static int /* convert columns to power series */
cols(projUV **c, projUV **d, int nu, int nv) {
projUV *sv, **dd;
int j, k;
dd = (projUV **)vector2(nu, nv, sizeof(projUV));
if (!dd)
return 0;
sv = (projUV *)vector1(nv, sizeof(projUV));
if (!sv) {
freev2((void **)dd, nu);
return 0;
}
bclear(d, nu, nv);
bclear(dd, nu, nv);
bmove(d[0], c[nu-1], nv);
for (j = nu-2; j >= 1; --j) {
for (k = nu-j; k >= 1; --k) {
bmove(sv, d[k], nv);
submop(d[k], 2., d[k-1], dd[k], nv);
bmove(dd[k], sv, nv);
}
bmove(sv, d[0], nv);
subop(d[0], c[j], dd[0], nv);
bmove(dd[0], sv, nv);
}
for (j = nu-1; j >= 1; --j)
subop(d[j], d[j-1], dd[j], nv);
submop(d[0], .5, c[0], dd[0], nv);
freev2((void **) dd, nu);
pj_dalloc(sv);
return 1;
}
static void /* convert columns to power series */
cols(UV **c, UV **d, int nu, int nv) {
UV *sv, **dd;
int j, k;
dd = (UV **)vector2(nu, nv, sizeof(UV));
sv = (UV *)vector1(nv, sizeof(UV));
bclear(d, nu, nv);
bclear(dd, nu, nv);
bmove(d[0], c[nu-1], nv);
for (j = nu-2; j >= 1; --j) {
for (k = nu-j; k >= 1; --k) {
bmove(sv, d[k], nv);
submop(d[k], 2., d[k-1], dd[k], nv);
bmove(dd[k], sv, nv);
}
bmove(sv, d[0], nv);
subop(d[0], c[j], dd[0], nv);
bmove(dd[0], sv, nv);
}
for (j = nu-1; j >= 1; --j)
subop(d[j], d[j-1], dd[j], nv);
submop(d[0], .5, c[0], dd[0], nv);
freev2(dd, nu);
pj_dalloc(sv);
}
int /* entry point */
bch2bps(projUV a, projUV b, projUV **c, int nu, int nv) {
projUV **d;
int i;
if (nu < 1 || nv < 1 || !(d = (projUV **)vector2(nu, nv, sizeof(projUV))))
return 0;
/* do rows to power series */
for (i = 0; i < nu; ++i) {
rows(c[i], d[i], nv);
rowshft(a.v, b.v, d[i], nv);
}
/* do columns to power series */
cols(d, c, nu, nv);
colshft(a.u, b.u, c, nu, nv);
freev2((void **) d, nu);
return 1;
}
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;
}
