Analyze test coverage and identify improvement areas

test/unit/FiniteDifferenceStencilsTests.wl

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+(* ::Package:: *)
+
+(* FiniteDifferenceStencilsTests.wl *)
+(* Unit tests for Generato`FiniteDifferenceStencils module *)
+
+Print["Loading FiniteDifferenceStencilsTests.wl..."];
+
+(* Load Generato *)
+Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl"}]];
+
+(* ========================================= *)
+(* Test: GetCenteringStencils *)
+(* ========================================= *)
+
+VerificationTest[
+  (* Order 2 should return {-1, 0, 1} *)
+  GetCenteringStencils[2],
+  {-1, 0, 1},
+  TestID -> "GetCenteringStencils-Order2"
+];
+
+VerificationTest[
+  (* Order 4 should return {-2, -1, 0, 1, 2} *)
+  GetCenteringStencils[4],
+  {-2, -1, 0, 1, 2},
+  TestID -> "GetCenteringStencils-Order4"
+];
+
+VerificationTest[
+  (* Order 6 should return {-3, -2, -1, 0, 1, 2, 3} *)
+  GetCenteringStencils[6],
+  {-3, -2, -1, 0, 1, 2, 3},
+  TestID -> "GetCenteringStencils-Order6"
+];
+
+VerificationTest[
+  (* Order 8 should return {-4, -3, -2, -1, 0, 1, 2, 3, 4} *)
+  GetCenteringStencils[8],
+  {-4, -3, -2, -1, 0, 1, 2, 3, 4},
+  TestID -> "GetCenteringStencils-Order8"
+];
+
+VerificationTest[
+  (* Order 12 should have 13 points *)
+  Length[GetCenteringStencils[12]],
+  13,
+  TestID -> "GetCenteringStencils-Order12-Length"
+];
+
+(* ========================================= *)
+(* Test: GetFiniteDifferenceCoefficients *)
+(* ========================================= *)
+
+VerificationTest[
+  (* First derivative, order 2: coefficients should be -1/2, 0, 1/2 *)
+  coeffs = GetFiniteDifferenceCoefficients[{-1, 0, 1}, 1];
+  {Subscript[c, -1], Subscript[c, 0], Subscript[c, 1]} /. coeffs,
+  {-1/2, 0, 1/2},
+  TestID -> "GetFDCoefficients-FirstDeriv-Order2"
+];
+
+VerificationTest[
+  (* Second derivative, order 2: coefficients should be 1, -2, 1 *)
+  coeffs = GetFiniteDifferenceCoefficients[{-1, 0, 1}, 2];
+  {Subscript[c, -1], Subscript[c, 0], Subscript[c, 1]} /. coeffs,
+  {1, -2, 1},
+  TestID -> "GetFDCoefficients-SecondDeriv-Order2"
+];
+
+VerificationTest[
+  (* First derivative, order 4: known coefficients *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 1];
+  {Subscript[c, -2], Subscript[c, -1], Subscript[c, 0], Subscript[c, 1], Subscript[c, 2]} /. coeffs,
+  {1/12, -2/3, 0, 2/3, -1/12},
+  TestID -> "GetFDCoefficients-FirstDeriv-Order4"
+];
+
+VerificationTest[
+  (* Second derivative, order 4: known coefficients *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 2];
+  {Subscript[c, -2], Subscript[c, -1], Subscript[c, 0], Subscript[c, 1], Subscript[c, 2]} /. coeffs,
+  {-1/12, 4/3, -5/2, 4/3, -1/12},
+  TestID -> "GetFDCoefficients-SecondDeriv-Order4"
+];
+
+VerificationTest[
+  (* Coefficients should be returned as a list of rules *)
+  coeffs = GetFiniteDifferenceCoefficients[{-1, 0, 1}, 1];
+  MatchQ[coeffs, {__Rule}],
+  True,
+  TestID -> "GetFDCoefficients-ReturnsRules"
+];
+
+VerificationTest[
+  (* Order 6 first derivative center coefficient should be 0 *)
+  coeffs = GetFiniteDifferenceCoefficients[{-3, -2, -1, 0, 1, 2, 3}, 1];
+  Subscript[c, 0] /. coeffs,
+  0,
+  TestID -> "GetFDCoefficients-Order6-CenterIsZero"
+];
+
+VerificationTest[
+  (* Coefficients should sum to 0 for first derivative *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 1];
+  Total[{Subscript[c, -2], Subscript[c, -1], Subscript[c, 0], Subscript[c, 1], Subscript[c, 2]} /. coeffs],
+  0,
+  TestID -> "GetFDCoefficients-FirstDeriv-SumToZero"
+];
+
+VerificationTest[
+  (* Coefficients should sum to 0 for second derivative *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 2];
+  Total[{Subscript[c, -2], Subscript[c, -1], Subscript[c, 0], Subscript[c, 1], Subscript[c, 2]} /. coeffs],
+  0,
+  TestID -> "GetFDCoefficients-SecondDeriv-SumToZero"
+];
+
+VerificationTest[
+  (* First derivative coefficients should be antisymmetric *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 1];
+  cm2 = Subscript[c, -2] /. coeffs;
+  cp2 = Subscript[c, 2] /. coeffs;
+  cm2 == -cp2,
+  True,
+  TestID -> "GetFDCoefficients-FirstDeriv-Antisymmetric"
+];
+
+VerificationTest[
+  (* Second derivative coefficients should be symmetric *)
+  coeffs = GetFiniteDifferenceCoefficients[{-2, -1, 0, 1, 2}, 2];
+  cm2 = Subscript[c, -2] /. coeffs;
+  cp2 = Subscript[c, 2] /. coeffs;
+  cm2 == cp2,
+  True,
+  TestID -> "GetFDCoefficients-SecondDeriv-Symmetric"
+];
+
+Print["FiniteDifferenceStencilsTests.wl completed."];