java.lang.Object
- com.opengamma.strata.math.impl.interpolation.CubicSplineNakSolver

```
public class CubicSplineNakSolver
extends Object
```
Solves cubic spline problem with Not-A-Knot endpoint conditions, where the third derivative at the endpoints is the same as that of their adjacent points.

Constructor Summary

Constructors
Constructor Description

CubicSplineNakSolver()

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`protected DoubleArray[]`	`combinedMatrixEqnSolver(double[][] doubMat1, double[] doubVec, double[][] doubMat2)`	Cubic spline and its node sensitivity are respectively obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector and AN=L where N,L are matrices
`protected DoubleMatrix[]`	`getCommonCoefficientWithSensitivity(double[] xValues, double[] yValues, double[] intervals, double[][] toBeInv, double[] commonVector, double[][] commonVecSensitivity)`	Cubic spline and its node sensitivity are respectively obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector and AN=L where N,L are matrices
`protected double[][]`	`getCommonMatrixElements(double[] intervals)`	Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector
`protected DoubleMatrix[]`	`getCommonSensitivityCoeffs(double[] intervals, double[][] solnMatrix)`
`protected DoubleMatrix`	`getCommonSplineCoeffs(double[] xValues, double[] yValues, double[] intervals, double[] solnVector)`
`protected double[]`	`getCommonVectorElements(double[] yValues, double[] intervals)`	Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector
`protected double[][]`	`getCommonVectorSensitivity(double[] intervals)`	Node sensitivity is obtained by solving a linear problem AN = L where A,N,L are matrices
`protected double[]`	`getDiffs(double[] xValues)`
`DoubleArray`	`getKnotsMat1D(double[] xValues)`
`protected double[]`	`matrixEqnSolver(double[][] doubMat, double[] doubVec)`	Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector This can be done by LU decomposition
`DoubleMatrix`	`solve(double[] xValues, double[] yValues)`	One-dimensional cubic spline If (xValues length) = (yValues length), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValues length), Clamped endpoint conditions are used
`DoubleMatrix[]`	`solveMultiDim(double[] xValues, DoubleMatrix yValuesMatrix)`	Multi-dimensional cubic spline If (xValues length) = (yValuesMatrix NumberOfColumn), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValuesMatrix NumberOfColumn), Clamped endpoint conditions are used
`DoubleMatrix[]`	`solveWithSensitivity(double[] xValues, double[] yValues)`	One-dimensional cubic spline If (xValues length) = (yValues length), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValues length), Clamped endpoint conditions are used

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - CubicSplineNakSolver
```
public CubicSplineNakSolver()
```
- Method Detail
  - solve
```
public DoubleMatrix solve(double[] xValues,
                          double[] yValues)
```
    One-dimensional cubic spline If (xValues length) = (yValues length), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValues length), Clamped endpoint conditions are used
    
    Parameters:
    
    xValues - X values of data
    
    yValues - Y values of data
    
    Returns:
    
    Coefficient matrix whose i-th row vector is (a_0,a_1,...) for i-th intervals, where a_0,a_1,... are coefficients of f(x) = a_0 + a_1 x^1 + .... Note that the degree of polynomial is NOT necessarily 3
  - solveWithSensitivity
```
public DoubleMatrix[] solveWithSensitivity(double[] xValues,
                                           double[] yValues)
```
    One-dimensional cubic spline If (xValues length) = (yValues length), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValues length), Clamped endpoint conditions are used
    
    Parameters:
    
    xValues - X values of data
    
    yValues - Y values of data
    
    Returns:
    
    Array of matrices: the 0-th element is Coefficient Matrix (same as the solve method above), the i-th element is \frac{\partial a^{i-1}_j}{\partial yValues_k} where a_0^i,a_1^i,... are coefficients of f^i(x) = a_0^i + a_1^i (x - xValues_{i}) + .... with x \in [xValues_{i}, xValues_{i+1}]
  - solveMultiDim
```
public DoubleMatrix[] solveMultiDim(double[] xValues,
                                    DoubleMatrix yValuesMatrix)
```
    Multi-dimensional cubic spline If (xValues length) = (yValuesMatrix NumberOfColumn), Not-A-Knot endpoint conditions are used If (xValues length) + 2 = (yValuesMatrix NumberOfColumn), Clamped endpoint conditions are used
    
    Parameters:
    
    xValues - X values of data
    
    yValuesMatrix - Y values of data, where NumberOfRow defines dimension of the spline
    
    Returns:
    
    A set of coefficient matrices whose i-th row vector is (a_0,a_1,...) for the i-th interval, where a_0,a_1,... are coefficients of f(x) = a_0 + a_1 x^1 + .... Each matrix corresponds to an interpolation (xValues, yValuesMatrix RowVector) Note that the degree of polynomial is NOT necessarily 3
  - getKnotsMat1D
```
public DoubleArray getKnotsMat1D(double[] xValues)
```
    Parameters:
    
    xValues - X values of data
    
    Returns:
    
    X values of knots (Note that these are NOT necessarily xValues if nDataPts=2,3)
  - getDiffs
```
protected double[] getDiffs(double[] xValues)
```
    Parameters:
    
    xValues - X values of Data
    
    Returns:
    
    {xValues[1]-xValues[0], xValues[2]-xValues[1],...} xValues (and corresponding yValues) should be sorted before calling this method
  - getCommonSplineCoeffs
```
protected DoubleMatrix getCommonSplineCoeffs(double[] xValues,
                                             double[] yValues,
                                             double[] intervals,
                                             double[] solnVector)
```
    Parameters:
    
    xValues - X values of Data
    
    yValues - Y values of Data
    
    intervals - {xValues[1]-xValues[0], xValues[2]-xValues[1],...}
    
    solnVector - Values of second derivative at knots
    
    Returns:
    
    Coefficient matrix whose i-th row vector is {a_0,a_1,...} for i-th intervals, where a_0,a_1,... are coefficients of f(x) = a_0 + a_1 x^1 + ....
  - getCommonSensitivityCoeffs
```
protected DoubleMatrix[] getCommonSensitivityCoeffs(double[] intervals,
                                                    double[][] solnMatrix)
```
    Parameters:
    
    intervals - {xValues[1]-xValues[0], xValues[2]-xValues[1],...}
    
    solnMatrix - Sensitivity of second derivatives (x 0.5)
    
    Returns:
    
    Array of i coefficient matrices \frac{\partial a^i_j}{\partial y_k}
  - getCommonCoefficientWithSensitivity
```
protected DoubleMatrix[] getCommonCoefficientWithSensitivity(double[] xValues,
                                                             double[] yValues,
                                                             double[] intervals,
                                                             double[][] toBeInv,
                                                             double[] commonVector,
                                                             double[][] commonVecSensitivity)
```
    Cubic spline and its node sensitivity are respectively obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector and AN=L where N,L are matrices
    
    Parameters:
    
    xValues - X values of data
    
    yValues - Y values of data
    
    intervals - {xValues[1]-xValues[0], xValues[2]-xValues[1],...}
    
    toBeInv - The matrix A
    
    commonVector - The vector b
    
    commonVecSensitivity - The matrix L
    
    Returns:
    
    Coefficient matrices of interpolant (x) and its node sensitivity (N)
  - getCommonMatrixElements
```
protected double[][] getCommonMatrixElements(double[] intervals)
```
    Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector
    
    Parameters:
    
    intervals - the intervals
    
    Returns:
    
    Endpoint-independent part of the matrix A
  - getCommonVectorElements
```
protected double[] getCommonVectorElements(double[] yValues,
                                           double[] intervals)
```
    Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector
    
    Parameters:
    
    yValues - Y values of Data
    
    intervals - {xValues[1]-xValues[0], xValues[2]-xValues[1],...}
    
    Returns:
    
    Endpoint-independent part of vector b
  - getCommonVectorSensitivity
```
protected double[][] getCommonVectorSensitivity(double[] intervals)
```
    Node sensitivity is obtained by solving a linear problem AN = L where A,N,L are matrices
    
    Parameters:
    
    intervals - {xValues[1]-xValues[0], xValues[2]-xValues[1],...}
    
    Returns:
    
    The matrix L
  - matrixEqnSolver
```
protected double[] matrixEqnSolver(double[][] doubMat,
                                   double[] doubVec)
```
    Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector This can be done by LU decomposition
    
    Parameters:
    
    doubMat - Matrix A
    
    doubVec - Vector B
    
    Returns:
    
    Solution to the linear equation, x
  - combinedMatrixEqnSolver
```
protected DoubleArray[] combinedMatrixEqnSolver(double[][] doubMat1,
                                                double[] doubVec,
                                                double[][] doubMat2)
```
    Cubic spline and its node sensitivity are respectively obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector and AN=L where N,L are matrices
    
    Parameters:
    
    doubMat1 - The matrix A
    
    doubVec - The vector b
    
    doubMat2 - The matrix L
    
    Returns:
    
    The solutions to the linear systems, x,N

Class CubicSplineNakSolver

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

CubicSplineNakSolver

Method Detail

solve

solveWithSensitivity

solveMultiDim

getKnotsMat1D

getDiffs

getCommonSplineCoeffs

getCommonSensitivityCoeffs

getCommonCoefficientWithSensitivity

getCommonMatrixElements

getCommonVectorElements

getCommonVectorSensitivity

matrixEqnSolver

combinedMatrixEqnSolver