OpenBLAS/lapack-netlib/SRC/slasq2.c

1189 lines
31 KiB
C

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static integer c__2 = 2;
/* > \brief \b SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc
iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SLASQ2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasq2.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasq2.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasq2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SLASQ2( N, Z, INFO ) */
/* INTEGER INFO, N */
/* REAL Z( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLASQ2 computes all the eigenvalues of the symmetric positive */
/* > definite tridiagonal matrix associated with the qd array Z to high */
/* > relative accuracy are computed to high relative accuracy, in the */
/* > absence of denormalization, underflow and overflow. */
/* > */
/* > To see the relation of Z to the tridiagonal matrix, let L be a */
/* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */
/* > let U be an upper bidiagonal matrix with 1's above and diagonal */
/* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */
/* > symmetric tridiagonal to which it is similar. */
/* > */
/* > Note : SLASQ2 defines a logical variable, IEEE, which is true */
/* > on machines which follow ieee-754 floating-point standard in their */
/* > handling of infinities and NaNs, and false otherwise. This variable */
/* > is passed to SLASQ3. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of rows and columns in the matrix. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is REAL array, dimension ( 4*N ) */
/* > On entry Z holds the qd array. On exit, entries 1 to N hold */
/* > the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */
/* > trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */
/* > N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */
/* > holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */
/* > shifts that failed. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if the i-th argument is a scalar and had an illegal */
/* > value, then INFO = -i, if the i-th argument is an */
/* > array and the j-entry had an illegal value, then */
/* > INFO = -(i*100+j) */
/* > > 0: the algorithm failed */
/* > = 1, a split was marked by a positive value in E */
/* > = 2, current block of Z not diagonalized after 100*N */
/* > iterations (in inner while loop). On exit Z holds */
/* > a qd array with the same eigenvalues as the given Z. */
/* > = 3, termination criterion of outer while loop not met */
/* > (program created more than N unreduced blocks) */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup auxOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Local Variables: I0:N0 defines a current unreduced segment of Z. */
/* > The shifts are accumulated in SIGMA. Iteration count is in ITER. */
/* > Ping-pong is controlled by PP (alternates between 0 and 1). */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void slasq2_(integer *n, real *z__, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3;
real r__1, r__2;
/* Local variables */
logical ieee;
integer nbig;
real dmin__, emin, emax;
integer kmin, ndiv, iter;
real qmin, temp, qmax, zmax;
integer splt;
real dmin1, dmin2, d__, e, g;
integer k;
real s, t;
integer nfail;
real desig, trace, sigma;
integer iinfo;
real tempe, tempq;
integer i0, i1, i4, n0, n1, ttype;
extern /* Subroutine */ void slasq3_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, integer *, integer *, integer *
, logical *, integer *, real *, real *, real *, real *, real *,
real *, real *);
real dn;
integer pp;
real deemin;
extern real slamch_(char *);
integer iwhila, iwhilb;
real oldemn, safmin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
real dn1, dn2;
extern /* Subroutine */ void slasrt_(char *, integer *, real *, integer *);
real dee, eps, tau, tol;
integer ipn4;
real tol2;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Test the input arguments. */
/* (in case SLASQ2 is not called by SLASQ1) */
/* Parameter adjustments */
--z__;
/* Function Body */
*info = 0;
eps = slamch_("Precision");
safmin = slamch_("Safe minimum");
tol = eps * 100.f;
/* Computing 2nd power */
r__1 = tol;
tol2 = r__1 * r__1;
if (*n < 0) {
*info = -1;
xerbla_("SLASQ2", &c__1, (ftnlen)6);
return;
} else if (*n == 0) {
return;
} else if (*n == 1) {
/* 1-by-1 case. */
if (z__[1] < 0.f) {
*info = -201;
xerbla_("SLASQ2", &c__2, (ftnlen)6);
}
return;
} else if (*n == 2) {
/* 2-by-2 case. */
if (z__[1] < 0.f) {
*info = -201;
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
} else if (z__[2] < 0.f) {
*info = -202;
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
} else if (z__[3] < 0.f) {
*info = -203;
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
} else if (z__[3] > z__[1]) {
d__ = z__[3];
z__[3] = z__[1];
z__[1] = d__;
}
z__[5] = z__[1] + z__[2] + z__[3];
if (z__[2] > z__[3] * tol2) {
t = (z__[1] - z__[3] + z__[2]) * .5f;
s = z__[3] * (z__[2] / t);
if (s <= t) {
s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.f) + 1.f)));
} else {
s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[1] + (s + z__[2]);
z__[3] *= z__[1] / t;
z__[1] = t;
}
z__[2] = z__[3];
z__[6] = z__[2] + z__[1];
return;
}
/* Check for negative data and compute sums of q's and e's. */
z__[*n * 2] = 0.f;
emin = z__[2];
qmax = 0.f;
zmax = 0.f;
d__ = 0.f;
e = 0.f;
i__1 = *n - 1 << 1;
for (k = 1; k <= i__1; k += 2) {
if (z__[k] < 0.f) {
*info = -(k + 200);
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
} else if (z__[k + 1] < 0.f) {
*info = -(k + 201);
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
}
d__ += z__[k];
e += z__[k + 1];
/* Computing MAX */
r__1 = qmax, r__2 = z__[k];
qmax = f2cmax(r__1,r__2);
/* Computing MIN */
r__1 = emin, r__2 = z__[k + 1];
emin = f2cmin(r__1,r__2);
/* Computing MAX */
r__1 = f2cmax(qmax,zmax), r__2 = z__[k + 1];
zmax = f2cmax(r__1,r__2);
/* L10: */
}
if (z__[(*n << 1) - 1] < 0.f) {
*info = -((*n << 1) + 199);
xerbla_("SLASQ2", &c__2, (ftnlen)6);
return;
}
d__ += z__[(*n << 1) - 1];
/* Computing MAX */
r__1 = qmax, r__2 = z__[(*n << 1) - 1];
qmax = f2cmax(r__1,r__2);
zmax = f2cmax(qmax,zmax);
/* Check for diagonality. */
if (e == 0.f) {
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
z__[k] = z__[(k << 1) - 1];
/* L20: */
}
slasrt_("D", n, &z__[1], &iinfo);
z__[(*n << 1) - 1] = d__;
return;
}
trace = d__ + e;
/* Check for zero data. */
if (trace == 0.f) {
z__[(*n << 1) - 1] = 0.f;
return;
}
/* Check whether the machine is IEEE conformable. */
/* IEEE = ILAENV( 10, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND. */
/* $ ILAENV( 11, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 */
/* [11/15/2008] The case IEEE=.TRUE. has a problem in single precision with */
/* some the test matrices of type 16. The double precision code is fine. */
ieee = FALSE_;
/* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */
for (k = *n << 1; k >= 2; k += -2) {
z__[k * 2] = 0.f;
z__[(k << 1) - 1] = z__[k];
z__[(k << 1) - 2] = 0.f;
z__[(k << 1) - 3] = z__[k - 1];
/* L30: */
}
i0 = 1;
n0 = *n;
/* Reverse the qd-array, if warranted. */
if (z__[(i0 << 2) - 3] * 1.5f < z__[(n0 << 2) - 3]) {
ipn4 = i0 + n0 << 2;
i__1 = i0 + n0 - 1 << 1;
for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {
temp = z__[i4 - 3];
z__[i4 - 3] = z__[ipn4 - i4 - 3];
z__[ipn4 - i4 - 3] = temp;
temp = z__[i4 - 1];
z__[i4 - 1] = z__[ipn4 - i4 - 5];
z__[ipn4 - i4 - 5] = temp;
/* L40: */
}
}
/* Initial split checking via dqd and Li's test. */
pp = 0;
for (k = 1; k <= 2; ++k) {
d__ = z__[(n0 << 2) + pp - 3];
i__1 = (i0 << 2) + pp;
for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) {
if (z__[i4 - 1] <= tol2 * d__) {
z__[i4 - 1] = 0.f;
d__ = z__[i4 - 3];
} else {
d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));
}
/* L50: */
}
/* dqd maps Z to ZZ plus Li's test. */
emin = z__[(i0 << 2) + pp + 1];
d__ = z__[(i0 << 2) + pp - 3];
i__1 = (n0 - 1 << 2) + pp;
for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {
z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];
if (z__[i4 - 1] <= tol2 * d__) {
z__[i4 - 1] = 0.f;
z__[i4 - (pp << 1) - 2] = d__;
z__[i4 - (pp << 1)] = 0.f;
d__ = z__[i4 + 1];
} else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] &&
safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {
temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];
z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;
d__ *= temp;
} else {
z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (
pp << 1) - 2]);
d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);
}
/* Computing MIN */
r__1 = emin, r__2 = z__[i4 - (pp << 1)];
emin = f2cmin(r__1,r__2);
/* L60: */
}
z__[(n0 << 2) - pp - 2] = d__;
/* Now find qmax. */
qmax = z__[(i0 << 2) - pp - 2];
i__1 = (n0 << 2) - pp - 2;
for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {
/* Computing MAX */
r__1 = qmax, r__2 = z__[i4];
qmax = f2cmax(r__1,r__2);
/* L70: */
}
/* Prepare for the next iteration on K. */
pp = 1 - pp;
/* L80: */
}
/* Initialise variables to pass to SLASQ3. */
ttype = 0;
dmin1 = 0.f;
dmin2 = 0.f;
dn = 0.f;
dn1 = 0.f;
dn2 = 0.f;
g = 0.f;
tau = 0.f;
iter = 2;
nfail = 0;
ndiv = n0 - i0 << 1;
i__1 = *n + 1;
for (iwhila = 1; iwhila <= i__1; ++iwhila) {
if (n0 < 1) {
goto L170;
}
/* While array unfinished do */
/* E(N0) holds the value of SIGMA when submatrix in I0:N0 */
/* splits from the rest of the array, but is negated. */
desig = 0.f;
if (n0 == *n) {
sigma = 0.f;
} else {
sigma = -z__[(n0 << 2) - 1];
}
if (sigma < 0.f) {
*info = 1;
return;
}
/* Find last unreduced submatrix's top index I0, find QMAX and */
/* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */
emax = 0.f;
if (n0 > i0) {
emin = (r__1 = z__[(n0 << 2) - 5], abs(r__1));
} else {
emin = 0.f;
}
qmin = z__[(n0 << 2) - 3];
qmax = qmin;
for (i4 = n0 << 2; i4 >= 8; i4 += -4) {
if (z__[i4 - 5] <= 0.f) {
goto L100;
}
if (qmin >= emax * 4.f) {
/* Computing MIN */
r__1 = qmin, r__2 = z__[i4 - 3];
qmin = f2cmin(r__1,r__2);
/* Computing MAX */
r__1 = emax, r__2 = z__[i4 - 5];
emax = f2cmax(r__1,r__2);
}
/* Computing MAX */
r__1 = qmax, r__2 = z__[i4 - 7] + z__[i4 - 5];
qmax = f2cmax(r__1,r__2);
/* Computing MIN */
r__1 = emin, r__2 = z__[i4 - 5];
emin = f2cmin(r__1,r__2);
/* L90: */
}
i4 = 4;
L100:
i0 = i4 / 4;
pp = 0;
if (n0 - i0 > 1) {
dee = z__[(i0 << 2) - 3];
deemin = dee;
kmin = i0;
i__2 = (n0 << 2) - 3;
for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) {
dee = z__[i4] * (dee / (dee + z__[i4 - 2]));
if (dee <= deemin) {
deemin = dee;
kmin = (i4 + 3) / 4;
}
/* L110: */
}
if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] *
.5f) {
ipn4 = i0 + n0 << 2;
pp = 2;
i__2 = i0 + n0 - 1 << 1;
for (i4 = i0 << 2; i4 <= i__2; i4 += 4) {
temp = z__[i4 - 3];
z__[i4 - 3] = z__[ipn4 - i4 - 3];
z__[ipn4 - i4 - 3] = temp;
temp = z__[i4 - 2];
z__[i4 - 2] = z__[ipn4 - i4 - 2];
z__[ipn4 - i4 - 2] = temp;
temp = z__[i4 - 1];
z__[i4 - 1] = z__[ipn4 - i4 - 5];
z__[ipn4 - i4 - 5] = temp;
temp = z__[i4];
z__[i4] = z__[ipn4 - i4 - 4];
z__[ipn4 - i4 - 4] = temp;
/* L120: */
}
}
}
/* Put -(initial shift) into DMIN. */
/* Computing MAX */
r__1 = 0.f, r__2 = qmin - sqrt(qmin) * 2.f * sqrt(emax);
dmin__ = -f2cmax(r__1,r__2);
/* Now I0:N0 is unreduced. */
/* PP = 0 for ping, PP = 1 for pong. */
/* PP = 2 indicates that flipping was applied to the Z array and */
/* and that the tests for deflation upon entry in SLASQ3 */
/* should not be performed. */
nbig = (n0 - i0 + 1) * 100;
i__2 = nbig;
for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) {
if (i0 > n0) {
goto L150;
}
/* While submatrix unfinished take a good dqds step. */
slasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &
nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, &
dn1, &dn2, &g, &tau);
pp = 1 - pp;
/* When EMIN is very small check for splits. */
if (pp == 0 && n0 - i0 >= 3) {
if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 *
sigma) {
splt = i0 - 1;
qmax = z__[(i0 << 2) - 3];
emin = z__[(i0 << 2) - 1];
oldemn = z__[i0 * 4];
i__3 = n0 - 3 << 2;
for (i4 = i0 << 2; i4 <= i__3; i4 += 4) {
if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <=
tol2 * sigma) {
z__[i4 - 1] = -sigma;
splt = i4 / 4;
qmax = 0.f;
emin = z__[i4 + 3];
oldemn = z__[i4 + 4];
} else {
/* Computing MAX */
r__1 = qmax, r__2 = z__[i4 + 1];
qmax = f2cmax(r__1,r__2);
/* Computing MIN */
r__1 = emin, r__2 = z__[i4 - 1];
emin = f2cmin(r__1,r__2);
/* Computing MIN */
r__1 = oldemn, r__2 = z__[i4];
oldemn = f2cmin(r__1,r__2);
}
/* L130: */
}
z__[(n0 << 2) - 1] = emin;
z__[n0 * 4] = oldemn;
i0 = splt + 1;
}
}
/* L140: */
}
*info = 2;
/* Maximum number of iterations exceeded, restore the shift */
/* SIGMA and place the new d's and e's in a qd array. */
/* This might need to be done for several blocks */
i1 = i0;
n1 = n0;
L145:
tempq = z__[(i0 << 2) - 3];
z__[(i0 << 2) - 3] += sigma;
i__2 = n0;
for (k = i0 + 1; k <= i__2; ++k) {
tempe = z__[(k << 2) - 5];
z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7];
tempq = z__[(k << 2) - 3];
z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k <<
2) - 5];
}
/* Prepare to do this on the previous block if there is one */
if (i1 > 1) {
n1 = i1 - 1;
while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.f) {
--i1;
}
if (i1 >= 1) {
sigma = -z__[(n1 << 2) - 1];
goto L145;
}
}
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
z__[(k << 1) - 1] = z__[(k << 2) - 3];
/* Only the block 1..N0 is unfinished. The rest of the e's */
/* must be essentially zero, although sometimes other data */
/* has been stored in them. */
if (k < n0) {
z__[k * 2] = z__[(k << 2) - 1];
} else {
z__[k * 2] = 0.f;
}
}
return;
/* end IWHILB */
L150:
/* L160: */
;
}
*info = 3;
return;
/* end IWHILA */
L170:
/* Move q's to the front. */
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
z__[k] = z__[(k << 2) - 3];
/* L180: */
}
/* Sort and compute sum of eigenvalues. */
slasrt_("D", n, &z__[1], &iinfo);
e = 0.f;
for (k = *n; k >= 1; --k) {
e += z__[k];
/* L190: */
}
/* Store trace, sum(eigenvalues) and information on performance. */
z__[(*n << 1) + 1] = trace;
z__[(*n << 1) + 2] = e;
z__[(*n << 1) + 3] = (real) iter;
/* Computing 2nd power */
i__1 = *n;
z__[(*n << 1) + 4] = (real) ndiv / (real) (i__1 * i__1);
z__[(*n << 1) + 5] = nfail * 100.f / (real) iter;
return;
/* End of SLASQ2 */
} /* slasq2_ */