Spline2DLeastSquares Class |
Namespace: Imsl.Math
The Spline2DLeastSquares type exposes the following members.
Name | Description | |
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Spline2DLeastSquares |
Constructor for Spline2DLeastSquares.
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Name | Description | |
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Compute | Computes a two-dimensional, tensor-product spline
approximant using least squares.
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Derivative(Double, Double, Int32, Int32) | Returns the value of the partial derivative of the tensor-product spline
at the point (x, y).
(Inherited from Spline2D.) | |
Derivative(Double, Double, Int32, Int32) | Returns the values of the partial derivative of the tensor-product spline
of an array of points.
(Inherited from Spline2D.) | |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetCoefficients | Returns the coefficients for the tensor-product spline.
(Inherited from Spline2D.) | |
GetErrorSumOfSquares | Returns the weighted error sum of squares.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetXKnots |
Returns the knot sequences in the x-direction.
(Inherited from Spline2D.) | |
GetXOrder | Returns the order of the spline in the x-direction.
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GetXWeights | Returns the weights for the least-squares fit in the
x-direction.
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GetYKnots | Returns the knot sequences in the y-direction.
(Inherited from Spline2D.) | |
GetYOrder | Returns the order of the spline in the y-direction.
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GetYWeights | Returns the weights for the least-squares fit in the
y-direction.
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Integral | Returns the value of an integral of a tensor-product spline
on a rectangular domain. (Inherited from Spline2D.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
SetXKnots | Sets the knot sequences of the spline in the
x-direction.
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SetXOrder | Sets the order of the spline in the x-direction.
| |
SetXWeights | Sets the weights for the least-squares fit in the
x-direction.
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SetYKnots | Sets the knot sequences of the spline in the
y-direction.
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SetYOrder | Sets the order of the spline in the y-direction.
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SetYWeights | Sets the weights for the least-squares fit in the y-direction.
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ToString | Returns a string that represents the current object. (Inherited from Object.) | |
Value(Double, Double) | Returns the value of the tensor-product spline at the point (x, y).
(Inherited from Spline2D.) | |
Value(Double, Double) | Returns the values of the tensor-product spline of an array of points.
(Inherited from Spline2D.) |
The Spline2DLeastSquares class computes a tensor-product spline
least-squares approximation to weighted tensor-product data. The input
consists of data vectors to specify the tensor-product grid for the
data, two vectors with the weights, the values of the surface on the
grid, and the specification for the tensor-product spline. The grid is
specified by the two vectors x = xData and y
= yData of length
n = xData.Length and
m = yData.Length, respectively. A two-dimensional array
f = fData contains the data values which are to be fit.
The two vectors = xWeights and
= yWeights contain the weights for the
weighted least-squares problem. The information for the approximating
tensor-product spline can be provided using the SetXOrder,
SetYOrder, SetXKnots and SetYKnots methods. This
information is contained in = xOrder,
= xKnots, and N =
xSplineSpaceDim for the spline in the first variable, and in
= yOrder, =
yKnots and M = ySplineSpaceDim for the spline in
the second variable. This class computes coefficients for the
tensor-product spline by solving the normal equations in tensor-product
form as discussed in de Boor (1978, Chapter 17). The interested reader
might also want to study the paper by Grosse (1980).
As the computation proceeds, we obtain coefficients c minimizing
where the function is the tensor-product of two B-splines of order and . Specifically, we have The spline and its partial derivatives can be evaluated using the Value method.