1503 lines
36 KiB
C
1503 lines
36 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 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]/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++ */
|
|
|
|
#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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b SLAED4 used by sstedc. Finds a single root of the secular equation. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLAED4 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaed4.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaed4.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaed4.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) */
|
|
|
|
/* INTEGER I, INFO, N */
|
|
/* REAL DLAM, RHO */
|
|
/* REAL D( * ), DELTA( * ), Z( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > This subroutine computes the I-th updated eigenvalue of a symmetric */
|
|
/* > rank-one modification to a diagonal matrix whose elements are */
|
|
/* > given in the array d, and that */
|
|
/* > */
|
|
/* > D(i) < D(j) for i < j */
|
|
/* > */
|
|
/* > and that RHO > 0. This is arranged by the calling routine, and is */
|
|
/* > no loss in generality. The rank-one modified system is thus */
|
|
/* > */
|
|
/* > diag( D ) + RHO * Z * Z_transpose. */
|
|
/* > */
|
|
/* > where we assume the Euclidean norm of Z is 1. */
|
|
/* > */
|
|
/* > The method consists of approximating the rational functions in the */
|
|
/* > secular equation by simpler interpolating rational functions. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The length of all arrays. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] I */
|
|
/* > \verbatim */
|
|
/* > I is INTEGER */
|
|
/* > The index of the eigenvalue to be computed. 1 <= I <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > The original eigenvalues. It is assumed that they are in */
|
|
/* > order, D(I) < D(J) for I < J. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Z */
|
|
/* > \verbatim */
|
|
/* > Z is REAL array, dimension (N) */
|
|
/* > The components of the updating vector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DELTA */
|
|
/* > \verbatim */
|
|
/* > DELTA is REAL array, dimension (N) */
|
|
/* > If N > 2, DELTA contains (D(j) - lambda_I) in its j-th */
|
|
/* > component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 */
|
|
/* > for detail. The vector DELTA contains the information necessary */
|
|
/* > to construct the eigenvectors by SLAED3 and SLAED9. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RHO */
|
|
/* > \verbatim */
|
|
/* > RHO is REAL */
|
|
/* > The scalar in the symmetric updating formula. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DLAM */
|
|
/* > \verbatim */
|
|
/* > DLAM is REAL */
|
|
/* > The computed lambda_I, the I-th updated eigenvalue. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > > 0: if INFO = 1, the updating process failed. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */
|
|
/* > whether D(i) or D(i+1) is treated as the origin. */
|
|
/* > */
|
|
/* > ORGATI = .true. origin at i */
|
|
/* > ORGATI = .false. origin at i+1 */
|
|
/* > */
|
|
/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */
|
|
/* > if we are working with THREE poles! */
|
|
/* > */
|
|
/* > MAXIT is the maximum number of iterations allowed for each */
|
|
/* > eigenvalue. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup auxOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ren-Cang Li, Computer Science Division, University of California */
|
|
/* > at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int slaed4_(integer *n, integer *i__, real *d__, real *z__,
|
|
real *delta, real *rho, real *dlam, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
real dphi, dpsi;
|
|
integer iter;
|
|
real temp, prew, temp1, a, b, c__;
|
|
integer j;
|
|
real w, dltlb, dltub, midpt;
|
|
integer niter;
|
|
logical swtch;
|
|
extern /* Subroutine */ int slaed5_(integer *, real *, real *, real *,
|
|
real *, real *), slaed6_(integer *, logical *, real *, real *,
|
|
real *, real *, real *, integer *);
|
|
logical swtch3;
|
|
integer ii;
|
|
real dw;
|
|
extern real slamch_(char *);
|
|
real zz[3];
|
|
logical orgati;
|
|
real erretm, rhoinv;
|
|
integer ip1;
|
|
real del, eta, phi, eps, tau, psi;
|
|
integer iim1, iip1;
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Since this routine is called in an inner loop, we do no argument */
|
|
/* checking. */
|
|
|
|
/* Quick return for N=1 and 2. */
|
|
|
|
/* Parameter adjustments */
|
|
--delta;
|
|
--z__;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (*n == 1) {
|
|
|
|
/* Presumably, I=1 upon entry */
|
|
|
|
*dlam = d__[1] + *rho * z__[1] * z__[1];
|
|
delta[1] = 1.f;
|
|
return 0;
|
|
}
|
|
if (*n == 2) {
|
|
slaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam);
|
|
return 0;
|
|
}
|
|
|
|
/* Compute machine epsilon */
|
|
|
|
eps = slamch_("Epsilon");
|
|
rhoinv = 1.f / *rho;
|
|
|
|
/* The case I = N */
|
|
|
|
if (*i__ == *n) {
|
|
|
|
/* Initialize some basic variables */
|
|
|
|
ii = *n - 1;
|
|
niter = 1;
|
|
|
|
/* Calculate initial guess */
|
|
|
|
midpt = *rho / 2.f;
|
|
|
|
/* If ||Z||_2 is not one, then TEMP should be set to */
|
|
/* RHO * ||Z||_2^2 / TWO */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[*i__] - midpt;
|
|
/* L10: */
|
|
}
|
|
|
|
psi = 0.f;
|
|
i__1 = *n - 2;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
psi += z__[j] * z__[j] / delta[j];
|
|
/* L20: */
|
|
}
|
|
|
|
c__ = rhoinv + psi;
|
|
w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[*
|
|
n];
|
|
|
|
if (w <= 0.f) {
|
|
temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho)
|
|
+ z__[*n] * z__[*n] / *rho;
|
|
if (c__ <= temp) {
|
|
tau = *rho;
|
|
} else {
|
|
del = d__[*n] - d__[*n - 1];
|
|
a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]
|
|
;
|
|
b = z__[*n] * z__[*n] * del;
|
|
if (a < 0.f) {
|
|
tau = b * 2.f / (sqrt(a * a + b * 4.f * c__) - a);
|
|
} else {
|
|
tau = (a + sqrt(a * a + b * 4.f * c__)) / (c__ * 2.f);
|
|
}
|
|
}
|
|
|
|
/* It can be proved that */
|
|
/* D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO */
|
|
|
|
dltlb = midpt;
|
|
dltub = *rho;
|
|
} else {
|
|
del = d__[*n] - d__[*n - 1];
|
|
a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n];
|
|
b = z__[*n] * z__[*n] * del;
|
|
if (a < 0.f) {
|
|
tau = b * 2.f / (sqrt(a * a + b * 4.f * c__) - a);
|
|
} else {
|
|
tau = (a + sqrt(a * a + b * 4.f * c__)) / (c__ * 2.f);
|
|
}
|
|
|
|
/* It can be proved that */
|
|
/* D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 */
|
|
|
|
dltlb = 0.f;
|
|
dltub = midpt;
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[*i__] - tau;
|
|
/* L30: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L40: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
temp = z__[*n] / delta[*n];
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8.f + erretm - phi + rhoinv + abs(tau) * (
|
|
dpsi + dphi);
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
*dlam = d__[*i__] + tau;
|
|
goto L250;
|
|
}
|
|
|
|
if (w <= 0.f) {
|
|
dltlb = f2cmax(dltlb,tau);
|
|
} else {
|
|
dltub = f2cmin(dltub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
++niter;
|
|
c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi;
|
|
a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * (
|
|
dpsi + dphi);
|
|
b = delta[*n - 1] * delta[*n] * w;
|
|
if (c__ < 0.f) {
|
|
c__ = abs(c__);
|
|
}
|
|
if (c__ == 0.f) {
|
|
/* ETA = B/A */
|
|
/* ETA = RHO - TAU */
|
|
eta = dltub - tau;
|
|
} else if (a >= 0.f) {
|
|
eta = (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) / (
|
|
c__ * 2.f);
|
|
} else {
|
|
eta = b * 2.f / (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)
|
|
)));
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta > 0.f) {
|
|
eta = -w / (dpsi + dphi);
|
|
}
|
|
temp = tau + eta;
|
|
if (temp > dltub || temp < dltlb) {
|
|
if (w < 0.f) {
|
|
eta = (dltub - tau) / 2.f;
|
|
} else {
|
|
eta = (dltlb - tau) / 2.f;
|
|
}
|
|
}
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
/* L50: */
|
|
}
|
|
|
|
tau += eta;
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L60: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
temp = z__[*n] / delta[*n];
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8.f + erretm - phi + rhoinv + abs(tau) * (
|
|
dpsi + dphi);
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* Main loop to update the values of the array DELTA */
|
|
|
|
iter = niter + 1;
|
|
|
|
for (niter = iter; niter <= 30; ++niter) {
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
*dlam = d__[*i__] + tau;
|
|
goto L250;
|
|
}
|
|
|
|
if (w <= 0.f) {
|
|
dltlb = f2cmax(dltlb,tau);
|
|
} else {
|
|
dltub = f2cmin(dltub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi;
|
|
a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] *
|
|
(dpsi + dphi);
|
|
b = delta[*n - 1] * delta[*n] * w;
|
|
if (a >= 0.f) {
|
|
eta = (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) /
|
|
(c__ * 2.f);
|
|
} else {
|
|
eta = b * 2.f / (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(
|
|
r__1))));
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta > 0.f) {
|
|
eta = -w / (dpsi + dphi);
|
|
}
|
|
temp = tau + eta;
|
|
if (temp > dltub || temp < dltlb) {
|
|
if (w < 0.f) {
|
|
eta = (dltub - tau) / 2.f;
|
|
} else {
|
|
eta = (dltlb - tau) / 2.f;
|
|
}
|
|
}
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
/* L70: */
|
|
}
|
|
|
|
tau += eta;
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L80: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
temp = z__[*n] / delta[*n];
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8.f + erretm - phi + rhoinv + abs(tau) * (
|
|
dpsi + dphi);
|
|
|
|
w = rhoinv + phi + psi;
|
|
/* L90: */
|
|
}
|
|
|
|
/* Return with INFO = 1, NITER = MAXIT and not converged */
|
|
|
|
*info = 1;
|
|
*dlam = d__[*i__] + tau;
|
|
goto L250;
|
|
|
|
/* End for the case I = N */
|
|
|
|
} else {
|
|
|
|
/* The case for I < N */
|
|
|
|
niter = 1;
|
|
ip1 = *i__ + 1;
|
|
|
|
/* Calculate initial guess */
|
|
|
|
del = d__[ip1] - d__[*i__];
|
|
midpt = del / 2.f;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[*i__] - midpt;
|
|
/* L100: */
|
|
}
|
|
|
|
psi = 0.f;
|
|
i__1 = *i__ - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
psi += z__[j] * z__[j] / delta[j];
|
|
/* L110: */
|
|
}
|
|
|
|
phi = 0.f;
|
|
i__1 = *i__ + 2;
|
|
for (j = *n; j >= i__1; --j) {
|
|
phi += z__[j] * z__[j] / delta[j];
|
|
/* L120: */
|
|
}
|
|
c__ = rhoinv + psi + phi;
|
|
w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] /
|
|
delta[ip1];
|
|
|
|
if (w > 0.f) {
|
|
|
|
/* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 */
|
|
|
|
/* We choose d(i) as origin. */
|
|
|
|
orgati = TRUE_;
|
|
a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1];
|
|
b = z__[*i__] * z__[*i__] * del;
|
|
if (a > 0.f) {
|
|
tau = b * 2.f / (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(
|
|
r__1))));
|
|
} else {
|
|
tau = (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) /
|
|
(c__ * 2.f);
|
|
}
|
|
dltlb = 0.f;
|
|
dltub = midpt;
|
|
} else {
|
|
|
|
/* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) */
|
|
|
|
/* We choose d(i+1) as origin. */
|
|
|
|
orgati = FALSE_;
|
|
a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1];
|
|
b = z__[ip1] * z__[ip1] * del;
|
|
if (a < 0.f) {
|
|
tau = b * 2.f / (a - sqrt((r__1 = a * a + b * 4.f * c__, abs(
|
|
r__1))));
|
|
} else {
|
|
tau = -(a + sqrt((r__1 = a * a + b * 4.f * c__, abs(r__1)))) /
|
|
(c__ * 2.f);
|
|
}
|
|
dltlb = -midpt;
|
|
dltub = 0.f;
|
|
}
|
|
|
|
if (orgati) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[*i__] - tau;
|
|
/* L130: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[ip1] - tau;
|
|
/* L140: */
|
|
}
|
|
}
|
|
if (orgati) {
|
|
ii = *i__;
|
|
} else {
|
|
ii = *i__ + 1;
|
|
}
|
|
iim1 = ii - 1;
|
|
iip1 = ii + 1;
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L150: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.f;
|
|
phi = 0.f;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / delta[j];
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L160: */
|
|
}
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* W is the value of the secular function with */
|
|
/* its ii-th element removed. */
|
|
|
|
swtch3 = FALSE_;
|
|
if (orgati) {
|
|
if (w < 0.f) {
|
|
swtch3 = TRUE_;
|
|
}
|
|
} else {
|
|
if (w > 0.f) {
|
|
swtch3 = TRUE_;
|
|
}
|
|
}
|
|
if (ii == 1 || ii == *n) {
|
|
swtch3 = FALSE_;
|
|
}
|
|
|
|
temp = z__[ii] / delta[ii];
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w += temp;
|
|
erretm = (phi - psi) * 8.f + erretm + rhoinv * 2.f + abs(temp) * 3.f
|
|
+ abs(tau) * dw;
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
if (orgati) {
|
|
*dlam = d__[*i__] + tau;
|
|
} else {
|
|
*dlam = d__[ip1] + tau;
|
|
}
|
|
goto L250;
|
|
}
|
|
|
|
if (w <= 0.f) {
|
|
dltlb = f2cmax(dltlb,tau);
|
|
} else {
|
|
dltub = f2cmin(dltub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
++niter;
|
|
if (! swtch3) {
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
r__1 = z__[*i__] / delta[*i__];
|
|
c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (r__1 *
|
|
r__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
r__1 = z__[ip1] / delta[ip1];
|
|
c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (r__1 *
|
|
r__1);
|
|
}
|
|
a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] *
|
|
dw;
|
|
b = delta[*i__] * delta[ip1] * w;
|
|
if (c__ == 0.f) {
|
|
if (a == 0.f) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] *
|
|
(dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] *
|
|
(dpsi + dphi);
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.f) {
|
|
eta = (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) /
|
|
(c__ * 2.f);
|
|
} else {
|
|
eta = b * 2.f / (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(
|
|
r__1))));
|
|
}
|
|
} else {
|
|
|
|
/* Interpolation using THREE most relevant poles */
|
|
|
|
temp = rhoinv + psi + phi;
|
|
if (orgati) {
|
|
temp1 = z__[iim1] / delta[iim1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[
|
|
iip1]) * temp1;
|
|
zz[0] = z__[iim1] * z__[iim1];
|
|
zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi);
|
|
} else {
|
|
temp1 = z__[iip1] / delta[iip1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[
|
|
iim1]) * temp1;
|
|
zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1));
|
|
zz[2] = z__[iip1] * z__[iip1];
|
|
}
|
|
zz[1] = z__[ii] * z__[ii];
|
|
slaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info);
|
|
if (*info != 0) {
|
|
goto L250;
|
|
}
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta >= 0.f) {
|
|
eta = -w / dw;
|
|
}
|
|
temp = tau + eta;
|
|
if (temp > dltub || temp < dltlb) {
|
|
if (w < 0.f) {
|
|
eta = (dltub - tau) / 2.f;
|
|
} else {
|
|
eta = (dltlb - tau) / 2.f;
|
|
}
|
|
}
|
|
|
|
prew = w;
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
/* L180: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L190: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.f;
|
|
phi = 0.f;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / delta[j];
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L200: */
|
|
}
|
|
|
|
temp = z__[ii] / delta[ii];
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w = rhoinv + phi + psi + temp;
|
|
erretm = (phi - psi) * 8.f + erretm + rhoinv * 2.f + abs(temp) * 3.f
|
|
+ (r__1 = tau + eta, abs(r__1)) * dw;
|
|
|
|
swtch = FALSE_;
|
|
if (orgati) {
|
|
if (-w > abs(prew) / 10.f) {
|
|
swtch = TRUE_;
|
|
}
|
|
} else {
|
|
if (w > abs(prew) / 10.f) {
|
|
swtch = TRUE_;
|
|
}
|
|
}
|
|
|
|
tau += eta;
|
|
|
|
/* Main loop to update the values of the array DELTA */
|
|
|
|
iter = niter + 1;
|
|
|
|
for (niter = iter; niter <= 30; ++niter) {
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
if (orgati) {
|
|
*dlam = d__[*i__] + tau;
|
|
} else {
|
|
*dlam = d__[ip1] + tau;
|
|
}
|
|
goto L250;
|
|
}
|
|
|
|
if (w <= 0.f) {
|
|
dltlb = f2cmax(dltlb,tau);
|
|
} else {
|
|
dltub = f2cmin(dltub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
if (! swtch3) {
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
r__1 = z__[*i__] / delta[*i__];
|
|
c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (
|
|
r__1 * r__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
r__1 = z__[ip1] / delta[ip1];
|
|
c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) *
|
|
(r__1 * r__1);
|
|
}
|
|
} else {
|
|
temp = z__[ii] / delta[ii];
|
|
if (orgati) {
|
|
dpsi += temp * temp;
|
|
} else {
|
|
dphi += temp * temp;
|
|
}
|
|
c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi;
|
|
}
|
|
a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1]
|
|
* dw;
|
|
b = delta[*i__] * delta[ip1] * w;
|
|
if (c__ == 0.f) {
|
|
if (a == 0.f) {
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + delta[ip1] *
|
|
delta[ip1] * (dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + delta[*i__] * delta[
|
|
*i__] * (dpsi + dphi);
|
|
}
|
|
} else {
|
|
a = delta[*i__] * delta[*i__] * dpsi + delta[ip1]
|
|
* delta[ip1] * dphi;
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.f) {
|
|
eta = (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))
|
|
) / (c__ * 2.f);
|
|
} else {
|
|
eta = b * 2.f / (a + sqrt((r__1 = a * a - b * 4.f * c__,
|
|
abs(r__1))));
|
|
}
|
|
} else {
|
|
|
|
/* Interpolation using THREE most relevant poles */
|
|
|
|
temp = rhoinv + psi + phi;
|
|
if (swtch) {
|
|
c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi;
|
|
zz[0] = delta[iim1] * delta[iim1] * dpsi;
|
|
zz[2] = delta[iip1] * delta[iip1] * dphi;
|
|
} else {
|
|
if (orgati) {
|
|
temp1 = z__[iim1] / delta[iim1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1]
|
|
- d__[iip1]) * temp1;
|
|
zz[0] = z__[iim1] * z__[iim1];
|
|
zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 +
|
|
dphi);
|
|
} else {
|
|
temp1 = z__[iip1] / delta[iip1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1]
|
|
- d__[iim1]) * temp1;
|
|
zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi -
|
|
temp1));
|
|
zz[2] = z__[iip1] * z__[iip1];
|
|
}
|
|
}
|
|
slaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta,
|
|
info);
|
|
if (*info != 0) {
|
|
goto L250;
|
|
}
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta >= 0.f) {
|
|
eta = -w / dw;
|
|
}
|
|
temp = tau + eta;
|
|
if (temp > dltub || temp < dltlb) {
|
|
if (w < 0.f) {
|
|
eta = (dltub - tau) / 2.f;
|
|
} else {
|
|
eta = (dltlb - tau) / 2.f;
|
|
}
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
/* L210: */
|
|
}
|
|
|
|
tau += eta;
|
|
prew = w;
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.f;
|
|
psi = 0.f;
|
|
erretm = 0.f;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L220: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.f;
|
|
phi = 0.f;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / delta[j];
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L230: */
|
|
}
|
|
|
|
temp = z__[ii] / delta[ii];
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w = rhoinv + phi + psi + temp;
|
|
erretm = (phi - psi) * 8.f + erretm + rhoinv * 2.f + abs(temp) *
|
|
3.f + abs(tau) * dw;
|
|
if (w * prew > 0.f && abs(w) > abs(prew) / 10.f) {
|
|
swtch = ! swtch;
|
|
}
|
|
|
|
/* L240: */
|
|
}
|
|
|
|
/* Return with INFO = 1, NITER = MAXIT and not converged */
|
|
|
|
*info = 1;
|
|
if (orgati) {
|
|
*dlam = d__[*i__] + tau;
|
|
} else {
|
|
*dlam = d__[ip1] + tau;
|
|
}
|
|
|
|
}
|
|
|
|
L250:
|
|
|
|
return 0;
|
|
|
|
/* End of SLAED4 */
|
|
|
|
} /* slaed4_ */
|
|
|