/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.math4.legacy.analysis.interpolation;
  
  import java.util.function.DoubleBinaryOperator;
  import org.apache.commons.math4.legacy.analysis.BivariateFunction;
  import org.apache.commons.math4.legacy.analysis.interpolation.BicubicInterpolatingFunction.BicubicFunction;
  import org.apache.commons.statistics.distribution.ContinuousDistribution;
  import org.apache.commons.statistics.distribution.UniformContinuousDistribution;
  import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.simple.RandomSource;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.apache.commons.numbers.core.Precision;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test case for the bicubic function.
   */
  public final class BicubicInterpolatingFunctionTest {
      /**
       * Test preconditions.
       */
      @Test
      public void testPreconditions() {
          double[] xval = new double[] {3, 4, 5, 6.5};
          double[] yval = new double[] {-4, -3, -1, 2.5};
          double[][] zval = new double[xval.length][yval.length];
  
          @SuppressWarnings("unused")
          BivariateFunction bcf = new BicubicInterpolatingFunction(xval, yval, zval,
                                                                   zval, zval, zval);
  
          double[] wxval = new double[] {3, 2, 5, 6.5};
          try {
              bcf = new BicubicInterpolatingFunction(wxval, yval, zval, zval, zval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (MathIllegalArgumentException e) {
              // Expected
          }
          double[] wyval = new double[] {-4, -1, -1, 2.5};
          try {
              bcf = new BicubicInterpolatingFunction(xval, wyval, zval, zval, zval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (MathIllegalArgumentException e) {
              // Expected
          }
          double[][] wzval = new double[xval.length][yval.length - 1];
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (DimensionMismatchException e) {
              // Expected
          }
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (DimensionMismatchException e) {
              // Expected
          }
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (DimensionMismatchException e) {
              // Expected
          }
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
              Assert.fail("an exception should have been thrown");
          } catch (DimensionMismatchException e) {
              // Expected
          }
  
          wzval = new double[xval.length - 1][yval.length];
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
              Assert.fail("an exception should have been thrown");
          } catch (DimensionMismatchException e) {
              // Expected
          }
          try {
              bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
             Assert.fail("an exception should have been thrown");
         } catch (DimensionMismatchException e) {
             // Expected
         }
         try {
             bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
             Assert.fail("an exception should have been thrown");
         } catch (DimensionMismatchException e) {
             // Expected
         }
         try {
             bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
             Assert.fail("an exception should have been thrown");
         } catch (DimensionMismatchException e) {
             // Expected
         }
     }
 
     @Test
     public void testIsValidPoint() {
         final double xMin = -12;
         final double xMax = 34;
         final double yMin = 5;
         final double yMax = 67;
         final double[] xval = new double[] { xMin, xMax };
         final double[] yval = new double[] { yMin, yMax };
         final double[][] f = new double[][] { { 1, 2 },
                                               { 3, 4 } };
         final double[][] dFdX = f;
         final double[][] dFdY = f;
         final double[][] dFdXdY = f;
 
         final BicubicInterpolatingFunction bcf
             = new BicubicInterpolatingFunction(xval, yval, f,
                                                      dFdX, dFdY, dFdXdY);
 
         double x = xMin;
         double y = yMin;
         Assert.assertTrue(bcf.isValidPoint(x, y));
         // Ensure that no exception is thrown.
         bcf.value(x, y);
 
         x = xMax;
         y = yMax;
         Assert.assertTrue(bcf.isValidPoint(x, y));
         // Ensure that no exception is thrown.
         bcf.value(x, y);
 
         final double xRange = xMax - xMin;
         final double yRange = yMax - yMin;
         x = xMin + xRange / 3.4;
         y = yMin + yRange / 1.2;
         Assert.assertTrue(bcf.isValidPoint(x, y));
         // Ensure that no exception is thrown.
         bcf.value(x, y);
 
         final double small = 1e-8;
         x = xMin - small;
         y = yMax;
         Assert.assertFalse(bcf.isValidPoint(x, y));
         // Ensure that an exception would have been thrown.
         try {
             bcf.value(x, y);
             Assert.fail("OutOfRangeException expected");
         } catch (OutOfRangeException expected) {}
 
         x = xMin;
         y = yMax + small;
         Assert.assertFalse(bcf.isValidPoint(x, y));
         // Ensure that an exception would have been thrown.
         try {
             bcf.value(x, y);
             Assert.fail("OutOfRangeException expected");
         } catch (OutOfRangeException expected) {}
     }
 
     /**
      * Interpolating a plane.
      * \[
      *   z = 2 x - 3 y + 5
      * \]
      */
     @Test
     public void testPlane() {
         final int numberOfElements = 10;
         final double minimumX = -10;
         final double maximumX = 10;
         final double minimumY = -10;
         final double maximumY = 10;
         final int numberOfSamples = 1000;
 
         final double interpolationTolerance = 1e-15;
         final double maxTolerance = 1e-14;
 
         // Function values
         BivariateFunction f = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 2 * x - 3 * y + 5;
                 }
             };
         BivariateFunction dfdx = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 2;
                 }
             };
         BivariateFunction dfdy = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return -3;
                 }
             };
         BivariateFunction d2fdxdy = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 0;
                 }
             };
 
         testInterpolation(minimumX,
                           maximumX,
                           minimumY,
                           maximumY,
                           numberOfElements,
                           numberOfSamples,
                           f,
                           dfdx,
                           dfdy,
                           d2fdxdy,
                           interpolationTolerance,
                           maxTolerance,
                           false);
     }
 
     /**
      * Interpolating a paraboloid.
      * \[
      *   z = 2 x^2 - 3 y^2 + 4 x y - 5
      * \]
      */
     @Test
     public void testParaboloid() {
         final int numberOfElements = 10;
         final double minimumX = -10;
         final double maximumX = 10;
         final double minimumY = -10;
         final double maximumY = 10;
         final int numberOfSamples = 1000;
 
         final double interpolationTolerance = 2e-14;
         final double maxTolerance = 1e-12;
 
         // Function values
         BivariateFunction f = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 2 * x * x - 3 * y * y + 4 * x * y - 5;
                 }
             };
         BivariateFunction dfdx = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 4 * (x + y);
                 }
             };
         BivariateFunction dfdy = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 4 * x - 6 * y;
                 }
             };
         BivariateFunction d2fdxdy = new BivariateFunction() {
                 @Override
                 public double value(double x, double y) {
                     return 4;
                 }
             };
 
         testInterpolation(minimumX,
                           maximumX,
                           minimumY,
                           maximumY,
                           numberOfElements,
                           numberOfSamples,
                           f,
                           dfdx,
                           dfdy,
                           d2fdxdy,
                           interpolationTolerance,
                           maxTolerance,
                           false);
     }
 
     /**
      * Test for partial derivatives of {@link BicubicFunction}.
      * \[
      *   f(x, y) = \Sigma_i \Sigma_j (i+1) (j+2) x^i y^j
      * \]
      */
     @Test
     public void testSplinePartialDerivatives() {
         final int N = 4;
         final double[] coeff = new double[16];
 
         for (int i = 0; i < N; i++) {
             for (int j = 0; j < N; j++) {
                 coeff[i + N * j] = (i + 1) * (j + 2);
             }
         }
 
         final BicubicFunction f = new BicubicFunction(coeff, 1, 1, true);
         BivariateFunction derivative;
         final double x = 0.435;
         final double y = 0.776;
         final double tol = 1e-13;
 
         derivative = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double y2 = y * y;
                     final double y3 = y2 * y;
                     final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3;
                     return yFactor * (2 + 6 * x + 12 * x2);
                 }
             };
         Assert.assertEquals("dFdX", derivative.value(x, y),
                             f.partialDerivativeX().value(x, y), tol);
 
         derivative = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double x3 = x2 * x;
                     final double y2 = y * y;
                     final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3;
                     return xFactor * (3 + 8 * y + 15 * y2);
                 }
             };
         Assert.assertEquals("dFdY", derivative.value(x, y),
                             f.partialDerivativeY().value(x, y), tol);
 
         derivative = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double y2 = y * y;
                     final double y3 = y2 * y;
                     final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3;
                     return yFactor * (6 + 24 * x);
                 }
             };
         Assert.assertEquals("d2FdX2", derivative.value(x, y),
                             f.partialDerivativeXX().value(x, y), tol);
 
         derivative = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double x3 = x2 * x;
                     final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3;
                     return xFactor * (8 + 30 * y);
                 }
             };
         Assert.assertEquals("d2FdY2", derivative.value(x, y),
                             f.partialDerivativeYY().value(x, y), tol);
 
         derivative = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double y2 = y * y;
                     final double yFactor = 3 + 8 * y + 15 * y2;
                     return yFactor * (2 + 6 * x + 12 * x2);
                 }
             };
         Assert.assertEquals("d2FdXdY", derivative.value(x, y),
                             f.partialDerivativeXY().value(x, y), tol);
     }
 
     /**
      * Test that the partial derivatives computed from a
      * {@link BicubicInterpolatingFunction} match the input data.
      * \[
      *   f(x, y) = 5
      *             - 3 x + 2 y
      *             - x y + 2 x^2 - 3 y^2
      *             + 4 x^2 y - x y^2 - 3 x^3 + y^3
      * \]
      */
     @Test
     public void testMatchingPartialDerivatives() {
         final int sz = 21;
         double[] xval = new double[sz];
         double[] yval = new double[sz];
         // Coordinate values
         final double delta = 1d / (sz - 1);
         for (int i = 0; i < sz; i++) {
             xval[i] = i * delta;
             yval[i] = i * delta / 3;
         }
         // Function values
         BivariateFunction f = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double x3 = x2 * x;
                     final double y2 = y * y;
                     final double y3 = y2 * y;
 
                     return 5
                         - 3 * x + 2 * y
                         - x * y + 2 * x2 - 3 * y2
                         + 4 * x2 * y - x * y2 - 3 * x3 + y3;
                 }
             };
         double[][] fval = new double[sz][sz];
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 fval[i][j] = f.value(xval[i], yval[j]);
             }
         }
         // Partial derivatives with respect to x
         double[][] dFdX = new double[sz][sz];
         BivariateFunction dfdX = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double y2 = y * y;
                     return - 3 - y + 4 * x + 8 * x * y - y2 - 9 * x2;
                 }
             };
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 dFdX[i][j] = dfdX.value(xval[i], yval[j]);
             }
         }
         // Partial derivatives with respect to y
         double[][] dFdY = new double[sz][sz];
         BivariateFunction dfdY = new BivariateFunction() {
                 public double value(double x, double y) {
                     final double x2 = x * x;
                     final double y2 = y * y;
                     return 2 - x - 6 * y + 4 * x2 - 2 * x * y + 3 * y2;
                 }
             };
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 dFdY[i][j] = dfdY.value(xval[i], yval[j]);
             }
         }
         // Second partial derivatives with respect to x
         double[][] d2Fd2X = new double[sz][sz];
         BivariateFunction d2fd2X = new BivariateFunction() {
                 public double value(double x, double y) {
                     return 4 + 8 * y - 18 * x;
                 }
             };
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 d2Fd2X[i][j] = d2fd2X.value(xval[i], yval[j]);
             }
         }
         // Second partial derivatives with respect to y
         double[][] d2Fd2Y = new double[sz][sz];
         BivariateFunction d2fd2Y = new BivariateFunction() {
                 public double value(double x, double y) {
                     return - 6 - 2 * x + 6 * y;
                 }
             };
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 d2Fd2Y[i][j] = d2fd2Y.value(xval[i], yval[j]);
             }
         }
         // Partial cross-derivatives
         double[][] d2FdXdY = new double[sz][sz];
         BivariateFunction d2fdXdY = new BivariateFunction() {
                 public double value(double x, double y) {
                     return -1 + 8 * x - 2 * y;
                 }
             };
         for (int i = 0; i < sz; i++) {
             for (int j = 0; j < sz; j++) {
                 d2FdXdY[i][j] = d2fdXdY.value(xval[i], yval[j]);
             }
         }
 
         BicubicInterpolatingFunction bcf
             = new BicubicInterpolatingFunction(xval, yval, fval, dFdX, dFdY, d2FdXdY, true);
         DoubleBinaryOperator partialDerivativeX = bcf.partialDerivativeX();
         DoubleBinaryOperator partialDerivativeY = bcf.partialDerivativeY();
         DoubleBinaryOperator partialDerivativeXX = bcf.partialDerivativeXX();
         DoubleBinaryOperator partialDerivativeYY = bcf.partialDerivativeYY();
         DoubleBinaryOperator partialDerivativeXY = bcf.partialDerivativeXY();
 
         double x;
         double y;
         double expected;
         double result;
 
         final double tol = 1e-10;
         for (int i = 0; i < sz; i++) {
             x = xval[i];
             for (int j = 0; j < sz; j++) {
                 y = yval[j];
 
                 expected = dfdX.value(x, y);
                 result = partialDerivativeX.applyAsDouble(x, y);
                 Assert.assertEquals(x + " " + y + " dFdX", expected, result, tol);
 
                 expected = dfdY.value(x, y);
                 result = partialDerivativeY.applyAsDouble(x, y);
                 Assert.assertEquals(x + " " + y + " dFdY", expected, result, tol);
 
                 expected = d2fd2X.value(x, y);
                 result = partialDerivativeXX.applyAsDouble(x, y);
                 Assert.assertEquals(x + " " + y + " d2Fd2X", expected, result, tol);
 
                 expected = d2fd2Y.value(x, y);
                 result = partialDerivativeYY.applyAsDouble(x, y);
                 Assert.assertEquals(x + " " + y + " d2Fd2Y", expected, result, tol);
 
                 expected = d2fdXdY.value(x, y);
                 result = partialDerivativeXY.applyAsDouble(x, y);
                 Assert.assertEquals(x + " " + y + " d2FdXdY", expected, result, tol);
             }
         }
     }
 
     /**
      * @param minimumX Lower bound of interpolation range along the x-coordinate.
      * @param maximumX Higher bound of interpolation range along the x-coordinate.
      * @param minimumY Lower bound of interpolation range along the y-coordinate.
      * @param maximumY Higher bound of interpolation range along the y-coordinate.
      * @param numberOfElements Number of data points (along each dimension).
      * @param numberOfSamples Number of test points.
      * @param f Function to test.
      * @param dfdx Partial derivative w.r.t. x of the function to test.
      * @param dfdy Partial derivative w.r.t. y of the function to test.
      * @param d2fdxdy Second partial cross-derivative of the function to test.
      * @param meanTolerance Allowed average error (mean error on all interpolated values).
      * @param maxTolerance Allowed error on each interpolated value.
      */
     private void testInterpolation(double minimumX,
                                    double maximumX,
                                    double minimumY,
                                    double maximumY,
                                    int numberOfElements,
                                    int numberOfSamples,
                                    BivariateFunction f,
                                    BivariateFunction dfdx,
                                    BivariateFunction dfdy,
                                    BivariateFunction d2fdxdy,
                                    double meanTolerance,
                                    double maxTolerance,
                                    boolean print) {
         double expected;
         double actual;
         double currentX;
         double currentY;
         final double deltaX = (maximumX - minimumX) / numberOfElements;
         final double deltaY = (maximumY - minimumY) / numberOfElements;
         final double[] xValues = new double[numberOfElements];
         final double[] yValues = new double[numberOfElements];
         final double[][] zValues = new double[numberOfElements][numberOfElements];
         final double[][] dzdx = new double[numberOfElements][numberOfElements];
         final double[][] dzdy = new double[numberOfElements][numberOfElements];
         final double[][] d2zdxdy = new double[numberOfElements][numberOfElements];
 
         for (int i = 0; i < numberOfElements; i++) {
             xValues[i] = minimumX + deltaX * i;
             final double x = xValues[i];
             for (int j = 0; j < numberOfElements; j++) {
                 yValues[j] = minimumY + deltaY * j;
                 final double y = yValues[j];
                 zValues[i][j] = f.value(x, y);
                 dzdx[i][j] = dfdx.value(x, y);
                 dzdy[i][j] = dfdy.value(x, y);
                 d2zdxdy[i][j] = d2fdxdy.value(x, y);
             }
         }
 
         final BivariateFunction interpolation
             = new BicubicInterpolatingFunction(xValues,
                                                yValues,
                                                zValues,
                                                dzdx,
                                                dzdy,
                                                d2zdxdy);
 
         for (int i = 0; i < numberOfElements; i++) {
             currentX = xValues[i];
             for (int j = 0; j < numberOfElements; j++) {
                 currentY = yValues[j];
                 expected = f.value(currentX, currentY);
                 actual = interpolation.value(currentX, currentY);
                 Assert.assertTrue("On data point: " + expected + " != " + actual,
                                   Precision.equals(expected, actual));
             }
         }
 
         final UniformRandomProvider rng = RandomSource.WELL_19937_C.create(1234567L);
         final ContinuousDistribution.Sampler distX = UniformContinuousDistribution.of(xValues[0], xValues[xValues.length - 1]).createSampler(rng);
         final ContinuousDistribution.Sampler distY = UniformContinuousDistribution.of(yValues[0], yValues[yValues.length - 1]).createSampler(rng);
 
         double sumError = 0;
         for (int i = 0; i < numberOfSamples; i++) {
             currentX = distX.sample();
             currentY = distY.sample();
             expected = f.value(currentX, currentY);
 
             if (print) {
                 System.out.println(currentX + " " + currentY + " -> ");
             }
 
             actual = interpolation.value(currentX, currentY);
             sumError += JdkMath.abs(actual - expected);
 
             if (print) {
                 System.out.println(actual + " (diff=" + (expected - actual) + ")");
             }
 
             Assert.assertEquals(expected, actual, maxTolerance);
         }
 
         final double meanError = sumError / numberOfSamples;
         Assert.assertEquals(0, meanError, meanTolerance);
     }
 }