WIP #1034 new ClenshawCurtisRule, GaussLobattoRule,NewtonCotesRule

method options for NIntegrate

Author: axkr

symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/NIntegrate.java

@@ -29,6 +29,9 @@
 import org.matheclipse.core.interfaces.IExpr;
 import org.matheclipse.core.interfaces.IReal;
 import org.matheclipse.core.interfaces.ISymbol;
+import org.matheclipse.core.numerics.integral.ClenshawCurtis;
+import org.matheclipse.core.numerics.integral.GaussLobatto;
+import org.matheclipse.core.numerics.integral.NewtonCotes;
 import org.matheclipse.core.numerics.integral.Quadrature;
 import org.matheclipse.core.numerics.integral.Quadrature.QuadratureResult;
 import org.matheclipse.core.numerics.integral.TanhSinh;
@@ -127,17 +130,39 @@ public static double integrate(String method, IAST list, final double min, final
       integrator = new TrapezoidIntegrator();
     } else if ("GaussKronrod".equalsIgnoreCase(method)) {
       return gausKronrodRule(maxIterations, f, min, max);
+    } else if ("ClenshawCurtisRule".equalsIgnoreCase(method)) {
+      Quadrature quadrature = new ClenshawCurtis(Config.SPECIAL_FUNCTIONS_TOLERANCE, 1000);
+      QuadratureResult result = quadrature.integrate(f, min, max);
+      if (result.converged) {
+        return result.estimate;
+      }
+      // NIntegrate failed to converge after `1` refinements in `2` in the region `3`.
+      throw new ArgumentTypeException("ncvi", F.List(F.ZZ(result.evaluations), xVar, list.rest()));
     } else if ("DoubleExponential".equalsIgnoreCase(method)) {
-      Quadrature quadrature = new TanhSinh(1e-8, 1000);
+      Quadrature quadrature = new TanhSinh(Config.SPECIAL_FUNCTIONS_TOLERANCE, maxIterations);
+      QuadratureResult result = quadrature.integrate(f, min, max);
+      if (result.converged) {
+        return result.estimate;
+      }
+      // NIntegrate failed to converge after `1` refinements in `2` in the region `3`.
+      throw new ArgumentTypeException("ncvi", F.List(F.ZZ(result.evaluations), xVar, list.rest()));
+    } else if ("GaussLobatto".equalsIgnoreCase(method)) {
+      Quadrature quadrature = new GaussLobatto(Config.SPECIAL_FUNCTIONS_TOLERANCE, 1000);
+      QuadratureResult result = quadrature.integrate(f, min, max);
+      if (result.converged) {
+        return result.estimate;
+      }
+      // NIntegrate failed to converge after `1` refinements in `2` in the region `3`.
+      throw new ArgumentTypeException("ncvi", F.List(F.ZZ(result.evaluations), xVar, list.rest()));
+
+    } else if ("NewtonCotesRule".equalsIgnoreCase(method)) {
+      Quadrature quadrature = new NewtonCotes(Config.SPECIAL_FUNCTIONS_TOLERANCE, 1000);
       QuadratureResult result = quadrature.integrate(f, min, max);
       if (result.converged) {
         return result.estimate;
       }
       // NIntegrate failed to converge after `1` refinements in `2` in the region `3`.
       throw new ArgumentTypeException("ncvi", F.List(F.ZZ(result.evaluations), xVar, list.rest()));
-      // Errors. printMessage(S.NIntegrate, "ncvi", F.List(F.ZZ(result.evaluations), xVar,
-      // list.rest()),
-      // engine);
     } else {
       if (maxPoints > 1000) {
         // github 150 - avoid StackOverflow from recursion

symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/IntegrateTest.java

@@ -296,6 +296,14 @@ public void testIntegrate() {
 
   @Test
   public void testNIntegrate() {
+    // avoid Indeterminate at 0
+    checkNumeric("NIntegrate(1/Sqrt(x), {x, 0.001, 1}, Method -> \"GaussLobatto\")", //
+        "1.9367544467966367");
+    checkNumeric("NIntegrate(1/Sqrt(x), {x, 0.001, 1}, Method -> \"NewtonCotesRule\")", //
+        "1.936754446797901");
+    checkNumeric("NIntegrate(Sqrt(x), {x, 0, 1}, Method -> \"ClenshawCurtisRule\")", //
+        "0.6666666666773636");
+
     // "tanh-sinh" strategy
     checkNumeric("NIntegrate(Exp(x)/x, {x, -Infinity, -1}, Method ->DoubleExponential)", //
         "-0.2193839343955203");