Returns an array of length n, which contains the second derivatives of the spline interpolating function g(x) at the tabulated points x_{i}, where i = 0, 1, ..., n - 1.
You can use interpolant as an input to the Spline Interpolation node to interpolate y at any value of ${x}_{0}\le x\le {x}_{n-1}$.
Dependent value.
This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
When x and y are 1D arrays of double-precision, floating-point numbers, if the number of elements in x is different from the number of elements in y, this node sets the output interpolant to an empty array and returns an error.
Independent value.
This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.
When x and y are 1D arrays of double-precision, floating-point numbers, if the number of elements in x is different from the number of elements in y, this node sets the output interpolant to an empty array and returns an error.
The first derivative of interpolating function g(x) at x_{0}, g'(x_{0}).
Default: 1E+30, which causes this node to set the initial boundary condition for a natural spline.
The first derivative of interpolating function g(x) at x_{n - 1}, g'(x_{n - 1}).
Default: 1E+30, which causes this node to set the final boundary condition for a natural spline.
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Default: No error
Length of each set of data. The node performs computation for each set of data.
sample length must be greater than zero.
This input is available only if you wire a double-precision, floating-point number to x or y.
Default: 100
The second derivative of interpolating function g(x) at points x_{i}, i = 0, 1, ..., n - 1.
Error information.
The node produces this output according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Input arrays x and y are of length n and contain a tabulated function where x_{0} < x_{1} < ... < x_{n-1}, as shown in the following equation:
f(x_{i}) = y_{i}
The interpolating function g(x) is a piecewise function in the following equation:
The function p_{i}(x) is a third-order polynomial that must satisfy the following conditions:
With the third condition, you can derive the following equation:
where i = 1, ..., n - 2. According to this equation, n - 2 linear equations exist for n unknown g"(x_{i}).
This node computes two equations for the derivatives at x_{o} and x_{n-1} in the following equation:
Consider the following equations:
The initial boundary is the equation
and the final boundary is the equation
For these equations, initial boundary and final boundary are the first derivative of g(x) at points x_{0} and x_{n - 1}, respectively. If initial boundary and final boundary are equal to or greater than 10^{30}, this node sets the corresponding boundary condition for a natural spline, with no second derivatives on the boundary.
This node solves g"(x_{i}) from n equations when i = 0, 1, …, n - 1. g"(x_{i}) is the interpolant output.
Where This Node Can Run:
Desktop OS: Windows
FPGA: This product does not support FPGA devices