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OpenBLAS/lapack-netlib/SRC/slasyf_aa.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 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 real c_b6 = -1.f;
static integer c__1 = 1;
static real c_b8 = 1.f;
static real c_b22 = 0.f;
/* > \brief \b SLASYF_AA */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SLASYF_AA + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasyf_
aa.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasyf_
aa.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasyf_
aa.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV, */
/* H, LDH, WORK ) */
/* CHARACTER UPLO */
/* INTEGER J1, M, NB, LDA, LDH */
/* INTEGER IPIV( * ) */
/* REAL A( LDA, * ), H( LDH, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLATRF_AA factorizes a panel of a real symmetric matrix A using */
/* > the Aasen's algorithm. The panel consists of a set of NB rows of A */
/* > when UPLO is U, or a set of NB columns when UPLO is L. */
/* > */
/* > In order to factorize the panel, the Aasen's algorithm requires the */
/* > last row, or column, of the previous panel. The first row, or column, */
/* > of A is set to be the first row, or column, of an identity matrix, */
/* > which is used to factorize the first panel. */
/* > */
/* > The resulting J-th row of U, or J-th column of L, is stored in the */
/* > (J-1)-th row, or column, of A (without the unit diagonals), while */
/* > the diagonal and subdiagonal of A are overwritten by those of T. */
/* > */
/* > \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] J1 */
/* > \verbatim */
/* > J1 is INTEGER */
/* > The location of the first row, or column, of the panel */
/* > within the submatrix of A, passed to this routine, e.g., */
/* > when called by SSYTRF_AA, for the first panel, J1 is 1, */
/* > while for the remaining panels, J1 is 2. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The dimension of the submatrix. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* > NB is INTEGER */
/* > The dimension of the panel to be facotorized. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,M) for */
/* > the first panel, while dimension (LDA,M+1) for the */
/* > remaining panels. */
/* > */
/* > On entry, A contains the last row, or column, of */
/* > the previous panel, and the trailing submatrix of A */
/* > to be factorized, except for the first panel, only */
/* > the panel is passed. */
/* > */
/* > On exit, the leading panel is factorized. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (M) */
/* > Details of the row and column interchanges, */
/* > the row and column k were interchanged with the row and */
/* > column IPIV(k). */
/* > \endverbatim */
/* > */
/* > \param[in,out] H */
/* > \verbatim */
/* > H is REAL workspace, dimension (LDH,NB). */
/* > */
/* > \endverbatim */
/* > */
/* > \param[in] LDH */
/* > \verbatim */
/* > LDH is INTEGER */
/* > The leading dimension of the workspace H. LDH >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL workspace, dimension (M). */
/* > \endverbatim */
/* > */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2017 */
/* > \ingroup realSYcomputational */
/* ===================================================================== */
/* Subroutine */ void slasyf_aa_(char *uplo, integer *j1, integer *m, integer
*nb, real *a, integer *lda, integer *ipiv, real *h__, integer *ldh,
real *work)
{
/* System generated locals */
integer a_dim1, a_offset, h_dim1, h_offset, i__1;
/* Local variables */
integer j, k;
real alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *),
sgemv_(char *, integer *, integer *, real *, real *, integer *,
real *, integer *, real *, real *, integer *);
integer i1, k1, i2;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *), sswap_(integer *, real *, integer *, real *, integer *
), saxpy_(integer *, real *, real *, integer *, real *, integer *)
;
integer mj;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ void slaset_(char *, integer *, integer *, real *,
real *, real *, integer *);
real piv;
/* -- 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 */
/* ===================================================================== */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
h_dim1 = *ldh;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
--work;
/* Function Body */
j = 1;
/* K1 is the first column of the panel to be factorized */
/* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks */
k1 = 2 - *j1 + 1;
if (lsame_(uplo, "U")) {
/* ..................................................... */
/* Factorize A as U**T*D*U using the upper triangle of A */
/* ..................................................... */
L10:
if (j > f2cmin(*m,*nb)) {
goto L20;
}
/* K is the column to be factorized */
/* when being called from SSYTRF_AA, */
/* > for the first block column, J1 is 1, hence J1+J-1 is J, */
/* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */
k = *j1 + j - 1;
if (j == *m) {
/* Only need to compute T(J, J) */
mj = 1;
} else {
mj = *m - j + 1;
}
/* H(J:M, J) := A(J, J:M) - H(J:M, 1:(J-1)) * L(J1:(J-1), J), */
/* where H(J:M, J) has been initialized to be A(J, J:M) */
if (k > 2) {
/* K is the column to be factorized */
/* > for the first block column, K is J, skipping the first two */
/* columns */
/* > for the rest of the columns, K is J+1, skipping only the */
/* first column */
i__1 = j - k1;
sgemv_("No transpose", &mj, &i__1, &c_b6, &h__[j + k1 * h_dim1],
ldh, &a[j * a_dim1 + 1], &c__1, &c_b8, &h__[j + j *
h_dim1], &c__1);
}
/* Copy H(i:M, i) into WORK */
scopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);
if (j > k1) {
/* Compute WORK := WORK - L(J-1, J:M) * T(J-1,J), */
/* where A(J-1, J) stores T(J-1, J) and A(J-2, J:M) stores U(J-1, J:M) */
alpha = -a[k - 1 + j * a_dim1];
saxpy_(&mj, &alpha, &a[k - 2 + j * a_dim1], lda, &work[1], &c__1);
}
/* Set A(J, J) = T(J, J) */
a[k + j * a_dim1] = work[1];
if (j < *m) {
/* Compute WORK(2:M) = T(J, J) L(J, (J+1):M) */
/* where A(J, J) stores T(J, J) and A(J-1, (J+1):M) stores U(J, (J+1):M) */
if (k > 1) {
alpha = -a[k + j * a_dim1];
i__1 = *m - j;
saxpy_(&i__1, &alpha, &a[k - 1 + (j + 1) * a_dim1], lda, &
work[2], &c__1);
}
/* Find f2cmax(|WORK(2:M)|) */
i__1 = *m - j;
i2 = isamax_(&i__1, &work[2], &c__1) + 1;
piv = work[i2];
/* Apply symmetric pivot */
if (i2 != 2 && piv != 0.f) {
/* Swap WORK(I1) and WORK(I2) */
i1 = 2;
work[i2] = work[i1];
work[i1] = piv;
/* Swap A(I1, I1+1:M) with A(I1+1:M, I2) */
i1 = i1 + j - 1;
i2 = i2 + j - 1;
i__1 = i2 - i1 - 1;
sswap_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda, &a[*
j1 + i1 + i2 * a_dim1], &c__1);
/* Swap A(I1, I2+1:M) with A(I2, I2+1:M) */
if (i2 < *m) {
i__1 = *m - i2;
sswap_(&i__1, &a[*j1 + i1 - 1 + (i2 + 1) * a_dim1], lda, &
a[*j1 + i2 - 1 + (i2 + 1) * a_dim1], lda);
}
/* Swap A(I1, I1) with A(I2,I2) */
piv = a[i1 + *j1 - 1 + i1 * a_dim1];
a[*j1 + i1 - 1 + i1 * a_dim1] = a[*j1 + i2 - 1 + i2 * a_dim1];
a[*j1 + i2 - 1 + i2 * a_dim1] = piv;
/* Swap H(I1, 1:J1) with H(I2, 1:J1) */
i__1 = i1 - 1;
sswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
ipiv[i1] = i2;
if (i1 > k1 - 1) {
/* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
/* skipping the first column */
i__1 = i1 - k1 + 1;
sswap_(&i__1, &a[i1 * a_dim1 + 1], &c__1, &a[i2 * a_dim1
+ 1], &c__1);
}
} else {
ipiv[j + 1] = j + 1;
}
/* Set A(J, J+1) = T(J, J+1) */
a[k + (j + 1) * a_dim1] = work[2];
if (j < *nb) {
/* Copy A(J+1:M, J+1) into H(J:M, J), */
i__1 = *m - j;
scopy_(&i__1, &a[k + 1 + (j + 1) * a_dim1], lda, &h__[j + 1 +
(j + 1) * h_dim1], &c__1);
}
/* Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1), */
/* where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1) */
if (j < *m - 1) {
if (a[k + (j + 1) * a_dim1] != 0.f) {
alpha = 1.f / a[k + (j + 1) * a_dim1];
i__1 = *m - j - 1;
scopy_(&i__1, &work[3], &c__1, &a[k + (j + 2) * a_dim1],
lda);
i__1 = *m - j - 1;
sscal_(&i__1, &alpha, &a[k + (j + 2) * a_dim1], lda);
} else {
i__1 = *m - j - 1;
slaset_("Full", &c__1, &i__1, &c_b22, &c_b22, &a[k + (j +
2) * a_dim1], lda);
}
}
}
++j;
goto L10;
L20:
;
} else {
/* ..................................................... */
/* Factorize A as L*D*L**T using the lower triangle of A */
/* ..................................................... */
L30:
if (j > f2cmin(*m,*nb)) {
goto L40;
}
/* K is the column to be factorized */
/* when being called from SSYTRF_AA, */
/* > for the first block column, J1 is 1, hence J1+J-1 is J, */
/* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */
k = *j1 + j - 1;
if (j == *m) {
/* Only need to compute T(J, J) */
mj = 1;
} else {
mj = *m - j + 1;
}
/* H(J:M, J) := A(J:M, J) - H(J:M, 1:(J-1)) * L(J, J1:(J-1))^T, */
/* where H(J:M, J) has been initialized to be A(J:M, J) */
if (k > 2) {
/* K is the column to be factorized */
/* > for the first block column, K is J, skipping the first two */
/* columns */
/* > for the rest of the columns, K is J+1, skipping only the */
/* first column */
i__1 = j - k1;
sgemv_("No transpose", &mj, &i__1, &c_b6, &h__[j + k1 * h_dim1],
ldh, &a[j + a_dim1], lda, &c_b8, &h__[j + j * h_dim1], &
c__1);
}
/* Copy H(J:M, J) into WORK */
scopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);
if (j > k1) {
/* Compute WORK := WORK - L(J:M, J-1) * T(J-1,J), */
/* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) */
alpha = -a[j + (k - 1) * a_dim1];
saxpy_(&mj, &alpha, &a[j + (k - 2) * a_dim1], &c__1, &work[1], &
c__1);
}
/* Set A(J, J) = T(J, J) */
a[j + k * a_dim1] = work[1];
if (j < *m) {
/* Compute WORK(2:M) = T(J, J) L((J+1):M, J) */
/* where A(J, J) = T(J, J) and A((J+1):M, J-1) = L((J+1):M, J) */
if (k > 1) {
alpha = -a[j + k * a_dim1];
i__1 = *m - j;
saxpy_(&i__1, &alpha, &a[j + 1 + (k - 1) * a_dim1], &c__1, &
work[2], &c__1);
}
/* Find f2cmax(|WORK(2:M)|) */
i__1 = *m - j;
i2 = isamax_(&i__1, &work[2], &c__1) + 1;
piv = work[i2];
/* Apply symmetric pivot */
if (i2 != 2 && piv != 0.f) {
/* Swap WORK(I1) and WORK(I2) */
i1 = 2;
work[i2] = work[i1];
work[i1] = piv;
/* Swap A(I1+1:M, I1) with A(I2, I1+1:M) */
i1 = i1 + j - 1;
i2 = i2 + j - 1;
i__1 = i2 - i1 - 1;
sswap_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1, &a[
i2 + (*j1 + i1) * a_dim1], lda);
/* Swap A(I2+1:M, I1) with A(I2+1:M, I2) */
if (i2 < *m) {
i__1 = *m - i2;
sswap_(&i__1, &a[i2 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1,
&a[i2 + 1 + (*j1 + i2 - 1) * a_dim1], &c__1);
}
/* Swap A(I1, I1) with A(I2, I2) */
piv = a[i1 + (*j1 + i1 - 1) * a_dim1];
a[i1 + (*j1 + i1 - 1) * a_dim1] = a[i2 + (*j1 + i2 - 1) *
a_dim1];
a[i2 + (*j1 + i2 - 1) * a_dim1] = piv;
/* Swap H(I1, I1:J1) with H(I2, I2:J1) */
i__1 = i1 - 1;
sswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
ipiv[i1] = i2;
if (i1 > k1 - 1) {
/* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
/* skipping the first column */
i__1 = i1 - k1 + 1;
sswap_(&i__1, &a[i1 + a_dim1], lda, &a[i2 + a_dim1], lda);
}
} else {
ipiv[j + 1] = j + 1;
}
/* Set A(J+1, J) = T(J+1, J) */
a[j + 1 + k * a_dim1] = work[2];
if (j < *nb) {
/* Copy A(J+1:M, J+1) into H(J+1:M, J), */
i__1 = *m - j;
scopy_(&i__1, &a[j + 1 + (k + 1) * a_dim1], &c__1, &h__[j + 1
+ (j + 1) * h_dim1], &c__1);
}
/* Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1), */
/* where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1) */
if (j < *m - 1) {
if (a[j + 1 + k * a_dim1] != 0.f) {
alpha = 1.f / a[j + 1 + k * a_dim1];
i__1 = *m - j - 1;
scopy_(&i__1, &work[3], &c__1, &a[j + 2 + k * a_dim1], &
c__1);
i__1 = *m - j - 1;
sscal_(&i__1, &alpha, &a[j + 2 + k * a_dim1], &c__1);
} else {
i__1 = *m - j - 1;
slaset_("Full", &i__1, &c__1, &c_b22, &c_b22, &a[j + 2 +
k * a_dim1], lda);
}
}
}
++j;
goto L30;
L40:
;
}
return;
/* End of SLASYF_AA */
} /* slasyf_aa__ */
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