c__1, &work[ki + 1 + iv * *n], &
c__1);
i__4 = j - ki - 1;
work[j + 1 + iv * *n] -= sdot_(&i__4, &t[ki + 1 + (j
+ 1) * t_dim1], &c__1, &work[ki + 1 + iv * *n]
, &c__1);
/* Solve */
/* [ T(J,J)-WR T(J,J+1) ]**T * X = SCALE*( WORK1 ) */
/* [ T(J+1,J) T(J+1,J+1)-WR ] ( WORK2 ) */
slaln2_(&c_true, &c__2, &c__1, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j +
iv * *n], n, &wr, &c_b17, x, &c__2, &scale, &
xnorm, &ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1);
}
work[j + iv * *n] = x[0];
work[j + 1 + iv * *n] = x[1];
/* Computing MAX */
r__3 = (r__1 = work[j + iv * *n], abs(r__1)), r__4 = (
r__2 = work[j + 1 + iv * *n], abs(r__2)),
r__3 = f2cmax(r__3,r__4);
vmax = f2cmax(r__3,vmax);
vcrit = bignum / vmax;
}
L170:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
/* ------------------------------ */
/* no back-transform: copy x to VL and normalize. */
i__3 = *n - ki + 1;
scopy_(&i__3, &work[ki + iv * *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__3 = *n - ki + 1;
ii = isamax_(&i__3, &vl[ki + is * vl_dim1], &c__1) + ki -
1;
remax = 1.f / (r__1 = vl[ii + is * vl_dim1], abs(r__1));
i__3 = *n - ki + 1;
sscal_(&i__3, &remax, &vl[ki + is * vl_dim1], &c__1);
i__3 = ki - 1;
for (k = 1; k <= i__3; ++k) {
vl[k + is * vl_dim1] = 0.f;
/* L180: */
}
} else if (nb == 1) {
/* ------------------------------ */
/* version 1: back-transform each vector with GEMV, Q*x. */
if (ki < *n) {
i__3 = *n - ki;
sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 1) * vl_dim1
+ 1], ldvl, &work[ki + 1 + iv * *n], &c__1, &
work[ki + iv * *n], &vl[ki * vl_dim1 + 1], &
c__1);
}
ii = isamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vl[ii + ki * vl_dim1], abs(r__1));
sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
} else {
/* ------------------------------ */
/* version 2: back-transform block of vectors with GEMM */
/* zero out above vector */
/* could go from KI-NV+1 to KI-1 */
i__3 = ki - 1;
for (k = 1; k <= i__3; ++k) {
work[k + iv * *n] = 0.f;
}
iscomplex[iv - 1] = ip;
/* back-transform and normalization is done below */
}
} else {
/* -------------------------------------------------------- */
/* Complex left eigenvector. */
/* Initial solve: */
/* [ ( T(KI,KI) T(KI,KI+1) )**T - (WR - I* WI) ]*X = 0. */
/* [ ( T(KI+1,KI) T(KI+1,KI+1) ) ] */
if ((r__1 = t[ki + (ki + 1) * t_dim1], abs(r__1)) >= (r__2 =
t[ki + 1 + ki * t_dim1], abs(r__2))) {
work[ki + iv * *n] = wi / t[ki + (ki + 1) * t_dim1];
work[ki + 1 + (iv + 1) * *n] = 1.f;
} else {
work[ki + iv * *n] = 1.f;
work[ki + 1 + (iv + 1) * *n] = -wi / t[ki + 1 + ki *
t_dim1];
}
work[ki + 1 + iv * *n] = 0.f;
work[ki + (iv + 1) * *n] = 0.f;
/* Form right-hand side. */
i__3 = *n;
for (k = ki + 2; k <= i__3; ++k) {
work[k + iv * *n] = -work[ki + iv * *n] * t[ki + k *
t_dim1];
work[k + (iv + 1) * *n] = -work[ki + 1 + (iv + 1) * *n] *
t[ki + 1 + k * t_dim1];
/* L190: */
}
/* Solve transposed quasi-triangular system: */
/* [ T(KI+2:N,KI+2:N)**T - (WR-i*WI) ]*X = WORK1+i*WORK2 */
vmax = 1.f;
vcrit = bignum;
jnxt = ki + 2;
i__3 = *n;
for (j = ki + 2; j <= i__3; ++j) {
if (j < jnxt) {
goto L200;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.f) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
/* Scale if necessary to avoid overflow when */
/* forming the right-hand side elements. */
if (work[j] > vcrit) {
rec = 1.f / vmax;
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1);
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + (iv + 1) * *n], &
c__1);
vmax = 1.f;
vcrit = bignum;
}
i__4 = j - ki - 2;
work[j + iv * *n] -= sdot_(&i__4, &t[ki + 2 + j *
t_dim1], &c__1, &work[ki + 2 + iv * *n], &
c__1);
i__4 = j - ki - 2;
work[j + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2 + j
* t_dim1], &c__1, &work[ki + 2 + (iv + 1) * *
n], &c__1);
/* Solve [ T(J,J)-(WR-i*WI) ]*(X11+i*X12)= WK+I*WK2 */
r__1 = -wi;
slaln2_(&c_false, &c__1, &c__2, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j +
iv * *n], n, &wr, &r__1, x, &c__2, &scale, &
xnorm, &ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1);
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + (iv + 1) * *n], &
c__1);
}
work[j + iv * *n] = x[0];
work[j + (iv + 1) * *n] = x[2];
/* Computing MAX */
r__3 = (r__1 = work[j + iv * *n], abs(r__1)), r__4 = (
r__2 = work[j + (iv + 1) * *n], abs(r__2)),
r__3 = f2cmax(r__3,r__4);
vmax = f2cmax(r__3,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side elements. */
/* Computing MAX */
r__1 = work[j], r__2 = work[j + 1];
beta = f2cmax(r__1,r__2);
if (beta > vcrit) {
rec = 1.f / vmax;
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + iv * *n], &c__1);
i__4 = *n - ki + 1;
sscal_(&i__4, &rec, &work[ki + (iv + 1) * *n], &
c__1);
vmax = 1.f;
vcrit = bignum;
}
i__4 = j - ki - 2;
work[j + iv * *n] -= sdot_(&i__4, &t[ki + 2 + j *
t_dim1], &c__1, &work[ki + 2 + iv * *n], &
c__1);
i__4 = j - ki - 2;
work[j + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2 + j
* t_dim1], &c__1, &work[ki + 2 + (iv + 1) * *
n], &c__1);
i__4 = j - ki - 2;
work[j + 1 + iv * *n] -= sdot_(&i__4, &t[ki + 2 + (j
+ 1) * t_dim1], &c__1, &work[ki + 2 + iv * *n]
, &c__1);
i__4 = j - ki - 2;
work[j + 1 + (iv + 1) * *n] -= sdot_(&i__4, &t[ki + 2
+ (j + 1) * t_dim1], &c__1, &work[ki + 2 + (
iv + 1) * *n], &c__1);
/* Solve 2-by-2 complex linear equation */
/* [ (T(j,j) T(j,j+1) )**T - (wr-i*wi)*I ]*X = SCALE*B */
/* [ (T(j+1,j) T(j+1,j+1)) ] */
r__1 = -wi;
slaln2_(&c_true, &c__2, &c__2, &smin, &c_b29, &t[j +
j * t_dim1], ldt, &c_b29, &c_b29, &work[j +
iv * *n], n, &wr, &r__1, x, &c__2, &scale, &
xnorm, &ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + iv * *n], &c__1);
i__4 = *n - ki + 1;
sscal_(&i__4, &scale, &work[ki + (iv + 1) * *n], &
c__1);
}
work[j + iv * *n] = x[0];
work[j + (iv + 1) * *n] = x[2];
work[j + 1 + iv * *n] = x[1];
work[j + 1 + (iv + 1) * *n] = x[3];
/* Computing MAX */
r__1 = abs(x[0]), r__2 = abs(x[2]), r__1 = f2cmax(r__1,
r__2), r__2 = abs(x[1]), r__1 = f2cmax(r__1,r__2)
, r__2 = abs(x[3]), r__1 = f2cmax(r__1,r__2);
vmax = f2cmax(r__1,vmax);
vcrit = bignum / vmax;
}
L200:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
/* ------------------------------ */
/* no back-transform: copy x to VL and normalize. */
i__3 = *n - ki + 1;
scopy_(&i__3, &work[ki + iv * *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__3 = *n - ki + 1;
scopy_(&i__3, &work[ki + (iv + 1) * *n], &c__1, &vl[ki + (
is + 1) * vl_dim1], &c__1);
emax = 0.f;
i__3 = *n;
for (k = ki; k <= i__3; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vl[k + is * vl_dim1], abs(
r__1)) + (r__2 = vl[k + (is + 1) * vl_dim1],
abs(r__2));
emax = f2cmax(r__3,r__4);
/* L220: */
}
remax = 1.f / emax;
i__3 = *n - ki + 1;
sscal_(&i__3, &remax, &vl[ki + is * vl_dim1], &c__1);
i__3 = *n - ki + 1;
sscal_(&i__3, &remax, &vl[ki + (is + 1) * vl_dim1], &c__1)
;
i__3 = ki - 1;
for (k = 1; k <= i__3; ++k) {
vl[k + is * vl_dim1] = 0.f;
vl[k + (is + 1) * vl_dim1] = 0.f;
/* L230: */
}
} else if (nb == 1) {
/* ------------------------------ */
/* version 1: back-transform each vector with GEMV, Q*x. */
if (ki < *n - 1) {
i__3 = *n - ki - 1;
sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + iv * *n], &c__1, &
work[ki + iv * *n], &vl[ki * vl_dim1 + 1], &
c__1);
i__3 = *n - ki - 1;
sgemv_("N", n, &i__3, &c_b29, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + (iv + 1) * *n], &
c__1, &work[ki + 1 + (iv + 1) * *n], &vl[(ki
+ 1) * vl_dim1 + 1], &c__1);
} else {
sscal_(n, &work[ki + iv * *n], &vl[ki * vl_dim1 + 1],
&c__1);
sscal_(n, &work[ki + 1 + (iv + 1) * *n], &vl[(ki + 1)
* vl_dim1 + 1], &c__1);
}
emax = 0.f;
i__3 = *n;
for (k = 1; k <= i__3; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vl[k + ki * vl_dim1], abs(
r__1)) + (r__2 = vl[k + (ki + 1) * vl_dim1],
abs(r__2));
emax = f2cmax(r__3,r__4);
/* L240: */
}
remax = 1.f / emax;
sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
sscal_(n, &remax, &vl[(ki + 1) * vl_dim1 + 1], &c__1);
} else {
/* ------------------------------ */
/* version 2: back-transform block of vectors with GEMM */
/* zero out above vector */
/* could go from KI-NV+1 to KI-1 */
i__3 = ki - 1;
for (k = 1; k <= i__3; ++k) {
work[k + iv * *n] = 0.f;
work[k + (iv + 1) * *n] = 0.f;
}
iscomplex[iv - 1] = ip;
iscomplex[iv] = -ip;
++iv;
/* back-transform and normalization is done below */
}
}
if (nb > 1) {
/* -------------------------------------------------------- */
/* Blocked version of back-transform */
/* For complex case, KI2 includes both vectors (KI and KI+1) */
if (ip == 0) {
ki2 = ki;
} else {
ki2 = ki + 1;
}
/* Columns 1:IV of work are valid vectors. */
/* When the number of vectors stored reaches NB-1 or NB, */
/* or if this was last vector, do the GEMM */
if (iv >= nb - 1 || ki2 == *n) {
i__3 = *n - ki2 + iv;
sgemm_("N", "N", n, &iv, &i__3, &c_b29, &vl[(ki2 - iv + 1)
* vl_dim1 + 1], ldvl, &work[ki2 - iv + 1 + *n],
n, &c_b17, &work[(nb + 1) * *n + 1], n);
/* normalize vectors */
i__3 = iv;
for (k = 1; k <= i__3; ++k) {
if (iscomplex[k - 1] == 0) {
/* real eigenvector */
ii = isamax_(n, &work[(nb + k) * *n + 1], &c__1);
remax = 1.f / (r__1 = work[ii + (nb + k) * *n],
abs(r__1));
} else if (iscomplex[k - 1] == 1) {
/* first eigenvector of conjugate pair */
emax = 0.f;
i__4 = *n;
for (ii = 1; ii <= i__4; ++ii) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = work[ii + (nb + k)
* *n], abs(r__1)) + (r__2 = work[ii
+ (nb + k + 1) * *n], abs(r__2));
emax = f2cmax(r__3,r__4);
}
remax = 1.f / emax;
/* else if ISCOMPLEX(K).EQ.-1 */
/* second eigenvector of conjugate pair */
/* reuse same REMAX as previous K */
}
sscal_(n, &remax, &work[(nb + k) * *n + 1], &c__1);
}
slacpy_("F", n, &iv, &work[(nb + 1) * *n + 1], n, &vl[(
ki2 - iv + 1) * vl_dim1 + 1], ldvl);
iv = 1;
} else {
++iv;
}
}
/* blocked back-transform */
++is;
if (ip != 0) {
++is;
}
L260:
;
}
}
return;
/* End of STREVC3 */
} /* strevc3_ */
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