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OpenBLAS/lapack-netlib/SRC/zsytf2.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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++ */
#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
/* > \brief \b ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal piv
oting method (unblocked algorithm). */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZSYTF2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytf2.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytf2.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytf2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO ) */
/* CHARACTER UPLO */
/* INTEGER INFO, LDA, N */
/* INTEGER IPIV( * ) */
/* COMPLEX*16 A( LDA, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZSYTF2 computes the factorization of a complex symmetric matrix A */
/* > using the Bunch-Kaufman diagonal pivoting method: */
/* > */
/* > A = U*D*U**T or A = L*D*L**T */
/* > */
/* > where U (or L) is a product of permutation and unit upper (lower) */
/* > triangular matrices, U**T is the transpose of U, and D is symmetric and */
/* > block diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
/* > */
/* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */
/* > \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,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, the block diagonal matrix D and the multipliers used */
/* > to obtain the factor U or L (see below for further details). */
/* > \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': */
/* > 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': */
/* > 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] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -k, the k-th argument had an illegal value */
/* > > 0: if INFO = k, D(k,k) is exactly zero. 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. */
/* > \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 Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > If UPLO = 'U', then A = U*D*U**T, where */
/* > U = P(n)*U(n)* ... *P(k)U(k)* ..., */
/* > i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
/* > 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
/* > defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
/* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
/* > */
/* > ( I v 0 ) k-s */
/* > U(k) = ( 0 I 0 ) s */
/* > ( 0 0 I ) n-k */
/* > k-s s n-k */
/* > */
/* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
/* > If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
/* > and A(k,k), and v overwrites A(1:k-2,k-1:k). */
/* > */
/* > If UPLO = 'L', then A = L*D*L**T, where */
/* > L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
/* > i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
/* > n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
/* > defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
/* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
/* > */
/* > ( I 0 0 ) k-1 */
/* > L(k) = ( 0 I 0 ) s */
/* > ( 0 v I ) n-k-s+1 */
/* > k-1 s n-k-s+1 */
/* > */
/* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
/* > If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
/* > and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > \verbatim */
/* > */
/* > 09-29-06 - patch from */
/* > Bobby Cheng, MathWorks */
/* > */
/* > Replace l.209 and l.377 */
/* > IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN */
/* > by */
/* > IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN */
/* > */
/* > 1-96 - Based on modifications by J. Lewis, Boeing Computer Services */
/* > Company */
/* > \endverbatim */
/* ===================================================================== */
/* Subroutine */ void zsytf2_(char *uplo, integer *n, doublecomplex *a,
integer *lda, integer *ipiv, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
integer imax, jmax;
extern /* Subroutine */ void zsyr_(char *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
integer i__, j, k;
doublecomplex t;
doublereal alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
integer kstep;
logical upper;
doublecomplex r1;
extern /* Subroutine */ void zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
doublecomplex d11, d12, d21, d22;
integer kk, kp;
doublereal absakk;
doublecomplex wk;
extern logical disnan_(doublereal *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
doublereal colmax;
extern integer izamax_(integer *, doublecomplex *, integer *);
doublereal rowmax;
doublecomplex wkm1, wkp1;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < f2cmax(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZSYTF2", &i__1, (ftnlen)6);
return;
}
/* Initialize ALPHA for use in choosing pivot block size. */
alpha = (sqrt(17.) + 1.) / 8.;
if (upper) {
/* Factorize A as U*D*U**T using the upper triangle of A */
/* K is the main loop index, decreasing from N to 1 in steps of */
/* 1 or 2 */
k = *n;
L10:
/* If K < 1, exit from loop */
if (k < 1) {
goto L70;
}
kstep = 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 * a_dim1;
absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k *
a_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, &a[k * a_dim1 + 1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax +
k * a_dim1]), abs(d__2));
} else {
colmax = 0.;
}
if (f2cmax(absakk,colmax) == 0. || disnan_(&absakk)) {
/* Column K is zero or underflow, or contains a NaN: */
/* 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 {
/* 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 + izamax_(&i__1, &a[imax + (imax + 1) * a_dim1],
lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[
imax + jmax * a_dim1]), abs(d__2));
if (imax > 1) {
i__1 = imax - 1;
jmax = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
/* Computing MAX */
i__1 = jmax + imax * a_dim1;
d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) + (
d__2 = d_imag(&a[jmax + imax * a_dim1]), abs(d__2)
);
rowmax = f2cmax(d__3,d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = imax + imax * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[
imax + imax * a_dim1]), abs(d__2)) >= alpha *
rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1 */
/* pivot block */
kp = imax;
} else {
/* interchange rows and columns K-1 and IMAX, use 2-by-2 */
/* pivot block */
kp = imax;
kstep = 2;
}
}
}
kk = k - kstep + 1;
if (kp != kk) {
/* Interchange rows and columns KK and KP in the leading */
/* submatrix A(1:k,1:k) */
i__1 = kp - 1;
zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1],
&c__1);
i__1 = kk - kp - 1;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
1) * a_dim1], lda);
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
if (kstep == 2) {
i__1 = k - 1 + k * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = k - 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + k * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
}
}
/* Update the leading submatrix */
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k now holds */
/* W(k) = U(k)*D(k) */
/* where U(k) is the k-th column of U */
/* Perform a rank-1 update of A(1:k-1,1:k-1) as */
/* A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T */
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;
z__1.r = -r1.r, z__1.i = -r1.i;
zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, &a[
a_offset], lda);
/* Store U(k) in column k */
i__1 = k - 1;
zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
} else {
/* 2-by-2 pivot block D(k): columns k and k-1 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 */
/* Perform a rank-2 update of A(1:k-2,1:k-2) as */
/* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T */
/* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T */
if (k > 2) {
i__1 = k - 1 + k * a_dim1;
d12.r = a[i__1].r, d12.i = a[i__1].i;
z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &d12);
d22.r = z__1.r, d22.i = z__1.i;
z_div(&z__1, &a[k + k * a_dim1], &d12);
d11.r = z__1.r, d11.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;
z_div(&z__1, &t, &d12);
d12.r = z__1.r, d12.i = z__1.i;
for (j = k - 2; j >= 1; --j) {
i__1 = j + (k - 1) * a_dim1;
z__3.r = d11.r * a[i__1].r - d11.i * a[i__1].i,
z__3.i = d11.r * a[i__1].i + d11.i * a[i__1]
.r;
i__2 = j + k * a_dim1;
z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
.i;
z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i =
d12.r * z__2.i + d12.i * z__2.r;
wkm1.r = z__1.r, wkm1.i = z__1.i;
i__1 = j + k * a_dim1;
z__3.r = d22.r * a[i__1].r - d22.i * a[i__1].i,
z__3.i = d22.r * a[i__1].i + d22.i * a[i__1]
.r;
i__2 = j + (k - 1) * a_dim1;
z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
.i;
z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i =
d12.r * z__2.i + d12.i * z__2.r;
wk.r = z__1.r, wk.i = z__1.i;
for (i__ = j; i__ >= 1; --i__) {
i__1 = i__ + j * a_dim1;
i__2 = i__ + j * a_dim1;
i__3 = i__ + k * a_dim1;
z__3.r = a[i__3].r * wk.r - a[i__3].i * wk.i,
z__3.i = a[i__3].r * wk.i + a[i__3].i *
wk.r;
z__2.r = a[i__2].r - z__3.r, z__2.i = a[i__2].i -
z__3.i;
i__4 = i__ + (k - 1) * a_dim1;
z__4.r = a[i__4].r * wkm1.r - a[i__4].i * wkm1.i,
z__4.i = a[i__4].r * wkm1.i + a[i__4].i *
wkm1.r;
z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* L20: */
}
i__1 = j + k * a_dim1;
a[i__1].r = wk.r, a[i__1].i = wk.i;
i__1 = j + (k - 1) * a_dim1;
a[i__1].r = wkm1.r, a[i__1].i = wkm1.i;
/* L30: */
}
}
}
}
/* 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;
} else {
/* Factorize A as L*D*L**T using the lower triangle of A */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2 */
k = 1;
L40:
/* If K > N, exit from loop */
if (k > *n) {
goto L70;
}
kstep = 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 * a_dim1;
absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k *
a_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, &a[k + 1 + k * a_dim1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax +
k * a_dim1]), abs(d__2));
} else {
colmax = 0.;
}
if (f2cmax(absakk,colmax) == 0. || disnan_(&absakk)) {
/* Column K is zero or underflow, or contains a NaN: */
/* 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 {
/* 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 + izamax_(&i__1, &a[imax + k * a_dim1], lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[
imax + jmax * a_dim1]), abs(d__2));
if (imax < *n) {
i__1 = *n - imax;
jmax = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1],
&c__1);
/* Computing MAX */
i__1 = jmax + imax * a_dim1;
d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) + (
d__2 = d_imag(&a[jmax + imax * a_dim1]), abs(d__2)
);
rowmax = f2cmax(d__3,d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = imax + imax * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[
imax + imax * a_dim1]), abs(d__2)) >= alpha *
rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1 */
/* pivot block */
kp = imax;
} else {
/* interchange rows and columns K+1 and IMAX, use 2-by-2 */
/* pivot block */
kp = imax;
kstep = 2;
}
}
}
kk = k + kstep - 1;
if (kp != kk) {
/* Interchange rows and columns KK and KP in the trailing */
/* submatrix A(k:n,k:n) */
if (kp < *n) {
i__1 = *n - kp;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+ kp * a_dim1], &c__1);
}
i__1 = kp - kk - 1;
zswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
1) * a_dim1], lda);
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
if (kstep == 2) {
i__1 = k + 1 + k * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = k + 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + k * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
}
}
/* Update the trailing submatrix */
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k now holds */
/* W(k) = L(k)*D(k) */
/* where L(k) is the k-th column of L */
if (k < *n) {
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
/* A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T */
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;
z__1.r = -r1.r, z__1.i = -r1.i;
zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], &c__1, &
a[k + 1 + (k + 1) * a_dim1], lda);
/* Store L(k) in column K */
i__1 = *n - k;
zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
}
} else {
/* 2-by-2 pivot block D(k) */
if (k < *n - 1) {
/* Perform a rank-2 update of A(k+2:n,k+2:n) as */
/* A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T */
/* = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T */
/* where L(k) and L(k+1) are the k-th and (k+1)-th */
/* columns of L */
i__1 = k + 1 + k * a_dim1;
d21.r = a[i__1].r, d21.i = a[i__1].i;
z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &d21);
d11.r = z__1.r, d11.i = z__1.i;
z_div(&z__1, &a[k + k * a_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;
z_div(&z__1, &t, &d21);
d21.r = z__1.r, d21.i = z__1.i;
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
z__3.r = d11.r * a[i__2].r - d11.i * a[i__2].i,
z__3.i = d11.r * a[i__2].i + d11.i * a[i__2]
.r;
i__3 = j + (k + 1) * a_dim1;
z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
.i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
d21.r * z__2.i + d21.i * z__2.r;
wk.r = z__1.r, wk.i = z__1.i;
i__2 = j + (k + 1) * a_dim1;
z__3.r = d22.r * a[i__2].r - d22.i * a[i__2].i,
z__3.i = d22.r * a[i__2].i + d22.i * a[i__2]
.r;
i__3 = j + k * a_dim1;
z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
.i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
d21.r * z__2.i + d21.i * z__2.r;
wkp1.r = z__1.r, wkp1.i = z__1.i;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__ + k * a_dim1;
z__3.r = a[i__5].r * wk.r - a[i__5].i * wk.i,
z__3.i = a[i__5].r * wk.i + a[i__5].i *
wk.r;
z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i -
z__3.i;
i__6 = i__ + (k + 1) * a_dim1;
z__4.r = a[i__6].r * wkp1.r - a[i__6].i * wkp1.i,
z__4.i = a[i__6].r * wkp1.i + a[i__6].i *
wkp1.r;
z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L50: */
}
i__2 = j + k * a_dim1;
a[i__2].r = wk.r, a[i__2].i = wk.i;
i__2 = j + (k + 1) * a_dim1;
a[i__2].r = wkp1.r, a[i__2].i = wkp1.i;
/* L60: */
}
}
}
}
/* 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 L40;
}
L70:
return;
/* End of ZSYTF2 */
} /* zsytf2_ */
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