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OpenBLAS/lapack-netlib/SRC/slasyf.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 integer c__1 = 1;
static real c_b8 = -1.f;
static real c_b9 = 1.f;
/* > \brief \b SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diag
onal pivoting method. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SLASYF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasyf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasyf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasyf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) */
/* CHARACTER UPLO */
/* INTEGER INFO, KB, LDA, LDW, N, NB */
/* INTEGER IPIV( * ) */
/* REAL A( LDA, * ), W( LDW, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLASYF computes a partial factorization of a real symmetric matrix A */
/* > using the Bunch-Kaufman diagonal pivoting method. The partial */
/* > factorization has the form: */
/* > */
/* > A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: */
/* > ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) */
/* > */
/* > A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' */
/* > ( L21 I ) ( 0 A22 ) ( 0 I ) */
/* > */
/* > where the order of D is at most NB. The actual order is returned in */
/* > the argument KB, and is either NB or NB-1, or N if N <= NB. */
/* > */
/* > SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code */
/* > (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or */
/* > A22 (if UPLO = 'L'). */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > Specifies whether the upper or lower triangular part of the */
/* > symmetric matrix A is stored: */
/* > = 'U': Upper triangular */
/* > = 'L': Lower triangular */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* > NB is INTEGER */
/* > The maximum number of columns of the matrix A that should be */
/* > factored. NB should be at least 2 to allow for 2-by-2 pivot */
/* > blocks. */
/* > \endverbatim */
/* > */
/* > \param[out] KB */
/* > \verbatim */
/* > KB is INTEGER */
/* > The number of columns of A that were actually factored. */
/* > KB is either NB-1 or NB, or N if N <= NB. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,N) */
/* > On entry, the symmetric 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, A contains details of the partial factorization. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > Details of the interchanges and the block structure of D. */
/* > */
/* > If UPLO = 'U': */
/* > Only the last KB elements of IPIV are set. */
/* > */
/* > If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* > interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* > */
/* > If IPIV(k) = IPIV(k-1) < 0, then rows and columns */
/* > k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/* > is a 2-by-2 diagonal block. */
/* > */
/* > If UPLO = 'L': */
/* > Only the first KB elements of IPIV are set. */
/* > */
/* > If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* > interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* > */
/* > If IPIV(k) = IPIV(k+1) < 0, then rows and columns */
/* > k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) */
/* > is a 2-by-2 diagonal block. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is REAL array, dimension (LDW,NB) */
/* > \endverbatim */
/* > */
/* > \param[in] LDW */
/* > \verbatim */
/* > LDW is INTEGER */
/* > The leading dimension of the array W. LDW >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > > 0: if INFO = k, D(k,k) is exactly zero. The factorization */
/* > has been completed, but the block diagonal matrix D is */
/* > exactly singular. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2013 */
/* > \ingroup realSYcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > \verbatim */
/* > */
/* > November 2013, Igor Kozachenko, */
/* > Computer Science Division, */
/* > University of California, Berkeley */
/* > \endverbatim */
/* ===================================================================== */
/* Subroutine */ void slasyf_(char *uplo, integer *n, integer *nb, integer *kb,
real *a, integer *lda, integer *ipiv, real *w, integer *ldw, integer
*info)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3;
/* Local variables */
integer imax, jmax, j, k;
real t, alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *),
sgemm_(char *, char *, integer *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
integer kstep;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *), sswap_(integer *, real *, integer *, real *, integer *
);
real r1, d11, d21, d22;
integer jb, jj, kk, jp, kp;
real absakk;
integer kw;
extern integer isamax_(integer *, real *, integer *);
real colmax, rowmax;
integer kkw;
/* -- LAPACK computational routine (version 3.5.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2013 */
/* ===================================================================== */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
w_dim1 = *ldw;
w_offset = 1 + w_dim1 * 1;
w -= w_offset;
/* Function Body */
*info = 0;
/* Initialize ALPHA for use in choosing pivot block size. */
alpha = (sqrt(17.f) + 1.f) / 8.f;
if (lsame_(uplo, "U")) {
/* Factorize the trailing columns of A using the upper triangle */
/* of A and working backwards, and compute the matrix W = U12*D */
/* for use in updating A11 */
/* K is the main loop index, decreasing from N in steps of 1 or 2 */
/* KW is the column of W which corresponds to column K of A */
k = *n;
L10:
kw = *nb + k - *n;
/* Exit from loop */
if (k <= *n - *nb + 1 && *nb < *n || k < 1) {
goto L30;
}
/* Copy column K of A to column KW of W and update it */
scopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
if (k < *n) {
i__1 = *n - k;
sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1],
lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b9, &w[kw *
w_dim1 + 1], &c__1);
}
kstep = 1;
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
absakk = (r__1 = w[k + kw * w_dim1], abs(r__1));
/* IMAX is the row-index of the largest off-diagonal element in */
/* column K, and COLMAX is its absolute value. */
/* Determine both COLMAX and IMAX. */
if (k > 1) {
i__1 = k - 1;
imax = isamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
colmax = (r__1 = w[imax + kw * w_dim1], abs(r__1));
} else {
colmax = 0.f;
}
if (f2cmax(absakk,colmax) == 0.f) {
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
} else {
if (absakk >= alpha * colmax) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
/* Copy column IMAX to column KW-1 of W and update it */
scopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
w_dim1 + 1], &c__1);
i__1 = k - imax;
scopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
1 + (kw - 1) * w_dim1], &c__1);
if (k < *n) {
i__1 = *n - k;
sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) *
a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
ldw, &c_b9, &w[(kw - 1) * w_dim1 + 1], &c__1);
}
/* JMAX is the column-index of the largest off-diagonal */
/* element in row IMAX, and ROWMAX is its absolute value */
i__1 = k - imax;
jmax = imax + isamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
&c__1);
rowmax = (r__1 = w[jmax + (kw - 1) * w_dim1], abs(r__1));
if (imax > 1) {
i__1 = imax - 1;
jmax = isamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
/* Computing MAX */
r__2 = rowmax, r__3 = (r__1 = w[jmax + (kw - 1) * w_dim1],
abs(r__1));
rowmax = f2cmax(r__2,r__3);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else if ((r__1 = w[imax + (kw - 1) * w_dim1], abs(r__1)) >=
alpha * rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1 */
/* pivot block */
kp = imax;
/* copy column KW-1 of W to column KW of W */
scopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
w_dim1 + 1], &c__1);
} else {
/* interchange rows and columns K-1 and IMAX, use 2-by-2 */
/* pivot block */
kp = imax;
kstep = 2;
}
}
/* ============================================================ */
/* KK is the column of A where pivoting step stopped */
kk = k - kstep + 1;
/* KKW is the column of W which corresponds to column KK of A */
kkw = *nb + kk - *n;
/* Interchange rows and columns KP and KK. */
/* Updated column KP is already stored in column KKW of W. */
if (kp != kk) {
/* Copy non-updated column KK to column KP of submatrix A */
/* at step K. No need to copy element into column K */
/* (or K and K-1 for 2-by-2 pivot) of A, since these columns */
/* will be later overwritten. */
a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
i__1 = kk - 1 - kp;
scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
1) * a_dim1], lda);
if (kp > 1) {
i__1 = kp - 1;
scopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+ 1], &c__1);
}
/* Interchange rows KK and KP in last K+1 to N columns of A */
/* (columns K (or K and K-1 for 2-by-2 pivot) of A will be */
/* later overwritten). Interchange rows KK and KP */
/* in last KKW to NB columns of W. */
if (k < *n) {
i__1 = *n - k;
sswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+ 1) * a_dim1], lda);
}
i__1 = *n - kk + 1;
sswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
w_dim1], ldw);
}
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column kw of W now holds */
/* W(kw) = U(k)*D(k), */
/* where U(k) is the k-th column of U */
/* Store subdiag. elements of column U(k) */
/* and 1-by-1 block D(k) in column k of A. */
/* NOTE: Diagonal element U(k,k) is a UNIT element */
/* and not stored. */
/* A(k,k) := D(k,k) = W(k,kw) */
/* A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k) */
scopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
c__1);
r1 = 1.f / a[k + k * a_dim1];
i__1 = k - 1;
sscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
} else {
/* 2-by-2 pivot block D(k): columns kw and kw-1 of W now hold */
/* ( W(kw-1) W(kw) ) = ( U(k-1) U(k) )*D(k) */
/* where U(k) and U(k-1) are the k-th and (k-1)-th columns */
/* of U */
/* Store U(1:k-2,k-1) and U(1:k-2,k) and 2-by-2 */
/* block D(k-1:k,k-1:k) in columns k-1 and k of A. */
/* NOTE: 2-by-2 diagonal block U(k-1:k,k-1:k) is a UNIT */
/* block and not stored. */
/* A(k-1:k,k-1:k) := D(k-1:k,k-1:k) = W(k-1:k,kw-1:kw) */
/* A(1:k-2,k-1:k) := U(1:k-2,k:k-1:k) = */
/* = W(1:k-2,kw-1:kw) * ( D(k-1:k,k-1:k)**(-1) ) */
if (k > 2) {
/* Compose the columns of the inverse of 2-by-2 pivot */
/* block D in the following way to reduce the number */
/* of FLOPS when we myltiply panel ( W(kw-1) W(kw) ) by */
/* this inverse */
/* D**(-1) = ( d11 d21 )**(-1) = */
/* ( d21 d22 ) */
/* = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) = */
/* ( (-d21 ) ( d11 ) ) */
/* = 1/d21 * 1/((d11/d21)*(d22/d21)-1) * */
/* * ( ( d22/d21 ) ( -1 ) ) = */
/* ( ( -1 ) ( d11/d21 ) ) */
/* = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) ( -1 ) ) = */
/* ( ( -1 ) ( D22 ) ) */
/* = 1/d21 * T * ( ( D11 ) ( -1 ) ) */
/* ( ( -1 ) ( D22 ) ) */
/* = D21 * ( ( D11 ) ( -1 ) ) */
/* ( ( -1 ) ( D22 ) ) */
d21 = w[k - 1 + kw * w_dim1];
d11 = w[k + kw * w_dim1] / d21;
d22 = w[k - 1 + (kw - 1) * w_dim1] / d21;
t = 1.f / (d11 * d22 - 1.f);
d21 = t / d21;
/* Update elements in columns A(k-1) and A(k) as */
/* dot products of rows of ( W(kw-1) W(kw) ) and columns */
/* of D**(-1) */
i__1 = k - 2;
for (j = 1; j <= i__1; ++j) {
a[j + (k - 1) * a_dim1] = d21 * (d11 * w[j + (kw - 1)
* w_dim1] - w[j + kw * w_dim1]);
a[j + k * a_dim1] = d21 * (d22 * w[j + kw * w_dim1] -
w[j + (kw - 1) * w_dim1]);
/* L20: */
}
}
/* Copy D(k) to A */
a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
a[k + k * a_dim1] = w[k + kw * w_dim1];
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -kp;
ipiv[k - 1] = -kp;
}
/* Decrease K and return to the start of the main loop */
k -= kstep;
goto L10;
L30:
/* Update the upper triangle of A11 (= A(1:k,1:k)) as */
/* A11 := A11 - U12*D*U12**T = A11 - U12*W**T */
/* computing blocks of NB columns at a time */
i__1 = -(*nb);
for (j = (k - 1) / *nb * *nb + 1; i__1 < 0 ? j >= 1 : j <= 1; j +=
i__1) {
/* Computing MIN */
i__2 = *nb, i__3 = k - j + 1;
jb = f2cmin(i__2,i__3);
/* Update the upper triangle of the diagonal block */
i__2 = j + jb - 1;
for (jj = j; jj <= i__2; ++jj) {
i__3 = jj - j + 1;
i__4 = *n - k;
sgemv_("No transpose", &i__3, &i__4, &c_b8, &a[j + (k + 1) *
a_dim1], lda, &w[jj + (kw + 1) * w_dim1], ldw, &c_b9,
&a[j + jj * a_dim1], &c__1);
/* L40: */
}
/* Update the rectangular superdiagonal block */
i__2 = j - 1;
i__3 = *n - k;
sgemm_("No transpose", "Transpose", &i__2, &jb, &i__3, &c_b8, &a[(
k + 1) * a_dim1 + 1], lda, &w[j + (kw + 1) * w_dim1], ldw,
&c_b9, &a[j * a_dim1 + 1], lda);
/* L50: */
}
/* Put U12 in standard form by partially undoing the interchanges */
/* in columns k+1:n looping backwards from k+1 to n */
j = k + 1;
L60:
/* Undo the interchanges (if any) of rows JJ and JP at each */
/* step J */
/* (Here, J is a diagonal index) */
jj = j;
jp = ipiv[j];
if (jp < 0) {
jp = -jp;
/* (Here, J is a diagonal index) */
++j;
}
/* (NOTE: Here, J is used to determine row length. Length N-J+1 */
/* of the rows to swap back doesn't include diagonal element) */
++j;
if (jp != jj && j <= *n) {
i__1 = *n - j + 1;
sswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
}
if (j < *n) {
goto L60;
}
/* Set KB to the number of columns factorized */
*kb = *n - k;
} else {
/* Factorize the leading columns of A using the lower triangle */
/* of A and working forwards, and compute the matrix W = L21*D */
/* for use in updating A22 */
/* K is the main loop index, increasing from 1 in steps of 1 or 2 */
k = 1;
L70:
/* Exit from loop */
if (k >= *nb && *nb < *n || k > *n) {
goto L90;
}
/* Copy column K of A to column K of W and update it */
i__1 = *n - k + 1;
scopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
i__1 = *n - k + 1;
i__2 = k - 1;
sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[k
+ w_dim1], ldw, &c_b9, &w[k + k * w_dim1], &c__1);
kstep = 1;
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
absakk = (r__1 = w[k + k * w_dim1], abs(r__1));
/* IMAX is the row-index of the largest off-diagonal element in */
/* column K, and COLMAX is its absolute value. */
/* Determine both COLMAX and IMAX. */
if (k < *n) {
i__1 = *n - k;
imax = k + isamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
colmax = (r__1 = w[imax + k * w_dim1], abs(r__1));
} else {
colmax = 0.f;
}
if (f2cmax(absakk,colmax) == 0.f) {
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
} else {
if (absakk >= alpha * colmax) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
/* Copy column IMAX to column K+1 of W and update it */
i__1 = imax - k;
scopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
w_dim1], &c__1);
i__1 = *n - imax + 1;
scopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
1) * w_dim1], &c__1);
i__1 = *n - k + 1;
i__2 = k - 1;
sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1],
lda, &w[imax + w_dim1], ldw, &c_b9, &w[k + (k + 1) *
w_dim1], &c__1);
/* JMAX is the column-index of the largest off-diagonal */
/* element in row IMAX, and ROWMAX is its absolute value */
i__1 = imax - k;
jmax = k - 1 + isamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
;
rowmax = (r__1 = w[jmax + (k + 1) * w_dim1], abs(r__1));
if (imax < *n) {
i__1 = *n - imax;
jmax = imax + isamax_(&i__1, &w[imax + 1 + (k + 1) *
w_dim1], &c__1);
/* Computing MAX */
r__2 = rowmax, r__3 = (r__1 = w[jmax + (k + 1) * w_dim1],
abs(r__1));
rowmax = f2cmax(r__2,r__3);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else if ((r__1 = w[imax + (k + 1) * w_dim1], abs(r__1)) >=
alpha * rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1 */
/* pivot block */
kp = imax;
/* copy column K+1 of W to column K of W */
i__1 = *n - k + 1;
scopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
w_dim1], &c__1);
} else {
/* interchange rows and columns K+1 and IMAX, use 2-by-2 */
/* pivot block */
kp = imax;
kstep = 2;
}
}
/* ============================================================ */
/* KK is the column of A where pivoting step stopped */
kk = k + kstep - 1;
/* Interchange rows and columns KP and KK. */
/* Updated column KP is already stored in column KK of W. */
if (kp != kk) {
/* Copy non-updated column KK to column KP of submatrix A */
/* at step K. No need to copy element into column K */
/* (or K and K+1 for 2-by-2 pivot) of A, since these columns */
/* will be later overwritten. */
a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
i__1 = kp - kk - 1;
scopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
1) * a_dim1], lda);
if (kp < *n) {
i__1 = *n - kp;
scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+ kp * a_dim1], &c__1);
}
/* Interchange rows KK and KP in first K-1 columns of A */
/* (columns K (or K and K+1 for 2-by-2 pivot) of A will be */
/* later overwritten). Interchange rows KK and KP */
/* in first KK columns of W. */
if (k > 1) {
i__1 = k - 1;
sswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
}
sswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
}
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k of W now holds */
/* W(k) = L(k)*D(k), */
/* where L(k) is the k-th column of L */
/* Store subdiag. elements of column L(k) */
/* and 1-by-1 block D(k) in column k of A. */
/* (NOTE: Diagonal element L(k,k) is a UNIT element */
/* and not stored) */
/* A(k,k) := D(k,k) = W(k,k) */
/* A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k) */
i__1 = *n - k + 1;
scopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
c__1);
if (k < *n) {
r1 = 1.f / a[k + k * a_dim1];
i__1 = *n - k;
sscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
}
} else {
/* 2-by-2 pivot block D(k): columns k and k+1 of W now hold */
/* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
/* where L(k) and L(k+1) are the k-th and (k+1)-th columns */
/* of L */
/* Store L(k+2:N,k) and L(k+2:N,k+1) and 2-by-2 */
/* block D(k:k+1,k:k+1) in columns k and k+1 of A. */
/* (NOTE: 2-by-2 diagonal block L(k:k+1,k:k+1) is a UNIT */
/* block and not stored) */
/* A(k:k+1,k:k+1) := D(k:k+1,k:k+1) = W(k:k+1,k:k+1) */
/* A(k+2:N,k:k+1) := L(k+2:N,k:k+1) = */
/* = W(k+2:N,k:k+1) * ( D(k:k+1,k:k+1)**(-1) ) */
if (k < *n - 1) {
/* Compose the columns of the inverse of 2-by-2 pivot */
/* block D in the following way to reduce the number */
/* of FLOPS when we myltiply panel ( W(k) W(k+1) ) by */
/* this inverse */
/* D**(-1) = ( d11 d21 )**(-1) = */
/* ( d21 d22 ) */
/* = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) = */
/* ( (-d21 ) ( d11 ) ) */
/* = 1/d21 * 1/((d11/d21)*(d22/d21)-1) * */
/* * ( ( d22/d21 ) ( -1 ) ) = */
/* ( ( -1 ) ( d11/d21 ) ) */
/* = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) ( -1 ) ) = */
/* ( ( -1 ) ( D22 ) ) */
/* = 1/d21 * T * ( ( D11 ) ( -1 ) ) */
/* ( ( -1 ) ( D22 ) ) */
/* = D21 * ( ( D11 ) ( -1 ) ) */
/* ( ( -1 ) ( D22 ) ) */
d21 = w[k + 1 + k * w_dim1];
d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
d22 = w[k + k * w_dim1] / d21;
t = 1.f / (d11 * d22 - 1.f);
d21 = t / d21;
/* Update elements in columns A(k) and A(k+1) as */
/* dot products of rows of ( W(k) W(k+1) ) and columns */
/* of D**(-1) */
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
a[j + k * a_dim1] = d21 * (d11 * w[j + k * w_dim1] -
w[j + (k + 1) * w_dim1]);
a[j + (k + 1) * a_dim1] = d21 * (d22 * w[j + (k + 1) *
w_dim1] - w[j + k * w_dim1]);
/* L80: */
}
}
/* Copy D(k) to A */
a[k + k * a_dim1] = w[k + k * w_dim1];
a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -kp;
ipiv[k + 1] = -kp;
}
/* Increase K and return to the start of the main loop */
k += kstep;
goto L70;
L90:
/* Update the lower triangle of A22 (= A(k:n,k:n)) as */
/* A22 := A22 - L21*D*L21**T = A22 - L21*W**T */
/* computing blocks of NB columns at a time */
i__1 = *n;
i__2 = *nb;
for (j = k; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
i__3 = *nb, i__4 = *n - j + 1;
jb = f2cmin(i__3,i__4);
/* Update the lower triangle of the diagonal block */
i__3 = j + jb - 1;
for (jj = j; jj <= i__3; ++jj) {
i__4 = j + jb - jj;
i__5 = k - 1;
sgemv_("No transpose", &i__4, &i__5, &c_b8, &a[jj + a_dim1],
lda, &w[jj + w_dim1], ldw, &c_b9, &a[jj + jj * a_dim1]
, &c__1);
/* L100: */
}
/* Update the rectangular subdiagonal block */
if (j + jb <= *n) {
i__3 = *n - j - jb + 1;
i__4 = k - 1;
sgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, &c_b8,
&a[j + jb + a_dim1], lda, &w[j + w_dim1], ldw, &c_b9,
&a[j + jb + j * a_dim1], lda);
}
/* L110: */
}
/* Put L21 in standard form by partially undoing the interchanges */
/* of rows in columns 1:k-1 looping backwards from k-1 to 1 */
j = k - 1;
L120:
/* Undo the interchanges (if any) of rows JJ and JP at each */
/* step J */
/* (Here, J is a diagonal index) */
jj = j;
jp = ipiv[j];
if (jp < 0) {
jp = -jp;
/* (Here, J is a diagonal index) */
--j;
}
/* (NOTE: Here, J is used to determine row length. Length J */
/* of the rows to swap back doesn't include diagonal element) */
--j;
if (jp != jj && j >= 1) {
sswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
}
if (j > 1) {
goto L120;
}
/* Set KB to the number of columns factorized */
*kb = k - 1;
}
return;
/* End of SLASYF */
} /* slasyf_ */
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