913 lines
26 KiB
C
913 lines
26 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 complex c_b1 = {1.f,0.f};
|
|
static complex c_b2 = {0.f,0.f};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b CGGHRD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGGHRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgghrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgghrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgghrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, */
|
|
/* LDQ, Z, LDZ, INFO ) */
|
|
|
|
/* CHARACTER COMPQ, COMPZ */
|
|
/* INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N */
|
|
/* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
|
|
/* $ Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGGHRD reduces a pair of complex matrices (A,B) to generalized upper */
|
|
/* > Hessenberg form using unitary transformations, where A is a */
|
|
/* > general matrix and B is upper triangular. The form of the generalized */
|
|
/* > eigenvalue problem is */
|
|
/* > A*x = lambda*B*x, */
|
|
/* > and B is typically made upper triangular by computing its QR */
|
|
/* > factorization and moving the unitary matrix Q to the left side */
|
|
/* > of the equation. */
|
|
/* > */
|
|
/* > This subroutine simultaneously reduces A to a Hessenberg matrix H: */
|
|
/* > Q**H*A*Z = H */
|
|
/* > and transforms B to another upper triangular matrix T: */
|
|
/* > Q**H*B*Z = T */
|
|
/* > in order to reduce the problem to its standard form */
|
|
/* > H*y = lambda*T*y */
|
|
/* > where y = Z**H*x. */
|
|
/* > */
|
|
/* > The unitary matrices Q and Z are determined as products of Givens */
|
|
/* > rotations. They may either be formed explicitly, or they may be */
|
|
/* > postmultiplied into input matrices Q1 and Z1, so that */
|
|
/* > Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H */
|
|
/* > Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H */
|
|
/* > If Q1 is the unitary matrix from the QR factorization of B in the */
|
|
/* > original equation A*x = lambda*B*x, then CGGHRD reduces the original */
|
|
/* > problem to generalized Hessenberg form. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] COMPQ */
|
|
/* > \verbatim */
|
|
/* > COMPQ is CHARACTER*1 */
|
|
/* > = 'N': do not compute Q; */
|
|
/* > = 'I': Q is initialized to the unit matrix, and the */
|
|
/* > unitary matrix Q is returned; */
|
|
/* > = 'V': Q must contain a unitary matrix Q1 on entry, */
|
|
/* > and the product Q1*Q is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPZ */
|
|
/* > \verbatim */
|
|
/* > COMPZ is CHARACTER*1 */
|
|
/* > = 'N': do not compute Z; */
|
|
/* > = 'I': Z is initialized to the unit matrix, and the */
|
|
/* > unitary matrix Z is returned; */
|
|
/* > = 'V': Z must contain a unitary matrix Z1 on entry, */
|
|
/* > and the product Z1*Z is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > */
|
|
/* > ILO and IHI mark the rows and columns of A which are to be */
|
|
/* > reduced. It is assumed that A is already upper triangular */
|
|
/* > in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are */
|
|
/* > normally set by a previous call to CGGBAL; otherwise they */
|
|
/* > should be set to 1 and N respectively. */
|
|
/* > 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA, N) */
|
|
/* > On entry, the N-by-N general matrix to be reduced. */
|
|
/* > On exit, the upper triangle and the first subdiagonal of A */
|
|
/* > are overwritten with the upper Hessenberg matrix H, and the */
|
|
/* > rest is set to zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX array, dimension (LDB, N) */
|
|
/* > On entry, the N-by-N upper triangular matrix B. */
|
|
/* > On exit, the upper triangular matrix T = Q**H B Z. The */
|
|
/* > elements below the diagonal are set to zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX array, dimension (LDQ, N) */
|
|
/* > On entry, if COMPQ = 'V', the unitary matrix Q1, typically */
|
|
/* > from the QR factorization of B. */
|
|
/* > On exit, if COMPQ='I', the unitary matrix Q, and if */
|
|
/* > COMPQ = 'V', the product Q1*Q. */
|
|
/* > Not referenced if COMPQ='N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. */
|
|
/* > LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX array, dimension (LDZ, N) */
|
|
/* > On entry, if COMPZ = 'V', the unitary matrix Z1. */
|
|
/* > On exit, if COMPZ='I', the unitary matrix Z, and if */
|
|
/* > COMPZ = 'V', the product Z1*Z. */
|
|
/* > Not referenced if COMPZ='N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. */
|
|
/* > LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > This routine reduces A to Hessenberg and B to triangular form by */
|
|
/* > an unblocked reduction, as described in _Matrix_Computations_, */
|
|
/* > by Golub and van Loan (Johns Hopkins Press). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cgghrd_(char *compq, char *compz, integer *n, integer *
|
|
ilo, integer *ihi, complex *a, integer *lda, complex *b, integer *ldb,
|
|
complex *q, integer *ldq, complex *z__, integer *ldz, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
|
|
z_offset, i__1, i__2, i__3;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
integer jcol;
|
|
extern /* Subroutine */ void crot_(integer *, complex *, integer *,
|
|
complex *, integer *, real *, complex *);
|
|
integer jrow;
|
|
real c__;
|
|
complex s;
|
|
extern logical lsame_(char *, char *);
|
|
complex ctemp;
|
|
extern /* Subroutine */ void claset_(char *, integer *, integer *, complex
|
|
*, complex *, complex *, integer *), clartg_(complex *,
|
|
complex *, real *, complex *, complex *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer icompq, icompz;
|
|
logical ilq, ilz;
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode COMPQ */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
|
|
/* Function Body */
|
|
if (lsame_(compq, "N")) {
|
|
ilq = FALSE_;
|
|
icompq = 1;
|
|
} else if (lsame_(compq, "V")) {
|
|
ilq = TRUE_;
|
|
icompq = 2;
|
|
} else if (lsame_(compq, "I")) {
|
|
ilq = TRUE_;
|
|
icompq = 3;
|
|
} else {
|
|
icompq = 0;
|
|
}
|
|
|
|
/* Decode COMPZ */
|
|
|
|
if (lsame_(compz, "N")) {
|
|
ilz = FALSE_;
|
|
icompz = 1;
|
|
} else if (lsame_(compz, "V")) {
|
|
ilz = TRUE_;
|
|
icompz = 2;
|
|
} else if (lsame_(compz, "I")) {
|
|
ilz = TRUE_;
|
|
icompz = 3;
|
|
} else {
|
|
icompz = 0;
|
|
}
|
|
|
|
/* Test the input parameters. */
|
|
|
|
*info = 0;
|
|
if (icompq <= 0) {
|
|
*info = -1;
|
|
} else if (icompz <= 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ilo < 1) {
|
|
*info = -4;
|
|
} else if (*ihi > *n || *ihi < *ilo - 1) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (ilq && *ldq < *n || *ldq < 1) {
|
|
*info = -11;
|
|
} else if (ilz && *ldz < *n || *ldz < 1) {
|
|
*info = -13;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CGGHRD", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q and Z if desired. */
|
|
|
|
if (icompq == 3) {
|
|
claset_("Full", n, n, &c_b2, &c_b1, &q[q_offset], ldq);
|
|
}
|
|
if (icompz == 3) {
|
|
claset_("Full", n, n, &c_b2, &c_b1, &z__[z_offset], ldz);
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 1) {
|
|
return;
|
|
}
|
|
|
|
/* Zero out lower triangle of B */
|
|
|
|
i__1 = *n - 1;
|
|
for (jcol = 1; jcol <= i__1; ++jcol) {
|
|
i__2 = *n;
|
|
for (jrow = jcol + 1; jrow <= i__2; ++jrow) {
|
|
i__3 = jrow + jcol * b_dim1;
|
|
b[i__3].r = 0.f, b[i__3].i = 0.f;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* Reduce A and B */
|
|
|
|
i__1 = *ihi - 2;
|
|
for (jcol = *ilo; jcol <= i__1; ++jcol) {
|
|
|
|
i__2 = jcol + 2;
|
|
for (jrow = *ihi; jrow >= i__2; --jrow) {
|
|
|
|
/* Step 1: rotate rows JROW-1, JROW to kill A(JROW,JCOL) */
|
|
|
|
i__3 = jrow - 1 + jcol * a_dim1;
|
|
ctemp.r = a[i__3].r, ctemp.i = a[i__3].i;
|
|
clartg_(&ctemp, &a[jrow + jcol * a_dim1], &c__, &s, &a[jrow - 1 +
|
|
jcol * a_dim1]);
|
|
i__3 = jrow + jcol * a_dim1;
|
|
a[i__3].r = 0.f, a[i__3].i = 0.f;
|
|
i__3 = *n - jcol;
|
|
crot_(&i__3, &a[jrow - 1 + (jcol + 1) * a_dim1], lda, &a[jrow + (
|
|
jcol + 1) * a_dim1], lda, &c__, &s);
|
|
i__3 = *n + 2 - jrow;
|
|
crot_(&i__3, &b[jrow - 1 + (jrow - 1) * b_dim1], ldb, &b[jrow + (
|
|
jrow - 1) * b_dim1], ldb, &c__, &s);
|
|
if (ilq) {
|
|
r_cnjg(&q__1, &s);
|
|
crot_(n, &q[(jrow - 1) * q_dim1 + 1], &c__1, &q[jrow * q_dim1
|
|
+ 1], &c__1, &c__, &q__1);
|
|
}
|
|
|
|
/* Step 2: rotate columns JROW, JROW-1 to kill B(JROW,JROW-1) */
|
|
|
|
i__3 = jrow + jrow * b_dim1;
|
|
ctemp.r = b[i__3].r, ctemp.i = b[i__3].i;
|
|
clartg_(&ctemp, &b[jrow + (jrow - 1) * b_dim1], &c__, &s, &b[jrow
|
|
+ jrow * b_dim1]);
|
|
i__3 = jrow + (jrow - 1) * b_dim1;
|
|
b[i__3].r = 0.f, b[i__3].i = 0.f;
|
|
crot_(ihi, &a[jrow * a_dim1 + 1], &c__1, &a[(jrow - 1) * a_dim1 +
|
|
1], &c__1, &c__, &s);
|
|
i__3 = jrow - 1;
|
|
crot_(&i__3, &b[jrow * b_dim1 + 1], &c__1, &b[(jrow - 1) * b_dim1
|
|
+ 1], &c__1, &c__, &s);
|
|
if (ilz) {
|
|
crot_(n, &z__[jrow * z_dim1 + 1], &c__1, &z__[(jrow - 1) *
|
|
z_dim1 + 1], &c__1, &c__, &s);
|
|
}
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CGGHRD */
|
|
|
|
} /* cgghrd_ */
|
|
|