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Posted to issues@commons.apache.org by GitBox <gi...@apache.org> on 2022/07/25 14:28:16 UTC
[GitHub] [commons-math] aherbert commented on a diff in pull request #210: Derivative computations for BicubicInterpolator
aherbert commented on code in PR #210:
URL: https://github.com/apache/commons-math/pull/210#discussion_r928911104
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunction.java:
##########
@@ -317,49 +325,6 @@ private int searchIndex(double c, double[] val) {
return r;
}
- /**
- * Compute the spline coefficients from the list of function values and
- * function partial derivatives values at the four corners of a grid
- * element. They must be specified in the following order:
- * <ul>
- * <li>f(0,0)</li>
- * <li>f(1,0)</li>
- * <li>f(0,1)</li>
- * <li>f(1,1)</li>
- * <li>f<sub>x</sub>(0,0)</li>
- * <li>f<sub>x</sub>(1,0)</li>
- * <li>f<sub>x</sub>(0,1)</li>
- * <li>f<sub>x</sub>(1,1)</li>
- * <li>f<sub>y</sub>(0,0)</li>
- * <li>f<sub>y</sub>(1,0)</li>
- * <li>f<sub>y</sub>(0,1)</li>
- * <li>f<sub>y</sub>(1,1)</li>
- * <li>f<sub>xy</sub>(0,0)</li>
- * <li>f<sub>xy</sub>(1,0)</li>
- * <li>f<sub>xy</sub>(0,1)</li>
- * <li>f<sub>xy</sub>(1,1)</li>
- * </ul>
- * where the subscripts indicate the partial derivative with respect to
- * the corresponding variable(s).
- *
- * @param beta List of function values and function partial derivatives
- * values.
- * @return the spline coefficients.
- */
- private double[] computeSplineCoefficients(double[] beta) {
- final double[] a = new double[NUM_COEFF];
-
- for (int i = 0; i < NUM_COEFF; i++) {
- double result = 0;
- final double[] row = AINV[i];
Review Comment:
Q. Why has this been replaced with the matrix multiply?
Using the Matrix objects is far less efficient.
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunction.java:
##########
@@ -322,4 +485,40 @@ private double apply(double[] pX, double[] pY, double[][] coeff) {
return result;
}
+
+ /**
+ * @return the partial derivative wrt {@code x}.
+ */
+ public BivariateFunction partialDerivativeX() {
Review Comment:
These can all drop the public keyword.
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunction.java:
##########
@@ -181,6 +226,75 @@ public boolean isValidPoint(double x, double y) {
y > yval[yval.length - 1]);
}
+ /**
+ * @return the first partial derivative respect to x.
+ * @throws NullPointerException if the internal data were not initialized
+ * (cf. {@link #BicubicSplineInterpolatingFunction(double[],double[],double[][],
Review Comment:
`BicubicSplineInterpolatingFunction` does not exist. Please update all 5 references in the javadoc of this class to `BicubicInterpolatingFunction`
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolator.java:
##########
@@ -41,6 +41,30 @@
*/
public class BicubicInterpolator
implements BivariateGridInterpolator {
+ /** Whether to initialize internal data used to compute the analytical
+ derivatives of the splines. */
+ private final boolean initializeDerivatives;
+
+ /**
+ * Default constructor.
+ * The argument {@link #BicubicSplineInterpolator(boolean) initializeDerivatives}
Review Comment:
`BicubicSplineInterpolator` does not exist
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolator.java:
##########
@@ -41,6 +41,30 @@
*/
public class BicubicInterpolator
implements BivariateGridInterpolator {
+ /** Whether to initialize internal data used to compute the analytical
+ derivatives of the splines. */
Review Comment:
Add ` * ` at the start of the line for correct javadoc formatting
##########
commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunctionTest.java:
##########
@@ -304,7 +304,7 @@ public void testSplinePartialDerivatives() {
}
}
- final BicubicFunction f = new BicubicFunction(coeff, true);
+ final BicubicFunction f = new BicubicFunction(coeff, 1, 1, true);
Review Comment:
Have you tested this when `xR` and `yR` are not 1? I would suggest simply repeating the test with `xR` and `yR` as 0.5 and 2 then testing the derivative is correctly scaled.
##########
commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunctionTest.java:
##########
@@ -286,6 +287,231 @@ public double value(double x, double y) {
maxTolerance,
false);
}
+
+ /**
+ * Test for partial derivatives of {@link BicubicSplineFunction}.
Review Comment:
`BicubicSplineFunction` does not exist; it should be `BicubicFunction`
##########
commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolatingFunctionTest.java:
##########
@@ -286,6 +287,231 @@ public double value(double x, double y) {
maxTolerance,
false);
}
+
+ /**
+ * Test for partial derivatives of {@link BicubicSplineFunction}.
+ * <p>
+ * f(x, y) = Σ<sub>i</sub>Σ<sub>j</sub> (i+1) (j+2) x<sup>i</sup> y<sup>j</sup>
+ */
+ @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 BicubicSplineInterpolatingFunction} match the input data.
Review Comment:
`BicubicSplineInterpolatingFunction` does not exist
##########
commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/BicubicInterpolator.java:
##########
@@ -41,6 +41,30 @@
*/
public class BicubicInterpolator
implements BivariateGridInterpolator {
+ /** Whether to initialize internal data used to compute the analytical
+ derivatives of the splines. */
+ private final boolean initializeDerivatives;
+
+ /**
+ * Default constructor.
+ * The argument {@link #BicubicSplineInterpolator(boolean) initializeDerivatives}
+ * is set to {@code false}.
+ */
+ public BicubicInterpolator() {
+ this(false);
+ }
+
+ /**
+ * Creates an interpolator.
+ *
+ * @param initializeDerivatives Whether to initialize the internal data
+ * needed for calling any of the methods that compute the partial derivatives
+ * of the {@link BicubicSplineInterpolatingFunction function} returned from
Review Comment:
`BicubicSplineInterpolatingFunction` does not exist
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