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added Algorithm for computing Natural Cubic Splines

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Modified algorithm from Wikipedia to work with integer x_i and x_i >= 0:
https://en.wikipedia.org/wiki/Spline_(mathematics)#Algorithm_for_computing_natural_cubic_splines
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Ahmet Inan 2018-03-28 16:29:46 +02:00
commit 9bd5546470
2 changed files with 62 additions and 0 deletions
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5
README.md
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@ -33,3 +33,8 @@ Interface for reading and writing [PCM](https://en.wikipedia.org/wiki/Pulse-code
Read and write [WAV](https://en.wikipedia.org/wiki/WAV) files
### [spline.hh](spline.hh)
Algorithm for computing uniform and [natural cubic splines](https://en.wikipedia.org/wiki/Spline_(mathematics)#Algorithm_for_computing_natural_cubic_splines)
Very useful for data interpolation.

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spline.hh Normal file
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@ -0,0 +1,57 @@
/*
Some spline algorithms
Copyright 2018 Ahmet Inan <inan@aicodix.de>
*/
#ifndef SPLINE_HH
#define SPLINE_HH
namespace DSP {
template <int KNOTS, typename OTYPE, typename ITYPE>
class UniformNaturalCubicSpline
{
OTYPE A[KNOTS], B[KNOTS], C[KNOTS], D[KNOTS];
public:
UniformNaturalCubicSpline(OTYPE *y, int STRIDE = 1)
{
for (int i = 0; i < KNOTS; ++i)
A[i] = y[i * STRIDE];
ITYPE u[KNOTS], l[KNOTS];
u[0] = 0;
l[0] = l[KNOTS-1] = 1;
OTYPE z[KNOTS];
z[0] = z[KNOTS-1] = 0;
for (int i = 1; i < KNOTS - 1; ++i) {
l[i] = ITYPE(4) - u[i-1];
u[i] = ITYPE(1) / l[i];
z[i] = (ITYPE(3) * (A[i+1] - ITYPE(2) * A[i] + A[i-1]) - z[i-1]) / l[i];
}
C[KNOTS-1] = 0;
for (int i = KNOTS - 2; i >= 0; --i) {
C[i] = z[i] - u[i] * C[i+1];
B[i] = A[i+1] - A[i] - (C[i+1] + ITYPE(2) * C[i]) / ITYPE(3);
D[i] = (C[i+1] - C[i]) / ITYPE(3);
}
}
OTYPE operator () (ITYPE x)
{
int k = x;
ITYPE t = x - ITYPE(k);
if (k < 0) {
t = x;
k = 0;
}
if (k >= KNOTS - 1) {
t = x - ITYPE(KNOTS-2);
k = KNOTS-2;
}
return A[k] + t * (B[k] + t * (C[k] + t * D[k]));
}
};
}
#endif