Deprecated
as a consequence of DifferentiableUnivariateFunction being deprecated. See corresponding docs for further information.
sinc(x) = 1 if x = 0,
sin(x) / x otherwise.
| Modifier and Type | Field and Description |
|---|---|
| private final boolean | normalized
For normalized sinc function. |
| private static final double | SHORTCUT
Value below which the computations are done using Taylor series. |
| Access | Constructor and Description |
|---|---|
| public | |
| public | Sinc(boolean
If normalized)true, the function is
sin(πx) / πx, otherwise sin(x) / x.Instantiates the sinc function. |
| Modifier and Type | Method and Description |
|---|---|
| public UnivariateFunction | derivative()
Implements org.
Deprecated
as of 3.1, replaced by
value(DerivativeStructure)
Returns the derivative of the function |
| public double | value(final double
Point at which the function value should be computed. x)Implements org. Compute the value of the function. |
| public DerivativeStructure | value(final DerivativeStructure
function input value t)Implements org. Simple mathematical function. |
| normalized | back to summary |
|---|---|
| private final boolean normalized For normalized sinc function. | |
| SHORTCUT | back to summary |
|---|---|
| private static final double SHORTCUT Value below which the computations are done using Taylor series. The Taylor series for sinc even order derivatives are:
d^(2n)sinc/dx^(2n) = Sum_(k>=0) (-1)^(n+k) / ((2k)!(2n+2k+1)) x^(2k)
= (-1)^n [ 1/(2n+1) - x^2/(4n+6) + x^4/(48n+120) - x^6/(1440n+5040) + O(x^8) ]
The Taylor series for sinc odd order derivatives are:
d^(2n+1)sinc/dx^(2n+1) = Sum_(k>=0) (-1)^(n+k+1) / ((2k+1)!(2n+2k+3)) x^(2k+1)
= (-1)^(n+1) [ x/(2n+3) - x^3/(12n+30) + x^5/(240n+840) - x^7/(10080n+45360) + O(x^9) ]
So the ratio of the fourth term with respect to the first term is always smaller than x^6/720, for all derivative orders. This implies that neglecting this term and using only the first three terms induces a relative error bounded by x^6/720. The SHORTCUT value is chosen such that this relative error is below double precision accuracy when |x| <= SHORTCUT. | |
| Sinc | back to summary |
|---|---|
| public Sinc() The sinc function, | |
| Sinc | back to summary |
|---|---|
| public Sinc(boolean normalized) Instantiates the sinc function.
| |
| derivative | back to summary |
|---|---|
| public UnivariateFunction derivative() Implements org. Doc from org. Deprecated as of 3.1, replaced by Returns the derivative of the function
| |
| value | back to summary |
|---|---|
| public double value(final double x) Implements org. Doc from org. Compute the value of the function.
| |
| value | back to summary |
|---|---|
| public DerivativeStructure value(final DerivativeStructure t) throws DimensionMismatchException Implements org. Doc from org. Simple mathematical function.
| |