advanced with new splines, updated readme todo

splines.hpp

@@ -0,0 +1,90 @@
+#ifndef SPLINES_HPP
+#define SPLINES_HPP
+
+#include <cstddef>
+
+namespace splines1d
+{
+
+template <typename real>
+constexpr real faculty( size_t n ) noexcept
+{
+   return  (n > 1) ? real(n)*faculty<real>(n-1) : real(1);
+}
+
+template <typename real, size_t order, size_t derivative = 0>
+void N( real x, real *result, size_t stride = 1 ) noexcept
+{
+    static_assert( order > 0, "Splines must have order greater than zero." );
+    constexpr int n { order      };
+    constexpr int d { derivative };
+
+    if ( derivative >= order )
+        for ( size_t i = 0; i < order; ++i )
+            result[ i*stride ] = 0;
+
+    if ( n == 1 )
+    {
+        *result = 1;
+        return;
+    }
+
+    real v[n]; v[n-1] = 1;
+    for ( int k = 1; k < n - d; ++k )
+    {
+        v[n-k-1] = (1-x)*v[n-k];
+
+        for ( int i = 1-k; i < 0; ++i )
+            v[n-1+i] = (x-i)*v[n-1+i] + (k+1+i-x)*v[n+i];
+
+        v[n-1] *= x;
+    }
+
+    // Differentiate if necessary.
+    for ( size_t j = derivative; j-- > 0;  )
+    {
+        v[j] = -v[j+1];
+        for ( size_t i = j + 1; i < order - 1; ++i )
+            v[i] = v[i] - v[i+1];
+    }
+
+    constexpr real factor = real(1) / faculty<real>(order-derivative-1);
+    for ( size_t i = 0; i < order; ++i )
+        result[i*stride] = v[i]*factor;
+}
+
+template <typename real, size_t order, size_t derivative = 0>
+real eval( real x, const real *coefficients, size_t stride = 1 ) noexcept
+{
+    static_assert( order > 0, "Splines must have order greater than zero." );
+    static_assert( order > derivative, "Too high derivative requested." );
+    constexpr size_t n { order };
+    constexpr size_t d { derivative };
+
+    if ( d >= n ) return 0;
+    if ( n == 1 ) return *coefficients;
+
+    // Gather coefficients.
+    real c[ order ];
+    for ( size_t j = 0; j < order; ++j )
+        c[j] = coefficients[ stride * j ];
+
+    // Differentiate if necessary.
+    for ( size_t j = 1; j <= d; ++j )
+        for ( size_t i = n; i-- > j; )
+            c[i] = c[i] - c[i-1];
+
+    // Evaluate using de Boor’s algorithm.
+    for ( size_t j = 1; j < n-d; ++j )
+        for ( size_t i = n-d; i-- > j; )
+            c[d+i] = (x+n-d-1-i)*c[d+i] + (i-j+1-x)*c[d+i-1];
+
+    constexpr real factor = real(1) / faculty<real>(order-derivative-1);
+    return factor*c[n-1];
+}
+
+}
+
+#endif
+
+