Table Of Contents

Rational Interpolation (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Interpolates or extrapolates a function f at a specific value using a rational function. The rational function passes through all the points formed by arrays of dependent and independent values.

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    Y

    Dependent values.

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    X

    Independent values.

    If the number of elements in X is different from the number of elements in Y, this node sets interpolation value and interpolation error to NaN and returns an error.

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    x value

    Point at which the interpolation or extrapolation is performed.

    If x value is in the range of X, this node performs interpolation. Otherwise, this node performs extrapolation. If x value is too far from the range of X, the extrapolation error may be large. It is not a satisfactory extrapolation.

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    error in

    Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

    Default: No error

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    interpolation value

    Interpolation of the function f at the point you specified.

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    interpolation error

    An estimate of the error in the interpolation.

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    error out

    Error information. The node produces this output according to standard error behavior.

    Algorithm for Calculating the Interpolation Value

    The rational function

    P ( x i ) Q ( x i ) = p 0 + p 1 x i + ... p m x i m q 0 + q 1 x i + ... q m x i m

    passes through all the points formed by Y and X. P and Q are polynomials, and the rational function is unique, given a set of n points (xiyi), where f(xi) = yi, f is any function, and given a number x in the range of the xi values.

    This node calculates interpolation value y using

    P ( x ) Q ( x )

    If the number of points is odd, the degrees of freedom of P and Q are using n 1 2 . If the number of points is even, the degrees of freedom of P are n 2 1 , and the degrees of freedom of Q are n 2 , where n is the total number of points formed by Y and X.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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