OpenBLAS/lapack-netlib/SRC/dsytrd_sb2st.c

1071 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__2 = 2;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__4 = 4;
static doublereal c_b26 = 0.;
/* > \brief \b DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSYTRD_SB2ST + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd_
sb2st.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd_
sb2st.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd_
sb2st.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSYTRD_SB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, */
/* D, E, HOUS, LHOUS, WORK, LWORK, INFO ) */
/* #if defined(_OPENMP) */
/* use omp_lib */
/* #endif */
/* IMPLICIT NONE */
/* CHARACTER STAGE1, UPLO, VECT */
/* INTEGER N, KD, IB, LDAB, LHOUS, LWORK, INFO */
/* DOUBLE PRECISION D( * ), E( * ) */
/* DOUBLE PRECISION AB( LDAB, * ), HOUS( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric */
/* > tridiagonal form T by a orthogonal similarity transformation: */
/* > Q**T * A * Q = T. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] STAGE1 */
/* > \verbatim */
/* > STAGE1 is CHARACTER*1 */
/* > = 'N': "No": to mention that the stage 1 of the reduction */
/* > from dense to band using the dsytrd_sy2sb routine */
/* > was not called before this routine to reproduce AB. */
/* > In other term this routine is called as standalone. */
/* > = 'Y': "Yes": to mention that the stage 1 of the */
/* > reduction from dense to band using the dsytrd_sy2sb */
/* > routine has been called to produce AB (e.g., AB is */
/* > the output of dsytrd_sy2sb. */
/* > \endverbatim */
/* > */
/* > \param[in] VECT */
/* > \verbatim */
/* > VECT is CHARACTER*1 */
/* > = 'N': No need for the Housholder representation, */
/* > and thus LHOUS is of size f2cmax(1, 4*N); */
/* > = 'V': the Householder representation is needed to */
/* > either generate or to apply Q later on, */
/* > then LHOUS is to be queried and computed. */
/* > (NOT AVAILABLE IN THIS RELEASE). */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > = 'U': Upper triangle of A is stored; */
/* > = 'L': Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KD */
/* > \verbatim */
/* > KD is INTEGER */
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AB */
/* > \verbatim */
/* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
/* > On entry, the upper or lower triangle of the symmetric band */
/* > matrix A, stored in the first KD+1 rows of the array. The */
/* > j-th column of A is stored in the j-th column of the array AB */
/* > as follows: */
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
/* > On exit, the diagonal elements of AB are overwritten by the */
/* > diagonal elements of the tridiagonal matrix T; if KD > 0, the */
/* > elements on the first superdiagonal (if UPLO = 'U') or the */
/* > first subdiagonal (if UPLO = 'L') are overwritten by the */
/* > off-diagonal elements of T; the rest of AB is overwritten by */
/* > values generated during the reduction. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array AB. LDAB >= KD+1. */
/* > \endverbatim */
/* > */
/* > \param[out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > The diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N-1) */
/* > The off-diagonal elements of the tridiagonal matrix T: */
/* > E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */
/* > \endverbatim */
/* > */
/* > \param[out] HOUS */
/* > \verbatim */
/* > HOUS is DOUBLE PRECISION array, dimension LHOUS, that */
/* > store the Householder representation. */
/* > \endverbatim */
/* > */
/* > \param[in] LHOUS */
/* > \verbatim */
/* > LHOUS is INTEGER */
/* > The dimension of the array HOUS. LHOUS = MAX(1, dimension) */
/* > If LWORK = -1, or LHOUS=-1, */
/* > then a query is assumed; the routine */
/* > only calculates the optimal size of the HOUS array, returns */
/* > this value as the first entry of the HOUS array, and no error */
/* > message related to LHOUS is issued by XERBLA. */
/* > LHOUS = MAX(1, dimension) where */
/* > dimension = 4*N if VECT='N' */
/* > not available now if VECT='H' */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK = MAX(1, dimension) */
/* > If LWORK = -1, or LHOUS=-1, */
/* > then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > LWORK = MAX(1, dimension) where */
/* > dimension = (2KD+1)*N + KD*NTHREADS */
/* > where KD is the blocking size of the reduction, */
/* > FACTOPTNB is the blocking used by the QR or LQ */
/* > algorithm, usually FACTOPTNB=128 is a good choice */
/* > NTHREADS is the number of threads used when */
/* > openMP compilation is enabled, otherwise =1. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2017 */
/* > \ingroup real16OTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Implemented by Azzam Haidar. */
/* > */
/* > All details are available on technical report, SC11, SC13 papers. */
/* > */
/* > Azzam Haidar, Hatem Ltaief, and Jack Dongarra. */
/* > Parallel reduction to condensed forms for symmetric eigenvalue problems */
/* > using aggregated fine-grained and memory-aware kernels. In Proceedings */
/* > of 2011 International Conference for High Performance Computing, */
/* > Networking, Storage and Analysis (SC '11), New York, NY, USA, */
/* > Article 8 , 11 pages. */
/* > http://doi.acm.org/10.1145/2063384.2063394 */
/* > */
/* > A. Haidar, J. Kurzak, P. Luszczek, 2013. */
/* > An improved parallel singular value algorithm and its implementation */
/* > for multicore hardware, In Proceedings of 2013 International Conference */
/* > for High Performance Computing, Networking, Storage and Analysis (SC '13). */
/* > Denver, Colorado, USA, 2013. */
/* > Article 90, 12 pages. */
/* > http://doi.acm.org/10.1145/2503210.2503292 */
/* > */
/* > A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. */
/* > A novel hybrid CPU-GPU generalized eigensolver for electronic structure */
/* > calculations based on fine-grained memory aware tasks. */
/* > International Journal of High Performance Computing Applications. */
/* > Volume 28 Issue 2, Pages 196-209, May 2014. */
/* > http://hpc.sagepub.com/content/28/2/196 */
/* > */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void dsytrd_sb2st_(char *stage1, char *vect, char *uplo,
integer *n, integer *kd, doublereal *ab, integer *ldab, doublereal *
d__, doublereal *e, doublereal *hous, integer *lhous, doublereal *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
real r__1;
/* Local variables */
integer inda;
extern integer ilaenv2stage_(integer *, char *, char *, integer *,
integer *, integer *, integer *);
integer thed, indv, myid, indw, apos, dpos, abofdpos, nthreads, i__, k, m,
edind, debug;
extern logical lsame_(char *, char *);
integer lhmin, sidev, sizea, shift, stind, colpt, lwmin, awpos;
logical wantq, upper;
integer grsiz, ttype, stepercol, ed, ib, st, abdpos;
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
integer thgrid;
extern /* Subroutine */ void dsb2st_kernels_(char *, logical *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *);
integer thgrnb, indtau, ofdpos, blklastind;
extern /* Subroutine */ void mecago_();
logical lquery, afters1;
integer lda, tid, ldv, stt, sweepid, nbtiles, sizetau, thgrsiz;
/* -- LAPACK computational routine (version 3.8.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2017 */
/* ===================================================================== */
/* Determine the minimal workspace size required. */
/* Test the input parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--d__;
--e;
--hous;
--work;
/* Function Body */
debug = 0;
*info = 0;
afters1 = lsame_(stage1, "Y");
wantq = lsame_(vect, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1 || *lhous == -1;
/* Determine the block size, the workspace size and the hous size. */
ib = ilaenv2stage_(&c__2, "DSYTRD_SB2ST", vect, n, kd, &c_n1, &c_n1);
lhmin = ilaenv2stage_(&c__3, "DSYTRD_SB2ST", vect, n, kd, &ib, &c_n1);
lwmin = ilaenv2stage_(&c__4, "DSYTRD_SB2ST", vect, n, kd, &ib, &c_n1);
if (! afters1 && ! lsame_(stage1, "N")) {
*info = -1;
} else if (! lsame_(vect, "N")) {
*info = -2;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*kd < 0) {
*info = -5;
} else if (*ldab < *kd + 1) {
*info = -7;
} else if (*lhous < lhmin && ! lquery) {
*info = -11;
} else if (*lwork < lwmin && ! lquery) {
*info = -13;
}
if (*info == 0) {
hous[1] = (doublereal) lhmin;
work[1] = (doublereal) lwmin;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSYTRD_SB2ST", &i__1, (ftnlen)12);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n == 0) {
hous[1] = 1.;
work[1] = 1.;
return;
}
/* Determine pointer position */
ldv = *kd + ib;
sizetau = *n << 1;
sidev = *n << 1;
indtau = 1;
indv = indtau + sizetau;
lda = (*kd << 1) + 1;
sizea = lda * *n;
inda = 1;
indw = inda + sizea;
nthreads = 1;
tid = 0;
if (upper) {
apos = inda + *kd;
awpos = inda;
dpos = apos + *kd;
ofdpos = dpos - 1;
abdpos = *kd + 1;
abofdpos = *kd;
} else {
apos = inda;
awpos = inda + *kd + 1;
dpos = apos;
ofdpos = dpos + 1;
abdpos = 1;
abofdpos = 2;
}
/* Case KD=0: */
/* The matrix is diagonal. We just copy it (convert to "real" for */
/* real because D is double and the imaginary part should be 0) */
/* and store it in D. A sequential code here is better or */
/* in a parallel environment it might need two cores for D and E */
if (*kd == 0) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[abdpos + i__ * ab_dim1];
/* L30: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = 0.;
/* L40: */
}
hous[1] = 1.;
work[1] = 1.;
return;
}
/* Case KD=1: */
/* The matrix is already Tridiagonal. We have to make diagonal */
/* and offdiagonal elements real, and store them in D and E. */
/* For that, for real precision just copy the diag and offdiag */
/* to D and E while for the COMPLEX case the bulge chasing is */
/* performed to convert the hermetian tridiagonal to symmetric */
/* tridiagonal. A simpler coversion formula might be used, but then */
/* updating the Q matrix will be required and based if Q is generated */
/* or not this might complicate the story. */
if (*kd == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[abdpos + i__ * ab_dim1];
/* L50: */
}
if (upper) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = ab[abofdpos + (i__ + 1) * ab_dim1];
/* L60: */
}
} else {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = ab[abofdpos + i__ * ab_dim1];
/* L70: */
}
}
hous[1] = 1.;
work[1] = 1.;
return;
}
/* Main code start here. */
/* Reduce the symmetric band of A to a tridiagonal matrix. */
thgrsiz = *n;
grsiz = 1;
shift = 3;
r__1 = (real) (*n) / (real) (*kd) + .5f;
nbtiles = r_int(&r__1);
r__1 = (real) shift / (real) grsiz + .5f;
stepercol = r_int(&r__1);
r__1 = (real) (*n - 1) / (real) thgrsiz + .5f;
thgrnb = r_int(&r__1);
i__1 = *kd + 1;
dlacpy_("A", &i__1, n, &ab[ab_offset], ldab, &work[apos], &lda)
;
dlaset_("A", kd, n, &c_b26, &c_b26, &work[awpos], &lda);
/* openMP parallelisation start here */
/* main bulge chasing loop */
i__1 = thgrnb;
for (thgrid = 1; thgrid <= i__1; ++thgrid) {
stt = (thgrid - 1) * thgrsiz + 1;
/* Computing MIN */
i__2 = stt + thgrsiz - 1, i__3 = *n - 1;
thed = f2cmin(i__2,i__3);
i__2 = *n - 1;
for (i__ = stt; i__ <= i__2; ++i__) {
ed = f2cmin(i__,thed);
if (stt > ed) {
myexit_();
}
i__3 = stepercol;
for (m = 1; m <= i__3; ++m) {
st = stt;
i__4 = ed;
for (sweepid = st; sweepid <= i__4; ++sweepid) {
i__5 = grsiz;
for (k = 1; k <= i__5; ++k) {
myid = (i__ - sweepid) * (stepercol * grsiz) + (m - 1)
* grsiz + k;
if (myid == 1) {
ttype = 1;
} else {
ttype = myid % 2 + 2;
}
if (ttype == 2) {
colpt = myid / 2 * *kd + sweepid;
stind = colpt - *kd + 1;
edind = f2cmin(colpt,*n);
blklastind = colpt;
} else {
colpt = (myid + 1) / 2 * *kd + sweepid;
stind = colpt - *kd + 1;
edind = f2cmin(colpt,*n);
if (stind >= edind - 1 && edind == *n) {
blklastind = *n;
} else {
blklastind = 0;
}
}
/* Call the kernel */
dsb2st_kernels_(uplo, &wantq, &ttype, &stind, &edind,
&sweepid, n, kd, &ib, &work[inda], &lda, &
hous[indv], &hous[indtau], &ldv, &work[indw +
tid * *kd]);
if (blklastind >= *n - 1) {
++stt;
myexit_();
}
/* L140: */
}
/* L130: */
}
/* L120: */
}
/* L110: */
}
/* L100: */
}
/* Copy the diagonal from A to D. Note that D is REAL thus only */
/* the Real part is needed, the imaginary part should be zero. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = work[dpos + (i__ - 1) * lda];
/* L150: */
}
/* Copy the off diagonal from A to E. Note that E is REAL thus only */
/* the Real part is needed, the imaginary part should be zero. */
if (upper) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = work[ofdpos + i__ * lda];
/* L160: */
}
} else {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = work[ofdpos + (i__ - 1) * lda];
/* L170: */
}
}
hous[1] = (doublereal) lhmin;
work[1] = (doublereal) lwmin;
return;
/* End of DSYTRD_SB2ST */
} /* dsytrd_sb2st__ */