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OpenBLAS/lapack-netlib/SRC/dstebz.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__3 = 3;
static integer c__2 = 2;
static integer c__0 = 0;
/* > \brief \b DSTEBZ */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSTEBZ + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstebz.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstebz.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstebz.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, */
/* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, */
/* INFO ) */
/* CHARACTER ORDER, RANGE */
/* INTEGER IL, INFO, IU, M, N, NSPLIT */
/* DOUBLE PRECISION ABSTOL, VL, VU */
/* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) */
/* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSTEBZ computes the eigenvalues of a symmetric tridiagonal */
/* > matrix T. The user may ask for all eigenvalues, all eigenvalues */
/* > in the half-open interval (VL, VU], or the IL-th through IU-th */
/* > eigenvalues. */
/* > */
/* > To avoid overflow, the matrix must be scaled so that its */
/* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
*/
/* > accuracy, it should not be much smaller than that. */
/* > */
/* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
/* > Matrix", Report CS41, Computer Science Dept., Stanford */
/* > University, July 21, 1966. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] RANGE */
/* > \verbatim */
/* > RANGE is CHARACTER*1 */
/* > = 'A': ("All") all eigenvalues will be found. */
/* > = 'V': ("Value") all eigenvalues in the half-open interval */
/* > (VL, VU] will be found. */
/* > = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
/* > entire matrix) will be found. */
/* > \endverbatim */
/* > */
/* > \param[in] ORDER */
/* > \verbatim */
/* > ORDER is CHARACTER*1 */
/* > = 'B': ("By Block") the eigenvalues will be grouped by */
/* > split-off block (see IBLOCK, ISPLIT) and */
/* > ordered from smallest to largest within */
/* > the block. */
/* > = 'E': ("Entire matrix") */
/* > the eigenvalues for the entire matrix */
/* > will be ordered from smallest to */
/* > largest. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the tridiagonal matrix T. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] VL */
/* > \verbatim */
/* > VL is DOUBLE PRECISION */
/* > */
/* > If RANGE='V', the lower bound of the interval to */
/* > be searched for eigenvalues. Eigenvalues less than or equal */
/* > to VL, or greater than VU, will not be returned. VL < VU. */
/* > Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] VU */
/* > \verbatim */
/* > VU is DOUBLE PRECISION */
/* > */
/* > If RANGE='V', the upper bound of the interval to */
/* > be searched for eigenvalues. Eigenvalues less than or equal */
/* > to VL, or greater than VU, will not be returned. VL < VU. */
/* > Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* > IL is INTEGER */
/* > */
/* > If RANGE='I', the index of the */
/* > smallest eigenvalue to be returned. */
/* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* > Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* > IU is INTEGER */
/* > */
/* > If RANGE='I', the index of the */
/* > largest eigenvalue to be returned. */
/* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* > Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] ABSTOL */
/* > \verbatim */
/* > ABSTOL is DOUBLE PRECISION */
/* > The absolute tolerance for the eigenvalues. An eigenvalue */
/* > (or cluster) is considered to be located if it has been */
/* > determined to lie in an interval whose width is ABSTOL or */
/* > less. If ABSTOL is less than or equal to zero, then ULP*|T| */
/* > will be used, where |T| means the 1-norm of T. */
/* > */
/* > Eigenvalues will be computed most accurately when ABSTOL is */
/* > set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > The n diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N-1) */
/* > The (n-1) off-diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The actual number of eigenvalues found. 0 <= M <= N. */
/* > (See also the description of INFO=2,3.) */
/* > \endverbatim */
/* > */
/* > \param[out] NSPLIT */
/* > \verbatim */
/* > NSPLIT is INTEGER */
/* > The number of diagonal blocks in the matrix T. */
/* > 1 <= NSPLIT <= N. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is DOUBLE PRECISION array, dimension (N) */
/* > On exit, the first M elements of W will contain the */
/* > eigenvalues. (DSTEBZ may use the remaining N-M elements as */
/* > workspace.) */
/* > \endverbatim */
/* > */
/* > \param[out] IBLOCK */
/* > \verbatim */
/* > IBLOCK is INTEGER array, dimension (N) */
/* > At each row/column j where E(j) is zero or small, the */
/* > matrix T is considered to split into a block diagonal */
/* > matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
/* > block (from 1 to the number of blocks) the eigenvalue W(i) */
/* > belongs. (DSTEBZ may use the remaining N-M elements as */
/* > workspace.) */
/* > \endverbatim */
/* > */
/* > \param[out] ISPLIT */
/* > \verbatim */
/* > ISPLIT is INTEGER array, dimension (N) */
/* > The splitting points, at which T breaks up into submatrices. */
/* > The first submatrix consists of rows/columns 1 to ISPLIT(1), */
/* > the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
/* > etc., and the NSPLIT-th consists of rows/columns */
/* > ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
/* > (Only the first NSPLIT elements will actually be used, but */
/* > since the user cannot know a priori what value NSPLIT will */
/* > have, N words must be reserved for ISPLIT.) */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (3*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > > 0: some or all of the eigenvalues failed to converge or */
/* > were not computed: */
/* > =1 or 3: Bisection failed to converge for some */
/* > eigenvalues; these eigenvalues are flagged by a */
/* > negative block number. The effect is that the */
/* > eigenvalues may not be as accurate as the */
/* > absolute and relative tolerances. This is */
/* > generally caused by unexpectedly inaccurate */
/* > arithmetic. */
/* > =2 or 3: RANGE='I' only: Not all of the eigenvalues */
/* > IL:IU were found. */
/* > Effect: M < IU+1-IL */
/* > Cause: non-monotonic arithmetic, causing the */
/* > Sturm sequence to be non-monotonic. */
/* > Cure: recalculate, using RANGE='A', and pick */
/* > out eigenvalues IL:IU. In some cases, */
/* > increasing the PARAMETER "FUDGE" may */
/* > make things work. */
/* > = 4: RANGE='I', and the Gershgorin interval */
/* > initially used was too small. No eigenvalues */
/* > were computed. */
/* > Probable cause: your machine has sloppy */
/* > floating-point arithmetic. */
/* > Cure: Increase the PARAMETER "FUDGE", */
/* > recompile, and try again. */
/* > \endverbatim */
/* > \par Internal Parameters: */
/* ========================= */
/* > */
/* > \verbatim */
/* > RELFAC DOUBLE PRECISION, default = 2.0e0 */
/* > The relative tolerance. An interval (a,b] lies within */
/* > "relative tolerance" if b-a < RELFAC*ulp*f2cmax(|a|,|b|), */
/* > where "ulp" is the machine precision (distance from 1 to */
/* > the next larger floating point number.) */
/* > */
/* > FUDGE DOUBLE PRECISION, default = 2 */
/* > A "fudge factor" to widen the Gershgorin intervals. Ideally, */
/* > a value of 1 should work, but on machines with sloppy */
/* > arithmetic, this needs to be larger. The default for */
/* > publicly released versions should be large enough to handle */
/* > the worst machine around. Note that this has no effect */
/* > on accuracy of the solution. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup auxOTHERcomputational */
/* ===================================================================== */
/* Subroutine */ int dstebz_(char *range, char *order, integer *n, doublereal
*vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
doublereal *d__, doublereal *e, integer *m, integer *nsplit,
doublereal *w, integer *iblock, integer *isplit, doublereal *work,
integer *iwork, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1, d__2, d__3, d__4, d__5;
/* Local variables */
integer iend, ioff, iout, itmp1, j, jdisc;
extern logical lsame_(char *, char *);
integer iinfo;
doublereal atoli;
integer iwoff;
doublereal bnorm;
integer itmax;
doublereal wkill, rtoli, tnorm;
integer ib, jb, ie, je, nb;
doublereal gl;
integer im, in;
extern doublereal dlamch_(char *);
integer ibegin;
doublereal gu;
integer iw;
extern /* Subroutine */ int dlaebz_(integer *, integer *, integer *,
integer *, integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
doublereal wl;
integer irange, idiscl;
doublereal safemn, wu;
integer idumma[1];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
integer idiscu, iorder;
logical ncnvrg;
doublereal pivmin;
logical toofew;
integer nwl;
doublereal ulp, wlu, wul;
integer nwu;
doublereal tmp1, tmp2;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* Parameter adjustments */
--iwork;
--work;
--isplit;
--iblock;
--w;
--e;
--d__;
/* Function Body */
*info = 0;
/* Decode RANGE */
if (lsame_(range, "A")) {
irange = 1;
} else if (lsame_(range, "V")) {
irange = 2;
} else if (lsame_(range, "I")) {
irange = 3;
} else {
irange = 0;
}
/* Decode ORDER */
if (lsame_(order, "B")) {
iorder = 2;
} else if (lsame_(order, "E")) {
iorder = 1;
} else {
iorder = 0;
}
/* Check for Errors */
if (irange <= 0) {
*info = -1;
} else if (iorder <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (irange == 2) {
if (*vl >= *vu) {
*info = -5;
}
} else if (irange == 3 && (*il < 1 || *il > f2cmax(1,*n))) {
*info = -6;
} else if (irange == 3 && (*iu < f2cmin(*n,*il) || *iu > *n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSTEBZ", &i__1, (ftnlen)6);
return 0;
}
/* Initialize error flags */
*info = 0;
ncnvrg = FALSE_;
toofew = FALSE_;
/* Quick return if possible */
*m = 0;
if (*n == 0) {
return 0;
}
/* Simplifications: */
if (irange == 3 && *il == 1 && *iu == *n) {
irange = 1;
}
/* Get machine constants */
/* NB is the minimum vector length for vector bisection, or 0 */
/* if only scalar is to be done. */
safemn = dlamch_("S");
ulp = dlamch_("P");
rtoli = ulp * 2.;
nb = ilaenv_(&c__1, "DSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1) {
nb = 0;
}
/* Special Case when N=1 */
if (*n == 1) {
*nsplit = 1;
isplit[1] = 1;
if (irange == 2 && (*vl >= d__[1] || *vu < d__[1])) {
*m = 0;
} else {
w[1] = d__[1];
iblock[1] = 1;
*m = 1;
}
return 0;
}
/* Compute Splitting Points */
*nsplit = 1;
work[*n] = 0.;
pivmin = 1.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
/* Computing 2nd power */
d__1 = e[j - 1];
tmp1 = d__1 * d__1;
/* Computing 2nd power */
d__2 = ulp;
if ((d__1 = d__[j] * d__[j - 1], abs(d__1)) * (d__2 * d__2) + safemn
> tmp1) {
isplit[*nsplit] = j - 1;
++(*nsplit);
work[j - 1] = 0.;
} else {
work[j - 1] = tmp1;
pivmin = f2cmax(pivmin,tmp1);
}
/* L10: */
}
isplit[*nsplit] = *n;
pivmin *= safemn;
/* Compute Interval and ATOLI */
if (irange == 3) {
/* RANGE='I': Compute the interval containing eigenvalues */
/* IL through IU. */
/* Compute Gershgorin interval for entire (split) matrix */
/* and use it as the initial interval */
gu = d__[1];
gl = d__[1];
tmp1 = 0.;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
tmp2 = sqrt(work[j]);
/* Computing MAX */
d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
gu = f2cmax(d__1,d__2);
/* Computing MIN */
d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
gl = f2cmin(d__1,d__2);
tmp1 = tmp2;
/* L20: */
}
/* Computing MAX */
d__1 = gu, d__2 = d__[*n] + tmp1;
gu = f2cmax(d__1,d__2);
/* Computing MIN */
d__1 = gl, d__2 = d__[*n] - tmp1;
gl = f2cmin(d__1,d__2);
/* Computing MAX */
d__1 = abs(gl), d__2 = abs(gu);
tnorm = f2cmax(d__1,d__2);
gl = gl - tnorm * 2.1 * ulp * *n - pivmin * 4.2000000000000002;
gu = gu + tnorm * 2.1 * ulp * *n + pivmin * 2.1;
/* Compute Iteration parameters */
itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.)) + 2;
if (*abstol <= 0.) {
atoli = ulp * tnorm;
} else {
atoli = *abstol;
}
work[*n + 1] = gl;
work[*n + 2] = gl;
work[*n + 3] = gu;
work[*n + 4] = gu;
work[*n + 5] = gl;
work[*n + 6] = gu;
iwork[1] = -1;
iwork[2] = -1;
iwork[3] = *n + 1;
iwork[4] = *n + 1;
iwork[5] = *il - 1;
iwork[6] = *iu;
dlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
&d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
+ 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
if (iwork[6] == *iu) {
wl = work[*n + 1];
wlu = work[*n + 3];
nwl = iwork[1];
wu = work[*n + 4];
wul = work[*n + 2];
nwu = iwork[4];
} else {
wl = work[*n + 2];
wlu = work[*n + 4];
nwl = iwork[2];
wu = work[*n + 3];
wul = work[*n + 1];
nwu = iwork[3];
}
if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
*info = 4;
return 0;
}
} else {
/* RANGE='A' or 'V' -- Set ATOLI */
/* Computing MAX */
d__3 = abs(d__[1]) + abs(e[1]), d__4 = (d__1 = d__[*n], abs(d__1)) + (
d__2 = e[*n - 1], abs(d__2));
tnorm = f2cmax(d__3,d__4);
i__1 = *n - 1;
for (j = 2; j <= i__1; ++j) {
/* Computing MAX */
d__4 = tnorm, d__5 = (d__1 = d__[j], abs(d__1)) + (d__2 = e[j - 1]
, abs(d__2)) + (d__3 = e[j], abs(d__3));
tnorm = f2cmax(d__4,d__5);
/* L30: */
}
if (*abstol <= 0.) {
atoli = ulp * tnorm;
} else {
atoli = *abstol;
}
if (irange == 2) {
wl = *vl;
wu = *vu;
} else {
wl = 0.;
wu = 0.;
}
}
/* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. */
/* NWL accumulates the number of eigenvalues .le. WL, */
/* NWU accumulates the number of eigenvalues .le. WU */
*m = 0;
iend = 0;
*info = 0;
nwl = 0;
nwu = 0;
i__1 = *nsplit;
for (jb = 1; jb <= i__1; ++jb) {
ioff = iend;
ibegin = ioff + 1;
iend = isplit[jb];
in = iend - ioff;
if (in == 1) {
/* Special Case -- IN=1 */
if (irange == 1 || wl >= d__[ibegin] - pivmin) {
++nwl;
}
if (irange == 1 || wu >= d__[ibegin] - pivmin) {
++nwu;
}
if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
- pivmin) {
++(*m);
w[*m] = d__[ibegin];
iblock[*m] = jb;
}
} else {
/* General Case -- IN > 1 */
/* Compute Gershgorin Interval */
/* and use it as the initial interval */
gu = d__[ibegin];
gl = d__[ibegin];
tmp1 = 0.;
i__2 = iend - 1;
for (j = ibegin; j <= i__2; ++j) {
tmp2 = (d__1 = e[j], abs(d__1));
/* Computing MAX */
d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
gu = f2cmax(d__1,d__2);
/* Computing MIN */
d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
gl = f2cmin(d__1,d__2);
tmp1 = tmp2;
/* L40: */
}
/* Computing MAX */
d__1 = gu, d__2 = d__[iend] + tmp1;
gu = f2cmax(d__1,d__2);
/* Computing MIN */
d__1 = gl, d__2 = d__[iend] - tmp1;
gl = f2cmin(d__1,d__2);
/* Computing MAX */
d__1 = abs(gl), d__2 = abs(gu);
bnorm = f2cmax(d__1,d__2);
gl = gl - bnorm * 2.1 * ulp * in - pivmin * 2.1;
gu = gu + bnorm * 2.1 * ulp * in + pivmin * 2.1;
/* Compute ATOLI for the current submatrix */
if (*abstol <= 0.) {
/* Computing MAX */
d__1 = abs(gl), d__2 = abs(gu);
atoli = ulp * f2cmax(d__1,d__2);
} else {
atoli = *abstol;
}
if (irange > 1) {
if (gu < wl) {
nwl += in;
nwu += in;
goto L70;
}
gl = f2cmax(gl,wl);
gu = f2cmin(gu,wu);
if (gl >= gu) {
goto L70;
}
}
/* Set Up Initial Interval */
work[*n + 1] = gl;
work[*n + in + 1] = gu;
dlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
w[*m + 1], &iblock[*m + 1], &iinfo);
nwl += iwork[1];
nwu += iwork[in + 1];
iwoff = *m - iwork[1];
/* Compute Eigenvalues */
itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(2.)
) + 2;
dlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
&w[*m + 1], &iblock[*m + 1], &iinfo);
/* Copy Eigenvalues Into W and IBLOCK */
/* Use -JB for block number for unconverged eigenvalues. */
i__2 = iout;
for (j = 1; j <= i__2; ++j) {
tmp1 = (work[j + *n] + work[j + in + *n]) * .5;
/* Flag non-convergence. */
if (j > iout - iinfo) {
ncnvrg = TRUE_;
ib = -jb;
} else {
ib = jb;
}
i__3 = iwork[j + in] + iwoff;
for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
w[je] = tmp1;
iblock[je] = ib;
/* L50: */
}
/* L60: */
}
*m += im;
}
L70:
;
}
/* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
/* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
if (irange == 3) {
im = 0;
idiscl = *il - 1 - nwl;
idiscu = nwu - *iu;
if (idiscl > 0 || idiscu > 0) {
i__1 = *m;
for (je = 1; je <= i__1; ++je) {
if (w[je] <= wlu && idiscl > 0) {
--idiscl;
} else if (w[je] >= wul && idiscu > 0) {
--idiscu;
} else {
++im;
w[im] = w[je];
iblock[im] = iblock[je];
}
/* L80: */
}
*m = im;
}
if (idiscl > 0 || idiscu > 0) {
/* Code to deal with effects of bad arithmetic: */
/* Some low eigenvalues to be discarded are not in (WL,WLU], */
/* or high eigenvalues to be discarded are not in (WUL,WU] */
/* so just kill off the smallest IDISCL/largest IDISCU */
/* eigenvalues, by simply finding the smallest/largest */
/* eigenvalue(s). */
/* (If N(w) is monotone non-decreasing, this should never */
/* happen.) */
if (idiscl > 0) {
wkill = wu;
i__1 = idiscl;
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
iw = 0;
i__2 = *m;
for (je = 1; je <= i__2; ++je) {
if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
iw = je;
wkill = w[je];
}
/* L90: */
}
iblock[iw] = 0;
/* L100: */
}
}
if (idiscu > 0) {
wkill = wl;
i__1 = idiscu;
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
iw = 0;
i__2 = *m;
for (je = 1; je <= i__2; ++je) {
if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
iw = je;
wkill = w[je];
}
/* L110: */
}
iblock[iw] = 0;
/* L120: */
}
}
im = 0;
i__1 = *m;
for (je = 1; je <= i__1; ++je) {
if (iblock[je] != 0) {
++im;
w[im] = w[je];
iblock[im] = iblock[je];
}
/* L130: */
}
*m = im;
}
if (idiscl < 0 || idiscu < 0) {
toofew = TRUE_;
}
}
/* If ORDER='B', do nothing -- the eigenvalues are already sorted */
/* by block. */
/* If ORDER='E', sort the eigenvalues from smallest to largest */
if (iorder == 1 && *nsplit > 1) {
i__1 = *m - 1;
for (je = 1; je <= i__1; ++je) {
ie = 0;
tmp1 = w[je];
i__2 = *m;
for (j = je + 1; j <= i__2; ++j) {
if (w[j] < tmp1) {
ie = j;
tmp1 = w[j];
}
/* L140: */
}
if (ie != 0) {
itmp1 = iblock[ie];
w[ie] = w[je];
iblock[ie] = iblock[je];
w[je] = tmp1;
iblock[je] = itmp1;
}
/* L150: */
}
}
*info = 0;
if (ncnvrg) {
++(*info);
}
if (toofew) {
*info += 2;
}
return 0;
/* End of DSTEBZ */
} /* dstebz_ */
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