Consider the time series of measurements m = [40.0, 41.0, 40.0, 45.0] and time points t1 = [0.0, 1.1, 1.9, 3.0] respectively and another sequence of time points t2 = [0.4, 0.7, 1.8, 2.9, 3.3].
Write a function to, where possible, return the one-dimensional interpolated values of m at t2.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | double interpolated(double targetValue, double x1, double x2, double y1, double y2) { auto x = x2 - x1; return (targetValue - x1) / x * y1 + (x2 - targetValue) / x * y2; } // assume m and t1 is sorted in non-descending order vector<double> linearPolated(const vector<double> &t1, const vector<double> &m, const vector<double> &t2) { auto sz_t1 = t1.size(); auto sz_m = m.size(); // input sizes of t1 and m should be equal assert(sz_t1 == sz_m); auto sz_t2 = t2.size(); vector<double> r; r.reserve(sz_t2); for (const auto &n: t2) { int j = 0; for (int i = 0; i < sz_t1 - 1; ++ i) { if (n >= t1[i] && n <= t1[i + 1]) { j = i; break; } } // TODO: check how interpolation actually works. auto nv = interpolated(n, t1[j], t1[j + 1], m[j], m[j + 1]); r.push_back(nv); } return r; } |
double interpolated(double targetValue, double x1, double x2, double y1, double y2) { auto x = x2 - x1; return (targetValue - x1) / x * y1 + (x2 - targetValue) / x * y2; } // assume m and t1 is sorted in non-descending order vector<double> linearPolated(const vector<double> &t1, const vector<double> &m, const vector<double> &t2) { auto sz_t1 = t1.size(); auto sz_m = m.size(); // input sizes of t1 and m should be equal assert(sz_t1 == sz_m); auto sz_t2 = t2.size(); vector<double> r; r.reserve(sz_t2); for (const auto &n: t2) { int j = 0; for (int i = 0; i < sz_t1 - 1; ++ i) { if (n >= t1[i] && n <= t1[i + 1]) { j = i; break; } } // TODO: check how interpolation actually works. auto nv = interpolated(n, t1[j], t1[j + 1], m[j], m[j + 1]); r.push_back(nv); } return r; }
Note: above C++ code may not have been tested.
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