Examples of org.jquantlib.math.interpolations.CubicInterpolation

Package org.jquantlib.math.interpolations

Examples of org.jquantlib.math.interpolations.CubicInterpolation

org.jquantlib.math.interpolations.CubicInterpolation
Cubic interpolation between discrete points.
Cubic interpolation is fully defined when the ${f_i}$ function values at points ${x_i}$ are supplemented with ${f_i}$ function derivative values.
Different type of first derivative approximations are implemented, both local and non-local. Local schemes (Fourth-order, Parabolic, Modified Parabolic, Fritsch-Butland, Akima, Kruger) use only $f$ values near $x_i$ to calculate $f_i$. Non-local schemes (Spline with different boundary conditions) use all ${f_i}$ values and obtain ${f_i}$ by solving a linear system of equations. Local schemes produce $C^1$ interpolants, while the spline scheme generates $C^2$ interpolants.
Hyman's monotonicity constraint filter is also implemented: it can be applied to all schemes to ensure that in the regions of local monotoniticity of the input (three successive increasing or decreasing values) the interpolating cubic remains monotonic. If the interpolating cubic is already monotonic, the Hyman filter leaves it unchanged preserving all its original features.
In the case of $C^2$ interpolants the Hyman filter ensures local monotonicity at the expense of the second derivative of the interpolant which will no longer be continuous in the points where the filter has been applied.
While some non-linear schemes (Modified Parabolic, Fritsch-Butland, Kruger) are guaranteed to be locally monotone in their original approximation, all other schemes must be filtered according to the Hyman criteria at the expense of their linearity.
See R. L. Dougherty, A. Edelman, and J. M. Hyman, "Nonnegativity-, Monotonicity-, or Convexity-Preserving CubicSpline and Quintic Hermite Interpolation" Mathematics Of Computation, v. 52, n. 186, April 1989, pp. 471-494.
@todo implement missing schemes (FourthOrder and ModifiedParabolic) andmissing boundary conditions (Periodic and Lagrange). @test to be adapted from old ones. @author Richard Gomes

          final Array x = xRange(-1.7, 1.9, n);
          final Array y = gaussian(x);
          double result;


          // Not-a-knot
          CubicInterpolation f = new CubicInterpolation(
                  x, y,
                    CubicInterpolation.DerivativeApprox.Spline, false,
                    CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL,
                    CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL);
          f.update();


          result = Math.sqrt(integral.op(makeErrorFunction(f), -1.7, 1.9));
          result /= scaleFactor;
            assertFalse("Not-a-knot spline interpolation "
                    +"\n    sample points:      "+n
                    +"\n    norm of difference: "+result
                    +"\n    it should be:       "+tabulatedErrors[i],
                    abs(result-tabulatedErrors[i]) > toleranceOnTabErr[i]);


          // MC not-a-knot
          f = new CubicInterpolation(
                  x, y,
                    CubicInterpolation.DerivativeApprox.Spline, true,
                    CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL,
                    CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL);
          f.update();


            result = Math.sqrt(integral.op(makeErrorFunction(f), -1.7, 1.9));
          result /= scaleFactor;
            assertFalse ("MC Not-a-knot spline interpolation "
                    + "\n    sample points:      "

View Full Code Here


    double interpolated;




      // Natural spline
      CubicInterpolation f = new CubicInterpolation(
                                RPN15A_x, RPN15A_y,
                                CubicInterpolation.DerivativeApprox.Spline, false,
                                CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0,
                                CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0);
      f.update();


      checkValues("Natural spline", f, RPN15A_x, RPN15A_y);
      check2ndDerivativeValue("Natural spline", f, RPN15A_x.first(), 0.0);
      check2ndDerivativeValue("Natural spline", f, RPN15A_x.last(),  0.0);


      // poor performance
      final double x_bad = 11.0;
      interpolated = f.op(x_bad);
        assertFalse("Natural spline interpolation poor performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated<1.0);




      // Clamped spline
      f = new CubicInterpolation(
                RPN15A_x, RPN15A_y,
                CubicInterpolation.DerivativeApprox.Spline, false,
                CubicInterpolation.BoundaryCondition.FirstDerivative, 0.0,
                CubicInterpolation.BoundaryCondition.FirstDerivative, 0.0);
      f.update();


      checkValues("Clamped spline", f, RPN15A_x, RPN15A_y);
      check1stDerivativeValue("Clamped spline", f, RPN15A_x.first(), 0.0);
      check1stDerivativeValue("Clamped spline", f, RPN15A_x.last(),  0.0);


      // poor performance
      interpolated = f.op(x_bad);
        assertFalse("Clamped spline interpolation poor performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated<1.0);




      // Not-a-knot spline
        f = new CubicInterpolation(
                RPN15A_x, RPN15A_y,
                CubicInterpolation.DerivativeApprox.Spline, false,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL);
      f.update();


      checkValues("Not-a-knot spline", f, RPN15A_x, RPN15A_y);
      checkNotAKnotCondition("Not-a-knot spline", f);


      // poor performance
      interpolated = f.op(x_bad);
        assertFalse("Not-a-knot spline interpolation poor performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated<1.0);






      // MC natural spline values
        f = new CubicInterpolation(
                RPN15A_x, RPN15A_y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0,
                CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0);
      f.update();


      checkValues("MC natural spline", f, RPN15A_x, RPN15A_y);


      // good performance
      interpolated = f.op(x_bad);
        assertFalse("MC natural spline interpolation good performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated>1.0);




      // MC clamped spline values
        f = new CubicInterpolation(
                RPN15A_x, RPN15A_y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.FirstDerivative, 0.0,
                CubicInterpolation.BoundaryCondition.FirstDerivative, 0.0);
      f.update();


      checkValues("MC clamped spline", f, RPN15A_x, RPN15A_y);
      check1stDerivativeValue("MC clamped spline", f, RPN15A_x.first(), 0.0);
      check1stDerivativeValue("MC clamped spline", f, RPN15A_x.last(),  0.0);


      // good performance
      interpolated = f.op(x_bad);
        assertFalse("MC clamped spline interpolation good performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated>1.0);




      // MC not-a-knot spline values
        f = new CubicInterpolation(
                RPN15A_x, RPN15A_y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL);
      f.update();


      checkValues("MC not-a-knot spline", f, RPN15A_x, RPN15A_y);


      // good performance
      interpolated = f.op(x_bad);
        assertFalse("MC clamped spline interpolation good performance unverified"
                +"\n    at x = "+x_bad
                +"\n    interpolated value: "+interpolated
                +"\n    expected value > 1.0",
                interpolated>1.0);

View Full Code Here

        for (double start = -1.9, j=0; j<2; start+=0.2, j++) {
            x = xRange(start, start+3.6, n);
            y = gaussian(x);


            // Not-a-knot spline
            CubicInterpolation f = new CubicInterpolation(
                    x, y,
                    CubicInterpolation.DerivativeApprox.Spline, false,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0);


            checkValues("Not-a-knot spline", f, x, y);
            checkNotAKnotCondition("Not-a-knot spline", f);
            // bad performance
            interpolated  = f.op(x1_bad);
            interpolated2 = f.op(x2_bad);
            assertFalse("Not-a-knot spline interpolation bad performance unverified"
                    +"\n    at x = "+x1_bad
                    +"\n    interpolated value: "+interpolated
                    +"\n    at x = "+x2_bad
                    +"\n    interpolated value: "+interpolated2
                    +"\n    at least one of them was expected to be < 0.0",
                    interpolated>0.0 && interpolated2>0.0);


            // MC not-a-knot spline
            f = new CubicInterpolation(
                    x, y,
                    CubicInterpolation.DerivativeApprox.Spline, true,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0);
            f.update();


            checkValues("MC not-a-knot spline", f, x, y);


            // bad performance
            interpolated  = f.op(x1_bad);
            interpolated2 = f.op(x2_bad);
            assertFalse("Not-a-knot spline interpolation "
                        + "bad performance unverified"
                        + "\nat x = " + x1_bad
                        + " interpolated value: " + interpolated
                        + "\nat x = " + x2_bad
                        + " interpolated value: " + interpolated
                        + "\n at least one of them was expected to be < 0.0",
                        interpolated<=0.0 || interpolated2<=0.0);
        }




        QL.info("Testing spline interpolation on a Gaussian data set...");


        for (double start = -1.9, j=0; j<2; start+=0.2, j++) {
            x = xRange(start, start+3.6, n);
            y = gaussian(x);


            // MC not-a-knot spline
            final CubicInterpolation interpolation = new CubicInterpolation(
                    x, y,
                    CubicInterpolation.DerivativeApprox.Spline, true,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0,
                    CubicInterpolation.BoundaryCondition.NotAKnot, 0.0);
            interpolation.update();


            checkValues("MC not-a-knot spline", interpolation, x, y);


            // bad performance
            interpolated  = interpolation.op(x1_bad);
            interpolated2 = interpolation.op(x2_bad);
            if (interpolated>0.0 && interpolated2>0.0 ) {
                assertFalse("Not-a-knot spline interpolation "
                            + "bad performance unverified"
                            + "\nat x = " + x1_bad
                            + " interpolated value: " + interpolated

View Full Code Here

        final double zero=0.0;
        double interpolated;
        final double expected=0.0;


        // MC Not-a-knot spline
        CubicInterpolation f = new CubicInterpolation(
                x, y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.NotAKnot, 0.0,
                CubicInterpolation.BoundaryCondition.NotAKnot, 0.0);


        interpolated = f.op(zero);
        assertFalse("MC not-a-knot spline interpolation failed at x = "+zero
                    +"\n    interpolated value: "+interpolated
                    +"\n    expected value:     "+expected
                    +"\n    error:              "+abs(interpolated-expected),
                    abs(interpolated-expected) > 1e-15);




        // MC Clamped spline
        f = new CubicInterpolation(
                x, y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.FirstDerivative,  4.0,
                CubicInterpolation.BoundaryCondition.FirstDerivative, -4.0);


        interpolated =  f.op(zero);
        assertFalse("MC clamped spline interpolation failed at x = "+zero
                +"\n    interpolated value: "+interpolated
                +"\n    expected value:     "+expected
                +"\n    error:              "+abs(interpolated-expected),
                abs(interpolated-expected) > 1e-15);




        // MC SecondDerivative spline
        f = new CubicInterpolation(
                x, y,
                CubicInterpolation.DerivativeApprox.Spline, true,
                CubicInterpolation.BoundaryCondition.SecondDerivative, -2.0,
                CubicInterpolation.BoundaryCondition.SecondDerivative, -2.0);


        interpolated =  f.op(zero);
        assertFalse("MC SecondDerivative spline interpolation failed at x = "+zero
                +"\n    interpolated value: "+interpolated
                +"\n    expected value:     "+expected
                +"\n    error:              "+abs(interpolated-expected),
                abs(interpolated-expected) > 1e-15);

View Full Code Here

    @Override
    public final int requiredPoints() { return 2; }


    @Override
    public final Interpolation interpolate(final Array vx, final Array vy) /* @ReadOnly */ {
        return new CubicInterpolation(vx, vy, da, monotonic, leftType, leftValue, rightType, rightValue);
    }

View Full Code Here

        } else {
            transformed = this.grid.clone().transform(f);
            newValues = newGrid.clone().transform(f);
        }


        final CubicInterpolation priceSpline = new NaturalCubicInterpolation(transformed, values);


        priceSpline.update();
        for (int i=0; i<newValues.size(); i++) {
            newValues.set(i, priceSpline.op(newValues.get(i), true) );
        }


        this.grid.swap(newGrid);
        this.values.swap(newValues);
    }

View Full Code Here

        double interpolated, error;
        final int n = generic_x.size();
        final double[] x35 = new double[3];


        // Natural spline
        CubicInterpolation f = new CubicInterpolation(
                generic_x, generic_y,
                CubicInterpolation.DerivativeApprox.Spline, false,
                CubicInterpolation.BoundaryCondition.SecondDerivative, generic_natural_y2.first(),
                CubicInterpolation.BoundaryCondition.SecondDerivative, generic_natural_y2.last());
        f.update();


        checkValues("Natural spline", f, generic_x, generic_y);
        // cached second derivative
        for (int i=0; i<n; i++) {
            interpolated = f.secondDerivative(generic_x.get(i));
            error = interpolated - generic_natural_y2.get(i);
            assertFalse("Natural spline interpolation "
                  +"second derivative failed at x="+generic_x.get(i)
                  +"\n interpolated value: "+interpolated
                  +"\n expected value:     "+generic_natural_y2.get(i)
                  +"\n error:              "+error,
                  abs(error) > 3e-16);
        }
        x35[1] = f.op(3.5);




        // Clamped spline
        final double y1a = 0.0;
        final double y1b = 0.0;
        f = new CubicInterpolation(
                generic_x, generic_y,
                CubicInterpolation.DerivativeApprox.Spline, false,
                CubicInterpolation.BoundaryCondition.FirstDerivative, y1a,
                CubicInterpolation.BoundaryCondition.FirstDerivative, y1b);
        f.update();


        checkValues("Clamped spline", f, generic_x, generic_y);
        check1stDerivativeValue("Clamped spline", f, generic_x.first(), 0.0);
        check1stDerivativeValue("Clamped spline", f, generic_x.last(),  0.0);
        x35[0] = f.op(3.5);




        // Not-a-knot spline
        f = new CubicInterpolation(
                generic_x, generic_y,
                CubicInterpolation.DerivativeApprox.Spline, false,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL,
                CubicInterpolation.BoundaryCondition.NotAKnot, Constants.NULL_REAL);
        f.update();


        checkValues("Not-a-knot spline", f, generic_x, generic_y);
        checkNotAKnotCondition("Not-a-knot spline", f);
        x35[2] = f.op(3.5);


        assertFalse("Spline interpolation failure"
            +"\n at x = "+3.5
            +"\n clamped spline    "+x35[0]
            +"\n natural spline    "+x35[1]

View Full Code Here

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