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Owning Class: polynomials
Requires: MathScript RT Module
[b, a] = residue(r, p, k)
[r2, p2, k2] = residue(b2, a2)
Computes the partial fraction expansion of two polynomials or transforms a given partial fraction expansion into the original polynomial representation.
Name | Description |
---|---|
r | Specifies the residues of the partial fraction expansion. r is a real or complex vector. |
p | Specifies the poles of the partial fraction expansion. p is a real or complex vector. |
k | Specifies the coefficients in descending order of power of the quotient polynomial of a and b. |
b2 | Specifies the coefficients in descending order of power of the numerator polynomial. |
a2 | Specifies the coefficients in descending order of power of the denominator polynomial. |
Name | Description |
---|---|
b | Returns the coefficients in descending order of power of the numerator polynomial. |
a | Returns the coefficients in descending order of power of the denominator polynomial. |
r2 | Returns the residues of the partial fraction expansion. r2 is a real or complex vector. |
p2 | Returns the poles of the partial fraction expansion. p2 is a real or complex vector. |
k2 | Returns the coefficients in descending order of power of the quotient polynomial of a2 and b2. |
LabVIEW computes a and b using the following equation if no multiple roots exist:
b_{s}/a_{s} = (r_{1}/(s-p_{1})) + (r_{2}/(s-p_{2})) + ... + (r_{n}/(s-p_{n})) + k_{s}
where s is the power and n is the number of elements in the partial fraction expansion.
If multiple poles exist, that is, if p_{j} = ... = p_{j}_{+}_{m}_{-}_{1} where j is the element index and m is the multiple, then the partial fraction expansion includes the following terms: (r_{j}/(s-p_{j})) + (r_{j}_{+1}/(s-p_{j}))^{2} + ... + (r_{j}_{+}_{m}_{-1}/(s-p_{j}))^{m}.
The following table lists the support characteristics of this function.
Supported in the LabVIEW Run-Time Engine | Yes |
Supported on RT targets | Yes |
Suitable for bounded execution times on RT | Not characterized |
B = [1, 2, 3, 4]
A = [1, 1]
[R, P, K] = residue(B, A)