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OpenBLAS/lapack-netlib/SRC/dlaqr5.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]/Cd(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 doublereal c_b7 = 0.;
static doublereal c_b8 = 1.;
static integer c__2 = 2;
static integer c__1 = 1;
static integer c__3 = 3;
/* > \brief \b DLAQR5 performs a single small-bulge multi-shift QR sweep. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLAQR5 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr5.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr5.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr5.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, */
/* SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, */
/* LDU, NV, WV, LDWV, NH, WH, LDWH ) */
/* INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV, */
/* $ LDWH, LDWV, LDZ, N, NH, NSHFTS, NV */
/* LOGICAL WANTT, WANTZ */
/* DOUBLE PRECISION H( LDH, * ), SI( * ), SR( * ), U( LDU, * ), */
/* $ V( LDV, * ), WH( LDWH, * ), WV( LDWV, * ), */
/* $ Z( LDZ, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAQR5, called by DLAQR0, performs a */
/* > single small-bulge multi-shift QR sweep. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] WANTT */
/* > \verbatim */
/* > WANTT is LOGICAL */
/* > WANTT = .true. if the quasi-triangular Schur factor */
/* > is being computed. WANTT is set to .false. otherwise. */
/* > \endverbatim */
/* > */
/* > \param[in] WANTZ */
/* > \verbatim */
/* > WANTZ is LOGICAL */
/* > WANTZ = .true. if the orthogonal Schur factor is being */
/* > computed. WANTZ is set to .false. otherwise. */
/* > \endverbatim */
/* > */
/* > \param[in] KACC22 */
/* > \verbatim */
/* > KACC22 is INTEGER with value 0, 1, or 2. */
/* > Specifies the computation mode of far-from-diagonal */
/* > orthogonal updates. */
/* > = 0: DLAQR5 does not accumulate reflections and does not */
/* > use matrix-matrix multiply to update far-from-diagonal */
/* > matrix entries. */
/* > = 1: DLAQR5 accumulates reflections and uses matrix-matrix */
/* > multiply to update the far-from-diagonal matrix entries. */
/* > = 2: Same as KACC22 = 1. This option used to enable exploiting */
/* > the 2-by-2 structure during matrix multiplications, but */
/* > this is no longer supported. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > N is the order of the Hessenberg matrix H upon which this */
/* > subroutine operates. */
/* > \endverbatim */
/* > */
/* > \param[in] KTOP */
/* > \verbatim */
/* > KTOP is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] KBOT */
/* > \verbatim */
/* > KBOT is INTEGER */
/* > These are the first and last rows and columns of an */
/* > isolated diagonal block upon which the QR sweep is to be */
/* > applied. It is assumed without a check that */
/* > either KTOP = 1 or H(KTOP,KTOP-1) = 0 */
/* > and */
/* > either KBOT = N or H(KBOT+1,KBOT) = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NSHFTS */
/* > \verbatim */
/* > NSHFTS is INTEGER */
/* > NSHFTS gives the number of simultaneous shifts. NSHFTS */
/* > must be positive and even. */
/* > \endverbatim */
/* > */
/* > \param[in,out] SR */
/* > \verbatim */
/* > SR is DOUBLE PRECISION array, dimension (NSHFTS) */
/* > \endverbatim */
/* > */
/* > \param[in,out] SI */
/* > \verbatim */
/* > SI is DOUBLE PRECISION array, dimension (NSHFTS) */
/* > SR contains the real parts and SI contains the imaginary */
/* > parts of the NSHFTS shifts of origin that define the */
/* > multi-shift QR sweep. On output SR and SI may be */
/* > reordered. */
/* > \endverbatim */
/* > */
/* > \param[in,out] H */
/* > \verbatim */
/* > H is DOUBLE PRECISION array, dimension (LDH,N) */
/* > On input H contains a Hessenberg matrix. On output a */
/* > multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied */
/* > to the isolated diagonal block in rows and columns KTOP */
/* > through KBOT. */
/* > \endverbatim */
/* > */
/* > \param[in] LDH */
/* > \verbatim */
/* > LDH is INTEGER */
/* > LDH is the leading dimension of H just as declared in the */
/* > calling procedure. LDH >= MAX(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] ILOZ */
/* > \verbatim */
/* > ILOZ is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] IHIZ */
/* > \verbatim */
/* > IHIZ is INTEGER */
/* > Specify the rows of Z to which transformations must be */
/* > applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is DOUBLE PRECISION array, dimension (LDZ,IHIZ) */
/* > If WANTZ = .TRUE., then the QR Sweep orthogonal */
/* > similarity transformation is accumulated into */
/* > Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. */
/* > If WANTZ = .FALSE., then Z is unreferenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* > LDZ is INTEGER */
/* > LDA is the leading dimension of Z just as declared in */
/* > the calling procedure. LDZ >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] V */
/* > \verbatim */
/* > V is DOUBLE PRECISION array, dimension (LDV,NSHFTS/2) */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > LDV is the leading dimension of V as declared in the */
/* > calling procedure. LDV >= 3. */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is DOUBLE PRECISION array, dimension (LDU,2*NSHFTS) */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > LDU is the leading dimension of U just as declared in the */
/* > in the calling subroutine. LDU >= 2*NSHFTS. */
/* > \endverbatim */
/* > */
/* > \param[in] NV */
/* > \verbatim */
/* > NV is INTEGER */
/* > NV is the number of rows in WV agailable for workspace. */
/* > NV >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] WV */
/* > \verbatim */
/* > WV is DOUBLE PRECISION array, dimension (LDWV,2*NSHFTS) */
/* > \endverbatim */
/* > */
/* > \param[in] LDWV */
/* > \verbatim */
/* > LDWV is INTEGER */
/* > LDWV is the leading dimension of WV as declared in the */
/* > in the calling subroutine. LDWV >= NV. */
/* > \endverbatim */
/* > \param[in] NH */
/* > \verbatim */
/* > NH is INTEGER */
/* > NH is the number of columns in array WH available for */
/* > workspace. NH >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] WH */
/* > \verbatim */
/* > WH is DOUBLE PRECISION array, dimension (LDWH,NH) */
/* > \endverbatim */
/* > */
/* > \param[in] LDWH */
/* > \verbatim */
/* > LDWH is INTEGER */
/* > Leading dimension of WH just as declared in the */
/* > calling procedure. LDWH >= 2*NSHFTS. */
/* > \endverbatim */
/* > */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date January 2021 */
/* > \ingroup doubleOTHERauxiliary */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Karen Braman and Ralph Byers, Department of Mathematics, */
/* > University of Kansas, USA */
/* > */
/* > Lars Karlsson, Daniel Kressner, and Bruno Lang */
/* > */
/* > Thijs Steel, Department of Computer science, */
/* > KU Leuven, Belgium */
/* > \par References: */
/* ================ */
/* > */
/* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
/* > Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
/* > Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
/* > 929--947, 2002. */
/* > */
/* > Lars Karlsson, Daniel Kressner, and Bruno Lang, Optimally packed */
/* > chains of bulges in multishift QR algorithms. */
/* > ACM Trans. Math. Softw. 40, 2, Article 12 (February 2014). */
/* > */
/* ===================================================================== */
/* Subroutine */ void dlaqr5_(logical *wantt, logical *wantz, integer *kacc22,
integer *n, integer *ktop, integer *kbot, integer *nshfts, doublereal
*sr, doublereal *si, doublereal *h__, integer *ldh, integer *iloz,
integer *ihiz, doublereal *z__, integer *ldz, doublereal *v, integer *
ldv, doublereal *u, integer *ldu, integer *nv, doublereal *wv,
integer *ldwv, integer *nh, doublereal *wh, integer *ldwh)
{
/* System generated locals */
integer h_dim1, h_offset, u_dim1, u_offset, v_dim1, v_offset, wh_dim1,
wh_offset, wv_dim1, wv_offset, z_dim1, z_offset, i__1, i__2, i__3,
i__4, i__5, i__6, i__7;
doublereal d__1, d__2, d__3, d__4, d__5;
/* Local variables */
doublereal beta;
logical bmp22;
integer jcol, jlen, jbot, mbot;
doublereal swap;
integer jtop, jrow, mtop, i__, j, k, m;
doublereal alpha;
logical accum;
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
integer ndcol, incol, krcol, nbmps, i2, k1, i4;
extern /* Subroutine */ void dlaqr1_(integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), dlabad_(doublereal *, doublereal *);
doublereal h11, h12, h21, h22;
integer m22;
extern doublereal dlamch_(char *);
extern /* Subroutine */ void dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *);
integer ns, nu;
doublereal vt[3];
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
doublereal safmin, safmax;
extern /* Subroutine */ void dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
doublereal refsum, smlnum, scl;
integer kdu, kms;
doublereal ulp;
doublereal tst1, tst2;
/* -- LAPACK auxiliary routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ================================================================ */
/* ==== If there are no shifts, then there is nothing to do. ==== */
/* Parameter adjustments */
--sr;
--si;
h_dim1 = *ldh;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1 * 1;
wv -= wv_offset;
wh_dim1 = *ldwh;
wh_offset = 1 + wh_dim1 * 1;
wh -= wh_offset;
/* Function Body */
if (*nshfts < 2) {
return;
}
/* ==== If the active block is empty or 1-by-1, then there */
/* . is nothing to do. ==== */
if (*ktop >= *kbot) {
return;
}
/* ==== Shuffle shifts into pairs of real shifts and pairs */
/* . of complex conjugate shifts assuming complex */
/* . conjugate shifts are already adjacent to one */
/* . another. ==== */
i__1 = *nshfts - 2;
for (i__ = 1; i__ <= i__1; i__ += 2) {
if (si[i__] != -si[i__ + 1]) {
swap = sr[i__];
sr[i__] = sr[i__ + 1];
sr[i__ + 1] = sr[i__ + 2];
sr[i__ + 2] = swap;
swap = si[i__];
si[i__] = si[i__ + 1];
si[i__ + 1] = si[i__ + 2];
si[i__ + 2] = swap;
}
/* L10: */
}
/* ==== NSHFTS is supposed to be even, but if it is odd, */
/* . then simply reduce it by one. The shuffle above */
/* . ensures that the dropped shift is real and that */
/* . the remaining shifts are paired. ==== */
ns = *nshfts - *nshfts % 2;
/* ==== Machine constants for deflation ==== */
safmin = dlamch_("SAFE MINIMUM");
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulp = dlamch_("PRECISION");
smlnum = safmin * ((doublereal) (*n) / ulp);
/* ==== Use accumulated reflections to update far-from-diagonal */
/* . entries ? ==== */
accum = *kacc22 == 1 || *kacc22 == 2;
/* ==== clear trash ==== */
if (*ktop + 2 <= *kbot) {
h__[*ktop + 2 + *ktop * h_dim1] = 0.;
}
/* ==== NBMPS = number of 2-shift bulges in the chain ==== */
nbmps = ns / 2;
/* ==== KDU = width of slab ==== */
kdu = nbmps << 2;
/* ==== Create and chase chains of NBMPS bulges ==== */
i__1 = *kbot - 2;
i__2 = nbmps << 1;
for (incol = *ktop - (nbmps << 1) + 1; i__2 < 0 ? incol >= i__1 : incol <=
i__1; incol += i__2) {
/* JTOP = Index from which updates from the right start. */
if (accum) {
jtop = f2cmax(*ktop,incol);
} else if (*wantt) {
jtop = 1;
} else {
jtop = *ktop;
}
ndcol = incol + kdu;
if (accum) {
dlaset_("ALL", &kdu, &kdu, &c_b7, &c_b8, &u[u_offset], ldu);
}
/* ==== Near-the-diagonal bulge chase. The following loop */
/* . performs the near-the-diagonal part of a small bulge */
/* . multi-shift QR sweep. Each 4*NBMPS column diagonal */
/* . chunk extends from column INCOL to column NDCOL */
/* . (including both column INCOL and column NDCOL). The */
/* . following loop chases a 2*NBMPS+1 column long chain of */
/* . NBMPS bulges 2*NBMPS columns to the right. (INCOL */
/* . may be less than KTOP and and NDCOL may be greater than */
/* . KBOT indicating phantom columns from which to chase */
/* . bulges before they are actually introduced or to which */
/* . to chase bulges beyond column KBOT.) ==== */
/* Computing MIN */
i__4 = incol + (nbmps << 1) - 1, i__5 = *kbot - 2;
i__3 = f2cmin(i__4,i__5);
for (krcol = incol; krcol <= i__3; ++krcol) {
/* ==== Bulges number MTOP to MBOT are active double implicit */
/* . shift bulges. There may or may not also be small */
/* . 2-by-2 bulge, if there is room. The inactive bulges */
/* . (if any) must wait until the active bulges have moved */
/* . down the diagonal to make room. The phantom matrix */
/* . paradigm described above helps keep track. ==== */
/* Computing MAX */
i__4 = 1, i__5 = (*ktop - krcol) / 2 + 1;
mtop = f2cmax(i__4,i__5);
/* Computing MIN */
i__4 = nbmps, i__5 = (*kbot - krcol - 1) / 2;
mbot = f2cmin(i__4,i__5);
m22 = mbot + 1;
bmp22 = mbot < nbmps && krcol + (m22 - 1 << 1) == *kbot - 2;
/* ==== Generate reflections to chase the chain right */
/* . one column. (The minimum value of K is KTOP-1.) ==== */
if (bmp22) {
/* ==== Special case: 2-by-2 reflection at bottom treated */
/* . separately ==== */
k = krcol + (m22 - 1 << 1);
if (k == *ktop - 1) {
dlaqr1_(&c__2, &h__[k + 1 + (k + 1) * h_dim1], ldh, &sr[(
m22 << 1) - 1], &si[(m22 << 1) - 1], &sr[m22 * 2],
&si[m22 * 2], &v[m22 * v_dim1 + 1]);
beta = v[m22 * v_dim1 + 1];
dlarfg_(&c__2, &beta, &v[m22 * v_dim1 + 2], &c__1, &v[m22
* v_dim1 + 1]);
} else {
beta = h__[k + 1 + k * h_dim1];
v[m22 * v_dim1 + 2] = h__[k + 2 + k * h_dim1];
dlarfg_(&c__2, &beta, &v[m22 * v_dim1 + 2], &c__1, &v[m22
* v_dim1 + 1]);
h__[k + 1 + k * h_dim1] = beta;
h__[k + 2 + k * h_dim1] = 0.;
}
/* ==== Perform update from right within */
/* . computational window. ==== */
/* Computing MIN */
i__5 = *kbot, i__6 = k + 3;
i__4 = f2cmin(i__5,i__6);
for (j = jtop; j <= i__4; ++j) {
refsum = v[m22 * v_dim1 + 1] * (h__[j + (k + 1) * h_dim1]
+ v[m22 * v_dim1 + 2] * h__[j + (k + 2) * h_dim1])
;
h__[j + (k + 1) * h_dim1] -= refsum;
h__[j + (k + 2) * h_dim1] -= refsum * v[m22 * v_dim1 + 2];
/* L30: */
}
/* ==== Perform update from left within */
/* . computational window. ==== */
if (accum) {
jbot = f2cmin(ndcol,*kbot);
} else if (*wantt) {
jbot = *n;
} else {
jbot = *kbot;
}
i__4 = jbot;
for (j = k + 1; j <= i__4; ++j) {
refsum = v[m22 * v_dim1 + 1] * (h__[k + 1 + j * h_dim1] +
v[m22 * v_dim1 + 2] * h__[k + 2 + j * h_dim1]);
h__[k + 1 + j * h_dim1] -= refsum;
h__[k + 2 + j * h_dim1] -= refsum * v[m22 * v_dim1 + 2];
/* L40: */
}
/* ==== The following convergence test requires that */
/* . the tradition small-compared-to-nearby-diagonals */
/* . criterion and the Ahues & Tisseur (LAWN 122, 1997) */
/* . criteria both be satisfied. The latter improves */
/* . accuracy in some examples. Falling back on an */
/* . alternate convergence criterion when TST1 or TST2 */
/* . is zero (as done here) is traditional but probably */
/* . unnecessary. ==== */
if (k >= *ktop) {
if (h__[k + 1 + k * h_dim1] != 0.) {
tst1 = (d__1 = h__[k + k * h_dim1], abs(d__1)) + (
d__2 = h__[k + 1 + (k + 1) * h_dim1], abs(
d__2));
if (tst1 == 0.) {
if (k >= *ktop + 1) {
tst1 += (d__1 = h__[k + (k - 1) * h_dim1],
abs(d__1));
}
if (k >= *ktop + 2) {
tst1 += (d__1 = h__[k + (k - 2) * h_dim1],
abs(d__1));
}
if (k >= *ktop + 3) {
tst1 += (d__1 = h__[k + (k - 3) * h_dim1],
abs(d__1));
}
if (k <= *kbot - 2) {
tst1 += (d__1 = h__[k + 2 + (k + 1) * h_dim1],
abs(d__1));
}
if (k <= *kbot - 3) {
tst1 += (d__1 = h__[k + 3 + (k + 1) * h_dim1],
abs(d__1));
}
if (k <= *kbot - 4) {
tst1 += (d__1 = h__[k + 4 + (k + 1) * h_dim1],
abs(d__1));
}
}
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * tst1;
if ((d__1 = h__[k + 1 + k * h_dim1], abs(d__1)) <=
f2cmax(d__2,d__3)) {
/* Computing MAX */
d__3 = (d__1 = h__[k + 1 + k * h_dim1], abs(d__1))
, d__4 = (d__2 = h__[k + (k + 1) * h_dim1]
, abs(d__2));
h12 = f2cmax(d__3,d__4);
/* Computing MIN */
d__3 = (d__1 = h__[k + 1 + k * h_dim1], abs(d__1))
, d__4 = (d__2 = h__[k + (k + 1) * h_dim1]
, abs(d__2));
h21 = f2cmin(d__3,d__4);
/* Computing MAX */
d__3 = (d__1 = h__[k + 1 + (k + 1) * h_dim1], abs(
d__1)), d__4 = (d__2 = h__[k + k * h_dim1]
- h__[k + 1 + (k + 1) * h_dim1], abs(
d__2));
h11 = f2cmax(d__3,d__4);
/* Computing MIN */
d__3 = (d__1 = h__[k + 1 + (k + 1) * h_dim1], abs(
d__1)), d__4 = (d__2 = h__[k + k * h_dim1]
- h__[k + 1 + (k + 1) * h_dim1], abs(
d__2));
h22 = f2cmin(d__3,d__4);
scl = h11 + h12;
tst2 = h22 * (h11 / scl);
/* Computing MAX */
d__1 = smlnum, d__2 = ulp * tst2;
if (tst2 == 0. || h21 * (h12 / scl) <= f2cmax(d__1,
d__2)) {
h__[k + 1 + k * h_dim1] = 0.;
}
}
}
}
/* ==== Accumulate orthogonal transformations. ==== */
if (accum) {
kms = k - incol;
/* Computing MAX */
i__4 = 1, i__5 = *ktop - incol;
i__6 = kdu;
for (j = f2cmax(i__4,i__5); j <= i__6; ++j) {
refsum = v[m22 * v_dim1 + 1] * (u[j + (kms + 1) *
u_dim1] + v[m22 * v_dim1 + 2] * u[j + (kms +
2) * u_dim1]);
u[j + (kms + 1) * u_dim1] -= refsum;
u[j + (kms + 2) * u_dim1] -= refsum * v[m22 * v_dim1
+ 2];
/* L50: */
}
} else if (*wantz) {
i__6 = *ihiz;
for (j = *iloz; j <= i__6; ++j) {
refsum = v[m22 * v_dim1 + 1] * (z__[j + (k + 1) *
z_dim1] + v[m22 * v_dim1 + 2] * z__[j + (k +
2) * z_dim1]);
z__[j + (k + 1) * z_dim1] -= refsum;
z__[j + (k + 2) * z_dim1] -= refsum * v[m22 * v_dim1
+ 2];
/* L60: */
}
}
}
/* ==== Normal case: Chain of 3-by-3 reflections ==== */
i__6 = mtop;
for (m = mbot; m >= i__6; --m) {
k = krcol + (m - 1 << 1);
if (k == *ktop - 1) {
dlaqr1_(&c__3, &h__[*ktop + *ktop * h_dim1], ldh, &sr[(m
<< 1) - 1], &si[(m << 1) - 1], &sr[m * 2], &si[m *
2], &v[m * v_dim1 + 1]);
alpha = v[m * v_dim1 + 1];
dlarfg_(&c__3, &alpha, &v[m * v_dim1 + 2], &c__1, &v[m *
v_dim1 + 1]);
} else {
/* ==== Perform delayed transformation of row below */
/* . Mth bulge. Exploit fact that first two elements */
/* . of row are actually zero. ==== */
refsum = v[m * v_dim1 + 1] * v[m * v_dim1 + 3] * h__[k +
3 + (k + 2) * h_dim1];
h__[k + 3 + k * h_dim1] = -refsum;
h__[k + 3 + (k + 1) * h_dim1] = -refsum * v[m * v_dim1 +
2];
h__[k + 3 + (k + 2) * h_dim1] -= refsum * v[m * v_dim1 +
3];
/* ==== Calculate reflection to move */
/* . Mth bulge one step. ==== */
beta = h__[k + 1 + k * h_dim1];
v[m * v_dim1 + 2] = h__[k + 2 + k * h_dim1];
v[m * v_dim1 + 3] = h__[k + 3 + k * h_dim1];
dlarfg_(&c__3, &beta, &v[m * v_dim1 + 2], &c__1, &v[m *
v_dim1 + 1]);
/* ==== A Bulge may collapse because of vigilant */
/* . deflation or destructive underflow. In the */
/* . underflow case, try the two-small-subdiagonals */
/* . trick to try to reinflate the bulge. ==== */
if (h__[k + 3 + k * h_dim1] != 0. || h__[k + 3 + (k + 1) *
h_dim1] != 0. || h__[k + 3 + (k + 2) * h_dim1] ==
0.) {
/* ==== Typical case: not collapsed (yet). ==== */
h__[k + 1 + k * h_dim1] = beta;
h__[k + 2 + k * h_dim1] = 0.;
h__[k + 3 + k * h_dim1] = 0.;
} else {
/* ==== Atypical case: collapsed. Attempt to */
/* . reintroduce ignoring H(K+1,K) and H(K+2,K). */
/* . If the fill resulting from the new */
/* . reflector is too large, then abandon it. */
/* . Otherwise, use the new one. ==== */
dlaqr1_(&c__3, &h__[k + 1 + (k + 1) * h_dim1], ldh, &
sr[(m << 1) - 1], &si[(m << 1) - 1], &sr[m *
2], &si[m * 2], vt);
alpha = vt[0];
dlarfg_(&c__3, &alpha, &vt[1], &c__1, vt);
refsum = vt[0] * (h__[k + 1 + k * h_dim1] + vt[1] *
h__[k + 2 + k * h_dim1]);
if ((d__1 = h__[k + 2 + k * h_dim1] - refsum * vt[1],
abs(d__1)) + (d__2 = refsum * vt[2], abs(d__2)
) > ulp * ((d__3 = h__[k + k * h_dim1], abs(
d__3)) + (d__4 = h__[k + 1 + (k + 1) * h_dim1]
, abs(d__4)) + (d__5 = h__[k + 2 + (k + 2) *
h_dim1], abs(d__5)))) {
/* ==== Starting a new bulge here would */
/* . create non-negligible fill. Use */
/* . the old one with trepidation. ==== */
h__[k + 1 + k * h_dim1] = beta;
h__[k + 2 + k * h_dim1] = 0.;
h__[k + 3 + k * h_dim1] = 0.;
} else {
/* ==== Starting a new bulge here would */
/* . create only negligible fill. */
/* . Replace the old reflector with */
/* . the new one. ==== */
h__[k + 1 + k * h_dim1] -= refsum;
h__[k + 2 + k * h_dim1] = 0.;
h__[k + 3 + k * h_dim1] = 0.;
v[m * v_dim1 + 1] = vt[0];
v[m * v_dim1 + 2] = vt[1];
v[m * v_dim1 + 3] = vt[2];
}
}
}
/* ==== Apply reflection from the right and */
/* . the first column of update from the left. */
/* . These updates are required for the vigilant */
/* . deflation check. We still delay most of the */
/* . updates from the left for efficiency. ==== */
/* Computing MIN */
i__5 = *kbot, i__7 = k + 3;
i__4 = f2cmin(i__5,i__7);
for (j = jtop; j <= i__4; ++j) {
refsum = v[m * v_dim1 + 1] * (h__[j + (k + 1) * h_dim1] +
v[m * v_dim1 + 2] * h__[j + (k + 2) * h_dim1] + v[
m * v_dim1 + 3] * h__[j + (k + 3) * h_dim1]);
h__[j + (k + 1) * h_dim1] -= refsum;
h__[j + (k + 2) * h_dim1] -= refsum * v[m * v_dim1 + 2];
h__[j + (k + 3) * h_dim1] -= refsum * v[m * v_dim1 + 3];
/* L70: */
}
/* ==== Perform update from left for subsequent */
/* . column. ==== */
refsum = v[m * v_dim1 + 1] * (h__[k + 1 + (k + 1) * h_dim1] +
v[m * v_dim1 + 2] * h__[k + 2 + (k + 1) * h_dim1] + v[
m * v_dim1 + 3] * h__[k + 3 + (k + 1) * h_dim1]);
h__[k + 1 + (k + 1) * h_dim1] -= refsum;
h__[k + 2 + (k + 1) * h_dim1] -= refsum * v[m * v_dim1 + 2];
h__[k + 3 + (k + 1) * h_dim1] -= refsum * v[m * v_dim1 + 3];
/* ==== The following convergence test requires that */
/* . the tradition small-compared-to-nearby-diagonals */
/* . criterion and the Ahues & Tisseur (LAWN 122, 1997) */
/* . criteria both be satisfied. The latter improves */
/* . accuracy in some examples. Falling back on an */
/* . alternate convergence criterion when TST1 or TST2 */
/* . is zero (as done here) is traditional but probably */
/* . unnecessary. ==== */
if (k < *ktop) {
mycycle_();
}
if (h__[k + 1 + k * h_dim1] != 0.) {
tst1 = (d__1 = h__[k + k * h_dim1], abs(d__1)) + (d__2 =
h__[k + 1 + (k + 1) * h_dim1], abs(d__2));
if (tst1 == 0.) {
if (k >= *ktop + 1) {
tst1 += (d__1 = h__[k + (k - 1) * h_dim1], abs(
d__1));
}
if (k >= *ktop + 2) {
tst1 += (d__1 = h__[k + (k - 2) * h_dim1], abs(
d__1));
}
if (k >= *ktop + 3) {
tst1 += (d__1 = h__[k + (k - 3) * h_dim1], abs(
d__1));
}
if (k <= *kbot - 2) {
tst1 += (d__1 = h__[k + 2 + (k + 1) * h_dim1],
abs(d__1));
}
if (k <= *kbot - 3) {
tst1 += (d__1 = h__[k + 3 + (k + 1) * h_dim1],
abs(d__1));
}
if (k <= *kbot - 4) {
tst1 += (d__1 = h__[k + 4 + (k + 1) * h_dim1],
abs(d__1));
}
}
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * tst1;
if ((d__1 = h__[k + 1 + k * h_dim1], abs(d__1)) <= f2cmax(
d__2,d__3)) {
/* Computing MAX */
d__3 = (d__1 = h__[k + 1 + k * h_dim1], abs(d__1)),
d__4 = (d__2 = h__[k + (k + 1) * h_dim1], abs(
d__2));
h12 = f2cmax(d__3,d__4);
/* Computing MIN */
d__3 = (d__1 = h__[k + 1 + k * h_dim1], abs(d__1)),
d__4 = (d__2 = h__[k + (k + 1) * h_dim1], abs(
d__2));
h21 = f2cmin(d__3,d__4);
/* Computing MAX */
d__3 = (d__1 = h__[k + 1 + (k + 1) * h_dim1], abs(
d__1)), d__4 = (d__2 = h__[k + k * h_dim1] -
h__[k + 1 + (k + 1) * h_dim1], abs(d__2));
h11 = f2cmax(d__3,d__4);
/* Computing MIN */
d__3 = (d__1 = h__[k + 1 + (k + 1) * h_dim1], abs(
d__1)), d__4 = (d__2 = h__[k + k * h_dim1] -
h__[k + 1 + (k + 1) * h_dim1], abs(d__2));
h22 = f2cmin(d__3,d__4);
scl = h11 + h12;
tst2 = h22 * (h11 / scl);
/* Computing MAX */
d__1 = smlnum, d__2 = ulp * tst2;
if (tst2 == 0. || h21 * (h12 / scl) <= f2cmax(d__1,d__2))
{
h__[k + 1 + k * h_dim1] = 0.;
}
}
}
/* L80: */
}
/* ==== Multiply H by reflections from the left ==== */
if (accum) {
jbot = f2cmin(ndcol,*kbot);
} else if (*wantt) {
jbot = *n;
} else {
jbot = *kbot;
}
i__6 = mtop;
for (m = mbot; m >= i__6; --m) {
k = krcol + (m - 1 << 1);
/* Computing MAX */
i__4 = *ktop, i__5 = krcol + (m << 1);
i__7 = jbot;
for (j = f2cmax(i__4,i__5); j <= i__7; ++j) {
refsum = v[m * v_dim1 + 1] * (h__[k + 1 + j * h_dim1] + v[
m * v_dim1 + 2] * h__[k + 2 + j * h_dim1] + v[m *
v_dim1 + 3] * h__[k + 3 + j * h_dim1]);
h__[k + 1 + j * h_dim1] -= refsum;
h__[k + 2 + j * h_dim1] -= refsum * v[m * v_dim1 + 2];
h__[k + 3 + j * h_dim1] -= refsum * v[m * v_dim1 + 3];
/* L90: */
}
/* L100: */
}
/* ==== Accumulate orthogonal transformations. ==== */
if (accum) {
/* ==== Accumulate U. (If needed, update Z later */
/* . with an efficient matrix-matrix */
/* . multiply.) ==== */
i__6 = mtop;
for (m = mbot; m >= i__6; --m) {
k = krcol + (m - 1 << 1);
kms = k - incol;
/* Computing MAX */
i__7 = 1, i__4 = *ktop - incol;
i2 = f2cmax(i__7,i__4);
/* Computing MAX */
i__7 = i2, i__4 = kms - (krcol - incol) + 1;
i2 = f2cmax(i__7,i__4);
/* Computing MIN */
i__7 = kdu, i__4 = krcol + (mbot - 1 << 1) - incol + 5;
i4 = f2cmin(i__7,i__4);
i__7 = i4;
for (j = i2; j <= i__7; ++j) {
refsum = v[m * v_dim1 + 1] * (u[j + (kms + 1) *
u_dim1] + v[m * v_dim1 + 2] * u[j + (kms + 2)
* u_dim1] + v[m * v_dim1 + 3] * u[j + (kms +
3) * u_dim1]);
u[j + (kms + 1) * u_dim1] -= refsum;
u[j + (kms + 2) * u_dim1] -= refsum * v[m * v_dim1 +
2];
u[j + (kms + 3) * u_dim1] -= refsum * v[m * v_dim1 +
3];
/* L110: */
}
/* L120: */
}
} else if (*wantz) {
/* ==== U is not accumulated, so update Z */
/* . now by multiplying by reflections */
/* . from the right. ==== */
i__6 = mtop;
for (m = mbot; m >= i__6; --m) {
k = krcol + (m - 1 << 1);
i__7 = *ihiz;
for (j = *iloz; j <= i__7; ++j) {
refsum = v[m * v_dim1 + 1] * (z__[j + (k + 1) *
z_dim1] + v[m * v_dim1 + 2] * z__[j + (k + 2)
* z_dim1] + v[m * v_dim1 + 3] * z__[j + (k +
3) * z_dim1]);
z__[j + (k + 1) * z_dim1] -= refsum;
z__[j + (k + 2) * z_dim1] -= refsum * v[m * v_dim1 +
2];
z__[j + (k + 3) * z_dim1] -= refsum * v[m * v_dim1 +
3];
/* L130: */
}
/* L140: */
}
}
/* ==== End of near-the-diagonal bulge chase. ==== */
/* L145: */
}
/* ==== Use U (if accumulated) to update far-from-diagonal */
/* . entries in H. If required, use U to update Z as */
/* . well. ==== */
if (accum) {
if (*wantt) {
jtop = 1;
jbot = *n;
} else {
jtop = *ktop;
jbot = *kbot;
}
/* Computing MAX */
i__3 = 1, i__6 = *ktop - incol;
k1 = f2cmax(i__3,i__6);
/* Computing MAX */
i__3 = 0, i__6 = ndcol - *kbot;
nu = kdu - f2cmax(i__3,i__6) - k1 + 1;
/* ==== Horizontal Multiply ==== */
i__3 = jbot;
i__6 = *nh;
for (jcol = f2cmin(ndcol,*kbot) + 1; i__6 < 0 ? jcol >= i__3 : jcol
<= i__3; jcol += i__6) {
/* Computing MIN */
i__7 = *nh, i__4 = jbot - jcol + 1;
jlen = f2cmin(i__7,i__4);
dgemm_("C", "N", &nu, &jlen, &nu, &c_b8, &u[k1 + k1 * u_dim1],
ldu, &h__[incol + k1 + jcol * h_dim1], ldh, &c_b7, &
wh[wh_offset], ldwh);
dlacpy_("ALL", &nu, &jlen, &wh[wh_offset], ldwh, &h__[incol +
k1 + jcol * h_dim1], ldh);
/* L150: */
}
/* ==== Vertical multiply ==== */
i__6 = f2cmax(*ktop,incol) - 1;
i__3 = *nv;
for (jrow = jtop; i__3 < 0 ? jrow >= i__6 : jrow <= i__6; jrow +=
i__3) {
/* Computing MIN */
i__7 = *nv, i__4 = f2cmax(*ktop,incol) - jrow;
jlen = f2cmin(i__7,i__4);
dgemm_("N", "N", &jlen, &nu, &nu, &c_b8, &h__[jrow + (incol +
k1) * h_dim1], ldh, &u[k1 + k1 * u_dim1], ldu, &c_b7,
&wv[wv_offset], ldwv);
dlacpy_("ALL", &jlen, &nu, &wv[wv_offset], ldwv, &h__[jrow + (
incol + k1) * h_dim1], ldh);
/* L160: */
}
/* ==== Z multiply (also vertical) ==== */
if (*wantz) {
i__3 = *ihiz;
i__6 = *nv;
for (jrow = *iloz; i__6 < 0 ? jrow >= i__3 : jrow <= i__3;
jrow += i__6) {
/* Computing MIN */
i__7 = *nv, i__4 = *ihiz - jrow + 1;
jlen = f2cmin(i__7,i__4);
dgemm_("N", "N", &jlen, &nu, &nu, &c_b8, &z__[jrow + (
incol + k1) * z_dim1], ldz, &u[k1 + k1 * u_dim1],
ldu, &c_b7, &wv[wv_offset], ldwv);
dlacpy_("ALL", &jlen, &nu, &wv[wv_offset], ldwv, &z__[
jrow + (incol + k1) * z_dim1], ldz);
/* L170: */
}
}
}
/* L180: */
}
/* ==== End of DLAQR5 ==== */
return;
} /* dlaqr5_ */
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