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OpenBLAS/lapack-netlib/SRC/chetrd_he2hb.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__4 = 4;
static integer c_n1 = -1;
static integer c__1 = 1;
static real c_b33 = 1.f;
/* > \brief \b CHETRD_HE2HB */
/* @generated from zhetrd_he2hb.f, fortran z -> c, Wed Dec 7 08:22:40 2016 */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CHETRD_HE2HB + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CHETRD_HE2HB( UPLO, N, KD, A, LDA, AB, LDAB, TAU, */
/* WORK, LWORK, INFO ) */
/* IMPLICIT NONE */
/* CHARACTER UPLO */
/* INTEGER INFO, LDA, LDAB, LWORK, N, KD */
/* COMPLEX A( LDA, * ), AB( LDAB, * ), */
/* TAU( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CHETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian */
/* > band-diagonal form AB by a unitary similarity transformation: */
/* > Q**H * A * Q = AB. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \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 reduced matrix if UPLO = 'U', */
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* > The reduced matrix is stored in the array AB. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA,N) */
/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */
/* > N-by-N upper triangular part of A contains the upper */
/* > triangular part of the matrix A, and the strictly lower */
/* > triangular part of A is not referenced. If UPLO = 'L', the */
/* > leading N-by-N lower triangular part of A contains the lower */
/* > triangular part of the matrix A, and the strictly upper */
/* > triangular part of A is not referenced. */
/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */
/* > of A are overwritten by the corresponding elements of the */
/* > tridiagonal matrix T, and the elements above the first */
/* > superdiagonal, with the array TAU, represent the unitary */
/* > matrix Q as a product of elementary reflectors; if UPLO */
/* > = 'L', the diagonal and first subdiagonal of A are over- */
/* > written by the corresponding elements of the tridiagonal */
/* > matrix T, and the elements below the first subdiagonal, with */
/* > the array TAU, represent the unitary matrix Q as a product */
/* > of elementary reflectors. See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] AB */
/* > \verbatim */
/* > AB is COMPLEX array, dimension (LDAB,N) */
/* > On exit, the upper or lower triangle of the Hermitian 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). */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array AB. LDAB >= KD+1. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* > TAU is COMPLEX array, dimension (N-KD) */
/* > The scalar factors of the elementary reflectors (see Further */
/* > Details). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension (LWORK) */
/* > On exit, if INFO = 0, or if LWORK=-1, */
/* > WORK(1) returns the size of LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK which should be calculated */
/* > by a workspace query. LWORK = MAX(1, LWORK_QUERY) */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > LWORK_QUERY = N*KD + N*f2cmax(KD,FACTOPTNB) + 2*KD*KD */
/* > where FACTOPTNB is the blocking used by the QR or LQ */
/* > algorithm, usually FACTOPTNB=128 is a good choice otherwise */
/* > putting LWORK=-1 will provide the size of WORK. */
/* > \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 complexHEcomputational */
/* > \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 */
/* > */
/* > \verbatim */
/* > */
/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* > reflectors */
/* > */
/* > Q = H(k)**H . . . H(2)**H H(1)**H, where k = n-kd. */
/* > */
/* > Each H(i) has the form */
/* > */
/* > H(i) = I - tau * v * v**H */
/* > */
/* > where tau is a complex scalar, and v is a complex vector with */
/* > v(1:i+kd-1) = 0 and v(i+kd) = 1; conjg(v(i+kd+1:n)) is stored on exit in */
/* > A(i,i+kd+1:n), and tau in TAU(i). */
/* > */
/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* > reflectors */
/* > */
/* > Q = H(1) H(2) . . . H(k), where k = n-kd. */
/* > */
/* > Each H(i) has the form */
/* > */
/* > H(i) = I - tau * v * v**H */
/* > */
/* > where tau is a complex scalar, and v is a complex vector with */
/* > v(kd+1:i) = 0 and v(i+kd+1) = 1; v(i+kd+2:n) is stored on exit in */
/* > A(i+kd+2:n,i), and tau in TAU(i). */
/* > */
/* > The contents of A on exit are illustrated by the following examples */
/* > with n = 5: */
/* > */
/* > if UPLO = 'U': if UPLO = 'L': */
/* > */
/* > ( ab ab/v1 v1 v1 v1 ) ( ab ) */
/* > ( ab ab/v2 v2 v2 ) ( ab/v1 ab ) */
/* > ( ab ab/v3 v3 ) ( v1 ab/v2 ab ) */
/* > ( ab ab/v4 ) ( v1 v2 ab/v3 ab ) */
/* > ( ab ) ( v1 v2 v3 ab/v4 ab ) */
/* > */
/* > where d and e denote diagonal and off-diagonal elements of T, and vi */
/* > denotes an element of the vector defining H(i). */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ int chetrd_he2hb_(char *uplo, integer *n, integer *kd,
complex *a, integer *lda, complex *ab, integer *ldab, complex *tau,
complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, ab_dim1, ab_offset, i__1, i__2, i__3, i__4,
i__5;
complex q__1;
/* Local variables */
extern integer ilaenv2stage_(integer *, char *, char *, integer *,
integer *, integer *, integer *);
integer tpos, wpos, s1pos, s2pos, i__, j;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *), chemm_(char *,
char *, integer *, integer *, complex *, complex *, integer *,
complex *, integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
integer lwmin;
logical upper;
extern /* Subroutine */ int cher2k_(char *, char *, integer *, integer *,
complex *, complex *, integer *, complex *, integer *, real *,
complex *, integer *);
integer lk, pk, pn, lt;
extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *);
integer lw;
extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), clarft_(
char *, char *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
integer ls1;
logical lquery;
integer ls2, ldt, ldw, lds1, lds2;
/* -- 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 */
/* and test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--tau;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
lwmin = ilaenv2stage_(&c__4, "CHETRD_HE2HB", "", n, kd, &c_n1, &c_n1);
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*lda < f2cmax(1,*n)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *kd + 1;
if (*ldab < f2cmax(i__1,i__2)) {
*info = -7;
} else if (*lwork < lwmin && ! lquery) {
*info = -10;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHETRD_HE2HB", &i__1, (ftnlen)12);
return 0;
} else if (lquery) {
work[1].r = (real) lwmin, work[1].i = 0.f;
return 0;
}
/* Quick return if possible */
/* Copy the upper/lower portion of A into AB */
if (*n <= *kd + 1) {
if (upper) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
i__2 = *kd + 1;
lk = f2cmin(i__2,i__);
ccopy_(&lk, &a[i__ - lk + 1 + i__ * a_dim1], &c__1, &ab[*kd +
1 - lk + 1 + i__ * ab_dim1], &c__1);
/* L100: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
i__2 = *kd + 1, i__3 = *n - i__ + 1;
lk = f2cmin(i__2,i__3);
ccopy_(&lk, &a[i__ + i__ * a_dim1], &c__1, &ab[i__ * ab_dim1
+ 1], &c__1);
/* L110: */
}
}
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
/* Determine the pointer position for the workspace */
ldt = *kd;
lds1 = *kd;
lt = ldt * *kd;
lw = *n * *kd;
ls1 = lds1 * *kd;
ls2 = lwmin - lt - lw - ls1;
/* LS2 = N*MAX(KD,FACTOPTNB) */
tpos = 1;
wpos = tpos + lt;
s1pos = wpos + lw;
s2pos = s1pos + ls1;
if (upper) {
ldw = *kd;
lds2 = *kd;
} else {
ldw = *n;
lds2 = *n;
}
/* Set the workspace of the triangular matrix T to zero once such a */
/* way every time T is generated the upper/lower portion will be always zero */
claset_("A", &ldt, kd, &c_b1, &c_b1, &work[tpos], &ldt);
if (upper) {
i__1 = *n - *kd;
i__2 = *kd;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
pn = *n - i__ - *kd + 1;
/* Computing MIN */
i__3 = *n - i__ - *kd + 1;
pk = f2cmin(i__3,*kd);
/* Compute the LQ factorization of the current block */
cgelqf_(kd, &pn, &a[i__ + (i__ + *kd) * a_dim1], lda, &tau[i__], &
work[s2pos], &ls2, &iinfo);
/* Copy the upper portion of A into AB */
i__3 = i__ + pk - 1;
for (j = i__; j <= i__3; ++j) {
/* Computing MIN */
i__4 = *kd, i__5 = *n - j;
lk = f2cmin(i__4,i__5) + 1;
i__4 = *ldab - 1;
ccopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j *
ab_dim1], &i__4);
/* L20: */
}
claset_("Lower", &pk, &pk, &c_b1, &c_b2, &a[i__ + (i__ + *kd) *
a_dim1], lda);
/* Form the matrix T */
clarft_("Forward", "Rowwise", &pn, &pk, &a[i__ + (i__ + *kd) *
a_dim1], lda, &tau[i__], &work[tpos], &ldt);
/* Compute W: */
cgemm_("Conjugate", "No transpose", &pk, &pn, &pk, &c_b2, &work[
tpos], &ldt, &a[i__ + (i__ + *kd) * a_dim1], lda, &c_b1, &
work[s2pos], &lds2);
chemm_("Right", uplo, &pk, &pn, &c_b2, &a[i__ + *kd + (i__ + *kd)
* a_dim1], lda, &work[s2pos], &lds2, &c_b1, &work[wpos], &
ldw);
cgemm_("No transpose", "Conjugate", &pk, &pk, &pn, &c_b2, &work[
wpos], &ldw, &work[s2pos], &lds2, &c_b1, &work[s1pos], &
lds1);
q__1.r = -.5f, q__1.i = 0.f;
cgemm_("No transpose", "No transpose", &pk, &pn, &pk, &q__1, &
work[s1pos], &lds1, &a[i__ + (i__ + *kd) * a_dim1], lda, &
c_b2, &work[wpos], &ldw);
/* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
/* an update of the form: A := A - V'*W - W'*V */
q__1.r = -1.f, q__1.i = 0.f;
cher2k_(uplo, "Conjugate", &pn, &pk, &q__1, &a[i__ + (i__ + *kd) *
a_dim1], lda, &work[wpos], &ldw, &c_b33, &a[i__ + *kd + (
i__ + *kd) * a_dim1], lda);
/* L10: */
}
/* Copy the upper band to AB which is the band storage matrix */
i__2 = *n;
for (j = *n - *kd + 1; j <= i__2; ++j) {
/* Computing MIN */
i__1 = *kd, i__3 = *n - j;
lk = f2cmin(i__1,i__3) + 1;
i__1 = *ldab - 1;
ccopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * ab_dim1], &
i__1);
/* L30: */
}
} else {
/* Reduce the lower triangle of A to lower band matrix */
i__2 = *n - *kd;
i__1 = *kd;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
pn = *n - i__ - *kd + 1;
/* Computing MIN */
i__3 = *n - i__ - *kd + 1;
pk = f2cmin(i__3,*kd);
/* Compute the QR factorization of the current block */
cgeqrf_(&pn, kd, &a[i__ + *kd + i__ * a_dim1], lda, &tau[i__], &
work[s2pos], &ls2, &iinfo);
/* Copy the upper portion of A into AB */
i__3 = i__ + pk - 1;
for (j = i__; j <= i__3; ++j) {
/* Computing MIN */
i__4 = *kd, i__5 = *n - j;
lk = f2cmin(i__4,i__5) + 1;
ccopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
c__1);
/* L50: */
}
claset_("Upper", &pk, &pk, &c_b1, &c_b2, &a[i__ + *kd + i__ *
a_dim1], lda);
/* Form the matrix T */
clarft_("Forward", "Columnwise", &pn, &pk, &a[i__ + *kd + i__ *
a_dim1], lda, &tau[i__], &work[tpos], &ldt);
/* Compute W: */
cgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b2, &a[
i__ + *kd + i__ * a_dim1], lda, &work[tpos], &ldt, &c_b1,
&work[s2pos], &lds2);
chemm_("Left", uplo, &pn, &pk, &c_b2, &a[i__ + *kd + (i__ + *kd) *
a_dim1], lda, &work[s2pos], &lds2, &c_b1, &work[wpos], &
ldw);
cgemm_("Conjugate", "No transpose", &pk, &pk, &pn, &c_b2, &work[
s2pos], &lds2, &work[wpos], &ldw, &c_b1, &work[s1pos], &
lds1);
q__1.r = -.5f, q__1.i = 0.f;
cgemm_("No transpose", "No transpose", &pn, &pk, &pk, &q__1, &a[
i__ + *kd + i__ * a_dim1], lda, &work[s1pos], &lds1, &
c_b2, &work[wpos], &ldw);
/* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
/* an update of the form: A := A - V*W' - W*V' */
q__1.r = -1.f, q__1.i = 0.f;
cher2k_(uplo, "No transpose", &pn, &pk, &q__1, &a[i__ + *kd + i__
* a_dim1], lda, &work[wpos], &ldw, &c_b33, &a[i__ + *kd +
(i__ + *kd) * a_dim1], lda);
/* ================================================================== */
/* RESTORE A FOR COMPARISON AND CHECKING TO BE REMOVED */
/* DO 45 J = I, I+PK-1 */
/* LK = MIN( KD, N-J ) + 1 */
/* CALL CCOPY( LK, AB( 1, J ), 1, A( J, J ), 1 ) */
/* 45 CONTINUE */
/* ================================================================== */
/* L40: */
}
/* Copy the lower band to AB which is the band storage matrix */
i__1 = *n;
for (j = *n - *kd + 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kd, i__3 = *n - j;
lk = f2cmin(i__2,i__3) + 1;
ccopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
c__1);
/* L60: */
}
}
work[1].r = (real) lwmin, work[1].i = 0.f;
return 0;
/* End of CHETRD_HE2HB */
} /* chetrd_he2hb__ */
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