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OpenBLAS/lapack-netlib/SRC/zlasyf_rk.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]/Cd(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 doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
/* > \brief \b ZLASYF_RK computes a partial factorization of a complex symmetric indefinite matrix using bound
ed Bunch-Kaufman (rook) diagonal pivoting method. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZLASYF_RK + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlasyf_
rk.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlasyf_
rk.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlasyf_
rk.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZLASYF_RK( UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW, */
/* INFO ) */
/* CHARACTER UPLO */
/* INTEGER INFO, KB, LDA, LDW, N, NB */
/* INTEGER IPIV( * ) */
/* COMPLEX*16 A( LDA, * ), E( * ), W( LDW, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > ZLASYF_RK computes a partial factorization of a complex symmetric */
/* > matrix A using the bounded Bunch-Kaufman (rook) 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. */
/* > */
/* > ZLASYF_RK is an auxiliary routine called by ZSYTRF_RK. 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 COMPLEX*16 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, contains: */
/* > a) ONLY diagonal elements of the symmetric block diagonal */
/* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
/* > (superdiagonal (or subdiagonal) elements of D */
/* > are stored on exit in array E), and */
/* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
/* > If UPLO = 'L': factor L in the subdiagonal part of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* > E is COMPLEX*16 array, dimension (N) */
/* > On exit, contains the superdiagonal (or subdiagonal) */
/* > elements of the symmetric block diagonal matrix D */
/* > with 1-by-1 or 2-by-2 diagonal blocks, where */
/* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; */
/* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0. */
/* > */
/* > NOTE: For 1-by-1 diagonal block D(k), where */
/* > 1 <= k <= N, the element E(k) is set to 0 in both */
/* > UPLO = 'U' or UPLO = 'L' cases. */
/* > \endverbatim */
/* > */
/* > \param[out] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > IPIV describes the permutation matrix P in the factorization */
/* > of matrix A as follows. The absolute value of IPIV(k) */
/* > represents the index of row and column that were */
/* > interchanged with the k-th row and column. The value of UPLO */
/* > describes the order in which the interchanges were applied. */
/* > Also, the sign of IPIV represents the block structure of */
/* > the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 */
/* > diagonal blocks which correspond to 1 or 2 interchanges */
/* > at each factorization step. */
/* > */
/* > If UPLO = 'U', */
/* > ( in factorization order, k decreases from N to 1 ): */
/* > a) A single positive entry IPIV(k) > 0 means: */
/* > D(k,k) is a 1-by-1 diagonal block. */
/* > If IPIV(k) != k, rows and columns k and IPIV(k) were */
/* > interchanged in the submatrix A(1:N,N-KB+1:N); */
/* > If IPIV(k) = k, no interchange occurred. */
/* > */
/* > */
/* > b) A pair of consecutive negative entries */
/* > IPIV(k) < 0 and IPIV(k-1) < 0 means: */
/* > D(k-1:k,k-1:k) is a 2-by-2 diagonal block. */
/* > (NOTE: negative entries in IPIV appear ONLY in pairs). */
/* > 1) If -IPIV(k) != k, rows and columns */
/* > k and -IPIV(k) were interchanged */
/* > in the matrix A(1:N,N-KB+1:N). */
/* > If -IPIV(k) = k, no interchange occurred. */
/* > 2) If -IPIV(k-1) != k-1, rows and columns */
/* > k-1 and -IPIV(k-1) were interchanged */
/* > in the submatrix A(1:N,N-KB+1:N). */
/* > If -IPIV(k-1) = k-1, no interchange occurred. */
/* > */
/* > c) In both cases a) and b) is always ABS( IPIV(k) ) <= k. */
/* > */
/* > d) NOTE: Any entry IPIV(k) is always NONZERO on output. */
/* > */
/* > If UPLO = 'L', */
/* > ( in factorization order, k increases from 1 to N ): */
/* > a) A single positive entry IPIV(k) > 0 means: */
/* > D(k,k) is a 1-by-1 diagonal block. */
/* > If IPIV(k) != k, rows and columns k and IPIV(k) were */
/* > interchanged in the submatrix A(1:N,1:KB). */
/* > If IPIV(k) = k, no interchange occurred. */
/* > */
/* > b) A pair of consecutive negative entries */
/* > IPIV(k) < 0 and IPIV(k+1) < 0 means: */
/* > D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
/* > (NOTE: negative entries in IPIV appear ONLY in pairs). */
/* > 1) If -IPIV(k) != k, rows and columns */
/* > k and -IPIV(k) were interchanged */
/* > in the submatrix A(1:N,1:KB). */
/* > If -IPIV(k) = k, no interchange occurred. */
/* > 2) If -IPIV(k+1) != k+1, rows and columns */
/* > k-1 and -IPIV(k-1) were interchanged */
/* > in the submatrix A(1:N,1:KB). */
/* > If -IPIV(k+1) = k+1, no interchange occurred. */
/* > */
/* > c) In both cases a) and b) is always ABS( IPIV(k) ) >= k. */
/* > */
/* > d) NOTE: Any entry IPIV(k) is always NONZERO on output. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is COMPLEX*16 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, the k-th argument had an illegal value */
/* > */
/* > > 0: If INFO = k, the matrix A is singular, because: */
/* > If UPLO = 'U': column k in the upper */
/* > triangular part of A contains all zeros. */
/* > If UPLO = 'L': column k in the lower */
/* > triangular part of A contains all zeros. */
/* > */
/* > Therefore D(k,k) is exactly zero, and superdiagonal */
/* > elements of column k of U (or subdiagonal elements of */
/* > column k of L ) are all zeros. The factorization has */
/* > been completed, but the block diagonal matrix D is */
/* > exactly singular, and division by zero will occur if */
/* > it is used to solve a system of equations. */
/* > */
/* > NOTE: INFO only stores the first occurrence of */
/* > a singularity, any subsequent occurrence of singularity */
/* > is not stored in INFO even though the factorization */
/* > always completes. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup complex16SYcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > \verbatim */
/* > */
/* > December 2016, Igor Kozachenko, */
/* > Computer Science Division, */
/* > University of California, Berkeley */
/* > */
/* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
/* > School of Mathematics, */
/* > University of Manchester */
/* > */
/* > \endverbatim */
/* ===================================================================== */
/* Subroutine */ void zlasyf_rk_(char *uplo, integer *n, integer *nb, integer
*kb, doublecomplex *a, integer *lda, doublecomplex *e, integer *ipiv,
doublecomplex *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;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
logical done;
integer imax, jmax, j, k, p;
doublecomplex t;
doublereal alpha;
extern logical lsame_(char *, char *);
doublereal dtemp, sfmin;
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
integer itemp;
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer kstep;
extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
doublecomplex r1;
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
doublecomplex d11, d12, d21, d22;
integer jb, ii, jj, kk;
extern doublereal dlamch_(char *);
integer kp;
doublereal absakk;
integer kw;
doublereal colmax;
extern integer izamax_(integer *, doublecomplex *, integer *);
doublereal rowmax;
integer kkw;
/* -- 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 */
/* ===================================================================== */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--e;
--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.) + 1.) / 8.;
/* Compute machine safe minimum */
sfmin = dlamch_("S");
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 */
/* Initialize the first entry of array E, where superdiagonal */
/* elements of D are stored */
e[1].r = 0., e[1].i = 0.;
/* K is the main loop index, decreasing from N in steps of 1 or 2 */
k = *n;
L10:
/* KW is the column of W which corresponds to column K of A */
kw = *nb + k - *n;
/* Exit from loop */
if (k <= *n - *nb + 1 && *nb < *n || k < 1) {
goto L30;
}
kstep = 1;
p = k;
/* Copy column K of A to column KW of W and update it */
zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
if (k < *n) {
i__1 = *n - k;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
w_dim1 + 1], &c__1);
}
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = k + kw * w_dim1;
absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + kw *
w_dim1]), abs(d__2));
/* 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 = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
i__1 = imax + kw * w_dim1;
colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
kw * w_dim1]), abs(d__2));
} else {
colmax = 0.;
}
if (f2cmax(absakk,colmax) == 0.) {
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
/* Set E( K ) to zero */
if (k > 1) {
i__1 = k;
e[i__1].r = 0., e[i__1].i = 0.;
}
} else {
/* ============================================================ */
/* Test for interchange */
/* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX */
/* (used to handle NaN and Inf) */
if (! (absakk < alpha * colmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
done = FALSE_;
/* Loop until pivot found */
L12:
/* Begin pivot search loop body */
/* Copy column IMAX to column KW-1 of W and update it */
zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
w_dim1 + 1], &c__1);
i__1 = k - imax;
zcopy_(&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;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
ldw, &c_b1, &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. */
/* Determine both ROWMAX and JMAX. */
if (imax != k) {
i__1 = k - imax;
jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) *
w_dim1], &c__1);
i__1 = jmax + (kw - 1) * w_dim1;
rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
w[jmax + (kw - 1) * w_dim1]), abs(d__2));
} else {
rowmax = 0.;
}
if (imax > 1) {
i__1 = imax - 1;
itemp = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
i__1 = itemp + (kw - 1) * w_dim1;
dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
itemp + (kw - 1) * w_dim1]), abs(d__2));
if (dtemp > rowmax) {
rowmax = dtemp;
jmax = itemp;
}
}
/* Equivalent to testing for */
/* CABS1( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX */
/* (used to handle NaN and Inf) */
i__1 = imax + (kw - 1) * w_dim1;
if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
+ (kw - 1) * w_dim1]), abs(d__2)) < 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 */
zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
w_dim1 + 1], &c__1);
done = TRUE_;
/* Equivalent to testing for ROWMAX.EQ.COLMAX, */
/* (used to handle NaN and Inf) */
} else if (p == jmax || rowmax <= colmax) {
/* interchange rows and columns K-1 and IMAX, */
/* use 2-by-2 pivot block */
kp = imax;
kstep = 2;
done = TRUE_;
} else {
/* Pivot not found: set params and repeat */
p = imax;
colmax = rowmax;
imax = jmax;
/* Copy updated JMAXth (next IMAXth) column to Kth of W */
zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
w_dim1 + 1], &c__1);
}
/* End pivot search loop body */
if (! done) {
goto L12;
}
}
/* ============================================================ */
kk = k - kstep + 1;
/* KKW is the column of W which corresponds to column KK of A */
kkw = *nb + kk - *n;
if (kstep == 2 && p != k) {
/* Copy non-updated column K to column P */
i__1 = k - p;
zcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
a_dim1], lda);
zcopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
c__1);
/* Interchange rows K and P in last N-K+1 columns of A */
/* and last N-K+2 columns of W */
i__1 = *n - k + 1;
zswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
lda);
i__1 = *n - kk + 1;
zswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
ldw);
}
/* Updated column KP is already stored in column KKW of W */
if (kp != kk) {
/* Copy non-updated column KK to column KP */
i__1 = kp + k * a_dim1;
i__2 = kk + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = k - 1 - kp;
zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
1) * a_dim1], lda);
zcopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
c__1);
/* Interchange rows KK and KP in last N-KK+1 columns */
/* of A and W */
i__1 = *n - kk + 1;
zswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
lda);
i__1 = *n - kk + 1;
zswap_(&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(k) = U(k)*D(k) */
/* where U(k) is the k-th column of U */
/* Store U(k) in column k of A */
zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
c__1);
if (k > 1) {
i__1 = k + k * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
k * a_dim1]), abs(d__2)) >= sfmin) {
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
r1.r = z__1.r, r1.i = z__1.i;
i__1 = k - 1;
zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
} else /* if(complicated condition) */ {
i__1 = k + k * a_dim1;
if (a[i__1].r != 0. || a[i__1].i != 0.) {
i__1 = k - 1;
for (ii = 1; ii <= i__1; ++ii) {
i__2 = ii + k * a_dim1;
z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
a_dim1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L14: */
}
}
}
/* Store the superdiagonal element of D in array E */
i__1 = k;
e[i__1].r = 0., e[i__1].i = 0.;
}
} else {
/* 2-by-2 pivot block D(k): columns KW and KW-1 of W now */
/* hold */
/* ( W(k-1) W(k) ) = ( 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 */
if (k > 2) {
/* Store U(k) and U(k-1) in columns k and k-1 of A */
i__1 = k - 1 + kw * w_dim1;
d12.r = w[i__1].r, d12.i = w[i__1].i;
z_div(&z__1, &w[k + kw * w_dim1], &d12);
d11.r = z__1.r, d11.i = z__1.i;
z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d12);
d22.r = z__1.r, d22.i = z__1.i;
z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
d22.i + d11.i * d22.r;
z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r, t.i = z__1.i;
i__1 = k - 2;
for (j = 1; j <= i__1; ++j) {
i__2 = j + (k - 1) * a_dim1;
i__3 = j + (kw - 1) * w_dim1;
z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
.r;
i__4 = j + kw * w_dim1;
z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
.i;
z_div(&z__2, &z__3, &d12);
z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
z__2.i + t.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = j + k * a_dim1;
i__3 = j + kw * w_dim1;
z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
.r;
i__4 = j + (kw - 1) * w_dim1;
z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
.i;
z_div(&z__2, &z__3, &d12);
z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
z__2.i + t.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L20: */
}
}
/* Copy diagonal elements of D(K) to A, */
/* copy superdiagonal element of D(K) to E(K) and */
/* ZERO out superdiagonal entry of A */
i__1 = k - 1 + (k - 1) * a_dim1;
i__2 = k - 1 + (kw - 1) * w_dim1;
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
i__1 = k - 1 + k * a_dim1;
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = k + k * a_dim1;
i__2 = k + kw * w_dim1;
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
i__1 = k;
i__2 = k - 1 + kw * w_dim1;
e[i__1].r = w[i__2].r, e[i__1].i = w[i__2].i;
i__1 = k - 1;
e[i__1].r = 0., e[i__1].i = 0.;
}
/* End column K is nonsingular */
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -p;
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;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &i__3, &i__4, &z__1, &a[j + (k + 1) *
a_dim1], lda, &w[jj + (kw + 1) * w_dim1], ldw, &c_b1,
&a[j + jj * a_dim1], &c__1);
/* L40: */
}
/* Update the rectangular superdiagonal block */
if (j >= 2) {
i__2 = j - 1;
i__3 = *n - k;
z__1.r = -1., z__1.i = 0.;
zgemm_("No transpose", "Transpose", &i__2, &jb, &i__3, &z__1,
&a[(k + 1) * a_dim1 + 1], lda, &w[j + (kw + 1) *
w_dim1], ldw, &c_b1, &a[j * a_dim1 + 1], lda);
}
/* L50: */
}
/* 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 */
/* Initialize the unused last entry of the subdiagonal array E. */
i__1 = *n;
e[i__1].r = 0., e[i__1].i = 0.;
/* 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;
}
kstep = 1;
p = k;
/* Copy column K of A to column K of W and update it */
i__1 = *n - k + 1;
zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
if (k > 1) {
i__1 = *n - k + 1;
i__2 = k - 1;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &
w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1);
}
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = k + k * w_dim1;
absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + k *
w_dim1]), abs(d__2));
/* 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 + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
i__1 = imax + k * w_dim1;
colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
k * w_dim1]), abs(d__2));
} else {
colmax = 0.;
}
if (f2cmax(absakk,colmax) == 0.) {
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
i__1 = *n - k + 1;
zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
c__1);
/* Set E( K ) to zero */
if (k < *n) {
i__1 = k;
e[i__1].r = 0., e[i__1].i = 0.;
}
} else {
/* ============================================================ */
/* Test for interchange */
/* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX */
/* (used to handle NaN and Inf) */
if (! (absakk < alpha * colmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
done = FALSE_;
/* Loop until pivot found */
L72:
/* Begin pivot search loop body */
/* Copy column IMAX to column K+1 of W and update it */
i__1 = imax - k;
zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
w_dim1], &c__1);
i__1 = *n - imax + 1;
zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
1) * w_dim1], &c__1);
if (k > 1) {
i__1 = *n - k + 1;
i__2 = k - 1;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1]
, lda, &w[imax + w_dim1], ldw, &c_b1, &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. */
/* Determine both ROWMAX and JMAX. */
if (imax != k) {
i__1 = imax - k;
jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &
c__1);
i__1 = jmax + (k + 1) * w_dim1;
rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
w[jmax + (k + 1) * w_dim1]), abs(d__2));
} else {
rowmax = 0.;
}
if (imax < *n) {
i__1 = *n - imax;
itemp = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
w_dim1], &c__1);
i__1 = itemp + (k + 1) * w_dim1;
dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
itemp + (k + 1) * w_dim1]), abs(d__2));
if (dtemp > rowmax) {
rowmax = dtemp;
jmax = itemp;
}
}
/* Equivalent to testing for */
/* CABS1( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX */
/* (used to handle NaN and Inf) */
i__1 = imax + (k + 1) * w_dim1;
if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
+ (k + 1) * w_dim1]), abs(d__2)) < 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;
zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
w_dim1], &c__1);
done = TRUE_;
/* Equivalent to testing for ROWMAX.EQ.COLMAX, */
/* (used to handle NaN and Inf) */
} else if (p == jmax || rowmax <= colmax) {
/* interchange rows and columns K+1 and IMAX, */
/* use 2-by-2 pivot block */
kp = imax;
kstep = 2;
done = TRUE_;
} else {
/* Pivot not found: set params and repeat */
p = imax;
colmax = rowmax;
imax = jmax;
/* Copy updated JMAXth (next IMAXth) column to Kth of W */
i__1 = *n - k + 1;
zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
w_dim1], &c__1);
}
/* End pivot search loop body */
if (! done) {
goto L72;
}
}
/* ============================================================ */
kk = k + kstep - 1;
if (kstep == 2 && p != k) {
/* Copy non-updated column K to column P */
i__1 = p - k;
zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
lda);
i__1 = *n - p + 1;
zcopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
c__1);
/* Interchange rows K and P in first K columns of A */
/* and first K+1 columns of W */
zswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
zswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
}
/* Updated column KP is already stored in column KK of W */
if (kp != kk) {
/* Copy non-updated column KK to column KP */
i__1 = kp + k * a_dim1;
i__2 = kk + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp - k - 1;
zcopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
* a_dim1], lda);
i__1 = *n - kp + 1;
zcopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
a_dim1], &c__1);
/* Interchange rows KK and KP in first KK columns of A and W */
zswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
zswap_(&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 L(k) in column k of A */
i__1 = *n - k + 1;
zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
c__1);
if (k < *n) {
i__1 = k + k * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
k * a_dim1]), abs(d__2)) >= sfmin) {
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
r1.r = z__1.r, r1.i = z__1.i;
i__1 = *n - k;
zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
} else /* if(complicated condition) */ {
i__1 = k + k * a_dim1;
if (a[i__1].r != 0. || a[i__1].i != 0.) {
i__1 = *n;
for (ii = k + 1; ii <= i__1; ++ii) {
i__2 = ii + k * a_dim1;
z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
a_dim1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L74: */
}
}
}
/* Store the subdiagonal element of D in array E */
i__1 = k;
e[i__1].r = 0., e[i__1].i = 0.;
}
} 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 */
if (k < *n - 1) {
/* Store L(k) and L(k+1) in columns k and k+1 of A */
i__1 = k + 1 + k * w_dim1;
d21.r = w[i__1].r, d21.i = w[i__1].i;
z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
d11.r = z__1.r, d11.i = z__1.i;
z_div(&z__1, &w[k + k * w_dim1], &d21);
d22.r = z__1.r, d22.i = z__1.i;
z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
d22.i + d11.i * d22.r;
z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r, t.i = z__1.i;
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
i__3 = j + k * w_dim1;
z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
.r;
i__4 = j + (k + 1) * w_dim1;
z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
.i;
z_div(&z__2, &z__3, &d21);
z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
z__2.i + t.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = j + (k + 1) * a_dim1;
i__3 = j + (k + 1) * w_dim1;
z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
.r;
i__4 = j + k * w_dim1;
z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
.i;
z_div(&z__2, &z__3, &d21);
z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
z__2.i + t.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L80: */
}
}
/* Copy diagonal elements of D(K) to A, */
/* copy subdiagonal element of D(K) to E(K) and */
/* ZERO out subdiagonal entry of A */
i__1 = k + k * a_dim1;
i__2 = k + k * w_dim1;
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
i__1 = k + 1 + k * a_dim1;
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = k + 1 + (k + 1) * a_dim1;
i__2 = k + 1 + (k + 1) * w_dim1;
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
i__1 = k;
i__2 = k + 1 + k * w_dim1;
e[i__1].r = w[i__2].r, e[i__1].i = w[i__2].i;
i__1 = k + 1;
e[i__1].r = 0., e[i__1].i = 0.;
}
/* End column K is nonsingular */
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -p;
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;
z__1.r = -1., z__1.i = 0.;
zgemv_("No transpose", &i__4, &i__5, &z__1, &a[jj + a_dim1],
lda, &w[jj + w_dim1], ldw, &c_b1, &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;
z__1.r = -1., z__1.i = 0.;
zgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, &z__1,
&a[j + jb + a_dim1], lda, &w[j + w_dim1], ldw, &c_b1,
&a[j + jb + j * a_dim1], lda);
}
/* L110: */
}
/* Set KB to the number of columns factorized */
*kb = k - 1;
}
return;
/* End of ZLASYF_RK */
} /* zlasyf_rk__ */
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