844 lines
25 KiB
C
844 lines
25 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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c_n1 = -1;
|
|
|
|
/* > \brief <b> DSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DSYSV_RK + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsysv_r
|
|
k.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsysv_r
|
|
k.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysv_r
|
|
k.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DSYSV_RK( UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, */
|
|
/* WORK, LWORK, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, LDA, LDB, LWORK, N, NRHS */
|
|
/* INTEGER IPIV( * ) */
|
|
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), E( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > DSYSV_RK computes the solution to a real system of linear */
|
|
/* > equations A * X = B, where A is an N-by-N symmetric matrix */
|
|
/* > and X and B are N-by-NRHS matrices. */
|
|
/* > */
|
|
/* > The bounded Bunch-Kaufman (rook) diagonal pivoting method is used */
|
|
/* > to factor A as */
|
|
/* > A = P*U*D*(U**T)*(P**T), if UPLO = 'U', or */
|
|
/* > A = P*L*D*(L**T)*(P**T), if UPLO = 'L', */
|
|
/* > where U (or L) is unit upper (or lower) triangular matrix, */
|
|
/* > U**T (or L**T) is the transpose of U (or L), P is a permutation */
|
|
/* > matrix, P**T is the transpose of P, and D is symmetric and block */
|
|
/* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
|
|
/* > */
|
|
/* > DSYTRF_RK is called to compute the factorization of a real */
|
|
/* > symmetric matrix. The factored form of A is then used to solve */
|
|
/* > the system of equations A * X = B by calling BLAS3 routine DSYTRS_3. */
|
|
/* > \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 triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of linear equations, i.e., the order of the */
|
|
/* > matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of right hand sides, i.e., the number of columns */
|
|
/* > of the matrix B. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION 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, if INFO = 0, diagonal of the block diagonal */
|
|
/* > matrix D and factors U or L as computed by DSYTRF_RK: */
|
|
/* > a) ONLY diagonal elements of the symmetric block diagonal */
|
|
/* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
|
|
/* > (superdiagonal (or subdiagonal) elements of D */
|
|
/* > are stored on exit in array E), and */
|
|
/* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
|
|
/* > If UPLO = 'L': factor L in the subdiagonal part of A. */
|
|
/* > */
|
|
/* > For more info see the description of DSYTRF_RK routine. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On exit, contains the output computed by the factorization */
|
|
/* > routine DSYTRF_RK, i.e. the superdiagonal (or subdiagonal) */
|
|
/* > elements of the symmetric block diagonal matrix D */
|
|
/* > with 1-by-1 or 2-by-2 diagonal blocks, where */
|
|
/* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; */
|
|
/* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0. */
|
|
/* > */
|
|
/* > NOTE: For 1-by-1 diagonal block D(k), where */
|
|
/* > 1 <= k <= N, the element E(k) is set to 0 in both */
|
|
/* > UPLO = 'U' or UPLO = 'L' cases. */
|
|
/* > */
|
|
/* > For more info see the description of DSYTRF_RK routine. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > Details of the interchanges and the block structure of D, */
|
|
/* > as determined by DSYTRF_RK. */
|
|
/* > */
|
|
/* > For more info see the description of DSYTRF_RK routine. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
|
|
/* > On entry, the N-by-NRHS right hand side matrix B. */
|
|
/* > On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension ( MAX(1,LWORK) ). */
|
|
/* > Work array used in the factorization stage. */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The length of WORK. LWORK >= 1. For best performance */
|
|
/* > of factorization stage LWORK >= f2cmax(1,N*NB), where NB is */
|
|
/* > the optimal blocksize for DSYTRF_RK. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; */
|
|
/* > the routine only calculates the optimal size of the WORK */
|
|
/* > array for factorization stage, returns this value as */
|
|
/* > the first entry of the WORK array, and no error message */
|
|
/* > related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > */
|
|
/* > < 0: If INFO = -k, the k-th argument had an illegal value */
|
|
/* > */
|
|
/* > > 0: If INFO = k, the matrix A is singular, because: */
|
|
/* > If UPLO = 'U': column k in the upper */
|
|
/* > triangular part of A contains all zeros. */
|
|
/* > If UPLO = 'L': column k in the lower */
|
|
/* > triangular part of A contains all zeros. */
|
|
/* > */
|
|
/* > Therefore D(k,k) is exactly zero, and superdiagonal */
|
|
/* > elements of column k of U (or subdiagonal elements of */
|
|
/* > column k of L ) are all zeros. The factorization has */
|
|
/* > been completed, but the block diagonal matrix D is */
|
|
/* > exactly singular, and division by zero will occur if */
|
|
/* > it is used to solve a system of equations. */
|
|
/* > */
|
|
/* > NOTE: INFO only stores the first occurrence of */
|
|
/* > a singularity, any subsequent occurrence of singularity */
|
|
/* > is not stored in INFO even though the factorization */
|
|
/* > always completes. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleSYsolve */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > December 2016, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
|
|
/* > School of Mathematics, */
|
|
/* > University of Manchester */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dsysv_rk_(char *uplo, integer *n, integer *nrhs,
|
|
doublereal *a, integer *lda, doublereal *e, integer *ipiv, doublereal
|
|
*b, integer *ldb, doublereal *work, integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
|
|
|
|
/* Local variables */
|
|
extern /* Subroutine */ void dsytrs_3_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dsytrf_rk_(char *, integer *, doublereal *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer lwkopt;
|
|
logical lquery;
|
|
|
|
|
|
/* -- LAPACK driver 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;
|
|
--e;
|
|
--ipiv;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*nrhs < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -5;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (*lwork < 1 && ! lquery) {
|
|
*info = -11;
|
|
}
|
|
|
|
if (*info == 0) {
|
|
if (*n == 0) {
|
|
lwkopt = 1;
|
|
} else {
|
|
dsytrf_rk_(uplo, n, &a[a_offset], lda, &e[1], &ipiv[1], &work[1],
|
|
&c_n1, info);
|
|
lwkopt = (integer) work[1];
|
|
}
|
|
work[1] = (doublereal) lwkopt;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DSYSV_RK ", &i__1, (ftnlen)9);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Compute the factorization A = P*U*D*(U**T)*(P**T) or */
|
|
/* A = P*U*D*(U**T)*(P**T). */
|
|
|
|
dsytrf_rk_(uplo, n, &a[a_offset], lda, &e[1], &ipiv[1], &work[1], lwork,
|
|
info);
|
|
|
|
if (*info == 0) {
|
|
|
|
/* Solve the system A*X = B with BLAS3 solver, overwriting B with X. */
|
|
|
|
dsytrs_3_(uplo, n, nrhs, &a[a_offset], lda, &e[1], &ipiv[1], &b[
|
|
b_offset], ldb, info);
|
|
|
|
}
|
|
|
|
work[1] = (doublereal) lwkopt;
|
|
|
|
return;
|
|
|
|
/* End of DSYSV_RK */
|
|
|
|
} /* dsysv_rk__ */
|
|
|