File: [local] / OpenXM_contrib2 / asir2000 / builtin / bfaux.c (download)
Revision 1.15, Thu Aug 31 04:21:48 2017 UTC (7 years ago) by noro
Branch: MAIN
Changes since 1.14: +123 -11
lines
todouble() now accepts structured data such as polynomial, rational function,
vector etc.
In ox_plot, coefficients of polynomials are converted to double by using todouble().
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/* $OpenXM: OpenXM_contrib2/asir2000/builtin/bfaux.c,v 1.15 2017/08/31 04:21:48 noro Exp $ */
#include "ca.h"
#include "parse.h"
void Peval(), Psetprec(), Psetbprec(), Ptodouble(), Psetround();
void Pmpfr_ai();
void Pmpfr_eint(), Pmpfr_erf(), Pmpfr_erfc(), Pmpfr_li2();
void Pmpfr_zeta();
void Pmpfr_j0(), Pmpfr_j1();
void Pmpfr_y0(), Pmpfr_y1();
void Pmpfr_gamma(), Pmpfr_lngamma(), Pmpfr_digamma();
void Pmpfr_floor(), Pmpfr_round(), Pmpfr_ceil();
void Prk_ratmat();
void mp_sin(),mp_cos(),mp_tan(),mp_asin(),mp_acos(),mp_atan();
void mp_sinh(),mp_cosh(),mp_tanh(),mp_asinh(),mp_acosh(),mp_atanh();
void mp_exp(),mp_log(),mp_pow();
struct ftab bf_tab[] = {
{"eval",Peval,-2},
{"setprec",Psetprec,-1},
{"setbprec",Psetbprec,-1},
{"setround",Psetround,-1},
{"todouble",Ptodouble,1},
{"mpfr_sin",mp_sin,-2},
{"mpfr_cos",mp_cos,-2},
{"mpfr_tan",mp_tan,-2},
{"mpfr_asin",mp_asin,-2},
{"mpfr_acos",mp_acos,-2},
{"mpfr_atan",mp_atan,-2},
{"mpfr_sinh",mp_sinh,-2},
{"mpfr_cosh",mp_cosh,-2},
{"mpfr_tanh",mp_tanh,-2},
{"mpfr_asinh",mp_asinh,-2},
{"mpfr_acosh",mp_acosh,-2},
{"mpfr_atanh",mp_atanh,-2},
{"mpfr_exp",mp_exp,-2},
{"mpfr_log",mp_log,-2},
{"mpfr_pow",mp_pow,-3},
{"mpfr_ai",Pmpfr_ai,-2},
{"mpfr_zeta",Pmpfr_zeta,-2},
{"mpfr_j0",Pmpfr_j0,-2},
{"mpfr_j1",Pmpfr_j1,-2},
{"mpfr_y0",Pmpfr_y0,-2},
{"mpfr_y1",Pmpfr_y1,-2},
{"mpfr_eint",Pmpfr_eint,-2},
{"mpfr_erf",Pmpfr_erf,-2},
{"mpfr_erfc",Pmpfr_erfc,-2},
{"mpfr_li2",Pmpfr_li2,-2},
{"mpfr_gamma",Pmpfr_gamma,-2},
{"mpfr_lngamma",Pmpfr_gamma,-2},
{"mpfr_digamma",Pmpfr_gamma,-2},
{"mpfr_floor",Pmpfr_floor,-2},
{"mpfr_ceil",Pmpfr_ceil,-2},
{"mpfr_round",Pmpfr_round,-2},
{"rk_ratmat",Prk_ratmat,7},
{0,0,0},
};
int mpfr_roundmode = MPFR_RNDN;
void todoublen(Num a,Num *rp)
{
double r,i;
Real real,imag;
if ( !a ) {
*rp = 0;
return;
}
switch ( NID(a) ) {
case N_R: case N_Q: case N_B:
r = ToReal(a);
MKReal(r,real);
*rp = (Num)real;
break;
case N_C:
r = ToReal(((C)a)->r);
i = ToReal(((C)a)->i);
MKReal(r,real);
MKReal(i,imag);
reimtocplx((Num)real,(Num)imag,rp);
break;
default:
*rp = a;
break;
}
}
void todoublep(P a,P *rp)
{
DCP dc,dcr,dcr0;
if ( !a ) *rp = 0;
else if ( OID(a) == O_N ) todoublen((Num)a,(Num *)rp);
else {
for ( dcr0 = 0, dc = DC(a); dc; dc = NEXT(dc) ) {
NEXTDC(dcr0,dcr);
DEG(dcr) = DEG(dc);
todoublep(COEF(dc),&COEF(dcr));
}
NEXT(dcr) = 0;
MKP(VR(a),dcr0,*rp);
}
}
void todoubler(R a,R *rp)
{
R b;
if ( !a ) *rp = 0;
else if ( OID(a) <= O_P ) todoublep((P)a,(P *)rp);
else {
NEWR(b);
todoublep(a->nm,&b->nm);
todoublep(a->dn,&b->dn);
*rp = b;
}
}
void todouble(Obj a,Obj *b)
{
Obj t;
LIST l;
V v;
int row,col,len;
VECT vect;
MAT mat;
int i,j;
NODE n0,n,nd;
MP m,mp,mp0;
DP d;
if ( !a ) {
*b = 0;
return;
}
switch ( OID(a) ) {
case O_N:
todoublen((Num)a,(Num *)b);
break;
case O_P:
todoublep((P)a,(P *)b);
break;
case O_R:
todoubler((R)a,(R *)b);
break;
case O_LIST:
n0 = 0;
for ( nd = BDY((LIST)a); nd; nd = NEXT(nd) ) {
NEXTNODE(n0,n);
todouble((Obj)BDY(nd),(Obj *)&BDY(n));
}
if ( n0 )
NEXT(n) = 0;
MKLIST(l,n0);
*b = (Obj)l;
break;
case O_VECT:
len = ((VECT)a)->len;
MKVECT(vect,len);
for ( i = 0; i < len; i++ ) {
todouble((Obj)BDY((VECT)a)[i],(Obj *)&BDY(vect)[i]);
}
*b = (Obj)vect;
break;
case O_MAT:
row = ((MAT)a)->row;
col = ((MAT)a)->col;
MKMAT(mat,row,col);
for ( i = 0; i < row; i++ )
for ( j = 0; j < col; j++ ) {
todouble((Obj)BDY((MAT)a)[i][j],(Obj *)&BDY(mat)[i][j]);
}
*b = (Obj)mat;
break;
case O_DP:
mp0 = 0;
for ( m = BDY((DP)a); m; m = NEXT(m) ) {
todouble(C(m),&t);
if ( t ) {
NEXTMP(mp0,mp);
C(mp) = t;
mp->dl = m->dl;
}
}
if ( mp0 ) {
MKDP(NV((DP)a),mp0,d);
d->sugar = ((DP)a)->sugar;
*b = (Obj)d;
} else
*b = 0;
break;
default:
error("todouble : invalid argument");
}
}
void Ptodouble(NODE arg,Obj *rp)
{
todouble((Obj)ARG0(arg),rp);
}
void Peval(NODE arg,Obj *rp)
{
int prec;
asir_assert(ARG0(arg),O_R,"eval");
if ( argc(arg) == 2 ) {
prec = QTOS((Q)ARG1(arg))*3.32193;
if ( prec < MPFR_PREC_MIN ) prec = MPFR_PREC_MIN;
else if ( prec > MPFR_PREC_MAX ) prec = MPFR_PREC_MAX;
} else
prec = 0;
evalr(CO,(Obj)ARG0(arg),prec,rp);
}
/* set/get decimal precision */
void Psetprec(NODE arg,Obj *rp)
{
int p;
Q q;
int prec,dprec;
prec = mpfr_get_default_prec();
/* decimal precision */
dprec = prec*0.30103;
STOQ(dprec,q); *rp = (Obj)q;
if ( arg ) {
asir_assert(ARG0(arg),O_N,"setprec");
p = QTOS((Q)ARG0(arg))*3.32193;
if ( p > 0 )
prec = p;
}
if ( prec < MPFR_PREC_MIN ) prec = MPFR_PREC_MIN;
else if ( prec > MPFR_PREC_MAX ) prec = MPFR_PREC_MAX;
mpfr_set_default_prec(prec);
}
/* set/get bit precision */
void Psetbprec(NODE arg,Obj *rp)
{
int p;
Q q;
int prec;
prec = mpfr_get_default_prec();
STOQ(prec,q); *rp = (Obj)q;
if ( arg ) {
asir_assert(ARG0(arg),O_N,"setbprec");
p = QTOS((Q)ARG0(arg));
if ( p > 0 )
prec = p;
}
if ( prec < MPFR_PREC_MIN ) prec = MPFR_PREC_MIN;
else if ( prec > MPFR_PREC_MAX ) prec = MPFR_PREC_MAX;
mpfr_set_default_prec(prec);
}
void Psetround(NODE arg,Q *rp)
{
int round;
STOQ(mpfr_roundmode,*rp);
if ( arg ) {
asir_assert(ARG0(arg),O_N,"setround");
round = QTOS((Q)ARG0(arg));
switch ( round ) {
case 0:
mpfr_roundmode = MPFR_RNDN;
break;
case 1:
mpfr_roundmode = MPFR_RNDZ;
break;
case 2:
mpfr_roundmode = MPFR_RNDU;
break;
case 3:
mpfr_roundmode = MPFR_RNDD;
break;
case 4:
mpfr_roundmode = MPFR_RNDA;
break;
case 5:
mpfr_roundmode = MPFR_RNDF;
break;
case 6:
mpfr_roundmode = MPFR_RNDNA;
break;
default:
error("setround : invalid rounding mode");
break;
}
}
}
Num tobf(Num a,int prec);
void mp_pi(NODE arg,BF *rp)
{
int prec;
BF r;
prec = arg ? QTOS((Q)ARG0(arg)) : 0;
NEWBF(r);
prec ? mpfr_init2(r->body,prec) : mpfr_init(r->body);
mpfr_const_pi(r->body,mpfr_roundmode);
if ( !cmpbf((Num)r,0) ) r = 0;
*rp = r;
}
void mp_e(NODE arg,BF *rp)
{
int prec;
mpfr_t one;
BF r;
prec = arg ? QTOS((Q)ARG0(arg)) : 0;
NEWBF(r);
prec ? mpfr_init2(r->body,prec) : mpfr_init(r->body);
mpfr_init(one);
mpfr_set_ui(one,1,mpfr_roundmode);
mpfr_exp(r->body,one,mpfr_roundmode);
if ( !cmpbf((Num)r,0) ) r = 0;
*rp = r;
}
void mpfr_or_mpc(NODE arg,int (*mpfr_f)(),int (*mpc_f)(),Num *rp)
{
Num a;
int prec;
BF r,re,im;
C c;
mpc_t mpc,a1;
prec = NEXT(arg) ? QTOS((Q)ARG1(arg)) : mpfr_get_default_prec();
a = tobf(ARG0(arg),prec);
if ( a && NID(a)==N_C ) {
mpc_init2(mpc,prec); mpc_init2(a1,prec);
re = (BF)((C)a)->r; im = (BF)((C)a)->i;
mpc_set_fr_fr(a1,re->body,im->body,mpfr_roundmode);
(*mpc_f)(mpc,a1,mpfr_roundmode);
MPFRTOBF(mpc_realref(mpc),re);
MPFRTOBF(mpc_imagref(mpc),im);
if ( !cmpbf((Num)re,0) ) re = 0;
if ( !cmpbf((Num)im,0) ) im = 0;
if ( !im )
*rp = (Num)re;
else {
NEWC(c); c->r = (Num)re; c->i = (Num)im;
*rp = (Num)c;
}
} else {
NEWBF(r);
mpfr_init2(r->body,prec);
(*mpfr_f)(r->body,((BF)a)->body,mpfr_roundmode);
if ( !cmpbf((Num)r,0) ) r = 0;
*rp = (Num)r;
}
}
void mp_sin(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_sin,mpc_sin,rp);
}
void mp_cos(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_cos,mpc_cos,rp);
}
void mp_tan(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_tan,mpc_tan,rp);
}
void mp_asin(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_asin,mpc_asin,rp);
}
void mp_acos(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_acos,mpc_acos,rp);
}
void mp_atan(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_atan,mpc_atan,rp);
}
void mp_sinh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_sinh,mpc_sinh,rp);
}
void mp_cosh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_cosh,mpc_cosh,rp);
}
void mp_tanh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_tanh,mpc_tanh,rp);
}
void mp_asinh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_asinh,mpc_asinh,rp);
}
void mp_acosh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_acosh,mpc_acosh,rp);
}
void mp_atanh(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_atanh,mpc_atanh,rp);
}
void mp_exp(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_exp,mpc_exp,rp);
}
void mp_log(NODE arg,Num *rp)
{
mpfr_or_mpc(arg,mpfr_log,mpc_log,rp);
}
void mp_pow(NODE arg,Num *rp)
{
Num a,e;
int prec;
BF r,re,im;
C c;
mpc_t mpc,a1,e1;
prec = NEXT(NEXT(arg)) ? QTOS((Q)ARG2(arg)) : mpfr_get_default_prec();
a = tobf(ARG0(arg),prec);
e = tobf(ARG1(arg),prec);
if ( NID(a) == N_C || NID(e) == N_C || MPFR_SIGN(((BF)a)->body) < 0 ) {
mpc_init2(mpc,prec); mpc_init2(a1,prec); mpc_init2(e1,prec);
if ( NID(a) == N_C ) {
re = (BF)((C)a)->r; im = (BF)((C)a)->i;
mpc_set_fr_fr(a1,re->body,im->body,mpfr_roundmode);
} else {
re = (BF)a;
mpc_set_fr(a1,re->body,mpfr_roundmode);
}
if ( NID(e) == N_C ) {
re = (BF)((C)e)->r; im = (BF)((C)e)->i;
mpc_set_fr_fr(e1,re->body,im->body,mpfr_roundmode);
} else {
re = (BF)e;
mpc_set_fr(e1,re->body,mpfr_roundmode);
}
mpc_pow(mpc,a1,e1,mpfr_roundmode);
MPFRTOBF(mpc_realref(mpc),re);
MPFRTOBF(mpc_imagref(mpc),im);
if ( !cmpbf((Num)re,0) ) re = 0;
if ( !cmpbf((Num)im,0) ) im = 0;
if ( !im )
*rp = (Num)re;
else {
NEWC(c); c->r = (Num)re; c->i = (Num)im;
*rp = (Num)c;
}
} else {
NEWBF(r);
mpfr_init2(r->body,prec);
mpfr_pow(r->body,((BF)a)->body,((BF)e)->body,mpfr_roundmode);
*rp = (Num)r;
}
}
#define SETPREC \
(prec)=NEXT(arg)?QTOS((Q)ARG1(arg)):0;\
(prec)*=3.32193;\
(a)=tobf(ARG0(arg),prec);\
NEWBF(r);\
prec ? mpfr_init2(r->body,prec) : mpfr_init(r->body);
void Pmpfr_gamma(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_gamma(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_lngamma(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_lngamma(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_digamma(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_digamma(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_zeta(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_zeta(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_eint(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_eint(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_erf(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_erf(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_erfc(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_erfc(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_j0(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_j0(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_j1(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_j1(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_y0(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_y0(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_y1(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_y1(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_li2(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_li2(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_ai(NODE arg,BF *rp)
{
Num a;
int prec;
BF r;
SETPREC
mpfr_ai(r->body,((BF)a)->body,mpfr_roundmode);
*rp = r;
}
void Pmpfr_floor(NODE arg,Q *rp)
{
Num a;
int prec;
BF r;
mpz_t t;
GZ rz;
SETPREC
mpfr_floor(r->body,((BF)a)->body);
mpz_init(t);
mpfr_get_z(t,r->body,mpfr_roundmode);
MPZTOGZ(t,rz);
*rp = gztoz(rz);
}
void Pmpfr_ceil(NODE arg,Q *rp)
{
Num a;
int prec;
BF r;
mpz_t t;
GZ rz;
SETPREC
mpfr_ceil(r->body,((BF)a)->body);
mpz_init(t);
mpfr_get_z(t,r->body,mpfr_roundmode);
MPZTOGZ(t,rz);
*rp = gztoz(rz);
}
void Pmpfr_round(NODE arg,Q *rp)
{
Num a;
int prec;
BF r;
mpz_t t;
GZ rz;
SETPREC
mpfr_round(r->body,((BF)a)->body);
mpz_init(t);
mpfr_get_z(t,r->body,mpfr_roundmode);
MPZTOGZ(t,rz);
*rp = gztoz(rz);
}
double **almat_double(int n)
{
int i;
double **a;
a = (double **)MALLOC(n*sizeof(double *));
for ( i = 0; i < n; i++ )
a[i] = (double *)MALLOC(n*sizeof(double));
return a;
}
/*
* k <- (A(xi)-(sbeta-mn2/xi))f
* A(t) = (num[0]+num[1]t+...+num[d-1]*t^(d-1))/den(t)
*/
struct jv {
int j;
double v;
};
struct smat {
int *rlen;
struct jv **row;
};
void eval_pfaffian2(double *k,int n,int d,struct smat *num,P den,double xi,double *f)
{
struct smat ma;
struct jv *maj;
int i,j,l,s;
double t,dn;
P r;
Real u;
memset(k,0,n*sizeof(double));
for ( i = d-1; i >= 0; i-- ) {
ma = num[i];
for ( j = 0; j < n; j++ ) {
maj = ma.row[j];
l = ma.rlen[j];
for ( t = 0, s = 0; s < l; s++, maj++ ) t += maj->v*f[maj->j];
k[j] = k[j]*xi+t;
}
}
MKReal(xi,u);
substp(CO,den,den->v,(P)u,&r); dn = ToReal(r);
for ( j = 0; j < n; j++ )
k[j] /= dn;
}
void Prk_ratmat(NODE arg,LIST *rp)
{
VECT mat;
P den;
int ord;
double sbeta,x0,x1,xi,h,mn2,hd;
double a2,a3,a4,a5,a6;
double b21,b31,b32,b41,b42,b43,b51,b52,b53,b54,b61,b62,b63,b64,b65;
double c1,c2,c3,c4,c5,c6,c7;
VECT fv;
int step,j,i,k,n,d,len,s;
struct smat *num;
Obj **b;
MAT mati;
double *f,*w,*k1,*k2,*k3,*k4,*k5,*k6;
NODE nd,nd1;
Real x,t;
LIST l;
ord = QTOS((Q)ARG0(arg));
mat = (VECT)ARG1(arg); den = (P)ARG2(arg);
x0 = ToReal((Num)ARG3(arg)); x1 = ToReal((Num)ARG4(arg));
step = QTOS((Q)ARG5(arg)); fv = (VECT)ARG6(arg);
h = (x1-x0)/step;
n = fv->len;
d = mat->len;
num = (struct smat *)MALLOC(d*sizeof(struct smat));
for ( i = 0; i < d; i++ ) {
num[i].rlen = (int *)MALLOC_ATOMIC(n*sizeof(int));
num[i].row = (struct jv **)MALLOC(n*sizeof(struct jv *));
mati = (MAT)mat->body[i];
b = (Obj **)mati->body;
for ( j = 0; j < n; j++ ) {
for ( len = k = 0; k < n; k++ )
if ( b[j][k] ) len++;
num[i].rlen[j] = len;
if ( !len )
num[i].row[j] = 0;
else {
num[i].row[j] = (struct jv *)MALLOC_ATOMIC((len)*sizeof(struct jv));
for ( s = k = 0; k < n; k++ )
if ( b[j][k] ) {
num[i].row[j][s].j = k;
num[i].row[j][s].v = ToReal((Num)b[j][k]);
s++;
}
}
}
}
f = (double *)MALLOC_ATOMIC(n*sizeof(double));
for ( j = 0; j < n; j++ )
f[j] = ToReal((Num)fv->body[j]);
w = (double *)MALLOC_ATOMIC(n*sizeof(double));
k1 = (double *)MALLOC_ATOMIC(n*sizeof(double));
k2 = (double *)MALLOC_ATOMIC(n*sizeof(double));
k3 = (double *)MALLOC_ATOMIC(n*sizeof(double));
k4 = (double *)MALLOC_ATOMIC(n*sizeof(double));
k5 = (double *)MALLOC_ATOMIC(n*sizeof(double));
k6 = (double *)MALLOC(n*sizeof(double));
nd = 0;
switch ( ord ) {
case 4:
a2 = 1/2.0*h; b21 = 1/2.0*h;
a3 = 1/2.0*h; b31 = 0.0; b32 = 1/2.0*h;
a4 = 1.0*h; b41 = 0.0; b42 = 0.0; b43 = 1.0*h;
c1 = 1/6.0*h; c2 = 1/3.0*h; c3 = 1/3.0*h; c4 = 1/6.0*h;
for ( i = 0; i < step; i++ ) {
if ( !(i%100000) ) fprintf(stderr,"[%d]",i);
xi = x0+i*h;
eval_pfaffian2(k1,n,d,num,den,xi,f);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b21*k1[j];
eval_pfaffian2(k2,n,d,num,den,xi+a2,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b31*k1[j]+b32*k2[j];
eval_pfaffian2(k3,n,d,num,den,xi+a3,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b41*k1[j]+b42*k2[j]+b43*k3[j];
eval_pfaffian2(k4,n,d,num,den,xi+a4,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += c1*k1[j]+c2*k2[j]+c3*k3[j]+c4*k4[j];
memcpy(f,w,n*sizeof(double));
MKReal(f[0],t);
MKReal(xi+h,x);
nd1 = mknode(2,x,t);
MKLIST(l,nd1);
MKNODE(nd1,l,nd);
nd = nd1;
for ( hd = f[0], j = 0; j < n; j++ ) f[j] /= hd;
}
MKLIST(*rp,nd);
break;
case 5:
default:
a2 = 1/4.0*h; b21 = 1/4.0*h;
a3 = 1/4.0*h; b31 = 1/8.0*h; b32 = 1/8.0*h;
a4 = 1/2.0*h; b41 = 0.0; b42 = 0.0; b43 = 1/2.0*h;
a5 = 3/4.0*h; b51 = 3/16.0*h;b52 = -3/8.0*h; b53 = 3/8.0*h; b54 = 9/16.0*h;
a6 = 1.0*h; b61 = -3/7.0*h;b62 = 8/7.0*h; b63 = 6/7.0*h; b64 = -12/7.0*h; b65 = 8/7.0*h;
c1 = 7/90.0*h; c2 = 0.0; c3 = 16/45.0*h; c4 = 2/15.0*h; c5 = 16/45.0*h; c6 = 7/90.0*h;
for ( i = 0; i < step; i++ ) {
if ( !(i%100000) ) fprintf(stderr,"[%d]",i);
xi = x0+i*h;
eval_pfaffian2(k1,n,d,num,den,xi,f);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b21*k1[j];
eval_pfaffian2(k2,n,d,num,den,xi+a2,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b31*k1[j]+b32*k2[j];
eval_pfaffian2(k3,n,d,num,den,xi+a3,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b41*k1[j]+b42*k2[j]+b43*k3[j];
eval_pfaffian2(k4,n,d,num,den,xi+a4,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b51*k1[j]+b52*k2[j]+b53*k3[j]+b54*k4[j];
eval_pfaffian2(k5,n,d,num,den,xi+a5,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += b61*k1[j]+b62*k2[j]+b63*k3[j]+b64*k4[j]+b65*k5[j];
eval_pfaffian2(k6,n,d,num,den,xi+a6,w);
memcpy(w,f,n*sizeof(double)); for ( j = 0; j < n; j++ ) w[j] += c1*k1[j]+c2*k2[j]+c3*k3[j]+c4*k4[j]+c5*k5[j]+c6*k6[j];
memcpy(f,w,n*sizeof(double));
MKReal(f[0],t);
MKReal(xi+h,x);
nd1 = mknode(2,x,t);
MKLIST(l,nd1);
MKNODE(nd1,l,nd);
nd = nd1;
for ( hd = f[0], j = 0; j < n; j++ ) f[j] /= hd;
}
MKLIST(*rp,nd);
break;
}
}