Polynomials Composition VI

Owning Palette: Polynomial VIs

Requires: Full Development System

Computes the composition of polynomials P(x) and Q(x). The data types you wire to the P(x) and Q(x) inputs determine the polymorphic instance to use.

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Select an instance Polynomials Composition (DBL)Polynomials Composition (CDB)

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Polynomials Composition (DBL)

	P(x) contains the real polynomial coefficients in ascending order of power.
	Q(x) contains the real polynomial coefficients in ascending order of power.
	threshold specifies the level at which the VI removes from P(Q(x)) the trailing elements whose absolute values or relative values are less than or equal to threshold. If all the elements in P(Q(x)) are less than or equal to threshold, P(Q(x)) returns a one-element array.
	threshold type specifies how the VI removes the trailing elements from P(Q(x)). If threshold type is Absolute Value, the VI removes the trailing elements from P(Q(x)) whose absolute values are less than or equal to threshold. If threshold type is Relative Value, the VI removes the trailing elements from P(Q(x)) whose absolute values are less than or equal to threshold * |x|, where x is the coefficient which has the maximum absolute value in resulting polynomial. 0 Absolute Value (default) 1 Relative Value
	P(Q(x)) returns the real polynomial coefficients, in ascending order of power, for the polynomial that results from composing P(x) and Q(x).
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Polynomials Composition (CDB)

	P(x) contains the complex polynomial coefficients in ascending order of power.
	Q(x) contains the complex polynomial coefficients in ascending order of power.
	threshold specifies the level at which the VI removes from P(Q(x)) the trailing elements whose absolute values or relative values are less than or equal to threshold. If all the elements in P(Q(x)) are less than or equal to threshold, P(Q(x)) returns a one-element array.
	threshold type specifies how the VI removes the trailing elements from P(Q(x)). If threshold type is Absolute Value, the VI removes the trailing elements from P(Q(x)) whose absolute values are less than or equal to threshold. If threshold type is Relative Value, the VI removes the trailing elements from P(Q(x)) whose absolute values are less than or equal to threshold * |x|, where x is the coefficient which has the maximum absolute value in resulting polynomial. 0 Absolute Value (default) 1 Relative Value
	P(Q(x)) returns the complex polynomial coefficients, in ascending order of power, for the polynomial that results from composing P(x) and Q(x).
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Polynomials Composition Details

The following polynomial defines the nth order polynomial described by the (n + 1) element array P[0…n]:

The following polynomial defines the mth order polynomial described by the (m + 1) element array Q[0…m]:

The VI uses the following equation to compose P(x) and Q(x):

P(Q(x)) = P[n](Q[m]x^m + Q[m – 1]x^{m – 1} + … + Q[1]x + Q[0])ⁿ + P[n – 1](Q[m]x^m + Q[m – 1]x^{m – 1} + … + Q[1]x + Q[0])^{n – 1} + … + P[1](Q[m]x^m + Q[m – 1]x^{m – 1} + … + Q[1]x + Q[0]) + P[0]