class SmoothingB_F extends Error
The SmoothingB_F
class fits a time-dependent data vector 'y' to B-Splines.
y(t(i)) = x(t(i)) + ε(t(i)) x(t) = cΦ(t)
where 'x' is the signal, 'ε' is the noise, 'c' is a coefficient vector and 'Φ(t)' is a vector of basis functions. This version just used B-Splines.
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- new SmoothingB_F(y: VectoD, t: VectoD, ord: Int = 4, lambda: Double = -1, method: SmoothingMethod.SmoothingMethod = ROUGHNESS, technique: RegTechnique.RegTechnique = Cholesky)
- y
the (raw) data points/vector
- t
the data time points/vector
- ord
the order of the basis function (defaults to 4, cubic)
- lambda
the regularization parameter (>= 0 or -1 to use GCV)
- method
the smoothing method
- technique
the factorization technique
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- def calcCov(yy: VectorD, k: Int = 1): MatrixD
Calculate the correlation matrix for the basis functions.
Calculate the correlation matrix for the basis functions.
- yy
data vector
- k
lag parameter for auto-covariance
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- def d1predict(tv: VectoD): VectoD
Predict the 1st derivative values at all time points in vector 'tv'.
Predict the 1st derivative values at all time points in vector 'tv'.
- tv
the given vector of time points
- def d1predict(tt: Double): Double
Predict the 1st derivative value at time point 'tt'.
Predict the 1st derivative value at time point 'tt'.
- tt
the given time point
- def d2predict(tv: VectoD): VectoD
Predict the 2nd derivative values at all time points in vector 'tv'.
Predict the 2nd derivative values at all time points in vector 'tv'.
- tv
the given vector of time points
- def d2predict(tt: Double): Double
Predict the 2nd derivative value at time point 'tt'.
Predict the 2nd derivative value at time point 'tt'.
- tt
the given time point
- def dnpredict(n: Int, tv: VectoD): VectoD
Predict the n-th derivative values at all time points in vector 'tv'.
Predict the n-th derivative values at all time points in vector 'tv'.
- n
the n-th derivative to be computed
- tv
the given vector of time points
- def dnpredict(n: Int)(tt: Double): Double
Predict the n-th derivative value at time point 'tt'.
Predict the n-th derivative value at time point 'tt'.
- n
the n-th derivative to be computed
- tt
the given time point
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- def getBasis: DB_Spline
Get the Basis Function object
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- def plotBasis(tt: VectoD = t): Unit
Predict the the basis functions
Predict the the basis functions
- tt
the given vector of time points
- def predict(tv: VectoD): VectoD
Predict the y-values at all time points in vector 'tv'.
Predict the y-values at all time points in vector 'tv'.
- tv
the given vector of time points
- def predict(tt: Double): Double
Predict the y-value at time point 'tt'.
Predict the y-value at time point 'tt'.
- tt
the given time point
- def residual: VectoD
Return the vector of residuals/errors.
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- def train(): VectoD
Train the model, i.e., determine the optimal coeifficient 'c' for the basis functions by finding optimal Lamdba to minimize gcv.
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