mk_cheby.c
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#ifndef lint
static const char SCCSID[]="@(#)mk_cheby.c 4.5 94/03/22 GIE REL";
#endif
#include "projects.h"
static void /* sum coefficients less than res */
eval(projUV **w, int nu, int nv, double res, projUV *resid) {
int i, j;
double ab;
projUV *s;
resid->u = resid->v = 0.;
for (i = 0; i < nu; ++i)
for (s = w[i], j = 0; j < nv; ++j, ++s) {
if ((ab = fabs(s->u)) < res)
resid->u += ab;
if ((ab = fabs(s->v)) < res)
resid->v += ab;
}
}
static Tseries * /* create power series structure */
makeT(int nru, int nrv) {
Tseries *Ts;
int i;
if ((Ts = (Tseries *)pj_malloc(sizeof(Tseries))) &&
(Ts->cu = (struct PW_COEF *)pj_malloc(
sizeof(struct PW_COEF) * nru)) &&
(Ts->cv = (struct PW_COEF *)pj_malloc(
sizeof(struct PW_COEF) * nrv))) {
for (i = 0; i < nru; ++i)
Ts->cu[i].c = 0;
for (i = 0; i < nrv; ++i)
Ts->cv[i].c = 0;
return Ts;
} else
return 0;
}
Tseries *
mk_cheby(projUV a, projUV b, double res, projUV *resid, projUV (*func)(projUV),
int nu, int nv, int power) {
int j, i, nru, nrv, *ncu, *ncv;
Tseries *Ts = 0;
projUV **w;
double cutres;
if (!(w = (projUV **)vector2(nu, nv, sizeof(projUV))) ||
!(ncu = (int *)vector1(nu + nv, sizeof(int))))
return 0;
ncv = ncu + nu;
if (!bchgen(a, b, nu, nv, w, func)) {
projUV *s;
double *p;
/* analyse coefficients and adjust until residual OK */
cutres = res;
for (i = 4; i ; --i) {
eval(w, nu, nv, cutres, resid);
if (resid->u < res && resid->v < res)
break;
cutres *= 0.5;
}
if (i <= 0) /* warn of too many tries */
resid->u = - resid->u;
/* apply cut resolution and set pointers */
nru = nrv = 0;
for (j = 0; j < nu; ++j) {
ncu[j] = ncv[j] = 0; /* clear column maxes */
for (s = w[j], i = 0; i < nv; ++i, ++s) {
if (fabs(s->u) < cutres) /* < resolution ? */
s->u = 0.; /* clear coefficient */
else
ncu[j] = i + 1; /* update column max */
if (fabs(s->v) < cutres) /* same for v coef's */
s->v = 0.;
else
ncv[j] = i + 1;
}
if (ncu[j]) nru = j + 1; /* update row max */
if (ncv[j]) nrv = j + 1;
}
if (power) { /* convert to bivariate power series */
if (!bch2bps(a, b, w, nu, nv))
goto error;
/* possible change in some row counts, so readjust */
nru = nrv = 0;
for (j = 0; j < nu; ++j) {
ncu[j] = ncv[j] = 0; /* clear column maxes */
for (s = w[j], i = 0; i < nv; ++i, ++s) {
if (s->u)
ncu[j] = i + 1; /* update column max */
if (s->v)
ncv[j] = i + 1;
}
if (ncu[j]) nru = j + 1; /* update row max */
if (ncv[j]) nrv = j + 1;
}
Ts = makeT(nru, nrv);
if (Ts) {
Ts->a = a;
Ts->b = b;
Ts->mu = nru - 1;
Ts->mv = nrv - 1;
Ts->power = 1;
for (i = 0; i < nru; ++i) /* store coefficient rows for u */
Ts->cu[i].m = ncu[i];
if (Ts->cu[i].m)
if ((p = Ts->cu[i].c =
(double *)pj_malloc(sizeof(double) * ncu[i])))
for (j = 0; j < ncu[i]; ++j)
*p++ = (w[i] + j)->u;
else
goto error;
for (i = 0; i < nrv; ++i) /* same for v */
Ts->cv[i].m = ncv[i];
if (Ts->cv[i].m)
if ((p = Ts->cv[i].c =
(double *)pj_malloc(sizeof(double) * ncv[i])))
for (j = 0; j < ncv[i]; ++j)
*p++ = (w[i] + j)->v;
else
goto error;
}
} else if ((Ts = makeT(nru, nrv))) {
/* else make returned Chebyshev coefficient structure */
Ts->mu = nru - 1; /* save row degree */
Ts->mv = nrv - 1;
Ts->a.u = a.u + b.u; /* set argument scaling */
Ts->a.v = a.v + b.v;
Ts->b.u = 1. / (b.u - a.u);
Ts->b.v = 1. / (b.v - a.v);
Ts->power = 0;
for (i = 0; i < nru; ++i) /* store coefficient rows for u */
Ts->cu[i].m = ncu[i];
if (Ts->cu[i].m)
if ((p = Ts->cu[i].c =
(double *)pj_malloc(sizeof(double) * ncu[i])))
for (j = 0; j < ncu[i]; ++j)
*p++ = (w[i] + j)->u;
else
goto error;
for (i = 0; i < nrv; ++i) /* same for v */
Ts->cv[i].m = ncv[i];
if (Ts->cv[i].m)
if ((p = Ts->cv[i].c =
(double *)pj_malloc(sizeof(double) * ncv[i])))
for (j = 0; j < ncv[i]; ++j)
*p++ = (w[i] + j)->v;
else
goto error;
} else
goto error;
}
goto gohome;
error:
if (Ts) { /* pj_dalloc up possible allocations */
for (i = 0; i <= Ts->mu; ++i)
if (Ts->cu[i].c)
pj_dalloc(Ts->cu[i].c);
for (i = 0; i <= Ts->mv; ++i)
if (Ts->cv[i].c)
pj_dalloc(Ts->cv[i].c);
pj_dalloc(Ts);
}
Ts = 0;
gohome:
freev2((void **) w, nu);
pj_dalloc(ncu);
return Ts;
}