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| #include <Python.h>
static PyObject *interpolation_iaval(PyObject *self, PyObject *args)
{
double x;
PyObject *a, *fa;
PyObject *tmp;
unsigned n, i, j;
double *da, *dfa;
if (!PyArg_ParseTuple(args, "dOO", &x, &a, &fa))
return PyExc_AttributeError;
if(!(PyList_Check(a) || PyList_Check(fa)))
return PyExc_AttributeError;
n = PyList_Size(a);
if(n!=PyList_Size(fa))
return PyExc_IndexError;
da = (double *)malloc(n*sizeof(double));
dfa = (double *)malloc(n*sizeof(double));
if(da==NULL || dfa==NULL)
{
if(da) free(da);
if(dfa) free(dfa);
return PyErr_NoMemory();
}
for(i=0; i<n; i++)
{
tmp = PyList_GetItem(a, i);
if(!PyFloat_Check(tmp))
{
free(da);
free(dfa);
return PyExc_AttributeError;
}
da[i] = PyFloat_AsDouble(tmp);
tmp = PyList_GetItem(fa, i);
if(!PyFloat_Check(tmp))
{
free(da);
free(dfa);
return PyExc_AttributeError;
}
dfa[i] = PyFloat_AsDouble(tmp);
}
n--;
for(i=1; i<=n; i++)
for(j=n; j>=i; j--)
dfa[j] = ((x-da[j-i])*dfa[j]-(x-da[j])*dfa[j-1])/(da[j]-da[j-i]);
x = dfa[n];
free(da);
free(dfa);
return Py_BuildValue("d", x);
}
static PyObject *interpolation_divdif(PyObject *self, PyObject *args)
{
PyObject *a, *fa;
PyObject *tmp;
unsigned n, i, j;
double *da, *dfa;
if (!PyArg_ParseTuple(args, "OO", &a, &fa))
return PyExc_AttributeError;
if(!(PyList_Check(a) || PyList_Check(fa)))
return PyExc_AttributeError;
n = PyList_Size(a);
if(n!=PyList_Size(fa))
return PyExc_IndexError;
da = (double *)malloc(n*sizeof(double));
dfa = (double *)malloc(n*sizeof(double));
if(da==NULL || dfa==NULL)
{
if(da) free(da);
if(dfa) free(dfa);
return PyErr_NoMemory();
}
for(i=0; i<n; i++)
{
tmp = PyList_GetItem(a, i);
if(!PyFloat_Check(tmp))
{
free(da);
free(dfa);
return PyExc_AttributeError;
}
da[i] = PyFloat_AsDouble(tmp);
tmp = PyList_GetItem(fa, i);
if(!PyFloat_Check(tmp))
{
free(da);
free(dfa);
return PyExc_AttributeError;
}
dfa[i] = PyFloat_AsDouble(tmp);
}
n--;
for(i=1; i<=n; i++)
for(j=n; j>=i; j--)
dfa[j] = (dfa[j]-dfa[j-1])/(da[j]-da[j-i]);
n++;
tmp = PyList_New((Py_ssize_t)(n));
for(i=0; i<n; i++)
PyList_SetItem(tmp, (Py_ssize_t)i, PyFloat_FromDouble(dfa[i]));
return tmp;
}
static PyObject *interpolation_hermite(PyObject *self, PyObject *args)
{
PyObject *pa, *pfa;
PyObject *t1, *t2;
unsigned n, m, i, j, k, s;
double *a, **dfa, *dd, t;
unsigned *nf;
/* Codi de preparació pel còmput i de comprovacions */
// printf("Inici de les preparacions...\n");
if (!PyArg_ParseTuple(args, "OO", &pa, &pfa))
return PyExc_AttributeError;
if(!(PyList_Check(pa) || PyList_Check(pfa)))
return PyExc_AttributeError;
n = PyList_Size(pa);
if(n!=PyList_Size(pfa))
return PyExc_IndexError;
nf = (unsigned *)malloc(n*sizeof(unsigned));
dfa = (double **)malloc(n*sizeof(double*));
if(dfa==NULL || nf ==NULL)
{
if(dfa) free(dfa);
if(nf) free(nf);
return PyErr_NoMemory();
}
m = 0;
for(i=0; i<n; i++)
{
t1 = PyList_GetItem(pfa, i);
if(!PyList_Check(t1))
{
free(dfa);
free(nf);
return PyExc_AttributeError;
}
nf[i] = (unsigned)PyList_Size(t1);
m += nf[i];
dfa[i] = (double *)malloc(sizeof(double)*nf[i]);
if(dfa[i]==NULL)
{
for(k=0; k<=i; k++)
free(dfa[k]);
free(dfa);
free(nf);
return PyErr_NoMemory();
}
for(j=0; j<nf[i]; j++)
{
t2 = PyList_GetItem(t1, j);
if(!PyFloat_Check(t2))
{
for(k=0; k<=i; k++)
free(dfa[k]);
free(dfa);
free(nf);
return PyExc_AttributeError;
}
dfa[i][j] = PyFloat_AsDouble(t2);
}
}
dd = (double *)malloc(sizeof(double)*m);
a = (double *)malloc(sizeof(double)*m);
if(a == NULL || dd == NULL)
{
if(a) free(a);
if(dd) free(dd);
for(i=0; i<n; i++)
free(dfa[i]);
free(dfa);
free(nf);
return PyErr_NoMemory();
}
for(k=0, i=0; i<n; i++)
{
t2 = PyList_GetItem(pa, i);
if(!PyFloat_Check(t2))
{
if(a) free(a);
if(dd) free(dd);
for(i=0; i<n; i++)
free(dfa[i]);
free(dfa);
free(nf);
return PyExc_AttributeError;
}
t = PyFloat_AsDouble(t2);
for(j=0; j<nf[i]; j++, k++)
{
a[k] = t;
dd[k] = dfa[i][0];
}
}
/* Final de les comprovacions i de la preparació del còmput */
// printf("Final de les comprovacions...\n");
// printf("Inici del còmput...\n");
/* Inici del còmput */
m--;
for(i=1; i<=m; i++)
for(j=m; j>=i; j--)
{
if(a[j]!=a[j-i])
dd[j] = (dd[j]-dd[j-1])/(a[j]-a[j-i]);
else
{
t = a[0];
for(s=k=0; k<n; k++)
{
if(a[k]==a[j])
break;
if(a[k]!=t)
{
t = a[k];
s++;
}
}
dd[j] = dfa[s][i]/((double)fact(i));
}
}
// printf("Final del comput...\n");
// printf("Conversio de tipus...\n");
m++;
t1 = PyList_New((Py_ssize_t)(m));
for(i=0; i<m; i++)
PyList_SetItem(t1, (Py_ssize_t)i, PyFloat_FromDouble(dd[i]));
// printf("Conversio realitzada...\n");
// printf("Alliberant memòria...\n");
free(nf);
free(dd);
for(i=0; i<n; i++)
free(dfa[i]);
free(dfa);
// printf("Memoria alliberada...\n");
return t1;
}
static PyMethodDef interpolationmethods[] = {
{"iaval", interpolation_iaval, METH_VARARGS,
"float iaval(x,[x1,x2,...,xn], [f(x1),f(x2),..,f(xn)])\n"
"Neville's method for Lagrange's interpolation\n"
"This function returns the value of the interpolation polynomial on the given point (x)." },
{"divdif", interpolation_divdif, METH_VARARGS,
"divdif([x1,x2,...,xn], [f(x1),f(x2),...,f(xn)])\n"
"Newton's Divided differences method for Lagrange's Interpolation\n"
"This function returns the divided differences of the Newton's divided differences interpolation polynomial."},
{"hermite", interpolation_hermite, METH_VARARGS,
"hermite([x1,x2,...,xn], [[f(x1),f'(x1),...,f(m1)(x1)],...,[f(xn),f'(xn),...,f(mn)(xn)]])\n"
"Hermite's method for Lagrange's Interpolation\n"
"This function returns the divided differences of the Hermite's divided differences interpolation polynomial."},
{NULL, NULL} /* sentinel */
};
DL_EXPORT(void) initinterpolation()
{
Py_InitModule("interpolation", interpolationmethods);
} |
:
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