Package com.opengamma.analytics.math.function

Examples of com.opengamma.analytics.math.function.PiecewisePolynomialFunction1D

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    }

    final double[][] coefsMatExp = new double[][] { {0., 0., 1. / 7., yValues[0] }, {0., 0., 1. / 7., yValues[1] }, {0., 0., 1. / 7., yValues[2] }, {0., 0., 1. / 7., yValues[3] },
        {0., 0., 1. / 7., yValues[4] } };

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    assertEquals(result.getDimensions(), 1);
    assertEquals(result.getNumberOfIntervals(), 5);
    assertEquals(result.getOrder(), 4);

    for (int i = 0; i < result.getNumberOfIntervals(); ++i) {
      for (int j = 0; j < result.getOrder(); ++j) {
        final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
        assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
      }
    }

    final int nKeys = 101;
    for (int i = 0; i < nKeys; ++i) {
      final double key = 1. + 5. / (nKeys - 1) * i;
      final double ref = key / 7. + 1 / 11.;
      assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
    }
  }
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    final double[][] coefsMatExp = new double[][] { {0., 1. / 7., 2. / 7. * xValues[0] + 1. / 13., yValues[0] }, {0., 1. / 7., 2. / 7. * xValues[1] + 1. / 13., yValues[1] },
        {0., 1. / 7., 2. / 7. * xValues[2] + 1. / 13., yValues[2] },
        {0., 1. / 7., 2. / 7. * xValues[3] + 1. / 13., yValues[3] },
        {0., 1. / 7., 2. / 7. * xValues[4] + 1. / 13., yValues[4] } };

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    assertEquals(result.getDimensions(), 1);
    assertEquals(result.getNumberOfIntervals(), 5);
    assertEquals(result.getOrder(), 4);

    for (int i = 0; i < result.getNumberOfIntervals(); ++i) {
      for (int j = 0; j < result.getOrder(); ++j) {
        final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
        assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
      }
    }

    final int nKeys = 101;
    for (int i = 0; i < nKeys; ++i) {
      final double key = 1. + 5. / (nKeys - 1) * i;
      final double ref = key * key / 7. + key / 13. + 1 / 11.;
      assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
    }
  }
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        {0., 1. / 7., 2. / 7. * xValues[1] + 1. / 13., yValues[0][1] }, {0., 1. / 3., 2. / 3. * xValues[1] + 1. / 7., yValues[1][1] },
        {0., 1. / 7., 2. / 7. * xValues[2] + 1. / 13., yValues[0][2] }, {0., 1. / 3., 2. / 3. * xValues[2] + 1. / 7., yValues[1][2] },
        {0., 1. / 7., 2. / 7. * xValues[3] + 1. / 13., yValues[0][3] }, {0., 1. / 3., 2. / 3. * xValues[3] + 1. / 7., yValues[1][3] },
        {0., 1. / 7., 2. / 7. * xValues[4] + 1. / 13., yValues[0][4] }, {0., 1. / 3., 2. / 3. * xValues[4] + 1. / 7., yValues[1][4] } };

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    assertEquals(result.getDimensions(), 2);
    assertEquals(result.getNumberOfIntervals(), 5);
    assertEquals(result.getOrder(), 4);

    for (int i = 0; i < result.getNumberOfIntervals() * 2; ++i) {
      for (int j = 0; j < result.getOrder(); ++j) {
        final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
        assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
      }
    }

    final int nKeys = 101;
    for (int i = 0; i < nKeys; ++i) {
      final double key = 1. + 5. / (nKeys - 1) * i;
      final double ref = key * key / 7. + key / 13. + 1 / 11.;
      assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
    }
  }
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    final double[] xValues = new double[] {0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10. };
    final double[] yValues = new double[] {10., 10., 10., 10., 10., 10., 10.5, 15., 50., 60., 85. };

    final double[][] coefsMatPartExp = new double[][] { {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. } };

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    assertEquals(result.getDimensions(), 1);
    assertEquals(result.getNumberOfIntervals(), 10);
    assertEquals(result.getOrder(), 4);

    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 4; ++j) {
        final double ref = Math.abs(coefsMatPartExp[i][j]) == 0. ? 1. : Math.abs(coefsMatPartExp[i][j]);
        assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatPartExp[i][j], ref * EPS);
      }
    }

    final int nKeys = 101;
    double key0 = 5.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 5. + 5. / (nKeys - 1) * i;
      assertTrue(function.evaluate(result, key).getData()[0] - function.evaluate(result, key0).getData()[0] >= 0.);
      key0 = 5. + 5. / (nKeys - 1) * i;
    }

    key0 = 0.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 0. + 5. / (nKeys - 1) * i;
      assertTrue(function.evaluate(result, key).getData()[0] - function.evaluate(result, key0).getData()[0] == 0.);
      key0 = 0. + 5. / (nKeys - 1) * i;
    }

  }
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    final double[][] yValues = new double[][] {{8.1, 7., 4.4, 7., 4., 3. } };

    PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
    System.out.println(resultPos.getCoefMatrix());

    final int nKeys = 101;
    for (int i = 0; i < nKeys; ++i) {
      final double key = +30. / (nKeys - 1) * i;
      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
    }

  }
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    final double[] yValues = new double[] {3. * 1, 3. * 8. };

    PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
    PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
    System.out.println(resultPos.getCoefMatrix());

    final int nKeys = 101;
    for (int i = 0; i < nKeys; ++i) {
      final double key = 1. + 5. / (nKeys - 1) * i;
      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
    }

  }
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    final Interpolator1D[] wrappedInterp = new PiecewisePolynomialInterpolator1D[] {new ClampedCubicSplineInterpolator1D(), new ConstrainedCubicSplineInterpolator1D(),
        new MonotonicityPreservingCubicSplineInterpolator1D(), new MonotonicityPreservingQuinticSplineInterpolator1D(), new NaturalSplineInterpolator1D(),
        new NonnegativityPreservingCubicSplineInterpolator1D(), new NonnegativityPreservingQuinticSplineInterpolator1D(), new NotAKnotCubicSplineInterpolator1D(),
        new SemiLocalCubicSplineInterpolator1D(), new MonotoneConvexSplineInterpolator1D(), new ShapePreservingCubicSplineInterpolator1D() };
    final int nMethods = bareInterp.length;
    final PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    for (int i = 0; i < dim; ++i) {
      final double[] bareResClamp = function.differentiate(bareInterp[0].interpolate(xValues, yValuesForClamped[i]), xKeys).getData()[0];
      for (int j = 0; j < nKeys; ++j) {
        final Interpolator1DDataBundle dataBundleClamp = wrappedInterp[0].getDataBundleFromSortedArrays(xValues, yValues[i]);
        final double wrappedResClamp = wrappedInterp[0].firstDerivative(dataBundleClamp, xKeys[j]);
        assertEquals(wrappedResClamp, bareResClamp[j], Math.max(Math.abs(bareResClamp[j]), 1.) * 1.e-15);
      }

      for (int k = 1; k < nMethods; ++k) {
        final double[] bareRes = function.differentiate(bareInterp[k].interpolate(xValues, yValues[i]), xKeys).getData()[0];
        for (int j = 0; j < nKeys; ++j) {
          final Interpolator1DDataBundle dataBundle = wrappedInterp[k].getDataBundleFromSortedArrays(xValues, yValues[i]);
          final double wrappedRes = wrappedInterp[k].firstDerivative(dataBundle, xKeys[j]);
          assertEquals(wrappedRes, bareRes[j], Math.max(Math.abs(bareRes[j]), 1.) * 1.e-15);
        }
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      }
    }

    PiecewisePolynomialInterpolator method = new NaturalSplineInterpolator();
    MeshgridInterpolator2D interp = new MeshgridInterpolator2D(method);
    PiecewisePolynomialFunction1D func = new PiecewisePolynomialFunction1D();

    final int n0Keys = 10 * n0Data + 1;
    final int n1Keys = 10 * n1Data + 1;
    final double eps = 1.e-6;
    double[] x0Keys = new double[n0Keys];
    double[] x1Keys = new double[n1Keys];
    double[] x0KeysUp = new double[n0Keys];
    double[] x1KeysUp = new double[n1Keys];
    double[] x0KeysDown = new double[n0Keys];
    double[] x1KeysDown = new double[n1Keys];
    for (int i = 0; i < n0Keys; ++i) {
      x0Keys[i] = x0Values[0] + (x0Values[n0Data - 1] - x0Values[0]) / (n0Keys - 1) * i;
      x0KeysUp[i] = x0Keys[i] == 0. ? eps : x0Keys[i] * (1. + eps);
      x0KeysDown[i] = x0Keys[i] == 0. ? -eps : x0Keys[i] * (1. - eps);
    }
    for (int i = 0; i < n1Keys; ++i) {
      x1Keys[i] = x1Values[0] + (x1Values[n1Data - 1] - x1Values[0]) / (n1Keys - 1) * i;
      x1KeysUp[i] = x1Keys[i] == 0. ? eps : x1Keys[i] * (1. + eps);
      x1KeysDown[i] = x1Keys[i] == 0. ? -eps : x1Keys[i] * (1. - eps);
    }

    final double[][] knotsRes = interp.interpolate(x0Values, x1Values, yValues, x0Values, x1Values).getData();

    final double[][] res = interp.interpolate(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();
    final double[][] resX0 = interp.differentiateX0(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();
    final double[][] resX1 = interp.differentiateX1(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();
    final double[][] resX0Twice = interp.differentiateX0Twice(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();
    final double[][] resX1Twice = interp.differentiateX1Twice(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();

    final double[][] resTran = OG_ALGEBRA.getTranspose(interp.interpolate(x1Values, x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData(), x1Keys, x0Keys)).getData();
    final double[][] resX0Tran = OG_ALGEBRA.getTranspose(interp.differentiateX1(x1Values, x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData(), x1Keys, x0Keys)).getData();
    final double[][] resX1Tran = OG_ALGEBRA.getTranspose(interp.differentiateX0(x1Values, x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData(), x1Keys, x0Keys)).getData();
    final double[][] resX0TwiceTran = OG_ALGEBRA.getTranspose(interp.differentiateX1Twice(x1Values, x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData(), x1Keys, x0Keys))
        .getData();
    final double[][] resX1TwiceTran = OG_ALGEBRA.getTranspose(interp.differentiateX0Twice(x1Values, x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData(), x1Keys, x0Keys))
        .getData();

    for (int i = 0; i < n0Data; ++i) {
      for (int j = 0; j < n1Data; ++j) {
        double ref = Math.abs(yValues[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(yValues[i][j]);
        assertEquals(knotsRes[i][j], yValues[i][j], EPS * ref);
      }
    }
    {
      double ref = Math.abs(yValues[1][2]) < 0.1 * EPS ? 0.1 : Math.abs(yValues[1][2]);
      assertEquals(interp.interpolate(x0Values, x1Values, yValues, x0Values[1], x1Values[2]), yValues[1][2], EPS * ref);
    }
    for (int i = 0; i < n0Keys; ++i) {
      for (int j = 0; j < n1Keys; ++j) {
        double ref = Math.abs(res[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(res[i][j]);
        assertEquals(res[i][j], resTran[i][j], EPS * ref);
        ref = Math.abs(resX0[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(resX0[i][j]);
        assertEquals(resX0[i][j], resX0Tran[i][j], EPS * ref);
        ref = Math.abs(resX1[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(resX1[i][j]);
        assertEquals(resX1[i][j], resX1Tran[i][j], EPS * ref);
        ref = Math.abs(resX0Twice[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(resX0Twice[i][j]);
        assertEquals(resX0Twice[i][j], resX0TwiceTran[i][j], EPS * ref);
        ref = Math.abs(resX1Twice[i][j]) < 0.1 * EPS ? 0.1 : Math.abs(resX1Twice[i][j]);
        assertEquals(resX1Twice[i][j], resX1TwiceTran[i][j], EPS * ref);
      }
    }
    {
      final double val = func.differentiate(method.interpolate(x1Values, yValues[1]), x1Keys[2]).getData()[0];
      final double resVal = interp.differentiateX1(x0Values, x1Values, yValues, x0Values[1], x1Keys[2]);
      final double ref = Math.abs(val) < 0.1 * EPS ? 0.1 : Math.abs(val);
      assertEquals(resVal, val, EPS * ref);
    }
    {
      final double val = func.differentiate(method.interpolate(x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData()[1]), x0Keys[2]).getData()[0];
      final double resVal = interp.differentiateX0(x0Values, x1Values, yValues, x0Keys[2], x1Values[1]);
      final double ref = Math.abs(val) < 0.1 * EPS ? 0.1 : Math.abs(val);
      assertEquals(resVal, val, EPS * ref);
    }
    {
      final double val = func.differentiateTwice(method.interpolate(x1Values, yValues[1]), x1Keys[2]).getData()[0];
      final double resVal = interp.differentiateX1Twice(x0Values, x1Values, yValues, x0Values[1], x1Keys[2]);
      final double ref = Math.abs(val) < 0.1 * EPS ? 0.1 : Math.abs(val);
      assertEquals(resVal, val, EPS * ref);
    }
    {
      final double val = func.differentiateTwice(method.interpolate(x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData()[1]), x0Keys[2]).getData()[0];
      final double resVal = interp.differentiateX0Twice(x0Values, x1Values, yValues, x0Keys[2], x1Values[1]);
      final double ref = Math.abs(val) < 0.1 * EPS ? 0.1 : Math.abs(val);
      assertEquals(resVal, val, EPS * ref);
    }

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    final double[][] yValues = new double[][] { {1., 1., 2., 4., 4., 2., 1., 1. }, {10., 10., 6., 4., 4., 6., 10., 10. } };

    PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interpPos = new MonotonicityPreservingQuinticSplineInterpolator(interp);
    PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);

    //    System.out.println(resultPos.getCoefMatrix());

    assertEquals(resultPos.getDimensions(), result.getDimensions());
    assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
    assertEquals(resultPos.getOrder(), 6);

    //    for (int i = 0; i < 71; ++i) {
    //      final double key = 1. + 7. / (71 - 1) * i;
    //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
    //    }

    final int nKeys = 41;
    double key0 = 1.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 1. + 3. / (nKeys - 1) * i;
      assertTrue(function.evaluate(resultPos, key).getData()[0] - function.evaluate(resultPos, key0).getData()[0] >= 0.);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
      key0 = 1. + 3. / (nKeys - 1) * i;
    }
    key0 = 1.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 1. + 3. / (nKeys - 1) * i;
      assertTrue(function.evaluate(resultPos, key).getData()[1] - function.evaluate(resultPos, key0).getData()[1] <= 0.);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[1] + "\t" + function.evaluate(resultPos, key).getData()[1]);
      key0 = 1. + 3. / (nKeys - 1) * i;
    }
    key0 = 5.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 5. + 3. / (nKeys - 1) * i;
      assertTrue(function.evaluate(resultPos, key).getData()[0] - function.evaluate(resultPos, key0).getData()[0] <= 0.);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
      key0 = 5. + 3. / (nKeys - 1) * i;
    }
    key0 = 5.;
    for (int i = 1; i < nKeys; ++i) {
      final double key = 5. + 3. / (nKeys - 1) * i;
      assertTrue(function.evaluate(resultPos, key).getData()[1] - function.evaluate(resultPos, key0).getData()[1] >= 0.);
      //      System.out.println(key + "\t" + function.evaluate(result, key).getData()[1] + "\t" + function.evaluate(resultPos, key).getData()[1]);
      key0 = 5. + 3. / (nKeys - 1) * i;
    }
  }
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    final double[] yValues = new double[] {19., 17., 19., 2., 4., 5., 18. };

    PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
    PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);

    PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();

    PiecewisePolynomialInterpolator interpPos = new MonotonicityPreservingQuinticSplineInterpolator(interp);
    PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);

    assertEquals(resultPos.getDimensions(), result.getDimensions());
    assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
    assertEquals(resultPos.getOrder(), 6);

    final int len = 21;
    double key0 = 5.;
    for (int i = 1; i < len; ++i) {
      final double key = 5. + 1. / (len - 1) * i;
      assertTrue(function.evaluate(resultPos, key).getData()[0] - function.evaluate(resultPos, key0).getData()[0] >= 0.);
      key0 = 5. + 1. / (len - 1) * i;
    }

    //    final int nKeys = 61;
    //    for (int i = 0; i < nKeys; ++i) {
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