873 lines
25 KiB
C
873 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__1 = 1;
|
|
static integer c__4 = 4;
|
|
static integer c__12 = 12;
|
|
static integer c__8 = 8;
|
|
static integer c__40 = 40;
|
|
static integer c__2 = 2;
|
|
static integer c__3 = 3;
|
|
static integer c__60 = 60;
|
|
|
|
/* > \brief \b SLATM6 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, */
|
|
/* BETA, WX, WY, S, DIF ) */
|
|
|
|
/* INTEGER LDA, LDX, LDY, N, TYPE */
|
|
/* REAL ALPHA, BETA, WX, WY */
|
|
/* REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), */
|
|
/* $ X( LDX, * ), Y( LDY, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLATM6 generates test matrices for the generalized eigenvalue */
|
|
/* > problem, their corresponding right and left eigenvector matrices, */
|
|
/* > and also reciprocal condition numbers for all eigenvalues and */
|
|
/* > the reciprocal condition numbers of eigenvectors corresponding to */
|
|
/* > the 1th and 5th eigenvalues. */
|
|
/* > */
|
|
/* > Test Matrices */
|
|
/* > ============= */
|
|
/* > */
|
|
/* > Two kinds of test matrix pairs */
|
|
/* > */
|
|
/* > (A, B) = inverse(YH) * (Da, Db) * inverse(X) */
|
|
/* > */
|
|
/* > are used in the tests: */
|
|
/* > */
|
|
/* > Type 1: */
|
|
/* > Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 */
|
|
/* > 0 2+a 0 0 0 0 1 0 0 0 */
|
|
/* > 0 0 3+a 0 0 0 0 1 0 0 */
|
|
/* > 0 0 0 4+a 0 0 0 0 1 0 */
|
|
/* > 0 0 0 0 5+a , 0 0 0 0 1 , and */
|
|
/* > */
|
|
/* > Type 2: */
|
|
/* > Da = 1 -1 0 0 0 Db = 1 0 0 0 0 */
|
|
/* > 1 1 0 0 0 0 1 0 0 0 */
|
|
/* > 0 0 1 0 0 0 0 1 0 0 */
|
|
/* > 0 0 0 1+a 1+b 0 0 0 1 0 */
|
|
/* > 0 0 0 -1-b 1+a , 0 0 0 0 1 . */
|
|
/* > */
|
|
/* > In both cases the same inverse(YH) and inverse(X) are used to compute */
|
|
/* > (A, B), giving the exact eigenvectors to (A,B) as (YH, X): */
|
|
/* > */
|
|
/* > YH: = 1 0 -y y -y X = 1 0 -x -x x */
|
|
/* > 0 1 -y y -y 0 1 x -x -x */
|
|
/* > 0 0 1 0 0 0 0 1 0 0 */
|
|
/* > 0 0 0 1 0 0 0 0 1 0 */
|
|
/* > 0 0 0 0 1, 0 0 0 0 1 , */
|
|
/* > */
|
|
/* > where a, b, x and y will have all values independently of each other. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] TYPE */
|
|
/* > \verbatim */
|
|
/* > TYPE is INTEGER */
|
|
/* > Specifies the problem type (see further details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > Size of the matrices A and B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA, N). */
|
|
/* > On exit A N-by-N is initialized according to TYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of A and of B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDA, N). */
|
|
/* > On exit B N-by-N is initialized according to TYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] X */
|
|
/* > \verbatim */
|
|
/* > X is REAL array, dimension (LDX, N). */
|
|
/* > On exit X is the N-by-N matrix of right eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX */
|
|
/* > \verbatim */
|
|
/* > LDX is INTEGER */
|
|
/* > The leading dimension of X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Y */
|
|
/* > \verbatim */
|
|
/* > Y is REAL array, dimension (LDY, N). */
|
|
/* > On exit Y is the N-by-N matrix of left eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDY */
|
|
/* > \verbatim */
|
|
/* > LDY is INTEGER */
|
|
/* > The leading dimension of Y. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is REAL */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is REAL */
|
|
/* > */
|
|
/* > Weighting constants for matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WX */
|
|
/* > \verbatim */
|
|
/* > WX is REAL */
|
|
/* > Constant for right eigenvector matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WY */
|
|
/* > \verbatim */
|
|
/* > WY is REAL */
|
|
/* > Constant for left eigenvector matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension (N) */
|
|
/* > S(i) is the reciprocal condition number for eigenvalue i. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIF */
|
|
/* > \verbatim */
|
|
/* > DIF is REAL array, dimension (N) */
|
|
/* > DIF(i) is the reciprocal condition number for eigenvector i. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup real_matgen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int slatm6_(integer *type__, integer *n, real *a, integer *
|
|
lda, real *b, real *x, integer *ldx, real *y, integer *ldy, real *
|
|
alpha, real *beta, real *wx, real *wy, real *s, real *dif)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, y_dim1,
|
|
y_offset, i__1, i__2;
|
|
|
|
/* Local variables */
|
|
integer info;
|
|
real work[100];
|
|
integer i__, j;
|
|
real z__[144] /* was [12][12] */;
|
|
extern /* Subroutine */ int slakf2_(integer *, integer *, real *, integer
|
|
*, real *, real *, real *, real *, integer *), sgesvd_(char *,
|
|
char *, integer *, integer *, real *, integer *, real *, real *,
|
|
integer *, real *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *,
|
|
integer *, real *, integer *);
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Generate test problem ... */
|
|
/* (Da, Db) ... */
|
|
|
|
/* Parameter adjustments */
|
|
b_dim1 = *lda;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
x_dim1 = *ldx;
|
|
x_offset = 1 + x_dim1 * 1;
|
|
x -= x_offset;
|
|
y_dim1 = *ldy;
|
|
y_offset = 1 + y_dim1 * 1;
|
|
y -= y_offset;
|
|
--s;
|
|
--dif;
|
|
|
|
/* Function Body */
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
|
|
if (i__ == j) {
|
|
a[i__ + i__ * a_dim1] = (real) i__ + *alpha;
|
|
b[i__ + i__ * b_dim1] = 1.f;
|
|
} else {
|
|
a[i__ + j * a_dim1] = 0.f;
|
|
b[i__ + j * b_dim1] = 0.f;
|
|
}
|
|
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* Form X and Y */
|
|
|
|
slacpy_("F", n, n, &b[b_offset], lda, &y[y_offset], ldy);
|
|
y[y_dim1 + 3] = -(*wy);
|
|
y[y_dim1 + 4] = *wy;
|
|
y[y_dim1 + 5] = -(*wy);
|
|
y[(y_dim1 << 1) + 3] = -(*wy);
|
|
y[(y_dim1 << 1) + 4] = *wy;
|
|
y[(y_dim1 << 1) + 5] = -(*wy);
|
|
|
|
slacpy_("F", n, n, &b[b_offset], lda, &x[x_offset], ldx);
|
|
x[x_dim1 * 3 + 1] = -(*wx);
|
|
x[(x_dim1 << 2) + 1] = -(*wx);
|
|
x[x_dim1 * 5 + 1] = *wx;
|
|
x[x_dim1 * 3 + 2] = *wx;
|
|
x[(x_dim1 << 2) + 2] = -(*wx);
|
|
x[x_dim1 * 5 + 2] = -(*wx);
|
|
|
|
/* Form (A, B) */
|
|
|
|
b[b_dim1 * 3 + 1] = *wx + *wy;
|
|
b[b_dim1 * 3 + 2] = -(*wx) + *wy;
|
|
b[(b_dim1 << 2) + 1] = *wx - *wy;
|
|
b[(b_dim1 << 2) + 2] = *wx - *wy;
|
|
b[b_dim1 * 5 + 1] = -(*wx) + *wy;
|
|
b[b_dim1 * 5 + 2] = *wx + *wy;
|
|
if (*type__ == 1) {
|
|
a[a_dim1 * 3 + 1] = *wx * a[a_dim1 + 1] + *wy * a[a_dim1 * 3 + 3];
|
|
a[a_dim1 * 3 + 2] = -(*wx) * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 *
|
|
3 + 3];
|
|
a[(a_dim1 << 2) + 1] = *wx * a[a_dim1 + 1] - *wy * a[(a_dim1 << 2) +
|
|
4];
|
|
a[(a_dim1 << 2) + 2] = *wx * a[(a_dim1 << 1) + 2] - *wy * a[(a_dim1 <<
|
|
2) + 4];
|
|
a[a_dim1 * 5 + 1] = -(*wx) * a[a_dim1 + 1] + *wy * a[a_dim1 * 5 + 5];
|
|
a[a_dim1 * 5 + 2] = *wx * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 * 5 +
|
|
5];
|
|
} else if (*type__ == 2) {
|
|
a[a_dim1 * 3 + 1] = *wx * 2.f + *wy;
|
|
a[a_dim1 * 3 + 2] = *wy;
|
|
a[(a_dim1 << 2) + 1] = -(*wy) * (*alpha + 2.f + *beta);
|
|
a[(a_dim1 << 2) + 2] = *wx * 2.f - *wy * (*alpha + 2.f + *beta);
|
|
a[a_dim1 * 5 + 1] = *wx * -2.f + *wy * (*alpha - *beta);
|
|
a[a_dim1 * 5 + 2] = *wy * (*alpha - *beta);
|
|
a[a_dim1 + 1] = 1.f;
|
|
a[(a_dim1 << 1) + 1] = -1.f;
|
|
a[a_dim1 + 2] = 1.f;
|
|
a[(a_dim1 << 1) + 2] = a[a_dim1 + 1];
|
|
a[a_dim1 * 3 + 3] = 1.f;
|
|
a[(a_dim1 << 2) + 4] = *alpha + 1.f;
|
|
a[a_dim1 * 5 + 4] = *beta + 1.f;
|
|
a[(a_dim1 << 2) + 5] = -a[a_dim1 * 5 + 4];
|
|
a[a_dim1 * 5 + 5] = a[(a_dim1 << 2) + 4];
|
|
}
|
|
|
|
/* Compute condition numbers */
|
|
|
|
if (*type__ == 1) {
|
|
|
|
s[1] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[a_dim1 + 1] * a[a_dim1
|
|
+ 1] + 1.f));
|
|
s[2] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[(a_dim1 << 1) + 2] * a[
|
|
(a_dim1 << 1) + 2] + 1.f));
|
|
s[3] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 3 + 3] * a[
|
|
a_dim1 * 3 + 3] + 1.f));
|
|
s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[(a_dim1 << 2) + 4] * a[
|
|
(a_dim1 << 2) + 4] + 1.f));
|
|
s[5] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 5 + 5] * a[
|
|
a_dim1 * 5 + 5] + 1.f));
|
|
|
|
slakf2_(&c__1, &c__4, &a[a_offset], lda, &a[(a_dim1 << 1) + 2], &b[
|
|
b_offset], &b[(b_dim1 << 1) + 2], z__, &c__12);
|
|
sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, &
|
|
work[9], &c__1, &work[10], &c__40, &info);
|
|
dif[1] = work[7];
|
|
|
|
slakf2_(&c__4, &c__1, &a[a_offset], lda, &a[a_dim1 * 5 + 5], &b[
|
|
b_offset], &b[b_dim1 * 5 + 5], z__, &c__12);
|
|
sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, &
|
|
work[9], &c__1, &work[10], &c__40, &info);
|
|
dif[5] = work[7];
|
|
|
|
} else if (*type__ == 2) {
|
|
|
|
s[1] = 1.f / sqrt(*wy * *wy + .33333333333333331f);
|
|
s[2] = s[1];
|
|
s[3] = 1.f / sqrt(*wx * *wx + .5f);
|
|
s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / ((*alpha + 1.f) * (*alpha
|
|
+ 1.f) + 1.f + (*beta + 1.f) * (*beta + 1.f)));
|
|
s[5] = s[4];
|
|
|
|
slakf2_(&c__2, &c__3, &a[a_offset], lda, &a[a_dim1 * 3 + 3], &b[
|
|
b_offset], &b[b_dim1 * 3 + 3], z__, &c__12);
|
|
sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1,
|
|
&work[13], &c__1, &work[14], &c__60, &info);
|
|
dif[1] = work[11];
|
|
|
|
slakf2_(&c__3, &c__2, &a[a_offset], lda, &a[(a_dim1 << 2) + 4], &b[
|
|
b_offset], &b[(b_dim1 << 2) + 4], z__, &c__12);
|
|
sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1,
|
|
&work[13], &c__1, &work[14], &c__60, &info);
|
|
dif[5] = work[11];
|
|
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of SLATM6 */
|
|
|
|
} /* slatm6_ */
|
|
|