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OpenBLAS/lapack-netlib/SRC/sgehrd.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 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 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);}
#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)}
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__65 = 65;
static real c_b25 = -1.f;
static real c_b26 = 1.f;
/* > \brief \b SGEHRD */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGEHRD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgehrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgehrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgehrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) */
/* INTEGER IHI, ILO, INFO, LDA, LWORK, N */
/* REAL A( LDA, * ), TAU( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGEHRD reduces a real general matrix A to upper Hessenberg form H by */
/* > an orthogonal similarity transformation: Q**T * A * Q = H . */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] ILO */
/* > \verbatim */
/* > ILO is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] IHI */
/* > \verbatim */
/* > IHI is INTEGER */
/* > */
/* > It is assumed that A is already upper triangular in rows */
/* > and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* > set by a previous call to SGEBAL; otherwise they should be */
/* > set to 1 and N respectively. See Further Details. */
/* > 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,N) */
/* > On entry, the N-by-N general matrix to be reduced. */
/* > On exit, the upper triangle and the first subdiagonal of A */
/* > are overwritten with the upper Hessenberg matrix H, and the */
/* > elements below the first subdiagonal, with the array TAU, */
/* > represent the orthogonal 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] TAU */
/* > \verbatim */
/* > TAU is REAL array, dimension (N-1) */
/* > The scalar factors of the elementary reflectors (see Further */
/* > Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* > zero. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (LWORK) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The length of the array WORK. LWORK >= f2cmax(1,N). */
/* > For good performance, LWORK should generally be larger. */
/* > */
/* > 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. */
/* > \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 December 2016 */
/* > \ingroup realGEcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The matrix Q is represented as a product of (ihi-ilo) elementary */
/* > reflectors */
/* > */
/* > Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* > */
/* > Each H(i) has the form */
/* > */
/* > H(i) = I - tau * v * v**T */
/* > */
/* > where tau is a real scalar, and v is a real vector with */
/* > v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* > exit in A(i+2:ihi,i), and tau in TAU(i). */
/* > */
/* > The contents of A are illustrated by the following example, with */
/* > n = 7, ilo = 2 and ihi = 6: */
/* > */
/* > on entry, on exit, */
/* > */
/* > ( a a a a a a a ) ( a a h h h h a ) */
/* > ( a a a a a a ) ( a h h h h a ) */
/* > ( a a a a a a ) ( h h h h h h ) */
/* > ( a a a a a a ) ( v2 h h h h h ) */
/* > ( a a a a a a ) ( v2 v3 h h h h ) */
/* > ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* > ( a ) ( a ) */
/* > */
/* > where a denotes an element of the original matrix A, h denotes a */
/* > modified element of the upper Hessenberg matrix H, and vi denotes an */
/* > element of the vector defining H(i). */
/* > */
/* > This file is a slight modification of LAPACK-3.0's DGEHRD */
/* > subroutine incorporating improvements proposed by Quintana-Orti and */
/* > Van de Geijn (2006). (See DLAHR2.) */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void sgehrd_(integer *n, integer *ilo, integer *ihi, real *a,
integer *lda, real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, j, nbmin, iinfo;
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *), strmm_(char *, char *, char *,
char *, integer *, integer *, real *, real *, integer *, real *,
integer *), saxpy_(integer *,
real *, real *, integer *, real *, integer *), sgehd2_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
), slahr2_(integer *, integer *, integer *, real *, integer *,
real *, real *, integer *, real *, integer *);
integer ib;
real ei;
integer nb, nh, nx;
extern /* Subroutine */ void slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *);
extern int xerbla_(char *, integer *,ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, lwkopt;
logical lquery;
integer iwt;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
*info = -2;
} else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < f2cmax(1,*n)) {
*info = -5;
} else if (*lwork < f2cmax(1,*n) && ! lquery) {
*info = -8;
}
if (*info == 0) {
/* Compute the workspace requirements */
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "SGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = f2cmin(i__1,i__2);
lwkopt = *n * nb + 4160;
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEHRD", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
tau[i__] = 0.f;
/* L10: */
}
i__1 = *n - 1;
for (i__ = f2cmax(1,*ihi); i__ <= i__1; ++i__) {
tau[i__] = 0.f;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1] = 1.f;
return;
}
/* Determine the block size */
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "SGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = f2cmin(i__1,i__2);
nbmin = 2;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code) */
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "SGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = f2cmax(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code */
if (*lwork < *n * nb + 4160) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code */
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGEHRD", " ", n, ilo, ihi, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = f2cmax(i__1,i__2);
if (*lwork >= *n * nbmin + 4160) {
nb = (*lwork - 4160) / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
iwt = *n * nb + 1;
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = f2cmin(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V**T */
/* which performs the reduction, and also the matrix Y = A*V*T */
slahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], &
work[iwt], &c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set */
/* to 1 */
ei = a[i__ + ib + (i__ + ib - 1) * a_dim1];
a[i__ + ib + (i__ + ib - 1) * a_dim1] = 1.f;
i__3 = *ihi - i__ - ib + 1;
sgemm_("No transpose", "Transpose", ihi, &i__3, &ib, &c_b25, &
work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, &
c_b26, &a[(i__ + ib) * a_dim1 + 1], lda);
a[i__ + ib + (i__ + ib - 1) * a_dim1] = ei;
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
/* right */
i__3 = ib - 1;
strmm_("Right", "Lower", "Transpose", "Unit", &i__, &i__3, &c_b26,
&a[i__ + 1 + i__ * a_dim1], lda, &work[1], &ldwork);
i__3 = ib - 2;
for (j = 0; j <= i__3; ++j) {
saxpy_(&i__, &c_b25, &work[ldwork * j + 1], &c__1, &a[(i__ +
j + 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, &work[iwt], &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
sgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1] = (real) lwkopt;
return;
/* End of SGEHRD */
} /* sgehrd_ */
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