// bivariate power polynomial entry point
public static projUV bpseval(projUV @in, Tseries T)
{
projUV @out;
@[email protected]=0.0;
for(int i=T.mu; i>=0; --i)
{
double row=0.0;
int m=T.cu[i].m;
if(m!=0)
{
int c=m;
while((m--)!=0) row=T.cu[i].c[--c][email protected]*row;
}
@[email protected]*@out.u;
}
for(int i=T.mv; i>=0; --i)
{
double row=0.0;
int m=T.cv[i].m;
if(m!=0)
{
int c=m;
while((m--)!=0) row=T.cv[i].c[--c][email protected]*row;
}
@[email protected]*@out.v;
}
return @out;
}
// general entry point selecting evaluation mode
public static projUV biveval(projUV @in, Tseries T)
{
if (T.power != 0)
{
return(bpseval(@in, T));
}
return(bcheval(@in, T));
}
public static void p_series(Tseries T, TextWriter file, string fmt)
{
const int CUT = 60; // check length of line
string format = " {0:" + fmt + "}%n";
file.WriteLine("u: {0}", T.mu + 1);
for (int i = 0; i <= T.mu; i++)
{
if (T.cu[i].m != 0)
{
string tmp = string.Format("{0} {1}", i, T.cu[i].m);
file.Write(tmp);
int L = tmp.Length;
int n = 0;
for (int j = 0; j < T.cu[i].m; j++)
{
L += n;
if (L > CUT)
{
file.Write("\n ");
L = 1;
}
tmp = string.Format(format, T.cu[i].c[j]);
file.Write(tmp);
n = tmp.Length;
}
file.WriteLine();
}
}
file.WriteLine("v: {0}", T.mv + 1);
for (int i = 0; i <= T.mv; i++)
{
if (T.cv[i].m != 0)
{
string tmp = string.Format("{0} {1}", i, T.cv[i].m);
file.Write(tmp);
int L = tmp.Length;
int n = 0;
for (int j = 0; j < T.cv[i].m; j++)
{
L += n;
if (L > CUT)
{
file.Write("\n ");
L = 1;
}
tmp = string.Format(format, T.cv[i].c[j]);
file.Write(tmp);
n = tmp.Length;
}
file.WriteLine();
}
}
}
public static void p_series(Tseries T, TextWriter file, string fmt)
{
const int CUT=60; // check length of line
string format=" {0:"+fmt+"}%n";
file.WriteLine("u: {0}", T.mu+1);
for(int i=0; i<=T.mu; i++)
{
if(T.cu[i].m!=0)
{
string tmp=string.Format("{0} {1}", i, T.cu[i].m);
file.Write(tmp);
int L=tmp.Length;
int n=0;
for(int j=0; j<T.cu[i].m; j++)
{
L+=n;
if(L>CUT)
{
file.Write("\n ");
L=1;
}
tmp=string.Format(format, T.cu[i].c[j]);
file.Write(tmp);
n=tmp.Length;
}
file.WriteLine();
}
}
file.WriteLine("v: {0}", T.mv+1);
for(int i=0; i<=T.mv; i++)
{
if(T.cv[i].m!=0)
{
string tmp=string.Format("{0} {1}", i, T.cv[i].m);
file.Write(tmp);
int L=tmp.Length;
int n=0;
for(int j=0; j<T.cv[i].m; j++)
{
L+=n;
if(L>CUT)
{
file.Write("\n ");
L=1;
}
tmp=string.Format(format, T.cv[i].c[j]);
file.Write(tmp);
n=tmp.Length;
}
file.WriteLine();
}
}
}
// create power series structure
static Tseries makeT(int nru, int nrv)
{
try
{
Tseries T = new Tseries();
T.cu = new PW_COEF[nru];
T.cv = new PW_COEF[nrv];
for (int i = 0; i < nru; i++)
{
T.cu[i].c = null;
}
for (int i = 0; i < nrv; i++)
{
T.cv[i].c = null;
}
return(T);
}
catch
{
return(null);
}
}
// bivariate power polynomial entry point
public static projUV bpseval(projUV @in, Tseries T)
{
projUV @out;
@out.u = @out.v = 0.0;
for (int i = T.mu; i >= 0; --i)
{
double row = 0.0;
int m = T.cu[i].m;
if (m != 0)
{
int c = m;
while ((m--) != 0)
{
row = T.cu[i].c[--c] + @in.v * row;
}
}
@out.u = row + @in.u * @out.u;
}
for (int i = T.mv; i >= 0; --i)
{
double row = 0.0;
int m = T.cv[i].m;
if (m != 0)
{
int c = m;
while ((m--) != 0)
{
row = T.cv[i].c[--c] + @in.v * row;
}
}
@out.v = row + @in.u * @out.v;
}
return(@out);
}
// bivariate Chebyshev polynomial entry point
public static projUV bcheval(projUV @in, Tseries T)
{
projUV w2, w, @out;
// scale to +-1
w.u=(@[email protected])*T.b.u;
w.v=(@[email protected])*T.b.v;
if(Math.Abs(w.u)>NEAR_ONE||Math.Abs(w.v)>NEAR_ONE)
{
@[email protected]=Libc.HUGE_VAL;
Proj.pj_errno=-36;
}
else
{ // double evaluation
w2.u=w.u+w.u;
w2.v=w.v+w.v;
@out.u=ceval(T.cu, T.mu, w, w2);
@out.v=ceval(T.cv, T.mv, w, w2);
}
return @out;
}
// bivariate Chebyshev polynomial entry point
public static projUV bcheval(projUV @in, Tseries T)
{
projUV w2, w, @out;
// scale to +-1
w.u = (@in.u + @in.u - T.a.u) * T.b.u;
w.v = (@in.v + @in.v - T.a.v) * T.b.v;
if (Math.Abs(w.u) > NEAR_ONE || Math.Abs(w.v) > NEAR_ONE)
{
@out.u = @out.v = Libc.HUGE_VAL;
Proj.pj_errno = -36;
}
else
{ // double evaluation
w2.u = w.u + w.u;
w2.v = w.v + w.v;
@out.u = ceval(T.cu, T.mu, w, w2);
@out.v = ceval(T.cv, T.mv, w, w2);
}
return(@out);
}
// general entry point selecting evaluation mode
public static projUV biveval(projUV @in, Tseries T)
{
if(T.power!=0) return bpseval(@in, T);
return bcheval(@in, T);
}
public static Tseries mk_cheby(projUV a, projUV b, double res, ref projUV resid, ProjFunc func, int nu, int nv, bool power)
{
try
{
projUV[][] w = new projUV[nu][];
for (int k = 0; k < nu; k++)
{
w[k] = new projUV[nv];
}
if (bchgen(a, b, nu, nv, w, func))
{
return(null);
}
// analyse coefficients and adjust until residual OK
double cutres = res;
int i = 4;
for (; i > 0; i--)
{
eval(w, nu, nv, cutres, ref resid);
if (resid.u < res && resid.v < res)
{
break;
}
cutres *= 0.5;
}
// warn of too many tries
if (i <= 0)
{
resid.u = -resid.u;
}
double ab;
double[] p;
int[] ncu = new int[nu];
int[] ncv = new int[nv];
// apply cut resolution and set pointers
int nru = 0, nrv = 0;
for (int j = 0; j < nu; ++j)
{
ncu[j] = ncv[j] = 0; // clear column maxes
projUV[] s = w[j];
for (i = 0; i < nv; i++)
{
// < resolution ?
ab = Math.Abs(s[i].u);
if (ab < cutres)
{
s[i].u = 0.0; // clear coefficient
}
else
{
ncu[j] = i + 1; // update column max
}
ab = Math.Abs(s[i].v);
if (ab < cutres)
{
s[i].v = 0.0; // same for v coef's
}
else
{
ncv[j] = i + 1;
}
}
if (ncu[j] != 0)
{
nru = j + 1; // update row max
}
if (ncv[j] != 0)
{
nrv = j + 1;
}
}
if (power)
{ // convert to bivariate power series
if (!bch2bps(a, b, w, nu, nv))
{
return(null);
}
// possible change in some row counts, so readjust
nru = nrv = 0;
for (int j = 0; j < nu; ++j)
{
ncu[j] = ncv[j] = 0; // clear column maxes
projUV[] s = w[j];
for (i = 0; i < nv; i++)
{
if (s[i].u != 0)
{
ncu[j] = i + 1; // update column max
}
if (s[i].v != 0)
{
ncv[j] = i + 1;
}
}
if (ncu[j] != 0)
{
nru = j + 1; // update row max
}
if (ncv[j] != 0)
{
nrv = j + 1;
}
}
Tseries T = makeT(nru, nrv);
if (T != null)
{
T.a = a;
T.b = b;
T.mu = nru - 1;
T.mv = nrv - 1;
T.power = 1;
for (i = 0; i < nru; ++i) // store coefficient rows for u
{
T.cu[i].m = ncu[i];
if (T.cu[i].m != 0)
{
p = T.cu[i].c = new double[ncu[i]];
projUV[] s = w[i];
for (int j = 0; j < ncu[i]; j++)
{
p[j] = s[j].u;
}
}
}
for (i = 0; i < nrv; ++i) // same for v
{
T.cv[i].m = ncv[i];
if (T.cv[i].m != 0)
{
p = T.cv[i].c = new double[ncv[i]];
projUV[] s = w[i];
for (int j = 0; j < ncv[i]; j++)
{
p[j] = s[j].v;
}
}
}
}
return(T);
}
else
{
Tseries T = makeT(nru, nrv);
if (T != null)
{
// else make returned Chebyshev coefficient structure
T.mu = nru - 1; // save row degree
T.mv = nrv - 1;
T.a.u = a.u + b.u; // set argument scaling
T.a.v = a.v + b.v;
T.b.u = 1.0 / (b.u - a.u);
T.b.v = 1.0 / (b.v - a.v);
T.power = 0;
for (i = 0; i < nru; ++i) // store coefficient rows for u
{
T.cu[i].m = ncu[i];
if (T.cu[i].m != 0)
{
p = T.cu[i].c = new double[ncu[i]];
projUV[] s = w[i];
for (int j = 0; j < ncu[i]; j++)
{
p[j] = s[j].u;
}
}
}
for (i = 0; i < nrv; ++i) // same for v
{
T.cv[i].m = ncv[i];
if (T.cv[i].m != 0)
{
p = T.cv[i].c = new double[ncv[i]];
projUV[] s = w[i];
for (int j = 0; j < ncv[i]; j++)
{
p[j] = s[j].v;
}
}
}
}
return(T);
}
}
catch
{
return(null);
}
}
// create power series structure
static Tseries makeT(int nru, int nrv)
{
try
{
Tseries T=new Tseries();
T.cu=new PW_COEF[nru];
T.cv=new PW_COEF[nrv];
for(int i=0; i<nru; i++) T.cu[i].c=null;
for(int i=0; i<nrv; i++) T.cv[i].c=null;
return T;
}
catch
{
return null;
}
}
public static void gen_cheb(bool inverse, ProjFunc proj, string s, PJ P, int iargc, string[] iargv)
{
InputFunc input = Proj.dmstor;
if (inverse)
{
input = Libc.strtod;
}
int errin = 0;
projUV low, upp;
low.u = low.v = upp.u = upp.v = 0;
if (s.Length > 0)
{
low.u = input(s, out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
upp.u = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
low.v = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
upp.v = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (errin != 0)
{
emess(16, "null or absent -T parameters");
}
int NU = 15, NV = 15, res = -1;
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
res = Libc.strtol(s, out s, 10);
}
}
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
NU = Libc.strtol(s, out s, 10);
}
}
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
NV = Libc.strtol(s, out s, 10);
}
}
bool pwr = s.Length > 0 && s.StartsWith(",P");
Console.WriteLine("#proj_{0}\n#\trun-line:", pwr?"Power":"Chebyshev");
// proj execution audit trail
if (iargc > 0)
{
int n = 0;
for (int i = 0; i < iargc; i++)
{
string arg = iargv[i];
if (arg[0] != '+')
{
if (n == 0)
{
Console.Write("#");
n++;
}
Console.Write(" " + arg);
n += arg.Length + 1;
if (n > 50)
{
Console.WriteLine(); n = 0;
}
}
}
if (n != 0)
{
Console.WriteLine();
}
}
Console.WriteLine("# projection parameters");
Console.WriteLine("#" + P.DescriptionName);
Console.WriteLine("#" + P.DescriptionParameters);
Console.WriteLine("#" + P.DescriptionType);
Console.WriteLine("#" + P.ToProj4String());
if (low.u == upp.u || low.v >= upp.v)
{
emess(16, "approx. argument range error");
}
if (low.u > upp.u)
{
low.u -= Proj.TWOPI;
}
if (NU < 2 || NV < 2)
{
emess(16, "approx. work dimensions ({0} {1}) too small", NU, NV);
}
projUV resid = new projUV();
Tseries F = mk_cheby(low, upp, Math.Pow(10.0, res) * 0.5, ref resid, proj, NU, NV, pwr);
if (F == null)
{
emess(16, "generation of approx failed\nreason: {0}\n", Proj.pj_strerrno(Libc.errno));
}
Console.WriteLine("{0},{1:G12},{2:G12},{3:G12},{4:G12},{5:G12}", inverse?'I':'F', P.lam0 * Proj.RAD_TO_DEG,
low.u * (inverse?1.0:Proj.RAD_TO_DEG), upp.u * (inverse?1.0:Proj.RAD_TO_DEG),
low.v * (inverse?1.0:Proj.RAD_TO_DEG), upp.v * (inverse?1.0:Proj.RAD_TO_DEG));
string fmt;
if (pwr)
{
fmt = "G15";
}
else if (res <= 0)
{
fmt = string.Format("F{0}", -res + 1);
}
else
{
fmt = "F0";
}
p_series(F, Console.Out, fmt);
Console.WriteLine("# |u,v| sums {0} {1}\n#end_proj_{2}", resid.u, resid.v, pwr?"Power":"Chebyshev");
}