1174 lines
31 KiB
C
1174 lines
31 KiB
C
#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;
|
|
|
|
/* > \brief \b SSPTRF */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SSPTRF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssptrf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssptrf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssptrf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SSPTRF( UPLO, N, AP, IPIV, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, N */
|
|
/* INTEGER IPIV( * ) */
|
|
/* REAL AP( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SSPTRF computes the factorization of a real symmetric matrix A stored */
|
|
/* > in packed format 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, and D is symmetric and block diagonal with */
|
|
/* > 1-by-1 and 2-by-2 diagonal blocks. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AP */
|
|
/* > \verbatim */
|
|
/* > AP is REAL array, dimension (N*(N+1)/2) */
|
|
/* > On entry, the upper or lower triangle of the symmetric matrix */
|
|
/* > A, packed columnwise in a linear array. The j-th column of A */
|
|
/* > is stored in the array AP as follows: */
|
|
/* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
|
|
/* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
|
|
/* > */
|
|
/* > On exit, the block diagonal matrix D and the multipliers used */
|
|
/* > to obtain the factor U or L, stored as a packed triangular */
|
|
/* > matrix overwriting A (see below for further details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > Details of the interchanges and the block structure of D. */
|
|
/* > 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 UPLO = 'U' and 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' and 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 = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = i, D(i,i) 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 realOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > 5-96 - Based on modifications by J. Lewis, Boeing Computer Services */
|
|
/* > Company */
|
|
/* > */
|
|
/* > 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 */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ssptrf_(char *uplo, integer *n, real *ap, integer *ipiv,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1, i__2;
|
|
real r__1, r__2, r__3;
|
|
|
|
/* Local variables */
|
|
integer imax, jmax;
|
|
extern /* Subroutine */ void sspr_(char *, integer *, real *, real *,
|
|
integer *, real *);
|
|
integer i__, j, k;
|
|
real t, alpha;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
integer kstep;
|
|
logical upper;
|
|
extern /* Subroutine */ void sswap_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
real r1, d11, d12, d21, d22;
|
|
integer kc, kk, kp;
|
|
real absakk, wk;
|
|
integer kx;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer isamax_(integer *, real *, integer *);
|
|
real colmax, rowmax;
|
|
integer knc, kpc, npp;
|
|
real 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 */
|
|
--ipiv;
|
|
--ap;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
upper = lsame_(uplo, "U");
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SSPTRF", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Initialize ALPHA for use in choosing pivot block size. */
|
|
|
|
alpha = (sqrt(17.f) + 1.f) / 8.f;
|
|
|
|
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;
|
|
kc = (*n - 1) * *n / 2 + 1;
|
|
L10:
|
|
knc = kc;
|
|
|
|
/* If K < 1, exit from loop */
|
|
|
|
if (k < 1) {
|
|
goto L110;
|
|
}
|
|
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 = ap[kc + k - 1], abs(r__1));
|
|
|
|
/* IMAX is the row-index of the largest off-diagonal element in */
|
|
/* column K, and COLMAX is its absolute value */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
imax = isamax_(&i__1, &ap[kc], &c__1);
|
|
colmax = (r__1 = ap[kc + imax - 1], abs(r__1));
|
|
} else {
|
|
colmax = 0.f;
|
|
}
|
|
|
|
if (f2cmax(absakk,colmax) == 0.f) {
|
|
|
|
/* Column K is zero: 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 {
|
|
|
|
rowmax = 0.f;
|
|
jmax = imax;
|
|
kx = imax * (imax + 1) / 2 + imax;
|
|
i__1 = k;
|
|
for (j = imax + 1; j <= i__1; ++j) {
|
|
if ((r__1 = ap[kx], abs(r__1)) > rowmax) {
|
|
rowmax = (r__1 = ap[kx], abs(r__1));
|
|
jmax = j;
|
|
}
|
|
kx += j;
|
|
/* L20: */
|
|
}
|
|
kpc = (imax - 1) * imax / 2 + 1;
|
|
if (imax > 1) {
|
|
i__1 = imax - 1;
|
|
jmax = isamax_(&i__1, &ap[kpc], &c__1);
|
|
/* Computing MAX */
|
|
r__2 = rowmax, r__3 = (r__1 = ap[kpc + jmax - 1], 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 = ap[kpc + imax - 1], abs(r__1)) >= 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 (kstep == 2) {
|
|
knc = knc - k + 1;
|
|
}
|
|
if (kp != kk) {
|
|
|
|
/* Interchange rows and columns KK and KP in the leading */
|
|
/* submatrix A(1:k,1:k) */
|
|
|
|
i__1 = kp - 1;
|
|
sswap_(&i__1, &ap[knc], &c__1, &ap[kpc], &c__1);
|
|
kx = kpc + kp - 1;
|
|
i__1 = kk - 1;
|
|
for (j = kp + 1; j <= i__1; ++j) {
|
|
kx = kx + j - 1;
|
|
t = ap[knc + j - 1];
|
|
ap[knc + j - 1] = ap[kx];
|
|
ap[kx] = t;
|
|
/* L30: */
|
|
}
|
|
t = ap[knc + kk - 1];
|
|
ap[knc + kk - 1] = ap[kpc + kp - 1];
|
|
ap[kpc + kp - 1] = t;
|
|
if (kstep == 2) {
|
|
t = ap[kc + k - 2];
|
|
ap[kc + k - 2] = ap[kc + kp - 1];
|
|
ap[kc + kp - 1] = t;
|
|
}
|
|
}
|
|
|
|
/* 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 */
|
|
|
|
r1 = 1.f / ap[kc + k - 1];
|
|
i__1 = k - 1;
|
|
r__1 = -r1;
|
|
sspr_(uplo, &i__1, &r__1, &ap[kc], &c__1, &ap[1]);
|
|
|
|
/* Store U(k) in column k */
|
|
|
|
i__1 = k - 1;
|
|
sscal_(&i__1, &r1, &ap[kc], &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) {
|
|
|
|
d12 = ap[k - 1 + (k - 1) * k / 2];
|
|
d22 = ap[k - 1 + (k - 2) * (k - 1) / 2] / d12;
|
|
d11 = ap[k + (k - 1) * k / 2] / d12;
|
|
t = 1.f / (d11 * d22 - 1.f);
|
|
d12 = t / d12;
|
|
|
|
for (j = k - 2; j >= 1; --j) {
|
|
wkm1 = d12 * (d11 * ap[j + (k - 2) * (k - 1) / 2] -
|
|
ap[j + (k - 1) * k / 2]);
|
|
wk = d12 * (d22 * ap[j + (k - 1) * k / 2] - ap[j + (k
|
|
- 2) * (k - 1) / 2]);
|
|
for (i__ = j; i__ >= 1; --i__) {
|
|
ap[i__ + (j - 1) * j / 2] = ap[i__ + (j - 1) * j /
|
|
2] - ap[i__ + (k - 1) * k / 2] * wk - ap[
|
|
i__ + (k - 2) * (k - 1) / 2] * wkm1;
|
|
/* L40: */
|
|
}
|
|
ap[j + (k - 1) * k / 2] = wk;
|
|
ap[j + (k - 2) * (k - 1) / 2] = wkm1;
|
|
/* L50: */
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
/* 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;
|
|
kc = knc - k;
|
|
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;
|
|
kc = 1;
|
|
npp = *n * (*n + 1) / 2;
|
|
L60:
|
|
knc = kc;
|
|
|
|
/* If K > N, exit from loop */
|
|
|
|
if (k > *n) {
|
|
goto L110;
|
|
}
|
|
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 = ap[kc], abs(r__1));
|
|
|
|
/* IMAX is the row-index of the largest off-diagonal element in */
|
|
/* column K, and COLMAX is its absolute value */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
imax = k + isamax_(&i__1, &ap[kc + 1], &c__1);
|
|
colmax = (r__1 = ap[kc + imax - k], abs(r__1));
|
|
} else {
|
|
colmax = 0.f;
|
|
}
|
|
|
|
if (f2cmax(absakk,colmax) == 0.f) {
|
|
|
|
/* Column K is zero: 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 */
|
|
|
|
rowmax = 0.f;
|
|
kx = kc + imax - k;
|
|
i__1 = imax - 1;
|
|
for (j = k; j <= i__1; ++j) {
|
|
if ((r__1 = ap[kx], abs(r__1)) > rowmax) {
|
|
rowmax = (r__1 = ap[kx], abs(r__1));
|
|
jmax = j;
|
|
}
|
|
kx = kx + *n - j;
|
|
/* L70: */
|
|
}
|
|
kpc = npp - (*n - imax + 1) * (*n - imax + 2) / 2 + 1;
|
|
if (imax < *n) {
|
|
i__1 = *n - imax;
|
|
jmax = imax + isamax_(&i__1, &ap[kpc + 1], &c__1);
|
|
/* Computing MAX */
|
|
r__2 = rowmax, r__3 = (r__1 = ap[kpc + jmax - imax], 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 = ap[kpc], abs(r__1)) >= 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 (kstep == 2) {
|
|
knc = knc + *n - k + 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;
|
|
sswap_(&i__1, &ap[knc + kp - kk + 1], &c__1, &ap[kpc + 1],
|
|
&c__1);
|
|
}
|
|
kx = knc + kp - kk;
|
|
i__1 = kp - 1;
|
|
for (j = kk + 1; j <= i__1; ++j) {
|
|
kx = kx + *n - j + 1;
|
|
t = ap[knc + j - kk];
|
|
ap[knc + j - kk] = ap[kx];
|
|
ap[kx] = t;
|
|
/* L80: */
|
|
}
|
|
t = ap[knc];
|
|
ap[knc] = ap[kpc];
|
|
ap[kpc] = t;
|
|
if (kstep == 2) {
|
|
t = ap[kc + 1];
|
|
ap[kc + 1] = ap[kc + kp - k];
|
|
ap[kc + kp - k] = t;
|
|
}
|
|
}
|
|
|
|
/* 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 */
|
|
|
|
r1 = 1.f / ap[kc];
|
|
i__1 = *n - k;
|
|
r__1 = -r1;
|
|
sspr_(uplo, &i__1, &r__1, &ap[kc + 1], &c__1, &ap[kc + *n
|
|
- k + 1]);
|
|
|
|
/* Store L(k) in column K */
|
|
|
|
i__1 = *n - k;
|
|
sscal_(&i__1, &r1, &ap[kc + 1], &c__1);
|
|
}
|
|
} else {
|
|
|
|
/* 2-by-2 pivot block D(k): columns K and K+1 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) {
|
|
|
|
/* 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 */
|
|
|
|
d21 = ap[k + 1 + (k - 1) * ((*n << 1) - k) / 2];
|
|
d11 = ap[k + 1 + k * ((*n << 1) - k - 1) / 2] / d21;
|
|
d22 = ap[k + (k - 1) * ((*n << 1) - k) / 2] / d21;
|
|
t = 1.f / (d11 * d22 - 1.f);
|
|
d21 = t / d21;
|
|
|
|
i__1 = *n;
|
|
for (j = k + 2; j <= i__1; ++j) {
|
|
wk = d21 * (d11 * ap[j + (k - 1) * ((*n << 1) - k) /
|
|
2] - ap[j + k * ((*n << 1) - k - 1) / 2]);
|
|
wkp1 = d21 * (d22 * ap[j + k * ((*n << 1) - k - 1) /
|
|
2] - ap[j + (k - 1) * ((*n << 1) - k) / 2]);
|
|
|
|
i__2 = *n;
|
|
for (i__ = j; i__ <= i__2; ++i__) {
|
|
ap[i__ + (j - 1) * ((*n << 1) - j) / 2] = ap[i__
|
|
+ (j - 1) * ((*n << 1) - j) / 2] - ap[i__
|
|
+ (k - 1) * ((*n << 1) - k) / 2] * wk -
|
|
ap[i__ + k * ((*n << 1) - k - 1) / 2] *
|
|
wkp1;
|
|
/* L90: */
|
|
}
|
|
|
|
ap[j + (k - 1) * ((*n << 1) - k) / 2] = wk;
|
|
ap[j + k * ((*n << 1) - k - 1) / 2] = wkp1;
|
|
|
|
/* L100: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* 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;
|
|
kc = knc + *n - k + 2;
|
|
goto L60;
|
|
|
|
}
|
|
|
|
L110:
|
|
return;
|
|
|
|
/* End of SSPTRF */
|
|
|
|
} /* ssptrf_ */
|
|
|